--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/kerneltest/e32utils/nistsecurerng/src/math/erf.cpp Wed Sep 15 13:42:27 2010 +0300
@@ -0,0 +1,355 @@
+/*
+* Portions Copyright (c) 2006, 2009 Nokia Corporation and/or its subsidiary(-ies).
+* All rights reserved.
+* This component and the accompanying materials are made available
+* under the terms of "Eclipse Public License v1.0"
+* which accompanies this distribution, and is available
+* at the URL "http://www.eclipse.org/legal/epl-v10.html".
+*
+* Initial Contributors:
+* Nokia Corporation - initial contribution.
+*
+* Contributors:
+*
+* Description:
+*/
+
+/* @(#)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.
+ * ====================================================
+ */
+#ifndef __SYMBIAN32__
+#ifndef lint
+static char rcsid[] = "$FreeBSD: src/lib/msun/src/s_erf.c,v 1.7 2002/05/28 18:15:04 alfred Exp $";
+#endif
+#endif //__SYMBIAN32__
+
+#include <e32std.h>
+
+#include "openc.h"
+
+/* 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
+ */
+
+
+
+
+
+////--------------------------------------------------
+
+#define __ieee754_exp exp
+typedef TUint32 u_int32_t;
+typedef TInt32 int32_t;
+
+typedef union
+ {
+ double value;
+ struct
+ {
+ u_int32_t lsw;
+ u_int32_t msw;
+ } parts;
+ } ieee_double_shape_type;
+
+
+inline void GET_HIGH_WORD(int32_t& aHighWord, double aValue)
+ {
+ ieee_double_shape_type gh_u;
+ gh_u.value = aValue;
+ aHighWord = gh_u.parts.msw;
+ }
+
+inline void SET_LOW_WORD(double& aValue, int32_t aLowWord)
+ {
+ ieee_double_shape_type sl_u;
+ sl_u.value = aValue;
+ sl_u.parts.lsw = aLowWord;
+ aValue = sl_u.value;
+ }
+
+//----------------------------------------------------------------math_private.h
+
+static const double tiny = 1e-300;
+static const double tinySquare = 0.00; // tiny * tiny
+static const double half = 5.00000000000000000000e-01; /* 0x3FE00000, 0x00000000 */
+static const double one = 1.00000000000000000000e+00; /* 0x3FF00000, 0x00000000 */
+static const double two = 2.00000000000000000000e+00; /* 0x40000000, 0x00000000 */
+ /* c = (float)0.84506291151 */
+static const double erx = 8.45062911510467529297e-01; /* 0x3FEB0AC1, 0x60000000 */
+/*
+ * Coefficients for approximation to erf on [0,0.84375]
+ */
+static const double efx = 1.28379167095512586316e-01; /* 0x3FC06EBA, 0x8214DB69 */
+static const double efx8 = 1.02703333676410069053e+00; /* 0x3FF06EBA, 0x8214DB69 */
+static const double pp0 = 1.28379167095512558561e-01; /* 0x3FC06EBA, 0x8214DB68 */
+static const double pp1 = -3.25042107247001499370e-01; /* 0xBFD4CD7D, 0x691CB913 */
+static const double pp2 = -2.84817495755985104766e-02; /* 0xBF9D2A51, 0xDBD7194F */
+static const double pp3 = -5.77027029648944159157e-03; /* 0xBF77A291, 0x236668E4 */
+static const double pp4 = -2.37630166566501626084e-05; /* 0xBEF8EAD6, 0x120016AC */
+static const double qq1 = 3.97917223959155352819e-01; /* 0x3FD97779, 0xCDDADC09 */
+static const double qq2 = 6.50222499887672944485e-02; /* 0x3FB0A54C, 0x5536CEBA */
+static const double qq3 = 5.08130628187576562776e-03; /* 0x3F74D022, 0xC4D36B0F */
+static const double qq4 = 1.32494738004321644526e-04; /* 0x3F215DC9, 0x221C1A10 */
+static const double qq5 = -3.96022827877536812320e-06; /* 0xBED09C43, 0x42A26120 */
+/*
+ * Coefficients for approximation to erf in [0.84375,1.25]
+ */
+static const double pa0 = -2.36211856075265944077e-03; /* 0xBF6359B8, 0xBEF77538 */
+static const double pa1 = 4.14856118683748331666e-01; /* 0x3FDA8D00, 0xAD92B34D */
+static const double pa2 = -3.72207876035701323847e-01; /* 0xBFD7D240, 0xFBB8C3F1 */
+static const double pa3 = 3.18346619901161753674e-01; /* 0x3FD45FCA, 0x805120E4 */
+static const double pa4 = -1.10894694282396677476e-01; /* 0xBFBC6398, 0x3D3E28EC */
+static const double pa5 = 3.54783043256182359371e-02; /* 0x3FA22A36, 0x599795EB */
+static const double pa6 = -2.16637559486879084300e-03; /* 0xBF61BF38, 0x0A96073F */
+static const double qa1 = 1.06420880400844228286e-01; /* 0x3FBB3E66, 0x18EEE323 */
+static const double qa2 = 5.40397917702171048937e-01; /* 0x3FE14AF0, 0x92EB6F33 */
+static const double qa3 = 7.18286544141962662868e-02; /* 0x3FB2635C, 0xD99FE9A7 */
+static const double qa4 = 1.26171219808761642112e-01; /* 0x3FC02660, 0xE763351F */
+static const double qa5 = 1.36370839120290507362e-02; /* 0x3F8BEDC2, 0x6B51DD1C */
+static const double qa6 = 1.19844998467991074170e-02; /* 0x3F888B54, 0x5735151D */
+/*
+ * Coefficients for approximation to erfc in [1.25,1/0.35]
+ */
+static const double ra0 = -9.86494403484714822705e-03; /* 0xBF843412, 0x600D6435 */
+static const double ra1 = -6.93858572707181764372e-01; /* 0xBFE63416, 0xE4BA7360 */
+static const double ra2 = -1.05586262253232909814e+01; /* 0xC0251E04, 0x41B0E726 */
+static const double ra3 = -6.23753324503260060396e+01; /* 0xC04F300A, 0xE4CBA38D */
+static const double ra4 = -1.62396669462573470355e+02; /* 0xC0644CB1, 0x84282266 */
+static const double ra5 = -1.84605092906711035994e+02; /* 0xC067135C, 0xEBCCABB2 */
+static const double ra6 = -8.12874355063065934246e+01; /* 0xC0545265, 0x57E4D2F2 */
+static const double ra7 = -9.81432934416914548592e+00; /* 0xC023A0EF, 0xC69AC25C */
+static const double sa1 = 1.96512716674392571292e+01; /* 0x4033A6B9, 0xBD707687 */
+static const double sa2 = 1.37657754143519042600e+02; /* 0x4061350C, 0x526AE721 */
+static const double sa3 = 4.34565877475229228821e+02; /* 0x407B290D, 0xD58A1A71 */
+static const double sa4 = 6.45387271733267880336e+02; /* 0x40842B19, 0x21EC2868 */
+static const double sa5 = 4.29008140027567833386e+02; /* 0x407AD021, 0x57700314 */
+static const double sa6 = 1.08635005541779435134e+02; /* 0x405B28A3, 0xEE48AE2C */
+static const double sa7 = 6.57024977031928170135e+00; /* 0x401A47EF, 0x8E484A93 */
+static const double sa8 = -6.04244152148580987438e-02; /* 0xBFAEEFF2, 0xEE749A62 */
+/*
+ * Coefficients for approximation to erfc in [1/.35,28]
+ */
+static const double rb0 = -9.86494292470009928597e-03; /* 0xBF843412, 0x39E86F4A */
+static const double rb1 = -7.99283237680523006574e-01; /* 0xBFE993BA, 0x70C285DE */
+static const double rb2 = -1.77579549177547519889e+01; /* 0xC031C209, 0x555F995A */
+static const double rb3 = -1.60636384855821916062e+02; /* 0xC064145D, 0x43C5ED98 */
+static const double rb4 = -6.37566443368389627722e+02; /* 0xC083EC88, 0x1375F228 */
+static const double rb5 = -1.02509513161107724954e+03; /* 0xC0900461, 0x6A2E5992 */
+static const double rb6 = -4.83519191608651397019e+02; /* 0xC07E384E, 0x9BDC383F */
+static const double sb1 = 3.03380607434824582924e+01; /* 0x403E568B, 0x261D5190 */
+static const double sb2 = 3.25792512996573918826e+02; /* 0x40745CAE, 0x221B9F0A */
+static const double sb3 = 1.53672958608443695994e+03; /* 0x409802EB, 0x189D5118 */
+static const double sb4 = 3.19985821950859553908e+03; /* 0x40A8FFB7, 0x688C246A */
+static const double sb5 = 2.55305040643316442583e+03; /* 0x40A3F219, 0xCEDF3BE6 */
+static const double sb6 = 4.74528541206955367215e+02; /* 0x407DA874, 0xE79FE763 */
+static const double sb7 = -2.24409524465858183362e+01; /* 0xC03670E2, 0x42712D62 */
+
+double erf(double x)
+{
+ TInt32 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 = ((TUint32)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)
+ return 0.125*(8.0*x+efx8*x); /*avoid underflow */
+ 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;
+ 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;
+}
+
+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;
+ }
+
+ 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;
+ 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 tinySquare; else return two-tiny;
+ }
+}