是否可以使用SSE和SSE2生成128位宽的整数? [英] Is it possible to use SSE and SSE2 to make a 128-bit wide integer?

问题描述

我希望对SSE2的功能有更多的了解，并想知道是否可以制作一个128位宽的整数以支持加，减，XOR和乘法?

解决方案

SSE2没有进位标志，但是您可以像此处

这是基于上述想法的未经测试，未经优化的C代码.

 inline bool lessthan(__m128i a, __m128i b){
    a = _mm_xor_si128(a, _mm_set1_epi32(0x80000000));
    b = _mm_xor_si128(b, _mm_set1_epi32(0x80000000));
    __m128i t = _mm_cmplt_epi32(a, b);
    __m128i u = _mm_cmpgt_epi32(a, b);
    __m128i z = _mm_or_si128(t, _mm_shuffle_epi32(t, 177));
    z = _mm_andnot_si128(_mm_shuffle_epi32(u, 245),z);
    return _mm_cvtsi128_si32(z) & 1;
}

inline __m128i addi128(__m128i a, __m128i b)
{
    __m128i sum = _mm_add_epi64(a, b);
    __m128i mask = _mm_set1_epi64(0x8000000000000000);    
    if (lessthan(_mm_xor_si128(mask, sum), _mm_xor_si128(mask, a)))
    {
        __m128i ONE = _mm_setr_epi64(0, 1);
        sum = _mm_add_epi64(sum, ONE);
    }

    return sum;
}
 

如您所见，代码需要更多指令，即使经过优化，它仍可能比x8​​6_64中的简单2 add/adc对(或x86中的4条指令)长得多.

---

如果要并行添加多个128位整数，则

SSE2会有所帮助.但是，您需要适当地排列值的高和低部分，以便我们可以一次添加所有低部分，也可以一次添加所有高部分

另请参见

• 可以使用实用的BigNum AVX/SSE吗?
• 长整数例程可以从SSE中受益吗?

I'm looking to understand SSE2's capabilities a little more, and would like to know if one could make a 128-bit wide integer that supports addition, subtraction, XOR and multiplication?

解决方案

SSE2 has no carry flag but you can easily calculate the carry as carry = sum < a or carry = sum < b like this. Worse yet, SSE2 doesn't have 64-bit comparisons either, so you must use some workaround like the one here

Here is an untested, unoptimized C code based on the idea above.

inline bool lessthan(__m128i a, __m128i b){
    a = _mm_xor_si128(a, _mm_set1_epi32(0x80000000));
    b = _mm_xor_si128(b, _mm_set1_epi32(0x80000000));
    __m128i t = _mm_cmplt_epi32(a, b);
    __m128i u = _mm_cmpgt_epi32(a, b);
    __m128i z = _mm_or_si128(t, _mm_shuffle_epi32(t, 177));
    z = _mm_andnot_si128(_mm_shuffle_epi32(u, 245),z);
    return _mm_cvtsi128_si32(z) & 1;
}

inline __m128i addi128(__m128i a, __m128i b)
{
    __m128i sum = _mm_add_epi64(a, b);
    __m128i mask = _mm_set1_epi64(0x8000000000000000);    
    if (lessthan(_mm_xor_si128(mask, sum), _mm_xor_si128(mask, a)))
    {
        __m128i ONE = _mm_setr_epi64(0, 1);
        sum = _mm_add_epi64(sum, ONE);
    }

    return sum;
}

As you can see, the code requires many more instructions and even after optimizing it may still be much longer than a simple 2 add/adc pair in x86_64 (or 4 instructions in x86)

---

SSE2 will help though, if you have multiple 128-bit integers to add in parallel. However you need to arrange the high and low parts of the values properly so that we can add all the low parts at once, and all the high parts at once

See also

• practical BigNum AVX/SSE possible?
• Can long integer routines benefit from SSE?

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