`11210 libm should be cstyle(1ONBLD) clean`
 ``` `````` 5 * Common Development and Distribution License (the "License"). 6 * You may not use this file except in compliance with the License. 7 * 8 * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE 9 * or http://www.opensolaris.org/os/licensing. 10 * See the License for the specific language governing permissions 11 * and limitations under the License. 12 * 13 * When distributing Covered Code, include this CDDL HEADER in each 14 * file and include the License file at usr/src/OPENSOLARIS.LICENSE. 15 * If applicable, add the following below this CDDL HEADER, with the 16 * fields enclosed by brackets "[]" replaced with your own identifying 17 * information: Portions Copyright [yyyy] [name of copyright owner] 18 * 19 * CDDL HEADER END 20 */ 21 22 /* 23 * Copyright 2011 Nexenta Systems, Inc. All rights reserved. 24 */ 25 /* 26 * Copyright 2006 Sun Microsystems, Inc. All rights reserved. 27 * Use is subject to license terms. 28 */ 29 30 #pragma weak __erf = erf 31 #pragma weak __erfc = erfc 32 33 /* INDENT OFF */ 34 /* 35 * double erf(double x) 36 * double erfc(double x) 37 * x 38 * 2 |\ 39 * erf(x) = --------- | exp(-t*t)dt 40 * sqrt(pi) \| 41 * 0 42 * 43 * erfc(x) = 1-erf(x) 44 * Note that 45 * erf(-x) = -erf(x) 46 * erfc(-x) = 2 - erfc(x) 47 * 48 * Method: 49 * 1. For |x| in [0, 0.84375] 50 * erf(x) = x + x*R(x^2) 51 * erfc(x) = 1 - erf(x) if x in [-.84375,0.25] 52 * = 0.5 + ((0.5-x)-x*R) if x in [0.25,0.84375] 53 * where R = P/Q where P is an odd poly of degree 8 and `````` 108 * Here 4 and 5 make use of the asymptotic series 109 * exp(-x*x) 110 * erfc(x) ~ ---------- * ( 1 + Poly(1/x^2) ) 111 * x*sqrt(pi) 112 * We use rational approximation to approximate 113 * g(s)=f(1/x^2) = log(erfc(x)*x) - x*x + 0.5625 114 * Here is the error bound for R1/S1 and R2/S2 115 * |R1/S1 - f(x)| < 2**(-62.57) 116 * |R2/S2 - f(x)| < 2**(-61.52) 117 * 118 * 5. For inf > x >= 28 119 * erf(x) = sign(x) *(1 - tiny) (raise inexact) 120 * erfc(x) = tiny*tiny (raise underflow) if x > 0 121 * = 2 - tiny if x<0 122 * 123 * 7. Special case: 124 * erf(0) = 0, erf(inf) = 1, erf(-inf) = -1, 125 * erfc(0) = 1, erfc(inf) = 0, erfc(-inf) = 2, 126 * erfc/erf(NaN) is NaN 127 */ 128 /* INDENT ON */ 129 130 #include "libm_macros.h" 131 #include 132 133 static const double xxx[] = { 134 /* tiny */ 1e-300, 135 /* half */ 5.00000000000000000000e-01, /* 3FE00000, 00000000 */ 136 /* one */ 1.00000000000000000000e+00, /* 3FF00000, 00000000 */ 137 /* two */ 2.00000000000000000000e+00, /* 40000000, 00000000 */ 138 /* erx */ 8.45062911510467529297e-01, /* 3FEB0AC1, 60000000 */ 139 /* 140 * Coefficients for approximation to erf on [0,0.84375] 141 */ 142 /* efx */ 1.28379167095512586316e-01, /* 3FC06EBA, 8214DB69 */ 143 /* efx8 */ 1.02703333676410069053e+00, /* 3FF06EBA, 8214DB69 */ 144 /* pp0 */ 1.28379167095512558561e-01, /* 3FC06EBA, 8214DB68 */ 145 /* pp1 */ -3.25042107247001499370e-01, /* BFD4CD7D, 691CB913 */ 146 /* pp2 */ -2.84817495755985104766e-02, /* BF9D2A51, DBD7194F */ 147 /* pp3 */ -5.77027029648944159157e-03, /* BF77A291, 236668E4 */ 148 /* pp4 */ -2.37630166566501626084e-05, /* BEF8EAD6, 120016AC */ 149 /* qq1 */ 3.97917223959155352819e-01, /* 3FD97779, CDDADC09 */ 150 /* qq2 */ 6.50222499887672944485e-02, /* 3FB0A54C, 5536CEBA */ 151 /* qq3 */ 5.08130628187576562776e-03, /* 3F74D022, C4D36B0F */ 152 /* qq4 */ 1.32494738004321644526e-04, /* 3F215DC9, 221C1A10 */ 153 /* qq5 */ -3.96022827877536812320e-06, /* BED09C43, 42A26120 */ 154 /* 155 * Coefficients for approximation to erf in [0.84375,1.25] 156 */ 157 /* pa0 */ -2.36211856075265944077e-03, /* BF6359B8, BEF77538 */ 158 /* pa1 */ 4.14856118683748331666e-01, /* 3FDA8D00, AD92B34D */ 159 /* pa2 */ -3.72207876035701323847e-01, /* BFD7D240, FBB8C3F1 */ 160 /* pa3 */ 3.18346619901161753674e-01, /* 3FD45FCA, 805120E4 */ 161 /* pa4 */ -1.10894694282396677476e-01, /* BFBC6398, 3D3E28EC */ 162 /* pa5 */ 3.54783043256182359371e-02, /* 3FA22A36, 599795EB */ 163 /* pa6 */ -2.16637559486879084300e-03, /* BF61BF38, 0A96073F */ 164 /* qa1 */ 1.06420880400844228286e-01, /* 3FBB3E66, 18EEE323 */ 165 /* qa2 */ 5.40397917702171048937e-01, /* 3FE14AF0, 92EB6F33 */ 166 /* qa3 */ 7.18286544141962662868e-02, /* 3FB2635C, D99FE9A7 */ 167 /* qa4 */ 1.26171219808761642112e-01, /* 3FC02660, E763351F */ 168 /* qa5 */ 1.36370839120290507362e-02, /* 3F8BEDC2, 6B51DD1C */ 169 /* qa6 */ 1.19844998467991074170e-02, /* 3F888B54, 5735151D */ 170 /* 171 * Coefficients for approximation to erfc in [1.25,1/0.35] 172 */ 173 /* ra0 */ -9.86494403484714822705e-03, /* BF843412, 600D6435 */ 174 /* ra1 */ -6.93858572707181764372e-01, /* BFE63416, E4BA7360 */ 175 /* ra2 */ -1.05586262253232909814e+01, /* C0251E04, 41B0E726 */ 176 /* ra3 */ -6.23753324503260060396e+01, /* C04F300A, E4CBA38D */ 177 /* ra4 */ -1.62396669462573470355e+02, /* C0644CB1, 84282266 */ 178 /* ra5 */ -1.84605092906711035994e+02, /* C067135C, EBCCABB2 */ 179 /* ra6 */ -8.12874355063065934246e+01, /* C0545265, 57E4D2F2 */ 180 /* ra7 */ -9.81432934416914548592e+00, /* C023A0EF, C69AC25C */ 181 /* sa1 */ 1.96512716674392571292e+01, /* 4033A6B9, BD707687 */ 182 /* sa2 */ 1.37657754143519042600e+02, /* 4061350C, 526AE721 */ 183 /* sa3 */ 4.34565877475229228821e+02, /* 407B290D, D58A1A71 */ 184 /* sa4 */ 6.45387271733267880336e+02, /* 40842B19, 21EC2868 */ 185 /* sa5 */ 4.29008140027567833386e+02, /* 407AD021, 57700314 */ 186 /* sa6 */ 1.08635005541779435134e+02, /* 405B28A3, EE48AE2C */ 187 /* sa7 */ 6.57024977031928170135e+00, /* 401A47EF, 8E484A93 */ 188 /* sa8 */ -6.04244152148580987438e-02, /* BFAEEFF2, EE749A62 */ 189 /* 190 * Coefficients for approximation to erfc in [1/.35,28] 191 */ 192 /* rb0 */ -9.86494292470009928597e-03, /* BF843412, 39E86F4A */ 193 /* rb1 */ -7.99283237680523006574e-01, /* BFE993BA, 70C285DE */ 194 /* rb2 */ -1.77579549177547519889e+01, /* C031C209, 555F995A */ 195 /* rb3 */ -1.60636384855821916062e+02, /* C064145D, 43C5ED98 */ 196 /* rb4 */ -6.37566443368389627722e+02, /* C083EC88, 1375F228 */ 197 /* rb5 */ -1.02509513161107724954e+03, /* C0900461, 6A2E5992 */ 198 /* rb6 */ -4.83519191608651397019e+02, /* C07E384E, 9BDC383F */ 199 /* sb1 */ 3.03380607434824582924e+01, /* 403E568B, 261D5190 */ 200 /* sb2 */ 3.25792512996573918826e+02, /* 40745CAE, 221B9F0A */ 201 /* sb3 */ 1.53672958608443695994e+03, /* 409802EB, 189D5118 */ 202 /* sb4 */ 3.19985821950859553908e+03, /* 40A8FFB7, 688C246A */ 203 /* sb5 */ 2.55305040643316442583e+03, /* 40A3F219, CEDF3BE6 */ 204 /* sb6 */ 4.74528541206955367215e+02, /* 407DA874, E79FE763 */ 205 /* sb7 */ -2.24409524465858183362e+01 /* C03670E2, 42712D62 */ 206 }; 207 208 #define tiny xxx[0] 209 #define half xxx[1] 210 #define one xxx[2] 211 #define two xxx[3] 212 #define erx xxx[4] 213 /* 214 * Coefficients for approximation to erf on [0,0.84375] 215 */ 216 #define efx xxx[5] 217 #define efx8 xxx[6] 218 #define pp0 xxx[7] 219 #define pp1 xxx[8] 220 #define pp2 xxx[9] 221 #define pp3 xxx[10] 222 #define pp4 xxx[11] 223 #define qq1 xxx[12] 224 #define qq2 xxx[13] 225 #define qq3 xxx[14] 226 #define qq4 xxx[15] 227 #define qq5 xxx[16] 228 /* 229 * Coefficients for approximation to erf in [0.84375,1.25] 230 */ 231 #define pa0 xxx[17] 232 #define pa1 xxx[18] 233 #define pa2 xxx[19] 234 #define pa3 xxx[20] 235 #define pa4 xxx[21] 236 #define pa5 xxx[22] 237 #define pa6 xxx[23] 238 #define qa1 xxx[24] 239 #define qa2 xxx[25] 240 #define qa3 xxx[26] 241 #define qa4 xxx[27] 242 #define qa5 xxx[28] 243 #define qa6 xxx[29] 244 /* 245 * Coefficients for approximation to erfc in [1.25,1/0.35] 246 */ 247 #define ra0 xxx[30] 248 #define ra1 xxx[31] 249 #define ra2 xxx[32] 250 #define ra3 xxx[33] 251 #define ra4 xxx[34] 252 #define ra5 xxx[35] 253 #define ra6 xxx[36] 254 #define ra7 xxx[37] 255 #define sa1 xxx[38] 256 #define sa2 xxx[39] 257 #define sa3 xxx[40] 258 #define sa4 xxx[41] 259 #define sa5 xxx[42] 260 #define sa6 xxx[43] 261 #define sa7 xxx[44] 262 #define sa8 xxx[45] 263 /* 264 * Coefficients for approximation to erfc in [1/.35,28] 265 */ 266 #define rb0 xxx[46] 267 #define rb1 xxx[47] 268 #define rb2 xxx[48] 269 #define rb3 xxx[49] 270 #define rb4 xxx[50] 271 #define rb5 xxx[51] 272 #define rb6 xxx[52] 273 #define sb1 xxx[53] 274 #define sb2 xxx[54] 275 #define sb3 xxx[55] 276 #define sb4 xxx[56] 277 #define sb5 xxx[57] 278 #define sb6 xxx[58] 279 #define sb7 xxx[59] 280 281 double 282 erf(double x) { 283 int hx, ix, i; 284 double R, S, P, Q, s, y, z, r; 285 286 hx = ((int *) &x)[HIWORD]; 287 ix = hx & 0x7fffffff; 288 if (ix >= 0x7ff00000) { /* erf(nan)=nan */ 289 #if defined(FPADD_TRAPS_INCOMPLETE_ON_NAN) 290 if (ix >= 0x7ff80000) /* assumes sparc-like QNaN */ 291 return (x); 292 #endif 293 i = ((unsigned) hx >> 31) << 1; 294 return ((double) (1 - i) + one / x); /* erf(+-inf)=+-1 */ 295 } 296 297 if (ix < 0x3feb0000) { /* |x|<0.84375 */ 298 if (ix < 0x3e300000) { /* |x|<2**-28 */ 299 if (ix < 0x00800000) /* avoid underflow */ 300 return (0.125 * (8.0 * x + efx8 * x)); 301 return (x + efx * x); 302 } 303 z = x * x; 304 r = pp0 + z * (pp1 + z * (pp2 + z * (pp3 + z * pp4))); 305 s = one + 306 z *(qq1 + z * (qq2 + z * (qq3 + z * (qq4 + z * qq5)))); 307 y = r / s; 308 return (x + x * y); 309 } 310 if (ix < 0x3ff40000) { /* 0.84375 <= |x| < 1.25 */ 311 s = fabs(x) - one; 312 P = pa0 + s * (pa1 + s * (pa2 + s * (pa3 + s * (pa4 + 313 s * (pa5 + s * pa6))))); 314 Q = one + s * (qa1 + s * (qa2 + s * (qa3 + s * (qa4 + 315 s * (qa5 + s * qa6))))); 316 if (hx >= 0) 317 return (erx + P / Q); 318 else 319 return (-erx - P / Q); 320 } 321 if (ix >= 0x40180000) { /* inf > |x| >= 6 */ 322 if (hx >= 0) 323 return (one - tiny); 324 else 325 return (tiny - one); 326 } 327 x = fabs(x); 328 s = one / (x * x); 329 if (ix < 0x4006DB6E) { /* |x| < 1/0.35 */ 330 R = ra0 + s * (ra1 + s * (ra2 + s * (ra3 + s * (ra4 + 331 s * (ra5 + s * (ra6 + s * ra7)))))); 332 S = one + s * (sa1 + s * (sa2 + s * (sa3 + s * (sa4 + 333 s * (sa5 + s * (sa6 + s * (sa7 + s * sa8))))))); 334 } else { /* |x| >= 1/0.35 */ 335 R = rb0 + s * (rb1 + s * (rb2 + s * (rb3 + s * (rb4 + 336 s * (rb5 + s * rb6))))); 337 S = one + s * (sb1 + s * (sb2 + s * (sb3 + s * (sb4 + 338 s * (sb5 + s * (sb6 + s * sb7)))))); 339 } 340 z = x; 341 ((int *) &z)[LOWORD] = 0; 342 r = exp(-z * z - 0.5625) * exp((z - x) * (z + x) + R / S); 343 if (hx >= 0) 344 return (one - r / x); 345 else 346 return (r / x - one); 347 } 348 349 double 350 erfc(double x) { 351 int hx, ix; 352 double R, S, P, Q, s, y, z, r; 353 354 hx = ((int *) &x)[HIWORD]; 355 ix = hx & 0x7fffffff; 356 if (ix >= 0x7ff00000) { /* erfc(nan)=nan */ 357 #if defined(FPADD_TRAPS_INCOMPLETE_ON_NAN) 358 if (ix >= 0x7ff80000) /* assumes sparc-like QNaN */ 359 return (x); 360 #endif 361 /* erfc(+-inf)=0,2 */ 362 return ((double) (((unsigned) hx >> 31) << 1) + one / x); 363 } 364 365 if (ix < 0x3feb0000) { /* |x| < 0.84375 */ 366 if (ix < 0x3c700000) /* |x| < 2**-56 */ 367 return (one - x); 368 z = x * x; 369 r = pp0 + z * (pp1 + z * (pp2 + z * (pp3 + z * pp4))); 370 s = one + 371 z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 + z * qq5)))); 372 y = r / s; 373 if (hx < 0x3fd00000) { /* x < 1/4 */ 374 return (one - (x + x * y)); 375 } else { 376 r = x * y; 377 r += (x - half); 378 return (half - r); 379 } 380 } 381 if (ix < 0x3ff40000) { /* 0.84375 <= |x| < 1.25 */ 382 s = fabs(x) - one; 383 P = pa0 + s * (pa1 + s * (pa2 + s * (pa3 + s * (pa4 + 384 s * (pa5 + s * pa6))))); 385 Q = one + s * (qa1 + s * (qa2 + s * (qa3 + s * (qa4 + 386 s * (qa5 + s * qa6))))); 387 if (hx >= 0) { 388 z = one - erx; 389 return (z - P / Q); 390 } else { 391 z = erx + P / Q; 392 return (one + z); 393 } 394 } 395 if (ix < 0x403c0000) { /* |x|<28 */ 396 x = fabs(x); 397 s = one / (x * x); 398 if (ix < 0x4006DB6D) { /* |x| < 1/.35 ~ 2.857143 */ 399 R = ra0 + s * (ra1 + s * (ra2 + s * (ra3 + s * (ra4 + 400 s * (ra5 + s * (ra6 + s * ra7)))))); 401 S = one + s * (sa1 + s * (sa2 + s * (sa3 + s * (sa4 + 402 s * (sa5 + s * (sa6 + s * (sa7 + s * sa8))))))); 403 } else { 404 /* |x| >= 1/.35 ~ 2.857143 */ 405 if (hx < 0 && ix >= 0x40180000) 406 return (two - tiny); /* x < -6 */ 407 408 R = rb0 + s * (rb1 + s * (rb2 + s * (rb3 + s * (rb4 + 409 s * (rb5 + s * rb6))))); 410 S = one + s * (sb1 + s * (sb2 + s * (sb3 + s * (sb4 + 411 s * (sb5 + s * (sb6 + s * sb7)))))); 412 } 413 z = x; 414 ((int *) &z)[LOWORD] = 0; 415 r = exp(-z * z - 0.5625) * exp((z - x) * (z + x) + R / S); 416 if (hx > 0) 417 return (r / x); 418 else 419 return (two - r / x); 420 } else { 421 if (hx > 0) 422 return (tiny * tiny); 423 else 424 return (two - tiny); 425 } 426 } ``` ``` `````` 5 * Common Development and Distribution License (the "License"). 6 * You may not use this file except in compliance with the License. 7 * 8 * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE 9 * or http://www.opensolaris.org/os/licensing. 10 * See the License for the specific language governing permissions 11 * and limitations under the License. 12 * 13 * When distributing Covered Code, include this CDDL HEADER in each 14 * file and include the License file at usr/src/OPENSOLARIS.LICENSE. 15 * If applicable, add the following below this CDDL HEADER, with the 16 * fields enclosed by brackets "[]" replaced with your own identifying 17 * information: Portions Copyright [yyyy] [name of copyright owner] 18 * 19 * CDDL HEADER END 20 */ 21 22 /* 23 * Copyright 2011 Nexenta Systems, Inc. All rights reserved. 24 */ 25 26 /* 27 * Copyright 2006 Sun Microsystems, Inc. All rights reserved. 28 * Use is subject to license terms. 29 */ 30 31 #pragma weak __erf = erf 32 #pragma weak __erfc = erfc 33 34 35 /* 36 * double erf(double x) 37 * double erfc(double x) 38 * x 39 * 2 |\ 40 * erf(x) = --------- | exp(-t*t)dt 41 * sqrt(pi) \| 42 * 0 43 * 44 * erfc(x) = 1-erf(x) 45 * Note that 46 * erf(-x) = -erf(x) 47 * erfc(-x) = 2 - erfc(x) 48 * 49 * Method: 50 * 1. For |x| in [0, 0.84375] 51 * erf(x) = x + x*R(x^2) 52 * erfc(x) = 1 - erf(x) if x in [-.84375,0.25] 53 * = 0.5 + ((0.5-x)-x*R) if x in [0.25,0.84375] 54 * where R = P/Q where P is an odd poly of degree 8 and `````` 109 * Here 4 and 5 make use of the asymptotic series 110 * exp(-x*x) 111 * erfc(x) ~ ---------- * ( 1 + Poly(1/x^2) ) 112 * x*sqrt(pi) 113 * We use rational approximation to approximate 114 * g(s)=f(1/x^2) = log(erfc(x)*x) - x*x + 0.5625 115 * Here is the error bound for R1/S1 and R2/S2 116 * |R1/S1 - f(x)| < 2**(-62.57) 117 * |R2/S2 - f(x)| < 2**(-61.52) 118 * 119 * 5. For inf > x >= 28 120 * erf(x) = sign(x) *(1 - tiny) (raise inexact) 121 * erfc(x) = tiny*tiny (raise underflow) if x > 0 122 * = 2 - tiny if x<0 123 * 124 * 7. Special case: 125 * erf(0) = 0, erf(inf) = 1, erf(-inf) = -1, 126 * erfc(0) = 1, erfc(inf) = 0, erfc(-inf) = 2, 127 * erfc/erf(NaN) is NaN 128 */ 129 130 #include "libm_macros.h" 131 #include 132 133 static const double xxx[] = { 134 /* tiny */ 135 1e-300, 136 /* half */ 5.00000000000000000000e-01, /* 3FE00000, 00000000 */ 137 /* one */ 1.00000000000000000000e+00, /* 3FF00000, 00000000 */ 138 /* two */ 2.00000000000000000000e+00, /* 40000000, 00000000 */ 139 /* erx */ 8.45062911510467529297e-01, /* 3FEB0AC1, 60000000 */ 140 141 /* 142 * Coefficients for approximation to erf on [0,0.84375] 143 */ 144 /* efx */ 1.28379167095512586316e-01, /* 3FC06EBA, 8214DB69 */ 145 /* efx8 */ 1.02703333676410069053e+00, /* 3FF06EBA, 8214DB69 */ 146 /* pp0 */ 1.28379167095512558561e-01, /* 3FC06EBA, 8214DB68 */ 147 /* pp1 */ -3.25042107247001499370e-01, /* BFD4CD7D, 691CB913 */ 148 /* pp2 */ -2.84817495755985104766e-02, /* BF9D2A51, DBD7194F */ 149 /* pp3 */ -5.77027029648944159157e-03, /* BF77A291, 236668E4 */ 150 /* pp4 */ -2.37630166566501626084e-05, /* BEF8EAD6, 120016AC */ 151 /* qq1 */ 3.97917223959155352819e-01, /* 3FD97779, CDDADC09 */ 152 /* qq2 */ 6.50222499887672944485e-02, /* 3FB0A54C, 5536CEBA */ 153 /* qq3 */ 5.08130628187576562776e-03, /* 3F74D022, C4D36B0F */ 154 /* qq4 */ 1.32494738004321644526e-04, /* 3F215DC9, 221C1A10 */ 155 /* qq5 */ -3.96022827877536812320e-06, /* BED09C43, 42A26120 */ 156 157 /* 158 * Coefficients for approximation to erf in [0.84375,1.25] 159 */ 160 /* pa0 */ -2.36211856075265944077e-03, /* BF6359B8, BEF77538 */ 161 /* pa1 */ 4.14856118683748331666e-01, /* 3FDA8D00, AD92B34D */ 162 /* pa2 */ -3.72207876035701323847e-01, /* BFD7D240, FBB8C3F1 */ 163 /* pa3 */ 3.18346619901161753674e-01, /* 3FD45FCA, 805120E4 */ 164 /* pa4 */ -1.10894694282396677476e-01, /* BFBC6398, 3D3E28EC */ 165 /* pa5 */ 3.54783043256182359371e-02, /* 3FA22A36, 599795EB */ 166 /* pa6 */ -2.16637559486879084300e-03, /* BF61BF38, 0A96073F */ 167 /* qa1 */ 1.06420880400844228286e-01, /* 3FBB3E66, 18EEE323 */ 168 /* qa2 */ 5.40397917702171048937e-01, /* 3FE14AF0, 92EB6F33 */ 169 /* qa3 */ 7.18286544141962662868e-02, /* 3FB2635C, D99FE9A7 */ 170 /* qa4 */ 1.26171219808761642112e-01, /* 3FC02660, E763351F */ 171 /* qa5 */ 1.36370839120290507362e-02, /* 3F8BEDC2, 6B51DD1C */ 172 /* qa6 */ 1.19844998467991074170e-02, /* 3F888B54, 5735151D */ 173 174 /* 175 * Coefficients for approximation to erfc in [1.25,1/0.35] 176 */ 177 /* ra0 */ -9.86494403484714822705e-03, /* BF843412, 600D6435 */ 178 /* ra1 */ -6.93858572707181764372e-01, /* BFE63416, E4BA7360 */ 179 /* ra2 */ -1.05586262253232909814e+01, /* C0251E04, 41B0E726 */ 180 /* ra3 */ -6.23753324503260060396e+01, /* C04F300A, E4CBA38D */ 181 /* ra4 */ -1.62396669462573470355e+02, /* C0644CB1, 84282266 */ 182 /* ra5 */ -1.84605092906711035994e+02, /* C067135C, EBCCABB2 */ 183 /* ra6 */ -8.12874355063065934246e+01, /* C0545265, 57E4D2F2 */ 184 /* ra7 */ -9.81432934416914548592e+00, /* C023A0EF, C69AC25C */ 185 /* sa1 */ 1.96512716674392571292e+01, /* 4033A6B9, BD707687 */ 186 /* sa2 */ 1.37657754143519042600e+02, /* 4061350C, 526AE721 */ 187 /* sa3 */ 4.34565877475229228821e+02, /* 407B290D, D58A1A71 */ 188 /* sa4 */ 6.45387271733267880336e+02, /* 40842B19, 21EC2868 */ 189 /* sa5 */ 4.29008140027567833386e+02, /* 407AD021, 57700314 */ 190 /* sa6 */ 1.08635005541779435134e+02, /* 405B28A3, EE48AE2C */ 191 /* sa7 */ 6.57024977031928170135e+00, /* 401A47EF, 8E484A93 */ 192 /* sa8 */ -6.04244152148580987438e-02, /* BFAEEFF2, EE749A62 */ 193 194 /* 195 * Coefficients for approximation to erfc in [1/.35,28] 196 */ 197 /* rb0 */ -9.86494292470009928597e-03, /* BF843412, 39E86F4A */ 198 /* rb1 */ -7.99283237680523006574e-01, /* BFE993BA, 70C285DE */ 199 /* rb2 */ -1.77579549177547519889e+01, /* C031C209, 555F995A */ 200 /* rb3 */ -1.60636384855821916062e+02, /* C064145D, 43C5ED98 */ 201 /* rb4 */ -6.37566443368389627722e+02, /* C083EC88, 1375F228 */ 202 /* rb5 */ -1.02509513161107724954e+03, /* C0900461, 6A2E5992 */ 203 /* rb6 */ -4.83519191608651397019e+02, /* C07E384E, 9BDC383F */ 204 /* sb1 */ 3.03380607434824582924e+01, /* 403E568B, 261D5190 */ 205 /* sb2 */ 3.25792512996573918826e+02, /* 40745CAE, 221B9F0A */ 206 /* sb3 */ 1.53672958608443695994e+03, /* 409802EB, 189D5118 */ 207 /* sb4 */ 3.19985821950859553908e+03, /* 40A8FFB7, 688C246A */ 208 /* sb5 */ 2.55305040643316442583e+03, /* 40A3F219, CEDF3BE6 */ 209 /* sb6 */ 4.74528541206955367215e+02, /* 407DA874, E79FE763 */ 210 /* sb7 */ -2.24409524465858183362e+01 /* C03670E2, 42712D62 */ 211 }; 212 213 #define tiny xxx[0] 214 #define half xxx[1] 215 #define one xxx[2] 216 #define two xxx[3] 217 #define erx xxx[4] 218 219 /* 220 * Coefficients for approximation to erf on [0,0.84375] 221 */ 222 #define efx xxx[5] 223 #define efx8 xxx[6] 224 #define pp0 xxx[7] 225 #define pp1 xxx[8] 226 #define pp2 xxx[9] 227 #define pp3 xxx[10] 228 #define pp4 xxx[11] 229 #define qq1 xxx[12] 230 #define qq2 xxx[13] 231 #define qq3 xxx[14] 232 #define qq4 xxx[15] 233 #define qq5 xxx[16] 234 235 /* 236 * Coefficients for approximation to erf in [0.84375,1.25] 237 */ 238 #define pa0 xxx[17] 239 #define pa1 xxx[18] 240 #define pa2 xxx[19] 241 #define pa3 xxx[20] 242 #define pa4 xxx[21] 243 #define pa5 xxx[22] 244 #define pa6 xxx[23] 245 #define qa1 xxx[24] 246 #define qa2 xxx[25] 247 #define qa3 xxx[26] 248 #define qa4 xxx[27] 249 #define qa5 xxx[28] 250 #define qa6 xxx[29] 251 252 /* 253 * Coefficients for approximation to erfc in [1.25,1/0.35] 254 */ 255 #define ra0 xxx[30] 256 #define ra1 xxx[31] 257 #define ra2 xxx[32] 258 #define ra3 xxx[33] 259 #define ra4 xxx[34] 260 #define ra5 xxx[35] 261 #define ra6 xxx[36] 262 #define ra7 xxx[37] 263 #define sa1 xxx[38] 264 #define sa2 xxx[39] 265 #define sa3 xxx[40] 266 #define sa4 xxx[41] 267 #define sa5 xxx[42] 268 #define sa6 xxx[43] 269 #define sa7 xxx[44] 270 #define sa8 xxx[45] 271 272 /* 273 * Coefficients for approximation to erfc in [1/.35,28] 274 */ 275 #define rb0 xxx[46] 276 #define rb1 xxx[47] 277 #define rb2 xxx[48] 278 #define rb3 xxx[49] 279 #define rb4 xxx[50] 280 #define rb5 xxx[51] 281 #define rb6 xxx[52] 282 #define sb1 xxx[53] 283 #define sb2 xxx[54] 284 #define sb3 xxx[55] 285 #define sb4 xxx[56] 286 #define sb5 xxx[57] 287 #define sb6 xxx[58] 288 #define sb7 xxx[59] 289 290 double 291 erf(double x) 292 { 293 int hx, ix, i; 294 double R, S, P, Q, s, y, z, r; 295 296 hx = ((int *)&x)[HIWORD]; 297 ix = hx & 0x7fffffff; 298 299 if (ix >= 0x7ff00000) { /* erf(nan)=nan */ 300 #if defined(FPADD_TRAPS_INCOMPLETE_ON_NAN) 301 if (ix >= 0x7ff80000) /* assumes sparc-like QNaN */ 302 return (x); 303 #endif 304 i = ((unsigned)hx >> 31) << 1; 305 return ((double)(1 - i) + one / x); /* erf(+-inf)=+-1 */ 306 } 307 308 if (ix < 0x3feb0000) { /* |x|<0.84375 */ 309 if (ix < 0x3e300000) { /* |x|<2**-28 */ 310 if (ix < 0x00800000) /* avoid underflow */ 311 return (0.125 * (8.0 * x + efx8 * x)); 312 313 return (x + efx * x); 314 } 315 316 z = x * x; 317 r = pp0 + z * (pp1 + z * (pp2 + z * (pp3 + z * pp4))); 318 s = one + z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 + z * 319 qq5)))); 320 y = r / s; 321 return (x + x * y); 322 } 323 324 if (ix < 0x3ff40000) { /* 0.84375 <= |x| < 1.25 */ 325 s = fabs(x) - one; 326 P = pa0 + s * (pa1 + s * (pa2 + s * (pa3 + s * (pa4 + s * (pa5 + 327 s * pa6))))); 328 Q = one + s * (qa1 + s * (qa2 + s * (qa3 + s * (qa4 + s * (qa5 + 329 s * qa6))))); 330 331 if (hx >= 0) 332 return (erx + P / Q); 333 else 334 return (-erx - P / Q); 335 } 336 337 if (ix >= 0x40180000) { /* inf > |x| >= 6 */ 338 if (hx >= 0) 339 return (one - tiny); 340 else 341 return (tiny - one); 342 } 343 344 x = fabs(x); 345 s = one / (x * x); 346 347 if (ix < 0x4006DB6E) { /* |x| < 1/0.35 */ 348 R = ra0 + s * (ra1 + s * (ra2 + s * (ra3 + s * (ra4 + s * (ra5 + 349 s * (ra6 + s * ra7)))))); 350 S = one + s * (sa1 + s * (sa2 + s * (sa3 + s * (sa4 + s * (sa5 + 351 s * (sa6 + s * (sa7 + s * sa8))))))); 352 } else { /* |x| >= 1/0.35 */ 353 R = rb0 + s * (rb1 + s * (rb2 + s * (rb3 + s * (rb4 + s * (rb5 + 354 s * rb6))))); 355 S = one + s * (sb1 + s * (sb2 + s * (sb3 + s * (sb4 + s * (sb5 + 356 s * (sb6 + s * sb7)))))); 357 } 358 359 z = x; 360 ((int *)&z)[LOWORD] = 0; 361 r = exp(-z * z - 0.5625) * exp((z - x) * (z + x) + R / S); 362 363 if (hx >= 0) 364 return (one - r / x); 365 else 366 return (r / x - one); 367 } 368 369 double 370 erfc(double x) 371 { 372 int hx, ix; 373 double R, S, P, Q, s, y, z, r; 374 375 hx = ((int *)&x)[HIWORD]; 376 ix = hx & 0x7fffffff; 377 378 if (ix >= 0x7ff00000) { /* erfc(nan)=nan */ 379 #if defined(FPADD_TRAPS_INCOMPLETE_ON_NAN) 380 if (ix >= 0x7ff80000) /* assumes sparc-like QNaN */ 381 return (x); 382 #endif 383 /* erfc(+-inf)=0,2 */ 384 return ((double)(((unsigned)hx >> 31) << 1) + one / x); 385 } 386 387 if (ix < 0x3feb0000) { /* |x| < 0.84375 */ 388 if (ix < 0x3c700000) /* |x| < 2**-56 */ 389 return (one - x); 390 391 z = x * x; 392 r = pp0 + z * (pp1 + z * (pp2 + z * (pp3 + z * pp4))); 393 s = one + z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 + z * 394 qq5)))); 395 y = r / s; 396 397 if (hx < 0x3fd00000) { /* x < 1/4 */ 398 return (one - (x + x * y)); 399 } else { 400 r = x * y; 401 r += (x - half); 402 return (half - r); 403 } 404 } 405 406 if (ix < 0x3ff40000) { /* 0.84375 <= |x| < 1.25 */ 407 s = fabs(x) - one; 408 P = pa0 + s * (pa1 + s * (pa2 + s * (pa3 + s * (pa4 + s * (pa5 + 409 s * pa6))))); 410 Q = one + s * (qa1 + s * (qa2 + s * (qa3 + s * (qa4 + s * (qa5 + 411 s * qa6))))); 412 413 if (hx >= 0) { 414 z = one - erx; 415 return (z - P / Q); 416 } else { 417 z = erx + P / Q; 418 return (one + z); 419 } 420 } 421 422 if (ix < 0x403c0000) { /* |x|<28 */ 423 x = fabs(x); 424 s = one / (x * x); 425 426 if (ix < 0x4006DB6D) { /* |x| < 1/.35 ~ 2.857143 */ 427 R = ra0 + s * (ra1 + s * (ra2 + s * (ra3 + s * (ra4 + 428 s * (ra5 + s * (ra6 + s * ra7)))))); 429 S = one + s * (sa1 + s * (sa2 + s * (sa3 + s * (sa4 + 430 s * (sa5 + s * (sa6 + s * (sa7 + s * sa8))))))); 431 } else { 432 /* |x| >= 1/.35 ~ 2.857143 */ 433 if (hx < 0 && ix >= 0x40180000) 434 return (two - tiny); /* x < -6 */ 435 436 R = rb0 + s * (rb1 + s * (rb2 + s * (rb3 + s * (rb4 + 437 s * (rb5 + s * rb6))))); 438 S = one + s * (sb1 + s * (sb2 + s * (sb3 + s * (sb4 + 439 s * (sb5 + s * (sb6 + s * sb7)))))); 440 } 441 442 z = x; 443 ((int *)&z)[LOWORD] = 0; 444 r = exp(-z * z - 0.5625) * exp((z - x) * (z + x) + R / S); 445 446 if (hx > 0) 447 return (r / x); 448 else 449 return (two - r / x); 450 } else { 451 if (hx > 0) 452 return (tiny * tiny); 453 else 454 return (two - tiny); 455 } 456 } ```