mirror of
https://git.code.sf.net/p/quake/quakeforge
synced 2024-11-23 12:52:46 +00:00
8791b35e55
iqm and OpenGL use them, so they might come in handy. The tests use values from wikipedia and a couple extra.
833 lines
18 KiB
C
833 lines
18 KiB
C
/*
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mathlib.c
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math primitives
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Copyright (C) 1996-1997 Id Software, Inc.
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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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#ifdef HAVE_STRING_H
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# include <string.h>
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#endif
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#ifdef HAVE_STRINGS_H
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# include <strings.h>
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#endif
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#include <math.h>
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#define IMPLEMENT_R_Cull
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#define IMPLEMENT_VectorNormalize
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#include "QF/mathlib.h"
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#include "QF/qtypes.h"
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#include "QF/sys.h"
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VISIBLE int nanmask = 255 << 23;
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static plane_t _frustum[4];
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VISIBLE plane_t *const frustum = _frustum;
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static vec3_t _vec3_origin = { 0, 0, 0 };
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VISIBLE const vec_t * const vec3_origin = _vec3_origin;
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static vec3_t _quat_origin = { 0, 0, 0 };
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VISIBLE const vec_t * const quat_origin = _quat_origin;
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#define DEG2RAD(a) (a * (M_PI / 180.0))
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#define FMANTBITS 23
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#define FMANTMASK ((1 << FMANTBITS) - 1)
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#define FEXPBITS 8
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#define FEXPMASK ((1 << FEXPBITS) - 1)
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#define FBIAS (1 << (FEXPBITS - 1))
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#define FEXPMAX ((1 << FEXPBITS) - 1)
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#define HMANTBITS 10
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#define HMANTMASK ((1 << HMANTBITS) - 1)
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#define HEXPBITS 5
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#define HEXPMASK ((1 << HEXPBITS) - 1)
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#define HBIAS (1 << (HEXPBITS - 1))
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#define HEXPMAX ((1 << HEXPBITS) - 1)
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int16_t
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FloatToHalf (float x)
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{
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union {
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float f;
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uint32_t u;
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} uf;
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unsigned sign;
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int exp;
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unsigned mant;
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int16_t half;
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uf.f = x;
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sign = (uf.u >> (FEXPBITS + FMANTBITS)) & 1;
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exp = ((uf.u >> FMANTBITS) & FEXPMASK) - FBIAS + HBIAS;
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mant = (uf.u & FMANTMASK) >> (FMANTBITS - HMANTBITS);
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if (exp <= 0) {
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mant |= 1 << HMANTBITS;
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mant >>= min (1 - exp, HMANTBITS + 1);
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exp = 0;
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} else if (exp >= HEXPMAX) {
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mant = 0;
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exp = HEXPMAX;
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}
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half = (sign << (HEXPBITS + HMANTBITS)) | (exp << HMANTBITS) | mant;
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return half;
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}
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float
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HalfToFloat (int16_t x)
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{
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union {
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float f;
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uint32_t u;
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} uf;
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unsigned sign;
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int exp;
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unsigned mant;
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sign = (x >> (HEXPBITS + HMANTBITS)) & 1;
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exp = ((x >> HMANTBITS) & HEXPMASK);
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mant = (x & HMANTMASK) << (FMANTBITS - HMANTBITS);
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if (exp == 0) {
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if (mant) {
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while (mant < (1 << FMANTBITS)) {
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mant <<= 1;
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exp--;
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}
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mant &= (1 << FMANTBITS) - 1;
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exp += FBIAS - HBIAS + 1;
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}
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} else if (exp == HEXPMAX) {
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exp = FEXPMAX;
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} else {
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exp += FBIAS - HBIAS;
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}
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uf.u = (sign << (FEXPBITS + FMANTBITS)) | (exp << FMANTBITS) | mant;
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return uf.f;
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}
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static void
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ProjectPointOnPlane (vec3_t dst, const vec3_t p, const vec3_t normal)
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{
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float inv_denom, d;
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vec3_t n;
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inv_denom = 1.0F / DotProduct (normal, normal);
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d = DotProduct (normal, p) * inv_denom;
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VectorScale (normal, inv_denom * d, n);
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VectorSubtract (p, n, dst);
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}
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// assumes "src" is normalized
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static void
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PerpendicularVector (vec3_t dst, const vec3_t src)
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{
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int pos, i;
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float minelem = 1.0F;
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vec3_t tempvec;
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/* find the smallest magnitude axially aligned vector */
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for (pos = 0, i = 0; i < 3; i++) {
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if (fabs (src[i]) < minelem) {
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pos = i;
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minelem = fabs (src[i]);
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}
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}
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VectorZero (tempvec);
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tempvec[pos] = 1.0F;
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/* project the point onto the plane defined by src */
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ProjectPointOnPlane (dst, tempvec, src);
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/* normalize the result */
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VectorNormalize (dst);
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}
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#if defined(_WIN32) && !defined(__GNUC__)
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# pragma optimize( "", off )
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#endif
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VISIBLE void
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VectorVectors(const vec3_t forward, vec3_t right, vec3_t up)
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{
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float d;
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right[0] = forward[2];
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right[1] = -forward[0];
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right[2] = forward[1];
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d = DotProduct(forward, right);
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VectorMultSub (right, d, forward, right);
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VectorNormalize (right);
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CrossProduct(right, forward, up);
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}
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VISIBLE void
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RotatePointAroundVector (vec3_t dst, const vec3_t axis, const vec3_t point,
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float degrees)
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{
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float m[3][3];
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float im[3][3];
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float zrot[3][3];
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float tmpmat[3][3];
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float rot[3][3];
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int i;
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vec3_t vr, vup, vf;
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VectorCopy (axis, vf);
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PerpendicularVector (vr, axis);
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CrossProduct (vr, vf, vup);
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m[0][0] = vr[0];
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m[1][0] = vr[1];
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m[2][0] = vr[2];
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m[0][1] = vup[0];
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m[1][1] = vup[1];
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m[2][1] = vup[2];
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m[0][2] = vf[0];
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m[1][2] = vf[1];
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m[2][2] = vf[2];
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memcpy (im, m, sizeof (im));
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im[0][1] = m[1][0];
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im[0][2] = m[2][0];
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im[1][0] = m[0][1];
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im[1][2] = m[2][1];
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im[2][0] = m[0][2];
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im[2][1] = m[1][2];
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memset (zrot, 0, sizeof (zrot));
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zrot[0][0] = zrot[1][1] = zrot[2][2] = 1.0F;
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zrot[0][0] = cos (DEG2RAD (degrees));
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zrot[0][1] = sin (DEG2RAD (degrees));
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zrot[1][0] = -sin (DEG2RAD (degrees));
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zrot[1][1] = cos (DEG2RAD (degrees));
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R_ConcatRotations (m, zrot, tmpmat);
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R_ConcatRotations (tmpmat, im, rot);
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for (i = 0; i < 3; i++) {
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dst[i] = DotProduct (rot[i], point);
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}
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}
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VISIBLE void
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QuatMult (const quat_t q1, const quat_t q2, quat_t out)
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{
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vec_t s;
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vec3_t v;
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s = q1[0] * q2[0] - DotProduct (q1 + 1, q2 + 1);
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CrossProduct (q1 + 1, q2 + 1, v);
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VectorMultAdd (v, q1[0], q2 + 1, v);
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VectorMultAdd (v, q2[0], q1 + 1, out + 1);
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out[0] = s;
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}
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VISIBLE void
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QuatMultVec (const quat_t q, const vec3_t v, vec3_t out)
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{
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vec_t s;
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vec3_t tv;
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s = -DotProduct (q + 1, v);
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CrossProduct (q + 1, v, tv);
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VectorMultAdd (tv, q[0], v, tv);
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CrossProduct (q + 1, tv, out);
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VectorMultSub (out, s, q + 1, out);
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VectorMultAdd (out, q[0], tv, out);
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}
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VISIBLE void
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QuatInverse (const quat_t in, quat_t out)
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{
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quat_t q;
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vec_t m;
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m = QDotProduct (in, in); // in * in*
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QuatConj (in, q);
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QuatScale (q, 1 / m, out);
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}
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VISIBLE void
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QuatExp (const quat_t a, quat_t b)
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{
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vec3_t n;
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vec_t th;
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vec_t r;
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vec_t c, s;
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VectorCopy (a + 1, n);
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th = VectorNormalize (n);
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r = expf (a[0]);
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c = cosf (th);
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s = sinf (th);
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VectorScale (n, r * s, b + 1);
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b[0] = r * c;
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}
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VISIBLE void
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QuatToMatrix (const quat_t q, vec_t *m, int homogenous, int vertical)
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{
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vec_t aa, ab, ac, ad, bb, bc, bd, cc, cd, dd;
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vec_t *_m[4] = {
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m + (homogenous ? 0 : 0),
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m + (homogenous ? 4 : 3),
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m + (homogenous ? 8 : 6),
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m + (homogenous ? 12 : 9),
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};
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aa = q[0] * q[0];
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ab = q[0] * q[1];
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ac = q[0] * q[2];
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ad = q[0] * q[3];
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bb = q[1] * q[1];
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bc = q[1] * q[2];
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bd = q[1] * q[3];
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cc = q[2] * q[2];
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cd = q[2] * q[3];
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dd = q[3] * q[3];
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if (vertical) {
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VectorSet (aa + bb - cc - dd, 2 * (bc + ad), 2 * (bd - ac), _m[0]);
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VectorSet (2 * (bc - ad), aa - bb + cc - dd, 2 * (cd + ab), _m[1]);
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VectorSet (2 * (bd + ac), 2 * (cd - ab), aa - bb - cc + dd, _m[2]);
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} else {
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VectorSet (aa + bb - cc - dd, 2 * (bc - ad), 2 * (bd + ac), _m[0]);
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VectorSet (2 * (bc + ad), aa - bb + cc - dd, 2 * (cd - ab), _m[1]);
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VectorSet (2 * (bd - ac), 2 * (cd + ab), aa - bb - cc + dd, _m[2]);
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}
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if (homogenous) {
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_m[0][3] = 0;
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_m[1][3] = 0;
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_m[2][3] = 0;
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VectorZero (_m[3]);
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_m[3][3] = 1;
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}
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}
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#if defined(_WIN32) && !defined(__GNUC__)
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# pragma optimize( "", on )
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#endif
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VISIBLE float
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anglemod (float a)
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{
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a = (360.0 / 65536) * ((int) (a * (65536 / 360.0)) & 65535);
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return a;
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}
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/*
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BOPS_Error
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Split out like this for ASM to call.
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*/
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void __attribute__ ((noreturn)) BOPS_Error (void);
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VISIBLE void __attribute__ ((noreturn))
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BOPS_Error (void)
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{
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Sys_Error ("BoxOnPlaneSide: Bad signbits");
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}
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#ifndef USE_INTEL_ASM
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/*
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BoxOnPlaneSide
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Returns 1, 2, or 1 + 2
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*/
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VISIBLE int
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BoxOnPlaneSide (const vec3_t emins, const vec3_t emaxs, plane_t *p)
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{
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float dist1, dist2;
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int sides;
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#if 0
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// this is done by the BOX_ON_PLANE_SIDE macro before
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// calling this function
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// fast axial cases
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if (p->type < 3) {
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if (p->dist <= emins[p->type])
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return 1;
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if (p->dist >= emaxs[p->type])
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return 2;
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return 3;
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}
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#endif
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// general case
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switch (p->signbits) {
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case 0:
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dist1 = p->normal[0] * emaxs[0] + p->normal[1] * emaxs[1] +
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p->normal[2] * emaxs[2];
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dist2 = p->normal[0] * emins[0] + p->normal[1] * emins[1] +
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p->normal[2] * emins[2];
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break;
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case 1:
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dist1 = p->normal[0] * emins[0] + p->normal[1] * emaxs[1] +
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p->normal[2] * emaxs[2];
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dist2 = p->normal[0] * emaxs[0] + p->normal[1] * emins[1] +
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p->normal[2] * emins[2];
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break;
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case 2:
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dist1 = p->normal[0] * emaxs[0] + p->normal[1] * emins[1] +
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p->normal[2] * emaxs[2];
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dist2 = p->normal[0] * emins[0] + p->normal[1] * emaxs[1] +
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p->normal[2] * emins[2];
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break;
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case 3:
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dist1 = p->normal[0] * emins[0] + p->normal[1] * emins[1] +
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p->normal[2] * emaxs[2];
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dist2 = p->normal[0] * emaxs[0] + p->normal[1] * emaxs[1] +
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p->normal[2] * emins[2];
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break;
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case 4:
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dist1 = p->normal[0] * emaxs[0] + p->normal[1] * emaxs[1] +
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p->normal[2] * emins[2];
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dist2 = p->normal[0] * emins[0] + p->normal[1] * emins[1] +
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p->normal[2] * emaxs[2];
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break;
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case 5:
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dist1 = p->normal[0] * emins[0] + p->normal[1] * emaxs[1] +
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p->normal[2] * emins[2];
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dist2 = p->normal[0] * emaxs[0] + p->normal[1] * emins[1] +
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p->normal[2] * emaxs[2];
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break;
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case 6:
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dist1 = p->normal[0] * emaxs[0] + p->normal[1] * emins[1] +
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p->normal[2] * emins[2];
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dist2 = p->normal[0] * emins[0] + p->normal[1] * emaxs[1] +
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p->normal[2] * emaxs[2];
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break;
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case 7:
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dist1 = p->normal[0] * emins[0] + p->normal[1] * emins[1] +
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p->normal[2] * emins[2];
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dist2 = p->normal[0] * emaxs[0] + p->normal[1] * emaxs[1] +
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p->normal[2] * emaxs[2];
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break;
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default:
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BOPS_Error ();
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}
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#if 0
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int i;
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vec3_t corners[2];
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for (i = 0; i < 3; i++) {
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if (plane->normal[i] < 0) {
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corners[0][i] = emins[i];
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corners[1][i] = emaxs[i];
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} else {
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corners[1][i] = emins[i];
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corners[0][i] = emaxs[i];
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}
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}
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dist = DotProduct (plane->normal, corners[0]) - plane->dist;
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dist2 = DotProduct (plane->normal, corners[1]) - plane->dist;
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sides = 0;
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if (dist1 >= 0)
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sides = 1;
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if (dist2 < 0)
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sides |= 2;
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#endif
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sides = 0;
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if (dist1 >= p->dist)
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sides = 1;
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if (dist2 < p->dist)
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sides |= 2;
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#ifdef PARANOID
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if (sides == 0)
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Sys_Error ("BoxOnPlaneSide: sides==0");
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#endif
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return sides;
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}
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#endif
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/*
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angles is a left(?) handed system: 'pitch yaw roll' with x (pitch) axis to
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the right, y (yaw) axis up and z (roll) axis forward.
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the math in AngleVectors has the entity frame as left handed with x
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(forward) axis forward, y (right) axis to the right and z (up) up. However,
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the world is a right handed system with x to the right, y forward and
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z up.
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pitch =
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cp 0 -sp
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0 1 0
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sp 0 cp
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yaw =
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cy sy 0
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-sy cy 0
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0 0 1
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roll =
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1 0 0
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0 cr sr
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0 -sr cr
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final = roll * (pitch * yaw)
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final =
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[forward]
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[-right] -ve due to left handed to right handed conversion
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[up]
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*/
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VISIBLE void
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AngleVectors (const vec3_t angles, vec3_t forward, vec3_t right, vec3_t up)
|
|
{
|
|
float angle, sr, sp, sy, cr, cp, cy;
|
|
|
|
angle = angles[YAW] * (M_PI * 2 / 360);
|
|
sy = sin (angle);
|
|
cy = cos (angle);
|
|
angle = angles[PITCH] * (M_PI * 2 / 360);
|
|
sp = sin (angle);
|
|
cp = cos (angle);
|
|
angle = angles[ROLL] * (M_PI * 2 / 360);
|
|
sr = sin (angle);
|
|
cr = cos (angle);
|
|
|
|
forward[0] = cp * cy;
|
|
forward[1] = cp * sy;
|
|
forward[2] = -sp;
|
|
// need to flip right because it's a left handed system in a right handed
|
|
// world
|
|
right[0] = -1 * (sr * sp * cy + cr * -sy);
|
|
right[1] = -1 * (sr * sp * sy + cr * cy);
|
|
right[2] = -1 * (sr * cp);
|
|
up[0] = (cr * sp * cy + -sr * -sy);
|
|
up[1] = (cr * sp * sy + -sr * cy);
|
|
up[2] = cr * cp;
|
|
}
|
|
|
|
VISIBLE void
|
|
AngleQuat (const vec3_t angles, quat_t q)
|
|
{
|
|
float alpha, sr, sp, sy, cr, cp, cy;
|
|
|
|
// alpha is half the angle
|
|
alpha = angles[YAW] * (M_PI / 360);
|
|
sy = sin (alpha);
|
|
cy = cos (alpha);
|
|
alpha = angles[PITCH] * (M_PI / 360);
|
|
sp = sin (alpha);
|
|
cp = cos (alpha);
|
|
alpha = angles[ROLL] * (M_PI / 360);
|
|
sr = sin (alpha);
|
|
cr = cos (alpha);
|
|
|
|
QuatSet (cy * cp * cr + sy * sp * sr,
|
|
cy * cp * sr - sy * sp * cr,
|
|
cy * sp * cr + sy * cp * sr,
|
|
sy * cp * cr - cy * sp * sr,
|
|
q);
|
|
}
|
|
|
|
VISIBLE int
|
|
_VectorCompare (const vec3_t v1, const vec3_t v2)
|
|
{
|
|
int i;
|
|
|
|
for (i = 0; i < 3; i++)
|
|
if (fabs (v1[i] - v2[i]) > EQUAL_EPSILON)
|
|
return 0;
|
|
|
|
return 1;
|
|
}
|
|
|
|
VISIBLE void
|
|
_VectorMA (const vec3_t veca, float scale, const vec3_t vecb, vec3_t vecc)
|
|
{
|
|
vecc[0] = veca[0] + scale * vecb[0];
|
|
vecc[1] = veca[1] + scale * vecb[1];
|
|
vecc[2] = veca[2] + scale * vecb[2];
|
|
}
|
|
|
|
VISIBLE vec_t
|
|
_DotProduct (const vec3_t v1, const vec3_t v2)
|
|
{
|
|
return v1[0] * v2[0] + v1[1] * v2[1] + v1[2] * v2[2];
|
|
}
|
|
|
|
VISIBLE void
|
|
_VectorSubtract (const vec3_t veca, const vec3_t vecb, vec3_t out)
|
|
{
|
|
out[0] = veca[0] - vecb[0];
|
|
out[1] = veca[1] - vecb[1];
|
|
out[2] = veca[2] - vecb[2];
|
|
}
|
|
|
|
VISIBLE void
|
|
_VectorAdd (const vec3_t veca, const vec3_t vecb, vec3_t out)
|
|
{
|
|
out[0] = veca[0] + vecb[0];
|
|
out[1] = veca[1] + vecb[1];
|
|
out[2] = veca[2] + vecb[2];
|
|
}
|
|
|
|
VISIBLE void
|
|
_VectorCopy (const vec3_t in, vec3_t out)
|
|
{
|
|
out[0] = in[0];
|
|
out[1] = in[1];
|
|
out[2] = in[2];
|
|
}
|
|
|
|
VISIBLE void
|
|
CrossProduct (const vec3_t v1, const vec3_t v2, vec3_t cross)
|
|
{
|
|
float v10 = v1[0];
|
|
float v11 = v1[1];
|
|
float v12 = v1[2];
|
|
float v20 = v2[0];
|
|
float v21 = v2[1];
|
|
float v22 = v2[2];
|
|
|
|
cross[0] = v11 * v22 - v12 * v21;
|
|
cross[1] = v12 * v20 - v10 * v22;
|
|
cross[2] = v10 * v21 - v11 * v20;
|
|
}
|
|
|
|
VISIBLE vec_t
|
|
_VectorLength (const vec3_t v)
|
|
{
|
|
float length;
|
|
|
|
length = sqrt (DotProduct (v, v));
|
|
return length;
|
|
}
|
|
|
|
VISIBLE vec_t
|
|
_VectorNormalize (vec3_t v)
|
|
{
|
|
int i;
|
|
double length;
|
|
|
|
length = 0;
|
|
for (i = 0; i < 3; i++)
|
|
length += v[i] * v[i];
|
|
length = sqrt (length);
|
|
if (length == 0)
|
|
return 0;
|
|
|
|
for (i = 0; i < 3; i++)
|
|
v[i] /= length;
|
|
|
|
return length;
|
|
}
|
|
|
|
VISIBLE void
|
|
_VectorScale (const vec3_t in, vec_t scale, vec3_t out)
|
|
{
|
|
out[0] = in[0] * scale;
|
|
out[1] = in[1] * scale;
|
|
out[2] = in[2] * scale;
|
|
}
|
|
|
|
VISIBLE int
|
|
Q_log2 (int val)
|
|
{
|
|
int answer = 0;
|
|
|
|
while ((val >>= 1) != 0)
|
|
answer++;
|
|
return answer;
|
|
}
|
|
|
|
VISIBLE void
|
|
R_ConcatRotations (float in1[3][3], float in2[3][3], float out[3][3])
|
|
{
|
|
out[0][0] = in1[0][0] * in2[0][0] + in1[0][1] * in2[1][0] +
|
|
in1[0][2] * in2[2][0];
|
|
out[0][1] = in1[0][0] * in2[0][1] + in1[0][1] * in2[1][1] +
|
|
in1[0][2] * in2[2][1];
|
|
out[0][2] = in1[0][0] * in2[0][2] + in1[0][1] * in2[1][2] +
|
|
in1[0][2] * in2[2][2];
|
|
out[1][0] = in1[1][0] * in2[0][0] + in1[1][1] * in2[1][0] +
|
|
in1[1][2] * in2[2][0];
|
|
out[1][1] = in1[1][0] * in2[0][1] + in1[1][1] * in2[1][1] +
|
|
in1[1][2] * in2[2][1];
|
|
out[1][2] = in1[1][0] * in2[0][2] + in1[1][1] * in2[1][2] +
|
|
in1[1][2] * in2[2][2];
|
|
out[2][0] = in1[2][0] * in2[0][0] + in1[2][1] * in2[1][0] +
|
|
in1[2][2] * in2[2][0];
|
|
out[2][1] = in1[2][0] * in2[0][1] + in1[2][1] * in2[1][1] +
|
|
in1[2][2] * in2[2][1];
|
|
out[2][2] = in1[2][0] * in2[0][2] + in1[2][1] * in2[1][2] +
|
|
in1[2][2] * in2[2][2];
|
|
}
|
|
|
|
VISIBLE void
|
|
R_ConcatTransforms (float in1[3][4], float in2[3][4], float out[3][4])
|
|
{
|
|
out[0][0] = in1[0][0] * in2[0][0] + in1[0][1] * in2[1][0] +
|
|
in1[0][2] * in2[2][0];
|
|
out[0][1] = in1[0][0] * in2[0][1] + in1[0][1] * in2[1][1] +
|
|
in1[0][2] * in2[2][1];
|
|
out[0][2] = in1[0][0] * in2[0][2] + in1[0][1] * in2[1][2] +
|
|
in1[0][2] * in2[2][2];
|
|
out[0][3] = in1[0][0] * in2[0][3] + in1[0][1] * in2[1][3] +
|
|
in1[0][2] * in2[2][3] + in1[0][3];
|
|
out[1][0] = in1[1][0] * in2[0][0] + in1[1][1] * in2[1][0] +
|
|
in1[1][2] * in2[2][0];
|
|
out[1][1] = in1[1][0] * in2[0][1] + in1[1][1] * in2[1][1] +
|
|
in1[1][2] * in2[2][1];
|
|
out[1][2] = in1[1][0] * in2[0][2] + in1[1][1] * in2[1][2] +
|
|
in1[1][2] * in2[2][2];
|
|
out[1][3] = in1[1][0] * in2[0][3] + in1[1][1] * in2[1][3] +
|
|
in1[1][2] * in2[2][3] + in1[1][3];
|
|
out[2][0] = in1[2][0] * in2[0][0] + in1[2][1] * in2[1][0] +
|
|
in1[2][2] * in2[2][0];
|
|
out[2][1] = in1[2][0] * in2[0][1] + in1[2][1] * in2[1][1] +
|
|
in1[2][2] * in2[2][1];
|
|
out[2][2] = in1[2][0] * in2[0][2] + in1[2][1] * in2[1][2] +
|
|
in1[2][2] * in2[2][2];
|
|
out[2][3] = in1[2][0] * in2[0][3] + in1[2][1] * in2[1][3] +
|
|
in1[2][2] * in2[2][3] + in1[2][3];
|
|
}
|
|
|
|
/*
|
|
FloorDivMod
|
|
|
|
Returns mathematically correct (floor-based) quotient and remainder for
|
|
numer and denom, both of which should contain no fractional part. The
|
|
quotient must fit in 32 bits.
|
|
*/
|
|
VISIBLE void
|
|
FloorDivMod (double numer, double denom, int *quotient, int *rem)
|
|
{
|
|
double x;
|
|
int q, r;
|
|
|
|
#ifndef PARANOID
|
|
if (denom <= 0.0)
|
|
Sys_Error ("FloorDivMod: bad denominator %f", denom);
|
|
|
|
// if ((floor(numer) != numer) || (floor(denom) != denom))
|
|
// Sys_Error ("FloorDivMod: non-integer numer or denom %f %f",
|
|
// numer, denom);
|
|
#endif
|
|
|
|
if (numer >= 0.0) {
|
|
x = floor (numer / denom);
|
|
q = (int) x;
|
|
r = (int) floor (numer - (x * denom));
|
|
} else {
|
|
// perform operations with positive values, and fix mod to make
|
|
// floor-based
|
|
x = floor (-numer / denom);
|
|
q = -(int) x;
|
|
r = (int) floor (-numer - (x * denom));
|
|
if (r != 0) {
|
|
q--;
|
|
r = (int) denom - r;
|
|
}
|
|
}
|
|
|
|
*quotient = q;
|
|
*rem = r;
|
|
}
|
|
|
|
VISIBLE int
|
|
GreatestCommonDivisor (int i1, int i2)
|
|
{
|
|
if (i1 > i2) {
|
|
if (i2 == 0)
|
|
return (i1);
|
|
return GreatestCommonDivisor (i2, i1 % i2);
|
|
} else {
|
|
if (i1 == 0)
|
|
return (i2);
|
|
return GreatestCommonDivisor (i1, i2 % i1);
|
|
}
|
|
}
|
|
|
|
#ifndef USE_INTEL_ASM
|
|
/*
|
|
Invert24To16
|
|
|
|
Inverts an 8.24 value to a 16.16 value
|
|
*/
|
|
VISIBLE fixed16_t
|
|
Invert24To16 (fixed16_t val)
|
|
{
|
|
if (val < 256)
|
|
return (0xFFFFFFFF);
|
|
|
|
return (fixed16_t)
|
|
(((double) 0x10000 * (double) 0x1000000 / (double) val) + 0.5);
|
|
}
|
|
#endif
|
|
|
|
void
|
|
Mat4Transpose (const mat4_t a, mat4_t b)
|
|
{
|
|
vec_t t;
|
|
int i, j;
|
|
|
|
for (i = 0; i < 3; i++) {
|
|
b[i * 4 + i] = a[i * 4 + i]; // in case b != a
|
|
for (j = i + 1; j < 4; j++) {
|
|
t = a[i * 4 + j]; // in case b == a
|
|
b[i * 4 + j] = a[j * 4 + i];
|
|
b[j * 4 + i] = t;
|
|
}
|
|
}
|
|
b[i * 4 + i] = a[i * 4 + i]; // in case b != a
|
|
}
|
|
|
|
void
|
|
Mat4Mult (const mat4_t a, const mat4_t b, mat4_t c)
|
|
{
|
|
mat4_t ta, tb; // in case c == b or c == a
|
|
int i, j, k;
|
|
|
|
Mat4Transpose (a, ta); // transpose so we can use dot
|
|
Mat4Copy (b, tb);
|
|
|
|
k = 0;
|
|
for (i = 0; i < 4; i++) {
|
|
for (j = 0; j < 4; j++) {
|
|
c[k++] = QDotProduct (ta + 4 * j, tb + 4 * i);
|
|
}
|
|
}
|
|
}
|