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f7eac6eb RM |
1 | /* @(#)s_erf.c 5.1 93/09/24 */ |
2 | /* | |
3 | * ==================================================== | |
4 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. | |
5 | * | |
6 | * Developed at SunPro, a Sun Microsystems, Inc. business. | |
7 | * Permission to use, copy, modify, and distribute this | |
cccda09f | 8 | * software is freely granted, provided that this notice |
f7eac6eb RM |
9 | * is preserved. |
10 | * ==================================================== | |
11 | */ | |
923609d1 UD |
12 | /* Modified by Naohiko Shimizu/Tokai University, Japan 1997/08/25, |
13 | for performance improvement on pipelined processors. | |
14 | */ | |
f7eac6eb RM |
15 | |
16 | #if defined(LIBM_SCCS) && !defined(lint) | |
17 | static char rcsid[] = "$NetBSD: s_erf.c,v 1.8 1995/05/10 20:47:05 jtc Exp $"; | |
18 | #endif | |
19 | ||
20 | /* double erf(double x) | |
21 | * double erfc(double x) | |
22 | * x | |
23 | * 2 |\ | |
24 | * erf(x) = --------- | exp(-t*t)dt | |
cccda09f | 25 | * sqrt(pi) \| |
f7eac6eb RM |
26 | * 0 |
27 | * | |
28 | * erfc(x) = 1-erf(x) | |
cccda09f | 29 | * Note that |
f7eac6eb RM |
30 | * erf(-x) = -erf(x) |
31 | * erfc(-x) = 2 - erfc(x) | |
32 | * | |
33 | * Method: | |
34 | * 1. For |x| in [0, 0.84375] | |
35 | * erf(x) = x + x*R(x^2) | |
36 | * erfc(x) = 1 - erf(x) if x in [-.84375,0.25] | |
37 | * = 0.5 + ((0.5-x)-x*R) if x in [0.25,0.84375] | |
38 | * where R = P/Q where P is an odd poly of degree 8 and | |
39 | * Q is an odd poly of degree 10. | |
40 | * -57.90 | |
41 | * | R - (erf(x)-x)/x | <= 2 | |
cccda09f | 42 | * |
f7eac6eb RM |
43 | * |
44 | * Remark. The formula is derived by noting | |
45 | * erf(x) = (2/sqrt(pi))*(x - x^3/3 + x^5/10 - x^7/42 + ....) | |
46 | * and that | |
47 | * 2/sqrt(pi) = 1.128379167095512573896158903121545171688 | |
48 | * is close to one. The interval is chosen because the fix | |
49 | * point of erf(x) is near 0.6174 (i.e., erf(x)=x when x is | |
50 | * near 0.6174), and by some experiment, 0.84375 is chosen to | |
51 | * guarantee the error is less than one ulp for erf. | |
52 | * | |
53 | * 2. For |x| in [0.84375,1.25], let s = |x| - 1, and | |
54 | * c = 0.84506291151 rounded to single (24 bits) | |
55 | * erf(x) = sign(x) * (c + P1(s)/Q1(s)) | |
56 | * erfc(x) = (1-c) - P1(s)/Q1(s) if x > 0 | |
57 | * 1+(c+P1(s)/Q1(s)) if x < 0 | |
58 | * |P1/Q1 - (erf(|x|)-c)| <= 2**-59.06 | |
59 | * Remark: here we use the taylor series expansion at x=1. | |
60 | * erf(1+s) = erf(1) + s*Poly(s) | |
61 | * = 0.845.. + P1(s)/Q1(s) | |
62 | * That is, we use rational approximation to approximate | |
63 | * erf(1+s) - (c = (single)0.84506291151) | |
64 | * Note that |P1/Q1|< 0.078 for x in [0.84375,1.25] | |
cccda09f | 65 | * where |
f7eac6eb RM |
66 | * P1(s) = degree 6 poly in s |
67 | * Q1(s) = degree 6 poly in s | |
68 | * | |
cccda09f | 69 | * 3. For x in [1.25,1/0.35(~2.857143)], |
f7eac6eb RM |
70 | * erfc(x) = (1/x)*exp(-x*x-0.5625+R1/S1) |
71 | * erf(x) = 1 - erfc(x) | |
cccda09f | 72 | * where |
f7eac6eb RM |
73 | * R1(z) = degree 7 poly in z, (z=1/x^2) |
74 | * S1(z) = degree 8 poly in z | |
75 | * | |
76 | * 4. For x in [1/0.35,28] | |
77 | * erfc(x) = (1/x)*exp(-x*x-0.5625+R2/S2) if x > 0 | |
78 | * = 2.0 - (1/x)*exp(-x*x-0.5625+R2/S2) if -6<x<0 | |
79 | * = 2.0 - tiny (if x <= -6) | |
80 | * erf(x) = sign(x)*(1.0 - erfc(x)) if x < 6, else | |
81 | * erf(x) = sign(x)*(1.0 - tiny) | |
82 | * where | |
83 | * R2(z) = degree 6 poly in z, (z=1/x^2) | |
84 | * S2(z) = degree 7 poly in z | |
85 | * | |
86 | * Note1: | |
87 | * To compute exp(-x*x-0.5625+R/S), let s be a single | |
88 | * precision number and s := x; then | |
89 | * -x*x = -s*s + (s-x)*(s+x) | |
cccda09f | 90 | * exp(-x*x-0.5626+R/S) = |
f7eac6eb RM |
91 | * exp(-s*s-0.5625)*exp((s-x)*(s+x)+R/S); |
92 | * Note2: | |
93 | * Here 4 and 5 make use of the asymptotic series | |
94 | * exp(-x*x) | |
95 | * erfc(x) ~ ---------- * ( 1 + Poly(1/x^2) ) | |
96 | * x*sqrt(pi) | |
97 | * We use rational approximation to approximate | |
98 | * g(s)=f(1/x^2) = log(erfc(x)*x) - x*x + 0.5625 | |
99 | * Here is the error bound for R1/S1 and R2/S2 | |
100 | * |R1/S1 - f(x)| < 2**(-62.57) | |
101 | * |R2/S2 - f(x)| < 2**(-61.52) | |
102 | * | |
103 | * 5. For inf > x >= 28 | |
104 | * erf(x) = sign(x) *(1 - tiny) (raise inexact) | |
105 | * erfc(x) = tiny*tiny (raise underflow) if x > 0 | |
106 | * = 2 - tiny if x<0 | |
107 | * | |
108 | * 7. Special case: | |
109 | * erf(0) = 0, erf(inf) = 1, erf(-inf) = -1, | |
cccda09f | 110 | * erfc(0) = 1, erfc(inf) = 0, erfc(-inf) = 2, |
f7eac6eb RM |
111 | * erfc/erf(NaN) is NaN |
112 | */ | |
113 | ||
114 | ||
34e16df5 JM |
115 | #include <errno.h> |
116 | #include <float.h> | |
1ed0291c | 117 | #include <math.h> |
aaee3cd8 | 118 | #include <math-narrow-eval.h> |
1ed0291c | 119 | #include <math_private.h> |
8f5b00d3 | 120 | #include <math-underflow.h> |
1e2bffd0 | 121 | #include <libm-alias-double.h> |
bc375363 | 122 | #include <fix-int-fp-convert-zero.h> |
f7eac6eb | 123 | |
f7eac6eb | 124 | static const double |
c5d5d574 OB |
125 | tiny = 1e-300, |
126 | half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ | |
127 | one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ | |
128 | two = 2.00000000000000000000e+00, /* 0x40000000, 0x00000000 */ | |
129 | /* c = (float)0.84506291151 */ | |
130 | erx = 8.45062911510467529297e-01, /* 0x3FEB0AC1, 0x60000000 */ | |
f7eac6eb RM |
131 | /* |
132 | * Coefficients for approximation to erf on [0,0.84375] | |
133 | */ | |
c5d5d574 | 134 | efx = 1.28379167095512586316e-01, /* 0x3FC06EBA, 0x8214DB69 */ |
c5d5d574 OB |
135 | pp[] = { 1.28379167095512558561e-01, /* 0x3FC06EBA, 0x8214DB68 */ |
136 | -3.25042107247001499370e-01, /* 0xBFD4CD7D, 0x691CB913 */ | |
137 | -2.84817495755985104766e-02, /* 0xBF9D2A51, 0xDBD7194F */ | |
138 | -5.77027029648944159157e-03, /* 0xBF77A291, 0x236668E4 */ | |
139 | -2.37630166566501626084e-05 }, /* 0xBEF8EAD6, 0x120016AC */ | |
140 | qq[] = { 0.0, 3.97917223959155352819e-01, /* 0x3FD97779, 0xCDDADC09 */ | |
141 | 6.50222499887672944485e-02, /* 0x3FB0A54C, 0x5536CEBA */ | |
142 | 5.08130628187576562776e-03, /* 0x3F74D022, 0xC4D36B0F */ | |
143 | 1.32494738004321644526e-04, /* 0x3F215DC9, 0x221C1A10 */ | |
144 | -3.96022827877536812320e-06 }, /* 0xBED09C43, 0x42A26120 */ | |
f7eac6eb | 145 | /* |
cccda09f | 146 | * Coefficients for approximation to erf in [0.84375,1.25] |
f7eac6eb | 147 | */ |
c5d5d574 OB |
148 | pa[] = { -2.36211856075265944077e-03, /* 0xBF6359B8, 0xBEF77538 */ |
149 | 4.14856118683748331666e-01, /* 0x3FDA8D00, 0xAD92B34D */ | |
150 | -3.72207876035701323847e-01, /* 0xBFD7D240, 0xFBB8C3F1 */ | |
151 | 3.18346619901161753674e-01, /* 0x3FD45FCA, 0x805120E4 */ | |
152 | -1.10894694282396677476e-01, /* 0xBFBC6398, 0x3D3E28EC */ | |
153 | 3.54783043256182359371e-02, /* 0x3FA22A36, 0x599795EB */ | |
154 | -2.16637559486879084300e-03 }, /* 0xBF61BF38, 0x0A96073F */ | |
155 | qa[] = { 0.0, 1.06420880400844228286e-01, /* 0x3FBB3E66, 0x18EEE323 */ | |
156 | 5.40397917702171048937e-01, /* 0x3FE14AF0, 0x92EB6F33 */ | |
157 | 7.18286544141962662868e-02, /* 0x3FB2635C, 0xD99FE9A7 */ | |
158 | 1.26171219808761642112e-01, /* 0x3FC02660, 0xE763351F */ | |
159 | 1.36370839120290507362e-02, /* 0x3F8BEDC2, 0x6B51DD1C */ | |
160 | 1.19844998467991074170e-02 }, /* 0x3F888B54, 0x5735151D */ | |
f7eac6eb RM |
161 | /* |
162 | * Coefficients for approximation to erfc in [1.25,1/0.35] | |
163 | */ | |
c5d5d574 OB |
164 | ra[] = { -9.86494403484714822705e-03, /* 0xBF843412, 0x600D6435 */ |
165 | -6.93858572707181764372e-01, /* 0xBFE63416, 0xE4BA7360 */ | |
166 | -1.05586262253232909814e+01, /* 0xC0251E04, 0x41B0E726 */ | |
167 | -6.23753324503260060396e+01, /* 0xC04F300A, 0xE4CBA38D */ | |
168 | -1.62396669462573470355e+02, /* 0xC0644CB1, 0x84282266 */ | |
169 | -1.84605092906711035994e+02, /* 0xC067135C, 0xEBCCABB2 */ | |
170 | -8.12874355063065934246e+01, /* 0xC0545265, 0x57E4D2F2 */ | |
171 | -9.81432934416914548592e+00 }, /* 0xC023A0EF, 0xC69AC25C */ | |
172 | sa[] = { 0.0, 1.96512716674392571292e+01, /* 0x4033A6B9, 0xBD707687 */ | |
173 | 1.37657754143519042600e+02, /* 0x4061350C, 0x526AE721 */ | |
174 | 4.34565877475229228821e+02, /* 0x407B290D, 0xD58A1A71 */ | |
175 | 6.45387271733267880336e+02, /* 0x40842B19, 0x21EC2868 */ | |
176 | 4.29008140027567833386e+02, /* 0x407AD021, 0x57700314 */ | |
177 | 1.08635005541779435134e+02, /* 0x405B28A3, 0xEE48AE2C */ | |
178 | 6.57024977031928170135e+00, /* 0x401A47EF, 0x8E484A93 */ | |
179 | -6.04244152148580987438e-02 }, /* 0xBFAEEFF2, 0xEE749A62 */ | |
f7eac6eb RM |
180 | /* |
181 | * Coefficients for approximation to erfc in [1/.35,28] | |
182 | */ | |
c5d5d574 OB |
183 | rb[] = { -9.86494292470009928597e-03, /* 0xBF843412, 0x39E86F4A */ |
184 | -7.99283237680523006574e-01, /* 0xBFE993BA, 0x70C285DE */ | |
185 | -1.77579549177547519889e+01, /* 0xC031C209, 0x555F995A */ | |
186 | -1.60636384855821916062e+02, /* 0xC064145D, 0x43C5ED98 */ | |
187 | -6.37566443368389627722e+02, /* 0xC083EC88, 0x1375F228 */ | |
188 | -1.02509513161107724954e+03, /* 0xC0900461, 0x6A2E5992 */ | |
189 | -4.83519191608651397019e+02 }, /* 0xC07E384E, 0x9BDC383F */ | |
190 | sb[] = { 0.0, 3.03380607434824582924e+01, /* 0x403E568B, 0x261D5190 */ | |
191 | 3.25792512996573918826e+02, /* 0x40745CAE, 0x221B9F0A */ | |
192 | 1.53672958608443695994e+03, /* 0x409802EB, 0x189D5118 */ | |
193 | 3.19985821950859553908e+03, /* 0x40A8FFB7, 0x688C246A */ | |
194 | 2.55305040643316442583e+03, /* 0x40A3F219, 0xCEDF3BE6 */ | |
195 | 4.74528541206955367215e+02, /* 0x407DA874, 0xE79FE763 */ | |
196 | -2.24409524465858183362e+01 }; /* 0xC03670E2, 0x42712D62 */ | |
f7eac6eb | 197 | |
c5d5d574 OB |
198 | double |
199 | __erf (double x) | |
f7eac6eb | 200 | { |
c5d5d574 OB |
201 | int32_t hx, ix, i; |
202 | double R, S, P, Q, s, y, z, r; | |
203 | GET_HIGH_WORD (hx, x); | |
204 | ix = hx & 0x7fffffff; | |
205 | if (ix >= 0x7ff00000) /* erf(nan)=nan */ | |
206 | { | |
24ab7723 | 207 | i = ((uint32_t) hx >> 31) << 1; |
c5d5d574 OB |
208 | return (double) (1 - i) + one / x; /* erf(+-inf)=+-1 */ |
209 | } | |
f7eac6eb | 210 | |
c5d5d574 OB |
211 | if (ix < 0x3feb0000) /* |x|<0.84375 */ |
212 | { | |
213 | double r1, r2, s1, s2, s3, z2, z4; | |
214 | if (ix < 0x3e300000) /* |x|<2**-28 */ | |
215 | { | |
216 | if (ix < 0x00800000) | |
0bf061d3 JM |
217 | { |
218 | /* Avoid spurious underflow. */ | |
219 | double ret = 0.0625 * (16.0 * x + (16.0 * efx) * x); | |
d96164c3 | 220 | math_check_force_underflow (ret); |
0bf061d3 JM |
221 | return ret; |
222 | } | |
c5d5d574 | 223 | return x + efx * x; |
f7eac6eb | 224 | } |
c5d5d574 OB |
225 | z = x * x; |
226 | r1 = pp[0] + z * pp[1]; z2 = z * z; | |
227 | r2 = pp[2] + z * pp[3]; z4 = z2 * z2; | |
228 | s1 = one + z * qq[1]; | |
229 | s2 = qq[2] + z * qq[3]; | |
230 | s3 = qq[4] + z * qq[5]; | |
231 | r = r1 + z2 * r2 + z4 * pp[4]; | |
232 | s = s1 + z2 * s2 + z4 * s3; | |
233 | y = r / s; | |
234 | return x + x * y; | |
235 | } | |
236 | if (ix < 0x3ff40000) /* 0.84375 <= |x| < 1.25 */ | |
237 | { | |
238 | double s2, s4, s6, P1, P2, P3, P4, Q1, Q2, Q3, Q4; | |
239 | s = fabs (x) - one; | |
240 | P1 = pa[0] + s * pa[1]; s2 = s * s; | |
241 | Q1 = one + s * qa[1]; s4 = s2 * s2; | |
242 | P2 = pa[2] + s * pa[3]; s6 = s4 * s2; | |
243 | Q2 = qa[2] + s * qa[3]; | |
244 | P3 = pa[4] + s * pa[5]; | |
245 | Q3 = qa[4] + s * qa[5]; | |
246 | P4 = pa[6]; | |
247 | Q4 = qa[6]; | |
248 | P = P1 + s2 * P2 + s4 * P3 + s6 * P4; | |
249 | Q = Q1 + s2 * Q2 + s4 * Q3 + s6 * Q4; | |
250 | if (hx >= 0) | |
251 | return erx + P / Q; | |
252 | else | |
253 | return -erx - P / Q; | |
254 | } | |
255 | if (ix >= 0x40180000) /* inf>|x|>=6 */ | |
256 | { | |
257 | if (hx >= 0) | |
258 | return one - tiny; | |
259 | else | |
260 | return tiny - one; | |
261 | } | |
262 | x = fabs (x); | |
263 | s = one / (x * x); | |
264 | if (ix < 0x4006DB6E) /* |x| < 1/0.35 */ | |
265 | { | |
266 | double R1, R2, R3, R4, S1, S2, S3, S4, s2, s4, s6, s8; | |
267 | R1 = ra[0] + s * ra[1]; s2 = s * s; | |
268 | S1 = one + s * sa[1]; s4 = s2 * s2; | |
269 | R2 = ra[2] + s * ra[3]; s6 = s4 * s2; | |
270 | S2 = sa[2] + s * sa[3]; s8 = s4 * s4; | |
271 | R3 = ra[4] + s * ra[5]; | |
272 | S3 = sa[4] + s * sa[5]; | |
273 | R4 = ra[6] + s * ra[7]; | |
274 | S4 = sa[6] + s * sa[7]; | |
275 | R = R1 + s2 * R2 + s4 * R3 + s6 * R4; | |
276 | S = S1 + s2 * S2 + s4 * S3 + s6 * S4 + s8 * sa[8]; | |
277 | } | |
278 | else /* |x| >= 1/0.35 */ | |
279 | { | |
280 | double R1, R2, R3, S1, S2, S3, S4, s2, s4, s6; | |
281 | R1 = rb[0] + s * rb[1]; s2 = s * s; | |
282 | S1 = one + s * sb[1]; s4 = s2 * s2; | |
283 | R2 = rb[2] + s * rb[3]; s6 = s4 * s2; | |
284 | S2 = sb[2] + s * sb[3]; | |
285 | R3 = rb[4] + s * rb[5]; | |
286 | S3 = sb[4] + s * sb[5]; | |
287 | S4 = sb[6] + s * sb[7]; | |
288 | R = R1 + s2 * R2 + s4 * R3 + s6 * rb[6]; | |
289 | S = S1 + s2 * S2 + s4 * S3 + s6 * S4; | |
290 | } | |
291 | z = x; | |
292 | SET_LOW_WORD (z, 0); | |
293 | r = __ieee754_exp (-z * z - 0.5625) * | |
294 | __ieee754_exp ((z - x) * (z + x) + R / S); | |
295 | if (hx >= 0) | |
296 | return one - r / x; | |
297 | else | |
298 | return r / x - one; | |
f7eac6eb | 299 | } |
1e2bffd0 | 300 | libm_alias_double (__erf, erf) |
f7eac6eb | 301 | |
c5d5d574 OB |
302 | double |
303 | __erfc (double x) | |
f7eac6eb | 304 | { |
c5d5d574 OB |
305 | int32_t hx, ix; |
306 | double R, S, P, Q, s, y, z, r; | |
307 | GET_HIGH_WORD (hx, x); | |
308 | ix = hx & 0x7fffffff; | |
309 | if (ix >= 0x7ff00000) /* erfc(nan)=nan */ | |
310 | { /* erfc(+-inf)=0,2 */ | |
24ab7723 | 311 | double ret = (double) (((uint32_t) hx >> 31) << 1) + one / x; |
bc375363 JM |
312 | if (FIX_INT_FP_CONVERT_ZERO && ret == 0.0) |
313 | return 0.0; | |
314 | return ret; | |
c5d5d574 | 315 | } |
f7eac6eb | 316 | |
c5d5d574 OB |
317 | if (ix < 0x3feb0000) /* |x|<0.84375 */ |
318 | { | |
319 | double r1, r2, s1, s2, s3, z2, z4; | |
320 | if (ix < 0x3c700000) /* |x|<2**-56 */ | |
321 | return one - x; | |
322 | z = x * x; | |
323 | r1 = pp[0] + z * pp[1]; z2 = z * z; | |
324 | r2 = pp[2] + z * pp[3]; z4 = z2 * z2; | |
325 | s1 = one + z * qq[1]; | |
326 | s2 = qq[2] + z * qq[3]; | |
327 | s3 = qq[4] + z * qq[5]; | |
328 | r = r1 + z2 * r2 + z4 * pp[4]; | |
329 | s = s1 + z2 * s2 + z4 * s3; | |
330 | y = r / s; | |
331 | if (hx < 0x3fd00000) /* x<1/4 */ | |
332 | { | |
333 | return one - (x + x * y); | |
334 | } | |
335 | else | |
336 | { | |
337 | r = x * y; | |
338 | r += (x - half); | |
339 | return half - r; | |
340 | } | |
341 | } | |
342 | if (ix < 0x3ff40000) /* 0.84375 <= |x| < 1.25 */ | |
343 | { | |
344 | double s2, s4, s6, P1, P2, P3, P4, Q1, Q2, Q3, Q4; | |
345 | s = fabs (x) - one; | |
346 | P1 = pa[0] + s * pa[1]; s2 = s * s; | |
347 | Q1 = one + s * qa[1]; s4 = s2 * s2; | |
348 | P2 = pa[2] + s * pa[3]; s6 = s4 * s2; | |
349 | Q2 = qa[2] + s * qa[3]; | |
350 | P3 = pa[4] + s * pa[5]; | |
351 | Q3 = qa[4] + s * qa[5]; | |
352 | P4 = pa[6]; | |
353 | Q4 = qa[6]; | |
354 | P = P1 + s2 * P2 + s4 * P3 + s6 * P4; | |
355 | Q = Q1 + s2 * Q2 + s4 * Q3 + s6 * Q4; | |
356 | if (hx >= 0) | |
357 | { | |
358 | z = one - erx; return z - P / Q; | |
359 | } | |
360 | else | |
361 | { | |
362 | z = erx + P / Q; return one + z; | |
f7eac6eb | 363 | } |
c5d5d574 OB |
364 | } |
365 | if (ix < 0x403c0000) /* |x|<28 */ | |
366 | { | |
367 | x = fabs (x); | |
368 | s = one / (x * x); | |
369 | if (ix < 0x4006DB6D) /* |x| < 1/.35 ~ 2.857143*/ | |
370 | { | |
371 | double R1, R2, R3, R4, S1, S2, S3, S4, s2, s4, s6, s8; | |
372 | R1 = ra[0] + s * ra[1]; s2 = s * s; | |
373 | S1 = one + s * sa[1]; s4 = s2 * s2; | |
374 | R2 = ra[2] + s * ra[3]; s6 = s4 * s2; | |
375 | S2 = sa[2] + s * sa[3]; s8 = s4 * s4; | |
376 | R3 = ra[4] + s * ra[5]; | |
377 | S3 = sa[4] + s * sa[5]; | |
378 | R4 = ra[6] + s * ra[7]; | |
379 | S4 = sa[6] + s * sa[7]; | |
380 | R = R1 + s2 * R2 + s4 * R3 + s6 * R4; | |
381 | S = S1 + s2 * S2 + s4 * S3 + s6 * S4 + s8 * sa[8]; | |
f7eac6eb | 382 | } |
c5d5d574 OB |
383 | else /* |x| >= 1/.35 ~ 2.857143 */ |
384 | { | |
385 | double R1, R2, R3, S1, S2, S3, S4, s2, s4, s6; | |
386 | if (hx < 0 && ix >= 0x40180000) | |
387 | return two - tiny; /* x < -6 */ | |
388 | R1 = rb[0] + s * rb[1]; s2 = s * s; | |
389 | S1 = one + s * sb[1]; s4 = s2 * s2; | |
390 | R2 = rb[2] + s * rb[3]; s6 = s4 * s2; | |
391 | S2 = sb[2] + s * sb[3]; | |
392 | R3 = rb[4] + s * rb[5]; | |
393 | S3 = sb[4] + s * sb[5]; | |
394 | S4 = sb[6] + s * sb[7]; | |
395 | R = R1 + s2 * R2 + s4 * R3 + s6 * rb[6]; | |
396 | S = S1 + s2 * S2 + s4 * S3 + s6 * S4; | |
f7eac6eb | 397 | } |
c5d5d574 OB |
398 | z = x; |
399 | SET_LOW_WORD (z, 0); | |
400 | r = __ieee754_exp (-z * z - 0.5625) * | |
401 | __ieee754_exp ((z - x) * (z + x) + R / S); | |
402 | if (hx > 0) | |
34e16df5 | 403 | { |
54142c44 | 404 | double ret = math_narrow_eval (r / x); |
34e16df5 JM |
405 | if (ret == 0) |
406 | __set_errno (ERANGE); | |
407 | return ret; | |
408 | } | |
c5d5d574 OB |
409 | else |
410 | return two - r / x; | |
411 | } | |
412 | else | |
413 | { | |
414 | if (hx > 0) | |
34e16df5 JM |
415 | { |
416 | __set_errno (ERANGE); | |
417 | return tiny * tiny; | |
418 | } | |
c5d5d574 OB |
419 | else |
420 | return two - tiny; | |
421 | } | |
f7eac6eb | 422 | } |
1e2bffd0 | 423 | libm_alias_double (__erfc, erfc) |