在装配单纯高位乘法？ [英] Pure high-bit multiplication in assembly?

问题描述

要实现0和1之间的实数，人们通常使用ANSI漂浮或双打。但是，0和1（小数模1）之间的固定的precision号可以有效地实现32位的整数或16位字，其中新增像普通整数/词，而是乘走错了路，意思是当你乘X倍Y，您保持产品的高位。这相当于乘以0.X和0.Y，其中X的所有位都在小数点后面。同样，签署数字之间-1和1也可实现这种方式与一个额外的位和移位。

To implement real numbers between 0 and 1, one usually uses ANSI floats or doubles. But fixed precision numbers between 0 and 1 (decimals modulo 1) can be efficiently implemented as 32 bit integers or 16 bit words, which add like normal integers/words, but which multiply the "wrong way", meaning that when you multiply X times Y, you keep the high order bits of the product. This is equivalent to multiplying 0.X and 0.Y, where all the bits of X are behind the decimal point. Likewise, signed numbers between -1 and 1 are also implementable this way with one extra bit and a shift.

一个人怎么会实现（尤其是在使用MMX或SSE）固定precision MOD 1或2的MOD用C？
我觉得这再presentation可能是酉矩阵的高效再presentation有用的，数字密集型的物理模拟。它使更多的MMX / SSE有整数数量，但你需要更高PMULHW级别的访问。

How would one implement fixed-precision mod 1 or mod 2 in C (especially using MMX or SSE)? I think this representation could be useful for efficient representation of unitary matrices, for numerically intensive physics simulations. It makes for more MMX/SSE to have integer quantities, but you need higher level access to PMULHW.

推荐答案

如果16位定点运算就足够了，你是在x86或类似的架构，可以直接使用SSE。搜索结果

If 16 bit fixed point arithmetic is sufficient and you are on x86 or a similar architecture, you can directly use SSE.

SSE3指令 pmulhrsw 直接实现签约0.15定点算术乘法运算（模2正如你所说的，从-1 .. + 1）硬件。除了不低于标准的16位矢量操作不同，只是用 PADDW 。

The SSE3 instruction pmulhrsw directly implements signed 0.15 fixed point arithmetic multiplication (mod 2 as you call it, from -1..+1) in hardware. Addition is not different than the standard 16 bit vector operations, just using paddw.

因此​​，这一次只处理乘法和加法八个符号的16位定点变量的库看起来是这样的：

So a library which handles multiplication and addition of eight signed 16 bit fixed point variables at a time could look like this:

typedef __v8hi fixed16_t;

fixed16_t mul(fixed16_t a, fixed16_t b) {
    return _mm_mulhrs_epi16(a,b);
}

fixed16_t add(fixed16_t a, fixed16_t b) {
    return _mm_add_epi16(a,b);
}

权限授予任何你喜欢的方式来使用它; - ）

Permission granted to use it in any way you like ;-)

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