#include "blas_extended.h" #include "blas_extended_private.h" void BLAS_zgemv_z_d_x(enum blas_order_type order, enum blas_trans_type trans, int m, int n, const void *alpha, const void *a, int lda, const double *x, int incx, const void *beta, void *y, int incy, enum blas_prec_type prec) /* * Purpose * ======= * * Computes y = alpha * A * x + beta * y, where A is a general matrix. * * Arguments * ========= * * order (input) blas_order_type * Order of AP; row or column major * * trans (input) blas_trans_type * Transpose of AB; no trans, * trans, or conjugate trans * * m (input) int * Dimension of AB * * n (input) int * Dimension of AB and the length of vector x * * alpha (input) const void* * * A (input) const void* * * lda (input) int * Leading dimension of A * * x (input) const double* * * incx (input) int * The stride for vector x. * * beta (input) const void* * * y (input/output) void* * * incy (input) int * The 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. * */ { static const char routine_name[] = "BLAS_zgemv_z_d_x"; switch (prec) { case blas_prec_single: case blas_prec_double: case blas_prec_indigenous:{ int i, j; int iy, jx, kx, ky; int lenx, leny; int ai, aij; int incai, incaij; const double *a_i = (double *) a; const double *x_i = x; double *y_i = (double *) y; double *alpha_i = (double *) alpha; double *beta_i = (double *) beta; double a_elem[2]; double x_elem; double y_elem[2]; double prod[2]; double sum[2]; double tmp1[2]; double tmp2[2]; /* all error calls */ if (m < 0) BLAS_error(routine_name, -3, m, 0); else if (n <= 0) BLAS_error(routine_name, -4, n, 0); else if (incx == 0) BLAS_error(routine_name, -9, incx, 0); else if (incy == 0) BLAS_error(routine_name, -12, incy, 0); if ((order == blas_rowmajor) && (trans == blas_no_trans)) { lenx = n; leny = m; incai = lda; incaij = 1; } else if ((order == blas_rowmajor) && (trans != blas_no_trans)) { lenx = m; leny = n; incai = 1; incaij = lda; } else if ((order == blas_colmajor) && (trans == blas_no_trans)) { lenx = n; leny = m; incai = 1; incaij = lda; } else { /* colmajor and blas_trans */ lenx = m; leny = n; incai = lda; incaij = 1; } if (lda < leny) BLAS_error(routine_name, -7, lda, NULL); incy *= 2; incai *= 2; incaij *= 2; if (incx > 0) kx = 0; else kx = (1 - lenx) * incx; if (incy > 0) ky = 0; else ky = (1 - leny) * incy; /* No extra-precision needed for alpha = 0 */ if (alpha_i[0] == 0.0 && alpha_i[1] == 0.0) { if (beta_i[0] == 0.0 && beta_i[1] == 0.0) { iy = ky; for (i = 0; i < leny; i++) { y_i[iy] = 0.0; y_i[iy + 1] = 0.0; iy += incy; } } else if (!(beta_i[0] == 0.0 && beta_i[1] == 0.0)) { iy = ky; for (i = 0; i < leny; i++) { y_elem[0] = y_i[iy]; y_elem[1] = y_i[iy + 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[iy] = tmp1[0]; y_i[iy + 1] = tmp1[1]; iy += incy; } } } else { if (trans == blas_conj_trans) { /* if beta = 0, we can save m multiplies: y = alpha*A*x */ if (beta_i[0] == 0.0 && beta_i[1] == 0.0) { /* save m more multiplies if alpha = 1 */ if ((alpha_i[0] == 1.0 && alpha_i[1] == 0.0)) { ai = 0; iy = ky; for (i = 0; i < leny; i++) { sum[0] = sum[1] = 0.0; aij = ai; jx = kx; for (j = 0; j < lenx; j++) { a_elem[0] = a_i[aij]; a_elem[1] = a_i[aij + 1]; a_elem[1] = -a_elem[1]; x_elem = x_i[jx]; { prod[0] = a_elem[0] * x_elem; prod[1] = a_elem[1] * x_elem; } sum[0] = sum[0] + prod[0]; sum[1] = sum[1] + prod[1]; aij += incaij; jx += incx; } y_i[iy] = sum[0]; y_i[iy + 1] = sum[1]; ai += incai; iy += incy; } } else { ai = 0; iy = ky; for (i = 0; i < leny; i++) { sum[0] = sum[1] = 0.0; aij = ai; jx = kx; for (j = 0; j < lenx; j++) { a_elem[0] = a_i[aij]; a_elem[1] = a_i[aij + 1]; a_elem[1] = -a_elem[1]; x_elem = x_i[jx]; { prod[0] = a_elem[0] * x_elem; prod[1] = a_elem[1] * x_elem; } sum[0] = sum[0] + prod[0]; sum[1] = sum[1] + prod[1]; aij += incaij; jx += incx; } { 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]; } y_i[iy] = tmp1[0]; y_i[iy + 1] = tmp1[1]; ai += incai; iy += incy; } } } else { /* the most general form, y = alpha*A*x + beta*y */ ai = 0; iy = ky; for (i = 0; i < leny; i++) { sum[0] = sum[1] = 0.0;; aij = ai; jx = kx; for (j = 0; j < lenx; j++) { a_elem[0] = a_i[aij]; a_elem[1] = a_i[aij + 1]; a_elem[1] = -a_elem[1]; x_elem = x_i[jx]; { prod[0] = a_elem[0] * x_elem; prod[1] = a_elem[1] * x_elem; } sum[0] = sum[0] + prod[0]; sum[1] = sum[1] + prod[1]; aij += incaij; jx += incx; } { 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]; } y_elem[0] = y_i[iy]; y_elem[1] = y_i[iy + 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] = tmp1[0] + tmp2[0]; tmp1[1] = tmp1[1] + tmp2[1]; y_i[iy] = tmp1[0]; y_i[iy + 1] = tmp1[1]; ai += incai; iy += incy; } } } else { /* if beta = 0, we can save m multiplies: y = alpha*A*x */ if (beta_i[0] == 0.0 && beta_i[1] == 0.0) { /* save m more multiplies if alpha = 1 */ if ((alpha_i[0] == 1.0 && alpha_i[1] == 0.0)) { ai = 0; iy = ky; for (i = 0; i < leny; i++) { sum[0] = sum[1] = 0.0; aij = ai; jx = kx; for (j = 0; j < lenx; j++) { a_elem[0] = a_i[aij]; a_elem[1] = a_i[aij + 1]; x_elem = x_i[jx]; { prod[0] = a_elem[0] * x_elem; prod[1] = a_elem[1] * x_elem; } sum[0] = sum[0] + prod[0]; sum[1] = sum[1] + prod[1]; aij += incaij; jx += incx; } y_i[iy] = sum[0]; y_i[iy + 1] = sum[1]; ai += incai; iy += incy; } } else { ai = 0; iy = ky; for (i = 0; i < leny; i++) { sum[0] = sum[1] = 0.0; aij = ai; jx = kx; for (j = 0; j < lenx; j++) { a_elem[0] = a_i[aij]; a_elem[1] = a_i[aij + 1]; x_elem = x_i[jx]; { prod[0] = a_elem[0] * x_elem; prod[1] = a_elem[1] * x_elem; } sum[0] = sum[0] + prod[0]; sum[1] = sum[1] + prod[1]; aij += incaij; jx += incx; } { 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]; } y_i[iy] = tmp1[0]; y_i[iy + 1] = tmp1[1]; ai += incai; iy += incy; } } } else { /* the most general form, y = alpha*A*x + beta*y */ ai = 0; iy = ky; for (i = 0; i < leny; i++) { sum[0] = sum[1] = 0.0;; aij = ai; jx = kx; for (j = 0; j < lenx; j++) { a_elem[0] = a_i[aij]; a_elem[1] = a_i[aij + 1]; x_elem = x_i[jx]; { prod[0] = a_elem[0] * x_elem; prod[1] = a_elem[1] * x_elem; } sum[0] = sum[0] + prod[0]; sum[1] = sum[1] + prod[1]; aij += incaij; jx += incx; } { 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]; } y_elem[0] = y_i[iy]; y_elem[1] = y_i[iy + 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] = tmp1[0] + tmp2[0]; tmp1[1] = tmp1[1] + tmp2[1]; y_i[iy] = tmp1[0]; y_i[iy + 1] = tmp1[1]; ai += incai; iy += incy; } } } } break; } case blas_prec_extra:{ int i, j; int iy, jx, kx, ky; int lenx, leny; int ai, aij; int incai, incaij; const double *a_i = (double *) a; const double *x_i = x; double *y_i = (double *) y; double *alpha_i = (double *) alpha; double *beta_i = (double *) beta; double a_elem[2]; double x_elem; double 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; /* all error calls */ if (m < 0) BLAS_error(routine_name, -3, m, 0); else if (n <= 0) BLAS_error(routine_name, -4, n, 0); else if (incx == 0) BLAS_error(routine_name, -9, incx, 0); else if (incy == 0) BLAS_error(routine_name, -12, incy, 0); if ((order == blas_rowmajor) && (trans == blas_no_trans)) { lenx = n; leny = m; incai = lda; incaij = 1; } else if ((order == blas_rowmajor) && (trans != blas_no_trans)) { lenx = m; leny = n; incai = 1; incaij = lda; } else if ((order == blas_colmajor) && (trans == blas_no_trans)) { lenx = n; leny = m; incai = 1; incaij = lda; } else { /* colmajor and blas_trans */ lenx = m; leny = n; incai = lda; incaij = 1; } if (lda < leny) BLAS_error(routine_name, -7, lda, NULL); FPU_FIX_START; incy *= 2; incai *= 2; incaij *= 2; if (incx > 0) kx = 0; else kx = (1 - lenx) * incx; if (incy > 0) ky = 0; else ky = (1 - leny) * incy; /* No extra-precision needed for alpha = 0 */ if (alpha_i[0] == 0.0 && alpha_i[1] == 0.0) { if (beta_i[0] == 0.0 && beta_i[1] == 0.0) { iy = ky; for (i = 0; i < leny; i++) { y_i[iy] = 0.0; y_i[iy + 1] = 0.0; iy += incy; } } else if (!(beta_i[0] == 0.0 && beta_i[1] == 0.0)) { iy = ky; for (i = 0; i < leny; i++) { y_elem[0] = y_i[iy]; y_elem[1] = y_i[iy + 1]; { /* Compute complex-extra = complex-double * complex-double. */ double head_t1, tail_t1; double head_t2, tail_t2; /* Real part */ { /* Compute double_double = double * double. */ double a1, a2, b1, b2, con; con = y_elem[0] * split; a1 = con - y_elem[0]; a1 = con - a1; a2 = y_elem[0] - a1; con = beta_i[0] * split; b1 = con - beta_i[0]; b1 = con - b1; b2 = beta_i[0] - b1; head_t1 = y_elem[0] * beta_i[0]; tail_t1 = (((a1 * b1 - head_t1) + a1 * b2) + a2 * b1) + a2 * b2; } { /* Compute double_double = double * double. */ double a1, a2, b1, b2, con; con = y_elem[1] * split; a1 = con - y_elem[1]; a1 = con - a1; a2 = y_elem[1] - a1; con = beta_i[1] * split; b1 = con - beta_i[1]; b1 = con - b1; b2 = beta_i[1] - b1; head_t2 = y_elem[1] * beta_i[1]; tail_t2 = (((a1 * b1 - head_t2) + a1 * b2) + a2 * b1) + a2 * b2; } 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 a1, a2, b1, b2, con; con = y_elem[1] * split; a1 = con - y_elem[1]; a1 = con - a1; a2 = y_elem[1] - a1; con = beta_i[0] * split; b1 = con - beta_i[0]; b1 = con - b1; b2 = beta_i[0] - b1; head_t1 = y_elem[1] * beta_i[0]; tail_t1 = (((a1 * b1 - head_t1) + a1 * b2) + a2 * b1) + a2 * b2; } { /* Compute double_double = double * double. */ double a1, a2, b1, b2, con; con = y_elem[0] * split; a1 = con - y_elem[0]; a1 = con - a1; a2 = y_elem[0] - a1; con = beta_i[1] * split; b1 = con - beta_i[1]; b1 = con - b1; b2 = beta_i[1] - b1; head_t2 = y_elem[0] * beta_i[1]; tail_t2 = (((a1 * b1 - head_t2) + a1 * b2) + a2 * b1) + a2 * b2; } { /* 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; } y_i[iy] = head_tmp1[0]; y_i[iy + 1] = head_tmp1[1]; iy += incy; } } } else { if (trans == blas_conj_trans) { /* if beta = 0, we can save m multiplies: y = alpha*A*x */ if (beta_i[0] == 0.0 && beta_i[1] == 0.0) { /* save m more multiplies if alpha = 1 */ if ((alpha_i[0] == 1.0 && alpha_i[1] == 0.0)) { ai = 0; iy = ky; for (i = 0; i < leny; i++) { head_sum[0] = head_sum[1] = tail_sum[0] = tail_sum[1] = 0.0; aij = ai; jx = kx; for (j = 0; j < lenx; j++) { a_elem[0] = a_i[aij]; a_elem[1] = a_i[aij + 1]; a_elem[1] = -a_elem[1]; x_elem = x_i[jx]; { /* Compute complex-extra = complex-double * real. */ double head_t, tail_t; { /* Compute double_double = double * double. */ double a1, a2, b1, b2, con; con = x_elem * split; a1 = con - x_elem; a1 = con - a1; a2 = x_elem - a1; con = a_elem[0] * split; b1 = con - a_elem[0]; b1 = con - b1; b2 = a_elem[0] - b1; head_t = x_elem * a_elem[0]; tail_t = (((a1 * b1 - head_t) + a1 * b2) + a2 * b1) + a2 * b2; } head_prod[0] = head_t; tail_prod[0] = tail_t; { /* Compute double_double = double * double. */ double a1, a2, b1, b2, con; con = x_elem * split; a1 = con - x_elem; a1 = con - a1; a2 = x_elem - a1; con = a_elem[1] * split; b1 = con - a_elem[1]; b1 = con - b1; b2 = a_elem[1] - b1; head_t = x_elem * a_elem[1]; tail_t = (((a1 * b1 - head_t) + a1 * b2) + a2 * b1) + a2 * b2; } head_prod[1] = head_t; tail_prod[1] = tail_t; } { 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; } aij += incaij; jx += incx; } y_i[iy] = head_sum[0]; y_i[iy + 1] = head_sum[1]; ai += incai; iy += incy; } } else { ai = 0; iy = ky; for (i = 0; i < leny; i++) { head_sum[0] = head_sum[1] = tail_sum[0] = tail_sum[1] = 0.0; aij = ai; jx = kx; for (j = 0; j < lenx; j++) { a_elem[0] = a_i[aij]; a_elem[1] = a_i[aij + 1]; a_elem[1] = -a_elem[1]; x_elem = x_i[jx]; { /* Compute complex-extra = complex-double * real. */ double head_t, tail_t; { /* Compute double_double = double * double. */ double a1, a2, b1, b2, con; con = x_elem * split; a1 = con - x_elem; a1 = con - a1; a2 = x_elem - a1; con = a_elem[0] * split; b1 = con - a_elem[0]; b1 = con - b1; b2 = a_elem[0] - b1; head_t = x_elem * a_elem[0]; tail_t = (((a1 * b1 - head_t) + a1 * b2) + a2 * b1) + a2 * b2; } head_prod[0] = head_t; tail_prod[0] = tail_t; { /* Compute double_double = double * double. */ double a1, a2, b1, b2, con; con = x_elem * split; a1 = con - x_elem; a1 = con - a1; a2 = x_elem - a1; con = a_elem[1] * split; b1 = con - a_elem[1]; b1 = con - b1; b2 = a_elem[1] - b1; head_t = x_elem * a_elem[1]; tail_t = (((a1 * b1 - head_t) + a1 * b2) + a2 * b1) + a2 * b2; } head_prod[1] = head_t; tail_prod[1] = tail_t; } { 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; } aij += incaij; jx += incx; } { /* 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 = alpha_i[0] * split; b1 = con - alpha_i[0]; b1 = con - b1; b2 = alpha_i[0] - b1; c11 = head_a0 * alpha_i[0]; c21 = (((a11 * b1 - c11) + a11 * b2) + a21 * b1) + a21 * b2; c2 = tail_a0 * alpha_i[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 = alpha_i[1] * split; b1 = con - alpha_i[1]; b1 = con - b1; b2 = alpha_i[1] - b1; c11 = head_a1 * alpha_i[1]; c21 = (((a11 * b1 - c11) + a11 * b2) + a21 * b1) + a21 * b2; c2 = tail_a1 * alpha_i[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 = alpha_i[0] * split; b1 = con - alpha_i[0]; b1 = con - b1; b2 = alpha_i[0] - b1; c11 = head_a1 * alpha_i[0]; c21 = (((a11 * b1 - c11) + a11 * b2) + a21 * b1) + a21 * b2; c2 = tail_a1 * alpha_i[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 = alpha_i[1] * split; b1 = con - alpha_i[1]; b1 = con - b1; b2 = alpha_i[1] - b1; c11 = head_a0 * alpha_i[1]; c21 = (((a11 * b1 - c11) + a11 * b2) + a21 * b1) + a21 * b2; c2 = tail_a0 * alpha_i[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; } y_i[iy] = head_tmp1[0]; y_i[iy + 1] = head_tmp1[1]; ai += incai; iy += incy; } } } else { /* the most general form, y = alpha*A*x + beta*y */ ai = 0; iy = ky; for (i = 0; i < leny; i++) { head_sum[0] = head_sum[1] = tail_sum[0] = tail_sum[1] = 0.0;; aij = ai; jx = kx; for (j = 0; j < lenx; j++) { a_elem[0] = a_i[aij]; a_elem[1] = a_i[aij + 1]; a_elem[1] = -a_elem[1]; x_elem = x_i[jx]; { /* Compute complex-extra = complex-double * real. */ double head_t, tail_t; { /* Compute double_double = double * double. */ double a1, a2, b1, b2, con; con = x_elem * split; a1 = con - x_elem; a1 = con - a1; a2 = x_elem - a1; con = a_elem[0] * split; b1 = con - a_elem[0]; b1 = con - b1; b2 = a_elem[0] - b1; head_t = x_elem * a_elem[0]; tail_t = (((a1 * b1 - head_t) + a1 * b2) + a2 * b1) + a2 * b2; } head_prod[0] = head_t; tail_prod[0] = tail_t; { /* Compute double_double = double * double. */ double a1, a2, b1, b2, con; con = x_elem * split; a1 = con - x_elem; a1 = con - a1; a2 = x_elem - a1; con = a_elem[1] * split; b1 = con - a_elem[1]; b1 = con - b1; b2 = a_elem[1] - b1; head_t = x_elem * a_elem[1]; tail_t = (((a1 * b1 - head_t) + a1 * b2) + a2 * b1) + a2 * b2; } head_prod[1] = head_t; tail_prod[1] = tail_t; } { 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; } aij += incaij; jx += incx; } { /* 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 = alpha_i[0] * split; b1 = con - alpha_i[0]; b1 = con - b1; b2 = alpha_i[0] - b1; c11 = head_a0 * alpha_i[0]; c21 = (((a11 * b1 - c11) + a11 * b2) + a21 * b1) + a21 * b2; c2 = tail_a0 * alpha_i[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 = alpha_i[1] * split; b1 = con - alpha_i[1]; b1 = con - b1; b2 = alpha_i[1] - b1; c11 = head_a1 * alpha_i[1]; c21 = (((a11 * b1 - c11) + a11 * b2) + a21 * b1) + a21 * b2; c2 = tail_a1 * alpha_i[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 = alpha_i[0] * split; b1 = con - alpha_i[0]; b1 = con - b1; b2 = alpha_i[0] - b1; c11 = head_a1 * alpha_i[0]; c21 = (((a11 * b1 - c11) + a11 * b2) + a21 * b1) + a21 * b2; c2 = tail_a1 * alpha_i[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 = alpha_i[1] * split; b1 = con - alpha_i[1]; b1 = con - b1; b2 = alpha_i[1] - b1; c11 = head_a0 * alpha_i[1]; c21 = (((a11 * b1 - c11) + a11 * b2) + a21 * b1) + a21 * b2; c2 = tail_a0 * alpha_i[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; } y_elem[0] = y_i[iy]; y_elem[1] = y_i[iy + 1]; { /* Compute complex-extra = complex-double * complex-double. */ double head_t1, tail_t1; double head_t2, tail_t2; /* Real part */ { /* Compute double_double = double * double. */ double a1, a2, b1, b2, con; con = y_elem[0] * split; a1 = con - y_elem[0]; a1 = con - a1; a2 = y_elem[0] - a1; con = beta_i[0] * split; b1 = con - beta_i[0]; b1 = con - b1; b2 = beta_i[0] - b1; head_t1 = y_elem[0] * beta_i[0]; tail_t1 = (((a1 * b1 - head_t1) + a1 * b2) + a2 * b1) + a2 * b2; } { /* Compute double_double = double * double. */ double a1, a2, b1, b2, con; con = y_elem[1] * split; a1 = con - y_elem[1]; a1 = con - a1; a2 = y_elem[1] - a1; con = beta_i[1] * split; b1 = con - beta_i[1]; b1 = con - b1; b2 = beta_i[1] - b1; head_t2 = y_elem[1] * beta_i[1]; tail_t2 = (((a1 * b1 - head_t2) + a1 * b2) + a2 * b1) + a2 * b2; } 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_tmp2[0] = head_t1; tail_tmp2[0] = tail_t1; /* Imaginary part */ { /* Compute double_double = double * double. */ double a1, a2, b1, b2, con; con = y_elem[1] * split; a1 = con - y_elem[1]; a1 = con - a1; a2 = y_elem[1] - a1; con = beta_i[0] * split; b1 = con - beta_i[0]; b1 = con - b1; b2 = beta_i[0] - b1; head_t1 = y_elem[1] * beta_i[0]; tail_t1 = (((a1 * b1 - head_t1) + a1 * b2) + a2 * b1) + a2 * b2; } { /* Compute double_double = double * double. */ double a1, a2, b1, b2, con; con = y_elem[0] * split; a1 = con - y_elem[0]; a1 = con - a1; a2 = y_elem[0] - a1; con = beta_i[1] * split; b1 = con - beta_i[1]; b1 = con - b1; b2 = beta_i[1] - b1; head_t2 = y_elem[0] * beta_i[1]; tail_t2 = (((a1 * b1 - head_t2) + a1 * b2) + a2 * b1) + a2 * b2; } { /* 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_tmp2[1] = head_t1; tail_tmp2[1] = tail_t1; } { double head_t, tail_t; double head_a, tail_a; double head_b, tail_b; /* Real part */ head_a = head_tmp1[0]; tail_a = tail_tmp1[0]; head_b = head_tmp2[0]; tail_b = tail_tmp2[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_tmp1[1]; tail_a = tail_tmp1[1]; head_b = head_tmp2[1]; tail_b = tail_tmp2[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[iy] = head_tmp1[0]; y_i[iy + 1] = head_tmp1[1]; ai += incai; iy += incy; } } } else { /* if beta = 0, we can save m multiplies: y = alpha*A*x */ if (beta_i[0] == 0.0 && beta_i[1] == 0.0) { /* save m more multiplies if alpha = 1 */ if ((alpha_i[0] == 1.0 && alpha_i[1] == 0.0)) { ai = 0; iy = ky; for (i = 0; i < leny; i++) { head_sum[0] = head_sum[1] = tail_sum[0] = tail_sum[1] = 0.0; aij = ai; jx = kx; for (j = 0; j < lenx; j++) { a_elem[0] = a_i[aij]; a_elem[1] = a_i[aij + 1]; x_elem = x_i[jx]; { /* Compute complex-extra = complex-double * real. */ double head_t, tail_t; { /* Compute double_double = double * double. */ double a1, a2, b1, b2, con; con = x_elem * split; a1 = con - x_elem; a1 = con - a1; a2 = x_elem - a1; con = a_elem[0] * split; b1 = con - a_elem[0]; b1 = con - b1; b2 = a_elem[0] - b1; head_t = x_elem * a_elem[0]; tail_t = (((a1 * b1 - head_t) + a1 * b2) + a2 * b1) + a2 * b2; } head_prod[0] = head_t; tail_prod[0] = tail_t; { /* Compute double_double = double * double. */ double a1, a2, b1, b2, con; con = x_elem * split; a1 = con - x_elem; a1 = con - a1; a2 = x_elem - a1; con = a_elem[1] * split; b1 = con - a_elem[1]; b1 = con - b1; b2 = a_elem[1] - b1; head_t = x_elem * a_elem[1]; tail_t = (((a1 * b1 - head_t) + a1 * b2) + a2 * b1) + a2 * b2; } head_prod[1] = head_t; tail_prod[1] = tail_t; } { 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; } aij += incaij; jx += incx; } y_i[iy] = head_sum[0]; y_i[iy + 1] = head_sum[1]; ai += incai; iy += incy; } } else { ai = 0; iy = ky; for (i = 0; i < leny; i++) { head_sum[0] = head_sum[1] = tail_sum[0] = tail_sum[1] = 0.0; aij = ai; jx = kx; for (j = 0; j < lenx; j++) { a_elem[0] = a_i[aij]; a_elem[1] = a_i[aij + 1]; x_elem = x_i[jx]; { /* Compute complex-extra = complex-double * real. */ double head_t, tail_t; { /* Compute double_double = double * double. */ double a1, a2, b1, b2, con; con = x_elem * split; a1 = con - x_elem; a1 = con - a1; a2 = x_elem - a1; con = a_elem[0] * split; b1 = con - a_elem[0]; b1 = con - b1; b2 = a_elem[0] - b1; head_t = x_elem * a_elem[0]; tail_t = (((a1 * b1 - head_t) + a1 * b2) + a2 * b1) + a2 * b2; } head_prod[0] = head_t; tail_prod[0] = tail_t; { /* Compute double_double = double * double. */ double a1, a2, b1, b2, con; con = x_elem * split; a1 = con - x_elem; a1 = con - a1; a2 = x_elem - a1; con = a_elem[1] * split; b1 = con - a_elem[1]; b1 = con - b1; b2 = a_elem[1] - b1; head_t = x_elem * a_elem[1]; tail_t = (((a1 * b1 - head_t) + a1 * b2) + a2 * b1) + a2 * b2; } head_prod[1] = head_t; tail_prod[1] = tail_t; } { 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; } aij += incaij; jx += incx; } { /* 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 = alpha_i[0] * split; b1 = con - alpha_i[0]; b1 = con - b1; b2 = alpha_i[0] - b1; c11 = head_a0 * alpha_i[0]; c21 = (((a11 * b1 - c11) + a11 * b2) + a21 * b1) + a21 * b2; c2 = tail_a0 * alpha_i[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 = alpha_i[1] * split; b1 = con - alpha_i[1]; b1 = con - b1; b2 = alpha_i[1] - b1; c11 = head_a1 * alpha_i[1]; c21 = (((a11 * b1 - c11) + a11 * b2) + a21 * b1) + a21 * b2; c2 = tail_a1 * alpha_i[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 = alpha_i[0] * split; b1 = con - alpha_i[0]; b1 = con - b1; b2 = alpha_i[0] - b1; c11 = head_a1 * alpha_i[0]; c21 = (((a11 * b1 - c11) + a11 * b2) + a21 * b1) + a21 * b2; c2 = tail_a1 * alpha_i[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 = alpha_i[1] * split; b1 = con - alpha_i[1]; b1 = con - b1; b2 = alpha_i[1] - b1; c11 = head_a0 * alpha_i[1]; c21 = (((a11 * b1 - c11) + a11 * b2) + a21 * b1) + a21 * b2; c2 = tail_a0 * alpha_i[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; } y_i[iy] = head_tmp1[0]; y_i[iy + 1] = head_tmp1[1]; ai += incai; iy += incy; } } } else { /* the most general form, y = alpha*A*x + beta*y */ ai = 0; iy = ky; for (i = 0; i < leny; i++) { head_sum[0] = head_sum[1] = tail_sum[0] = tail_sum[1] = 0.0;; aij = ai; jx = kx; for (j = 0; j < lenx; j++) { a_elem[0] = a_i[aij]; a_elem[1] = a_i[aij + 1]; x_elem = x_i[jx]; { /* Compute complex-extra = complex-double * real. */ double head_t, tail_t; { /* Compute double_double = double * double. */ double a1, a2, b1, b2, con; con = x_elem * split; a1 = con - x_elem; a1 = con - a1; a2 = x_elem - a1; con = a_elem[0] * split; b1 = con - a_elem[0]; b1 = con - b1; b2 = a_elem[0] - b1; head_t = x_elem * a_elem[0]; tail_t = (((a1 * b1 - head_t) + a1 * b2) + a2 * b1) + a2 * b2; } head_prod[0] = head_t; tail_prod[0] = tail_t; { /* Compute double_double = double * double. */ double a1, a2, b1, b2, con; con = x_elem * split; a1 = con - x_elem; a1 = con - a1; a2 = x_elem - a1; con = a_elem[1] * split; b1 = con - a_elem[1]; b1 = con - b1; b2 = a_elem[1] - b1; head_t = x_elem * a_elem[1]; tail_t = (((a1 * b1 - head_t) + a1 * b2) + a2 * b1) + a2 * b2; } head_prod[1] = head_t; tail_prod[1] = tail_t; } { 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; } aij += incaij; jx += incx; } { /* 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 = alpha_i[0] * split; b1 = con - alpha_i[0]; b1 = con - b1; b2 = alpha_i[0] - b1; c11 = head_a0 * alpha_i[0]; c21 = (((a11 * b1 - c11) + a11 * b2) + a21 * b1) + a21 * b2; c2 = tail_a0 * alpha_i[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 = alpha_i[1] * split; b1 = con - alpha_i[1]; b1 = con - b1; b2 = alpha_i[1] - b1; c11 = head_a1 * alpha_i[1]; c21 = (((a11 * b1 - c11) + a11 * b2) + a21 * b1) + a21 * b2; c2 = tail_a1 * alpha_i[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 = alpha_i[0] * split; b1 = con - alpha_i[0]; b1 = con - b1; b2 = alpha_i[0] - b1; c11 = head_a1 * alpha_i[0]; c21 = (((a11 * b1 - c11) + a11 * b2) + a21 * b1) + a21 * b2; c2 = tail_a1 * alpha_i[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 = alpha_i[1] * split; b1 = con - alpha_i[1]; b1 = con - b1; b2 = alpha_i[1] - b1; c11 = head_a0 * alpha_i[1]; c21 = (((a11 * b1 - c11) + a11 * b2) + a21 * b1) + a21 * b2; c2 = tail_a0 * alpha_i[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; } y_elem[0] = y_i[iy]; y_elem[1] = y_i[iy + 1]; { /* Compute complex-extra = complex-double * complex-double. */ double head_t1, tail_t1; double head_t2, tail_t2; /* Real part */ { /* Compute double_double = double * double. */ double a1, a2, b1, b2, con; con = y_elem[0] * split; a1 = con - y_elem[0]; a1 = con - a1; a2 = y_elem[0] - a1; con = beta_i[0] * split; b1 = con - beta_i[0]; b1 = con - b1; b2 = beta_i[0] - b1; head_t1 = y_elem[0] * beta_i[0]; tail_t1 = (((a1 * b1 - head_t1) + a1 * b2) + a2 * b1) + a2 * b2; } { /* Compute double_double = double * double. */ double a1, a2, b1, b2, con; con = y_elem[1] * split; a1 = con - y_elem[1]; a1 = con - a1; a2 = y_elem[1] - a1; con = beta_i[1] * split; b1 = con - beta_i[1]; b1 = con - b1; b2 = beta_i[1] - b1; head_t2 = y_elem[1] * beta_i[1]; tail_t2 = (((a1 * b1 - head_t2) + a1 * b2) + a2 * b1) + a2 * b2; } 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_tmp2[0] = head_t1; tail_tmp2[0] = tail_t1; /* Imaginary part */ { /* Compute double_double = double * double. */ double a1, a2, b1, b2, con; con = y_elem[1] * split; a1 = con - y_elem[1]; a1 = con - a1; a2 = y_elem[1] - a1; con = beta_i[0] * split; b1 = con - beta_i[0]; b1 = con - b1; b2 = beta_i[0] - b1; head_t1 = y_elem[1] * beta_i[0]; tail_t1 = (((a1 * b1 - head_t1) + a1 * b2) + a2 * b1) + a2 * b2; } { /* Compute double_double = double * double. */ double a1, a2, b1, b2, con; con = y_elem[0] * split; a1 = con - y_elem[0]; a1 = con - a1; a2 = y_elem[0] - a1; con = beta_i[1] * split; b1 = con - beta_i[1]; b1 = con - b1; b2 = beta_i[1] - b1; head_t2 = y_elem[0] * beta_i[1]; tail_t2 = (((a1 * b1 - head_t2) + a1 * b2) + a2 * b1) + a2 * b2; } { /* 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_tmp2[1] = head_t1; tail_tmp2[1] = tail_t1; } { double head_t, tail_t; double head_a, tail_a; double head_b, tail_b; /* Real part */ head_a = head_tmp1[0]; tail_a = tail_tmp1[0]; head_b = head_tmp2[0]; tail_b = tail_tmp2[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_tmp1[1]; tail_a = tail_tmp1[1]; head_b = head_tmp2[1]; tail_b = tail_tmp2[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[iy] = head_tmp1[0]; y_i[iy + 1] = head_tmp1[1]; ai += incai; iy += incy; } } } } FPU_FIX_STOP; } break; } }