vrshoot: b2f14e535253 libs/vmath/vmath.c

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author	John Tsiombikas <nuclear@member.fsf.org>
date	Sat, 01 Feb 2014 19:58:19 +0200
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1 /*

2 libvmath - a vector math library

5 This program is free software: you can redistribute it and/or modify

6 it under the terms of the GNU Lesser General Public License as published

7 by the Free Software Foundation, either version 3 of the License, or

8 (at your option) any later version.

10 This program is distributed in the hope that it will be useful,

11 but WITHOUT ANY WARRANTY; without even the implied warranty of

12 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the

13 GNU Lesser General Public License for more details.

15 You should have received a copy of the GNU Lesser General Public License

16 along with this program. If not, see <http://www.gnu.org/licenses/>.

17 */

18 #include <stdlib.h>

19 #include <math.h>

20 #include "vmath.h"

22 #if defined(__APPLE__) && !defined(TARGET_IPHONE)

23 #include <xmmintrin.h>

25 void enable_fpexcept(void)

26 {

27 unsigned int bits;

28 bits = _MM_MASK_INVALID | _MM_MASK_DIV_ZERO | _MM_MASK_OVERFLOW | _MM_MASK_UNDERFLOW;

29 _MM_SET_EXCEPTION_MASK(_MM_GET_EXCEPTION_MASK() & ~bits);

30 }

32 void disable_fpexcept(void)

33 {

34 unsigned int bits;

35 bits = _MM_MASK_INVALID | _MM_MASK_DIV_ZERO | _MM_MASK_OVERFLOW | _MM_MASK_UNDERFLOW;

36 _MM_SET_EXCEPTION_MASK(_MM_GET_EXCEPTION_MASK() | bits);

37 }

39 #elif defined(__GNUC__) && !defined(TARGET_IPHONE)

40 #define __USE_GNU

41 #include <fenv.h>

43 void enable_fpexcept(void)

44 {

45 feenableexcept(FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW);

46 }

48 void disable_fpexcept(void)

49 {

50 fedisableexcept(FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW);

51 }

53 #elif defined(_MSC_VER)

54 #include <float.h>

56 void enable_fpexcept(void)

57 {

58 _clearfp();

59 _controlfp(_controlfp(0, 0) & ~(_EM_INVALID | _EM_ZERODIVIDE | _EM_OVERFLOW), _MCW_EM);

60 }

62 void disable_fpexcept(void)

63 {

64 _clearfp();

65 _controlfp(_controlfp(0, 0) | (_EM_INVALID | _EM_ZERODIVIDE | _EM_OVERFLOW), _MCW_EM);

66 }

67 #else

68 void enable_fpexcept(void) {}

69 void disable_fpexcept(void) {}

70 #endif

73 /** Numerical calculation of integrals using simpson's rule */

74 scalar_t integral(scalar_t (*f)(scalar_t), scalar_t low, scalar_t high, int samples)

75 {

76 int i;

77 scalar_t h = (high - low) / (scalar_t)samples;

78 scalar_t sum = 0.0;

80 for(i=0; i<samples+1; i++) {

81 scalar_t y = f((scalar_t)i * h + low);

82 sum += ((!i || i == samples) ? y : ((i % 2) ? 4.0 * y : 2.0 * y)) * (h / 3.0);

83 }

84 return sum;

85 }

87 /** Gaussuan function */

88 scalar_t gaussian(scalar_t x, scalar_t mean, scalar_t sdev)

89 {

90 scalar_t exponent = -SQ(x - mean) / (2.0 * SQ(sdev));

91 return 1.0 - -pow(M_E, exponent) / (sdev * sqrt(TWO_PI));

92 }

95 /** b-spline approximation */

96 scalar_t bspline(scalar_t a, scalar_t b, scalar_t c, scalar_t d, scalar_t t)

97 {

98 vec4_t tmp;

99 scalar_t tsq = t * t;

100

101 static mat4_t bspline_mat = {

102 {-1, 3, -3, 1},

103 {3, -6, 3, 0},

104 {-3, 0, 3, 0},

105 {1, 4, 1, 0}

106 };

107

108 tmp = v4_scale(v4_transform(v4_cons(a, b, c, d), bspline_mat), 1.0 / 6.0);

109 return v4_dot(v4_cons(tsq * t, tsq, t, 1.0), tmp);

110 }

111

112 /** Catmull-rom spline interpolation */

113 scalar_t spline(scalar_t a, scalar_t b, scalar_t c, scalar_t d, scalar_t t)

114 {

115 vec4_t tmp;

116 scalar_t tsq = t * t;

117

118 static mat4_t crspline_mat = {

119 {-1, 3, -3, 1},

120 {2, -5, 4, -1},

121 {-1, 0, 1, 0},

122 {0, 2, 0, 0}

123 };

124

125 tmp = v4_scale(v4_transform(v4_cons(a, b, c, d), crspline_mat), 0.5);

126 return v4_dot(v4_cons(tsq * t, tsq, t, 1.0), tmp);

127 }

128

129 /** Bezier interpolation */

130 scalar_t bezier(scalar_t a, scalar_t b, scalar_t c, scalar_t d, scalar_t t)

131 {

132 scalar_t omt, omt3, t3, f;

133 t3 = t * t * t;

134 omt = 1.0f - t;

135 omt3 = omt * omt * omt;

136 f = 3 * t * omt;

137

138 return (a * omt3) + (b * f * omt) + (c * f * t) + (d * t3);

139 }

140

141 /* ---- Ken Perlin's implementation of noise ---- */

142

143 #define B 0x100

144 #define BM 0xff

145 #define N 0x1000

146 #define NP 12 /* 2^N */

147 #define NM 0xfff

148

149 #define s_curve(t) (t * t * (3.0f - 2.0f * t))

150

151 #define setup(elem, b0, b1, r0, r1) \

152 do { \

153 scalar_t t = elem + N; \

154 b0 = ((int)t) & BM; \

155 b1 = (b0 + 1) & BM; \

156 r0 = t - (int)t; \

157 r1 = r0 - 1.0f; \

158 } while(0)

159

160

161 static int perm[B + B + 2]; /* permuted index from g_n onto themselves */

162 static vec3_t grad3[B + B + 2]; /* 3D random gradients */

163 static vec2_t grad2[B + B + 2]; /* 2D random gradients */

164 static scalar_t grad1[B + B + 2]; /* 1D random ... slopes */

165 static int tables_valid;

166

167 static void init_noise()

168 {

169 int i;

170

171 /* calculate random gradients */

172 for(i=0; i<B; i++) {

173 perm[i] = i; /* .. and initialize permutation mapping to identity */

174

175 grad1[i] = (scalar_t)((rand() % (B + B)) - B) / B;

176

177 grad2[i].x = (scalar_t)((rand() % (B + B)) - B) / B;

178 grad2[i].y = (scalar_t)((rand() % (B + B)) - B) / B;

179 grad2[i] = v2_normalize(grad2[i]);

180

181 grad3[i].x = (scalar_t)((rand() % (B + B)) - B) / B;

182 grad3[i].y = (scalar_t)((rand() % (B + B)) - B) / B;

183 grad3[i].z = (scalar_t)((rand() % (B + B)) - B) / B;

184 grad3[i] = v3_normalize(grad3[i]);

185 }

186

187 /* permute indices by swapping them randomly */

188 for(i=0; i<B; i++) {

189 int rand_idx = rand() % B;

190

191 int tmp = perm[i];

192 perm[i] = perm[rand_idx];

193 perm[rand_idx] = tmp;

194 }

195

196 /* fill up the rest of the arrays by duplicating the existing gradients */

197 /* and permutations */

198 for(i=0; i<B+2; i++) {

199 perm[B + i] = perm[i];

200 grad1[B + i] = grad1[i];

201 grad2[B + i] = grad2[i];

202 grad3[B + i] = grad3[i];

203 }

204 }

205

206 scalar_t noise1(scalar_t x)

207 {

208 int bx0, bx1;

209 scalar_t rx0, rx1, sx, u, v;

210

211 if(!tables_valid) {

212 init_noise();

213 tables_valid = 1;

214 }

215

216 setup(x, bx0, bx1, rx0, rx1);

217 sx = s_curve(rx0);

218 u = rx0 * grad1[perm[bx0]];

219 v = rx1 * grad1[perm[bx1]];

220

221 return lerp(u, v, sx);

222 }

223

224 scalar_t noise2(scalar_t x, scalar_t y)

225 {

226 int i, j, b00, b10, b01, b11;

227 int bx0, bx1, by0, by1;

228 scalar_t rx0, rx1, ry0, ry1;

229 scalar_t sx, sy, u, v, a, b;

230

231 if(!tables_valid) {

232 init_noise();

233 tables_valid = 1;

234 }

235

236 setup(x, bx0, bx1, rx0, rx1);

237 setup(y, by0, by1, ry0, ry1);

238

239 i = perm[bx0];

240 j = perm[bx1];

241

242 b00 = perm[i + by0];

243 b10 = perm[j + by0];

244 b01 = perm[i + by1];

245 b11 = perm[j + by1];

246

247 /* calculate hermite inteprolating factors */

248 sx = s_curve(rx0);

249 sy = s_curve(ry0);

250

251 /* interpolate along the left edge */

252 u = v2_dot(grad2[b00], v2_cons(rx0, ry0));

253 v = v2_dot(grad2[b10], v2_cons(rx1, ry0));

254 a = lerp(u, v, sx);

255

256 /* interpolate along the right edge */

257 u = v2_dot(grad2[b01], v2_cons(rx0, ry1));

258 v = v2_dot(grad2[b11], v2_cons(rx1, ry1));

259 b = lerp(u, v, sx);

260

261 /* interpolate between them */

262 return lerp(a, b, sy);

263 }

264

265 scalar_t noise3(scalar_t x, scalar_t y, scalar_t z)

266 {

267 int i, j;

268 int bx0, bx1, by0, by1, bz0, bz1;

269 int b00, b10, b01, b11;

270 scalar_t rx0, rx1, ry0, ry1, rz0, rz1;

271 scalar_t sx, sy, sz;

272 scalar_t u, v, a, b, c, d;

273

274 if(!tables_valid) {

275 init_noise();

276 tables_valid = 1;

277 }

278

279 setup(x, bx0, bx1, rx0, rx1);

280 setup(y, by0, by1, ry0, ry1);

281 setup(z, bz0, bz1, rz0, rz1);

282

283 i = perm[bx0];

284 j = perm[bx1];

285

286 b00 = perm[i + by0];

287 b10 = perm[j + by0];

288 b01 = perm[i + by1];

289 b11 = perm[j + by1];

290

291 /* calculate hermite interpolating factors */

292 sx = s_curve(rx0);

293 sy = s_curve(ry0);

294 sz = s_curve(rz0);

295

296 /* interpolate along the top slice of the cell */

297 u = v3_dot(grad3[b00 + bz0], v3_cons(rx0, ry0, rz0));

298 v = v3_dot(grad3[b10 + bz0], v3_cons(rx1, ry0, rz0));

299 a = lerp(u, v, sx);

300

301 u = v3_dot(grad3[b01 + bz0], v3_cons(rx0, ry1, rz0));

302 v = v3_dot(grad3[b11 + bz0], v3_cons(rx1, ry1, rz0));

303 b = lerp(u, v, sx);

304

305 c = lerp(a, b, sy);

306

307 /* interpolate along the bottom slice of the cell */

308 u = v3_dot(grad3[b00 + bz0], v3_cons(rx0, ry0, rz1));

309 v = v3_dot(grad3[b10 + bz0], v3_cons(rx1, ry0, rz1));

310 a = lerp(u, v, sx);

311

312 u = v3_dot(grad3[b01 + bz0], v3_cons(rx0, ry1, rz1));

313 v = v3_dot(grad3[b11 + bz0], v3_cons(rx1, ry1, rz1));

314 b = lerp(u, v, sx);

315

316 d = lerp(a, b, sy);

317

318 /* interpolate between slices */

319 return lerp(c, d, sz);

320 }

321

322 scalar_t fbm1(scalar_t x, int octaves)

323 {

324 int i;

325 scalar_t res = 0.0f, freq = 1.0f;

326 for(i=0; i<octaves; i++) {

327 res += noise1(x * freq) / freq;

328 freq *= 2.0f;

329 }

330 return res;

331 }

332

333 scalar_t fbm2(scalar_t x, scalar_t y, int octaves)

334 {

335 int i;

336 scalar_t res = 0.0f, freq = 1.0f;

337 for(i=0; i<octaves; i++) {

338 res += noise2(x * freq, y * freq) / freq;

339 freq *= 2.0f;

340 }

341 return res;

342 }

343

344 scalar_t fbm3(scalar_t x, scalar_t y, scalar_t z, int octaves)

345 {

346 int i;

347 scalar_t res = 0.0f, freq = 1.0f;

348 for(i=0; i<octaves; i++) {

349 res += noise3(x * freq, y * freq, z * freq) / freq;

350 freq *= 2.0f;

351 }

352 return res;

353 }

354

355 scalar_t turbulence1(scalar_t x, int octaves)

356 {

357 int i;

358 scalar_t res = 0.0f, freq = 1.0f;

359 for(i=0; i<octaves; i++) {

360 res += fabs(noise1(x * freq) / freq);

361 freq *= 2.0f;

362 }

363 return res;

364 }

365

366 scalar_t turbulence2(scalar_t x, scalar_t y, int octaves)

367 {

368 int i;

369 scalar_t res = 0.0f, freq = 1.0f;

370 for(i=0; i<octaves; i++) {

371 res += fabs(noise2(x * freq, y * freq) / freq);

372 freq *= 2.0f;

373 }

374 return res;

375 }

376

377 scalar_t turbulence3(scalar_t x, scalar_t y, scalar_t z, int octaves)

378 {

379 int i;

380 scalar_t res = 0.0f, freq = 1.0f;

381 for(i=0; i<octaves; i++) {

382 res += fabs(noise3(x * freq, y * freq, z * freq) / freq);

383 freq *= 2.0f;

384 }

385 return res;

386 }