我們如何使用 SSE2 在雙精度數和 64 位元整數之間高效轉換？

無需AVX512 的高效Double/Int64 轉換

SSE2 提供了在浮點數和32 位元整數之間進行轉換的指令，但缺少在浮點數和32 位元整數之間進行轉換的等效指令雙精確度數和64位整數。我們如何有效模擬此類轉換？

偷工減料轉換

如果範圍限制可以接受，以下技巧可以只用兩條指令執行轉換：

雙倍Int64

__m128i double_to_int64(__m128d x) {
    x = _mm_add_pd(x, _mm_set1_pd(0x0018000000000000));
    return _mm_sub_epi64(_mm_castpd_si128(x), _mm_castpd_si128(_mm_set1_pd(0x0018000000000000)));
}

雙精度到UInt64

__m128i double_to_uint64(__m128d x){
    x = _mm_add_pd(x, _mm_set1_pd(0x0010000000000000));
    return _mm_xor_si128(_mm_castpd_si128(x), _mm_castpd_si128(_mm_set1_pd(0x0010000000000000)));
}

Int64 到雙精確度

__m128d int64_to_double(__m128i x){
    x = _mm_add_epi64(x, _mm_castpd_si128(_mm_set1_pd(0x0018000000000000)));
    return _mm_sub_pd(_mm_castsi128_pd(x), _mm_set1_pd(0x0018000000000000));
}

UInt64到Double

__m128d uint64_to_double(__m128i x){
    x = _mm_or_si128(x, _mm_castpd_si128(_mm_set1_pd(0x0010000000000000)));
    return _mm_sub_pd(_mm_castsi128_pd(x), _mm_set1_pd(0x0010000000000000));
}

全範圍轉換

對於處理全範圍64 位元整數的轉換，以下是最佳化實作：

UInt64到雙精確度

__m128d uint64_to_double_full(__m128i x){
    __m128i xH = _mm_srli_epi64(x, 32);
    xH = _mm_or_si128(xH, _mm_castpd_si128(_mm_set1_pd(19342813113834066795298816.)));          //  2^84
    __m128i xL = _mm_blend_epi16(x, _mm_castpd_si128(_mm_set1_pd(0x0010000000000000)), 0xcc);   //  2^52
    __m128d f = _mm_sub_pd(_mm_castsi128_pd(xH), _mm_set1_pd(19342813118337666422669312.));     //  2^84 + 2^52
    return _mm_add_pd(f, _mm_castsi128_pd(xL));
}

Int64 轉雙精確度

__m128d int64_to_double_full(__m128i x){
    __m128i xH = _mm_srai_epi32(x, 16);
    xH = _mm_blend_epi16(xH, _mm_setzero_si128(), 0x33);
    xH = _mm_add_epi64(xH, _mm_castpd_si128(_mm_set1_pd(442721857769029238784.)));              //  3*2^67
    __m128i xL = _mm_blend_epi16(x, _mm_castpd_si128(_mm_set1_pd(0x0010000000000000)), 0x88);   //  2^52
    __m128d f = _mm_sub_pd(_mm_castsi128_pd(xH), _mm_set1_pd(442726361368656609280.));          //  3*2^67 + 2^52
    return _mm_add_pd(f, _mm_castsi128_pd(xL));
}

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