From 0e0ead5b0b45078c0009a0ce23ce4bd88a49bb13 Mon Sep 17 00:00:00 2001 From: Anton Khirnov Date: Thu, 27 Dec 2018 11:53:30 +0100 Subject: ell_relax: rewrite residual calculation The order-specific function now calculates the complete residual for an entire row, instead of the derivatives of u for a single point. This is done in preparation for upcoming SIMD. --- ell_relax.c | 167 ++++++++++++++++++++++++++++++++++++++++++++---------------- 1 file changed, 122 insertions(+), 45 deletions(-) diff --git a/ell_relax.c b/ell_relax.c index aa791d8..8d4cb34 100644 --- a/ell_relax.c +++ b/ell_relax.c @@ -39,7 +39,11 @@ struct EllRelaxInternal { double *boundary_val_base[4]; - void (*derivatives_calc)(EllRelaxContext *ctx, double *dst, ptrdiff_t idx, ptrdiff_t stride); + void (*residual_calc_line)(size_t linesize, double *dst, + ptrdiff_t stride, const double *u, const double *rhs, + const double * const diff_coeffs[ELL_RELAX_DIFF_COEFF_NB], + const double *fd_factors); + double fd_factors[ELL_RELAX_DIFF_COEFF_NB]; double relax_factor; }; @@ -65,59 +69,119 @@ static const struct { }, }; +static const double fd_denoms[][ELL_RELAX_DIFF_COEFF_NB] = { + { + [ELL_RELAX_DIFF_COEFF_00] = 1.0, + [ELL_RELAX_DIFF_COEFF_10] = 2.0, + [ELL_RELAX_DIFF_COEFF_01] = 2.0, + [ELL_RELAX_DIFF_COEFF_20] = 1.0, + [ELL_RELAX_DIFF_COEFF_02] = 1.0, + [ELL_RELAX_DIFF_COEFF_11] = 4.0, + }, + { + [ELL_RELAX_DIFF_COEFF_00] = 1.0, + [ELL_RELAX_DIFF_COEFF_10] = 12.0, + [ELL_RELAX_DIFF_COEFF_01] = 12.0, + [ELL_RELAX_DIFF_COEFF_20] = 12.0, + [ELL_RELAX_DIFF_COEFF_02] = 12.0, + [ELL_RELAX_DIFF_COEFF_11] = 144.0, + }, +}; + static void -derivatives_calc_s1(EllRelaxContext *ctx, double *dst, ptrdiff_t idx, ptrdiff_t stride) +derivatives_calc_s1(double *dst, const double *u, const double *fd_factors, ptrdiff_t stride) { - const double *u = ctx->u; - const double dx = ctx->step[0]; - const double dy = ctx->step[1]; - - dst[ELL_RELAX_DIFF_COEFF_00] = u[idx]; - dst[ELL_RELAX_DIFF_COEFF_10] = (u[idx + 1] - u[idx - 1]) / (2.0 * dx); - dst[ELL_RELAX_DIFF_COEFF_01] = (u[idx + stride] - u[idx - stride]) / (2.0 * dy); + dst[ELL_RELAX_DIFF_COEFF_00] = u[0]; + dst[ELL_RELAX_DIFF_COEFF_10] = (u[1] - u[-1]) * fd_factors[ELL_RELAX_DIFF_COEFF_10]; + dst[ELL_RELAX_DIFF_COEFF_01] = (u[stride] - u[-stride]) * fd_factors[ELL_RELAX_DIFF_COEFF_01]; - dst[ELL_RELAX_DIFF_COEFF_20] = (u[idx + 1] - 2.0 * u[idx] + u[idx - 1]) / (SQR(dx)); - dst[ELL_RELAX_DIFF_COEFF_02] = (u[idx + stride] - 2.0 * u[idx] + u[idx - stride]) / (SQR(dy)); + dst[ELL_RELAX_DIFF_COEFF_20] = (u[1] - 2.0 * u[0] + u[-1]) * fd_factors[ELL_RELAX_DIFF_COEFF_20]; + dst[ELL_RELAX_DIFF_COEFF_02] = (u[stride] - 2.0 * u[0] + u[-stride]) * fd_factors[ELL_RELAX_DIFF_COEFF_02]; - dst[ELL_RELAX_DIFF_COEFF_11] = (u[idx + 1 + stride] - u[idx + stride - 1] - u[idx - stride + 1] + u[idx - stride - 1]) / (4.0 * dx * dy); + dst[ELL_RELAX_DIFF_COEFF_11] = (u[1 + stride] - u[stride - 1] - u[-stride + 1] + u[-stride - 1]) * fd_factors[ELL_RELAX_DIFF_COEFF_11]; } static void -derivatives_calc_s2(EllRelaxContext *ctx, double *dst, ptrdiff_t idx, ptrdiff_t stride) +derivatives_calc_s2(double *dst, const double *u, const double *fd_factors, ptrdiff_t stride) { - const double *u = ctx->u; - const double dx = ctx->step[0]; - const double dy = ctx->step[1]; - - dst[ELL_RELAX_DIFF_COEFF_00] = u[idx]; - dst[ELL_RELAX_DIFF_COEFF_10] = (-1.0 * u[idx + 2] + 8.0 * u[idx + 1] - 8.0 * u[idx - 1] + 1.0 * u[idx - 2]) / (12.0 * dx); - dst[ELL_RELAX_DIFF_COEFF_01] = (-1.0 * u[idx + 2 * stride] + 8.0 * u[idx + stride] - 8.0 * u[idx - stride] + 1.0 * u[idx - 2 * stride]) / (12.0 * dy); - - dst[ELL_RELAX_DIFF_COEFF_20] = (-1.0 * u[idx + 2] + 16.0 * u[idx + 1] - 30.0 * u[idx] + 16.0 * u[idx - 1] - 1.0 * u[idx - 2]) / (12.0 * SQR(dx)); - dst[ELL_RELAX_DIFF_COEFF_02] = (-1.0 * u[idx + 2 * stride] + 16.0 * u[idx + stride] - 30.0 * u[idx] + 16.0 * u[idx - stride] - 1.0 * u[idx - 2 * stride]) / (12.0 * SQR(dy)); - - dst[ELL_RELAX_DIFF_COEFF_11] = ( 1.0 * u[idx + 2 + 2 * stride] - 8.0 * u[idx + 2 + stride] + 8.0 * u[idx + 2 - stride] - 1.0 * u[idx + 2 - 2 * stride] - -8.0 * u[idx + 1 + 2 * stride] + 64.0 * u[idx + 1 + stride] - 64.0 * u[idx + 1 - stride] + 8.0 * u[idx + 1 - 2 * stride] - +8.0 * u[idx - 1 + 2 * stride] - 64.0 * u[idx - 1 + stride] + 64.0 * u[idx - 1 - stride] - 8.0 * u[idx - 1 - 2 * stride] - -1.0 * u[idx - 2 + 2 * stride] + 8.0 * u[idx - 2 + stride] - 8.0 * u[idx - 2 - stride] + 1.0 * u[idx - 2 - 2 * stride]) - / (144.0 * dx * dy); + const double val = u[0]; + + const double valxp1 = u[ 1]; + const double valxp2 = u[ 2]; + const double valxm1 = u[-1]; + const double valxm2 = u[-2]; + const double valyp1 = u[ 1 * stride]; + const double valyp2 = u[ 2 * stride]; + const double valym1 = u[-1 * stride]; + const double valym2 = u[-2 * stride]; + + const double valxp1yp1 = u[ 1 + 1 * stride]; + const double valxp1yp2 = u[ 1 + 2 * stride]; + const double valxp1ym1 = u[ 1 - 1 * stride]; + const double valxp1ym2 = u[ 1 - 2 * stride]; + + const double valxp2yp1 = u[ 2 + 1 * stride]; + const double valxp2yp2 = u[ 2 + 2 * stride]; + const double valxp2ym1 = u[ 2 - 1 * stride]; + const double valxp2ym2 = u[ 2 - 2 * stride]; + + const double valxm1yp1 = u[-1 + 1 * stride]; + const double valxm1yp2 = u[-1 + 2 * stride]; + const double valxm1ym1 = u[-1 - 1 * stride]; + const double valxm1ym2 = u[-1 - 2 * stride]; + + const double valxm2yp1 = u[-2 + 1 * stride]; + const double valxm2yp2 = u[-2 + 2 * stride]; + const double valxm2ym1 = u[-2 - 1 * stride]; + const double valxm2ym2 = u[-2 - 2 * stride]; + + dst[ELL_RELAX_DIFF_COEFF_00] = val; + dst[ELL_RELAX_DIFF_COEFF_10] = (-1.0 * valxp2 + 8.0 * valxp1 - 8.0 * valxm1 + 1.0 * valxm2) * fd_factors[ELL_RELAX_DIFF_COEFF_10]; + dst[ELL_RELAX_DIFF_COEFF_01] = (-1.0 * valyp2 + 8.0 * valyp1 - 8.0 * valym1 + 1.0 * valym2) * fd_factors[ELL_RELAX_DIFF_COEFF_01]; + + dst[ELL_RELAX_DIFF_COEFF_20] = (-1.0 * valxp2 + 16.0 * valxp1 - 30.0 * val + 16.0 * valxm1 - 1.0 * valxm2) * fd_factors[ELL_RELAX_DIFF_COEFF_20]; + dst[ELL_RELAX_DIFF_COEFF_02] = (-1.0 * valyp2 + 16.0 * valyp1 - 30.0 * val + 16.0 * valym1 - 1.0 * valym2) * fd_factors[ELL_RELAX_DIFF_COEFF_02]; + + dst[ELL_RELAX_DIFF_COEFF_11] = ( 1.0 * valxp2yp2 - 8.0 * valxp2yp1 + 8.0 * valxp2ym1 - 1.0 * valxp2ym2 + -8.0 * valxp1yp2 + 64.0 * valxp1yp1 - 64.0 * valxp1ym1 + 8.0 * valxp1ym2 + +8.0 * valxm1yp2 - 64.0 * valxm1yp1 + 64.0 * valxm1ym1 - 8.0 * valxm1ym2 + -1.0 * valxm2yp2 + 8.0 * valxm2yp1 - 8.0 * valxm2ym1 + 1.0 * valxm2ym2) * fd_factors[ELL_RELAX_DIFF_COEFF_11]; } -static inline double residual_calc_kernel(EllRelaxContext *ctx, ptrdiff_t idx) +static void residual_calc_line_s1_c(size_t linesize, double *dst, + ptrdiff_t stride, const double *u, const double *rhs, + const double * const diff_coeffs[ELL_RELAX_DIFF_COEFF_NB], + const double *fd_factors) { - EllRelaxInternal *priv = ctx->priv; + for (size_t i = 0; i < linesize; i++) { + double u_vals[ELL_RELAX_DIFF_COEFF_NB]; + double res; - double u[ELL_RELAX_DIFF_COEFF_NB]; - double res; + derivatives_calc_s1(u_vals, u + i, fd_factors, stride); - priv->derivatives_calc(ctx, u, idx, priv->stride); + res = -rhs[i]; + for (int j = 0; j < ARRAY_ELEMS(u_vals); j++) + res += u_vals[j] * diff_coeffs[j][i]; + dst[i] = res; + } +} - res = -ctx->rhs[idx]; - for (int i = 0; i < ARRAY_ELEMS(u); i++) - res += u[i] * ctx->diff_coeffs[i][idx]; +static void residual_calc_line_s2_c(size_t linesize, double *dst, + ptrdiff_t stride, const double *u, const double *rhs, + const double * const diff_coeffs[ELL_RELAX_DIFF_COEFF_NB], + const double *fd_factors) +{ + for (size_t i = 0; i < linesize; i++) { + double u_vals[ELL_RELAX_DIFF_COEFF_NB]; + double res; - return res; + derivatives_calc_s2(u_vals, u + i, fd_factors, stride); + res = -rhs[i]; + for (int j = 0; j < ARRAY_ELEMS(u_vals); j++) + res += u_vals[j] * diff_coeffs[j][i]; + dst[i] = res; + } } static void residual_calc(EllRelaxContext *ctx) @@ -126,11 +190,17 @@ static void residual_calc(EllRelaxContext *ctx) int64_t start; start = gettime(); - for (int idx1 = 0; idx1 < ctx->domain_size[1]; idx1++) - for (int idx0 = 0; idx0 < ctx->domain_size[0]; idx0++) { - ptrdiff_t idx = idx1 * priv->stride + idx0; - ctx->residual[idx] = residual_calc_kernel(ctx, idx); - } + for (int idx1 = 0; idx1 < ctx->domain_size[1]; idx1++) { + const ptrdiff_t offset = idx1 * priv->stride; + const double *diff_coeffs[ELL_RELAX_DIFF_COEFF_NB]; + + for (int i = 0; i < ARRAY_ELEMS(diff_coeffs); i++) + diff_coeffs[i] = ctx->diff_coeffs[i] + offset; + + priv->residual_calc_line(ctx->domain_size[0], ctx->residual + offset, + priv->stride, ctx->u + offset, ctx->rhs + offset, + diff_coeffs, priv->fd_factors); + } for (int i = 0; i < ARRAY_ELEMS(ctx->boundaries); i++) { const ptrdiff_t strides[2] = { 1, priv->stride }; @@ -274,10 +344,10 @@ int mg2di_ell_relax_init(EllRelaxContext *ctx) switch (ctx->fd_stencil) { case 1: - priv->derivatives_calc = derivatives_calc_s1; + priv->residual_calc_line = residual_calc_line_s1_c; break; case 2: - priv->derivatives_calc = derivatives_calc_s2; + priv->residual_calc_line = residual_calc_line_s2_c; break; default: mg2di_log(&ctx->logger, 0, "Invalid finite difference stencil: %zd\n", @@ -295,6 +365,13 @@ int mg2di_ell_relax_init(EllRelaxContext *ctx) else priv->relax_factor = ctx->relax_factor; + priv->fd_factors[ELL_RELAX_DIFF_COEFF_00] = 1.0 / fd_denoms[ctx->fd_stencil - 1][ELL_RELAX_DIFF_COEFF_00]; + priv->fd_factors[ELL_RELAX_DIFF_COEFF_10] = 1.0 / (fd_denoms[ctx->fd_stencil - 1][ELL_RELAX_DIFF_COEFF_10] * ctx->step[0]); + priv->fd_factors[ELL_RELAX_DIFF_COEFF_01] = 1.0 / (fd_denoms[ctx->fd_stencil - 1][ELL_RELAX_DIFF_COEFF_01] * ctx->step[1]); + priv->fd_factors[ELL_RELAX_DIFF_COEFF_20] = 1.0 / (fd_denoms[ctx->fd_stencil - 1][ELL_RELAX_DIFF_COEFF_20] * SQR(ctx->step[0])); + priv->fd_factors[ELL_RELAX_DIFF_COEFF_02] = 1.0 / (fd_denoms[ctx->fd_stencil - 1][ELL_RELAX_DIFF_COEFF_02] * SQR(ctx->step[1])); + priv->fd_factors[ELL_RELAX_DIFF_COEFF_11] = 1.0 / (fd_denoms[ctx->fd_stencil - 1][ELL_RELAX_DIFF_COEFF_11] * ctx->step[0] * ctx->step[1]); + for (int i = 0; i < ARRAY_ELEMS(ctx->boundaries); i++) { if (ctx->boundaries[i].type == ELL_RELAX_BC_TYPE_FIXDIFF) { for (int k = 0; k < ctx->domain_size[boundary_def[i].stride_idx]; k++) -- cgit v1.2.3