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Clarification of "magic" constants #4

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Clarification of "magic" constants #4

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25b41ea
Constants clarified
jneb Sep 4, 2023
f66a0d2
All constants clarified
jneb Sep 5, 2023
6c4ace2
Clarification added to AVX512 version
jneb Sep 5, 2023
ceac2d4
Fixed typo
jneb Sep 5, 2023
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13 changes: 9 additions & 4 deletions Source/DigitViewer2/RawToDecKernels/Kernels_i64_to_dec_x64_AVX2.h
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Original file line number Diff line number Diff line change
Expand Up @@ -36,9 +36,11 @@ YM_FORCE_INLINE __m256i div_100000000(__m256i x0){

r3 = _mm256_shuffle_epi32(x0, 177);

r0 = _mm256_mul_epu32(x0, _mm256_set1_epi32(2882303761));
r1 = _mm256_mul_epu32(r3, _mm256_set1_epi32(2221002493));
r2 = _mm256_mul_epu32(x0, _mm256_set1_epi32(2221002493));
// 2**90 / 10**8 = 0xabcc77118461cefc.e
// round up and split in two values: 0xabcc7711 and 0x8461cefd
r0 = _mm256_mul_epu32(x0, _mm256_set1_epi32(0xabcc7711));
r1 = _mm256_mul_epu32(r3, _mm256_set1_epi32(0x8461cefd));
r2 = _mm256_mul_epu32(x0, _mm256_set1_epi32(0x8461cefd));

r2 = _mm256_srli_epi64(r2, 32);
r0 = _mm256_add_epi64(r0, r2);
Expand All @@ -48,7 +50,7 @@ YM_FORCE_INLINE __m256i div_100000000(__m256i x0){
r0 = _mm256_srli_epi64(r0, 32);
r1 = _mm256_srli_epi64(r1, 32);

r3 = _mm256_mul_epu32(r3, _mm256_set1_epi32(2882303761));
r3 = _mm256_mul_epu32(r3, _mm256_set1_epi32(0x8461cefd));
r3 = _mm256_add_epi64(r3, r0);
r3 = _mm256_add_epi64(r3, r1);

Expand Down Expand Up @@ -83,6 +85,7 @@ YM_FORCE_INLINE void i64_to_dec_x64_AVX2(

// Invariant multiply
hi = _mm256_shuffle_epi32(x0, 177);
// 3518437209 = 2**45 / 10000, rounded up
lo = _mm256_mul_epu32(x0, _mm256_set1_epi32(3518437209));
hi = _mm256_mul_epu32(hi, _mm256_set1_epi32(3518437209));

Expand All @@ -104,6 +107,7 @@ YM_FORCE_INLINE void i64_to_dec_x64_AVX2(

// Divide
hi = _mm256_srli_epi16(c0, 2);
// 5243 = 2**19 / 100, rounded up
hi = _mm256_mulhi_epu16(hi, _mm256_set1_epi16(5243));
hi = _mm256_srli_epi16(hi, 1);

Expand Down Expand Up @@ -135,6 +139,7 @@ YM_FORCE_INLINE void i64_to_dec_x64_AVX2(
__m256i lo, hi;

// Divide
// 205 = 2**11 / 10, rounded up
hi = _mm256_mullo_epi16(c0, _mm256_set1_epi16(205));
hi = _mm256_srli_epi16(hi, 11);

Expand Down
14 changes: 10 additions & 4 deletions Source/DigitViewer2/RawToDecKernels/Kernels_i64_to_dec_x64_AVX512-BW.h
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Original file line number Diff line number Diff line change
Expand Up @@ -35,10 +35,13 @@ YM_FORCE_INLINE __m512i div_100000000(__m512i x0){
__m512i r0, r1, r2, r3;

r3 = _mm512_shuffle_epi32(x0, _MM_PERM_CDAB);

// 2**90 / 10**8 = 0xabcc77118461cefc.e
// round up and split in two values: 0xabcc7711 and 0x8461cefd

r0 = _mm512_mul_epu32(x0, _mm512_set1_epi32(2882303761));
r1 = _mm512_mul_epu32(r3, _mm512_set1_epi32(2221002493));
r2 = _mm512_mul_epu32(x0, _mm512_set1_epi32(2221002493));
r0 = _mm512_mul_epu32(x0, _mm512_set1_epi32(0xabcc7711));
r1 = _mm512_mul_epu32(r3, _mm512_set1_epi32(0x8461cefd));
r2 = _mm512_mul_epu32(x0, _mm512_set1_epi32(0x8461cefd));

r2 = _mm512_srli_epi64(r2, 32);
r0 = _mm512_add_epi64(r0, r2);
Expand All @@ -48,7 +51,7 @@ YM_FORCE_INLINE __m512i div_100000000(__m512i x0){
r0 = _mm512_srli_epi64(r0, 32);
r1 = _mm512_srli_epi64(r1, 32);

r3 = _mm512_mul_epu32(r3, _mm512_set1_epi32(2882303761));
r3 = _mm512_mul_epu32(r3, _mm512_set1_epi32(0x8461cefd));
r3 = _mm512_add_epi64(r3, r0);
r3 = _mm512_add_epi64(r3, r1);

Expand Down Expand Up @@ -82,6 +85,7 @@ YM_FORCE_INLINE void i64_to_dec_x64_AVX512BW(

// Invariant multiply
hi = _mm512_shuffle_epi32(x0, _MM_PERM_CDAB);
// 3518437209 = 2**45 / 10000, rounded up
lo = _mm512_mul_epu32(x0, _mm512_set1_epi32(3518437209));
hi = _mm512_mul_epu32(hi, _mm512_set1_epi32(3518437209));
hi = _mm512_mask_shuffle_epi32(hi, 0x5555, lo, _MM_PERM_CDAB);
Expand All @@ -102,6 +106,7 @@ YM_FORCE_INLINE void i64_to_dec_x64_AVX512BW(

// Divide
hi = _mm512_srli_epi16(c0, 2);
// 5243 = 2**19 / 100, rounded up
hi = _mm512_mulhi_epu16(hi, _mm512_set1_epi16(5243));
hi = _mm512_srli_epi16(hi, 1);

Expand Down Expand Up @@ -134,6 +139,7 @@ YM_FORCE_INLINE void i64_to_dec_x64_AVX512BW(
__m512i hi;

// Divide
// 205 = 2**11 / 10, rounded up
hi = _mm512_mullo_epi16(c0, _mm512_set1_epi16(205));

#if 1
Expand Down