CG标准函数库 港控/mmm° 2022-07-13 14:48 132阅读 0赞 原文地址:[http://blog.csdn.net/lcbcsdn/article/details/46848125][http_blog.csdn.net_lcbcsdn_article_details_46848125] > ### (1)数学函数 ### <table style="width:948.333px; border-collapse:collapse; border-spacing:0px; border:1px solid rgb(238,238,238); color:rgb(85,85,85); font-family:'microsoft yahei'; font-size:14px; line-height:35px"> <thead style=""> <tr style=""> <th align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 函数</th> <th align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 功能描述</th> </tr> </thead> <tbody style=""> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> abs(x)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 返回输入参数的绝对值</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> acos(x)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 反余切函数,输入参数范围为[-1,1], 返回[0,π]区间的角度值</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> all(x)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 如果输入参数均不为0,则返回ture; 否则返回flase。&&运算</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> any(x)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 输入参数只要有其中一个不为0,则返回true。</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> asin(x)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 反正弦函数,输入参数取值区间为<span style="color:rgb(136,136,136)"></span><span style="display:inline; line-height:normal; font-size:14px; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> <span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:3.517em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:2.825em; height:0px; font-size:17.36px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.186em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Main">[</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Main">−</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Main">1</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Main">,</span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.176em; margin:0px; vertical-align:0px; font-family:MathJax_Main">1</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Main">]</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.192em"></span></span></span><span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.354em; overflow:hidden; width:0px; height:1.361em; color:rgb(255,255,255)"></span></span> </span>,返回角度值范围为, <span style="color:rgb(136,136,136)"></span><span style="display:inline; line-height:normal; font-size:14px; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> <span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:4.438em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:3.574em; height:0px; font-size:17.36px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-3.223em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0.003em"><span style="position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size2">[</span></span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px 0.118em; vertical-align:0px; width:1.155em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.516em; vertical-align:0px; top:-2.244em; left:10.013px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">−</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Math-italic">π</span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.17em; vertical-align:0px; top:-1.437em; left:10.013px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">2</span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.322em; left:0.003em"><span style="display:inline-block; position:static; border-width:0px 0px 0px 1.155em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:0.003em; overflow:hidden; width:0px; height:1.25px"></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.097em"></span></span></span></span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.176em; margin:0px; vertical-align:0px; font-family:MathJax_Main">,</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px 0.118em; vertical-align:0px; width:0.521em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.17em; vertical-align:0px; top:-2.071em; left:4.51823px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Math-italic">π</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.673em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.17em; vertical-align:0px; top:-1.437em; left:4.51823px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">2</span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.322em; left:0.003em"><span style="display:inline-block; position:static; border-width:0px 0px 0px 0.521em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:0.003em; overflow:hidden; width:0px; height:1.25px"></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.097em"></span></span></span></span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0.003em"><span style="position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size2">]</span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.229em"></span></span></span><span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.854em; overflow:hidden; width:0px; height:2.361em; color:rgb(255,255,255)"></span></span> </span></td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> atan(x)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 反正切函数,返回角度值范围为<span style="color:rgb(136,136,136)"></span><span style="display:inline; line-height:normal; font-size:14px; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> <span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:4.438em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:3.574em; height:0px; font-size:17.36px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-3.223em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0.003em"><span style="position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size2">[</span></span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px 0.118em; vertical-align:0px; width:1.155em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.516em; vertical-align:0px; top:-2.244em; left:10.013px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">−</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Math-italic">π</span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.17em; vertical-align:0px; top:-1.437em; left:10.013px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">2</span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.322em; left:0.003em"><span style="display:inline-block; position:static; border-width:0px 0px 0px 1.155em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:0.003em; overflow:hidden; width:0px; height:1.25px"></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.097em"></span></span></span></span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.176em; margin:0px; vertical-align:0px; font-family:MathJax_Main">,</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px 0.118em; vertical-align:0px; width:0.521em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.17em; vertical-align:0px; top:-2.071em; left:4.51823px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Math-italic">π</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.673em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.17em; vertical-align:0px; top:-1.437em; left:4.51823px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">2</span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.322em; left:0.003em"><span style="display:inline-block; position:static; border-width:0px 0px 0px 0.521em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:0.003em; overflow:hidden; width:0px; height:1.25px"></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.097em"></span></span></span></span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0.003em"><span style="position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size2">]</span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.229em"></span></span></span><span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.854em; overflow:hidden; width:0px; height:2.361em; color:rgb(255,255,255)"></span></span> </span></td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> atan2(y,x)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 计算y/x的反正切值。实际上和atan(x)函数功能完全一样,至少输入参数不同。atan(x) = atan2(x, float(1))。</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> ceil(x)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 对输入参数向上取整。例如: ceil(float(1.3)) ,其返回值为2.0</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> clamp(x,a,b)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 如果<span style="">x</span>值小于<span style="">a</span>,则返回<span style="">a</span>;<br style=""> 如果<span style="">x</span>值大于<span style="">b</span>,返回<span style="">b</span>;<br style=""> 否则,返回<span style="">x</span>。</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> cos(x)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 返回弧度<span style="">x</span>的余弦值。返回值范围为<span style="color:rgb(136,136,136)"></span><span style="display:inline; line-height:normal; font-size:14px; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> <span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:3.517em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:2.825em; height:0px; font-size:17.36px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.186em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Main">[</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Main">−</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Main">1</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Main">,</span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.176em; margin:0px; vertical-align:0px; font-family:MathJax_Main">1</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Main">]</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.192em"></span></span></span><span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.354em; overflow:hidden; width:0px; height:1.361em; color:rgb(255,255,255)"></span></span> </span></td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> cosh(x)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 双曲余弦(hyperbolic cosine)函数,计算<span style="">x</span>的双曲余弦值。</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> cross(A,B)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 返回两个三元向量的叉积(cross product)。注意,输入参数必须是三元向量!</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> degrees(x)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 输入参数为弧度值(radians),函数将其转换为角度值(degrees)</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> determinant(m)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 计算矩阵的行列式因子。</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> dot(A,B)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 返回<span style="">A</span>和<span style="">B</span>的点积(dot product)。参数<span style="">A</span>和<span style="">B</span>可以是标量,也可以是向量(输入参数方面,点积和叉积函数有很大不同)。</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> exp(x)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 计算<span style="color:rgb(136,136,136)"></span><span style="display:inline; line-height:normal; font-size:14px; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> <span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.213em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0.982em; height:0px; font-size:17.36px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-0.976em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0.925em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">e</span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.464em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Math-italic">x</span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.673em"></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:0.982em"></span></span></span><span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.068em; overflow:hidden; width:0px; height:1.004em; color:rgb(255,255,255)"></span></span> </span>的值,e=2.71828182845904523536</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> exp2(x)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 计算<span style="color:rgb(136,136,136)"></span><span style="display:inline; line-height:normal; font-size:14px; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> <span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.328em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.04em; height:0px; font-size:17.36px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-0.976em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0.982em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.186em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Main">2</span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.192em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.071em; left:0.521em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Math-italic">x</span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.673em"></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:0.982em"></span></span></span><span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.068em; overflow:hidden; width:0px; height:1.004em; color:rgb(255,255,255)"></span></span> </span>的值</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> floor(x)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 对输入参数向下取整。例如floor(float(1.3))返回的值为1.0;但是floor(float(-1.3))返回的值为-2.0。该函数与ceil(x)函数相对应。</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> fmod(x,y)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 返回<span style="">x/y</span>的余数。如果<span style="">y</span>为<span style="">0</span>,结果不可预料。</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> frac(x)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 返回标量或矢量的小数</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> frexp(x, out i)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 将浮点数x分解为尾数和指数,即<span style="color:rgb(136,136,136)"></span><span style="display:inline; line-height:normal; font-size:14px; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> <span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:5.59em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:4.496em; height:0px; font-size:17.36px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.301em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">x</span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.291em; margin:0px; vertical-align:0px; font-family:MathJax_Main">=</span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.291em; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">m</span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.233em; margin:0px; vertical-align:0px; font-family:MathJax_Main">∗</span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.233em; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0.809em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.186em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Main">2</span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.192em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.071em; left:0.521em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Math-italic">i</span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.673em"></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.307em"></span></span></span><span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.068em; overflow:hidden; width:0px; height:1.218em; color:rgb(255,255,255)"></span></span> </span>, 返回<span style="">m</span>,并将指数存入<span style="">i</span>中;如果<span style="">x</span>为<span style="">0</span>,则尾数和指数都返回<span style="">0</span></td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> isfinite(x)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 判断标量或者向量中的每个数据是否是有限数,如果是返回true;否则返回false;</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> isinf(x)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 判断标量或者向量中的每个数据是否是无限,如果是返回true;否则返回false;</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> isnan(x)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 判断标量或者向量中的每个数据是否是非数据(not-a-number NaN),如果是返回true;否则返回false;</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> ldexp(x, n)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 计算<span style="color:rgb(136,136,136)"></span><span style="display:inline; line-height:normal; font-size:14px; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> <span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:3.113em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:2.48em; height:0px; font-size:17.36px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.301em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">x</span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.233em; margin:0px; vertical-align:0px; font-family:MathJax_Main">∗</span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.233em; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0.982em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.186em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Main">2</span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.192em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.071em; left:0.521em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Math-italic">n</span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.673em"></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.307em"></span></span></span><span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.068em; overflow:hidden; width:0px; height:1.004em; color:rgb(255,255,255)"></span></span> </span>的值</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> lerp(a, b, f)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 计算<span style="color:rgb(136,136,136)"></span><span style="display:inline; line-height:normal; font-size:14px; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> <span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:9.335em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:7.491em; height:0px; font-size:17.36px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.186em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Main">(</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Main">1</span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.233em; margin:0px; vertical-align:0px; font-family:MathJax_Main">−</span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.233em; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">f<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Main">)</span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.233em; margin:0px; vertical-align:0px; font-family:MathJax_Main">∗</span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.233em; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">a</span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.233em; margin:0px; vertical-align:0px; font-family:MathJax_Main">+</span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.233em; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">b</span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.233em; margin:0px; vertical-align:0px; font-family:MathJax_Main">∗</span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.233em; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">f<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.192em"></span></span></span><span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.354em; overflow:hidden; width:0px; height:1.361em; color:rgb(255,255,255)"></span></span> </span>或者<span style="color:rgb(136,136,136)"></span><span style="display:inline; line-height:normal; font-size:14px; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> <span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:7.549em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:6.051em; height:0px; font-size:17.36px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.186em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">a</span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.233em; margin:0px; vertical-align:0px; font-family:MathJax_Main">+</span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.233em; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">f<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.233em; margin:0px; vertical-align:0px; font-family:MathJax_Main">∗</span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.233em; margin:0px; vertical-align:0px; font-family:MathJax_Main">(</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">b</span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.233em; margin:0px; vertical-align:0px; font-family:MathJax_Main">−</span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.233em; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">a</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Main">)</span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.192em"></span></span></span><span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.354em; overflow:hidden; width:0px; height:1.361em; color:rgb(255,255,255)"></span></span> </span>的值。即在下限<span style="">a</span>和上限<span style="">b</span>之间进行插值,<span style="">f</span>表示权值。注意,如果<span style="">a</span>和<span style="">b</span>是向量,则权值<span style="">f</span>必须是标量或者等长的向量。</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> lit(NdotL, NdotH, m)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> <span style="">N</span>表示法向量;<br style=""> <span style="">L</span>表示入射光向量;<br style=""> <span style="">H</span>表示半角向量;<br style=""> <span style="">m</span>表示高光系数。 <br style=""> 函数计算环境光、散射光、镜面光的贡献,返回的4元向量。 <br style=""> <span style="">X</span>位表示环境光的贡献,总是1.0; <br style=""> <span style="">Y</span>位代表散射光的贡献,如果 <span style="color:rgb(136,136,136)"></span><span style="display:inline; line-height:normal; font-size:14px; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> <span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:5.475em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:4.381em; height:0px; font-size:17.36px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.186em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">N<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.233em; margin:0px; vertical-align:0px; font-family:MathJax_Main">∙</span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.233em; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">L</span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.291em; margin:0px; vertical-align:0px; font-family:MathJax_Main"><</span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.291em; margin:0px; vertical-align:0px; font-family:MathJax_Main">0</span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.192em"></span></span></span><span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.139em; overflow:hidden; width:0px; height:1.075em; color:rgb(255,255,255)"></span></span> </span>,则为0;否则为<span style="color:rgb(136,136,136)"></span><span style="display:inline; line-height:normal; font-size:14px; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> <span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:3.113em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:2.48em; height:0px; font-size:17.36px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.186em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">N<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.233em; margin:0px; vertical-align:0px; font-family:MathJax_Main">∙</span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.233em; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">L</span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.192em"></span></span></span><span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.068em; overflow:hidden; width:0px; height:1.004em; color:rgb(255,255,255)"></span></span> </span> <br style=""> <span style="">Z</span>位代表镜面光的贡献,如果<span style="color:rgb(136,136,136)"></span><span style="display:inline; line-height:normal; font-size:14px; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> <span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:5.475em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:4.381em; height:0px; font-size:17.36px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.186em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">N<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.233em; margin:0px; vertical-align:0px; font-family:MathJax_Main">∙</span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.233em; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">L</span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.291em; margin:0px; vertical-align:0px; font-family:MathJax_Main"><</span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.291em; margin:0px; vertical-align:0px; font-family:MathJax_Main">0</span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.192em"></span></span></span><span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.139em; overflow:hidden; width:0px; height:1.075em; color:rgb(255,255,255)"></span></span> </span> 或者<span style="color:rgb(136,136,136)"></span><span style="display:inline; line-height:normal; font-size:14px; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> <span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:5.648em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:4.554em; height:0px; font-size:17.36px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.186em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">N<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.233em; margin:0px; vertical-align:0px; font-family:MathJax_Main">∙</span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.233em; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">H<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.291em; margin:0px; vertical-align:0px; font-family:MathJax_Main"><</span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.291em; margin:0px; vertical-align:0px; font-family:MathJax_Main">0</span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.192em"></span></span></span><span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.139em; overflow:hidden; width:0px; height:1.075em; color:rgb(255,255,255)"></span></span> </span>,则位0;否则为<span style="color:rgb(136,136,136)"></span><span style="display:inline; line-height:normal; font-size:14px; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> <span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:4.957em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:3.978em; height:0px; font-size:17.36px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.186em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Main">(</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">N<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.233em; margin:0px; vertical-align:0px; font-family:MathJax_Main">∙</span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.233em; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">L</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.097em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.186em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Main">)</span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.192em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.128em; left:0.406em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Math-italic">m</span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.673em"></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.192em"></span></span></span><span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.354em; overflow:hidden; width:0px; height:1.432em; color:rgb(255,255,255)"></span></span> </span>;<br style=""> <span style="">W</span>位始终位1.0</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> log(x)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 计算<span style="color:rgb(136,136,136)"></span><span style="display:inline; line-height:normal; font-size:14px; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> <span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:2.595em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:2.077em; height:0px; font-size:17.36px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">l</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.731em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">n</span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.186em; left:0.637em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">(</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Math-italic">x</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">)</span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span></span><span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.068em; overflow:hidden; width:0px; height:1.289em; color:rgb(255,255,255)"></span></span> </span>的值,<span style="">x</span>必须大于<span style="">0</span></td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> log2(x)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 计算<span style="color:rgb(136,136,136)"></span><span style="display:inline; line-height:normal; font-size:14px; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> <span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:3.113em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:2.48em; height:0px; font-size:17.36px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">l</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">o</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.673em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">g<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.003em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.359em; left:0.579em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">(</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Math-italic">x</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">)</span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.552em; left:0.521em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">2</span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span></span><span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.425em; overflow:hidden; width:0px; height:1.861em; color:rgb(255,255,255)"></span></span> </span>的值,<span style="">x</span>必须大于<span style="">0</span></td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> log10(x)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 计算<span style="color:rgb(136,136,136)"></span><span style="display:inline; line-height:normal; font-size:14px; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> <span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:3.113em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:2.48em; height:0px; font-size:17.36px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">l</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">o</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.673em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">g<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.003em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.359em; left:0.579em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">(</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Math-italic">x</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">)</span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.552em; left:0.521em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">10</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span></span><span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.496em; overflow:hidden; width:0px; height:1.861em; color:rgb(255,255,255)"></span></span> </span>的值,<span style="">x</span>必须大于<span style="">0</span></td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> max(a, b)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 比较两个标量或等长向量元素,返回最大值。</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> min(a,b)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 比较两个标量或等长向量元素,返回最小值。</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> modf(x, out ip)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 把<span style="">x</span>分解成整数和分数两部分,每部分都和<span style="">x</span>有着相同的符号,整数部分被保存在<span style="">ip</span>中,分数部分由函数返回</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> mul(M, N)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 矩阵<span style="">M</span>和矩阵<span style="">N</span>的积,计算方法如下<br style=""> <span style="color:rgb(136,136,136)"></span> <div style="text-align:center; margin:1em 0em; position:relative; max-width:none; max-height:none; min-width:0px; min-height:0px; width:782.5px"> <span style="display:inline; line-height:normal; font-size:14px; text-align:left; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> <span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:37.042em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:29.842em; height:0px; font-size:17.36px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-5.181em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">m</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">u</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">l</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Main">(</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">M<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Main">,</span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.176em; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">N<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Main">)</span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.291em; margin:0px; vertical-align:0px; font-family:MathJax_Main">=</span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.291em; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.291em; margin:0px; vertical-align:2.825em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0.694em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size4; top:-2.82em; left:0.003em">⎡<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size4; top:0.579em; left:0.003em">⎣<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size4; top:-1.61em; left:0.003em">⎢<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size4; top:-1.092em; left:0.003em">⎢<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size4; top:-0.516em; left:0.003em">⎢<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span></span></span><span style="display:inline; position:static; border:0px; padding:0px 0.176em; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:10.141em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-6.046em; left:0.003em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.789em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.861em; vertical-align:0px; top:-6.046em; left:15.5208px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.789em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">M<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.982em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">11</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.861em; vertical-align:0px; top:-4.605em; left:15.5208px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.789em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">M<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.982em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">12</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.861em; vertical-align:0px; top:-3.223em; left:15.5208px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.789em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">M<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.982em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">13</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.861em; vertical-align:0px; top:-1.84em; left:15.5208px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.789em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">M<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.982em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">14</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:6.051em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-6.046em; left:2.768em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.789em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.861em; vertical-align:0px; top:-6.046em; left:15.5208px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.789em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">M<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.982em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">21</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.861em; vertical-align:0px; top:-4.605em; left:15.5208px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; 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position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.982em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">31</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.861em; vertical-align:0px; top:-4.605em; left:15.5208px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.789em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">M<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.982em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">32</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.861em; vertical-align:0px; top:-3.223em; left:15.5208px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.789em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">M<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.982em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">33</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.861em; vertical-align:0px; top:-1.84em; left:15.5208px"><span style="display:inline; 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border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.982em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">34</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:6.051em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-6.046em; left:8.355em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.789em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.861em; vertical-align:0px; top:-6.046em; left:15.5208px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.789em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">M<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.982em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">41</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; 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border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.982em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">42</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; 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margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.982em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">43</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; 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overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.982em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">44</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:6.051em"></span></span></span></span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:2.825em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0.694em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size4; top:-2.82em; left:0.003em">⎤<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size4; top:0.579em; left:0.003em">⎦<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size4; top:-1.61em; left:0.003em">⎥<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size4; top:-1.092em; left:0.003em">⎥<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size4; top:-0.516em; left:0.003em">⎥<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span></span></span></span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.176em; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.176em; margin:0px; vertical-align:2.825em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0.694em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size4; top:-2.82em; left:0.003em">⎡<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size4; top:0.579em; left:0.003em">⎣<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size4; top:-1.61em; left:0.003em">⎢<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size4; top:-1.092em; left:0.003em">⎢<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size4; top:-0.516em; left:0.003em">⎢<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span></span></span><span style="display:inline; position:static; border:0px; padding:0px 0.176em; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:9.623em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-6.046em; left:0.003em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.673em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.804em; vertical-align:0px; top:-6.046em; left:14.5182px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.673em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">N<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.867em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">11</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.804em; vertical-align:0px; top:-4.605em; left:14.5182px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.673em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">N<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.867em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">12</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.804em; vertical-align:0px; top:-3.223em; left:14.5182px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.673em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">N<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.867em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">12</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.804em; vertical-align:0px; top:-1.84em; left:14.5182px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.673em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">N<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.867em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">13</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:6.051em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-6.046em; left:2.653em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.673em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.804em; vertical-align:0px; top:-6.046em; left:14.5182px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.673em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">N<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.867em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">21</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.804em; vertical-align:0px; top:-4.605em; left:14.5182px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.673em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">N<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.867em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">22</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.804em; vertical-align:0px; top:-3.223em; left:14.5182px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.673em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">N<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.867em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">23</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.804em; vertical-align:0px; top:-1.84em; left:14.5182px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.673em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">N<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.867em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">24</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:6.051em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-6.046em; left:5.302em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.673em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.804em; vertical-align:0px; top:-6.046em; left:14.5182px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.673em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">N<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.867em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">31</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.804em; vertical-align:0px; top:-4.605em; left:14.5182px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.673em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">N<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.867em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">32</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.804em; vertical-align:0px; top:-3.223em; left:14.5182px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.673em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">N<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.867em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">33</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.804em; vertical-align:0px; top:-1.84em; left:14.5182px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.673em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">N<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.867em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">34</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:6.051em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-6.046em; left:8.01em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.673em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.804em; vertical-align:0px; top:-6.046em; left:14.5182px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.673em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">N<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.867em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">41</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.804em; vertical-align:0px; top:-4.605em; left:14.5182px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.673em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">N<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.867em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">42</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.804em; vertical-align:0px; top:-3.223em; left:14.5182px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.673em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">N<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.867em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">43</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.804em; vertical-align:0px; top:-1.84em; left:14.5182px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.673em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">N<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.867em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">44</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:6.051em"></span></span></span></span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:2.825em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0.694em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size4; top:-2.82em; left:0.003em">⎤<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size4; top:0.579em; left:0.003em">⎦<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size4; top:-1.61em; left:0.003em">⎥<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size4; top:-1.092em; left:0.003em">⎥<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size4; top:-0.516em; left:0.003em">⎥<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:5.187em"></span></span></span><span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-2.996em; overflow:hidden; width:0px; height:6.575em; color:rgb(255,255,255)"></span></span> </span> </div> </td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> mul(M, v)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 矩阵<span style="">M</span>和列向量<span style="">v</span>的积,公式如下<br style=""> <span style="color:rgb(136,136,136)"></span> <div style="text-align:center; margin:1em 0em; position:relative; max-width:none; max-height:none; min-width:0px; min-height:0px; width:782.5px"> <span style="display:inline; line-height:normal; font-size:14px; text-align:left; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> <span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:25.925em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:20.913em; height:0px; font-size:17.36px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-5.181em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">m</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">u</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">l</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Main">(</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">M<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Main">,</span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.176em; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">v</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Main">)</span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.291em; margin:0px; vertical-align:0px; font-family:MathJax_Main">=</span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.291em; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.291em; margin:0px; vertical-align:2.825em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0.694em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size4; top:-2.82em; left:0.003em">⎡<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size4; top:0.579em; left:0.003em">⎣<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size4; top:-1.61em; left:0.003em">⎢<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size4; top:-1.092em; left:0.003em">⎢<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size4; top:-0.516em; left:0.003em">⎢<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span></span></span><span style="display:inline; position:static; border:0px; padding:0px 0.176em; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:10.141em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-6.046em; left:0.003em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.789em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.861em; vertical-align:0px; top:-6.046em; left:15.5208px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.789em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">M<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.982em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">11</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.861em; vertical-align:0px; top:-4.605em; left:15.5208px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.789em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">M<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.982em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">12</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.861em; vertical-align:0px; top:-3.223em; left:15.5208px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.789em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">M<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.982em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">13</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.861em; vertical-align:0px; top:-1.84em; left:15.5208px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.789em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">M<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.982em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">14</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:6.051em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-6.046em; left:2.768em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.789em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.861em; vertical-align:0px; top:-6.046em; left:15.5208px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.789em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">M<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.982em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">21</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.861em; vertical-align:0px; top:-4.605em; left:15.5208px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.789em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">M<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.982em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">22</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.861em; vertical-align:0px; top:-3.223em; left:15.5208px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.789em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">M<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.982em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">23</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.861em; vertical-align:0px; top:-1.84em; left:15.5208px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.789em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">M<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.982em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">24</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:6.051em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-6.046em; left:5.59em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.789em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.861em; vertical-align:0px; top:-6.046em; left:15.5208px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.789em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">M<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.982em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">31</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; 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margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.982em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">33</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; 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overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.982em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">34</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; 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font-size:12.2735px; font-family:MathJax_Main">41</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.861em; vertical-align:0px; top:-4.605em; left:15.5208px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.789em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">M<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.982em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">42</span></span></span><span style="display:inline-block; 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position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">M<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.982em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">43</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.861em; vertical-align:0px; top:-1.84em; left:15.5208px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.789em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">M<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.982em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">44</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:6.051em"></span></span></span></span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:2.825em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0.694em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size4; top:-2.82em; left:0.003em">⎤<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size4; top:0.579em; left:0.003em">⎦<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size4; top:-1.61em; left:0.003em">⎥<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size4; top:-1.092em; left:0.003em">⎥<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size4; top:-0.516em; left:0.003em">⎥<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span></span></span></span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.176em; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.176em; margin:0px; vertical-align:2.825em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0.694em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size4; top:-2.82em; left:0.003em">⎡<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size4; top:0.579em; left:0.003em">⎣<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size4; top:-1.61em; left:0.003em">⎢<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size4; top:-1.092em; left:0.003em">⎢<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size4; top:-0.516em; left:0.003em">⎢<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span></span></span><span style="display:inline; position:static; border:0px; padding:0px 0.176em; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.04em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-5.873em; left:0.003em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.04em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.516em; vertical-align:0px; top:-4.26em; left:9.02344px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">v</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Main">1</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.192em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.516em; vertical-align:0px; top:-2.82em; left:9.02344px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">v</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Main">2</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.192em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.516em; vertical-align:0px; top:-1.437em; left:9.02344px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">v</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Main">3</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.192em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.516em; vertical-align:0px; top:-0.055em; left:9.02344px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">v</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Main">4</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.192em"></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:5.878em"></span></span></span></span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:2.825em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0.694em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size4; top:-2.82em; left:0.003em">⎤<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size4; top:0.579em; left:0.003em">⎦<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size4; top:-1.61em; left:0.003em">⎥<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size4; top:-1.092em; left:0.003em">⎥<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size4; top:-0.516em; left:0.003em">⎥<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:5.187em"></span></span></span><span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-2.996em; overflow:hidden; width:0px; height:6.575em; color:rgb(255,255,255)"></span></span> </span> </div> </td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> mul(v, M)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 行向量<span style="">v</span>和矩阵<span style="">M</span>的积,公式如下<br style=""> <span style="color:rgb(136,136,136)"></span> <div style="text-align:center; margin:1em 0em; position:relative; max-width:none; max-height:none; min-width:0px; min-height:0px; width:782.5px"> <span style="display:inline; line-height:normal; font-size:14px; text-align:left; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> <span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:32.549em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:26.213em; height:0px; font-size:17.36px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-5.181em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">m</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">u</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">l</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Main">(</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">v</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Main">,</span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.176em; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">M<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Main">)</span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.291em; margin:0px; vertical-align:0px; font-family:MathJax_Main">=</span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.291em; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.291em; margin:0px; vertical-align:0px; font-family:MathJax_Main">[</span><span style="display:inline; position:static; border:0px; padding:0px 0.176em; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:7.146em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-3.972em; left:0.003em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.04em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.516em; vertical-align:0px; top:-2.128em; left:9.02344px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">v</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Main">1</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.192em"></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-3.972em; left:2.019em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.04em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.516em; vertical-align:0px; top:-2.128em; left:9.02344px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">v</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Main">2</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.192em"></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-3.972em; left:4.093em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.04em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.516em; vertical-align:0px; top:-2.128em; left:9.02344px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">v</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Main">3</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.192em"></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-3.972em; left:6.109em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.04em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.516em; vertical-align:0px; top:-2.128em; left:9.02344px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">v</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Main">4</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.192em"></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span></span></span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Main">]</span></span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.176em; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.176em; margin:0px; vertical-align:2.825em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0.694em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size4; top:-2.82em; left:0.003em">⎡<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size4; top:0.579em; left:0.003em">⎣<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size4; top:-1.61em; left:0.003em">⎢<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size4; top:-1.092em; left:0.003em">⎢<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size4; top:-0.516em; left:0.003em">⎢<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span></span></span><span style="display:inline; position:static; border:0px; padding:0px 0.176em; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:10.141em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-6.046em; left:0.003em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.789em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.861em; vertical-align:0px; top:-6.046em; left:15.5208px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.789em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">M<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.982em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">11</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.861em; vertical-align:0px; top:-4.605em; left:15.5208px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.789em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">M<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.982em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">12</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.861em; vertical-align:0px; top:-3.223em; left:15.5208px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.789em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">M<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.982em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">13</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.861em; vertical-align:0px; top:-1.84em; left:15.5208px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.789em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">M<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.982em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">14</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:6.051em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-6.046em; left:2.768em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.789em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.861em; vertical-align:0px; top:-6.046em; left:15.5208px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.789em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">M<span style="display:inline-block; 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margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.982em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">22</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; 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overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.982em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">23</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.861em; vertical-align:0px; top:-1.84em; left:15.5208px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.789em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">M<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.982em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">24</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span></span><span style="display:inline-block; 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margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">M<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.982em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">31</span></span></span><span style="display:inline-block; 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position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">M<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.982em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">32</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.861em; vertical-align:0px; top:-3.223em; left:15.5208px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.789em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">M<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.982em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">33</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.861em; vertical-align:0px; top:-1.84em; left:15.5208px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.789em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">M<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.982em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">34</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; 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padding:0px; margin:0px; vertical-align:0px; width:1.789em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">M<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.982em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">41</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.861em; vertical-align:0px; top:-4.605em; left:15.5208px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.789em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">M<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.982em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">42</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.861em; vertical-align:0px; top:-3.223em; left:15.5208px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.789em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">M<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.982em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">43</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -0.861em; vertical-align:0px; top:-1.84em; left:15.5208px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.789em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">M<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.668em; left:0.982em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">44</span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:6.051em"></span></span></span></span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:2.825em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0.694em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size4; top:-2.82em; left:0.003em">⎤<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size4; top:0.579em; left:0.003em">⎦<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size4; top:-1.61em; left:0.003em">⎥<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size4; top:-1.092em; left:0.003em">⎥<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Size4; top:-0.516em; left:0.003em">⎥<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:5.187em"></span></span></span><span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-2.996em; overflow:hidden; width:0px; height:6.575em; color:rgb(255,255,255)"></span></span> </span> </div> </td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> noise(x)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 根据它的参数类型,这个函数可以是一元、二元或三元噪音函数。返回的值在<span style="">0</span>和<span style="">1</span>之间,并且通常与给定的输入值一样</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> pow(x, y)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> <span style="color:rgb(136,136,136)"></span><span style="display:inline; line-height:normal; font-size:14px; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> <span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.328em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.04em; height:0px; font-size:17.36px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-0.976em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.04em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">x</span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.579em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Math-italic">y<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.003em"></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.673em"></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:0.982em"></span></span></span><span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.068em; overflow:hidden; width:0px; height:1.004em; color:rgb(255,255,255)"></span></span> </span></td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> radians(x)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 函数将角度值转换为弧度值</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> round(x)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 返回四舍五入值。</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> rsqrt(x)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> <span style="">x</span>的平方根的倒数,<span style="">x</span>必须大于<span style="">0</span></td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> saturate(x)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 把<span style="">x</span>限制到<span style="">[0,1]</span>之间</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> sign(x)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 如果<span style="color:rgb(136,136,136)"></span><span style="display:inline; line-height:normal; font-size:14px; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> <span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:3.113em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:2.48em; height:0px; font-size:17.36px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.186em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">x</span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.291em; margin:0px; vertical-align:0px; font-family:MathJax_Main">></span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.291em; margin:0px; vertical-align:0px; font-family:MathJax_Main">0</span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.192em"></span></span></span><span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.139em; overflow:hidden; width:0px; height:1.004em; color:rgb(255,255,255)"></span></span> </span>则返回<span style="">1</span>;否则返回<span style="">0</span></td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> sin(x)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 输入参数为弧度,计算正弦值,返回值范围 为<span style="">[-1,1]</span></td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> sincos(float x, out s, out c)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 该函数是同时计算x的sin值和cos值,其中<span style="">s</span>=<span style="">sin(x)</span>,<span style="">c</span>=<span style="">cos(x)</span>。该函数用于“同时需要计算sin值和cos值的情况”,比分别运算要快很多!</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> sinh(x)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 计算<span style="">x</span>的双曲正弦</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> smoothstep(min, max, x)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 值<span style="">x</span>位于<span style="">min</span>、<span style="">max</span>区间中。如果<span style="">x</span>=<span style="">min</span>,返回<span style="">0</span>;如果<span style="">x</span>=<span style="">max</span>,返回<span style="">1</span>;如果<span style="">x</span>在两者之间,按照下列公式返回数据:<br style=""> <span style="color:rgb(136,136,136)"></span><span style="display:inline; line-height:normal; font-size:14px; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> <span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:18.09em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:14.577em; height:0px; font-size:17.36px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.186em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Main">−</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Main">2</span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.233em; margin:0px; vertical-align:0px; font-family:MathJax_Main">∗</span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.233em; margin:0px; vertical-align:0px; font-family:MathJax_Main">(</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px 0.118em; vertical-align:0px; width:3.401em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -1.149em; vertical-align:0px; top:-2.244em; left:29.5182px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Math-italic">x</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">−</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Math-italic">m</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Math-italic">i</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Math-italic">n</span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -1.61em; vertical-align:0px; top:-1.437em; left:29.5182px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Math-italic">m</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Math-italic">a</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Math-italic">x</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">−</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Math-italic">m</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Math-italic">i</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Math-italic">n</span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.322em; left:0.003em"><span style="display:inline-block; position:static; border-width:0px 0px 0px 3.401em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:0.003em; overflow:hidden; width:0px; height:1.25px"></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.097em"></span></span></span></span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0.867em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.186em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Main">)</span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.192em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.301em; left:0.406em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">3</span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.233em; margin:0px; vertical-align:0px; font-family:MathJax_Main">+</span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.233em; margin:0px; vertical-align:0px; font-family:MathJax_Main">3</span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.233em; margin:0px; vertical-align:0px; font-family:MathJax_Main">∗</span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.233em; margin:0px; vertical-align:0px; font-family:MathJax_Main">(</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px 0.118em; vertical-align:0px; width:3.401em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -1.149em; vertical-align:0px; top:-2.244em; left:29.5182px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Math-italic">x</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">−</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Math-italic">m</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Math-italic">i</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Math-italic">n</span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px 0px 0px -1.61em; vertical-align:0px; top:-1.437em; left:29.5182px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Math-italic">m</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Math-italic">a</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Math-italic">x</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">−</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Math-italic">m</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Math-italic">i</span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Math-italic">n</span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.322em; left:0.003em"><span style="display:inline-block; position:static; border-width:0px 0px 0px 3.401em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:0.003em; overflow:hidden; width:0px; height:1.25px"></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.097em"></span></span></span></span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0.867em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.186em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Main">)</span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.192em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.301em; left:0.406em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-size:12.2735px; font-family:MathJax_Main">2</span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.846em"></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.192em"></span></span></span><span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.568em; overflow:hidden; width:0px; height:1.789em; color:rgb(255,255,255)"></span></span> </span></td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> step(a, x)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 如果<span style="color:rgb(136,136,136)"></span><span style="display:inline; line-height:normal; font-size:14px; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> <span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:3.113em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:2.48em; height:0px; font-size:17.36px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.186em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">x</span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.291em; margin:0px; vertical-align:0px; font-family:MathJax_Main"><</span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.291em; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">a</span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.192em"></span></span></span><span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.139em; overflow:hidden; width:0px; height:0.861em; color:rgb(255,255,255)"></span></span> </span>,返回<span style="">0</span>;否则,返回<span style="">1</span></td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> sqrt(x)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 求<span style="">x</span>的平方根,<span style="color:rgb(136,136,136)"></span><span style="display:inline; line-height:normal; font-size:14px; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> <span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.731em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.385em; height:0px; font-size:17.36px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-0.976em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:1.385em; height:0px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.013em; left:0.809em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">x</span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.019em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-1.783em; left:0.809em"><span style="display:inline-block; position:static; border-width:0px 0px 0px 0.579em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.055em; overflow:hidden; width:0px; height:1.25px"></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:1.097em"></span></span><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-3.914em; left:0.003em"><span style="position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Main">√</span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:3.978em"></span></span></span></span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:0.982em"></span></span></span><span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.425em; overflow:hidden; width:0px; height:1.361em; color:rgb(255,255,255)"></span></span> </span>,<span style="">x</span>必须大于<span style="">0</span></td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> tan(x)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 计算<span style="">x</span>正切值</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> tanh(x)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 计算<span style="">x</span>的双曲线切线</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> transpose(M)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 矩阵M的转置矩阵<br style=""> 如果M是一个AxB矩阵,M的转置是一个BxA矩阵,它的第一列是M的第一行,第二列是M的第二行,第三列是M的第三行,等等</td> </tr> </tbody> </table> > ### (2)几何函数 ### <table style="width:948.333px; border-collapse:collapse; border-spacing:0px; border:1px solid rgb(238,238,238); color:rgb(85,85,85); font-family:'microsoft yahei'; font-size:14px; line-height:35px"> <thead style=""> <tr style=""> <th align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 函数</th> <th align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 功能描述</th> </tr> </thead> <tbody style=""> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> distance(pt1, pt2)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 两点之间的欧几里德距离(Euclidean distance)</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> faceforward(N,I,Ng)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 如果<span style="color:rgb(136,136,136)"></span><span style="display:inline; line-height:normal; font-size:14px; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> <span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:5.821em"><span style="display:inline-block; position:relative; border:0px; padding:0px; margin:0px; vertical-align:0px; width:4.669em; height:0px; font-size:17.36px"><span style="position:absolute; border:0px; padding:0px; margin:0px; vertical-align:0px; top:-2.186em; left:0.003em"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px"><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">N<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">g<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.003em"></span></span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.233em; margin:0px; vertical-align:0px; font-family:MathJax_Main">∙</span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.233em; margin:0px; vertical-align:0px; font-family:MathJax_Math-italic">I<span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; overflow:hidden; height:1px; width:0.06em"></span></span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.291em; margin:0px; vertical-align:0px; font-family:MathJax_Main"><</span><span style="display:inline; position:static; border:0px; padding:0px 0px 0px 0.291em; margin:0px; vertical-align:0px; font-family:MathJax_Main">0</span></span><span style="display:inline-block; position:static; border:0px; padding:0px; margin:0px; vertical-align:0px; width:0px; height:2.192em"></span></span></span><span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.354em; overflow:hidden; width:0px; height:1.218em; color:rgb(255,255,255)"></span></span> </span>,返回<span style="">N</span>;否则返回<span style="">-N</span>。</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> length(v)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 返回一个向量的模,即sqrt(dot(v,v))</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> normalize(v)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 返回v向量的单位向量</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> reflect(I, N)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 根据入射光纤方向<span style="">I</span>和表面法向量<span style="">N</span>计算反射向量,仅对三元向量有效</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> refract(I,N,eta)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 根据入射光线方向<span style="">I</span>,表面法向量<span style="">N</span>和折射相对系数<span style="">eta</span>,计算折射向量。如果对给定的<span style="">eta</span>,<span style="">I</span>和<span style="">N</span>之间的角度太大,返回(0,0,0)。<br style=""> 只对三元向量有效</td> </tr> </tbody> </table> > ### (3)纹理映射函数 ### <table style="width:948.333px; border-collapse:collapse; border-spacing:0px; border:1px solid rgb(238,238,238); color:rgb(85,85,85); font-family:'microsoft yahei'; font-size:14px; line-height:35px"> <thead style=""> <tr style=""> <th align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 函数</th> <th align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 功能描述</th> </tr> </thead> <tbody style=""> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> tex1D(sampler1D tex, float s)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 一维纹理查询</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> tex1D(sampler1D tex, float s, float dsdx, float dsdy)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 使用导数值(derivatives)查询一维纹理</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> Tex1D(sampler1D tex, float2 sz)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 一维纹理查询,并进行深度值比较</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> Tex1D(sampler1D tex, float2 sz, float dsdx,float dsdy)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 使用导数值(derivatives)查询一维纹理, 并进行深度值比较</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> Tex1Dproj(sampler1D tex, float2 sq)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 一维投影纹理查询</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> Tex1Dproj(sampler1D tex, float3 szq)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 一维投影纹理查询,并比较深度值</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> Tex2D(sampler2D tex, float2 s)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 二维纹理查询</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> Tex2D(sampler2D tex, float2 s, float2 dsdx, float2 dsdy)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 使用导数值(derivatives)查询二维纹理</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> Tex2D(sampler2D tex, float3 sz)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 二维纹理查询,并进行深度值比较</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> Tex2D(sampler2D tex, float3 sz, float2 dsdx,float2 dsdy)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 使用导数值(derivatives)查询二维纹理,并进行深度值比较</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> Tex2Dproj(sampler2D tex, float3 sq)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 二维投影纹理查询</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> Tex2Dproj(sampler2D tex, float4 szq)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 二维投影纹理查询,并进行深度值比较</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> texRECT(samplerRECT tex, float2 s)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 二维非投影矩形纹理查询(OpenGL独有)</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> texRECT (samplerRECT tex, float3 sz, float2 dsdx,float2 dsdy)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 二维非投影使用导数的矩形纹理查询(OpenGL独有)</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> texRECT (samplerRECT tex, float3 sz)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 二维非投影深度比较矩形纹理查询(OpenGL独有)</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> texRECT (samplerRECT tex, float3 sz, float2 dsdx,float2 dsdy)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 二维非投影深度比较并使用导数的矩形纹理查询(OpenGL独有)</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> texRECT proj(samplerRECT tex, float3 sq)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 二维投影矩形纹理查询(OpenGL独有)</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> texRECT proj(samplerRECT tex, float3 szq)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 二维投影矩形纹理深度比较查询(OpenGL独有)</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> Tex3D(sampler3D tex, float s)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 三维纹理查询</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> Tex3D(sampler3D tex, float3 s, float3 dsdx, float3 dsdy)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 结合导数值(derivatives)查询三维纹理</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> Tex3Dproj(sampler3D tex, float4 szq)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 查询三维投影纹理,并进行深度值比较</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> texCUBE(samplerCUBE tex, float3 s)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 查询立方体纹理</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> texCUBE (samplerCUBE tex, float3 s, float3 dsdx, float3 dsdy)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 结合导数值(derivatives)查询立方体纹理</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> texCUBEproj (samplerCUBE tex, float4 sq)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 查询投影立方体纹理</td> </tr> </tbody> </table> 在这个表中,每个函数第二个参数的名字指明了在执行纹理查询的时候,它的值是如果被使用的: * s表示这是一个一元、二元或三元纹理坐标。 * z表示这是一个用来进行阴影贴图查找的深度比较值。 * q表示这是一个透视值,在进行纹理查找之前,它被用来除以纹理坐标(s)。 当你使用的纹理函数允许你指定一个深度比较值的时候,与之相关联的纹理单元必须被设置成深度比较纹理。否则,深度比较实际上不会被执行。 > ### (4)偏导函数 ### <table style="width:948.333px; border-collapse:collapse; border-spacing:0px; border:1px solid rgb(238,238,238); color:rgb(85,85,85); font-family:'microsoft yahei'; font-size:14px; line-height:35px"> <thead style=""> <tr style=""> <th align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 函数</th> <th align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 功能描述</th> </tr> </thead> <tbody style=""> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> ddx(a)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 近似<span style="">a</span>关于屏幕空间<span style="">x</span>轴的偏导数</td> </tr> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> ddy(a)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 近似<span style="">a</span>关于屏幕空间<span style="">y</span>轴的偏导数</td> </tr> </tbody> </table> > ### (5)调试函数 ### <table style="width:948.333px; border-collapse:collapse; border-spacing:0px; border:1px solid rgb(238,238,238); color:rgb(85,85,85); font-family:'microsoft yahei'; font-size:14px; line-height:35px"> <thead style=""> <tr style=""> <th align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 函数</th> <th align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 功能描述</th> </tr> </thead> <tbody style=""> <tr style=""> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> void debug(float4 x)</td> <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 如果在编译时设置了DEBUG,片段着 色程序中调用该函数可以将值x作为COLOR语义的最终输出;否则该函数什么也不做。</td> </tr> </tbody> </table> [http_blog.csdn.net_lcbcsdn_article_details_46848125]: http://blog.csdn.net/lcbcsdn/article/details/46848125
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