mirror of
https://git.code.sf.net/p/quake/quakeforge
synced 2024-11-23 04:42:32 +00:00
e2d812ab6a
It's implemented as the Hodge dual, which is probably reasonable until people complain. Both ⋆ and ! are supported, though the former is a little hard to see in Consola.
1619 lines
44 KiB
C
1619 lines
44 KiB
C
/*
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expr_algebra.c
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geometric algebra expressions
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Copyright (C) 2023 Bill Currie <bill@taniwha.org>
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This program is free software; you can redistribute it and/or
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modify it under the terms of the GNU General Public License
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as published by the Free Software Foundation; either version 2
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of the License, or (at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
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See the GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with this program; if not, write to:
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Free Software Foundation, Inc.
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59 Temple Place - Suite 330
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Boston, MA 02111-1307, USA
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*/
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#ifdef HAVE_CONFIG_H
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# include "config.h"
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#endif
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#include "QF/math/bitop.h"
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#include "tools/qfcc/include/algebra.h"
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#include "tools/qfcc/include/diagnostic.h"
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#include "tools/qfcc/include/expr.h"
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#include "tools/qfcc/include/type.h"
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#include "tools/qfcc/include/value.h"
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#include "tools/qfcc/source/qc-parse.h"
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static int __attribute__((pure))
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get_group (type_t *type, algebra_t *algebra)
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{
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auto layout = &algebra->layout;
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if (is_scalar (type) && !is_algebra (type)) {
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return layout->group_map[layout->mask_map[0]][0];
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}
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if (!is_algebra (type)) {
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internal_error (0, "non-algebra type");
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}
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pr_uint_t group_mask = (1u << (layout->count + 1)) - 1;
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if (type->type != ev_invalid) {
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group_mask = type->t.multivec->group_mask;
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}
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if (group_mask & (group_mask - 1)) {
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internal_error (0, "multi-group mult-vector");
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}
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return BITOP_LOG2 (group_mask);
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}
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static expr_t *
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offset_cast (type_t *type, expr_t *expr, int offset)
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{
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offset *= type_size (base_type (get_type (expr)));
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return new_offset_alias_expr (type, expr, offset);
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}
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static expr_t *
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mvec_expr (expr_t *expr, algebra_t *algebra)
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{
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auto mvtype = get_type (expr);
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if (expr->type == ex_multivec || is_scalar (mvtype)) {
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return expr;
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}
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if (!is_algebra (mvtype)) {
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return error (expr, "invalid operand for GA");
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}
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auto layout = &algebra->layout;
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pr_uint_t group_mask = (1u << (layout->count + 1)) - 1;
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if (mvtype->type != ev_invalid) {
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group_mask = mvtype->t.multivec->group_mask;
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}
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if (!(group_mask & (group_mask - 1))) {
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return expr;
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}
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auto mvec = new_expr ();
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mvec->type = ex_multivec;
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mvec->e.multivec = (ex_multivec_t) {
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.type = algebra_mvec_type (algebra, group_mask),
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.algebra = algebra,
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};
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expr_t **c = &mvec->e.multivec.components;
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int comp_offset = 0;
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for (int i = 0; i < layout->count; i++) {
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pr_uint_t mask = 1u << i;
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if (mask & group_mask) {
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auto comp_type = algebra_mvec_type (algebra, mask);
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*c = offset_cast (comp_type, expr, comp_offset);
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c = &(*c)->next;
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mvec->e.multivec.count++;
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comp_offset += algebra->layout.groups[i].count;
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}
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}
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return mvec;
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}
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static void
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mvec_scatter (expr_t **components, expr_t *mvec, algebra_t *algebra)
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{
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auto layout = &algebra->layout;
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int group;
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if (mvec->type != ex_multivec) {
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auto type = get_type (mvec);
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if (!is_algebra (type)) {
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group = layout->group_map[layout->mask_map[0]][0];
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} else {
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if (type->type == ev_invalid) {
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internal_error (mvec, "full algebra in mvec_scatter");
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}
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pr_uint_t mask = type->t.multivec->group_mask;
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if (mask & (mask - 1)) {
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internal_error (mvec, "bare multivector in mvec_scatter");
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}
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group = BITOP_LOG2 (mask);
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}
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components[group] = mvec;
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return;
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}
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for (auto c = mvec->e.multivec.components; c; c = c->next) {
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auto ct = get_type (c);
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if (!is_algebra (ct)) {
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group = layout->group_map[layout->mask_map[0]][0];
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components[group] = mvec;
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} else if (ct->meta == ty_algebra && ct->type != ev_invalid) {
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pr_uint_t mask = ct->t.multivec->group_mask;
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if (mask & (mask - 1)) {
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internal_error (mvec, "multivector in multivec expression");
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}
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group = BITOP_LOG2 (mask);
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} else {
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internal_error (mvec, "invalid type in multivec expression");
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}
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components[group] = c;
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}
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}
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static expr_t *
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mvec_gather (expr_t **components, algebra_t *algebra)
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{
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auto layout = &algebra->layout;
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pr_uint_t group_mask = 0;
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int count = 0;
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expr_t *mvec = 0;
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for (int i = 0; i < layout->count; i++) {
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if (components[i]) {
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count++;
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mvec = components[i];
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group_mask |= 1 << i;
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}
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}
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if (count == 1) {
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return mvec;
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}
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if (!count) {
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return new_zero_expr (algebra->type);
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}
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mvec = new_expr ();
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mvec->type = ex_multivec;
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mvec->e.multivec = (ex_multivec_t) {
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.type = algebra_mvec_type (algebra, group_mask),
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.algebra = algebra,
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};
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for (int i = layout->count; i-- > 0; ) {
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if (components[i]) {
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components[i]->next = mvec->e.multivec.components;
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mvec->e.multivec.components = components[i];
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mvec->e.multivec.count++;
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}
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}
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return mvec;
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}
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static expr_t *
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promote_scalar (type_t *dst_type, expr_t *scalar)
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{
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auto scalar_type = get_type (scalar);
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if (scalar_type != dst_type) {
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if (!type_promotes (dst_type, scalar_type)) {
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warning (scalar, "demoting %s to %s (use a cast)",
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get_type_string (scalar_type),
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get_type_string (dst_type));
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}
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scalar = cast_expr (dst_type, scalar);
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}
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return scalar;
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}
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static expr_t *
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scalar_product (expr_t *e1, expr_t *e2)
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{
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auto scalar = is_scalar (get_type (e1)) ? e1 : e2;
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auto vector = is_scalar (get_type (e1)) ? e2 : e1;
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auto algebra = algebra_get (get_type (vector));
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auto layout = &algebra->layout;
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scalar = promote_scalar (algebra->type, scalar);
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expr_t *components[layout->count] = {};
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vector = mvec_expr (vector, algebra);
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mvec_scatter (components, vector, algebra);
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for (int i = 0; i < layout->count; i++) {
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if (!components[i]) {
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continue;
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}
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auto comp_type = get_type (components[i]);
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if (type_width (comp_type) == 1) {
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auto prod = new_binary_expr ('*', components[i], scalar);
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prod->e.expr.type = comp_type;
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components[i] = fold_constants (prod);
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} else if (type_width (comp_type) > 4) {
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internal_error (vector, "scalar * %d-vector not implemented",
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type_width (comp_type));
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} else {
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auto prod = new_binary_expr (SCALE, components[i], scalar);
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prod->e.expr.type = comp_type;
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components[i] = fold_constants (prod);
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}
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}
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return mvec_gather (components, algebra);
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}
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static void
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component_sum (int op, expr_t **c, expr_t **a, expr_t **b,
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algebra_t *algebra)
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{
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auto layout = &algebra->layout;
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for (int i = 0; i < layout->count; i++) {
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if (a[i] && b[i]) {
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if (get_type (a[i]) != get_type (b[i])) {
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internal_error (a[i], "tangled multivec types");
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}
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auto sum_type = get_type (a[i]);
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c[i] = new_binary_expr (op, a[i], b[i]);
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c[i]->e.expr.type = sum_type;
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c[i] = fold_constants (c[i]);
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} else if (a[i]) {
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c[i] = a[i];
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} else if (b[i]) {
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if (op == '+') {
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c[i] = b[i];
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} else {
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c[i] = scalar_product (new_float_expr (-1), b[i]);
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c[i] = fold_constants (c[i]);
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}
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} else {
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c[i] = 0;
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}
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}
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}
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static expr_t *
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sum_expr (type_t *type, int op, expr_t *a, expr_t *b)
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{
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auto sum = new_binary_expr (op, a, b);
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sum->e.expr.type = type;
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return sum;
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}
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static expr_t *
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scale_expr (type_t *type, expr_t *a, expr_t *b)
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{
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if (!is_scalar (get_type (b)) || !is_real (get_type (b))) {
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internal_error (b, "not a real scalar type");
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}
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if (!is_real (get_type (a))) {
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internal_error (b, "not a real scalar type");
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}
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int op = is_scalar (get_type (a)) ? '*' : SCALE;
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auto scale = new_binary_expr (op, a, b);
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scale->e.expr.type = type;
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return fold_constants (scale);
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}
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static expr_t *
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dot_expr (type_t *type, expr_t *a, expr_t *b)
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{
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auto vec_type = get_type (a);
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auto dot = new_binary_expr (DOT, a, b);
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dot->e.expr.type = vector_type (vec_type, type_width (vec_type));
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dot = array_expr (dot, new_short_expr (0));
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dot->e.expr.type = type;
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return dot;
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}
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static expr_t *
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cross_expr (type_t *type, expr_t *a, expr_t *b)
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{
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auto cross = new_binary_expr (CROSS, a, b);
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cross->e.expr.type = type;
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return cross;
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}
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typedef void (*pga_func) (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg);
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static void
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scale_component (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
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{
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if (is_algebra (get_type (b))) {
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auto t = a;
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a = b;
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b = t;
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}
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if (!is_algebra (get_type (a))) {
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a = promote_scalar (alg->type, a);
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}
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auto scale_type = get_type (a);
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b = promote_scalar (alg->type, b);
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auto scale = scale_expr (scale_type, a, b);
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int group = get_group (scale_type, alg);
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c[group] = scale;
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}
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static void
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pga3_x_y_z_w_dot_x_y_z_w (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
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{
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auto stype = alg->type;
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auto vtype = vector_type (stype, 3);
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auto dot_type = algebra_mvec_type (alg, 0x04);
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auto va = offset_cast (vtype, a, 0);
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auto vb = offset_cast (vtype, b, 0);
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c[2] = dot_expr (dot_type, va, vb);
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}
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static void
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pga3_x_y_z_w_dot_yz_zx_xy (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
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{
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auto stype = alg->type;
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auto vtype = vector_type (stype, 3);
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auto dot_type = algebra_mvec_type (alg, 0x01);
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auto va = offset_cast (vtype, a, 0);
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c[2] = cross_expr (dot_type, b, va);
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}
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static void
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pga3_x_y_z_w_dot_wx_wy_wz (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
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{
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auto stype = alg->type;
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auto vtype = vector_type (stype, 3);
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auto va = offset_cast (vtype, a, 0);
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auto cs = unary_expr ('-', dot_expr (stype, b, va));
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c[0] = new_extend_expr (cs, algebra_mvec_type (alg, 0x01), 0, true);
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}
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static void
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pga3_x_y_z_w_dot_wxyz (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
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{
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auto stype = alg->type;
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auto vtype = vector_type (stype, 3);
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auto va = offset_cast (vtype, a, 0);
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auto sb = offset_cast (stype, b, 0);
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auto cv = scale_expr (vtype, va, sb);
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c[5] = new_extend_expr (cv, algebra_mvec_type (alg, 0x20), 0, false);
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}
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#define pga3_wzy_wxz_wyx_xyz_dot_x_y_z_w pga3_x_y_z_w_dot_wzy_wxz_wyx_xyz
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static void
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pga3_x_y_z_w_dot_wzy_wxz_wyx_xyz (expr_t **c, expr_t *a, expr_t *b,
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algebra_t *alg)
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{
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auto stype = alg->type;
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auto vtype = vector_type (stype, 3);
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auto bvtype = algebra_mvec_type (alg, 0x02);
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auto bmtype = algebra_mvec_type (alg, 0x08);
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auto va = offset_cast (bvtype, a, 0);
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auto vb = offset_cast (vtype, b, 0);
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auto sb = offset_cast (stype, b, 3);
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c[1] = scale_expr (bvtype, va, sb);
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c[3] = cross_expr (bmtype, vb, va);
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}
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static void
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pga3_yz_zx_xy_dot_x_y_z_w (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
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{
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auto stype = alg->type;
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auto vtype = vector_type (stype, 3);
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auto dot_type = algebra_mvec_type (alg, 0x01);
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auto vb = offset_cast (vtype, a, 0);
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c[2] = cross_expr (dot_type, a, vb);
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}
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static void
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pga3_yz_zx_xy_dot_yz_zx_xy (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
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{
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auto dot_type = algebra_mvec_type (alg, 0x04);
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c[2] = unary_expr ('-', dot_expr (dot_type, a, b));
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}
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#define pga3_wxyz_dot_yz_zx_xy pga3_yz_zx_xy_dot_wxyz
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static void
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pga3_yz_zx_xy_dot_wxyz (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
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{
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auto stype = alg->type;
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auto bmtype = algebra_mvec_type (alg, 0x08);
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auto va = offset_cast (bmtype, a, 0);
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auto sb = offset_cast (stype, b, 0);
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c[3] = scale_expr (bmtype, va, unary_expr ('-', sb));
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}
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#define pga3_wzy_wxz_wyx_xyz_dot_yz_zx_xy pga3_yz_zx_xy_dot_wzy_wxz_wyx_xyz
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static void
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pga3_yz_zx_xy_dot_wzy_wxz_wyx_xyz (expr_t **c, expr_t *a, expr_t *b,
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algebra_t *alg)
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{
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auto stype = alg->type;
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auto vtype = vector_type (stype, 3);
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auto dot_type = algebra_mvec_type (alg, 0x01);
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auto vb = offset_cast (vtype, b, 0);
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auto sb = offset_cast (stype, b, 3);
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auto cv = scale_expr (vtype, a, sb);
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auto cs = dot_expr (stype, a, vb);
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c[0] = sum_expr (dot_type, '-', new_extend_expr (cs, dot_type, 0, true),
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new_extend_expr (cv, dot_type, 0, false));
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}
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static void
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pga3_wx_wy_wz_dot_x_y_z_w (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
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{
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auto stype = alg->type;
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auto vtype = vector_type (stype, 3);
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auto va = offset_cast (vtype, a, 0);
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auto cs = dot_expr (stype, b, va);
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c[0] = new_extend_expr (cs, algebra_mvec_type (alg, 0x01), 0, true);
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}
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static void
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pga3_wxyz_dot_x_y_z_w (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
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{
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auto stype = alg->type;
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auto dot_type = algebra_mvec_type (alg, 0x20);
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auto vb = offset_cast (dot_type,
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new_swizzle_expr (b, "-x-y-z0"), 0);
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auto sa = offset_cast (stype, a, 0);
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c[5] = scale_expr (dot_type, vb, sa);
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}
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static void
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pga3_wxyz_dot_wzy_wxz_wyx_xyz (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
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{
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auto stype = alg->type;
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auto sa = offset_cast (stype, a, 0);
|
|
auto sb = offset_cast (stype, b, 3);
|
|
sb = unary_expr ('-', sb);
|
|
auto cs = scale_expr (stype, sa, sb);
|
|
c[0] = new_extend_expr (cs, algebra_mvec_type (alg, 0x01), 0, true);
|
|
}
|
|
|
|
static void
|
|
pga3_wzy_wxz_wyx_xyz_dot_wxyz (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
|
|
{
|
|
auto stype = alg->type;
|
|
auto sa = offset_cast (stype, a, 0);
|
|
auto sb = offset_cast (stype, b, 3);
|
|
auto cs = scale_expr (stype, sa, sb);
|
|
c[0] = new_extend_expr (cs, algebra_mvec_type (alg, 0x01), 0, true);
|
|
}
|
|
|
|
static void
|
|
pga3_wzy_wxz_wyx_xyz_dot_wzy_wxz_wyx_xyz (expr_t **c, expr_t *a, expr_t *b,
|
|
algebra_t *alg)
|
|
{
|
|
auto stype = alg->type;
|
|
auto sa = offset_cast (stype, a, 3);
|
|
auto sb = offset_cast (stype, b, 3);
|
|
c[0] = unary_expr ('-', scale_expr (stype, sa, sb));
|
|
}
|
|
|
|
static pga_func pga3_dot_funcs[6][6] = {
|
|
[0] = {
|
|
[0] = pga3_x_y_z_w_dot_x_y_z_w,
|
|
[1] = pga3_x_y_z_w_dot_yz_zx_xy,
|
|
[2] = scale_component,
|
|
[3] = pga3_x_y_z_w_dot_wx_wy_wz,
|
|
[4] = pga3_x_y_z_w_dot_wxyz,
|
|
[5] = pga3_x_y_z_w_dot_wzy_wxz_wyx_xyz,
|
|
},
|
|
[1] = {
|
|
[0] = pga3_yz_zx_xy_dot_x_y_z_w,
|
|
[1] = pga3_yz_zx_xy_dot_yz_zx_xy,
|
|
[2] = scale_component,
|
|
[4] = pga3_yz_zx_xy_dot_wxyz,
|
|
[5] = pga3_yz_zx_xy_dot_wzy_wxz_wyx_xyz,
|
|
},
|
|
[2] = {
|
|
[0] = scale_component,
|
|
[1] = scale_component,
|
|
[2] = scale_component,
|
|
[3] = scale_component,
|
|
[4] = scale_component,
|
|
[5] = scale_component,
|
|
},
|
|
[3] = {
|
|
[0] = pga3_wx_wy_wz_dot_x_y_z_w,
|
|
[2] = scale_component,
|
|
},
|
|
[4] = {
|
|
[0] = pga3_wxyz_dot_x_y_z_w,
|
|
[1] = pga3_wxyz_dot_yz_zx_xy,
|
|
[2] = scale_component,
|
|
[5] = pga3_wxyz_dot_wzy_wxz_wyx_xyz,
|
|
},
|
|
[5] = {
|
|
[0] = pga3_wzy_wxz_wyx_xyz_dot_x_y_z_w,
|
|
[1] = pga3_wzy_wxz_wyx_xyz_dot_yz_zx_xy,
|
|
[2] = scale_component,
|
|
[4] = pga3_wzy_wxz_wyx_xyz_dot_wxyz,
|
|
[5] = pga3_wzy_wxz_wyx_xyz_dot_wzy_wxz_wyx_xyz,
|
|
},
|
|
};
|
|
|
|
static void
|
|
pga2_yw_wx_xy_dot_yw_wx_xy (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
|
|
{
|
|
auto stype = alg->type;
|
|
auto sa = offset_cast (stype, a, 2);
|
|
auto sb = offset_cast (stype, b, 2);
|
|
|
|
c[1] = unary_expr ('-', scale_expr (stype, sa, sb));
|
|
}
|
|
|
|
static void
|
|
pga2_yw_wx_xy_dot_x_y_w (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
|
|
{
|
|
auto stype = alg->type;
|
|
auto vtype = vector_type (stype, 3);
|
|
auto dot_type = algebra_mvec_type (alg, 0x04);
|
|
auto vb = offset_cast (dot_type, new_swizzle_expr (b, "y-x0"), 0);
|
|
auto sa = offset_cast (stype, a, 2);
|
|
auto tmp = offset_cast (stype, cross_expr (vtype, b, a), 2);
|
|
tmp = new_extend_expr (tmp, dot_type, 0, true);
|
|
c[2] = sum_expr (dot_type, '+', scale_expr (dot_type, vb, sa), tmp);
|
|
}
|
|
|
|
static void
|
|
pga2_yw_wx_xy_dot_wxy (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
|
|
{
|
|
auto stype = alg->type;
|
|
auto sa = offset_cast (stype, a, 2);
|
|
auto sb = offset_cast (stype, b, 0);
|
|
sb = unary_expr ('-', sb);
|
|
auto cs = scale_expr (stype, sa, sb);
|
|
c[0] = new_extend_expr (cs, algebra_mvec_type (alg, 0x01), 0, true);
|
|
}
|
|
|
|
static void
|
|
pga2_x_y_w_dot_yw_wx_xy (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
|
|
{
|
|
auto stype = alg->type;
|
|
auto vtype = vector_type (stype, 3);
|
|
auto dot_type = algebra_mvec_type (alg, 0x04);
|
|
auto va = offset_cast (vtype, new_swizzle_expr (a, "-yx0"), 0);
|
|
auto sb = offset_cast (stype, b, 2);
|
|
auto tmp = offset_cast (stype, cross_expr (vtype, b, a), 2);
|
|
tmp = new_extend_expr (tmp, dot_type, 0, true);
|
|
c[2] = sum_expr (dot_type, '+', tmp, scale_expr (dot_type, va, sb));
|
|
}
|
|
|
|
static void
|
|
pga2_x_y_w_dot_x_y_w (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
|
|
{
|
|
auto stype = alg->type;
|
|
auto vtype = vector_type (stype, 2);
|
|
auto va = offset_cast (vtype, a, 0);
|
|
auto vb = offset_cast (vtype, b, 0);
|
|
auto cs = dot_expr (stype, va, vb);
|
|
c[1] = cs;
|
|
}
|
|
|
|
static void
|
|
pga2_x_y_w_dot_wxy (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
|
|
{
|
|
auto stype = alg->type;
|
|
auto vtype = vector_type (stype, 2);
|
|
auto dot_type = algebra_mvec_type (alg, 0x01);
|
|
auto va = offset_cast (vtype, a, 0);
|
|
auto cv = scale_expr (vtype, va, b);
|
|
|
|
c[0] = new_extend_expr (cv, dot_type, 0, false);
|
|
}
|
|
|
|
static void
|
|
pga2_wxy_dot_yw_wx_xy (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
|
|
{
|
|
auto stype = alg->type;
|
|
auto sa = offset_cast (stype, a, 0);
|
|
auto sb = offset_cast (stype, b, 2);
|
|
sb = unary_expr ('-', sb);
|
|
auto cs = scale_expr (stype, sa, sb);
|
|
c[0] = new_extend_expr (cs, algebra_mvec_type (alg, 0x01), 0, true);
|
|
}
|
|
|
|
static void
|
|
pga2_wxy_dot_x_y_w (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
|
|
{
|
|
auto stype = alg->type;
|
|
auto vtype = vector_type (stype, 2);
|
|
auto dot_type = algebra_mvec_type (alg, 0x01);
|
|
auto sa = offset_cast (stype, a, 0);
|
|
auto vb = offset_cast (vtype, b, 0);
|
|
auto cv = scale_expr (vtype, vb, sa);
|
|
c[0] = new_extend_expr (cv, dot_type, 0, false);
|
|
}
|
|
|
|
static pga_func pga2_dot_funcs[4][4] = {
|
|
[0] = {
|
|
[0] = pga2_yw_wx_xy_dot_yw_wx_xy,
|
|
[2] = pga2_yw_wx_xy_dot_x_y_w,
|
|
[3] = pga2_yw_wx_xy_dot_wxy,
|
|
},
|
|
[1] = {
|
|
[0] = scale_component,
|
|
[1] = scale_component,
|
|
[2] = scale_component,
|
|
[3] = scale_component,
|
|
},
|
|
[2] = {
|
|
[0] = pga2_x_y_w_dot_yw_wx_xy,
|
|
[2] = pga2_x_y_w_dot_x_y_w,
|
|
[3] = pga2_x_y_w_dot_wxy,
|
|
},
|
|
[3] = {
|
|
[0] = pga2_wxy_dot_yw_wx_xy,
|
|
[2] = pga2_wxy_dot_x_y_w,
|
|
},
|
|
};
|
|
|
|
static void
|
|
component_dot (expr_t **c, expr_t *a, expr_t *b, algebra_t *algebra)
|
|
{
|
|
int p = algebra->plus;
|
|
int m = algebra->minus;
|
|
int z = algebra->zero;
|
|
|
|
if (p == 3 && m == 0 && z == 1) {
|
|
int ga = get_group (get_type (a), algebra);
|
|
int gb = get_group (get_type (b), algebra);
|
|
if (pga3_dot_funcs[ga][gb]) {
|
|
pga3_dot_funcs[ga][gb] (c, a, b, algebra);
|
|
}
|
|
} else if (p == 2 && m == 0 && z == 1) {
|
|
int ga = get_group (get_type (a), algebra);
|
|
int gb = get_group (get_type (b), algebra);
|
|
if (pga2_dot_funcs[ga][gb]) {
|
|
pga2_dot_funcs[ga][gb] (c, a, b, algebra);
|
|
}
|
|
} else {
|
|
}
|
|
}
|
|
|
|
static expr_t *
|
|
inner_product (expr_t *e1, expr_t *e2)
|
|
{
|
|
auto t1 = get_type (e1);
|
|
auto t2 = get_type (e2);
|
|
auto algebra = is_algebra (t1) ? algebra_get (t1) : algebra_get (t2);
|
|
auto layout = &algebra->layout;
|
|
expr_t *a[layout->count] = {};
|
|
expr_t *b[layout->count] = {};
|
|
expr_t *c[layout->count] = {};
|
|
e1 = mvec_expr (e1, algebra);
|
|
e2 = mvec_expr (e2, algebra);
|
|
mvec_scatter (a, e1, algebra);
|
|
mvec_scatter (b, e2, algebra);
|
|
|
|
for (int i = 0; i < layout->count; i++) {
|
|
for (int j = 0; j < layout->count; j++) {
|
|
if (a[i] && b[j]) {
|
|
expr_t *w[layout->count] = {};
|
|
component_dot (w, a[i], b[j], algebra);
|
|
component_sum ('+', c, c, w, algebra);
|
|
}
|
|
}
|
|
}
|
|
return mvec_gather (c, algebra);
|
|
}
|
|
|
|
static void
|
|
pga3_x_y_z_w_wedge_x_y_z_w (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
|
|
{
|
|
auto stype = alg->type;
|
|
auto vtype = vector_type (stype, 3);
|
|
auto wedge_type = algebra_mvec_type (alg, 0x08);
|
|
auto va = offset_cast (vtype, a, 0);
|
|
auto vb = offset_cast (vtype, b, 0);
|
|
auto sa = offset_cast (stype, a, 3);
|
|
auto sb = offset_cast (stype, b, 3);
|
|
c[1] = cross_expr (algebra_mvec_type (alg, 0x02), va, vb);
|
|
c[3] = sum_expr (wedge_type, '-', scale_expr (wedge_type, vb, sa),
|
|
scale_expr (wedge_type, va, sb));
|
|
}
|
|
|
|
#define pga3_yz_zx_xy_wedge_x_y_z_w pga3_x_y_z_w_wedge_yz_zx_xy
|
|
static void
|
|
pga3_x_y_z_w_wedge_yz_zx_xy (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
|
|
{
|
|
auto stype = alg->type;
|
|
auto vtype = vector_type (stype, 3);
|
|
auto wedge_type = algebra_mvec_type (alg, 0x20);
|
|
auto va = offset_cast (vtype, a, 0);
|
|
auto sa = offset_cast (stype, a, 3);
|
|
auto cv = scale_expr (get_type (b), b, sa);
|
|
auto cs = dot_expr (stype, va, b);
|
|
|
|
c[5] = sum_expr (wedge_type, '-',
|
|
new_extend_expr (cs, wedge_type, 0, true),
|
|
new_extend_expr (cv, wedge_type, 0, false));
|
|
}
|
|
|
|
// vector-bivector wedge is commutative
|
|
#define pga3_wx_wy_wz_wedge_x_y_z_w pga3_x_y_z_w_wedge_wx_wy_wz
|
|
static void
|
|
pga3_x_y_z_w_wedge_wx_wy_wz (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
|
|
{
|
|
auto stype = alg->type;
|
|
auto vtype = vector_type (stype, 3);
|
|
auto wedge_type = algebra_mvec_type (alg, 0x20);
|
|
auto va = offset_cast (vtype, a, 0);
|
|
auto cv = cross_expr (vtype, va, b);
|
|
auto cs = new_zero_expr (stype);
|
|
c[5] = sum_expr (wedge_type, '+',
|
|
new_extend_expr (cs, wedge_type, 0, true),
|
|
new_extend_expr (cv, wedge_type, 0, false));
|
|
}
|
|
|
|
static void
|
|
pga3_x_y_z_w_wedge_wzy_wxz_wyx_xyz (expr_t **c, expr_t *a, expr_t *b,
|
|
algebra_t *alg)
|
|
{
|
|
c[4] = dot_expr (algebra_mvec_type (alg, 0x10), a, b);
|
|
}
|
|
|
|
// bivector-bivector wedge is commutative
|
|
#define pga3_wx_wy_wz_wedge_yz_zx_xy pga3_yz_zx_xy_wedge_wx_wy_wz
|
|
static void
|
|
pga3_yz_zx_xy_wedge_wx_wy_wz (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
|
|
{
|
|
c[4] = dot_expr (algebra_mvec_type (alg, 0x10), a, b);
|
|
}
|
|
|
|
static void
|
|
pga3_wzy_wxz_wyx_xyz_wedge_x_y_z_w (expr_t **c, expr_t *a, expr_t *b,
|
|
algebra_t *alg)
|
|
{
|
|
c[4] = unary_expr ('-', dot_expr (algebra_mvec_type (alg, 0x10), a, b));
|
|
}
|
|
|
|
static pga_func pga3_wedge_funcs[6][6] = {
|
|
[0] = {
|
|
[0] = pga3_x_y_z_w_wedge_x_y_z_w,
|
|
[1] = pga3_x_y_z_w_wedge_yz_zx_xy,
|
|
[2] = scale_component,
|
|
[3] = pga3_x_y_z_w_wedge_wx_wy_wz,
|
|
[5] = pga3_x_y_z_w_wedge_wzy_wxz_wyx_xyz,
|
|
},
|
|
[1] = {
|
|
[0] = pga3_yz_zx_xy_wedge_x_y_z_w,
|
|
[2] = scale_component,
|
|
[3] = pga3_yz_zx_xy_wedge_wx_wy_wz,
|
|
},
|
|
[2] = {
|
|
[0] = scale_component,
|
|
[1] = scale_component,
|
|
[2] = scale_component,
|
|
[3] = scale_component,
|
|
[4] = scale_component,
|
|
[5] = scale_component,
|
|
},
|
|
[3] = {
|
|
[0] = pga3_wx_wy_wz_wedge_x_y_z_w,
|
|
[1] = pga3_wx_wy_wz_wedge_yz_zx_xy,
|
|
[2] = scale_component,
|
|
},
|
|
[4] = {
|
|
[2] = scale_component,
|
|
},
|
|
[5] = {
|
|
[0] = pga3_wzy_wxz_wyx_xyz_wedge_x_y_z_w,
|
|
[2] = scale_component,
|
|
},
|
|
};
|
|
|
|
// vector-bivector wedge is commutative
|
|
#define pga2_x_y_w_wedge_yw_wx_xy pga2_yw_wx_xy_wedge_x_y_w
|
|
static void
|
|
pga2_yw_wx_xy_wedge_x_y_w (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
|
|
{
|
|
c[3] = dot_expr (algebra_mvec_type (alg, 0x08), a, b);
|
|
}
|
|
|
|
static void
|
|
pga2_x_y_w_wedge_x_y_w (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
|
|
{
|
|
auto wedge_type = algebra_mvec_type (alg, 0x01);
|
|
c[0] = cross_expr (wedge_type, a, b);
|
|
}
|
|
|
|
static pga_func pga2_wedge_funcs[4][4] = {
|
|
[0] = {
|
|
[1] = scale_component,
|
|
[2] = pga2_yw_wx_xy_wedge_x_y_w,
|
|
},
|
|
[1] = {
|
|
[0] = scale_component,
|
|
[1] = scale_component,
|
|
[2] = scale_component,
|
|
[3] = scale_component,
|
|
},
|
|
[2] = {
|
|
[0] = pga2_x_y_w_wedge_yw_wx_xy,
|
|
[1] = scale_component,
|
|
[2] = pga2_x_y_w_wedge_x_y_w,
|
|
},
|
|
[3] = {
|
|
[1] = scale_component,
|
|
},
|
|
};
|
|
|
|
static void
|
|
component_wedge (expr_t **c, expr_t *a, expr_t *b, algebra_t *algebra)
|
|
{
|
|
int p = algebra->plus;
|
|
int m = algebra->minus;
|
|
int z = algebra->zero;
|
|
|
|
if (p == 3 && m == 0 && z == 1) {
|
|
int ga = get_group (get_type (a), algebra);
|
|
int gb = get_group (get_type (b), algebra);
|
|
if (pga3_wedge_funcs[ga][gb]) {
|
|
pga3_wedge_funcs[ga][gb] (c, a, b, algebra);
|
|
}
|
|
} else if (p == 2 && m == 0 && z == 1) {
|
|
int ga = get_group (get_type (a), algebra);
|
|
int gb = get_group (get_type (b), algebra);
|
|
if (pga2_wedge_funcs[ga][gb]) {
|
|
pga2_wedge_funcs[ga][gb] (c, a, b, algebra);
|
|
}
|
|
} else {
|
|
}
|
|
}
|
|
|
|
static expr_t *
|
|
outer_product (expr_t *e1, expr_t *e2)
|
|
{
|
|
auto t1 = get_type (e1);
|
|
auto t2 = get_type (e2);
|
|
auto algebra = is_algebra (t1) ? algebra_get (t1) : algebra_get (t2);
|
|
auto layout = &algebra->layout;
|
|
expr_t *a[layout->count] = {};
|
|
expr_t *b[layout->count] = {};
|
|
expr_t *c[layout->count] = {};
|
|
e1 = mvec_expr (e1, algebra);
|
|
e2 = mvec_expr (e2, algebra);
|
|
mvec_scatter (a, e1, algebra);
|
|
mvec_scatter (b, e2, algebra);
|
|
|
|
for (int i = 0; i < layout->count; i++) {
|
|
for (int j = 0; j < layout->count; j++) {
|
|
if (a[i] && b[j]) {
|
|
expr_t *w[layout->count] = {};
|
|
component_wedge (w, a[i], b[j], algebra);
|
|
component_sum ('+', c, c, w, algebra);
|
|
}
|
|
}
|
|
}
|
|
return mvec_gather (c, algebra);
|
|
}
|
|
|
|
static void
|
|
pga3_x_y_z_w_geom_x_y_z_w (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
|
|
{
|
|
auto stype = alg->type;
|
|
auto vtype = vector_type (stype, 3);
|
|
auto geom_type = algebra_mvec_type (alg, 0x08);
|
|
auto va = offset_cast (vtype, a, 0);
|
|
auto vb = offset_cast (vtype, b, 0);
|
|
auto sa = offset_cast (stype, a, 3);
|
|
auto sb = offset_cast (stype, b, 3);
|
|
c[4] = dot_expr (stype, va, vb);
|
|
c[1] = cross_expr (algebra_mvec_type (alg, 0x02), va, vb);
|
|
c[3] = sum_expr (geom_type, '-', scale_expr (geom_type, vb, sa),
|
|
scale_expr (geom_type, va, sb));
|
|
}
|
|
|
|
static void
|
|
pga3_x_y_z_w_geom_yz_zx_xy (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
|
|
{
|
|
auto stype = alg->type;
|
|
auto vtype = vector_type (stype, 3);
|
|
auto geom_type = algebra_mvec_type (alg, 0x20);
|
|
auto va = offset_cast (vtype, a, 0);
|
|
auto sa = offset_cast (stype, a, 3);
|
|
auto cv = scale_expr (geom_type, b, sa);
|
|
auto cs = dot_expr (stype, va, b);
|
|
c[0] = cross_expr (algebra_mvec_type (alg, 0x01), b, va);
|
|
c[5] = sum_expr (geom_type, '+', new_extend_expr (cv, geom_type, 0, false),
|
|
new_extend_expr (cs, geom_type, 0, true));
|
|
c[5]->e.expr.type = geom_type;
|
|
}
|
|
|
|
static void
|
|
pga3_x_y_z_w_geom_wx_wy_wz (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
|
|
{
|
|
auto stype = alg->type;
|
|
auto vtype = vector_type (stype, 3);
|
|
auto geom_type = algebra_mvec_type (alg, 0x20);
|
|
auto va = offset_cast (vtype, a, 0);
|
|
auto cs = unary_expr ('-', dot_expr (stype, va, b));
|
|
c[0] = cross_expr (algebra_mvec_type (alg, 0x01), va, b);
|
|
c[5] = new_extend_expr (cs, geom_type, 0, true);
|
|
}
|
|
|
|
static void
|
|
pga3_x_y_z_w_geom_wxyz (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
|
|
{
|
|
auto stype = alg->type;
|
|
auto vtype = vector_type (stype, 3);
|
|
auto geom_type = algebra_mvec_type (alg, 0x20);
|
|
auto va = offset_cast (vtype, a, 0);
|
|
auto sb = offset_cast (stype, b, 0);
|
|
auto cv = scale_expr (geom_type, va, sb);
|
|
c[5] = new_extend_expr (cv, geom_type, 0, true);
|
|
}
|
|
|
|
static void
|
|
pga3_x_y_z_w_geom_wzy_wxz_wyx_xyz (expr_t **c, expr_t *a, expr_t *b,
|
|
algebra_t *alg)
|
|
{
|
|
auto stype = alg->type;
|
|
auto vtype = vector_type (stype, 3);
|
|
auto geom_type = algebra_mvec_type (alg, 0x10);
|
|
auto va = offset_cast (vtype, a, 0);
|
|
auto vb = offset_cast (vtype, b, 0);
|
|
auto sb = offset_cast (stype, b, 3);
|
|
c[1] = scale_expr (algebra_mvec_type (alg, 0x02), va, sb);
|
|
c[3] = cross_expr (algebra_mvec_type (alg, 0x80), vb, va);
|
|
c[4] = dot_expr (geom_type, a, b);
|
|
}
|
|
|
|
static void
|
|
pga3_yz_zx_xy_geom_x_y_z_w (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
|
|
{
|
|
auto stype = alg->type;
|
|
auto vtype = vector_type (stype, 3);
|
|
auto geom_type = algebra_mvec_type (alg, 0x20);
|
|
auto vb = offset_cast (vtype, b, 0);
|
|
auto sb = offset_cast (stype, b, 3);
|
|
auto cv = scale_expr (geom_type, a, sb);
|
|
auto cs = dot_expr (stype, vb, a);
|
|
c[0] = cross_expr (algebra_mvec_type (alg, 0x01), a, vb);
|
|
c[5] = sum_expr (geom_type, '-', new_extend_expr (cs, geom_type, 0, true),
|
|
new_extend_expr (cv, geom_type, 0, false));
|
|
}
|
|
|
|
static void
|
|
pga3_yz_zx_xy_geom_yz_zx_xy (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
|
|
{
|
|
c[1] = cross_expr (algebra_mvec_type (alg, 0x02), b, a);
|
|
c[2] = unary_expr ('-', dot_expr (algebra_mvec_type (alg, 0x04), b, a));
|
|
}
|
|
|
|
static void
|
|
pga3_yz_zx_xy_geom_wx_wy_wz (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
|
|
{
|
|
c[3] = cross_expr (algebra_mvec_type (alg, 0x08), b, a);
|
|
c[4] = dot_expr (algebra_mvec_type (alg, 0x10), b, a);
|
|
}
|
|
|
|
#define pga3_wxyz_geom_yz_zx_xy pga3_yz_zx_xy_geom_wxyz
|
|
static void
|
|
pga3_yz_zx_xy_geom_wxyz (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
|
|
{
|
|
auto stype = alg->type;
|
|
auto sb = offset_cast (stype, b, 0);
|
|
c[3] = scale_expr (algebra_mvec_type (alg, 0x08), a, unary_expr ('-', sb));
|
|
}
|
|
|
|
#define pga3_wzy_wxz_wyx_xyz_geom_yz_zx_xy pga3_yz_zx_xy_geom_wzy_wxz_wyx_xyz
|
|
static void
|
|
pga3_yz_zx_xy_geom_wzy_wxz_wyx_xyz (expr_t **c, expr_t *a, expr_t *b,
|
|
algebra_t *alg)
|
|
{
|
|
auto stype = alg->type;
|
|
auto vtype = vector_type (stype, 3);
|
|
auto geom_type = algebra_mvec_type (alg, 0x01);
|
|
auto vb = offset_cast (vtype, b, 0);
|
|
auto sb = offset_cast (stype, b, 3);
|
|
auto cv = scale_expr (geom_type, a, sb);
|
|
auto cs = dot_expr (stype, vb, a);
|
|
c[0] = sum_expr (geom_type, '-', new_extend_expr (cs, geom_type, 0, true),
|
|
new_extend_expr (cv, geom_type, 0, false));
|
|
c[5] = cross_expr (algebra_mvec_type (alg, 0x20), vb, a);
|
|
}
|
|
|
|
static void
|
|
pga3_wx_wy_wz_geom_x_y_z_w (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
|
|
{
|
|
auto stype = alg->type;
|
|
auto vtype = vector_type (stype, 3);
|
|
auto geom_type = algebra_mvec_type (alg, 0x20);
|
|
auto vb = offset_cast (vtype, b, 0);
|
|
auto cs = dot_expr (stype, vb, a);
|
|
c[0] = cross_expr (algebra_mvec_type (alg, 0x01), vb, a);
|
|
c[5] = new_extend_expr (cs, geom_type, 0, true);
|
|
}
|
|
|
|
static void
|
|
pga3_wx_wy_wz_geom_yz_zx_xy (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
|
|
{
|
|
c[3] = cross_expr (algebra_mvec_type (alg, 0x08), a, b);
|
|
c[4] = dot_expr (algebra_mvec_type (alg, 0x10), a, b);
|
|
}
|
|
|
|
static void
|
|
pga3_wx_wy_wz_geom_wzy_wxz_wyx_xyz (expr_t **c, expr_t *a, expr_t *b,
|
|
algebra_t *alg)
|
|
{
|
|
auto stype = alg->type;
|
|
auto geom_type = algebra_mvec_type (alg, 0x20);
|
|
auto vs = offset_cast (stype, b, 3);
|
|
auto cv = scale_expr (geom_type, a, unary_expr ('-', vs));
|
|
c[5] = new_extend_expr (cv, geom_type, 0, true);
|
|
}
|
|
|
|
static void
|
|
pga3_wxyz_geom_x_y_z_w (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
|
|
{
|
|
auto stype = alg->type;
|
|
auto vtype = vector_type (stype, 3);
|
|
auto geom_type = algebra_mvec_type (alg, 0x20);
|
|
auto sa = offset_cast (stype, a, 0);
|
|
auto vb = offset_cast (vtype, b, 0);
|
|
auto cv = scale_expr (geom_type, vb, unary_expr ('-', sa));
|
|
c[5] = new_extend_expr (cv, geom_type, 0, true);
|
|
}
|
|
|
|
static void
|
|
pga3_wxyz_geom_wzy_wxz_wyx_xyz (expr_t **c, expr_t *a, expr_t *b,
|
|
algebra_t *alg)
|
|
{
|
|
auto stype = alg->type;
|
|
auto sa = offset_cast (stype, a, 0);
|
|
auto sb = offset_cast (stype, b, 3);
|
|
auto geom_type = algebra_mvec_type (alg, 0x01);
|
|
auto cs = scale_expr (stype, sa, sb);
|
|
c[0] = new_extend_expr (unary_expr ('-', cs), geom_type, 0, true);
|
|
}
|
|
|
|
static void
|
|
pga3_wzy_wxz_wyx_xyz_geom_x_y_z_w (expr_t **c, expr_t *a, expr_t *b,
|
|
algebra_t *alg)
|
|
{
|
|
auto stype = alg->type;
|
|
auto vtype = vector_type (stype, 3);
|
|
auto geom_type = algebra_mvec_type (alg, 0x10);
|
|
auto va = offset_cast (vtype, a, 0);
|
|
auto sa = offset_cast (stype, a, 3);
|
|
auto vb = offset_cast (vtype, b, 0);
|
|
c[1] = scale_expr (algebra_mvec_type (alg, 0x02), vb, sa);
|
|
c[3] = cross_expr (algebra_mvec_type (alg, 0x08), vb, va);
|
|
c[0] = unary_expr ('-', dot_expr (geom_type, b, a));
|
|
}
|
|
|
|
static void
|
|
pga3_wzy_wxz_wyx_xyz_geom_wx_wy_wz (expr_t **c, expr_t *a, expr_t *b,
|
|
algebra_t *alg)
|
|
{
|
|
auto stype = alg->type;
|
|
auto geom_type = algebra_mvec_type (alg, 0x20);
|
|
auto vs = offset_cast (stype, b, 3);
|
|
auto cv = scale_expr (geom_type, a, vs);
|
|
c[5] = new_extend_expr (cv, geom_type, 0, true);
|
|
}
|
|
|
|
static void
|
|
pga3_wzy_wxz_wyx_xyz_geom_wxyz (expr_t **c, expr_t *a, expr_t *b,
|
|
algebra_t *alg)
|
|
{
|
|
auto stype = alg->type;
|
|
auto sa = offset_cast (stype, a, 0);
|
|
auto sb = offset_cast (stype, b, 3);
|
|
auto geom_type = algebra_mvec_type (alg, 0x01);
|
|
auto cs = scale_expr (stype, sa, sb);
|
|
c[0] = new_extend_expr (cs, geom_type, 0, true);
|
|
}
|
|
|
|
static void
|
|
pga3_wzy_wxz_wyx_xyz_geom_wzy_wxz_wyx_xyz (expr_t **c, expr_t *a, expr_t *b,
|
|
algebra_t *alg)
|
|
{
|
|
auto stype = alg->type;
|
|
auto vtype = vector_type (stype, 3);
|
|
auto geom_type = algebra_mvec_type (alg, 0x08);
|
|
auto va = offset_cast (vtype, a, 0);
|
|
auto vb = offset_cast (vtype, b, 0);
|
|
auto sa = offset_cast (stype, a, 3);
|
|
auto sb = offset_cast (stype, b, 3);
|
|
c[2] = unary_expr ('-', scale_expr (stype, sa, sb));
|
|
c[3] = sum_expr (geom_type, '-', scale_expr (geom_type, va, sb),
|
|
scale_expr (geom_type, vb, sa));
|
|
}
|
|
|
|
static pga_func pga3_geometric_funcs[6][6] = {
|
|
[0] = {
|
|
[0] = pga3_x_y_z_w_geom_x_y_z_w,
|
|
[1] = pga3_x_y_z_w_geom_yz_zx_xy,
|
|
[2] = scale_component,
|
|
[3] = pga3_x_y_z_w_geom_wx_wy_wz,
|
|
[4] = pga3_x_y_z_w_geom_wxyz,
|
|
[5] = pga3_x_y_z_w_geom_wzy_wxz_wyx_xyz,
|
|
},
|
|
[1] = {
|
|
[0] = pga3_yz_zx_xy_geom_x_y_z_w,
|
|
[1] = pga3_yz_zx_xy_geom_yz_zx_xy,
|
|
[2] = scale_component,
|
|
[3] = pga3_yz_zx_xy_geom_wx_wy_wz,
|
|
[4] = pga3_yz_zx_xy_geom_wxyz,
|
|
[5] = pga3_yz_zx_xy_geom_wzy_wxz_wyx_xyz,
|
|
},
|
|
[2] = {
|
|
[0] = scale_component,
|
|
[1] = scale_component,
|
|
[2] = scale_component,
|
|
[3] = scale_component,
|
|
[4] = scale_component,
|
|
[5] = scale_component,
|
|
},
|
|
[3] = {
|
|
[0] = pga3_wx_wy_wz_geom_x_y_z_w,
|
|
[1] = pga3_wx_wy_wz_geom_yz_zx_xy,
|
|
[2] = scale_component,
|
|
[5] = pga3_wx_wy_wz_geom_wzy_wxz_wyx_xyz,
|
|
},
|
|
[4] = {
|
|
[0] = pga3_wxyz_geom_x_y_z_w,
|
|
[1] = pga3_wxyz_geom_yz_zx_xy,
|
|
[2] = scale_component,
|
|
[5] = pga3_wxyz_geom_wzy_wxz_wyx_xyz,
|
|
},
|
|
[5] = {
|
|
[0] = pga3_wzy_wxz_wyx_xyz_geom_x_y_z_w,
|
|
[1] = pga3_wzy_wxz_wyx_xyz_geom_yz_zx_xy,
|
|
[2] = scale_component,
|
|
[3] = pga3_wzy_wxz_wyx_xyz_geom_wx_wy_wz,
|
|
[4] = pga3_wzy_wxz_wyx_xyz_geom_wxyz,
|
|
[5] = pga3_wzy_wxz_wyx_xyz_geom_wzy_wxz_wyx_xyz,
|
|
},
|
|
};
|
|
|
|
static void
|
|
pga2_yw_wx_xy_geom_yw_wx_xy (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
|
|
{
|
|
auto stype = alg->type;
|
|
auto geom_type = algebra_mvec_type (alg, 0x01);
|
|
auto sa = offset_cast (stype, a, 2);
|
|
auto sb = offset_cast (stype, b, 2);
|
|
auto cv = cross_expr (geom_type, b, a);
|
|
|
|
c[0] = offset_cast (geom_type, new_swizzle_expr (cv, "xy0"), 0);
|
|
c[1] = unary_expr ('-', scale_expr (algebra_mvec_type (alg, 0x02), sa, sb));
|
|
}
|
|
|
|
static void
|
|
pga2_yw_wx_xy_geom_x_y_w (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
|
|
{
|
|
auto stype = alg->type;
|
|
auto vtype = vector_type (stype, 3);
|
|
auto geom_type = algebra_mvec_type (alg, 0x04);
|
|
auto sa = offset_cast (stype, a, 2);
|
|
auto vb = offset_cast (vtype, new_swizzle_expr (b, "y-x0"), 0);
|
|
auto tmp = offset_cast (stype, cross_expr (vtype, b, a), 2);
|
|
tmp = new_extend_expr (tmp, geom_type, 0, true);
|
|
c[2] = sum_expr (geom_type, '+', tmp, scale_expr (geom_type, vb, sa));
|
|
c[3] = dot_expr (algebra_mvec_type (alg, 0x08), a, b);
|
|
}
|
|
|
|
static void
|
|
pga2_yw_wx_xy_geom_wxy (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
|
|
{
|
|
auto stype = alg->type;
|
|
auto sa = offset_cast (stype, a, 2);
|
|
auto sb = offset_cast (stype, b, 0);
|
|
sb = unary_expr ('-', sb);
|
|
auto cs = scale_expr (stype, sa, sb);
|
|
c[0] = new_extend_expr (cs, algebra_mvec_type (alg, 0x01), 0, true);
|
|
}
|
|
|
|
static void
|
|
pga2_x_y_w_geom_yw_wx_xy (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
|
|
{
|
|
auto stype = alg->type;
|
|
auto vtype = vector_type (stype, 3);
|
|
auto geom_type = algebra_mvec_type (alg, 0x04);
|
|
auto va = offset_cast (vtype, new_swizzle_expr (a, "-yx0"), 0);
|
|
auto sb = offset_cast (stype, b, 2);
|
|
auto tmp = offset_cast (stype, cross_expr (vtype, b, a), 2);
|
|
tmp = new_extend_expr (tmp, geom_type, 0, true);
|
|
c[2] = sum_expr (geom_type, '+', tmp, scale_expr (geom_type, va, sb));
|
|
c[3] = dot_expr (algebra_mvec_type (alg, 0x08), a, b);
|
|
}
|
|
|
|
static void
|
|
pga2_x_y_w_geom_x_y_w (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
|
|
{
|
|
auto stype = alg->type;
|
|
auto vtype = vector_type (stype, 2);
|
|
auto geom_type = algebra_mvec_type (alg, 0x01);
|
|
auto va = offset_cast (vtype, a, 0);
|
|
auto vb = offset_cast (vtype, b, 0);
|
|
c[1] = dot_expr (stype, va, vb);
|
|
c[0] = cross_expr (geom_type, a, b);
|
|
}
|
|
|
|
static void
|
|
pga2_x_y_w_geom_wxy (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
|
|
{
|
|
auto stype = alg->type;
|
|
auto vtype = vector_type (stype, 2);
|
|
auto geom_type = algebra_mvec_type (alg, 0x01);
|
|
auto va = offset_cast (vtype, a, 0);
|
|
auto cv = scale_expr (vtype, va, b);
|
|
|
|
c[0] = new_extend_expr (cv, geom_type, 0, false);
|
|
}
|
|
|
|
static void
|
|
pga2_wxy_geom_yw_wx_xy (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
|
|
{
|
|
auto stype = alg->type;
|
|
auto sa = offset_cast (stype, a, 0);
|
|
auto sb = offset_cast (stype, b, 2);
|
|
sb = unary_expr ('-', sb);
|
|
auto cs = scale_expr (stype, sa, sb);
|
|
c[0] = new_extend_expr (cs, algebra_mvec_type (alg, 0x01), 0, true);
|
|
}
|
|
|
|
static void
|
|
pga2_wxy_geom_x_y_w (expr_t **c, expr_t *a, expr_t *b, algebra_t *alg)
|
|
{
|
|
auto stype = alg->type;
|
|
auto vtype = vector_type (stype, 2);
|
|
auto geom_type = algebra_mvec_type (alg, 0x01);
|
|
auto vb = offset_cast (vtype, b, 0);
|
|
auto cv = scale_expr (vtype, vb, a);
|
|
|
|
c[0] = new_extend_expr (cv, geom_type, 0, false);
|
|
}
|
|
|
|
static pga_func pga2_geometric_funcs[6][6] = {
|
|
[0] = {
|
|
[0] = pga2_yw_wx_xy_geom_yw_wx_xy,
|
|
[1] = scale_component,
|
|
[2] = pga2_yw_wx_xy_geom_x_y_w,
|
|
[3] = pga2_yw_wx_xy_geom_wxy,
|
|
},
|
|
[1] = {
|
|
[0] = scale_component,
|
|
[1] = scale_component,
|
|
[2] = scale_component,
|
|
[3] = scale_component,
|
|
},
|
|
[2] = {
|
|
[0] = pga2_x_y_w_geom_yw_wx_xy,
|
|
[1] = scale_component,
|
|
[2] = pga2_x_y_w_geom_x_y_w,
|
|
[3] = pga2_x_y_w_geom_wxy,
|
|
},
|
|
[3] = {
|
|
[0] = pga2_wxy_geom_yw_wx_xy,
|
|
[1] = scale_component,
|
|
[2] = pga2_wxy_geom_x_y_w,
|
|
},
|
|
};
|
|
|
|
static void
|
|
component_geometric (expr_t **c, expr_t *a, expr_t *b, algebra_t *algebra)
|
|
{
|
|
int p = algebra->plus;
|
|
int m = algebra->minus;
|
|
int z = algebra->zero;
|
|
|
|
if (p == 3 && m == 0 && z == 1) {
|
|
int ga = get_group (get_type (a), algebra);
|
|
int gb = get_group (get_type (b), algebra);
|
|
if (pga3_geometric_funcs[ga][gb]) {
|
|
pga3_geometric_funcs[ga][gb] (c, a, b, algebra);
|
|
}
|
|
} else if (p == 2 && m == 0 && z == 1) {
|
|
int ga = get_group (get_type (a), algebra);
|
|
int gb = get_group (get_type (b), algebra);
|
|
if (pga2_geometric_funcs[ga][gb]) {
|
|
pga2_geometric_funcs[ga][gb] (c, a, b, algebra);
|
|
}
|
|
} else {
|
|
}
|
|
}
|
|
|
|
static expr_t *
|
|
geometric_product (expr_t *e1, expr_t *e2)
|
|
{
|
|
auto t1 = get_type (e1);
|
|
auto t2 = get_type (e2);
|
|
auto algebra = is_algebra (t1) ? algebra_get (t1) : algebra_get (t2);
|
|
auto layout = &algebra->layout;
|
|
expr_t *a[layout->count] = {};
|
|
expr_t *b[layout->count] = {};
|
|
expr_t *c[layout->count] = {};
|
|
e1 = mvec_expr (e1, algebra);
|
|
e2 = mvec_expr (e2, algebra);
|
|
mvec_scatter (a, e1, algebra);
|
|
mvec_scatter (b, e2, algebra);
|
|
|
|
for (int i = 0; i < layout->count; i++) {
|
|
for (int j = 0; j < layout->count; j++) {
|
|
if (a[i] && b[j]) {
|
|
expr_t *w[layout->count] = {};
|
|
component_geometric (w, a[i], b[j], algebra);
|
|
component_sum ('+', c, c, w, algebra);
|
|
}
|
|
}
|
|
}
|
|
return mvec_gather (c, algebra);
|
|
}
|
|
|
|
static expr_t *
|
|
regressive_product (expr_t *e1, expr_t *e2)
|
|
{
|
|
notice (e1, "not implemented");
|
|
return 0;
|
|
}
|
|
|
|
static expr_t *
|
|
multivector_sum (int op, expr_t *e1, expr_t *e2)
|
|
{
|
|
auto t1 = get_type (e1);
|
|
auto t2 = get_type (e2);
|
|
auto algebra = is_algebra (t1) ? algebra_get (t1) : algebra_get (t2);
|
|
auto layout = &algebra->layout;
|
|
expr_t *a[layout->count] = {};
|
|
expr_t *b[layout->count] = {};
|
|
expr_t *c[layout->count];
|
|
e1 = mvec_expr (e1, algebra);
|
|
e2 = mvec_expr (e2, algebra);
|
|
mvec_scatter (a, e1, algebra);
|
|
mvec_scatter (b, e2, algebra);
|
|
component_sum (op, c, a, b, algebra);
|
|
return mvec_gather (c, algebra);
|
|
}
|
|
|
|
static expr_t *
|
|
commutator_product (expr_t *e1, expr_t *e2)
|
|
{
|
|
auto ab = geometric_product (e1, e2);
|
|
auto ba = geometric_product (e2, e1);
|
|
return multivector_sum ('-', ab, ba);
|
|
}
|
|
|
|
static expr_t *
|
|
multivector_divide (expr_t *e1, expr_t *e2)
|
|
{
|
|
if (is_algebra (get_type (e2))) {
|
|
return error (e2, "Division is left-right ambiguous (and works only"
|
|
" for versors anyway). Use explicit reversion and divide"
|
|
" by square magnitude instead.");
|
|
}
|
|
if (!is_algebra (get_type (e1))) {
|
|
internal_error (e1, "wtw?");
|
|
}
|
|
auto t1 = get_type (e1);
|
|
auto algebra = algebra_get (t1);
|
|
auto layout = &algebra->layout;
|
|
auto stype = algebra->type;
|
|
expr_t *a[layout->count] = {};
|
|
e1 = mvec_expr (e1, algebra);
|
|
e2 = promote_scalar (algebra->type, e2);
|
|
mvec_scatter (a, e1, algebra);
|
|
|
|
for (int i = 0; i < layout->count; i++) {
|
|
if (!a[i]) {
|
|
continue;
|
|
}
|
|
auto den = e2;
|
|
auto ct = get_type (a[i]);
|
|
int width = type_width (ct);
|
|
if (width > 1) {
|
|
den = new_extend_expr (den, vector_type (stype, width), 2, false);
|
|
}
|
|
a[i] = new_binary_expr ('/', a[i], den);
|
|
a[i]->e.expr.type = ct;
|
|
}
|
|
return mvec_gather (a, algebra);
|
|
}
|
|
|
|
expr_t *
|
|
algebra_binary_expr (int op, expr_t *e1, expr_t *e2)
|
|
{
|
|
switch (op) {
|
|
case DOT:
|
|
return inner_product (e1, e2);
|
|
case WEDGE:
|
|
return outer_product (e1, e2);
|
|
case REGRESSIVE:
|
|
return regressive_product (e1, e2);
|
|
case CROSS:
|
|
return commutator_product (e1, e2);
|
|
case '+':
|
|
case '-':
|
|
return multivector_sum (op, e1, e2);
|
|
case '/':
|
|
return multivector_divide (e1, e2);
|
|
case '*':
|
|
case GEOMETRIC:
|
|
return geometric_product (e1, e2);
|
|
}
|
|
return error (e1, "invalid operator");
|
|
}
|
|
|
|
expr_t *
|
|
algebra_negate (expr_t *e)
|
|
{
|
|
auto t = get_type (e);
|
|
auto algebra = algebra_get (t);
|
|
auto layout = &algebra->layout;
|
|
expr_t *n[layout->count] = {};
|
|
e = mvec_expr (e, algebra);
|
|
mvec_scatter (n, e, algebra);
|
|
|
|
for (int i = 0; i < layout->count; i++) {
|
|
if (!n[i]) {
|
|
continue;
|
|
}
|
|
auto ct = get_type (n[i]);
|
|
if (is_algebra (ct)) {
|
|
n[i] = cast_expr (float_type (ct), n[i]);
|
|
}
|
|
n[i] = unary_expr ('-', n[i]);
|
|
n[i]->e.expr.type = ct;
|
|
}
|
|
return mvec_gather (n, algebra);
|
|
}
|
|
|
|
expr_t *
|
|
algebra_dual (expr_t *e)
|
|
{
|
|
if (!is_algebra (get_type (e))) {
|
|
//FIXME check for being in an @algebra { } block
|
|
return error (e, "cannot take the dual of a scalar without context");
|
|
}
|
|
auto algebra = algebra_get (get_type (e));
|
|
auto layout = &algebra->layout;
|
|
|
|
expr_t *a[layout->count] = {};
|
|
expr_t *b[layout->count] = {};
|
|
e = mvec_expr (e, algebra);
|
|
mvec_scatter (a, e, algebra);
|
|
|
|
pr_uint_t I_mask = (1u << algebra->dimension) - 1;
|
|
for (int i = 0; i < layout->count; i++) {
|
|
if (!a[i]) {
|
|
continue;
|
|
}
|
|
auto group = &layout->groups[i];
|
|
//FIXME assumes groups are mono-grade (either come up with something
|
|
//or reject mixed-grade groups)
|
|
pr_uint_t mask = I_mask ^ group->blades[0].mask;
|
|
int dual_ind = layout->group_map[layout->mask_map[mask]][0];
|
|
auto dual_group = &layout->groups[dual_ind];
|
|
auto dual_type = algebra_mvec_type (algebra, dual_group->group_mask);
|
|
auto dual = cast_expr (dual_type, a[i]);
|
|
if (algebra_count_flips (algebra, group->blades[0].mask, mask) & 1) {
|
|
b[dual_ind] = unary_expr ('-', dual);
|
|
} else {
|
|
b[dual_ind] = dual;
|
|
}
|
|
}
|
|
|
|
return mvec_gather (b, algebra);
|
|
}
|
|
|
|
static void
|
|
set_sign (pr_type_t *val, int sign, const type_t *type)
|
|
{
|
|
if (is_float (type)) {
|
|
(*(float *) val) = sign;
|
|
} else {
|
|
(*(double *) val) = sign;
|
|
}
|
|
}
|
|
|
|
expr_t *
|
|
algebra_reverse (expr_t *e)
|
|
{
|
|
auto t = get_type (e);
|
|
auto algebra = algebra_get (t);
|
|
auto layout = &algebra->layout;
|
|
expr_t *r[layout->count] = {};
|
|
e = mvec_expr (e, algebra);
|
|
mvec_scatter (r, e, algebra);
|
|
|
|
for (int i = 0; i < layout->count; i++) {
|
|
if (!r[i]) {
|
|
continue;
|
|
}
|
|
auto ct = get_type (r[i]);
|
|
if (is_mono_grade (ct)) {
|
|
int grade = algebra_get_grade (ct);
|
|
if (grade & 2) {
|
|
r[i] = unary_expr ('-', r[i]);
|
|
}
|
|
} else {
|
|
auto group = &layout->groups[i];
|
|
pr_type_t ones[group->count * type_size (algebra->type)];
|
|
bool neg = false;
|
|
for (int j = 0; j < group->count; j++) {
|
|
int grade = algebra_blade_grade (group->blades[i]);
|
|
int sign = grade & 2 ? -1 : 1;
|
|
if (sign < 0) {
|
|
neg = true;
|
|
}
|
|
set_sign (&ones[j * type_size (algebra->type)], sign, ct);
|
|
}
|
|
if (neg) {
|
|
auto rev = new_value_expr (new_type_value (ct, ones));
|
|
r[i] = new_binary_expr (HADAMARD, r[i], rev);
|
|
r[i]->e.expr.type = ct;
|
|
}
|
|
}
|
|
}
|
|
return mvec_gather (r, algebra);
|
|
}
|
|
|
|
expr_t *
|
|
algebra_cast_expr (type_t *dstType, expr_t *e)
|
|
{
|
|
type_t *srcType = get_type (e);
|
|
if (dstType->type == ev_invalid
|
|
|| srcType->type == ev_invalid
|
|
|| type_size (dstType) != type_size (srcType)
|
|
|| type_width (dstType) != type_width (srcType)) {
|
|
return cast_error (e, srcType, dstType);
|
|
}
|
|
return new_alias_expr (dstType, e);
|
|
}
|
|
|
|
static void
|
|
zero_components (expr_t *block, expr_t *dst, int memset_base, int memset_size)
|
|
{
|
|
auto base = new_offset_alias_expr (&type_int, dst, memset_base);
|
|
auto zero = new_int_expr (0);
|
|
auto size = new_int_expr (memset_size);
|
|
append_expr (block, new_memset_expr (base, zero, size));
|
|
}
|
|
|
|
expr_t *
|
|
algebra_assign_expr (expr_t *dst, expr_t *src)
|
|
{
|
|
type_t *srcType = get_type (src);
|
|
type_t *dstType = get_type (dst);
|
|
|
|
if (src->type != ex_multivec) {
|
|
if (type_size (srcType) == type_size (dstType)) {
|
|
return new_assign_expr (dst, src);
|
|
}
|
|
}
|
|
|
|
if (dstType->meta != ty_algebra && dstType != srcType) {
|
|
return 0;
|
|
}
|
|
auto algebra = algebra_get (dstType);
|
|
auto layout = &algebra->layout;
|
|
expr_t *components[layout->count] = {};
|
|
src = mvec_expr (src, algebra);
|
|
mvec_scatter (components, src, algebra);
|
|
|
|
auto block = new_block_expr ();
|
|
int memset_base = 0;
|
|
int memset_size = 0;
|
|
int offset = 0;
|
|
for (int i = 0; i < layout->count; i++) {
|
|
if (components[i]) {
|
|
if (memset_size) {
|
|
zero_components (block, dst, memset_base, memset_size);
|
|
memset_size = 0;
|
|
}
|
|
auto dst_type = algebra_mvec_type (algebra, 1 << i);
|
|
auto dst_alias = new_offset_alias_expr (dst_type, dst, offset);
|
|
append_expr (block, new_assign_expr (dst_alias, components[i]));
|
|
offset += type_size (dst_type);
|
|
memset_base = offset;
|
|
} else {
|
|
if (dstType->type == ev_invalid) {
|
|
auto dst_type = algebra_mvec_type (algebra, 1 << i);
|
|
offset += type_size (dst_type);
|
|
memset_size += type_size (dst_type);
|
|
}
|
|
}
|
|
}
|
|
if (memset_size) {
|
|
zero_components (block, dst, memset_base, memset_size);
|
|
}
|
|
return block;
|
|
}
|