#include "blas_extended.h" #include "blas_extended_private.h" void BLAS_csymv_s_c_x(enum blas_order_type order, enum blas_uplo_type uplo, int n, const void *alpha, const float *a, int lda, const void *x, int incx, const void *beta, void *y, int incy, enum blas_prec_type prec) /* * Purpose * ======= * * This routines computes the matrix product: * * y <- alpha * A * x + beta * y * * where A is a Symmetric matrix. * * Arguments * ========= * * order (input) enum blas_order_type * Storage format of input symmetric matrix A. * * uplo (input) enum blas_uplo_type * Determines which half of matrix A (upper or lower triangle) * is accessed. * * n (input) int * Dimension of A and size of vectors x, y. * * alpha (input) const void* * * a (input) float* * Matrix A. * * lda (input) int * Leading dimension of matrix A. * * x (input) void* * Vector x. * * incx (input) int * Stride for vector x. * * beta (input) const void* * * y (input/output) void* * Vector y. * * incy (input) int * Stride for vector y. * * prec (input) enum blas_prec_type * Specifies the internal precision to be used. * = blas_prec_single: single precision. * = blas_prec_double: double precision. * = blas_prec_extra : anything at least 1.5 times as accurate * than double, and wider than 80-bits. * We use double-double in our implementation. * */ { /* Routine name */ static const char routine_name[] = "BLAS_csymv_s_c_x"; switch (prec) { case blas_prec_single:{ /* Integer Index Variables */ int i, k; int xi, yi; int aik, astarti, x_starti, y_starti; int incai; int incaik, incaik2; int n_i; /* Input Matrices */ const float *a_i = a; const float *x_i = (float *) x; /* Output Vector */ float *y_i = (float *) y; /* Input Scalars */ float *alpha_i = (float *) alpha; float *beta_i = (float *) beta; /* Temporary Floating-Point Variables */ float a_elem; float x_elem[2]; float y_elem[2]; float prod[2]; float sum[2]; float tmp1[2]; float tmp2[2]; /* Test for no-op */ if (n <= 0) { return; } if (alpha_i[0] == 0.0 && alpha_i[1] == 0.0 && (beta_i[0] == 1.0 && beta_i[1] == 0.0)) { return; } /* Check for error conditions. */ if (lda < n) { BLAS_error(routine_name, -3, n, NULL); } if (incx == 0) { BLAS_error(routine_name, -8, incx, NULL); } if (incy == 0) { BLAS_error(routine_name, -11, incy, NULL); } /* Set Index Parameters */ n_i = n; if ((order == blas_colmajor && uplo == blas_upper) || (order == blas_rowmajor && uplo == blas_lower)) { incai = lda; incaik = 1; incaik2 = lda; } else { incai = 1; incaik = lda; incaik2 = 1; } /* Adjustment to increments (if any) */ incx *= 2; incy *= 2; if (incx < 0) { x_starti = (-n + 1) * incx; } else { x_starti = 0; } if (incy < 0) { y_starti = (-n + 1) * incy; } else { y_starti = 0; } /* alpha = 0. In this case, just return beta * y */ if (alpha_i[0] == 0.0 && alpha_i[1] == 0.0) { for (i = 0, yi = y_starti; i < n_i; i++, yi += incy) { y_elem[0] = y_i[yi]; y_elem[1] = y_i[yi + 1]; { tmp1[0] = y_elem[0] * beta_i[0] - y_elem[1] * beta_i[1]; tmp1[1] = y_elem[0] * beta_i[1] + y_elem[1] * beta_i[0]; } y_i[yi] = tmp1[0]; y_i[yi + 1] = tmp1[1]; } } else if ((alpha_i[0] == 1.0 && alpha_i[1] == 0.0)) { /* Case alpha == 1. */ if (beta_i[0] == 0.0 && beta_i[1] == 0.0) { /* Case alpha = 1, beta = 0. We compute y <--- A * x */ for (i = 0, yi = y_starti, astarti = 0; i < n_i; i++, yi += incy, astarti += incai) { sum[0] = sum[1] = 0.0; for (k = 0, aik = astarti, xi = x_starti; k < i; k++, aik += incaik, xi += incx) { a_elem = a_i[aik]; x_elem[0] = x_i[xi]; x_elem[1] = x_i[xi + 1]; { prod[0] = x_elem[0] * a_elem; prod[1] = x_elem[1] * a_elem; } sum[0] = sum[0] + prod[0]; sum[1] = sum[1] + prod[1]; } for (; k < n_i; k++, aik += incaik2, xi += incx) { a_elem = a_i[aik]; x_elem[0] = x_i[xi]; x_elem[1] = x_i[xi + 1]; { prod[0] = x_elem[0] * a_elem; prod[1] = x_elem[1] * a_elem; } sum[0] = sum[0] + prod[0]; sum[1] = sum[1] + prod[1]; } y_i[yi] = sum[0]; y_i[yi + 1] = sum[1]; } } else { /* Case alpha = 1, but beta != 0. We compute y <--- A * x + beta * y */ for (i = 0, yi = y_starti, astarti = 0; i < n_i; i++, yi += incy, astarti += incai) { sum[0] = sum[1] = 0.0; for (k = 0, aik = astarti, xi = x_starti; k < i; k++, aik += incaik, xi += incx) { a_elem = a_i[aik]; x_elem[0] = x_i[xi]; x_elem[1] = x_i[xi + 1]; { prod[0] = x_elem[0] * a_elem; prod[1] = x_elem[1] * a_elem; } sum[0] = sum[0] + prod[0]; sum[1] = sum[1] + prod[1]; } for (; k < n_i; k++, aik += incaik2, xi += incx) { a_elem = a_i[aik]; x_elem[0] = x_i[xi]; x_elem[1] = x_i[xi + 1]; { prod[0] = x_elem[0] * a_elem; prod[1] = x_elem[1] * a_elem; } sum[0] = sum[0] + prod[0]; sum[1] = sum[1] + prod[1]; } y_elem[0] = y_i[yi]; y_elem[1] = y_i[yi + 1]; { tmp2[0] = y_elem[0] * beta_i[0] - y_elem[1] * beta_i[1]; tmp2[1] = y_elem[0] * beta_i[1] + y_elem[1] * beta_i[0]; } tmp1[0] = sum[0]; tmp1[1] = sum[1]; tmp1[0] = tmp2[0] + tmp1[0]; tmp1[1] = tmp2[1] + tmp1[1]; y_i[yi] = tmp1[0]; y_i[yi + 1] = tmp1[1]; } } } else { /* The most general form, y <--- alpha * A * x + beta * y */ for (i = 0, yi = y_starti, astarti = 0; i < n_i; i++, yi += incy, astarti += incai) { sum[0] = sum[1] = 0.0; for (k = 0, aik = astarti, xi = x_starti; k < i; k++, aik += incaik, xi += incx) { a_elem = a_i[aik]; x_elem[0] = x_i[xi]; x_elem[1] = x_i[xi + 1]; { prod[0] = x_elem[0] * a_elem; prod[1] = x_elem[1] * a_elem; } sum[0] = sum[0] + prod[0]; sum[1] = sum[1] + prod[1]; } for (; k < n_i; k++, aik += incaik2, xi += incx) { a_elem = a_i[aik]; x_elem[0] = x_i[xi]; x_elem[1] = x_i[xi + 1]; { prod[0] = x_elem[0] * a_elem; prod[1] = x_elem[1] * a_elem; } sum[0] = sum[0] + prod[0]; sum[1] = sum[1] + prod[1]; } y_elem[0] = y_i[yi]; y_elem[1] = y_i[yi + 1]; { tmp2[0] = y_elem[0] * beta_i[0] - y_elem[1] * beta_i[1]; tmp2[1] = y_elem[0] * beta_i[1] + y_elem[1] * beta_i[0]; } { tmp1[0] = sum[0] * alpha_i[0] - sum[1] * alpha_i[1]; tmp1[1] = sum[0] * alpha_i[1] + sum[1] * alpha_i[0]; } tmp1[0] = tmp2[0] + tmp1[0]; tmp1[1] = tmp2[1] + tmp1[1]; y_i[yi] = tmp1[0]; y_i[yi + 1] = tmp1[1]; } } break; } case blas_prec_double: case blas_prec_indigenous:{ /* Integer Index Variables */ int i, k; int xi, yi; int aik, astarti, x_starti, y_starti; int incai; int incaik, incaik2; int n_i; /* Input Matrices */ const float *a_i = a; const float *x_i = (float *) x; /* Output Vector */ float *y_i = (float *) y; /* Input Scalars */ float *alpha_i = (float *) alpha; float *beta_i = (float *) beta; /* Temporary Floating-Point Variables */ float a_elem; float x_elem[2]; float y_elem[2]; double prod[2]; double sum[2]; double tmp1[2]; double tmp2[2]; /* Test for no-op */ if (n <= 0) { return; } if (alpha_i[0] == 0.0 && alpha_i[1] == 0.0 && (beta_i[0] == 1.0 && beta_i[1] == 0.0)) { return; } /* Check for error conditions. */ if (lda < n) { BLAS_error(routine_name, -3, n, NULL); } if (incx == 0) { BLAS_error(routine_name, -8, incx, NULL); } if (incy == 0) { BLAS_error(routine_name, -11, incy, NULL); } /* Set Index Parameters */ n_i = n; if ((order == blas_colmajor && uplo == blas_upper) || (order == blas_rowmajor && uplo == blas_lower)) { incai = lda; incaik = 1; incaik2 = lda; } else { incai = 1; incaik = lda; incaik2 = 1; } /* Adjustment to increments (if any) */ incx *= 2; incy *= 2; if (incx < 0) { x_starti = (-n + 1) * incx; } else { x_starti = 0; } if (incy < 0) { y_starti = (-n + 1) * incy; } else { y_starti = 0; } /* alpha = 0. In this case, just return beta * y */ if (alpha_i[0] == 0.0 && alpha_i[1] == 0.0) { for (i = 0, yi = y_starti; i < n_i; i++, yi += incy) { y_elem[0] = y_i[yi]; y_elem[1] = y_i[yi + 1]; { tmp1[0] = (double) y_elem[0] * beta_i[0] - (double) y_elem[1] * beta_i[1]; tmp1[1] = (double) y_elem[0] * beta_i[1] + (double) y_elem[1] * beta_i[0]; } y_i[yi] = tmp1[0]; y_i[yi + 1] = tmp1[1]; } } else if ((alpha_i[0] == 1.0 && alpha_i[1] == 0.0)) { /* Case alpha == 1. */ if (beta_i[0] == 0.0 && beta_i[1] == 0.0) { /* Case alpha = 1, beta = 0. We compute y <--- A * x */ for (i = 0, yi = y_starti, astarti = 0; i < n_i; i++, yi += incy, astarti += incai) { sum[0] = sum[1] = 0.0; for (k = 0, aik = astarti, xi = x_starti; k < i; k++, aik += incaik, xi += incx) { a_elem = a_i[aik]; x_elem[0] = x_i[xi]; x_elem[1] = x_i[xi + 1]; { prod[0] = (double) x_elem[0] * a_elem; prod[1] = (double) x_elem[1] * a_elem; } sum[0] = sum[0] + prod[0]; sum[1] = sum[1] + prod[1]; } for (; k < n_i; k++, aik += incaik2, xi += incx) { a_elem = a_i[aik]; x_elem[0] = x_i[xi]; x_elem[1] = x_i[xi + 1]; { prod[0] = (double) x_elem[0] * a_elem; prod[1] = (double) x_elem[1] * a_elem; } sum[0] = sum[0] + prod[0]; sum[1] = sum[1] + prod[1]; } y_i[yi] = sum[0]; y_i[yi + 1] = sum[1]; } } else { /* Case alpha = 1, but beta != 0. We compute y <--- A * x + beta * y */ for (i = 0, yi = y_starti, astarti = 0; i < n_i; i++, yi += incy, astarti += incai) { sum[0] = sum[1] = 0.0; for (k = 0, aik = astarti, xi = x_starti; k < i; k++, aik += incaik, xi += incx) { a_elem = a_i[aik]; x_elem[0] = x_i[xi]; x_elem[1] = x_i[xi + 1]; { prod[0] = (double) x_elem[0] * a_elem; prod[1] = (double) x_elem[1] * a_elem; } sum[0] = sum[0] + prod[0]; sum[1] = sum[1] + prod[1]; } for (; k < n_i; k++, aik += incaik2, xi += incx) { a_elem = a_i[aik]; x_elem[0] = x_i[xi]; x_elem[1] = x_i[xi + 1]; { prod[0] = (double) x_elem[0] * a_elem; prod[1] = (double) x_elem[1] * a_elem; } sum[0] = sum[0] + prod[0]; sum[1] = sum[1] + prod[1]; } y_elem[0] = y_i[yi]; y_elem[1] = y_i[yi + 1]; { tmp2[0] = (double) y_elem[0] * beta_i[0] - (double) y_elem[1] * beta_i[1]; tmp2[1] = (double) y_elem[0] * beta_i[1] + (double) y_elem[1] * beta_i[0]; } tmp1[0] = sum[0]; tmp1[1] = sum[1]; tmp1[0] = tmp2[0] + tmp1[0]; tmp1[1] = tmp2[1] + tmp1[1]; y_i[yi] = tmp1[0]; y_i[yi + 1] = tmp1[1]; } } } else { /* The most general form, y <--- alpha * A * x + beta * y */ for (i = 0, yi = y_starti, astarti = 0; i < n_i; i++, yi += incy, astarti += incai) { sum[0] = sum[1] = 0.0; for (k = 0, aik = astarti, xi = x_starti; k < i; k++, aik += incaik, xi += incx) { a_elem = a_i[aik]; x_elem[0] = x_i[xi]; x_elem[1] = x_i[xi + 1]; { prod[0] = (double) x_elem[0] * a_elem; prod[1] = (double) x_elem[1] * a_elem; } sum[0] = sum[0] + prod[0]; sum[1] = sum[1] + prod[1]; } for (; k < n_i; k++, aik += incaik2, xi += incx) { a_elem = a_i[aik]; x_elem[0] = x_i[xi]; x_elem[1] = x_i[xi + 1]; { prod[0] = (double) x_elem[0] * a_elem; prod[1] = (double) x_elem[1] * a_elem; } sum[0] = sum[0] + prod[0]; sum[1] = sum[1] + prod[1]; } y_elem[0] = y_i[yi]; y_elem[1] = y_i[yi + 1]; { tmp2[0] = (double) y_elem[0] * beta_i[0] - (double) y_elem[1] * beta_i[1]; tmp2[1] = (double) y_elem[0] * beta_i[1] + (double) y_elem[1] * beta_i[0]; } { tmp1[0] = (double) sum[0] * alpha_i[0] - (double) sum[1] * alpha_i[1]; tmp1[1] = (double) sum[0] * alpha_i[1] + (double) sum[1] * alpha_i[0]; } tmp1[0] = tmp2[0] + tmp1[0]; tmp1[1] = tmp2[1] + tmp1[1]; y_i[yi] = tmp1[0]; y_i[yi + 1] = tmp1[1]; } } break; } case blas_prec_extra:{ /* Integer Index Variables */ int i, k; int xi, yi; int aik, astarti, x_starti, y_starti; int incai; int incaik, incaik2; int n_i; /* Input Matrices */ const float *a_i = a; const float *x_i = (float *) x; /* Output Vector */ float *y_i = (float *) y; /* Input Scalars */ float *alpha_i = (float *) alpha; float *beta_i = (float *) beta; /* Temporary Floating-Point Variables */ float a_elem; float x_elem[2]; float y_elem[2]; double head_prod[2], tail_prod[2]; double head_sum[2], tail_sum[2]; double head_tmp1[2], tail_tmp1[2]; double head_tmp2[2], tail_tmp2[2]; FPU_FIX_DECL; /* Test for no-op */ if (n <= 0) { return; } if (alpha_i[0] == 0.0 && alpha_i[1] == 0.0 && (beta_i[0] == 1.0 && beta_i[1] == 0.0)) { return; } /* Check for error conditions. */ if (lda < n) { BLAS_error(routine_name, -3, n, NULL); } if (incx == 0) { BLAS_error(routine_name, -8, incx, NULL); } if (incy == 0) { BLAS_error(routine_name, -11, incy, NULL); } /* Set Index Parameters */ n_i = n; if ((order == blas_colmajor && uplo == blas_upper) || (order == blas_rowmajor && uplo == blas_lower)) { incai = lda; incaik = 1; incaik2 = lda; } else { incai = 1; incaik = lda; incaik2 = 1; } /* Adjustment to increments (if any) */ incx *= 2; incy *= 2; if (incx < 0) { x_starti = (-n + 1) * incx; } else { x_starti = 0; } if (incy < 0) { y_starti = (-n + 1) * incy; } else { y_starti = 0; } FPU_FIX_START; /* alpha = 0. In this case, just return beta * y */ if (alpha_i[0] == 0.0 && alpha_i[1] == 0.0) { for (i = 0, yi = y_starti; i < n_i; i++, yi += incy) { y_elem[0] = y_i[yi]; y_elem[1] = y_i[yi + 1]; { double head_e1, tail_e1; double d1; double d2; /* Real part */ d1 = (double) y_elem[0] * beta_i[0]; d2 = (double) -y_elem[1] * beta_i[1]; { /* Compute double-double = double + double. */ double e, t1, t2; /* Knuth trick. */ t1 = d1 + d2; e = t1 - d1; t2 = ((d2 - e) + (d1 - (t1 - e))); /* The result is t1 + t2, after normalization. */ head_e1 = t1 + t2; tail_e1 = t2 - (head_e1 - t1); } head_tmp1[0] = head_e1; tail_tmp1[0] = tail_e1; /* imaginary part */ d1 = (double) y_elem[0] * beta_i[1]; d2 = (double) y_elem[1] * beta_i[0]; { /* Compute double-double = double + double. */ double e, t1, t2; /* Knuth trick. */ t1 = d1 + d2; e = t1 - d1; t2 = ((d2 - e) + (d1 - (t1 - e))); /* The result is t1 + t2, after normalization. */ head_e1 = t1 + t2; tail_e1 = t2 - (head_e1 - t1); } head_tmp1[1] = head_e1; tail_tmp1[1] = tail_e1; } y_i[yi] = head_tmp1[0]; y_i[yi + 1] = head_tmp1[1]; } } else if ((alpha_i[0] == 1.0 && alpha_i[1] == 0.0)) { /* Case alpha == 1. */ if (beta_i[0] == 0.0 && beta_i[1] == 0.0) { /* Case alpha = 1, beta = 0. We compute y <--- A * x */ for (i = 0, yi = y_starti, astarti = 0; i < n_i; i++, yi += incy, astarti += incai) { head_sum[0] = head_sum[1] = tail_sum[0] = tail_sum[1] = 0.0; for (k = 0, aik = astarti, xi = x_starti; k < i; k++, aik += incaik, xi += incx) { a_elem = a_i[aik]; x_elem[0] = x_i[xi]; x_elem[1] = x_i[xi + 1]; { head_prod[0] = (double) x_elem[0] * a_elem; tail_prod[0] = 0.0; head_prod[1] = (double) x_elem[1] * a_elem; tail_prod[1] = 0.0; } { double head_t, tail_t; double head_a, tail_a; double head_b, tail_b; /* Real part */ head_a = head_sum[0]; tail_a = tail_sum[0]; head_b = head_prod[0]; tail_b = tail_prod[0]; { /* Compute double-double = double-double + double-double. */ double bv; double s1, s2, t1, t2; /* Add two hi words. */ s1 = head_a + head_b; bv = s1 - head_a; s2 = ((head_b - bv) + (head_a - (s1 - bv))); /* Add two lo words. */ t1 = tail_a + tail_b; bv = t1 - tail_a; t2 = ((tail_b - bv) + (tail_a - (t1 - bv))); s2 += t1; /* Renormalize (s1, s2) to (t1, s2) */ t1 = s1 + s2; s2 = s2 - (t1 - s1); t2 += s2; /* Renormalize (t1, t2) */ head_t = t1 + t2; tail_t = t2 - (head_t - t1); } head_sum[0] = head_t; tail_sum[0] = tail_t; /* Imaginary part */ head_a = head_sum[1]; tail_a = tail_sum[1]; head_b = head_prod[1]; tail_b = tail_prod[1]; { /* Compute double-double = double-double + double-double. */ double bv; double s1, s2, t1, t2; /* Add two hi words. */ s1 = head_a + head_b; bv = s1 - head_a; s2 = ((head_b - bv) + (head_a - (s1 - bv))); /* Add two lo words. */ t1 = tail_a + tail_b; bv = t1 - tail_a; t2 = ((tail_b - bv) + (tail_a - (t1 - bv))); s2 += t1; /* Renormalize (s1, s2) to (t1, s2) */ t1 = s1 + s2; s2 = s2 - (t1 - s1); t2 += s2; /* Renormalize (t1, t2) */ head_t = t1 + t2; tail_t = t2 - (head_t - t1); } head_sum[1] = head_t; tail_sum[1] = tail_t; } } for (; k < n_i; k++, aik += incaik2, xi += incx) { a_elem = a_i[aik]; x_elem[0] = x_i[xi]; x_elem[1] = x_i[xi + 1]; { head_prod[0] = (double) x_elem[0] * a_elem; tail_prod[0] = 0.0; head_prod[1] = (double) x_elem[1] * a_elem; tail_prod[1] = 0.0; } { double head_t, tail_t; double head_a, tail_a; double head_b, tail_b; /* Real part */ head_a = head_sum[0]; tail_a = tail_sum[0]; head_b = head_prod[0]; tail_b = tail_prod[0]; { /* Compute double-double = double-double + double-double. */ double bv; double s1, s2, t1, t2; /* Add two hi words. */ s1 = head_a + head_b; bv = s1 - head_a; s2 = ((head_b - bv) + (head_a - (s1 - bv))); /* Add two lo words. */ t1 = tail_a + tail_b; bv = t1 - tail_a; t2 = ((tail_b - bv) + (tail_a - (t1 - bv))); s2 += t1; /* Renormalize (s1, s2) to (t1, s2) */ t1 = s1 + s2; s2 = s2 - (t1 - s1); t2 += s2; /* Renormalize (t1, t2) */ head_t = t1 + t2; tail_t = t2 - (head_t - t1); } head_sum[0] = head_t; tail_sum[0] = tail_t; /* Imaginary part */ head_a = head_sum[1]; tail_a = tail_sum[1]; head_b = head_prod[1]; tail_b = tail_prod[1]; { /* Compute double-double = double-double + double-double. */ double bv; double s1, s2, t1, t2; /* Add two hi words. */ s1 = head_a + head_b; bv = s1 - head_a; s2 = ((head_b - bv) + (head_a - (s1 - bv))); /* Add two lo words. */ t1 = tail_a + tail_b; bv = t1 - tail_a; t2 = ((tail_b - bv) + (tail_a - (t1 - bv))); s2 += t1; /* Renormalize (s1, s2) to (t1, s2) */ t1 = s1 + s2; s2 = s2 - (t1 - s1); t2 += s2; /* Renormalize (t1, t2) */ head_t = t1 + t2; tail_t = t2 - (head_t - t1); } head_sum[1] = head_t; tail_sum[1] = tail_t; } } y_i[yi] = head_sum[0]; y_i[yi + 1] = head_sum[1]; } } else { /* Case alpha = 1, but beta != 0. We compute y <--- A * x + beta * y */ for (i = 0, yi = y_starti, astarti = 0; i < n_i; i++, yi += incy, astarti += incai) { head_sum[0] = head_sum[1] = tail_sum[0] = tail_sum[1] = 0.0; for (k = 0, aik = astarti, xi = x_starti; k < i; k++, aik += incaik, xi += incx) { a_elem = a_i[aik]; x_elem[0] = x_i[xi]; x_elem[1] = x_i[xi + 1]; { head_prod[0] = (double) x_elem[0] * a_elem; tail_prod[0] = 0.0; head_prod[1] = (double) x_elem[1] * a_elem; tail_prod[1] = 0.0; } { double head_t, tail_t; double head_a, tail_a; double head_b, tail_b; /* Real part */ head_a = head_sum[0]; tail_a = tail_sum[0]; head_b = head_prod[0]; tail_b = tail_prod[0]; { /* Compute double-double = double-double + double-double. */ double bv; double s1, s2, t1, t2; /* Add two hi words. */ s1 = head_a + head_b; bv = s1 - head_a; s2 = ((head_b - bv) + (head_a - (s1 - bv))); /* Add two lo words. */ t1 = tail_a + tail_b; bv = t1 - tail_a; t2 = ((tail_b - bv) + (tail_a - (t1 - bv))); s2 += t1; /* Renormalize (s1, s2) to (t1, s2) */ t1 = s1 + s2; s2 = s2 - (t1 - s1); t2 += s2; /* Renormalize (t1, t2) */ head_t = t1 + t2; tail_t = t2 - (head_t - t1); } head_sum[0] = head_t; tail_sum[0] = tail_t; /* Imaginary part */ head_a = head_sum[1]; tail_a = tail_sum[1]; head_b = head_prod[1]; tail_b = tail_prod[1]; { /* Compute double-double = double-double + double-double. */ double bv; double s1, s2, t1, t2; /* Add two hi words. */ s1 = head_a + head_b; bv = s1 - head_a; s2 = ((head_b - bv) + (head_a - (s1 - bv))); /* Add two lo words. */ t1 = tail_a + tail_b; bv = t1 - tail_a; t2 = ((tail_b - bv) + (tail_a - (t1 - bv))); s2 += t1; /* Renormalize (s1, s2) to (t1, s2) */ t1 = s1 + s2; s2 = s2 - (t1 - s1); t2 += s2; /* Renormalize (t1, t2) */ head_t = t1 + t2; tail_t = t2 - (head_t - t1); } head_sum[1] = head_t; tail_sum[1] = tail_t; } } for (; k < n_i; k++, aik += incaik2, xi += incx) { a_elem = a_i[aik]; x_elem[0] = x_i[xi]; x_elem[1] = x_i[xi + 1]; { head_prod[0] = (double) x_elem[0] * a_elem; tail_prod[0] = 0.0; head_prod[1] = (double) x_elem[1] * a_elem; tail_prod[1] = 0.0; } { double head_t, tail_t; double head_a, tail_a; double head_b, tail_b; /* Real part */ head_a = head_sum[0]; tail_a = tail_sum[0]; head_b = head_prod[0]; tail_b = tail_prod[0]; { /* Compute double-double = double-double + double-double. */ double bv; double s1, s2, t1, t2; /* Add two hi words. */ s1 = head_a + head_b; bv = s1 - head_a; s2 = ((head_b - bv) + (head_a - (s1 - bv))); /* Add two lo words. */ t1 = tail_a + tail_b; bv = t1 - tail_a; t2 = ((tail_b - bv) + (tail_a - (t1 - bv))); s2 += t1; /* Renormalize (s1, s2) to (t1, s2) */ t1 = s1 + s2; s2 = s2 - (t1 - s1); t2 += s2; /* Renormalize (t1, t2) */ head_t = t1 + t2; tail_t = t2 - (head_t - t1); } head_sum[0] = head_t; tail_sum[0] = tail_t; /* Imaginary part */ head_a = head_sum[1]; tail_a = tail_sum[1]; head_b = head_prod[1]; tail_b = tail_prod[1]; { /* Compute double-double = double-double + double-double. */ double bv; double s1, s2, t1, t2; /* Add two hi words. */ s1 = head_a + head_b; bv = s1 - head_a; s2 = ((head_b - bv) + (head_a - (s1 - bv))); /* Add two lo words. */ t1 = tail_a + tail_b; bv = t1 - tail_a; t2 = ((tail_b - bv) + (tail_a - (t1 - bv))); s2 += t1; /* Renormalize (s1, s2) to (t1, s2) */ t1 = s1 + s2; s2 = s2 - (t1 - s1); t2 += s2; /* Renormalize (t1, t2) */ head_t = t1 + t2; tail_t = t2 - (head_t - t1); } head_sum[1] = head_t; tail_sum[1] = tail_t; } } y_elem[0] = y_i[yi]; y_elem[1] = y_i[yi + 1]; { double head_e1, tail_e1; double d1; double d2; /* Real part */ d1 = (double) y_elem[0] * beta_i[0]; d2 = (double) -y_elem[1] * beta_i[1]; { /* Compute double-double = double + double. */ double e, t1, t2; /* Knuth trick. */ t1 = d1 + d2; e = t1 - d1; t2 = ((d2 - e) + (d1 - (t1 - e))); /* The result is t1 + t2, after normalization. */ head_e1 = t1 + t2; tail_e1 = t2 - (head_e1 - t1); } head_tmp2[0] = head_e1; tail_tmp2[0] = tail_e1; /* imaginary part */ d1 = (double) y_elem[0] * beta_i[1]; d2 = (double) y_elem[1] * beta_i[0]; { /* Compute double-double = double + double. */ double e, t1, t2; /* Knuth trick. */ t1 = d1 + d2; e = t1 - d1; t2 = ((d2 - e) + (d1 - (t1 - e))); /* The result is t1 + t2, after normalization. */ head_e1 = t1 + t2; tail_e1 = t2 - (head_e1 - t1); } head_tmp2[1] = head_e1; tail_tmp2[1] = tail_e1; } head_tmp1[0] = head_sum[0]; tail_tmp1[0] = tail_sum[0]; head_tmp1[1] = head_sum[1]; tail_tmp1[1] = tail_sum[1]; { double head_t, tail_t; double head_a, tail_a; double head_b, tail_b; /* Real part */ head_a = head_tmp2[0]; tail_a = tail_tmp2[0]; head_b = head_tmp1[0]; tail_b = tail_tmp1[0]; { /* Compute double-double = double-double + double-double. */ double bv; double s1, s2, t1, t2; /* Add two hi words. */ s1 = head_a + head_b; bv = s1 - head_a; s2 = ((head_b - bv) + (head_a - (s1 - bv))); /* Add two lo words. */ t1 = tail_a + tail_b; bv = t1 - tail_a; t2 = ((tail_b - bv) + (tail_a - (t1 - bv))); s2 += t1; /* Renormalize (s1, s2) to (t1, s2) */ t1 = s1 + s2; s2 = s2 - (t1 - s1); t2 += s2; /* Renormalize (t1, t2) */ head_t = t1 + t2; tail_t = t2 - (head_t - t1); } head_tmp1[0] = head_t; tail_tmp1[0] = tail_t; /* Imaginary part */ head_a = head_tmp2[1]; tail_a = tail_tmp2[1]; head_b = head_tmp1[1]; tail_b = tail_tmp1[1]; { /* Compute double-double = double-double + double-double. */ double bv; double s1, s2, t1, t2; /* Add two hi words. */ s1 = head_a + head_b; bv = s1 - head_a; s2 = ((head_b - bv) + (head_a - (s1 - bv))); /* Add two lo words. */ t1 = tail_a + tail_b; bv = t1 - tail_a; t2 = ((tail_b - bv) + (tail_a - (t1 - bv))); s2 += t1; /* Renormalize (s1, s2) to (t1, s2) */ t1 = s1 + s2; s2 = s2 - (t1 - s1); t2 += s2; /* Renormalize (t1, t2) */ head_t = t1 + t2; tail_t = t2 - (head_t - t1); } head_tmp1[1] = head_t; tail_tmp1[1] = tail_t; } y_i[yi] = head_tmp1[0]; y_i[yi + 1] = head_tmp1[1]; } } } else { /* The most general form, y <--- alpha * A * x + beta * y */ for (i = 0, yi = y_starti, astarti = 0; i < n_i; i++, yi += incy, astarti += incai) { head_sum[0] = head_sum[1] = tail_sum[0] = tail_sum[1] = 0.0; for (k = 0, aik = astarti, xi = x_starti; k < i; k++, aik += incaik, xi += incx) { a_elem = a_i[aik]; x_elem[0] = x_i[xi]; x_elem[1] = x_i[xi + 1]; { head_prod[0] = (double) x_elem[0] * a_elem; tail_prod[0] = 0.0; head_prod[1] = (double) x_elem[1] * a_elem; tail_prod[1] = 0.0; } { double head_t, tail_t; double head_a, tail_a; double head_b, tail_b; /* Real part */ head_a = head_sum[0]; tail_a = tail_sum[0]; head_b = head_prod[0]; tail_b = tail_prod[0]; { /* Compute double-double = double-double + double-double. */ double bv; double s1, s2, t1, t2; /* Add two hi words. */ s1 = head_a + head_b; bv = s1 - head_a; s2 = ((head_b - bv) + (head_a - (s1 - bv))); /* Add two lo words. */ t1 = tail_a + tail_b; bv = t1 - tail_a; t2 = ((tail_b - bv) + (tail_a - (t1 - bv))); s2 += t1; /* Renormalize (s1, s2) to (t1, s2) */ t1 = s1 + s2; s2 = s2 - (t1 - s1); t2 += s2; /* Renormalize (t1, t2) */ head_t = t1 + t2; tail_t = t2 - (head_t - t1); } head_sum[0] = head_t; tail_sum[0] = tail_t; /* Imaginary part */ head_a = head_sum[1]; tail_a = tail_sum[1]; head_b = head_prod[1]; tail_b = tail_prod[1]; { /* Compute double-double = double-double + double-double. */ double bv; double s1, s2, t1, t2; /* Add two hi words. */ s1 = head_a + head_b; bv = s1 - head_a; s2 = ((head_b - bv) + (head_a - (s1 - bv))); /* Add two lo words. */ t1 = tail_a + tail_b; bv = t1 - tail_a; t2 = ((tail_b - bv) + (tail_a - (t1 - bv))); s2 += t1; /* Renormalize (s1, s2) to (t1, s2) */ t1 = s1 + s2; s2 = s2 - (t1 - s1); t2 += s2; /* Renormalize (t1, t2) */ head_t = t1 + t2; tail_t = t2 - (head_t - t1); } head_sum[1] = head_t; tail_sum[1] = tail_t; } } for (; k < n_i; k++, aik += incaik2, xi += incx) { a_elem = a_i[aik]; x_elem[0] = x_i[xi]; x_elem[1] = x_i[xi + 1]; { head_prod[0] = (double) x_elem[0] * a_elem; tail_prod[0] = 0.0; head_prod[1] = (double) x_elem[1] * a_elem; tail_prod[1] = 0.0; } { double head_t, tail_t; double head_a, tail_a; double head_b, tail_b; /* Real part */ head_a = head_sum[0]; tail_a = tail_sum[0]; head_b = head_prod[0]; tail_b = tail_prod[0]; { /* Compute double-double = double-double + double-double. */ double bv; double s1, s2, t1, t2; /* Add two hi words. */ s1 = head_a + head_b; bv = s1 - head_a; s2 = ((head_b - bv) + (head_a - (s1 - bv))); /* Add two lo words. */ t1 = tail_a + tail_b; bv = t1 - tail_a; t2 = ((tail_b - bv) + (tail_a - (t1 - bv))); s2 += t1; /* Renormalize (s1, s2) to (t1, s2) */ t1 = s1 + s2; s2 = s2 - (t1 - s1); t2 += s2; /* Renormalize (t1, t2) */ head_t = t1 + t2; tail_t = t2 - (head_t - t1); } head_sum[0] = head_t; tail_sum[0] = tail_t; /* Imaginary part */ head_a = head_sum[1]; tail_a = tail_sum[1]; head_b = head_prod[1]; tail_b = tail_prod[1]; { /* Compute double-double = double-double + double-double. */ double bv; double s1, s2, t1, t2; /* Add two hi words. */ s1 = head_a + head_b; bv = s1 - head_a; s2 = ((head_b - bv) + (head_a - (s1 - bv))); /* Add two lo words. */ t1 = tail_a + tail_b; bv = t1 - tail_a; t2 = ((tail_b - bv) + (tail_a - (t1 - bv))); s2 += t1; /* Renormalize (s1, s2) to (t1, s2) */ t1 = s1 + s2; s2 = s2 - (t1 - s1); t2 += s2; /* Renormalize (t1, t2) */ head_t = t1 + t2; tail_t = t2 - (head_t - t1); } head_sum[1] = head_t; tail_sum[1] = tail_t; } } y_elem[0] = y_i[yi]; y_elem[1] = y_i[yi + 1]; { double head_e1, tail_e1; double d1; double d2; /* Real part */ d1 = (double) y_elem[0] * beta_i[0]; d2 = (double) -y_elem[1] * beta_i[1]; { /* Compute double-double = double + double. */ double e, t1, t2; /* Knuth trick. */ t1 = d1 + d2; e = t1 - d1; t2 = ((d2 - e) + (d1 - (t1 - e))); /* The result is t1 + t2, after normalization. */ head_e1 = t1 + t2; tail_e1 = t2 - (head_e1 - t1); } head_tmp2[0] = head_e1; tail_tmp2[0] = tail_e1; /* imaginary part */ d1 = (double) y_elem[0] * beta_i[1]; d2 = (double) y_elem[1] * beta_i[0]; { /* Compute double-double = double + double. */ double e, t1, t2; /* Knuth trick. */ t1 = d1 + d2; e = t1 - d1; t2 = ((d2 - e) + (d1 - (t1 - e))); /* The result is t1 + t2, after normalization. */ head_e1 = t1 + t2; tail_e1 = t2 - (head_e1 - t1); } head_tmp2[1] = head_e1; tail_tmp2[1] = tail_e1; } { double cd[2]; cd[0] = (double) alpha_i[0]; cd[1] = (double) alpha_i[1]; { /* Compute complex-extra = complex-extra * complex-double. */ double head_a0, tail_a0; double head_a1, tail_a1; double head_t1, tail_t1; double head_t2, tail_t2; head_a0 = head_sum[0]; tail_a0 = tail_sum[0]; head_a1 = head_sum[1]; tail_a1 = tail_sum[1]; /* real part */ { /* Compute double-double = double-double * double. */ double a11, a21, b1, b2, c11, c21, c2, con, t1, t2; con = head_a0 * split; a11 = con - head_a0; a11 = con - a11; a21 = head_a0 - a11; con = cd[0] * split; b1 = con - cd[0]; b1 = con - b1; b2 = cd[0] - b1; c11 = head_a0 * cd[0]; c21 = (((a11 * b1 - c11) + a11 * b2) + a21 * b1) + a21 * b2; c2 = tail_a0 * cd[0]; t1 = c11 + c2; t2 = (c2 - (t1 - c11)) + c21; head_t1 = t1 + t2; tail_t1 = t2 - (head_t1 - t1); } { /* Compute double-double = double-double * double. */ double a11, a21, b1, b2, c11, c21, c2, con, t1, t2; con = head_a1 * split; a11 = con - head_a1; a11 = con - a11; a21 = head_a1 - a11; con = cd[1] * split; b1 = con - cd[1]; b1 = con - b1; b2 = cd[1] - b1; c11 = head_a1 * cd[1]; c21 = (((a11 * b1 - c11) + a11 * b2) + a21 * b1) + a21 * b2; c2 = tail_a1 * cd[1]; t1 = c11 + c2; t2 = (c2 - (t1 - c11)) + c21; head_t2 = t1 + t2; tail_t2 = t2 - (head_t2 - t1); } head_t2 = -head_t2; tail_t2 = -tail_t2; { /* Compute double-double = double-double + double-double. */ double bv; double s1, s2, t1, t2; /* Add two hi words. */ s1 = head_t1 + head_t2; bv = s1 - head_t1; s2 = ((head_t2 - bv) + (head_t1 - (s1 - bv))); /* Add two lo words. */ t1 = tail_t1 + tail_t2; bv = t1 - tail_t1; t2 = ((tail_t2 - bv) + (tail_t1 - (t1 - bv))); s2 += t1; /* Renormalize (s1, s2) to (t1, s2) */ t1 = s1 + s2; s2 = s2 - (t1 - s1); t2 += s2; /* Renormalize (t1, t2) */ head_t1 = t1 + t2; tail_t1 = t2 - (head_t1 - t1); } head_tmp1[0] = head_t1; tail_tmp1[0] = tail_t1; /* imaginary part */ { /* Compute double-double = double-double * double. */ double a11, a21, b1, b2, c11, c21, c2, con, t1, t2; con = head_a1 * split; a11 = con - head_a1; a11 = con - a11; a21 = head_a1 - a11; con = cd[0] * split; b1 = con - cd[0]; b1 = con - b1; b2 = cd[0] - b1; c11 = head_a1 * cd[0]; c21 = (((a11 * b1 - c11) + a11 * b2) + a21 * b1) + a21 * b2; c2 = tail_a1 * cd[0]; t1 = c11 + c2; t2 = (c2 - (t1 - c11)) + c21; head_t1 = t1 + t2; tail_t1 = t2 - (head_t1 - t1); } { /* Compute double-double = double-double * double. */ double a11, a21, b1, b2, c11, c21, c2, con, t1, t2; con = head_a0 * split; a11 = con - head_a0; a11 = con - a11; a21 = head_a0 - a11; con = cd[1] * split; b1 = con - cd[1]; b1 = con - b1; b2 = cd[1] - b1; c11 = head_a0 * cd[1]; c21 = (((a11 * b1 - c11) + a11 * b2) + a21 * b1) + a21 * b2; c2 = tail_a0 * cd[1]; t1 = c11 + c2; t2 = (c2 - (t1 - c11)) + c21; head_t2 = t1 + t2; tail_t2 = t2 - (head_t2 - t1); } { /* Compute double-double = double-double + double-double. */ double bv; double s1, s2, t1, t2; /* Add two hi words. */ s1 = head_t1 + head_t2; bv = s1 - head_t1; s2 = ((head_t2 - bv) + (head_t1 - (s1 - bv))); /* Add two lo words. */ t1 = tail_t1 + tail_t2; bv = t1 - tail_t1; t2 = ((tail_t2 - bv) + (tail_t1 - (t1 - bv))); s2 += t1; /* Renormalize (s1, s2) to (t1, s2) */ t1 = s1 + s2; s2 = s2 - (t1 - s1); t2 += s2; /* Renormalize (t1, t2) */ head_t1 = t1 + t2; tail_t1 = t2 - (head_t1 - t1); } head_tmp1[1] = head_t1; tail_tmp1[1] = tail_t1; } } { double head_t, tail_t; double head_a, tail_a; double head_b, tail_b; /* Real part */ head_a = head_tmp2[0]; tail_a = tail_tmp2[0]; head_b = head_tmp1[0]; tail_b = tail_tmp1[0]; { /* Compute double-double = double-double + double-double. */ double bv; double s1, s2, t1, t2; /* Add two hi words. */ s1 = head_a + head_b; bv = s1 - head_a; s2 = ((head_b - bv) + (head_a - (s1 - bv))); /* Add two lo words. */ t1 = tail_a + tail_b; bv = t1 - tail_a; t2 = ((tail_b - bv) + (tail_a - (t1 - bv))); s2 += t1; /* Renormalize (s1, s2) to (t1, s2) */ t1 = s1 + s2; s2 = s2 - (t1 - s1); t2 += s2; /* Renormalize (t1, t2) */ head_t = t1 + t2; tail_t = t2 - (head_t - t1); } head_tmp1[0] = head_t; tail_tmp1[0] = tail_t; /* Imaginary part */ head_a = head_tmp2[1]; tail_a = tail_tmp2[1]; head_b = head_tmp1[1]; tail_b = tail_tmp1[1]; { /* Compute double-double = double-double + double-double. */ double bv; double s1, s2, t1, t2; /* Add two hi words. */ s1 = head_a + head_b; bv = s1 - head_a; s2 = ((head_b - bv) + (head_a - (s1 - bv))); /* Add two lo words. */ t1 = tail_a + tail_b; bv = t1 - tail_a; t2 = ((tail_b - bv) + (tail_a - (t1 - bv))); s2 += t1; /* Renormalize (s1, s2) to (t1, s2) */ t1 = s1 + s2; s2 = s2 - (t1 - s1); t2 += s2; /* Renormalize (t1, t2) */ head_t = t1 + t2; tail_t = t2 - (head_t - t1); } head_tmp1[1] = head_t; tail_tmp1[1] = tail_t; } y_i[yi] = head_tmp1[0]; y_i[yi + 1] = head_tmp1[1]; } } FPU_FIX_STOP; break; } } } /* end BLAS_csymv_s_c_x */