How Can I Efficiently Convert Between Double-Precision Floats and 64-bit Integers Using SSE/AVX Instructions?

Efficient Double/int64 Conversions with SSE/AVX

SSE2 provides intrinsics for converting vectors between single-precision floats and 32-bit integers, but lacks direct counterparts for double-precision floating-point and 64-bit integers. AVX does not offer these conversions either.

Methods for simulating intrinsics

1. For limited values:

If certain limitations are tolerated, conversions between doubles and int64 can be performed with just two statements:

• double -> ; uint64_t:

  __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))
    );
  }

• double -> int64_t:

  __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))
    );
  }

• uint64_t -> 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));
  }

• int64_t -> double:

  __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));
  }

2. Full range int64 -> double:

To convert full range int64 to double, 5 instructions are needed for uint64_t and 6 instructions for int64_t:

• uint64_t -> ; double:

  __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_t -> double:

  __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));
  }

AVX512

AVX512 does offer direct conversions to/from 64-bit integers, both signed and unsigned signed. These conversions are done using intrinsics such as _mm512_cvtpd_epi64 and _mm256_cvtpd_epi64.

Please note that these solutions are not provided as complete code. The reader is expected to complete them and optimize them as necessary to adapt them to their specific context.

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