diff options
Diffstat (limited to 'sysdeps/ieee754/dbl-64/s_erf.c')
| -rw-r--r-- | sysdeps/ieee754/dbl-64/s_erf.c | 475 |
1 files changed, 258 insertions, 217 deletions
diff --git a/sysdeps/ieee754/dbl-64/s_erf.c b/sysdeps/ieee754/dbl-64/s_erf.c index 0cf408c03c..aab4ed593e 100644 --- a/sysdeps/ieee754/dbl-64/s_erf.c +++ b/sysdeps/ieee754/dbl-64/s_erf.c @@ -116,157 +116,176 @@ static char rcsid[] = "$NetBSD: s_erf.c,v 1.8 1995/05/10 20:47:05 jtc Exp $"; #include <math_private.h> 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 */ + 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 */ /* * Coefficients for approximation to erf on [0,0.84375] */ -efx = 1.28379167095512586316e-01, /* 0x3FC06EBA, 0x8214DB69 */ -efx8= 1.02703333676410069053e+00, /* 0x3FF06EBA, 0x8214DB69 */ -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 */ + efx = 1.28379167095512586316e-01, /* 0x3FC06EBA, 0x8214DB69 */ + efx8 = 1.02703333676410069053e+00, /* 0x3FF06EBA, 0x8214DB69 */ + 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 */ + 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 */ + 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 */ + 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 __erf(double x) +double +__erf (double x) { - int32_t hx,ix,i; - double R,S,P,Q,s,y,z,r; - GET_HIGH_WORD(hx,x); - ix = hx&0x7fffffff; - if(ix>=0x7ff00000) { /* erf(nan)=nan */ - i = ((u_int32_t)hx>>31)<<1; - return (double)(1-i)+one/x; /* erf(+-inf)=+-1 */ - } + int32_t hx, ix, i; + double R, S, P, Q, s, y, z, r; + GET_HIGH_WORD (hx, x); + ix = hx & 0x7fffffff; + if (ix >= 0x7ff00000) /* erf(nan)=nan */ + { + i = ((u_int32_t) hx >> 31) << 1; + return (double) (1 - i) + one / x; /* erf(+-inf)=+-1 */ + } - if(ix < 0x3feb0000) { /* |x|<0.84375 */ - double r1,r2,s1,s2,s3,z2,z4; - if(ix < 0x3e300000) { /* |x|<2**-28 */ - if (ix < 0x00800000) - return 0.125*(8.0*x+efx8*x); /*avoid underflow */ - return x + efx*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; - return x + x*y; - } - 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) return erx + P/Q; else return -erx - P/Q; - } - if (ix >= 0x40180000) { /* inf>|x|>=6 */ - if(hx>=0) return one-tiny; else return tiny-one; - } - x = fabs(x); - s = one/(x*x); - if(ix< 0x4006DB6E) { /* |x| < 1/0.35 */ - 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| >= 1/0.35 */ - double R1,R2,R3,S1,S2,S3,S4,s2,s4,s6; - 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; + if (ix < 0x3feb0000) /* |x|<0.84375 */ + { + double r1, r2, s1, s2, s3, z2, z4; + if (ix < 0x3e300000) /* |x|<2**-28 */ + { + if (ix < 0x00800000) + return 0.125 * (8.0 * x + efx8 * x); /*avoid underflow */ + return x + efx * x; } - 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) return one-r/x; else return r/x-one; + 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; + return x + x * y; + } + 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) + return erx + P / Q; + else + return -erx - P / Q; + } + if (ix >= 0x40180000) /* inf>|x|>=6 */ + { + if (hx >= 0) + return one - tiny; + else + return tiny - one; + } + x = fabs (x); + s = one / (x * x); + if (ix < 0x4006DB6E) /* |x| < 1/0.35 */ + { + 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| >= 1/0.35 */ + { + double R1, R2, R3, S1, S2, S3, S4, s2, s4, s6; + 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) + return one - r / x; + else + return r / x - one; } weak_alias (__erf, erf) #ifdef NO_LONG_DOUBLE @@ -274,93 +293,115 @@ strong_alias (__erf, __erfl) weak_alias (__erf, erfl) #endif -double __erfc(double x) +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 */ - return (double)(((u_int32_t)hx>>31)<<1)+one/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 */ + return (double) (((u_int32_t) hx >> 31) << 1) + one / x; + } - 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 < 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 < 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]; } - 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) return r/x; else return two-r/x; - } else { - if(hx>0) return tiny*tiny; else return two-tiny; + 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) + return r / x; + else + return two - r / x; + } + else + { + if (hx > 0) + return tiny * tiny; + else + return two - tiny; + } } weak_alias (__erfc, erfc) #ifdef NO_LONG_DOUBLE |