[444] | 1 | |
---|
| 2 | /* @(#)s_erf.c 5.1 93/09/24 */ |
---|
| 3 | /* |
---|
| 4 | * ==================================================== |
---|
| 5 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
---|
| 6 | * |
---|
| 7 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
---|
| 8 | * Permission to use, copy, modify, and distribute this |
---|
| 9 | * software is freely granted, provided that this notice |
---|
| 10 | * is preserved. |
---|
| 11 | * ==================================================== |
---|
| 12 | */ |
---|
| 13 | |
---|
| 14 | /* |
---|
| 15 | FUNCTION |
---|
| 16 | <<erf>>, <<erff>>, <<erfc>>, <<erfcf>>---error function |
---|
| 17 | INDEX |
---|
| 18 | erf |
---|
| 19 | INDEX |
---|
| 20 | erff |
---|
| 21 | INDEX |
---|
| 22 | erfc |
---|
| 23 | INDEX |
---|
| 24 | erfcf |
---|
| 25 | |
---|
| 26 | SYNOPSIS |
---|
| 27 | #include <math.h> |
---|
| 28 | double erf(double <[x]>); |
---|
| 29 | float erff(float <[x]>); |
---|
| 30 | double erfc(double <[x]>); |
---|
| 31 | float erfcf(float <[x]>); |
---|
| 32 | |
---|
| 33 | DESCRIPTION |
---|
| 34 | <<erf>> calculates an approximation to the ``error function'', |
---|
| 35 | which estimates the probability that an observation will fall within |
---|
| 36 | <[x]> standard deviations of the mean (assuming a normal |
---|
| 37 | distribution). |
---|
| 38 | @tex |
---|
| 39 | The error function is defined as |
---|
| 40 | $${2\over\sqrt\pi}\times\int_0^x e^{-t^2}dt$$ |
---|
| 41 | @end tex |
---|
| 42 | |
---|
| 43 | <<erfc>> calculates the complementary probability; that is, |
---|
| 44 | <<erfc(<[x]>)>> is <<1 - erf(<[x]>)>>. <<erfc>> is computed directly, |
---|
| 45 | so that you can use it to avoid the loss of precision that would |
---|
| 46 | result from subtracting large probabilities (on large <[x]>) from 1. |
---|
| 47 | |
---|
| 48 | <<erff>> and <<erfcf>> differ from <<erf>> and <<erfc>> only in the |
---|
| 49 | argument and result types. |
---|
| 50 | |
---|
| 51 | RETURNS |
---|
| 52 | For positive arguments, <<erf>> and all its variants return a |
---|
| 53 | probability---a number between 0 and 1. |
---|
| 54 | |
---|
| 55 | PORTABILITY |
---|
| 56 | None of the variants of <<erf>> are ANSI C. |
---|
| 57 | */ |
---|
| 58 | |
---|
| 59 | /* double erf(double x) |
---|
| 60 | * double erfc(double x) |
---|
| 61 | * x |
---|
| 62 | * 2 |\ |
---|
| 63 | * erf(x) = --------- | exp(-t*t)dt |
---|
| 64 | * sqrt(pi) \| |
---|
| 65 | * 0 |
---|
| 66 | * |
---|
| 67 | * erfc(x) = 1-erf(x) |
---|
| 68 | * Note that |
---|
| 69 | * erf(-x) = -erf(x) |
---|
| 70 | * erfc(-x) = 2 - erfc(x) |
---|
| 71 | * |
---|
| 72 | * Method: |
---|
| 73 | * 1. For |x| in [0, 0.84375] |
---|
| 74 | * erf(x) = x + x*R(x^2) |
---|
| 75 | * erfc(x) = 1 - erf(x) if x in [-.84375,0.25] |
---|
| 76 | * = 0.5 + ((0.5-x)-x*R) if x in [0.25,0.84375] |
---|
| 77 | * where R = P/Q where P is an odd poly of degree 8 and |
---|
| 78 | * Q is an odd poly of degree 10. |
---|
| 79 | * -57.90 |
---|
| 80 | * | R - (erf(x)-x)/x | <= 2 |
---|
| 81 | * |
---|
| 82 | * |
---|
| 83 | * Remark. The formula is derived by noting |
---|
| 84 | * erf(x) = (2/sqrt(pi))*(x - x^3/3 + x^5/10 - x^7/42 + ....) |
---|
| 85 | * and that |
---|
| 86 | * 2/sqrt(pi) = 1.128379167095512573896158903121545171688 |
---|
| 87 | * is close to one. The interval is chosen because the fix |
---|
| 88 | * point of erf(x) is near 0.6174 (i.e., erf(x)=x when x is |
---|
| 89 | * near 0.6174), and by some experiment, 0.84375 is chosen to |
---|
| 90 | * guarantee the error is less than one ulp for erf. |
---|
| 91 | * |
---|
| 92 | * 2. For |x| in [0.84375,1.25], let s = |x| - 1, and |
---|
| 93 | * c = 0.84506291151 rounded to single (24 bits) |
---|
| 94 | * erf(x) = sign(x) * (c + P1(s)/Q1(s)) |
---|
| 95 | * erfc(x) = (1-c) - P1(s)/Q1(s) if x > 0 |
---|
| 96 | * 1+(c+P1(s)/Q1(s)) if x < 0 |
---|
| 97 | * |P1/Q1 - (erf(|x|)-c)| <= 2**-59.06 |
---|
| 98 | * Remark: here we use the taylor series expansion at x=1. |
---|
| 99 | * erf(1+s) = erf(1) + s*Poly(s) |
---|
| 100 | * = 0.845.. + P1(s)/Q1(s) |
---|
| 101 | * That is, we use rational approximation to approximate |
---|
| 102 | * erf(1+s) - (c = (single)0.84506291151) |
---|
| 103 | * Note that |P1/Q1|< 0.078 for x in [0.84375,1.25] |
---|
| 104 | * where |
---|
| 105 | * P1(s) = degree 6 poly in s |
---|
| 106 | * Q1(s) = degree 6 poly in s |
---|
| 107 | * |
---|
| 108 | * 3. For x in [1.25,1/0.35(~2.857143)], |
---|
| 109 | * erfc(x) = (1/x)*exp(-x*x-0.5625+R1/S1) |
---|
| 110 | * erf(x) = 1 - erfc(x) |
---|
| 111 | * where |
---|
| 112 | * R1(z) = degree 7 poly in z, (z=1/x^2) |
---|
| 113 | * S1(z) = degree 8 poly in z |
---|
| 114 | * |
---|
| 115 | * 4. For x in [1/0.35,28] |
---|
| 116 | * erfc(x) = (1/x)*exp(-x*x-0.5625+R2/S2) if x > 0 |
---|
| 117 | * = 2.0 - (1/x)*exp(-x*x-0.5625+R2/S2) if -6<x<0 |
---|
| 118 | * = 2.0 - tiny (if x <= -6) |
---|
| 119 | * erf(x) = sign(x)*(1.0 - erfc(x)) if x < 6, else |
---|
| 120 | * erf(x) = sign(x)*(1.0 - tiny) |
---|
| 121 | * where |
---|
| 122 | * R2(z) = degree 6 poly in z, (z=1/x^2) |
---|
| 123 | * S2(z) = degree 7 poly in z |
---|
| 124 | * |
---|
| 125 | * Note1: |
---|
| 126 | * To compute exp(-x*x-0.5625+R/S), let s be a single |
---|
| 127 | * precision number and s := x; then |
---|
| 128 | * -x*x = -s*s + (s-x)*(s+x) |
---|
| 129 | * exp(-x*x-0.5626+R/S) = |
---|
| 130 | * exp(-s*s-0.5625)*exp((s-x)*(s+x)+R/S); |
---|
| 131 | * Note2: |
---|
| 132 | * Here 4 and 5 make use of the asymptotic series |
---|
| 133 | * exp(-x*x) |
---|
| 134 | * erfc(x) ~ ---------- * ( 1 + Poly(1/x^2) ) |
---|
| 135 | * x*sqrt(pi) |
---|
| 136 | * We use rational approximation to approximate |
---|
| 137 | * g(s)=f(1/x^2) = log(erfc(x)*x) - x*x + 0.5625 |
---|
| 138 | * Here is the error bound for R1/S1 and R2/S2 |
---|
| 139 | * |R1/S1 - f(x)| < 2**(-62.57) |
---|
| 140 | * |R2/S2 - f(x)| < 2**(-61.52) |
---|
| 141 | * |
---|
| 142 | * 5. For inf > x >= 28 |
---|
| 143 | * erf(x) = sign(x) *(1 - tiny) (raise inexact) |
---|
| 144 | * erfc(x) = tiny*tiny (raise underflow) if x > 0 |
---|
| 145 | * = 2 - tiny if x<0 |
---|
| 146 | * |
---|
| 147 | * 7. Special case: |
---|
| 148 | * erf(0) = 0, erf(inf) = 1, erf(-inf) = -1, |
---|
| 149 | * erfc(0) = 1, erfc(inf) = 0, erfc(-inf) = 2, |
---|
| 150 | * erfc/erf(NaN) is NaN |
---|
| 151 | */ |
---|
| 152 | |
---|
| 153 | |
---|
| 154 | #include "fdlibm.h" |
---|
| 155 | |
---|
| 156 | #ifndef _DOUBLE_IS_32BITS |
---|
| 157 | |
---|
| 158 | #ifdef __STDC__ |
---|
| 159 | static const double |
---|
| 160 | #else |
---|
| 161 | static double |
---|
| 162 | #endif |
---|
| 163 | tiny = 1e-300, |
---|
| 164 | half= 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ |
---|
| 165 | one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ |
---|
| 166 | two = 2.00000000000000000000e+00, /* 0x40000000, 0x00000000 */ |
---|
| 167 | /* c = (float)0.84506291151 */ |
---|
| 168 | erx = 8.45062911510467529297e-01, /* 0x3FEB0AC1, 0x60000000 */ |
---|
| 169 | /* |
---|
| 170 | * Coefficients for approximation to erf on [0,0.84375] |
---|
| 171 | */ |
---|
| 172 | efx = 1.28379167095512586316e-01, /* 0x3FC06EBA, 0x8214DB69 */ |
---|
| 173 | efx8= 1.02703333676410069053e+00, /* 0x3FF06EBA, 0x8214DB69 */ |
---|
| 174 | pp0 = 1.28379167095512558561e-01, /* 0x3FC06EBA, 0x8214DB68 */ |
---|
| 175 | pp1 = -3.25042107247001499370e-01, /* 0xBFD4CD7D, 0x691CB913 */ |
---|
| 176 | pp2 = -2.84817495755985104766e-02, /* 0xBF9D2A51, 0xDBD7194F */ |
---|
| 177 | pp3 = -5.77027029648944159157e-03, /* 0xBF77A291, 0x236668E4 */ |
---|
| 178 | pp4 = -2.37630166566501626084e-05, /* 0xBEF8EAD6, 0x120016AC */ |
---|
| 179 | qq1 = 3.97917223959155352819e-01, /* 0x3FD97779, 0xCDDADC09 */ |
---|
| 180 | qq2 = 6.50222499887672944485e-02, /* 0x3FB0A54C, 0x5536CEBA */ |
---|
| 181 | qq3 = 5.08130628187576562776e-03, /* 0x3F74D022, 0xC4D36B0F */ |
---|
| 182 | qq4 = 1.32494738004321644526e-04, /* 0x3F215DC9, 0x221C1A10 */ |
---|
| 183 | qq5 = -3.96022827877536812320e-06, /* 0xBED09C43, 0x42A26120 */ |
---|
| 184 | /* |
---|
| 185 | * Coefficients for approximation to erf in [0.84375,1.25] |
---|
| 186 | */ |
---|
| 187 | pa0 = -2.36211856075265944077e-03, /* 0xBF6359B8, 0xBEF77538 */ |
---|
| 188 | pa1 = 4.14856118683748331666e-01, /* 0x3FDA8D00, 0xAD92B34D */ |
---|
| 189 | pa2 = -3.72207876035701323847e-01, /* 0xBFD7D240, 0xFBB8C3F1 */ |
---|
| 190 | pa3 = 3.18346619901161753674e-01, /* 0x3FD45FCA, 0x805120E4 */ |
---|
| 191 | pa4 = -1.10894694282396677476e-01, /* 0xBFBC6398, 0x3D3E28EC */ |
---|
| 192 | pa5 = 3.54783043256182359371e-02, /* 0x3FA22A36, 0x599795EB */ |
---|
| 193 | pa6 = -2.16637559486879084300e-03, /* 0xBF61BF38, 0x0A96073F */ |
---|
| 194 | qa1 = 1.06420880400844228286e-01, /* 0x3FBB3E66, 0x18EEE323 */ |
---|
| 195 | qa2 = 5.40397917702171048937e-01, /* 0x3FE14AF0, 0x92EB6F33 */ |
---|
| 196 | qa3 = 7.18286544141962662868e-02, /* 0x3FB2635C, 0xD99FE9A7 */ |
---|
| 197 | qa4 = 1.26171219808761642112e-01, /* 0x3FC02660, 0xE763351F */ |
---|
| 198 | qa5 = 1.36370839120290507362e-02, /* 0x3F8BEDC2, 0x6B51DD1C */ |
---|
| 199 | qa6 = 1.19844998467991074170e-02, /* 0x3F888B54, 0x5735151D */ |
---|
| 200 | /* |
---|
| 201 | * Coefficients for approximation to erfc in [1.25,1/0.35] |
---|
| 202 | */ |
---|
| 203 | ra0 = -9.86494403484714822705e-03, /* 0xBF843412, 0x600D6435 */ |
---|
| 204 | ra1 = -6.93858572707181764372e-01, /* 0xBFE63416, 0xE4BA7360 */ |
---|
| 205 | ra2 = -1.05586262253232909814e+01, /* 0xC0251E04, 0x41B0E726 */ |
---|
| 206 | ra3 = -6.23753324503260060396e+01, /* 0xC04F300A, 0xE4CBA38D */ |
---|
| 207 | ra4 = -1.62396669462573470355e+02, /* 0xC0644CB1, 0x84282266 */ |
---|
| 208 | ra5 = -1.84605092906711035994e+02, /* 0xC067135C, 0xEBCCABB2 */ |
---|
| 209 | ra6 = -8.12874355063065934246e+01, /* 0xC0545265, 0x57E4D2F2 */ |
---|
| 210 | ra7 = -9.81432934416914548592e+00, /* 0xC023A0EF, 0xC69AC25C */ |
---|
| 211 | sa1 = 1.96512716674392571292e+01, /* 0x4033A6B9, 0xBD707687 */ |
---|
| 212 | sa2 = 1.37657754143519042600e+02, /* 0x4061350C, 0x526AE721 */ |
---|
| 213 | sa3 = 4.34565877475229228821e+02, /* 0x407B290D, 0xD58A1A71 */ |
---|
| 214 | sa4 = 6.45387271733267880336e+02, /* 0x40842B19, 0x21EC2868 */ |
---|
| 215 | sa5 = 4.29008140027567833386e+02, /* 0x407AD021, 0x57700314 */ |
---|
| 216 | sa6 = 1.08635005541779435134e+02, /* 0x405B28A3, 0xEE48AE2C */ |
---|
| 217 | sa7 = 6.57024977031928170135e+00, /* 0x401A47EF, 0x8E484A93 */ |
---|
| 218 | sa8 = -6.04244152148580987438e-02, /* 0xBFAEEFF2, 0xEE749A62 */ |
---|
| 219 | /* |
---|
| 220 | * Coefficients for approximation to erfc in [1/.35,28] |
---|
| 221 | */ |
---|
| 222 | rb0 = -9.86494292470009928597e-03, /* 0xBF843412, 0x39E86F4A */ |
---|
| 223 | rb1 = -7.99283237680523006574e-01, /* 0xBFE993BA, 0x70C285DE */ |
---|
| 224 | rb2 = -1.77579549177547519889e+01, /* 0xC031C209, 0x555F995A */ |
---|
| 225 | rb3 = -1.60636384855821916062e+02, /* 0xC064145D, 0x43C5ED98 */ |
---|
| 226 | rb4 = -6.37566443368389627722e+02, /* 0xC083EC88, 0x1375F228 */ |
---|
| 227 | rb5 = -1.02509513161107724954e+03, /* 0xC0900461, 0x6A2E5992 */ |
---|
| 228 | rb6 = -4.83519191608651397019e+02, /* 0xC07E384E, 0x9BDC383F */ |
---|
| 229 | sb1 = 3.03380607434824582924e+01, /* 0x403E568B, 0x261D5190 */ |
---|
| 230 | sb2 = 3.25792512996573918826e+02, /* 0x40745CAE, 0x221B9F0A */ |
---|
| 231 | sb3 = 1.53672958608443695994e+03, /* 0x409802EB, 0x189D5118 */ |
---|
| 232 | sb4 = 3.19985821950859553908e+03, /* 0x40A8FFB7, 0x688C246A */ |
---|
| 233 | sb5 = 2.55305040643316442583e+03, /* 0x40A3F219, 0xCEDF3BE6 */ |
---|
| 234 | sb6 = 4.74528541206955367215e+02, /* 0x407DA874, 0xE79FE763 */ |
---|
| 235 | sb7 = -2.24409524465858183362e+01; /* 0xC03670E2, 0x42712D62 */ |
---|
| 236 | |
---|
| 237 | #ifdef __STDC__ |
---|
| 238 | double erf(double x) |
---|
| 239 | #else |
---|
| 240 | double erf(x) |
---|
| 241 | double x; |
---|
| 242 | #endif |
---|
| 243 | { |
---|
| 244 | __int32_t hx,ix,i; |
---|
| 245 | double R,S,P,Q,s,y,z,r; |
---|
| 246 | GET_HIGH_WORD(hx,x); |
---|
| 247 | ix = hx&0x7fffffff; |
---|
| 248 | if(ix>=0x7ff00000) { /* erf(nan)=nan */ |
---|
| 249 | i = ((__uint32_t)hx>>31)<<1; |
---|
| 250 | return (double)(1-i)+one/x; /* erf(+-inf)=+-1 */ |
---|
| 251 | } |
---|
| 252 | |
---|
| 253 | if(ix < 0x3feb0000) { /* |x|<0.84375 */ |
---|
| 254 | if(ix < 0x3e300000) { /* |x|<2**-28 */ |
---|
| 255 | if (ix < 0x00800000) |
---|
| 256 | return 0.125*(8.0*x+efx8*x); /*avoid underflow */ |
---|
| 257 | return x + efx*x; |
---|
| 258 | } |
---|
| 259 | z = x*x; |
---|
| 260 | r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4))); |
---|
| 261 | s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))); |
---|
| 262 | y = r/s; |
---|
| 263 | return x + x*y; |
---|
| 264 | } |
---|
| 265 | if(ix < 0x3ff40000) { /* 0.84375 <= |x| < 1.25 */ |
---|
| 266 | s = fabs(x)-one; |
---|
| 267 | P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6))))); |
---|
| 268 | Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6))))); |
---|
| 269 | if(hx>=0) return erx + P/Q; else return -erx - P/Q; |
---|
| 270 | } |
---|
| 271 | if (ix >= 0x40180000) { /* inf>|x|>=6 */ |
---|
| 272 | if(hx>=0) return one-tiny; else return tiny-one; |
---|
| 273 | } |
---|
| 274 | x = fabs(x); |
---|
| 275 | s = one/(x*x); |
---|
| 276 | if(ix< 0x4006DB6E) { /* |x| < 1/0.35 */ |
---|
| 277 | R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*( |
---|
| 278 | ra5+s*(ra6+s*ra7)))))); |
---|
| 279 | S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*( |
---|
| 280 | sa5+s*(sa6+s*(sa7+s*sa8))))))); |
---|
| 281 | } else { /* |x| >= 1/0.35 */ |
---|
| 282 | R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*( |
---|
| 283 | rb5+s*rb6))))); |
---|
| 284 | S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*( |
---|
| 285 | sb5+s*(sb6+s*sb7)))))); |
---|
| 286 | } |
---|
| 287 | z = x; |
---|
| 288 | SET_LOW_WORD(z,0); |
---|
| 289 | r = exp(-z*z-0.5625)*exp((z-x)*(z+x)+R/S); |
---|
| 290 | if(hx>=0) return one-r/x; else return r/x-one; |
---|
| 291 | } |
---|
| 292 | |
---|
| 293 | #ifdef __STDC__ |
---|
| 294 | double erfc(double x) |
---|
| 295 | #else |
---|
| 296 | double erfc(x) |
---|
| 297 | double x; |
---|
| 298 | #endif |
---|
| 299 | { |
---|
| 300 | __int32_t hx,ix; |
---|
| 301 | double R,S,P,Q,s,y,z,r; |
---|
| 302 | GET_HIGH_WORD(hx,x); |
---|
| 303 | ix = hx&0x7fffffff; |
---|
| 304 | if(ix>=0x7ff00000) { /* erfc(nan)=nan */ |
---|
| 305 | /* erfc(+-inf)=0,2 */ |
---|
| 306 | return (double)(((__uint32_t)hx>>31)<<1)+one/x; |
---|
| 307 | } |
---|
| 308 | |
---|
| 309 | if(ix < 0x3feb0000) { /* |x|<0.84375 */ |
---|
| 310 | if(ix < 0x3c700000) /* |x|<2**-56 */ |
---|
| 311 | return one-x; |
---|
| 312 | z = x*x; |
---|
| 313 | r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4))); |
---|
| 314 | s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))); |
---|
| 315 | y = r/s; |
---|
| 316 | if(hx < 0x3fd00000) { /* x<1/4 */ |
---|
| 317 | return one-(x+x*y); |
---|
| 318 | } else { |
---|
| 319 | r = x*y; |
---|
| 320 | r += (x-half); |
---|
| 321 | return half - r ; |
---|
| 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+s*pa6))))); |
---|
| 327 | Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6))))); |
---|
| 328 | if(hx>=0) { |
---|
| 329 | z = one-erx; return z - P/Q; |
---|
| 330 | } else { |
---|
| 331 | z = erx+P/Q; return one+z; |
---|
| 332 | } |
---|
| 333 | } |
---|
| 334 | if (ix < 0x403c0000) { /* |x|<28 */ |
---|
| 335 | x = fabs(x); |
---|
| 336 | s = one/(x*x); |
---|
| 337 | if(ix< 0x4006DB6D) { /* |x| < 1/.35 ~ 2.857143*/ |
---|
| 338 | R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*( |
---|
| 339 | ra5+s*(ra6+s*ra7)))))); |
---|
| 340 | S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*( |
---|
| 341 | sa5+s*(sa6+s*(sa7+s*sa8))))))); |
---|
| 342 | } else { /* |x| >= 1/.35 ~ 2.857143 */ |
---|
| 343 | if(hx<0&&ix>=0x40180000) return two-tiny;/* x < -6 */ |
---|
| 344 | R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*( |
---|
| 345 | rb5+s*rb6))))); |
---|
| 346 | S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*( |
---|
| 347 | sb5+s*(sb6+s*sb7)))))); |
---|
| 348 | } |
---|
| 349 | z = x; |
---|
| 350 | SET_LOW_WORD(z,0); |
---|
| 351 | r = exp(-z*z-0.5625)* |
---|
| 352 | exp((z-x)*(z+x)+R/S); |
---|
| 353 | if(hx>0) return r/x; else return two-r/x; |
---|
| 354 | } else { |
---|
| 355 | if(hx>0) return tiny*tiny; else return two-tiny; |
---|
| 356 | } |
---|
| 357 | } |
---|
| 358 | |
---|
| 359 | #endif /* _DOUBLE_IS_32BITS */ |
---|