static const double
tiny = 1e-300,
- half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
- two = 2.00000000000000000000e+00, /* 0x40000000, 0x00000000 */
/* c = (float)0.84506291151 */
erx = 8.45062911510467529297e-01, /* 0x3FEB0AC1, 0x60000000 */
/*
return r / x - one;
}
libm_alias_double (__erf, erf)
-
-double
-__erfc (double x)
-{
- int32_t hx, ix;
- double R, S, P, Q, s, y, z, r;
- GET_HIGH_WORD (hx, x);
- ix = hx & 0x7fffffff;
- if (ix >= 0x7ff00000) /* erfc(nan)=nan */
- { /* erfc(+-inf)=0,2 */
- double ret = (double) (((uint32_t) hx >> 31) << 1) + one / x;
- if (FIX_INT_FP_CONVERT_ZERO && ret == 0.0)
- return 0.0;
- return ret;
- }
-
- if (ix < 0x3feb0000) /* |x|<0.84375 */
- {
- double r1, r2, s1, s2, s3, z2, z4;
- if (ix < 0x3c700000) /* |x|<2**-56 */
- return one - x;
- z = x * x;
- r1 = pp[0] + z * pp[1]; z2 = z * z;
- r2 = pp[2] + z * pp[3]; z4 = z2 * z2;
- s1 = one + z * qq[1];
- s2 = qq[2] + z * qq[3];
- s3 = qq[4] + z * qq[5];
- r = r1 + z2 * r2 + z4 * pp[4];
- s = s1 + z2 * s2 + z4 * s3;
- y = r / s;
- if (hx < 0x3fd00000) /* x<1/4 */
- {
- return one - (x + x * y);
- }
- else
- {
- r = x * y;
- r += (x - half);
- return half - r;
- }
- }
- if (ix < 0x3ff40000) /* 0.84375 <= |x| < 1.25 */
- {
- double s2, s4, s6, P1, P2, P3, P4, Q1, Q2, Q3, Q4;
- s = fabs (x) - one;
- P1 = pa[0] + s * pa[1]; s2 = s * s;
- Q1 = one + s * qa[1]; s4 = s2 * s2;
- P2 = pa[2] + s * pa[3]; s6 = s4 * s2;
- Q2 = qa[2] + s * qa[3];
- P3 = pa[4] + s * pa[5];
- Q3 = qa[4] + s * qa[5];
- P4 = pa[6];
- Q4 = qa[6];
- P = P1 + s2 * P2 + s4 * P3 + s6 * P4;
- Q = Q1 + s2 * Q2 + s4 * Q3 + s6 * Q4;
- if (hx >= 0)
- {
- z = one - erx; return z - P / Q;
- }
- else
- {
- z = erx + P / Q; return one + z;
- }
- }
- if (ix < 0x403c0000) /* |x|<28 */
- {
- x = fabs (x);
- s = one / (x * x);
- if (ix < 0x4006DB6D) /* |x| < 1/.35 ~ 2.857143*/
- {
- double R1, R2, R3, R4, S1, S2, S3, S4, s2, s4, s6, s8;
- R1 = ra[0] + s * ra[1]; s2 = s * s;
- S1 = one + s * sa[1]; s4 = s2 * s2;
- R2 = ra[2] + s * ra[3]; s6 = s4 * s2;
- S2 = sa[2] + s * sa[3]; s8 = s4 * s4;
- R3 = ra[4] + s * ra[5];
- S3 = sa[4] + s * sa[5];
- R4 = ra[6] + s * ra[7];
- S4 = sa[6] + s * sa[7];
- R = R1 + s2 * R2 + s4 * R3 + s6 * R4;
- S = S1 + s2 * S2 + s4 * S3 + s6 * S4 + s8 * sa[8];
- }
- else /* |x| >= 1/.35 ~ 2.857143 */
- {
- double R1, R2, R3, S1, S2, S3, S4, s2, s4, s6;
- if (hx < 0 && ix >= 0x40180000)
- return two - tiny; /* x < -6 */
- R1 = rb[0] + s * rb[1]; s2 = s * s;
- S1 = one + s * sb[1]; s4 = s2 * s2;
- R2 = rb[2] + s * rb[3]; s6 = s4 * s2;
- S2 = sb[2] + s * sb[3];
- R3 = rb[4] + s * rb[5];
- S3 = sb[4] + s * sb[5];
- S4 = sb[6] + s * sb[7];
- R = R1 + s2 * R2 + s4 * R3 + s6 * rb[6];
- S = S1 + s2 * S2 + s4 * S3 + s6 * S4;
- }
- z = x;
- SET_LOW_WORD (z, 0);
- r = __ieee754_exp (-z * z - 0.5625) *
- __ieee754_exp ((z - x) * (z + x) + R / S);
- if (hx > 0)
- {
- double ret = math_narrow_eval (r / x);
- if (ret == 0)
- __set_errno (ERANGE);
- return ret;
- }
- else
- return two - r / x;
- }
- else
- {
- if (hx > 0)
- {
- __set_errno (ERANGE);
- return tiny * tiny;
- }
- else
- return two - tiny;
- }
-}
-libm_alias_double (__erfc, erfc)
-/* Not required. */
+/* @(#)s_erf.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.
+ * ====================================================
+ */
+/* Modified by Naohiko Shimizu/Tokai University, Japan 1997/08/25,
+ for performance improvement on pipelined processors.
+*/
+
+#include <errno.h>
+#include <math.h>
+#include <math_private.h>
+#include <math-narrow-eval.h>
+#include <libm-alias-double.h>
+#include <fix-int-fp-convert-zero.h>
+
+static const double
+ tiny = 1e-300,
+ one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
+ half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
+ two = 2.00000000000000000000e+00, /* 0x40000000, 0x00000000 */
+/* c = (float)0.84506291151 */
+ erx = 8.45062911510467529297e-01, /* 0x3FEB0AC1, 0x60000000 */
+/*
+ * Coefficients for approximation to erf on [0,0.84375]
+ */
+ pp[] = { 1.28379167095512558561e-01, /* 0x3FC06EBA, 0x8214DB68 */
+ -3.25042107247001499370e-01, /* 0xBFD4CD7D, 0x691CB913 */
+ -2.84817495755985104766e-02, /* 0xBF9D2A51, 0xDBD7194F */
+ -5.77027029648944159157e-03, /* 0xBF77A291, 0x236668E4 */
+ -2.37630166566501626084e-05 }, /* 0xBEF8EAD6, 0x120016AC */
+ qq[] = { 0.0, 3.97917223959155352819e-01, /* 0x3FD97779, 0xCDDADC09 */
+ 6.50222499887672944485e-02, /* 0x3FB0A54C, 0x5536CEBA */
+ 5.08130628187576562776e-03, /* 0x3F74D022, 0xC4D36B0F */
+ 1.32494738004321644526e-04, /* 0x3F215DC9, 0x221C1A10 */
+ -3.96022827877536812320e-06 }, /* 0xBED09C43, 0x42A26120 */
+/*
+ * Coefficients for approximation to erf in [0.84375,1.25]
+ */
+ pa[] = { -2.36211856075265944077e-03, /* 0xBF6359B8, 0xBEF77538 */
+ 4.14856118683748331666e-01, /* 0x3FDA8D00, 0xAD92B34D */
+ -3.72207876035701323847e-01, /* 0xBFD7D240, 0xFBB8C3F1 */
+ 3.18346619901161753674e-01, /* 0x3FD45FCA, 0x805120E4 */
+ -1.10894694282396677476e-01, /* 0xBFBC6398, 0x3D3E28EC */
+ 3.54783043256182359371e-02, /* 0x3FA22A36, 0x599795EB */
+ -2.16637559486879084300e-03 }, /* 0xBF61BF38, 0x0A96073F */
+ qa[] = { 0.0, 1.06420880400844228286e-01, /* 0x3FBB3E66, 0x18EEE323 */
+ 5.40397917702171048937e-01, /* 0x3FE14AF0, 0x92EB6F33 */
+ 7.18286544141962662868e-02, /* 0x3FB2635C, 0xD99FE9A7 */
+ 1.26171219808761642112e-01, /* 0x3FC02660, 0xE763351F */
+ 1.36370839120290507362e-02, /* 0x3F8BEDC2, 0x6B51DD1C */
+ 1.19844998467991074170e-02 }, /* 0x3F888B54, 0x5735151D */
+/*
+ * Coefficients for approximation to erfc in [1.25,1/0.35]
+ */
+ ra[] = { -9.86494403484714822705e-03, /* 0xBF843412, 0x600D6435 */
+ -6.93858572707181764372e-01, /* 0xBFE63416, 0xE4BA7360 */
+ -1.05586262253232909814e+01, /* 0xC0251E04, 0x41B0E726 */
+ -6.23753324503260060396e+01, /* 0xC04F300A, 0xE4CBA38D */
+ -1.62396669462573470355e+02, /* 0xC0644CB1, 0x84282266 */
+ -1.84605092906711035994e+02, /* 0xC067135C, 0xEBCCABB2 */
+ -8.12874355063065934246e+01, /* 0xC0545265, 0x57E4D2F2 */
+ -9.81432934416914548592e+00 }, /* 0xC023A0EF, 0xC69AC25C */
+ sa[] = { 0.0, 1.96512716674392571292e+01, /* 0x4033A6B9, 0xBD707687 */
+ 1.37657754143519042600e+02, /* 0x4061350C, 0x526AE721 */
+ 4.34565877475229228821e+02, /* 0x407B290D, 0xD58A1A71 */
+ 6.45387271733267880336e+02, /* 0x40842B19, 0x21EC2868 */
+ 4.29008140027567833386e+02, /* 0x407AD021, 0x57700314 */
+ 1.08635005541779435134e+02, /* 0x405B28A3, 0xEE48AE2C */
+ 6.57024977031928170135e+00, /* 0x401A47EF, 0x8E484A93 */
+ -6.04244152148580987438e-02 }, /* 0xBFAEEFF2, 0xEE749A62 */
+/*
+ * Coefficients for approximation to erfc in [1/.35,28]
+ */
+ rb[] = { -9.86494292470009928597e-03, /* 0xBF843412, 0x39E86F4A */
+ -7.99283237680523006574e-01, /* 0xBFE993BA, 0x70C285DE */
+ -1.77579549177547519889e+01, /* 0xC031C209, 0x555F995A */
+ -1.60636384855821916062e+02, /* 0xC064145D, 0x43C5ED98 */
+ -6.37566443368389627722e+02, /* 0xC083EC88, 0x1375F228 */
+ -1.02509513161107724954e+03, /* 0xC0900461, 0x6A2E5992 */
+ -4.83519191608651397019e+02 }, /* 0xC07E384E, 0x9BDC383F */
+ sb[] = { 0.0, 3.03380607434824582924e+01, /* 0x403E568B, 0x261D5190 */
+ 3.25792512996573918826e+02, /* 0x40745CAE, 0x221B9F0A */
+ 1.53672958608443695994e+03, /* 0x409802EB, 0x189D5118 */
+ 3.19985821950859553908e+03, /* 0x40A8FFB7, 0x688C246A */
+ 2.55305040643316442583e+03, /* 0x40A3F219, 0xCEDF3BE6 */
+ 4.74528541206955367215e+02, /* 0x407DA874, 0xE79FE763 */
+ -2.24409524465858183362e+01 }; /* 0xC03670E2, 0x42712D62 */
+
+double
+__erfc (double x)
+{
+ int32_t hx, ix;
+ double R, S, P, Q, s, y, z, r;
+ GET_HIGH_WORD (hx, x);
+ ix = hx & 0x7fffffff;
+ if (ix >= 0x7ff00000) /* erfc(nan)=nan */
+ { /* erfc(+-inf)=0,2 */
+ double ret = (double) (((uint32_t) hx >> 31) << 1) + one / x;
+ if (FIX_INT_FP_CONVERT_ZERO && ret == 0.0)
+ return 0.0;
+ return ret;
+ }
+
+ if (ix < 0x3feb0000) /* |x|<0.84375 */
+ {
+ double r1, r2, s1, s2, s3, z2, z4;
+ if (ix < 0x3c700000) /* |x|<2**-56 */
+ return one - x;
+ z = x * x;
+ r1 = pp[0] + z * pp[1]; z2 = z * z;
+ r2 = pp[2] + z * pp[3]; z4 = z2 * z2;
+ s1 = one + z * qq[1];
+ s2 = qq[2] + z * qq[3];
+ s3 = qq[4] + z * qq[5];
+ r = r1 + z2 * r2 + z4 * pp[4];
+ s = s1 + z2 * s2 + z4 * s3;
+ y = r / s;
+ if (hx < 0x3fd00000) /* x<1/4 */
+ {
+ return one - (x + x * y);
+ }
+ else
+ {
+ r = x * y;
+ r += (x - half);
+ return half - r;
+ }
+ }
+ if (ix < 0x3ff40000) /* 0.84375 <= |x| < 1.25 */
+ {
+ double s2, s4, s6, P1, P2, P3, P4, Q1, Q2, Q3, Q4;
+ s = fabs (x) - one;
+ P1 = pa[0] + s * pa[1]; s2 = s * s;
+ Q1 = one + s * qa[1]; s4 = s2 * s2;
+ P2 = pa[2] + s * pa[3]; s6 = s4 * s2;
+ Q2 = qa[2] + s * qa[3];
+ P3 = pa[4] + s * pa[5];
+ Q3 = qa[4] + s * qa[5];
+ P4 = pa[6];
+ Q4 = qa[6];
+ P = P1 + s2 * P2 + s4 * P3 + s6 * P4;
+ Q = Q1 + s2 * Q2 + s4 * Q3 + s6 * Q4;
+ if (hx >= 0)
+ {
+ z = one - erx; return z - P / Q;
+ }
+ else
+ {
+ z = erx + P / Q; return one + z;
+ }
+ }
+ if (ix < 0x403c0000) /* |x|<28 */
+ {
+ x = fabs (x);
+ s = one / (x * x);
+ if (ix < 0x4006DB6D) /* |x| < 1/.35 ~ 2.857143*/
+ {
+ double R1, R2, R3, R4, S1, S2, S3, S4, s2, s4, s6, s8;
+ R1 = ra[0] + s * ra[1]; s2 = s * s;
+ S1 = one + s * sa[1]; s4 = s2 * s2;
+ R2 = ra[2] + s * ra[3]; s6 = s4 * s2;
+ S2 = sa[2] + s * sa[3]; s8 = s4 * s4;
+ R3 = ra[4] + s * ra[5];
+ S3 = sa[4] + s * sa[5];
+ R4 = ra[6] + s * ra[7];
+ S4 = sa[6] + s * sa[7];
+ R = R1 + s2 * R2 + s4 * R3 + s6 * R4;
+ S = S1 + s2 * S2 + s4 * S3 + s6 * S4 + s8 * sa[8];
+ }
+ else /* |x| >= 1/.35 ~ 2.857143 */
+ {
+ double R1, R2, R3, S1, S2, S3, S4, s2, s4, s6;
+ if (hx < 0 && ix >= 0x40180000)
+ return two - tiny; /* x < -6 */
+ R1 = rb[0] + s * rb[1]; s2 = s * s;
+ S1 = one + s * sb[1]; s4 = s2 * s2;
+ R2 = rb[2] + s * rb[3]; s6 = s4 * s2;
+ S2 = sb[2] + s * sb[3];
+ R3 = rb[4] + s * rb[5];
+ S3 = sb[4] + s * sb[5];
+ S4 = sb[6] + s * sb[7];
+ R = R1 + s2 * R2 + s4 * R3 + s6 * rb[6];
+ S = S1 + s2 * S2 + s4 * S3 + s6 * S4;
+ }
+ z = x;
+ SET_LOW_WORD (z, 0);
+ r = __ieee754_exp (-z * z - 0.5625) *
+ __ieee754_exp ((z - x) * (z + x) + R / S);
+ if (hx > 0)
+ {
+ double ret = math_narrow_eval (r / x);
+ if (ret == 0)
+ __set_errno (ERANGE);
+ return ret;
+ }
+ else
+ return two - r / x;
+ }
+ else
+ {
+ if (hx > 0)
+ {
+ __set_errno (ERANGE);
+ return tiny * tiny;
+ }
+ else
+ return two - tiny;
+ }
+}
+libm_alias_double (__erfc, erfc)
projects / thirdparty / glibc.git / commitdiff
