kc3-lang/SDL/src/libm/e_pow.c
-
Show log
Commit
-
Hash : 3dcb451f
Author :
Date : 2014-04-09T21:29:19
Added a README file regarding WinRT support To note, this file is currently formatted with CRLF line endings, rather than LF, to allow the file to be viewed with Notepad.
-
src/libm/e_pow.c
-
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342
/* @(#)e_pow.c 5.1 93/09/24 */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. * ==================================================== */ #if defined(LIBM_SCCS) && !defined(lint) static char rcsid[] = "$NetBSD: e_pow.c,v 1.9 1995/05/12 04:57:32 jtc Exp $"; #endif /* __ieee754_pow(x,y) return x**y * * n * Method: Let x = 2 * (1+f) * 1. Compute and return log2(x) in two pieces: * log2(x) = w1 + w2, * where w1 has 53-24 = 29 bit trailing zeros. * 2. Perform y*log2(x) = n+y' by simulating muti-precision * arithmetic, where |y'|<=0.5. * 3. Return x**y = 2**n*exp(y'*log2) * * Special cases: * 1. (anything) ** 0 is 1 * 2. (anything) ** 1 is itself * 3. (anything) ** NAN is NAN * 4. NAN ** (anything except 0) is NAN * 5. +-(|x| > 1) ** +INF is +INF * 6. +-(|x| > 1) ** -INF is +0 * 7. +-(|x| < 1) ** +INF is +0 * 8. +-(|x| < 1) ** -INF is +INF * 9. +-1 ** +-INF is NAN * 10. +0 ** (+anything except 0, NAN) is +0 * 11. -0 ** (+anything except 0, NAN, odd integer) is +0 * 12. +0 ** (-anything except 0, NAN) is +INF * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF * 14. -0 ** (odd integer) = -( +0 ** (odd integer) ) * 15. +INF ** (+anything except 0,NAN) is +INF * 16. +INF ** (-anything except 0,NAN) is +0 * 17. -INF ** (anything) = -0 ** (-anything) * 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer) * 19. (-anything except 0 and inf) ** (non-integer) is NAN * * Accuracy: * pow(x,y) returns x**y nearly rounded. In particular * pow(integer,integer) * always returns the correct integer provided it is * representable. * * Constants : * The hexadecimal values are the intended ones for the following * constants. The decimal values may be used, provided that the * compiler will convert from decimal to binary accurately enough * to produce the hexadecimal values shown. */ #include "math_libm.h" #include "math_private.h" libm_hidden_proto(scalbn) libm_hidden_proto(fabs) #ifdef __STDC__ static const double #else static double #endif bp[] = { 1.0, 1.5, }, dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */ dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */ zero = 0.0, one = 1.0, two = 2.0, two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */ huge_val = 1.0e300, tiny = 1.0e-300, /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */ L1 = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */ L2 = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */ L3 = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */ L4 = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */ L5 = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */ L6 = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */ P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */ P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */ P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */ P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */ P5 = 4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */ lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */ lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */ ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */ cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */ cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */ cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h */ ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */ ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2 */ ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail */ #ifdef __STDC__ double attribute_hidden __ieee754_pow(double x, double y) #else double attribute_hidden __ieee754_pow(x, y) double x, y; #endif { double z, ax, z_h, z_l, p_h, p_l; double y1, t1, t2, r, s, t, u, v, w; int32_t i, j, k, yisint, n; int32_t hx, hy, ix, iy; u_int32_t lx, ly; EXTRACT_WORDS(hx, lx, x); EXTRACT_WORDS(hy, ly, y); ix = hx & 0x7fffffff; iy = hy & 0x7fffffff; /* y==zero: x**0 = 1 */ if ((iy | ly) == 0) return one; /* +-NaN return x+y */ if (ix > 0x7ff00000 || ((ix == 0x7ff00000) && (lx != 0)) || iy > 0x7ff00000 || ((iy == 0x7ff00000) && (ly != 0))) return x + y; /* determine if y is an odd int when x < 0 * yisint = 0 ... y is not an integer * yisint = 1 ... y is an odd int * yisint = 2 ... y is an even int */ yisint = 0; if (hx < 0) { if (iy >= 0x43400000) yisint = 2; /* even integer y */ else if (iy >= 0x3ff00000) { k = (iy >> 20) - 0x3ff; /* exponent */ if (k > 20) { j = ly >> (52 - k); if ((j << (52 - k)) == ly) yisint = 2 - (j & 1); } else if (ly == 0) { j = iy >> (20 - k); if ((j << (20 - k)) == iy) yisint = 2 - (j & 1); } } } /* special value of y */ if (ly == 0) { if (iy == 0x7ff00000) { /* y is +-inf */ if (((ix - 0x3ff00000) | lx) == 0) return y - y; /* inf**+-1 is NaN */ else if (ix >= 0x3ff00000) /* (|x|>1)**+-inf = inf,0 */ return (hy >= 0) ? y : zero; else /* (|x|<1)**-,+inf = inf,0 */ return (hy < 0) ? -y : zero; } if (iy == 0x3ff00000) { /* y is +-1 */ if (hy < 0) return one / x; else return x; } if (hy == 0x40000000) return x * x; /* y is 2 */ if (hy == 0x3fe00000) { /* y is 0.5 */ if (hx >= 0) /* x >= +0 */ return __ieee754_sqrt(x); } } ax = fabs(x); /* special value of x */ if (lx == 0) { if (ix == 0x7ff00000 || ix == 0 || ix == 0x3ff00000) { z = ax; /* x is +-0,+-inf,+-1 */ if (hy < 0) z = one / z; /* z = (1/|x|) */ if (hx < 0) { if (((ix - 0x3ff00000) | yisint) == 0) { z = (z - z) / (z - z); /* (-1)**non-int is NaN */ } else if (yisint == 1) z = -z; /* (x<0)**odd = -(|x|**odd) */ } return z; } } /* (x<0)**(non-int) is NaN */ if (((((u_int32_t) hx >> 31) - 1) | yisint) == 0) return (x - x) / (x - x); /* |y| is huge */ if (iy > 0x41e00000) { /* if |y| > 2**31 */ if (iy > 0x43f00000) { /* if |y| > 2**64, must o/uflow */ if (ix <= 0x3fefffff) return (hy < 0) ? huge_val * huge_val : tiny * tiny; if (ix >= 0x3ff00000) return (hy > 0) ? huge_val * huge_val : tiny * tiny; } /* over/underflow if x is not close to one */ if (ix < 0x3fefffff) return (hy < 0) ? huge_val * huge_val : tiny * tiny; if (ix > 0x3ff00000) return (hy > 0) ? huge_val * huge_val : tiny * tiny; /* now |1-x| is tiny <= 2**-20, suffice to compute log(x) by x-x^2/2+x^3/3-x^4/4 */ t = x - 1; /* t has 20 trailing zeros */ w = (t * t) * (0.5 - t * (0.3333333333333333333333 - t * 0.25)); u = ivln2_h * t; /* ivln2_h has 21 sig. bits */ v = t * ivln2_l - w * ivln2; t1 = u + v; SET_LOW_WORD(t1, 0); t2 = v - (t1 - u); } else { double s2, s_h, s_l, t_h, t_l; n = 0; /* take care subnormal number */ if (ix < 0x00100000) { ax *= two53; n -= 53; GET_HIGH_WORD(ix, ax); } n += ((ix) >> 20) - 0x3ff; j = ix & 0x000fffff; /* determine interval */ ix = j | 0x3ff00000; /* normalize ix */ if (j <= 0x3988E) k = 0; /* |x|<sqrt(3/2) */ else if (j < 0xBB67A) k = 1; /* |x|<sqrt(3) */ else { k = 0; n += 1; ix -= 0x00100000; } SET_HIGH_WORD(ax, ix); /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */ u = ax - bp[k]; /* bp[0]=1.0, bp[1]=1.5 */ v = one / (ax + bp[k]); s = u * v; s_h = s; SET_LOW_WORD(s_h, 0); /* t_h=ax+bp[k] High */ t_h = zero; SET_HIGH_WORD(t_h, ((ix >> 1) | 0x20000000) + 0x00080000 + (k << 18)); t_l = ax - (t_h - bp[k]); s_l = v * ((u - s_h * t_h) - s_h * t_l); /* compute log(ax) */ s2 = s * s; r = s2 * s2 * (L1 + s2 * (L2 + s2 * (L3 + s2 * (L4 + s2 * (L5 + s2 * L6))))); r += s_l * (s_h + s); s2 = s_h * s_h; t_h = 3.0 + s2 + r; SET_LOW_WORD(t_h, 0); t_l = r - ((t_h - 3.0) - s2); /* u+v = s*(1+...) */ u = s_h * t_h; v = s_l * t_h + t_l * s; /* 2/(3log2)*(s+...) */ p_h = u + v; SET_LOW_WORD(p_h, 0); p_l = v - (p_h - u); z_h = cp_h * p_h; /* cp_h+cp_l = 2/(3*log2) */ z_l = cp_l * p_h + p_l * cp + dp_l[k]; /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */ t = (double) n; t1 = (((z_h + z_l) + dp_h[k]) + t); SET_LOW_WORD(t1, 0); t2 = z_l - (((t1 - t) - dp_h[k]) - z_h); } s = one; /* s (sign of result -ve**odd) = -1 else = 1 */ if (((((u_int32_t) hx >> 31) - 1) | (yisint - 1)) == 0) s = -one; /* (-ve)**(odd int) */ /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */ y1 = y; SET_LOW_WORD(y1, 0); p_l = (y - y1) * t1 + y * t2; p_h = y1 * t1; z = p_l + p_h; EXTRACT_WORDS(j, i, z); if (j >= 0x40900000) { /* z >= 1024 */ if (((j - 0x40900000) | i) != 0) /* if z > 1024 */ return s * huge_val * huge_val; /* overflow */ else { if (p_l + ovt > z - p_h) return s * huge_val * huge_val; /* overflow */ } } else if ((j & 0x7fffffff) >= 0x4090cc00) { /* z <= -1075 */ if (((j - 0xc090cc00) | i) != 0) /* z < -1075 */ return s * tiny * tiny; /* underflow */ else { if (p_l <= z - p_h) return s * tiny * tiny; /* underflow */ } } /* * compute 2**(p_h+p_l) */ i = j & 0x7fffffff; k = (i >> 20) - 0x3ff; n = 0; if (i > 0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */ n = j + (0x00100000 >> (k + 1)); k = ((n & 0x7fffffff) >> 20) - 0x3ff; /* new k for n */ t = zero; SET_HIGH_WORD(t, n & ~(0x000fffff >> k)); n = ((n & 0x000fffff) | 0x00100000) >> (20 - k); if (j < 0) n = -n; p_h -= t; } t = p_l + p_h; SET_LOW_WORD(t, 0); u = t * lg2_h; v = (p_l - (t - p_h)) * lg2 + t * lg2_l; z = u + v; w = v - (z - u); t = z * z; t1 = z - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5)))); r = (z * t1) / (t1 - two) - (w + z * w); z = one - (r - z); GET_HIGH_WORD(j, z); j += (n << 20); if ((j >> 20) <= 0) z = scalbn(z, n); /* subnormal output */ else SET_HIGH_WORD(z, j); return s * z; }