浮点模运算 [英] Floating Point Modulo Operation

问题描述

我正在尝试实现三角函数的范围缩减操作.但相反，我认为对传入数据执行模 pi/2 运算可能会更好.我想知道存在哪些算法并且对​​于 32 位 IEEE 754 浮点的此操作有效?

I am trying to implement the range reduction operation for trigonometry. But instead I think it might be better to just perform a modulo pi/2 operation on incoming data. I was wondering what algorithms exist and are efficient for this operation for 32-bit IEEE 754 floating-point?

我必须在汇编中实现它，所以 fmod、除法、乘法等仅靠一条指令对我来说是不可用的.我的处理器使用 16 位字，我已经实现了 32 位浮点加法、减法、乘法、除法、平方根、余弦和正弦.我只需要范围缩小(模数)来输入余弦和正弦值.

I have to implement this in assembly, so fmod, division, multiplication, etc. aren't available to me with just one instruction. My processor uses 16-bit words and I have implemented 32-bit floating point addition, subtraction, multiplication, division, square root, cosine, and sine. I just need range reduction (modulus) for inputting values to cosine and sine.

推荐答案

我认为标准库的 fmod() 在大多数情况下会是最好的选择.这是一个链接，讨论了几种简单的算法.

I think standard library's fmod() will be the best choice in most cases. Here's a link to a discussion of several simple algorithms.

在我的机器上，fmod() 使用优化的内联汇编代码(/usr/include/bits/mathinline.h):

On my machine, fmod() uses optimized inline assembly code (/usr/include/bits/mathinline.h):

#if defined __FAST_MATH__ && !__GNUC_PREREQ (3, 5)
__inline_mathcodeNP2 (fmod, __x, __y, 
  register long double __value;                           
  __asm __volatile__                                  
    ("1:    fprem
	"                            
     "fnstsw    %%ax
	"                             
     "sahf
	"                                   
     "jp    1b"                               
     : "=t" (__value) : "0" (__x), "u" (__y) : "ax", "cc");           
  return __value)
#endif

所以它实际上使用专用的 CPU 指令 (fprem) 进行计算.

So it actually uses a dedicated CPU instruction (fprem) for the calculation.

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