Penukaran Double/Int64 yang Cekap tanpa AVX512
SSE2 menyediakan arahan untuk menukar antara apungan dan integer 32-bit, tetapi tidak mempunyai persamaan untuk menukar antara berganda dan integer 64-bit. Bagaimanakah kita boleh mensimulasikan penukaran sedemikian dengan cekap?
Penukaran Sudut Potong
Jika sekatan julat boleh diterima, helah berikut boleh melakukan penukaran hanya dalam dua arahan:
Berganda kepada 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))); }
Double kepada 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 to 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)); }
UInt64 ke Berganda
__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)); }
Penukaran Julat Penuh
Untuk penukaran yang mengendalikan julat penuh integer 64-bit, berikut ialah pelaksanaan yang dioptimumkan:
UInt64 ke Gandakan
__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 kepada Gandakan
__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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