bzr branch
http://suren.me/webbzr/ani/mrses
1
by Suren A. Chilingaryan
Initial import |
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#include <stdio.h> |
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#include <string.h> |
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#include <assert.h> |
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#include <blas_s.h> |
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#include <simdmath.h> |
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#include <libvector.h> |
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#include <simdmath/sqrtf4.h> |
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#include <simdmath/fmaxf4.h> |
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#include <simdmath/divf4.h> |
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#include <simdmath/divf4_fast.h> |
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#include <simdmath/rsqrtf4.h> |
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#include <simdmath/recipf4.h> |
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#include <simdmath/recipf4_fast.h> |
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#include <simdmath/logf4.h> |
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#ifdef __SPU__
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#include <spu_intrinsics.h> |
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#else /* not __SPU__ */ |
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#include <altivec.h> |
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#endif
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static vector float zero = {0, 0, 0, 0}; |
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static vector float two = {2, 2, 2, 2}; |
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static vector float four = {4, 4, 4, 4}; |
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static vector float eight = {8, 8, 8, 8}; |
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// fast versions does not bring significant performance benefits
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// fmaxf between nan and zero is zero
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#define spu_max _fmaxf4
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// divide by zero: nan, nan; in fast mode -0, -0
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#define spu_div _divf4
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//#define spu_div _divf4_fast
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// sqrt of negative: 0; in fast mode: undefined, sqrt of nan: big num, ?
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#define spu_sqrt(a) _sqrtf4(spu_max(a, zero))
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//#define spu_sqrt(a) sqrtf4_fast(spu_max(a, zero))
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#define spu_recip _recipf4
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//#define spu_recip _recipf4_fast
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#define spu_rsqrt _rsqrtf4
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#define spu_log _logf4
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#define VECTOR_PRINT(var, val) \
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printf("Vector %10s is: {% 6.4e, % 6.4e, % 6.4e, % 6.4e}\n", var, spu_extract(val, 0), spu_extract(val, 1), spu_extract(val, 2), spu_extract(val, 3));
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#define iVECTOR_PRINT(var, val) \
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printf("Vector %10s is: {%i, %i, %i, %i}\n", var, spu_extract(val, 0), spu_extract(val, 1), spu_extract(val, 2), spu_extract(val, 3));
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#define VECTOR_PRINT_MATRIX(num, fmt, MATRIX, width, n, m) \
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{ \
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int i, j; \
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for (i = 0; i < n; i++) { \
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for (j = 0; j < m; j++) \
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printf(fmt, spu_extract(MATRIX[i * width + j], num)); \
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printf("\n"); \
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} \
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printf("\n"); \
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}
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inline static vector unsigned int vec_potrfU_4(vector float *A, const short int lda) |
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{
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vector float *pA1=A+lda, *pA2=pA1+lda, *pA3=pA2+lda; |
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vector float L11 = *A, L21 = *pA1, L31 = *pA2, L41 = *pA3; |
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vector float L22 = pA1[1], L32 = pA2[1], L42 = pA3[1]; |
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vector float L33 = pA2[2], L43 = pA3[2]; |
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vector float L44 = pA3[3]; |
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vector unsigned int errors; |
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errors = spu_cmpgt(L11, zero); |
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L11 = spu_rsqrt(L11); |
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*A = spu_recip(L11); |
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L21 = spu_mul(L21, L11); |
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L31 = spu_mul(L31, L11); |
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L41 = spu_mul(L41, L11); |
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*pA1 = L21; |
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*pA2 = L31; |
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*pA3 = L41; |
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L22 = spu_nmsub(L21, L21, L22); // L22 -= L21*L21; |
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errors = spu_and(spu_cmpgt(L22, zero), errors); |
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L22 = spu_rsqrt(L22); |
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pA1[1] = spu_recip(L22); |
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L32 = spu_mul(L22, spu_nmsub(L31, L21, L32)); // (L32 - L31*L21) * L22; |
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L42 = spu_mul(L22, spu_nmsub(L41, L21, L42)); // (L42 - L41*L21) * L22; |
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L33 = spu_nmsub(L32, L32, spu_nmsub(L31, L31, L33)); // (L33 - L31*L31) - L32*L32; |
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pA2[1] = L32; |
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pA3[1] = L42; |
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errors = spu_and(spu_cmpgt(L33, zero), errors); |
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105 |
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L33 = spu_rsqrt(L33); |
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pA2[2] = spu_recip(L33); |
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108 |
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L43 = spu_mul(L33, spu_nmsub(L42, L32, spu_nmsub(L41, L31, L43))); // ((L43 - L41*L31) - L42*L32) * L33; |
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L44 = spu_nmsub(L43, L43, spu_nmsub(L42, L42, spu_nmsub(L41, L41, L44))); // (((L44 - L41*L41) - L42*L42) - L43*L43); |
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pA3[2] = L43; |
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errors = spu_and(spu_cmpgt(L44, zero), errors); |
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pA3[3] = spu_sqrt(L44); |
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115 |
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return errors; |
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}
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inline static vector unsigned int vec_potrfU_3(vector float *A, const short int lda) |
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{
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vector float *pA1=A+lda, *pA2=pA1+lda; |
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register vector float L11 = *A, L21 = *pA1, L31 = *pA2; |
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register vector float L22=pA1[1], L32=pA2[1]; |
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register vector float L33=pA2[2]; |
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vector unsigned int errors; |
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128 |
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errors = spu_cmpgt(L11, zero); |
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L11 = spu_rsqrt(L11); |
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*A = spu_recip(L11); |
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L21 = spu_mul(L21, L11); |
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L31 = spu_mul(L31, L11); |
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*pA1 = L21; |
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*pA2 = L31; |
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L22 = spu_nmsub(L21, L21, L22); |
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errors = spu_and(spu_cmpgt(L22, zero), errors); |
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L22 = spu_rsqrt(L22); |
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L32 = spu_mul( spu_nmsub(L31, L21, L32), L22); // (L32 - L31*L21) / sqrt(L22); |
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L33 = spu_nmsub(L32, L32, spu_nmsub(L31, L31, L33)); // (L33 - L31*L31) - L32 * L32; |
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errors = spu_and(spu_cmpgt(L33, zero), errors); |
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pA1[1] = spu_recip(L22); |
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pA2[1] = L32; |
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pA2[2] = spu_sqrt(L33); |
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return errors; |
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}
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inline static vector unsigned int vec_potrfU_2(vector float *A, const short int lda) |
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{
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vector float *pA1 = A + lda; |
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register vector float L11 = *A, L21 = *pA1, L22 = pA1[1]; |
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register vector unsigned int errors; |
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errors = spu_cmpgt(L11, zero); |
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L11 = spu_rsqrt(L11); |
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*A = spu_recip(L11); |
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*pA1 = L21 = spu_mul(L21, L11); // division by zero |
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L22 = spu_nmsub(L21, L21, L22); // L22 -= L21*L21; |
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errors = spu_and(spu_cmpgt(L22, zero), errors); |
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pA1[1] = spu_sqrt(L22); |
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return errors; |
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}
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inline static void vec_strsv_rlnn (short int N, const vector float *A, const int lda, vector float *X) { |
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register short int i, j; |
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183 |
for (i = 0; i < N; i++) { |
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vector float tmp = X[i]; |
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186 |
for (j = 0; j < i; j++) { |
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tmp = spu_nmsub(A[lda * i + j], X[j], tmp); // tmp -= A[lda * i + j] * X[j]; |
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}
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X[i] = spu_div(tmp, A[(lda + 1) * i]); // X[i] = tmp / A[lda * i + i]; |
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}
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}
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#define BLOCK_X 4
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#define BLOCK_Y 8
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#include <sum_across_float4.h> |
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#include "vec_potrf_mtxmul.h" |
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#define HSUM(r1,r2,r3,r4) \
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tmp1 = spu_rlqwbyte(r1, 8); \
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tmp2 = spu_rlqwbyte(r3, 8); \
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\
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tmp3 = spu_sel(r1, r3, mask1); \
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tmp4 = spu_sel(tmp1, tmp2, mask1); \
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tmp5 = spu_add(tmp3, tmp4); \
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\
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tmp1 = spu_rlqwbyte(r2, 8); \
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tmp2 = spu_rlqwbyte(r4, 8); \
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\
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tmp3 = spu_sel(r2, r4, mask1); \
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tmp4 = spu_sel(tmp1, tmp2, mask1); \
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tmp6 = spu_add(tmp3, tmp4); \
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\
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tmp1 = spu_rlqwbyte(tmp5, 4); \
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tmp2 = spu_rlqwbyte(tmp6, -4); \
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\
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tmp3 = spu_sel(tmp5, tmp6, mask2); \
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tmp4 = spu_sel(tmp1, tmp2, mask2); \
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\
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tmp5 = spu_add(tmp3, tmp4);
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#define DO_MATRIX(size) \
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DECLARE_R##size \
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for (k = 0; k < K; k += BLOCK_X) { \
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const vector float *B = A + k; \
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\
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DECLARE_T##size(B) \
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COMPUTE_T##size(C) \
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} \
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SUM_T##size(C)
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#include "tools.h" |
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void vec_ssyrk_rln_11 (short int N, short int K, const vector float *A, short int lda, float *C, short int ldc) |
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{
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register short int k; |
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register vector float tmp1, tmp2, tmp3, tmp4, tmp5, tmp6; |
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register vector unsigned int mask1 = {0, 0, 0xFFFFFFFF, 0xFFFFFFFF}; |
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register vector unsigned int mask2 = {0, 0xFFFFFFFF, 0, 0xFFFFFFFF}; |
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assert((K%16)==0); |
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K >>= 2; |
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lda >>= 2; |
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248 |
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249 |
if (N < 5) { |
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250 |
if (N < 3) { |
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251 |
if (N < 2) { |
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DO_MATRIX(1) |
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} else { |
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DO_MATRIX(2) |
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}
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} else { |
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if (N < 4) { |
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DO_MATRIX(3) |
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} else { |
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DO_MATRIX(4) |
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}
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}
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} else if (N < 9) { |
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if (N < 7) { |
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if (N < 6) { |
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DO_MATRIX(5) |
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} else { |
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DO_MATRIX(6) |
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}
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} else { |
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if (N < 8) { |
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DO_MATRIX(7) |
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} else { |
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DO_MATRIX(8) |
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}
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}
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} else if (N < 12) { |
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if (N < 11) { |
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279 |
if (N < 10) { |
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DO_MATRIX(9) |
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} else { |
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DO_MATRIX(10) |
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}
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} else { |
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285 |
if (N < 12) { |
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DO_MATRIX(11); |
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} else { |
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DO_MATRIX(12); |
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}
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}
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} else { |
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// assert((N%16)==0);
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// ldc is walloc, we can have N=ralloc smaller for memory optimization, but still should use walloc here to have multiple of 16
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294 |
memset(C, 0, N * ldc * sizeof(float)); |
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295 |
ssyrk_spu((float*)A, C, 1, /*N*/ldc, K * 4, lda * 4, ldc); |
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296 |
}
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297 |
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298 |
/*
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299 |
int i,j;
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300 |
for (i = 0; i < N; i++) {
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301 |
for (j = 0; j <= i; j++) {
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register vector float temp = zero;
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303 |
for (k = 0; k < K; k++) {
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temp = spu_madd(A[i * lda + k], A[j * lda + k], temp);
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305 |
}
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306 |
C[i * ldc + j] = spu_extract(temp, 0) + spu_extract(temp, 1) + spu_extract(temp, 2) + spu_extract(temp, 3);
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}
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}
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*/
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}
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311 |
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312 |
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313 |
#define DO_ROW(size) \
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314 |
DECLARE_VR##size \
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315 |
for (k = 0; k < K; k += BLOCK_X) { \
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const vector float *B = A + row * lda + k; \
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\
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318 |
DECLARE_VX(B) \
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319 |
COMPUTE_V##size((A + l * lda + k)) \
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320 |
} \
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321 |
SUM_V##size(((vector float*)(C+l)));
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322 |
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323 |
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void vec_update_row (short int row, short int N, short int K, const vector float *A, short int lda, float *C) { |
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int k, l; |
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326 |
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327 |
register vector float tmp1, tmp2, tmp3, tmp4, tmp5, tmp6; |
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328 |
register vector unsigned int mask1 = {0, 0, 0xFFFFFFFF, 0xFFFFFFFF}; |
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register vector unsigned int mask2 = {0, 0xFFFFFFFF, 0, 0xFFFFFFFF}; |
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// vector float temp;
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331 |
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332 |
assert((K%16)==0); |
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333 |
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K >>= 2; |
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lda >>= 2; |
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336 |
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337 |
for (l = 0; l < N; l+=16) { |
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338 |
short int rem = min(16, N - l); |
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339 |
||
340 |
if (rem < 9) { |
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341 |
if (rem < 5) { |
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342 |
if (rem < 3) { |
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343 |
if (rem < 2) { |
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344 |
DO_ROW(1) |
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345 |
} else { |
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346 |
DO_ROW(2) |
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347 |
}
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348 |
} else { |
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349 |
if (rem < 4) { |
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350 |
DO_ROW(3) |
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351 |
} else { |
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DO_ROW(4) |
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}
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354 |
}
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355 |
} else |
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356 |
if (rem < 7) { |
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357 |
if (rem < 6) { |
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358 |
DO_ROW(5) |
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359 |
} else { |
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360 |
DO_ROW(6) |
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361 |
}
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362 |
} else { |
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363 |
if (rem < 8) { |
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364 |
DO_ROW(7) |
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365 |
} else { |
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366 |
DO_ROW(8) |
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367 |
}
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368 |
}
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369 |
} else { |
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370 |
if (rem < 12) { |
|
371 |
if (rem < 11) { |
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372 |
if (rem < 10) { |
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373 |
DO_ROW(9) |
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374 |
} else { |
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375 |
DO_ROW(10) |
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376 |
}
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377 |
} else { |
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378 |
if (rem < 12) { |
|
379 |
DO_ROW(11); |
|
380 |
} else { |
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381 |
DO_ROW(12); |
|
382 |
}
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383 |
}
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384 |
} else { |
|
385 |
if (rem < 15) { |
|
386 |
if (rem < 14) { |
|
387 |
DO_ROW(13) |
|
388 |
} else { |
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389 |
DO_ROW(14) |
|
390 |
}
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391 |
} else { |
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392 |
if (rem < 16) { |
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393 |
DO_ROW(15); |
|
394 |
} else { |
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395 |
DO_ROW(16); |
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396 |
}
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397 |
}
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398 |
}
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399 |
}
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400 |
}
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401 |
||
402 |
||
403 |
/*
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404 |
DECLARE_VR5
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405 |
for (k = 0; k < K; k+= BLOCK_X) {
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406 |
const vector float *B = A + row * lda + k;
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407 |
||
408 |
DECLARE_VX(B)
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409 |
COMPUTE_V5((A + l * lda + k))
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410 |
}
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411 |
SUM_V5(((vector float*)(C+l)));
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412 |
*/
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413 |
||
414 |
||
415 |
/*
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|
416 |
vector float temp[N];
|
|
417 |
memset(temp, 0, sizeof(vector float)*N);
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|
418 |
for (k = 0; k < K; k++) {
|
|
419 |
||
420 |
register vector float Arow = A[row * lda + k];
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|
421 |
for (l = 0; l < N; l++) {
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|
422 |
temp[l] = spu_madd(Arow, A[l * lda + k], temp[l]);
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423 |
C[l] = spu_extract(temp[l], 0) + spu_extract(temp[l], 1) + spu_extract(temp[l], 2) + spu_extract(temp[l], 3);
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|
424 |
}
|
|
425 |
if ((k%4)==3) {
|
|
426 |
printf("Step: %i\n",k);
|
|
427 |
PRINT_MATRIX("% 6.4f ", C, 1, 1, 16);
|
|
428 |
}
|
|
429 |
}
|
|
430 |
for (l = 0; l < N; l++) {
|
|
431 |
C[l] = spu_extract(temp[l], 0) + spu_extract(temp[l], 1) + spu_extract(temp[l], 2) + spu_extract(temp[l], 3);
|
|
432 |
}
|
|
433 |
PRINT_MATRIX("% 6.4f ", C, 1, 1, 16);
|
|
434 |
*/
|
|
435 |
||
436 |
/*
|
|
437 |
for (l = 0; l < N; l++) {
|
|
438 |
if (l < row) {
|
|
439 |
i = l; j = row;
|
|
440 |
} else {
|
|
441 |
i = row; j = l;
|
|
442 |
}
|
|
443 |
||
444 |
register vector float tmp = zero;
|
|
445 |
for (k = 0; k < K; k++) {
|
|
446 |
tmp = spu_madd(A[i * lda + k], A[j * lda + k], tmp);
|
|
447 |
}
|
|
448 |
C[l] = spu_extract(tmp, 0) + spu_extract(tmp, 1) + spu_extract(tmp, 2) + spu_extract(tmp, 3);
|
|
449 |
}
|
|
450 |
||
451 |
PRINT_MATRIX("% 6.4f ", C, 1, 1, 16);
|
|
452 |
*/
|
|
453 |
}
|
|
454 |
||
455 |
||
456 |
inline static void vec_spotrf_step(const short int M, const short int N, vector float *A, const short int lda) { |
|
457 |
register short int i, j, k; |
|
458 |
||
459 |
vector float *B = A + M * lda; |
|
460 |
vector float *C = B + M; |
|
461 |
||
462 |
||
463 |
for (i = 0; i < N; i++) { |
|
464 |
for (j = 0; j < M; j++) { |
|
465 |
vector float sum = {0, 0, 0, 0}; |
|
466 |
||
467 |
for (k = 0; k < j; k++) { |
|
468 |
sum = spu_madd(A[j * lda + k], B[i * lda + k], sum); |
|
469 |
}
|
|
470 |
||
471 |
B[i * lda + j] = spu_div(spu_sub(B[i * lda + j], sum), A[j * lda + j]); |
|
472 |
}
|
|
473 |
||
474 |
for (j = 0; j <= i; j++) { |
|
475 |
vector float temp = {0, 0, 0, 0}; |
|
476 |
||
477 |
for (k = 0; k < M; k++) { |
|
478 |
temp = spu_madd(B[i * lda + k], B[j * lda + k], temp); |
|
479 |
}
|
|
480 |
||
481 |
C[i * lda + j] = spu_sub(C[i * lda + j], temp); |
|
482 |
}
|
|
483 |
}
|
|
484 |
}
|
|
485 |
||
486 |
||
487 |
// we ignore errors if it will lead to 0 determinant
|
|
488 |
vector unsigned int vec_spotrf_u(short int N, vector float *A, short int lda) { |
|
489 |
short int Nleft, Nright; |
|
490 |
||
491 |
vector unsigned int errors; |
|
492 |
||
493 |
//PRINT_MULTIMATRIX(0, "% 7.4f ", ((float*)A), 5, 5, 5);
|
|
494 |
||
495 |
if (N > 4) { |
|
496 |
Nleft = N >> 1; |
|
497 |
Nright = N - Nleft; |
|
498 |
||
499 |
// printf("passed matrix\n");
|
|
500 |
// VECTOR_PRINT_MATRIX(0, "% 8.4f ", A, 5, 5, 5);
|
|
501 |
||
502 |
errors = vec_spotrf_u(Nleft, A, lda); |
|
503 |
||
504 |
// printf("left\n");
|
|
505 |
// VECTOR_PRINT_MATRIX(0, "% 8.4f ", A, 5, 5, 5);
|
|
506 |
||
507 |
vec_spotrf_step(Nleft, Nright, A, lda); |
|
508 |
// printf("step\n");
|
|
509 |
// VECTOR_PRINT_MATRIX(0, "% 8.4f ", A, 5, 5, 5);
|
|
510 |
||
511 |
spu_and(vec_spotrf_u(Nright, A + (lda + 1) * Nleft, lda), errors); |
|
512 |
// printf("right\n");
|
|
513 |
// VECTOR_PRINT_MATRIX(0, "% 8.4f ", A, 5, 5, 5);
|
|
514 |
||
515 |
}
|
|
516 |
else if (N==4) errors = vec_potrfU_4(A, lda); |
|
517 |
else if (N==3) errors = vec_potrfU_3(A, lda); |
|
518 |
else if (N==2) errors = vec_potrfU_2(A, lda); |
|
519 |
else if (N==1) { |
|
520 |
errors = spu_cmpgt(*A, zero); |
|
521 |
*A = spu_sqrt(*A); |
|
522 |
} else return spu_cmpgt(zero, zero); // anything |
|
523 |
||
524 |
return errors; |
|
525 |
}
|
|
526 |
||
527 |
vector float vec_rcorr(short int N, vector float *C, vector float *Ca, vector float *Cb) { |
|
528 |
short int i; |
|
529 |
short int step = N + 1; |
|
530 |
short int end = N * N; |
|
531 |
vector float detC, detAB; |
|
532 |
||
533 |
// VECTOR_PRINT_MATRIX(1, "%6.4f", C, 5, 5, 5);
|
|
534 |
||
535 |
detC = C[0]; |
|
536 |
detAB = Ca[0] * Cb[0]; |
|
537 |
for (i = step; i < end; i+= step) { |
|
538 |
detAB = spu_mul(detAB, spu_mul(Ca[i], Cb[i])); |
|
539 |
detC = spu_mul(detC, C[i]); |
|
540 |
}
|
|
541 |
||
542 |
/*
|
|
543 |
VECTOR_PRINT("detAB", detAB);
|
|
544 |
VECTOR_PRINT("detC", detC);
|
|
545 |
VECTOR_PRINT("detC^2", spu_mul(detC, detC));
|
|
546 |
VECTOR_PRINT("C/AB", spu_div(spu_mul(detC, detC), detAB));
|
|
547 |
VECTOR_PRINT("log", spu_log(spu_div(spu_mul(detC, detC), detAB)));
|
|
548 |
*/
|
|
549 |
||
550 |
return spu_mul(two, spu_log(spu_div(spu_mul(detC, detC), detAB))); |
|
551 |
}
|
|
552 |
||
553 |
vector float vec_rmahal(short int N, vector float *C, vector float *X) { |
|
554 |
register short int i; |
|
555 |
vector float sum = zero; |
|
556 |
||
557 |
vec_strsv_rlnn(N, C, N, X); |
|
558 |
for (i = 0; i < N; i++) { |
|
559 |
vector float val = X[i]; |
|
560 |
sum = spu_madd(val, val, sum); |
|
561 |
}
|
|
562 |
||
563 |
return sum; |
|
564 |
}
|
|
565 |
||
566 |
vector float vec_bhata(vector float rcorr, vector float rmahal) { |
|
567 |
return spu_add(spu_div(rmahal, eight), spu_div(rcorr, four)); |
|
568 |
}
|
|
569 |