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-rw-r--r--usr/src/lib/libm/common/C/erf.c427
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diff --git a/usr/src/lib/libm/common/C/erf.c b/usr/src/lib/libm/common/C/erf.c
new file mode 100644
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+++ b/usr/src/lib/libm/common/C/erf.c
@@ -0,0 +1,427 @@
+/*
+ * CDDL HEADER START
+ *
+ * The contents of this file are subject to the terms of the
+ * Common Development and Distribution License (the "License").
+ * You may not use this file except in compliance with the License.
+ *
+ * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
+ * or http://www.opensolaris.org/os/licensing.
+ * See the License for the specific language governing permissions
+ * and limitations under the License.
+ *
+ * When distributing Covered Code, include this CDDL HEADER in each
+ * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
+ * If applicable, add the following below this CDDL HEADER, with the
+ * fields enclosed by brackets "[]" replaced with your own identifying
+ * information: Portions Copyright [yyyy] [name of copyright owner]
+ *
+ * CDDL HEADER END
+ */
+
+/*
+ * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
+ */
+/*
+ * Copyright 2006 Sun Microsystems, Inc. All rights reserved.
+ * Use is subject to license terms.
+ */
+
+#pragma weak erf = __erf
+#pragma weak erfc = __erfc
+
+/* INDENT OFF */
+/*
+ * double erf(double x)
+ * double erfc(double x)
+ * x
+ * 2 |\
+ * erf(x) = --------- | exp(-t*t)dt
+ * sqrt(pi) \|
+ * 0
+ *
+ * erfc(x) = 1-erf(x)
+ * Note that
+ * erf(-x) = -erf(x)
+ * erfc(-x) = 2 - erfc(x)
+ *
+ * Method:
+ * 1. For |x| in [0, 0.84375]
+ * erf(x) = x + x*R(x^2)
+ * erfc(x) = 1 - erf(x) if x in [-.84375,0.25]
+ * = 0.5 + ((0.5-x)-x*R) if x in [0.25,0.84375]
+ * where R = P/Q where P is an odd poly of degree 8 and
+ * Q is an odd poly of degree 10.
+ * -57.90
+ * | R - (erf(x)-x)/x | <= 2
+ *
+ *
+ * Remark. The formula is derived by noting
+ * erf(x) = (2/sqrt(pi))*(x - x^3/3 + x^5/10 - x^7/42 + ....)
+ * and that
+ * 2/sqrt(pi) = 1.128379167095512573896158903121545171688
+ * is close to one. The interval is chosen because the fix
+ * point of erf(x) is near 0.6174 (i.e., erf(x)=x when x is
+ * near 0.6174), and by some experiment, 0.84375 is chosen to
+ * guarantee the error is less than one ulp for erf.
+ *
+ * 2. For |x| in [0.84375,1.25], let s = |x| - 1, and
+ * c = 0.84506291151 rounded to single (24 bits)
+ * erf(x) = sign(x) * (c + P1(s)/Q1(s))
+ * erfc(x) = (1-c) - P1(s)/Q1(s) if x > 0
+ * 1+(c+P1(s)/Q1(s)) if x < 0
+ * |P1/Q1 - (erf(|x|)-c)| <= 2**-59.06
+ * Remark: here we use the taylor series expansion at x=1.
+ * erf(1+s) = erf(1) + s*Poly(s)
+ * = 0.845.. + P1(s)/Q1(s)
+ * That is, we use rational approximation to approximate
+ * erf(1+s) - (c = (single)0.84506291151)
+ * Note that |P1/Q1|< 0.078 for x in [0.84375,1.25]
+ * where
+ * P1(s) = degree 6 poly in s
+ * Q1(s) = degree 6 poly in s
+ *
+ * 3. For x in [1.25,1/0.35(~2.857143)],
+ * erfc(x) = (1/x)*exp(-x*x-0.5625+R1/S1)
+ * erf(x) = 1 - erfc(x)
+ * where
+ * R1(z) = degree 7 poly in z, (z=1/x^2)
+ * S1(z) = degree 8 poly in z
+ *
+ * 4. For x in [1/0.35,28]
+ * erfc(x) = (1/x)*exp(-x*x-0.5625+R2/S2) if x > 0
+ * = 2.0 - (1/x)*exp(-x*x-0.5625+R2/S2) if -6<x<0
+ * = 2.0 - tiny (if x <= -6)
+ * erf(x) = sign(x)*(1.0 - erfc(x)) if x < 6, else
+ * erf(x) = sign(x)*(1.0 - tiny)
+ * where
+ * R2(z) = degree 6 poly in z, (z=1/x^2)
+ * S2(z) = degree 7 poly in z
+ *
+ * Note1:
+ * To compute exp(-x*x-0.5625+R/S), let s be a single
+ * precision number and s := x; then
+ * -x*x = -s*s + (s-x)*(s+x)
+ * exp(-x*x-0.5626+R/S) =
+ * exp(-s*s-0.5625)*exp((s-x)*(s+x)+R/S);
+ * Note2:
+ * Here 4 and 5 make use of the asymptotic series
+ * exp(-x*x)
+ * erfc(x) ~ ---------- * ( 1 + Poly(1/x^2) )
+ * x*sqrt(pi)
+ * We use rational approximation to approximate
+ * g(s)=f(1/x^2) = log(erfc(x)*x) - x*x + 0.5625
+ * Here is the error bound for R1/S1 and R2/S2
+ * |R1/S1 - f(x)| < 2**(-62.57)
+ * |R2/S2 - f(x)| < 2**(-61.52)
+ *
+ * 5. For inf > x >= 28
+ * erf(x) = sign(x) *(1 - tiny) (raise inexact)
+ * erfc(x) = tiny*tiny (raise underflow) if x > 0
+ * = 2 - tiny if x<0
+ *
+ * 7. Special case:
+ * erf(0) = 0, erf(inf) = 1, erf(-inf) = -1,
+ * erfc(0) = 1, erfc(inf) = 0, erfc(-inf) = 2,
+ * erfc/erf(NaN) is NaN
+ */
+/* INDENT ON */
+
+#include "libm_synonyms.h" /* __erf, __erfc, __exp */
+#include "libm_macros.h"
+#include <math.h>
+
+static const double xxx[] = {
+/* tiny */ 1e-300,
+/* half */ 5.00000000000000000000e-01, /* 3FE00000, 00000000 */
+/* one */ 1.00000000000000000000e+00, /* 3FF00000, 00000000 */
+/* two */ 2.00000000000000000000e+00, /* 40000000, 00000000 */
+/* erx */ 8.45062911510467529297e-01, /* 3FEB0AC1, 60000000 */
+/*
+ * Coefficients for approximation to erf on [0,0.84375]
+ */
+/* efx */ 1.28379167095512586316e-01, /* 3FC06EBA, 8214DB69 */
+/* efx8 */ 1.02703333676410069053e+00, /* 3FF06EBA, 8214DB69 */
+/* pp0 */ 1.28379167095512558561e-01, /* 3FC06EBA, 8214DB68 */
+/* pp1 */ -3.25042107247001499370e-01, /* BFD4CD7D, 691CB913 */
+/* pp2 */ -2.84817495755985104766e-02, /* BF9D2A51, DBD7194F */
+/* pp3 */ -5.77027029648944159157e-03, /* BF77A291, 236668E4 */
+/* pp4 */ -2.37630166566501626084e-05, /* BEF8EAD6, 120016AC */
+/* qq1 */ 3.97917223959155352819e-01, /* 3FD97779, CDDADC09 */
+/* qq2 */ 6.50222499887672944485e-02, /* 3FB0A54C, 5536CEBA */
+/* qq3 */ 5.08130628187576562776e-03, /* 3F74D022, C4D36B0F */
+/* qq4 */ 1.32494738004321644526e-04, /* 3F215DC9, 221C1A10 */
+/* qq5 */ -3.96022827877536812320e-06, /* BED09C43, 42A26120 */
+/*
+ * Coefficients for approximation to erf in [0.84375,1.25]
+ */
+/* pa0 */ -2.36211856075265944077e-03, /* BF6359B8, BEF77538 */
+/* pa1 */ 4.14856118683748331666e-01, /* 3FDA8D00, AD92B34D */
+/* pa2 */ -3.72207876035701323847e-01, /* BFD7D240, FBB8C3F1 */
+/* pa3 */ 3.18346619901161753674e-01, /* 3FD45FCA, 805120E4 */
+/* pa4 */ -1.10894694282396677476e-01, /* BFBC6398, 3D3E28EC */
+/* pa5 */ 3.54783043256182359371e-02, /* 3FA22A36, 599795EB */
+/* pa6 */ -2.16637559486879084300e-03, /* BF61BF38, 0A96073F */
+/* qa1 */ 1.06420880400844228286e-01, /* 3FBB3E66, 18EEE323 */
+/* qa2 */ 5.40397917702171048937e-01, /* 3FE14AF0, 92EB6F33 */
+/* qa3 */ 7.18286544141962662868e-02, /* 3FB2635C, D99FE9A7 */
+/* qa4 */ 1.26171219808761642112e-01, /* 3FC02660, E763351F */
+/* qa5 */ 1.36370839120290507362e-02, /* 3F8BEDC2, 6B51DD1C */
+/* qa6 */ 1.19844998467991074170e-02, /* 3F888B54, 5735151D */
+/*
+ * Coefficients for approximation to erfc in [1.25,1/0.35]
+ */
+/* ra0 */ -9.86494403484714822705e-03, /* BF843412, 600D6435 */
+/* ra1 */ -6.93858572707181764372e-01, /* BFE63416, E4BA7360 */
+/* ra2 */ -1.05586262253232909814e+01, /* C0251E04, 41B0E726 */
+/* ra3 */ -6.23753324503260060396e+01, /* C04F300A, E4CBA38D */
+/* ra4 */ -1.62396669462573470355e+02, /* C0644CB1, 84282266 */
+/* ra5 */ -1.84605092906711035994e+02, /* C067135C, EBCCABB2 */
+/* ra6 */ -8.12874355063065934246e+01, /* C0545265, 57E4D2F2 */
+/* ra7 */ -9.81432934416914548592e+00, /* C023A0EF, C69AC25C */
+/* sa1 */ 1.96512716674392571292e+01, /* 4033A6B9, BD707687 */
+/* sa2 */ 1.37657754143519042600e+02, /* 4061350C, 526AE721 */
+/* sa3 */ 4.34565877475229228821e+02, /* 407B290D, D58A1A71 */
+/* sa4 */ 6.45387271733267880336e+02, /* 40842B19, 21EC2868 */
+/* sa5 */ 4.29008140027567833386e+02, /* 407AD021, 57700314 */
+/* sa6 */ 1.08635005541779435134e+02, /* 405B28A3, EE48AE2C */
+/* sa7 */ 6.57024977031928170135e+00, /* 401A47EF, 8E484A93 */
+/* sa8 */ -6.04244152148580987438e-02, /* BFAEEFF2, EE749A62 */
+/*
+ * Coefficients for approximation to erfc in [1/.35,28]
+ */
+/* rb0 */ -9.86494292470009928597e-03, /* BF843412, 39E86F4A */
+/* rb1 */ -7.99283237680523006574e-01, /* BFE993BA, 70C285DE */
+/* rb2 */ -1.77579549177547519889e+01, /* C031C209, 555F995A */
+/* rb3 */ -1.60636384855821916062e+02, /* C064145D, 43C5ED98 */
+/* rb4 */ -6.37566443368389627722e+02, /* C083EC88, 1375F228 */
+/* rb5 */ -1.02509513161107724954e+03, /* C0900461, 6A2E5992 */
+/* rb6 */ -4.83519191608651397019e+02, /* C07E384E, 9BDC383F */
+/* sb1 */ 3.03380607434824582924e+01, /* 403E568B, 261D5190 */
+/* sb2 */ 3.25792512996573918826e+02, /* 40745CAE, 221B9F0A */
+/* sb3 */ 1.53672958608443695994e+03, /* 409802EB, 189D5118 */
+/* sb4 */ 3.19985821950859553908e+03, /* 40A8FFB7, 688C246A */
+/* sb5 */ 2.55305040643316442583e+03, /* 40A3F219, CEDF3BE6 */
+/* sb6 */ 4.74528541206955367215e+02, /* 407DA874, E79FE763 */
+/* sb7 */ -2.24409524465858183362e+01 /* C03670E2, 42712D62 */
+};
+
+#define tiny xxx[0]
+#define half xxx[1]
+#define one xxx[2]
+#define two xxx[3]
+#define erx xxx[4]
+/*
+ * Coefficients for approximation to erf on [0,0.84375]
+ */
+#define efx xxx[5]
+#define efx8 xxx[6]
+#define pp0 xxx[7]
+#define pp1 xxx[8]
+#define pp2 xxx[9]
+#define pp3 xxx[10]
+#define pp4 xxx[11]
+#define qq1 xxx[12]
+#define qq2 xxx[13]
+#define qq3 xxx[14]
+#define qq4 xxx[15]
+#define qq5 xxx[16]
+/*
+ * Coefficients for approximation to erf in [0.84375,1.25]
+ */
+#define pa0 xxx[17]
+#define pa1 xxx[18]
+#define pa2 xxx[19]
+#define pa3 xxx[20]
+#define pa4 xxx[21]
+#define pa5 xxx[22]
+#define pa6 xxx[23]
+#define qa1 xxx[24]
+#define qa2 xxx[25]
+#define qa3 xxx[26]
+#define qa4 xxx[27]
+#define qa5 xxx[28]
+#define qa6 xxx[29]
+/*
+ * Coefficients for approximation to erfc in [1.25,1/0.35]
+ */
+#define ra0 xxx[30]
+#define ra1 xxx[31]
+#define ra2 xxx[32]
+#define ra3 xxx[33]
+#define ra4 xxx[34]
+#define ra5 xxx[35]
+#define ra6 xxx[36]
+#define ra7 xxx[37]
+#define sa1 xxx[38]
+#define sa2 xxx[39]
+#define sa3 xxx[40]
+#define sa4 xxx[41]
+#define sa5 xxx[42]
+#define sa6 xxx[43]
+#define sa7 xxx[44]
+#define sa8 xxx[45]
+/*
+ * Coefficients for approximation to erfc in [1/.35,28]
+ */
+#define rb0 xxx[46]
+#define rb1 xxx[47]
+#define rb2 xxx[48]
+#define rb3 xxx[49]
+#define rb4 xxx[50]
+#define rb5 xxx[51]
+#define rb6 xxx[52]
+#define sb1 xxx[53]
+#define sb2 xxx[54]
+#define sb3 xxx[55]
+#define sb4 xxx[56]
+#define sb5 xxx[57]
+#define sb6 xxx[58]
+#define sb7 xxx[59]
+
+double
+erf(double x) {
+ int hx, ix, i;
+ double R, S, P, Q, s, y, z, r;
+
+ hx = ((int *) &x)[HIWORD];
+ ix = hx & 0x7fffffff;
+ if (ix >= 0x7ff00000) { /* erf(nan)=nan */
+#if defined(FPADD_TRAPS_INCOMPLETE_ON_NAN)
+ if (ix >= 0x7ff80000) /* assumes sparc-like QNaN */
+ return (x);
+#endif
+ i = ((unsigned) hx >> 31) << 1;
+ return ((double) (1 - i) + one / x); /* erf(+-inf)=+-1 */
+ }
+
+ if (ix < 0x3feb0000) { /* |x|<0.84375 */
+ if (ix < 0x3e300000) { /* |x|<2**-28 */
+ if (ix < 0x00800000) /* avoid underflow */
+ return (0.125 * (8.0 * x + efx8 * x));
+ return (x + efx * x);
+ }
+ z = x * x;
+ r = pp0 + z * (pp1 + z * (pp2 + z * (pp3 + z * pp4)));
+ s = one +
+ z *(qq1 + z * (qq2 + z * (qq3 + z * (qq4 + z * qq5))));
+ y = r / s;
+ return (x + x * y);
+ }
+ if (ix < 0x3ff40000) { /* 0.84375 <= |x| < 1.25 */
+ s = fabs(x) - one;
+ P = pa0 + s * (pa1 + s * (pa2 + s * (pa3 + s * (pa4 +
+ s * (pa5 + s * pa6)))));
+ Q = one + s * (qa1 + s * (qa2 + s * (qa3 + s * (qa4 +
+ s * (qa5 + s * qa6)))));
+ 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 */
+ R = ra0 + s * (ra1 + s * (ra2 + s * (ra3 + s * (ra4 +
+ s * (ra5 + s * (ra6 + s * ra7))))));
+ S = one + s * (sa1 + s * (sa2 + s * (sa3 + s * (sa4 +
+ s * (sa5 + s * (sa6 + s * (sa7 + s * sa8)))))));
+ } else { /* |x| >= 1/0.35 */
+ R = rb0 + s * (rb1 + s * (rb2 + s * (rb3 + s * (rb4 +
+ s * (rb5 + s * rb6)))));
+ S = one + s * (sb1 + s * (sb2 + s * (sb3 + s * (sb4 +
+ s * (sb5 + s * (sb6 + s * sb7))))));
+ }
+ z = x;
+ ((int *) &z)[LOWORD] = 0;
+ r = exp(-z * z - 0.5625) * exp((z - x) * (z + x) + R / S);
+ if (hx >= 0)
+ return (one - r / x);
+ else
+ return (r / x - one);
+}
+
+double
+erfc(double x) {
+ int hx, ix;
+ double R, S, P, Q, s, y, z, r;
+
+ hx = ((int *) &x)[HIWORD];
+ ix = hx & 0x7fffffff;
+ if (ix >= 0x7ff00000) { /* erfc(nan)=nan */
+#if defined(FPADD_TRAPS_INCOMPLETE_ON_NAN)
+ if (ix >= 0x7ff80000) /* assumes sparc-like QNaN */
+ return (x);
+#endif
+ /* erfc(+-inf)=0,2 */
+ return ((double) (((unsigned) hx >> 31) << 1) + one / x);
+ }
+
+ if (ix < 0x3feb0000) { /* |x| < 0.84375 */
+ if (ix < 0x3c700000) /* |x| < 2**-56 */
+ return (one - x);
+ z = x * x;
+ r = pp0 + z * (pp1 + z * (pp2 + z * (pp3 + z * pp4)));
+ s = one +
+ z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 + z * qq5))));
+ 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 */
+ s = fabs(x) - one;
+ P = pa0 + s * (pa1 + s * (pa2 + s * (pa3 + s * (pa4 +
+ s * (pa5 + s * pa6)))));
+ Q = one + s * (qa1 + s * (qa2 + s * (qa3 + s * (qa4 +
+ s * (qa5 + s * qa6)))));
+ 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 */
+ R = ra0 + s * (ra1 + s * (ra2 + s * (ra3 + s * (ra4 +
+ s * (ra5 + s * (ra6 + s * ra7))))));
+ S = one + s * (sa1 + s * (sa2 + s * (sa3 + s * (sa4 +
+ s * (sa5 + s * (sa6 + s * (sa7 + s * sa8)))))));
+ } else {
+ /* |x| >= 1/.35 ~ 2.857143 */
+ if (hx < 0 && ix >= 0x40180000)
+ return (two - tiny); /* x < -6 */
+
+ R = rb0 + s * (rb1 + s * (rb2 + s * (rb3 + s * (rb4 +
+ s * (rb5 + s * rb6)))));
+ S = one + s * (sb1 + s * (sb2 + s * (sb3 + s * (sb4 +
+ s * (sb5 + s * (sb6 + s * sb7))))));
+ }
+ z = x;
+ ((int *) &z)[LOWORD] = 0;
+ r = exp(-z * z - 0.5625) * 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);
+ }
+}
generated by cgit v1.2.3 (git 2.46.0) at 2025-10-21 19:53:41 +0000