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11210 libm should be cstyle(1ONBLD) clean
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--- old/usr/src/lib/libm/common/C/erf.c
+++ new/usr/src/lib/libm/common/C/erf.c
1 1 /*
2 2 * CDDL HEADER START
3 3 *
4 4 * The contents of this file are subject to the terms of the
5 5 * Common Development and Distribution License (the "License").
6 6 * You may not use this file except in compliance with the License.
7 7 *
8 8 * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
9 9 * or http://www.opensolaris.org/os/licensing.
10 10 * See the License for the specific language governing permissions
11 11 * and limitations under the License.
12 12 *
13 13 * When distributing Covered Code, include this CDDL HEADER in each
14 14 * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
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15 15 * If applicable, add the following below this CDDL HEADER, with the
16 16 * fields enclosed by brackets "[]" replaced with your own identifying
17 17 * information: Portions Copyright [yyyy] [name of copyright owner]
18 18 *
19 19 * CDDL HEADER END
20 20 */
21 21
22 22 /*
23 23 * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
24 24 */
25 +
25 26 /*
26 27 * Copyright 2006 Sun Microsystems, Inc. All rights reserved.
27 28 * Use is subject to license terms.
28 29 */
29 30
30 31 #pragma weak __erf = erf
31 32 #pragma weak __erfc = erfc
32 33
33 -/* INDENT OFF */
34 +
34 35 /*
35 36 * double erf(double x)
36 37 * double erfc(double x)
37 38 * x
38 39 * 2 |\
39 40 * erf(x) = --------- | exp(-t*t)dt
40 41 * sqrt(pi) \|
41 42 * 0
42 43 *
43 44 * erfc(x) = 1-erf(x)
44 45 * Note that
45 46 * erf(-x) = -erf(x)
46 47 * erfc(-x) = 2 - erfc(x)
47 48 *
48 49 * Method:
49 50 * 1. For |x| in [0, 0.84375]
50 51 * erf(x) = x + x*R(x^2)
51 52 * erfc(x) = 1 - erf(x) if x in [-.84375,0.25]
52 53 * = 0.5 + ((0.5-x)-x*R) if x in [0.25,0.84375]
53 54 * where R = P/Q where P is an odd poly of degree 8 and
54 55 * Q is an odd poly of degree 10.
55 56 * -57.90
56 57 * | R - (erf(x)-x)/x | <= 2
57 58 *
58 59 *
59 60 * Remark. The formula is derived by noting
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60 61 * erf(x) = (2/sqrt(pi))*(x - x^3/3 + x^5/10 - x^7/42 + ....)
61 62 * and that
62 63 * 2/sqrt(pi) = 1.128379167095512573896158903121545171688
63 64 * is close to one. The interval is chosen because the fix
64 65 * point of erf(x) is near 0.6174 (i.e., erf(x)=x when x is
65 66 * near 0.6174), and by some experiment, 0.84375 is chosen to
66 67 * guarantee the error is less than one ulp for erf.
67 68 *
68 69 * 2. For |x| in [0.84375,1.25], let s = |x| - 1, and
69 70 * c = 0.84506291151 rounded to single (24 bits)
70 - * erf(x) = sign(x) * (c + P1(s)/Q1(s))
71 - * erfc(x) = (1-c) - P1(s)/Q1(s) if x > 0
71 + * erf(x) = sign(x) * (c + P1(s)/Q1(s))
72 + * erfc(x) = (1-c) - P1(s)/Q1(s) if x > 0
72 73 * 1+(c+P1(s)/Q1(s)) if x < 0
73 - * |P1/Q1 - (erf(|x|)-c)| <= 2**-59.06
74 + * |P1/Q1 - (erf(|x|)-c)| <= 2**-59.06
74 75 * Remark: here we use the taylor series expansion at x=1.
75 76 * erf(1+s) = erf(1) + s*Poly(s)
76 77 * = 0.845.. + P1(s)/Q1(s)
77 78 * That is, we use rational approximation to approximate
78 79 * erf(1+s) - (c = (single)0.84506291151)
79 80 * Note that |P1/Q1|< 0.078 for x in [0.84375,1.25]
80 81 * where
81 82 * P1(s) = degree 6 poly in s
82 83 * Q1(s) = degree 6 poly in s
83 84 *
84 85 * 3. For x in [1.25,1/0.35(~2.857143)],
85 - * erfc(x) = (1/x)*exp(-x*x-0.5625+R1/S1)
86 - * erf(x) = 1 - erfc(x)
86 + * erfc(x) = (1/x)*exp(-x*x-0.5625+R1/S1)
87 + * erf(x) = 1 - erfc(x)
87 88 * where
88 89 * R1(z) = degree 7 poly in z, (z=1/x^2)
89 90 * S1(z) = degree 8 poly in z
90 91 *
91 92 * 4. For x in [1/0.35,28]
92 - * erfc(x) = (1/x)*exp(-x*x-0.5625+R2/S2) if x > 0
93 + * erfc(x) = (1/x)*exp(-x*x-0.5625+R2/S2) if x > 0
93 94 * = 2.0 - (1/x)*exp(-x*x-0.5625+R2/S2) if -6<x<0
94 95 * = 2.0 - tiny (if x <= -6)
95 - * erf(x) = sign(x)*(1.0 - erfc(x)) if x < 6, else
96 - * erf(x) = sign(x)*(1.0 - tiny)
96 + * erf(x) = sign(x)*(1.0 - erfc(x)) if x < 6, else
97 + * erf(x) = sign(x)*(1.0 - tiny)
97 98 * where
98 99 * R2(z) = degree 6 poly in z, (z=1/x^2)
99 100 * S2(z) = degree 7 poly in z
100 101 *
101 102 * Note1:
102 103 * To compute exp(-x*x-0.5625+R/S), let s be a single
103 104 * precision number and s := x; then
104 105 * -x*x = -s*s + (s-x)*(s+x)
105 106 * exp(-x*x-0.5626+R/S) =
106 107 * exp(-s*s-0.5625)*exp((s-x)*(s+x)+R/S);
107 108 * Note2:
108 109 * Here 4 and 5 make use of the asymptotic series
109 110 * exp(-x*x)
110 111 * erfc(x) ~ ---------- * ( 1 + Poly(1/x^2) )
111 112 * x*sqrt(pi)
112 113 * We use rational approximation to approximate
113 - * g(s)=f(1/x^2) = log(erfc(x)*x) - x*x + 0.5625
114 + * g(s)=f(1/x^2) = log(erfc(x)*x) - x*x + 0.5625
114 115 * 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)
116 + * |R1/S1 - f(x)| < 2**(-62.57)
117 + * |R2/S2 - f(x)| < 2**(-61.52)
117 118 *
118 119 * 5. For inf > x >= 28
119 - * erf(x) = sign(x) *(1 - tiny) (raise inexact)
120 - * erfc(x) = tiny*tiny (raise underflow) if x > 0
120 + * erf(x) = sign(x) *(1 - tiny) (raise inexact)
121 + * erfc(x) = tiny*tiny (raise underflow) if x > 0
121 122 * = 2 - tiny if x<0
122 123 *
123 124 * 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
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
127 128 */
128 -/* INDENT ON */
129 129
130 130 #include "libm_macros.h"
131 131 #include <math.h>
132 132
133 133 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 */
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 +
139 141 /*
140 142 * Coefficients for approximation to erf on [0,0.84375]
141 143 */
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 */
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 +
154 157 /*
155 158 * Coefficients for approximation to erf in [0.84375,1.25]
156 159 */
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 */
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 +
170 174 /*
171 175 * Coefficients for approximation to erfc in [1.25,1/0.35]
172 176 */
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 */
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 +
189 194 /*
190 195 * Coefficients for approximation to erfc in [1/.35,28]
191 196 */
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 */
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 */
206 211 };
207 212
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 +#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 +
213 219 /*
214 220 * Coefficients for approximation to erf on [0,0.84375]
215 221 */
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]
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 +
228 235 /*
229 236 * Coefficients for approximation to erf in [0.84375,1.25]
230 237 */
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]
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 +
244 252 /*
245 253 * Coefficients for approximation to erfc in [1.25,1/0.35]
246 254 */
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]
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 +
263 272 /*
264 273 * Coefficients for approximation to erfc in [1/.35,28]
265 274 */
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]
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]
280 289
281 290 double
282 -erf(double x) {
291 +erf(double x)
292 +{
283 293 int hx, ix, i;
284 294 double R, S, P, Q, s, y, z, r;
285 295
286 - hx = ((int *) &x)[HIWORD];
296 + hx = ((int *)&x)[HIWORD];
287 297 ix = hx & 0x7fffffff;
288 - if (ix >= 0x7ff00000) { /* erf(nan)=nan */
298 +
299 + if (ix >= 0x7ff00000) { /* erf(nan)=nan */
289 300 #if defined(FPADD_TRAPS_INCOMPLETE_ON_NAN)
290 - if (ix >= 0x7ff80000) /* assumes sparc-like QNaN */
301 + if (ix >= 0x7ff80000) /* assumes sparc-like QNaN */
291 302 return (x);
292 303 #endif
293 - i = ((unsigned) hx >> 31) << 1;
294 - return ((double) (1 - i) + one / x); /* erf(+-inf)=+-1 */
304 + i = ((unsigned)hx >> 31) << 1;
305 + return ((double)(1 - i) + one / x); /* erf(+-inf)=+-1 */
295 306 }
296 307
297 - if (ix < 0x3feb0000) { /* |x|<0.84375 */
298 - if (ix < 0x3e300000) { /* |x|<2**-28 */
299 - if (ix < 0x00800000) /* avoid underflow */
308 + if (ix < 0x3feb0000) { /* |x|<0.84375 */
309 + if (ix < 0x3e300000) { /* |x|<2**-28 */
310 + if (ix < 0x00800000) /* avoid underflow */
300 311 return (0.125 * (8.0 * x + efx8 * x));
312 +
301 313 return (x + efx * x);
302 314 }
315 +
303 316 z = x * x;
304 317 r = pp0 + z * (pp1 + z * (pp2 + z * (pp3 + z * pp4)));
305 - s = one +
306 - z *(qq1 + z * (qq2 + z * (qq3 + z * (qq4 + z * qq5))));
318 + s = one + z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 + z *
319 + qq5))));
307 320 y = r / s;
308 321 return (x + x * y);
309 322 }
310 - if (ix < 0x3ff40000) { /* 0.84375 <= |x| < 1.25 */
323 +
324 + if (ix < 0x3ff40000) { /* 0.84375 <= |x| < 1.25 */
311 325 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)))));
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 +
316 331 if (hx >= 0)
317 332 return (erx + P / Q);
318 333 else
319 334 return (-erx - P / Q);
320 335 }
321 - if (ix >= 0x40180000) { /* inf > |x| >= 6 */
336 +
337 + if (ix >= 0x40180000) { /* inf > |x| >= 6 */
322 338 if (hx >= 0)
323 339 return (one - tiny);
324 340 else
325 341 return (tiny - one);
326 342 }
343 +
327 344 x = fabs(x);
328 345 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)))))));
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)))))));
334 352 } 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))))));
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))))));
339 357 }
358 +
340 359 z = x;
341 - ((int *) &z)[LOWORD] = 0;
360 + ((int *)&z)[LOWORD] = 0;
342 361 r = exp(-z * z - 0.5625) * exp((z - x) * (z + x) + R / S);
362 +
343 363 if (hx >= 0)
344 364 return (one - r / x);
345 365 else
346 366 return (r / x - one);
347 367 }
348 368
349 369 double
350 -erfc(double x) {
370 +erfc(double x)
371 +{
351 372 int hx, ix;
352 373 double R, S, P, Q, s, y, z, r;
353 374
354 - hx = ((int *) &x)[HIWORD];
375 + hx = ((int *)&x)[HIWORD];
355 376 ix = hx & 0x7fffffff;
356 - if (ix >= 0x7ff00000) { /* erfc(nan)=nan */
377 +
378 + if (ix >= 0x7ff00000) { /* erfc(nan)=nan */
357 379 #if defined(FPADD_TRAPS_INCOMPLETE_ON_NAN)
358 - if (ix >= 0x7ff80000) /* assumes sparc-like QNaN */
380 + if (ix >= 0x7ff80000) /* assumes sparc-like QNaN */
359 381 return (x);
360 382 #endif
361 383 /* erfc(+-inf)=0,2 */
362 - return ((double) (((unsigned) hx >> 31) << 1) + one / x);
384 + return ((double)(((unsigned)hx >> 31) << 1) + one / x);
363 385 }
364 386
365 - if (ix < 0x3feb0000) { /* |x| < 0.84375 */
387 + if (ix < 0x3feb0000) { /* |x| < 0.84375 */
366 388 if (ix < 0x3c700000) /* |x| < 2**-56 */
367 389 return (one - x);
390 +
368 391 z = x * x;
369 392 r = pp0 + z * (pp1 + z * (pp2 + z * (pp3 + z * pp4)));
370 - s = one +
371 - z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 + z * qq5))));
393 + s = one + z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 + z *
394 + qq5))));
372 395 y = r / s;
396 +
373 397 if (hx < 0x3fd00000) { /* x < 1/4 */
374 398 return (one - (x + x * y));
375 399 } else {
376 400 r = x * y;
377 401 r += (x - half);
378 402 return (half - r);
379 403 }
380 404 }
381 - if (ix < 0x3ff40000) { /* 0.84375 <= |x| < 1.25 */
405 +
406 + if (ix < 0x3ff40000) { /* 0.84375 <= |x| < 1.25 */
382 407 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)))));
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 +
387 413 if (hx >= 0) {
388 414 z = one - erx;
389 415 return (z - P / Q);
390 416 } else {
391 417 z = erx + P / Q;
392 418 return (one + z);
393 419 }
394 420 }
395 - if (ix < 0x403c0000) { /* |x|<28 */
421 +
422 + if (ix < 0x403c0000) { /* |x|<28 */
396 423 x = fabs(x);
397 424 s = one / (x * x);
425 +
398 426 if (ix < 0x4006DB6D) { /* |x| < 1/.35 ~ 2.857143 */
399 427 R = ra0 + s * (ra1 + s * (ra2 + s * (ra3 + s * (ra4 +
400 - s * (ra5 + s * (ra6 + s * ra7))))));
428 + s * (ra5 + s * (ra6 + s * ra7))))));
401 429 S = one + s * (sa1 + s * (sa2 + s * (sa3 + s * (sa4 +
402 - s * (sa5 + s * (sa6 + s * (sa7 + s * sa8)))))));
430 + s * (sa5 + s * (sa6 + s * (sa7 + s * sa8)))))));
403 431 } else {
404 432 /* |x| >= 1/.35 ~ 2.857143 */
405 433 if (hx < 0 && ix >= 0x40180000)
406 434 return (two - tiny); /* x < -6 */
407 435
408 436 R = rb0 + s * (rb1 + s * (rb2 + s * (rb3 + s * (rb4 +
409 - s * (rb5 + s * rb6)))));
437 + s * (rb5 + s * rb6)))));
410 438 S = one + s * (sb1 + s * (sb2 + s * (sb3 + s * (sb4 +
411 - s * (sb5 + s * (sb6 + s * sb7))))));
439 + s * (sb5 + s * (sb6 + s * sb7))))));
412 440 }
441 +
413 442 z = x;
414 - ((int *) &z)[LOWORD] = 0;
443 + ((int *)&z)[LOWORD] = 0;
415 444 r = exp(-z * z - 0.5625) * exp((z - x) * (z + x) + R / S);
445 +
416 446 if (hx > 0)
417 447 return (r / x);
418 448 else
419 449 return (two - r / x);
420 450 } else {
421 451 if (hx > 0)
422 452 return (tiny * tiny);
423 453 else
424 454 return (two - tiny);
425 455 }
426 456 }
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