Mercurial > hg > openjdk > jdk8u > jdk
changeset 4445:b9fffbe98230
7075098: Remove unused fdlibm files
Reviewed-by: alanb, mduigou
| author | darcy |
|---|---|
| date | Sat, 06 Aug 2011 14:35:58 -0700 |
| parents | 565555e89034 |
| children | a5f825ef8587 |
| files | make/java/fdlibm/FILES_c.gmk src/share/native/java/lang/fdlibm/include/fdlibm.h src/share/native/java/lang/fdlibm/include/jfdlibm.h src/share/native/java/lang/fdlibm/src/e_acosh.c src/share/native/java/lang/fdlibm/src/e_gamma.c src/share/native/java/lang/fdlibm/src/e_gamma_r.c src/share/native/java/lang/fdlibm/src/e_j0.c src/share/native/java/lang/fdlibm/src/e_j1.c src/share/native/java/lang/fdlibm/src/e_jn.c src/share/native/java/lang/fdlibm/src/e_lgamma.c src/share/native/java/lang/fdlibm/src/e_lgamma_r.c src/share/native/java/lang/fdlibm/src/s_asinh.c src/share/native/java/lang/fdlibm/src/s_erf.c src/share/native/java/lang/fdlibm/src/w_acosh.c src/share/native/java/lang/fdlibm/src/w_gamma.c src/share/native/java/lang/fdlibm/src/w_gamma_r.c src/share/native/java/lang/fdlibm/src/w_j0.c src/share/native/java/lang/fdlibm/src/w_j1.c src/share/native/java/lang/fdlibm/src/w_jn.c src/share/native/java/lang/fdlibm/src/w_lgamma.c src/share/native/java/lang/fdlibm/src/w_lgamma_r.c |
| diffstat | 21 files changed, 0 insertions(+), 2786 deletions(-) [+] |
line wrap: on
line diff
--- a/make/java/fdlibm/FILES_c.gmk Thu Aug 04 08:53:16 2011 -0700 +++ b/make/java/fdlibm/FILES_c.gmk Sat Aug 06 14:35:58 2011 -0700 @@ -30,21 +30,13 @@ k_sin.c \ k_tan.c \ e_acos.c \ - e_acosh.c \ e_asin.c \ e_atan2.c \ e_atanh.c \ e_cosh.c \ e_exp.c \ e_fmod.c \ - e_gamma.c \ - e_gamma_r.c \ e_hypot.c \ - e_j0.c \ - e_j1.c \ - e_jn.c \ - e_lgamma.c \ - e_lgamma_r.c \ e_log.c \ e_log10.c \ e_pow.c \ @@ -54,21 +46,13 @@ e_sinh.c \ e_sqrt.c \ w_acos.c \ - w_acosh.c \ w_asin.c \ w_atan2.c \ w_atanh.c \ w_cosh.c \ w_exp.c \ w_fmod.c \ - w_gamma.c \ - w_gamma_r.c \ w_hypot.c \ - w_j0.c \ - w_j1.c \ - w_jn.c \ - w_lgamma.c \ - w_lgamma_r.c \ w_log.c \ w_log10.c \ w_pow.c \ @@ -76,13 +60,11 @@ w_scalb.c \ w_sinh.c \ w_sqrt.c \ - s_asinh.c \ s_atan.c \ s_cbrt.c \ s_ceil.c \ s_copysign.c \ s_cos.c \ - s_erf.c \ s_expm1.c \ s_fabs.c \ s_finite.c \
--- a/src/share/native/java/lang/fdlibm/include/fdlibm.h Thu Aug 04 08:53:16 2011 -0700 +++ b/src/share/native/java/lang/fdlibm/include/fdlibm.h Sat Aug 06 14:35:58 2011 -0700 @@ -135,22 +135,10 @@ extern double floor __P((double)); extern double fmod __P((double, double)); -extern double erf __P((double)); -extern double erfc __P((double)); -extern double gamma __P((double)); extern double hypot __P((double, double)); extern int isnan __P((double)); extern int finite __P((double)); -extern double j0 __P((double)); -extern double j1 __P((double)); -extern double jn __P((int, double)); -extern double lgamma __P((double)); -extern double y0 __P((double)); -extern double y1 __P((double)); -extern double yn __P((int, double)); -extern double acosh __P((double)); -extern double asinh __P((double)); extern double atanh __P((double)); extern double cbrt __P((double)); extern double logb __P((double)); @@ -183,19 +171,9 @@ extern double expm1 __P((double)); extern double log1p __P((double)); -/* - * Reentrant version of gamma & lgamma; passes signgam back by reference - * as the second argument; user must allocate space for signgam. - */ -#ifdef _REENTRANT -extern double gamma_r __P((double, int *)); -extern double lgamma_r __P((double, int *)); -#endif /* _REENTRANT */ - /* ieee style elementary functions */ extern double __ieee754_sqrt __P((double)); extern double __ieee754_acos __P((double)); -extern double __ieee754_acosh __P((double)); extern double __ieee754_log __P((double)); extern double __ieee754_atanh __P((double)); extern double __ieee754_asin __P((double)); @@ -204,19 +182,9 @@ extern double __ieee754_cosh __P((double)); extern double __ieee754_fmod __P((double,double)); extern double __ieee754_pow __P((double,double)); -extern double __ieee754_lgamma_r __P((double,int *)); -extern double __ieee754_gamma_r __P((double,int *)); -extern double __ieee754_lgamma __P((double)); -extern double __ieee754_gamma __P((double)); extern double __ieee754_log10 __P((double)); extern double __ieee754_sinh __P((double)); extern double __ieee754_hypot __P((double,double)); -extern double __ieee754_j0 __P((double)); -extern double __ieee754_j1 __P((double)); -extern double __ieee754_y0 __P((double)); -extern double __ieee754_y1 __P((double)); -extern double __ieee754_jn __P((int,double)); -extern double __ieee754_yn __P((int,double)); extern double __ieee754_remainder __P((double,double)); extern int __ieee754_rem_pio2 __P((double,double*)); #ifdef _SCALB_INT
--- a/src/share/native/java/lang/fdlibm/include/jfdlibm.h Thu Aug 04 08:53:16 2011 -0700 +++ b/src/share/native/java/lang/fdlibm/include/jfdlibm.h Sat Aug 06 14:35:58 2011 -0700 @@ -64,7 +64,6 @@ #ifdef __linux__ #define __ieee754_sqrt __j__ieee754_sqrt #define __ieee754_acos __j__ieee754_acos -#define __ieee754_acosh __j__ieee754_acosh #define __ieee754_log __j__ieee754_log #define __ieee754_atanh __j__ieee754_atanh #define __ieee754_asin __j__ieee754_asin @@ -73,19 +72,9 @@ #define __ieee754_cosh __j__ieee754_cosh #define __ieee754_fmod __j__ieee754_fmod #define __ieee754_pow __j__ieee754_pow -#define __ieee754_lgamma_r __j__ieee754_lgamma_r -#define __ieee754_gamma_r __j__ieee754_gamma_r -#define __ieee754_lgamma __j__ieee754_lgamma -#define __ieee754_gamma __j__ieee754_gamma #define __ieee754_log10 __j__ieee754_log10 #define __ieee754_sinh __j__ieee754_sinh #define __ieee754_hypot __j__ieee754_hypot -#define __ieee754_j0 __j__ieee754_j0 -#define __ieee754_j1 __j__ieee754_j1 -#define __ieee754_y0 __j__ieee754_y0 -#define __ieee754_y1 __j__ieee754_y1 -#define __ieee754_jn __j__ieee754_jn -#define __ieee754_yn __j__ieee754_yn #define __ieee754_remainder __j__ieee754_remainder #define __ieee754_rem_pio2 __j__ieee754_rem_pio2 #define __ieee754_scalb __j__ieee754_scalb
--- a/src/share/native/java/lang/fdlibm/src/e_acosh.c Thu Aug 04 08:53:16 2011 -0700 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,77 +0,0 @@ - -/* - * Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved. - * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. - * - * This code is free software; you can redistribute it and/or modify it - * under the terms of the GNU General Public License version 2 only, as - * published by the Free Software Foundation. Oracle designates this - * particular file as subject to the "Classpath" exception as provided - * by Oracle in the LICENSE file that accompanied this code. - * - * This code is distributed in the hope that it will be useful, but WITHOUT - * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or - * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License - * version 2 for more details (a copy is included in the LICENSE file that - * accompanied this code). - * - * You should have received a copy of the GNU General Public License version - * 2 along with this work; if not, write to the Free Software Foundation, - * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. - * - * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA - * or visit www.oracle.com if you need additional information or have any - * questions. - */ - -/* __ieee754_acosh(x) - * Method : - * Based on - * acosh(x) = log [ x + sqrt(x*x-1) ] - * we have - * acosh(x) := log(x)+ln2, if x is large; else - * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else - * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1. - * - * Special cases: - * acosh(x) is NaN with signal if x<1. - * acosh(NaN) is NaN without signal. - */ - -#include "fdlibm.h" - -#ifdef __STDC__ -static const double -#else -static double -#endif -one = 1.0, -ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */ - -#ifdef __STDC__ - double __ieee754_acosh(double x) -#else - double __ieee754_acosh(x) - double x; -#endif -{ - double t; - int hx; - hx = __HI(x); - if(hx<0x3ff00000) { /* x < 1 */ - return (x-x)/(x-x); - } else if(hx >=0x41b00000) { /* x > 2**28 */ - if(hx >=0x7ff00000) { /* x is inf of NaN */ - return x+x; - } else - return __ieee754_log(x)+ln2; /* acosh(huge)=log(2x) */ - } else if(((hx-0x3ff00000)|__LO(x))==0) { - return 0.0; /* acosh(1) = 0 */ - } else if (hx > 0x40000000) { /* 2**28 > x > 2 */ - t=x*x; - return __ieee754_log(2.0*x-one/(x+sqrt(t-one))); - } else { /* 1<x<2 */ - t = x-one; - return log1p(t+sqrt(2.0*t+t*t)); - } -}
--- a/src/share/native/java/lang/fdlibm/src/e_gamma.c Thu Aug 04 08:53:16 2011 -0700 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,45 +0,0 @@ - -/* - * Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved. - * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. - * - * This code is free software; you can redistribute it and/or modify it - * under the terms of the GNU General Public License version 2 only, as - * published by the Free Software Foundation. Oracle designates this - * particular file as subject to the "Classpath" exception as provided - * by Oracle in the LICENSE file that accompanied this code. - * - * This code is distributed in the hope that it will be useful, but WITHOUT - * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or - * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License - * version 2 for more details (a copy is included in the LICENSE file that - * accompanied this code). - * - * You should have received a copy of the GNU General Public License version - * 2 along with this work; if not, write to the Free Software Foundation, - * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. - * - * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA - * or visit www.oracle.com if you need additional information or have any - * questions. - */ - -/* __ieee754_gamma(x) - * Return the logarithm of the Gamma function of x. - * - * Method: call __ieee754_gamma_r - */ - -#include "fdlibm.h" - -extern int signgam; - -#ifdef __STDC__ - double __ieee754_gamma(double x) -#else - double __ieee754_gamma(x) - double x; -#endif -{ - return __ieee754_gamma_r(x,&signgam); -}
--- a/src/share/native/java/lang/fdlibm/src/e_gamma_r.c Thu Aug 04 08:53:16 2011 -0700 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,44 +0,0 @@ - -/* - * Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved. - * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. - * - * This code is free software; you can redistribute it and/or modify it - * under the terms of the GNU General Public License version 2 only, as - * published by the Free Software Foundation. Oracle designates this - * particular file as subject to the "Classpath" exception as provided - * by Oracle in the LICENSE file that accompanied this code. - * - * This code is distributed in the hope that it will be useful, but WITHOUT - * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or - * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License - * version 2 for more details (a copy is included in the LICENSE file that - * accompanied this code). - * - * You should have received a copy of the GNU General Public License version - * 2 along with this work; if not, write to the Free Software Foundation, - * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. - * - * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA - * or visit www.oracle.com if you need additional information or have any - * questions. - */ - -/* __ieee754_gamma_r(x, signgamp) - * Reentrant version of the logarithm of the Gamma function - * with user provide pointer for the sign of Gamma(x). - * - * Method: See __ieee754_lgamma_r - */ - -#include "fdlibm.h" - -#ifdef __STDC__ - double __ieee754_gamma_r(double x, int *signgamp) -#else - double __ieee754_gamma_r(x,signgamp) - double x; int *signgamp; -#endif -{ - return __ieee754_lgamma_r(x,signgamp); -}
--- a/src/share/native/java/lang/fdlibm/src/e_j0.c Thu Aug 04 08:53:16 2011 -0700 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,491 +0,0 @@ - -/* - * Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved. - * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. - * - * This code is free software; you can redistribute it and/or modify it - * under the terms of the GNU General Public License version 2 only, as - * published by the Free Software Foundation. Oracle designates this - * particular file as subject to the "Classpath" exception as provided - * by Oracle in the LICENSE file that accompanied this code. - * - * This code is distributed in the hope that it will be useful, but WITHOUT - * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or - * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License - * version 2 for more details (a copy is included in the LICENSE file that - * accompanied this code). - * - * You should have received a copy of the GNU General Public License version - * 2 along with this work; if not, write to the Free Software Foundation, - * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. - * - * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA - * or visit www.oracle.com if you need additional information or have any - * questions. - */ - -/* __ieee754_j0(x), __ieee754_y0(x) - * Bessel function of the first and second kinds of order zero. - * Method -- j0(x): - * 1. For tiny x, we use j0(x) = 1 - x^2/4 + x^4/64 - ... - * 2. Reduce x to |x| since j0(x)=j0(-x), and - * for x in (0,2) - * j0(x) = 1-z/4+ z^2*R0/S0, where z = x*x; - * (precision: |j0-1+z/4-z^2R0/S0 |<2**-63.67 ) - * for x in (2,inf) - * j0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)-q0(x)*sin(x0)) - * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0) - * as follow: - * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4) - * = 1/sqrt(2) * (cos(x) + sin(x)) - * sin(x0) = sin(x)cos(pi/4)-cos(x)sin(pi/4) - * = 1/sqrt(2) * (sin(x) - cos(x)) - * (To avoid cancellation, use - * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) - * to compute the worse one.) - * - * 3 Special cases - * j0(nan)= nan - * j0(0) = 1 - * j0(inf) = 0 - * - * Method -- y0(x): - * 1. For x<2. - * Since - * y0(x) = 2/pi*(j0(x)*(ln(x/2)+Euler) + x^2/4 - ...) - * therefore y0(x)-2/pi*j0(x)*ln(x) is an even function. - * We use the following function to approximate y0, - * y0(x) = U(z)/V(z) + (2/pi)*(j0(x)*ln(x)), z= x^2 - * where - * U(z) = u00 + u01*z + ... + u06*z^6 - * V(z) = 1 + v01*z + ... + v04*z^4 - * with absolute approximation error bounded by 2**-72. - * Note: For tiny x, U/V = u0 and j0(x)~1, hence - * y0(tiny) = u0 + (2/pi)*ln(tiny), (choose tiny<2**-27) - * 2. For x>=2. - * y0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)+q0(x)*sin(x0)) - * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0) - * by the method mentioned above. - * 3. Special cases: y0(0)=-inf, y0(x<0)=NaN, y0(inf)=0. - */ - -#include "fdlibm.h" - -#ifdef __STDC__ -static double pzero(double), qzero(double); -#else -static double pzero(), qzero(); -#endif - -#ifdef __STDC__ -static const double -#else -static double -#endif -huge = 1e300, -one = 1.0, -invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ -tpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ - /* R0/S0 on [0, 2.00] */ -R02 = 1.56249999999999947958e-02, /* 0x3F8FFFFF, 0xFFFFFFFD */ -R03 = -1.89979294238854721751e-04, /* 0xBF28E6A5, 0xB61AC6E9 */ -R04 = 1.82954049532700665670e-06, /* 0x3EBEB1D1, 0x0C503919 */ -R05 = -4.61832688532103189199e-09, /* 0xBE33D5E7, 0x73D63FCE */ -S01 = 1.56191029464890010492e-02, /* 0x3F8FFCE8, 0x82C8C2A4 */ -S02 = 1.16926784663337450260e-04, /* 0x3F1EA6D2, 0xDD57DBF4 */ -S03 = 5.13546550207318111446e-07, /* 0x3EA13B54, 0xCE84D5A9 */ -S04 = 1.16614003333790000205e-09; /* 0x3E1408BC, 0xF4745D8F */ - -static double zero = 0.0; - -#ifdef __STDC__ - double __ieee754_j0(double x) -#else - double __ieee754_j0(x) - double x; -#endif -{ - double z, s,c,ss,cc,r,u,v; - int hx,ix; - - hx = __HI(x); - ix = hx&0x7fffffff; - if(ix>=0x7ff00000) return one/(x*x); - x = fabs(x); - if(ix >= 0x40000000) { /* |x| >= 2.0 */ - s = sin(x); - c = cos(x); - ss = s-c; - cc = s+c; - if(ix<0x7fe00000) { /* make sure x+x not overflow */ - z = -cos(x+x); - if ((s*c)<zero) cc = z/ss; - else ss = z/cc; - } - /* - * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) - * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) - */ - if(ix>0x48000000) z = (invsqrtpi*cc)/sqrt(x); - else { - u = pzero(x); v = qzero(x); - z = invsqrtpi*(u*cc-v*ss)/sqrt(x); - } - return z; - } - if(ix<0x3f200000) { /* |x| < 2**-13 */ - if(huge+x>one) { /* raise inexact if x != 0 */ - if(ix<0x3e400000) return one; /* |x|<2**-27 */ - else return one - 0.25*x*x; - } - } - z = x*x; - r = z*(R02+z*(R03+z*(R04+z*R05))); - s = one+z*(S01+z*(S02+z*(S03+z*S04))); - if(ix < 0x3FF00000) { /* |x| < 1.00 */ - return one + z*(-0.25+(r/s)); - } else { - u = 0.5*x; - return((one+u)*(one-u)+z*(r/s)); - } -} - -#ifdef __STDC__ -static const double -#else -static double -#endif -u00 = -7.38042951086872317523e-02, /* 0xBFB2E4D6, 0x99CBD01F */ -u01 = 1.76666452509181115538e-01, /* 0x3FC69D01, 0x9DE9E3FC */ -u02 = -1.38185671945596898896e-02, /* 0xBF8C4CE8, 0xB16CFA97 */ -u03 = 3.47453432093683650238e-04, /* 0x3F36C54D, 0x20B29B6B */ -u04 = -3.81407053724364161125e-06, /* 0xBECFFEA7, 0x73D25CAD */ -u05 = 1.95590137035022920206e-08, /* 0x3E550057, 0x3B4EABD4 */ -u06 = -3.98205194132103398453e-11, /* 0xBDC5E43D, 0x693FB3C8 */ -v01 = 1.27304834834123699328e-02, /* 0x3F8A1270, 0x91C9C71A */ -v02 = 7.60068627350353253702e-05, /* 0x3F13ECBB, 0xF578C6C1 */ -v03 = 2.59150851840457805467e-07, /* 0x3E91642D, 0x7FF202FD */ -v04 = 4.41110311332675467403e-10; /* 0x3DFE5018, 0x3BD6D9EF */ - -#ifdef __STDC__ - double __ieee754_y0(double x) -#else - double __ieee754_y0(x) - double x; -#endif -{ - double z, s,c,ss,cc,u,v; - int hx,ix,lx; - - hx = __HI(x); - ix = 0x7fffffff&hx; - lx = __LO(x); - /* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0 */ - if(ix>=0x7ff00000) return one/(x+x*x); - if((ix|lx)==0) return -one/zero; - if(hx<0) return zero/zero; - if(ix >= 0x40000000) { /* |x| >= 2.0 */ - /* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0)) - * where x0 = x-pi/4 - * Better formula: - * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4) - * = 1/sqrt(2) * (sin(x) + cos(x)) - * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) - * = 1/sqrt(2) * (sin(x) - cos(x)) - * To avoid cancellation, use - * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) - * to compute the worse one. - */ - s = sin(x); - c = cos(x); - ss = s-c; - cc = s+c; - /* - * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) - * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) - */ - if(ix<0x7fe00000) { /* make sure x+x not overflow */ - z = -cos(x+x); - if ((s*c)<zero) cc = z/ss; - else ss = z/cc; - } - if(ix>0x48000000) z = (invsqrtpi*ss)/sqrt(x); - else { - u = pzero(x); v = qzero(x); - z = invsqrtpi*(u*ss+v*cc)/sqrt(x); - } - return z; - } - if(ix<=0x3e400000) { /* x < 2**-27 */ - return(u00 + tpi*__ieee754_log(x)); - } - z = x*x; - u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06))))); - v = one+z*(v01+z*(v02+z*(v03+z*v04))); - return(u/v + tpi*(__ieee754_j0(x)*__ieee754_log(x))); -} - -/* The asymptotic expansions of pzero is - * 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x. - * For x >= 2, We approximate pzero by - * pzero(x) = 1 + (R/S) - * where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10 - * S = 1 + pS0*s^2 + ... + pS4*s^10 - * and - * | pzero(x)-1-R/S | <= 2 ** ( -60.26) - */ -#ifdef __STDC__ -static const double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ -#else -static double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ -#endif - 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ - -7.03124999999900357484e-02, /* 0xBFB1FFFF, 0xFFFFFD32 */ - -8.08167041275349795626e+00, /* 0xC02029D0, 0xB44FA779 */ - -2.57063105679704847262e+02, /* 0xC0701102, 0x7B19E863 */ - -2.48521641009428822144e+03, /* 0xC0A36A6E, 0xCD4DCAFC */ - -5.25304380490729545272e+03, /* 0xC0B4850B, 0x36CC643D */ -}; -#ifdef __STDC__ -static const double pS8[5] = { -#else -static double pS8[5] = { -#endif - 1.16534364619668181717e+02, /* 0x405D2233, 0x07A96751 */ - 3.83374475364121826715e+03, /* 0x40ADF37D, 0x50596938 */ - 4.05978572648472545552e+04, /* 0x40E3D2BB, 0x6EB6B05F */ - 1.16752972564375915681e+05, /* 0x40FC810F, 0x8F9FA9BD */ - 4.76277284146730962675e+04, /* 0x40E74177, 0x4F2C49DC */ -}; - -#ifdef __STDC__ -static const double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ -#else -static double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ -#endif - -1.14125464691894502584e-11, /* 0xBDA918B1, 0x47E495CC */ - -7.03124940873599280078e-02, /* 0xBFB1FFFF, 0xE69AFBC6 */ - -4.15961064470587782438e+00, /* 0xC010A370, 0xF90C6BBF */ - -6.76747652265167261021e+01, /* 0xC050EB2F, 0x5A7D1783 */ - -3.31231299649172967747e+02, /* 0xC074B3B3, 0x6742CC63 */ - -3.46433388365604912451e+02, /* 0xC075A6EF, 0x28A38BD7 */ -}; -#ifdef __STDC__ -static const double pS5[5] = { -#else -static double pS5[5] = { -#endif - 6.07539382692300335975e+01, /* 0x404E6081, 0x0C98C5DE */ - 1.05125230595704579173e+03, /* 0x40906D02, 0x5C7E2864 */ - 5.97897094333855784498e+03, /* 0x40B75AF8, 0x8FBE1D60 */ - 9.62544514357774460223e+03, /* 0x40C2CCB8, 0xFA76FA38 */ - 2.40605815922939109441e+03, /* 0x40A2CC1D, 0xC70BE864 */ -}; - -#ifdef __STDC__ -static const double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ -#else -static double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ -#endif - -2.54704601771951915620e-09, /* 0xBE25E103, 0x6FE1AA86 */ - -7.03119616381481654654e-02, /* 0xBFB1FFF6, 0xF7C0E24B */ - -2.40903221549529611423e+00, /* 0xC00345B2, 0xAEA48074 */ - -2.19659774734883086467e+01, /* 0xC035F74A, 0x4CB94E14 */ - -5.80791704701737572236e+01, /* 0xC04D0A22, 0x420A1A45 */ - -3.14479470594888503854e+01, /* 0xC03F72AC, 0xA892D80F */ -}; -#ifdef __STDC__ -static const double pS3[5] = { -#else -static double pS3[5] = { -#endif - 3.58560338055209726349e+01, /* 0x4041ED92, 0x84077DD3 */ - 3.61513983050303863820e+02, /* 0x40769839, 0x464A7C0E */ - 1.19360783792111533330e+03, /* 0x4092A66E, 0x6D1061D6 */ - 1.12799679856907414432e+03, /* 0x40919FFC, 0xB8C39B7E */ - 1.73580930813335754692e+02, /* 0x4065B296, 0xFC379081 */ -}; - -#ifdef __STDC__ -static const double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ -#else -static double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ -#endif - -8.87534333032526411254e-08, /* 0xBE77D316, 0xE927026D */ - -7.03030995483624743247e-02, /* 0xBFB1FF62, 0x495E1E42 */ - -1.45073846780952986357e+00, /* 0xBFF73639, 0x8A24A843 */ - -7.63569613823527770791e+00, /* 0xC01E8AF3, 0xEDAFA7F3 */ - -1.11931668860356747786e+01, /* 0xC02662E6, 0xC5246303 */ - -3.23364579351335335033e+00, /* 0xC009DE81, 0xAF8FE70F */ -}; -#ifdef __STDC__ -static const double pS2[5] = { -#else -static double pS2[5] = { -#endif - 2.22202997532088808441e+01, /* 0x40363865, 0x908B5959 */ - 1.36206794218215208048e+02, /* 0x4061069E, 0x0EE8878F */ - 2.70470278658083486789e+02, /* 0x4070E786, 0x42EA079B */ - 1.53875394208320329881e+02, /* 0x40633C03, 0x3AB6FAFF */ - 1.46576176948256193810e+01, /* 0x402D50B3, 0x44391809 */ -}; - -#ifdef __STDC__ - static double pzero(double x) -#else - static double pzero(x) - double x; -#endif -{ -#ifdef __STDC__ - const double *p=(void*)0,*q=(void*)0; -#else - double *p,*q; -#endif - double z,r,s; - int ix; - ix = 0x7fffffff&__HI(x); - if(ix>=0x40200000) {p = pR8; q= pS8;} - else if(ix>=0x40122E8B){p = pR5; q= pS5;} - else if(ix>=0x4006DB6D){p = pR3; q= pS3;} - else if(ix>=0x40000000){p = pR2; q= pS2;} - z = one/(x*x); - r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); - s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); - return one+ r/s; -} - - -/* For x >= 8, the asymptotic expansions of qzero is - * -1/8 s + 75/1024 s^3 - ..., where s = 1/x. - * We approximate pzero by - * qzero(x) = s*(-1.25 + (R/S)) - * where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10 - * S = 1 + qS0*s^2 + ... + qS5*s^12 - * and - * | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22) - */ -#ifdef __STDC__ -static const double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ -#else -static double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ -#endif - 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ - 7.32421874999935051953e-02, /* 0x3FB2BFFF, 0xFFFFFE2C */ - 1.17682064682252693899e+01, /* 0x40278952, 0x5BB334D6 */ - 5.57673380256401856059e+02, /* 0x40816D63, 0x15301825 */ - 8.85919720756468632317e+03, /* 0x40C14D99, 0x3E18F46D */ - 3.70146267776887834771e+04, /* 0x40E212D4, 0x0E901566 */ -}; -#ifdef __STDC__ -static const double qS8[6] = { -#else -static double qS8[6] = { -#endif - 1.63776026895689824414e+02, /* 0x406478D5, 0x365B39BC */ - 8.09834494656449805916e+03, /* 0x40BFA258, 0x4E6B0563 */ - 1.42538291419120476348e+05, /* 0x41016652, 0x54D38C3F */ - 8.03309257119514397345e+05, /* 0x412883DA, 0x83A52B43 */ - 8.40501579819060512818e+05, /* 0x4129A66B, 0x28DE0B3D */ - -3.43899293537866615225e+05, /* 0xC114FD6D, 0x2C9530C5 */ -}; - -#ifdef __STDC__ -static const double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ -#else -static double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ -#endif - 1.84085963594515531381e-11, /* 0x3DB43D8F, 0x29CC8CD9 */ - 7.32421766612684765896e-02, /* 0x3FB2BFFF, 0xD172B04C */ - 5.83563508962056953777e+00, /* 0x401757B0, 0xB9953DD3 */ - 1.35111577286449829671e+02, /* 0x4060E392, 0x0A8788E9 */ - 1.02724376596164097464e+03, /* 0x40900CF9, 0x9DC8C481 */ - 1.98997785864605384631e+03, /* 0x409F17E9, 0x53C6E3A6 */ -}; -#ifdef __STDC__ -static const double qS5[6] = { -#else -static double qS5[6] = { -#endif - 8.27766102236537761883e+01, /* 0x4054B1B3, 0xFB5E1543 */ - 2.07781416421392987104e+03, /* 0x40A03BA0, 0xDA21C0CE */ - 1.88472887785718085070e+04, /* 0x40D267D2, 0x7B591E6D */ - 5.67511122894947329769e+04, /* 0x40EBB5E3, 0x97E02372 */ - 3.59767538425114471465e+04, /* 0x40E19118, 0x1F7A54A0 */ - -5.35434275601944773371e+03, /* 0xC0B4EA57, 0xBEDBC609 */ -}; - -#ifdef __STDC__ -static const double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ -#else -static double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ -#endif - 4.37741014089738620906e-09, /* 0x3E32CD03, 0x6ADECB82 */ - 7.32411180042911447163e-02, /* 0x3FB2BFEE, 0x0E8D0842 */ - 3.34423137516170720929e+00, /* 0x400AC0FC, 0x61149CF5 */ - 4.26218440745412650017e+01, /* 0x40454F98, 0x962DAEDD */ - 1.70808091340565596283e+02, /* 0x406559DB, 0xE25EFD1F */ - 1.66733948696651168575e+02, /* 0x4064D77C, 0x81FA21E0 */ -}; -#ifdef __STDC__ -static const double qS3[6] = { -#else -static double qS3[6] = { -#endif - 4.87588729724587182091e+01, /* 0x40486122, 0xBFE343A6 */ - 7.09689221056606015736e+02, /* 0x40862D83, 0x86544EB3 */ - 3.70414822620111362994e+03, /* 0x40ACF04B, 0xE44DFC63 */ - 6.46042516752568917582e+03, /* 0x40B93C6C, 0xD7C76A28 */ - 2.51633368920368957333e+03, /* 0x40A3A8AA, 0xD94FB1C0 */ - -1.49247451836156386662e+02, /* 0xC062A7EB, 0x201CF40F */ -}; - -#ifdef __STDC__ -static const double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ -#else -static double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ -#endif - 1.50444444886983272379e-07, /* 0x3E84313B, 0x54F76BDB */ - 7.32234265963079278272e-02, /* 0x3FB2BEC5, 0x3E883E34 */ - 1.99819174093815998816e+00, /* 0x3FFFF897, 0xE727779C */ - 1.44956029347885735348e+01, /* 0x402CFDBF, 0xAAF96FE5 */ - 3.16662317504781540833e+01, /* 0x403FAA8E, 0x29FBDC4A */ - 1.62527075710929267416e+01, /* 0x403040B1, 0x71814BB4 */ -}; -#ifdef __STDC__ -static const double qS2[6] = { -#else -static double qS2[6] = { -#endif - 3.03655848355219184498e+01, /* 0x403E5D96, 0xF7C07AED */ - 2.69348118608049844624e+02, /* 0x4070D591, 0xE4D14B40 */ - 8.44783757595320139444e+02, /* 0x408A6645, 0x22B3BF22 */ - 8.82935845112488550512e+02, /* 0x408B977C, 0x9C5CC214 */ - 2.12666388511798828631e+02, /* 0x406A9553, 0x0E001365 */ - -5.31095493882666946917e+00, /* 0xC0153E6A, 0xF8B32931 */ -}; - -#ifdef __STDC__ - static double qzero(double x) -#else - static double qzero(x) - double x; -#endif -{ -#ifdef __STDC__ - const double *p=(void*)0,*q=(void*)0; -#else - double *p,*q; -#endif - double s,r,z; - int ix; - ix = 0x7fffffff&__HI(x); - if(ix>=0x40200000) {p = qR8; q= qS8;} - else if(ix>=0x40122E8B){p = qR5; q= qS5;} - else if(ix>=0x4006DB6D){p = qR3; q= qS3;} - else if(ix>=0x40000000){p = qR2; q= qS2;} - z = one/(x*x); - r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); - s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); - return (-.125 + r/s)/x; -}
--- a/src/share/native/java/lang/fdlibm/src/e_j1.c Thu Aug 04 08:53:16 2011 -0700 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,490 +0,0 @@ - -/* - * Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved. - * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. - * - * This code is free software; you can redistribute it and/or modify it - * under the terms of the GNU General Public License version 2 only, as - * published by the Free Software Foundation. Oracle designates this - * particular file as subject to the "Classpath" exception as provided - * by Oracle in the LICENSE file that accompanied this code. - * - * This code is distributed in the hope that it will be useful, but WITHOUT - * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or - * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License - * version 2 for more details (a copy is included in the LICENSE file that - * accompanied this code). - * - * You should have received a copy of the GNU General Public License version - * 2 along with this work; if not, write to the Free Software Foundation, - * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. - * - * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA - * or visit www.oracle.com if you need additional information or have any - * questions. - */ - -/* __ieee754_j1(x), __ieee754_y1(x) - * Bessel function of the first and second kinds of order zero. - * Method -- j1(x): - * 1. For tiny x, we use j1(x) = x/2 - x^3/16 + x^5/384 - ... - * 2. Reduce x to |x| since j1(x)=-j1(-x), and - * for x in (0,2) - * j1(x) = x/2 + x*z*R0/S0, where z = x*x; - * (precision: |j1/x - 1/2 - R0/S0 |<2**-61.51 ) - * for x in (2,inf) - * j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x1)-q1(x)*sin(x1)) - * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1)) - * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1) - * as follow: - * cos(x1) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) - * = 1/sqrt(2) * (sin(x) - cos(x)) - * sin(x1) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) - * = -1/sqrt(2) * (sin(x) + cos(x)) - * (To avoid cancellation, use - * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) - * to compute the worse one.) - * - * 3 Special cases - * j1(nan)= nan - * j1(0) = 0 - * j1(inf) = 0 - * - * Method -- y1(x): - * 1. screen out x<=0 cases: y1(0)=-inf, y1(x<0)=NaN - * 2. For x<2. - * Since - * y1(x) = 2/pi*(j1(x)*(ln(x/2)+Euler)-1/x-x/2+5/64*x^3-...) - * therefore y1(x)-2/pi*j1(x)*ln(x)-1/x is an odd function. - * We use the following function to approximate y1, - * y1(x) = x*U(z)/V(z) + (2/pi)*(j1(x)*ln(x)-1/x), z= x^2 - * where for x in [0,2] (abs err less than 2**-65.89) - * U(z) = U0[0] + U0[1]*z + ... + U0[4]*z^4 - * V(z) = 1 + v0[0]*z + ... + v0[4]*z^5 - * Note: For tiny x, 1/x dominate y1 and hence - * y1(tiny) = -2/pi/tiny, (choose tiny<2**-54) - * 3. For x>=2. - * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1)) - * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1) - * by method mentioned above. - */ - -#include "fdlibm.h" - -#ifdef __STDC__ -static double pone(double), qone(double); -#else -static double pone(), qone(); -#endif - -#ifdef __STDC__ -static const double -#else -static double -#endif -huge = 1e300, -one = 1.0, -invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ -tpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ - /* R0/S0 on [0,2] */ -r00 = -6.25000000000000000000e-02, /* 0xBFB00000, 0x00000000 */ -r01 = 1.40705666955189706048e-03, /* 0x3F570D9F, 0x98472C61 */ -r02 = -1.59955631084035597520e-05, /* 0xBEF0C5C6, 0xBA169668 */ -r03 = 4.96727999609584448412e-08, /* 0x3E6AAAFA, 0x46CA0BD9 */ -s01 = 1.91537599538363460805e-02, /* 0x3F939D0B, 0x12637E53 */ -s02 = 1.85946785588630915560e-04, /* 0x3F285F56, 0xB9CDF664 */ -s03 = 1.17718464042623683263e-06, /* 0x3EB3BFF8, 0x333F8498 */ -s04 = 5.04636257076217042715e-09, /* 0x3E35AC88, 0xC97DFF2C */ -s05 = 1.23542274426137913908e-11; /* 0x3DAB2ACF, 0xCFB97ED8 */ - -static double zero = 0.0; - -#ifdef __STDC__ - double __ieee754_j1(double x) -#else - double __ieee754_j1(x) - double x; -#endif -{ - double z, s,c,ss,cc,r,u,v,y; - int hx,ix; - - hx = __HI(x); - ix = hx&0x7fffffff; - if(ix>=0x7ff00000) return one/x; - y = fabs(x); - if(ix >= 0x40000000) { /* |x| >= 2.0 */ - s = sin(y); - c = cos(y); - ss = -s-c; - cc = s-c; - if(ix<0x7fe00000) { /* make sure y+y not overflow */ - z = cos(y+y); - if ((s*c)>zero) cc = z/ss; - else ss = z/cc; - } - /* - * j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x) - * y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x) - */ - if(ix>0x48000000) z = (invsqrtpi*cc)/sqrt(y); - else { - u = pone(y); v = qone(y); - z = invsqrtpi*(u*cc-v*ss)/sqrt(y); - } - if(hx<0) return -z; - else return z; - } - if(ix<0x3e400000) { /* |x|<2**-27 */ - if(huge+x>one) return 0.5*x;/* inexact if x!=0 necessary */ - } - z = x*x; - r = z*(r00+z*(r01+z*(r02+z*r03))); - s = one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05)))); - r *= x; - return(x*0.5+r/s); -} - -#ifdef __STDC__ -static const double U0[5] = { -#else -static double U0[5] = { -#endif - -1.96057090646238940668e-01, /* 0xBFC91866, 0x143CBC8A */ - 5.04438716639811282616e-02, /* 0x3FA9D3C7, 0x76292CD1 */ - -1.91256895875763547298e-03, /* 0xBF5F55E5, 0x4844F50F */ - 2.35252600561610495928e-05, /* 0x3EF8AB03, 0x8FA6B88E */ - -9.19099158039878874504e-08, /* 0xBE78AC00, 0x569105B8 */ -}; -#ifdef __STDC__ -static const double V0[5] = { -#else -static double V0[5] = { -#endif - 1.99167318236649903973e-02, /* 0x3F94650D, 0x3F4DA9F0 */ - 2.02552581025135171496e-04, /* 0x3F2A8C89, 0x6C257764 */ - 1.35608801097516229404e-06, /* 0x3EB6C05A, 0x894E8CA6 */ - 6.22741452364621501295e-09, /* 0x3E3ABF1D, 0x5BA69A86 */ - 1.66559246207992079114e-11, /* 0x3DB25039, 0xDACA772A */ -}; - -#ifdef __STDC__ - double __ieee754_y1(double x) -#else - double __ieee754_y1(x) - double x; -#endif -{ - double z, s,c,ss,cc,u,v; - int hx,ix,lx; - - hx = __HI(x); - ix = 0x7fffffff&hx; - lx = __LO(x); - /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */ - if(ix>=0x7ff00000) return one/(x+x*x); - if((ix|lx)==0) return -one/zero; - if(hx<0) return zero/zero; - if(ix >= 0x40000000) { /* |x| >= 2.0 */ - s = sin(x); - c = cos(x); - ss = -s-c; - cc = s-c; - if(ix<0x7fe00000) { /* make sure x+x not overflow */ - z = cos(x+x); - if ((s*c)>zero) cc = z/ss; - else ss = z/cc; - } - /* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0)) - * where x0 = x-3pi/4 - * Better formula: - * cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) - * = 1/sqrt(2) * (sin(x) - cos(x)) - * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) - * = -1/sqrt(2) * (cos(x) + sin(x)) - * To avoid cancellation, use - * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) - * to compute the worse one. - */ - if(ix>0x48000000) z = (invsqrtpi*ss)/sqrt(x); - else { - u = pone(x); v = qone(x); - z = invsqrtpi*(u*ss+v*cc)/sqrt(x); - } - return z; - } - if(ix<=0x3c900000) { /* x < 2**-54 */ - return(-tpi/x); - } - z = x*x; - u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4]))); - v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4])))); - return(x*(u/v) + tpi*(__ieee754_j1(x)*__ieee754_log(x)-one/x)); -} - -/* For x >= 8, the asymptotic expansions of pone is - * 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x. - * We approximate pone by - * pone(x) = 1 + (R/S) - * where R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10 - * S = 1 + ps0*s^2 + ... + ps4*s^10 - * and - * | pone(x)-1-R/S | <= 2 ** ( -60.06) - */ - -#ifdef __STDC__ -static const double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ -#else -static double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ -#endif - 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ - 1.17187499999988647970e-01, /* 0x3FBDFFFF, 0xFFFFFCCE */ - 1.32394806593073575129e+01, /* 0x402A7A9D, 0x357F7FCE */ - 4.12051854307378562225e+02, /* 0x4079C0D4, 0x652EA590 */ - 3.87474538913960532227e+03, /* 0x40AE457D, 0xA3A532CC */ - 7.91447954031891731574e+03, /* 0x40BEEA7A, 0xC32782DD */ -}; -#ifdef __STDC__ -static const double ps8[5] = { -#else -static double ps8[5] = { -#endif - 1.14207370375678408436e+02, /* 0x405C8D45, 0x8E656CAC */ - 3.65093083420853463394e+03, /* 0x40AC85DC, 0x964D274F */ - 3.69562060269033463555e+04, /* 0x40E20B86, 0x97C5BB7F */ - 9.76027935934950801311e+04, /* 0x40F7D42C, 0xB28F17BB */ - 3.08042720627888811578e+04, /* 0x40DE1511, 0x697A0B2D */ -}; - -#ifdef __STDC__ -static const double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ -#else -static double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ -#endif - 1.31990519556243522749e-11, /* 0x3DAD0667, 0xDAE1CA7D */ - 1.17187493190614097638e-01, /* 0x3FBDFFFF, 0xE2C10043 */ - 6.80275127868432871736e+00, /* 0x401B3604, 0x6E6315E3 */ - 1.08308182990189109773e+02, /* 0x405B13B9, 0x452602ED */ - 5.17636139533199752805e+02, /* 0x40802D16, 0xD052D649 */ - 5.28715201363337541807e+02, /* 0x408085B8, 0xBB7E0CB7 */ -}; -#ifdef __STDC__ -static const double ps5[5] = { -#else -static double ps5[5] = { -#endif - 5.92805987221131331921e+01, /* 0x404DA3EA, 0xA8AF633D */ - 9.91401418733614377743e+02, /* 0x408EFB36, 0x1B066701 */ - 5.35326695291487976647e+03, /* 0x40B4E944, 0x5706B6FB */ - 7.84469031749551231769e+03, /* 0x40BEA4B0, 0xB8A5BB15 */ - 1.50404688810361062679e+03, /* 0x40978030, 0x036F5E51 */ -}; - -#ifdef __STDC__ -static const double pr3[6] = { -#else -static double pr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ -#endif - 3.02503916137373618024e-09, /* 0x3E29FC21, 0xA7AD9EDD */ - 1.17186865567253592491e-01, /* 0x3FBDFFF5, 0x5B21D17B */ - 3.93297750033315640650e+00, /* 0x400F76BC, 0xE85EAD8A */ - 3.51194035591636932736e+01, /* 0x40418F48, 0x9DA6D129 */ - 9.10550110750781271918e+01, /* 0x4056C385, 0x4D2C1837 */ - 4.85590685197364919645e+01, /* 0x4048478F, 0x8EA83EE5 */ -}; -#ifdef __STDC__ -static const double ps3[5] = { -#else -static double ps3[5] = { -#endif - 3.47913095001251519989e+01, /* 0x40416549, 0xA134069C */ - 3.36762458747825746741e+02, /* 0x40750C33, 0x07F1A75F */ - 1.04687139975775130551e+03, /* 0x40905B7C, 0x5037D523 */ - 8.90811346398256432622e+02, /* 0x408BD67D, 0xA32E31E9 */ - 1.03787932439639277504e+02, /* 0x4059F26D, 0x7C2EED53 */ -}; - -#ifdef __STDC__ -static const double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ -#else -static double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ -#endif - 1.07710830106873743082e-07, /* 0x3E7CE9D4, 0xF65544F4 */ - 1.17176219462683348094e-01, /* 0x3FBDFF42, 0xBE760D83 */ - 2.36851496667608785174e+00, /* 0x4002F2B7, 0xF98FAEC0 */ - 1.22426109148261232917e+01, /* 0x40287C37, 0x7F71A964 */ - 1.76939711271687727390e+01, /* 0x4031B1A8, 0x177F8EE2 */ - 5.07352312588818499250e+00, /* 0x40144B49, 0xA574C1FE */ -}; -#ifdef __STDC__ -static const double ps2[5] = { -#else -static double ps2[5] = { -#endif - 2.14364859363821409488e+01, /* 0x40356FBD, 0x8AD5ECDC */ - 1.25290227168402751090e+02, /* 0x405F5293, 0x14F92CD5 */ - 2.32276469057162813669e+02, /* 0x406D08D8, 0xD5A2DBD9 */ - 1.17679373287147100768e+02, /* 0x405D6B7A, 0xDA1884A9 */ - 8.36463893371618283368e+00, /* 0x4020BAB1, 0xF44E5192 */ -}; - -#ifdef __STDC__ - static double pone(double x) -#else - static double pone(x) - double x; -#endif -{ -#ifdef __STDC__ - const double *p=(void*)0,*q=(void*)0; -#else - double *p,*q; -#endif - double z,r,s; - int ix; - ix = 0x7fffffff&__HI(x); - if(ix>=0x40200000) {p = pr8; q= ps8;} - else if(ix>=0x40122E8B){p = pr5; q= ps5;} - else if(ix>=0x4006DB6D){p = pr3; q= ps3;} - else if(ix>=0x40000000){p = pr2; q= ps2;} - z = one/(x*x); - r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); - s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); - return one+ r/s; -} - - -/* For x >= 8, the asymptotic expansions of qone is - * 3/8 s - 105/1024 s^3 - ..., where s = 1/x. - * We approximate pone by - * qone(x) = s*(0.375 + (R/S)) - * where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10 - * S = 1 + qs1*s^2 + ... + qs6*s^12 - * and - * | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13) - */ - -#ifdef __STDC__ -static const double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ -#else -static double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ -#endif - 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ - -1.02539062499992714161e-01, /* 0xBFBA3FFF, 0xFFFFFDF3 */ - -1.62717534544589987888e+01, /* 0xC0304591, 0xA26779F7 */ - -7.59601722513950107896e+02, /* 0xC087BCD0, 0x53E4B576 */ - -1.18498066702429587167e+04, /* 0xC0C724E7, 0x40F87415 */ - -4.84385124285750353010e+04, /* 0xC0E7A6D0, 0x65D09C6A */ -}; -#ifdef __STDC__ -static const double qs8[6] = { -#else -static double qs8[6] = { -#endif - 1.61395369700722909556e+02, /* 0x40642CA6, 0xDE5BCDE5 */ - 7.82538599923348465381e+03, /* 0x40BE9162, 0xD0D88419 */ - 1.33875336287249578163e+05, /* 0x4100579A, 0xB0B75E98 */ - 7.19657723683240939863e+05, /* 0x4125F653, 0x72869C19 */ - 6.66601232617776375264e+05, /* 0x412457D2, 0x7719AD5C */ - -2.94490264303834643215e+05, /* 0xC111F969, 0x0EA5AA18 */ -}; - -#ifdef __STDC__ -static const double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ -#else -static double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ -#endif - -2.08979931141764104297e-11, /* 0xBDB6FA43, 0x1AA1A098 */ - -1.02539050241375426231e-01, /* 0xBFBA3FFF, 0xCB597FEF */ - -8.05644828123936029840e+00, /* 0xC0201CE6, 0xCA03AD4B */ - -1.83669607474888380239e+02, /* 0xC066F56D, 0x6CA7B9B0 */ - -1.37319376065508163265e+03, /* 0xC09574C6, 0x6931734F */ - -2.61244440453215656817e+03, /* 0xC0A468E3, 0x88FDA79D */ -}; -#ifdef __STDC__ -static const double qs5[6] = { -#else -static double qs5[6] = { -#endif - 8.12765501384335777857e+01, /* 0x405451B2, 0xFF5A11B2 */ - 1.99179873460485964642e+03, /* 0x409F1F31, 0xE77BF839 */ - 1.74684851924908907677e+04, /* 0x40D10F1F, 0x0D64CE29 */ - 4.98514270910352279316e+04, /* 0x40E8576D, 0xAABAD197 */ - 2.79480751638918118260e+04, /* 0x40DB4B04, 0xCF7C364B */ - -4.71918354795128470869e+03, /* 0xC0B26F2E, 0xFCFFA004 */ -}; - -#ifdef __STDC__ -static const double qr3[6] = { -#else -static double qr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ -#endif - -5.07831226461766561369e-09, /* 0xBE35CFA9, 0xD38FC84F */ - -1.02537829820837089745e-01, /* 0xBFBA3FEB, 0x51AEED54 */ - -4.61011581139473403113e+00, /* 0xC01270C2, 0x3302D9FF */ - -5.78472216562783643212e+01, /* 0xC04CEC71, 0xC25D16DA */ - -2.28244540737631695038e+02, /* 0xC06C87D3, 0x4718D55F */ - -2.19210128478909325622e+02, /* 0xC06B66B9, 0x5F5C1BF6 */ -}; -#ifdef __STDC__ -static const double qs3[6] = { -#else -static double qs3[6] = { -#endif - 4.76651550323729509273e+01, /* 0x4047D523, 0xCCD367E4 */ - 6.73865112676699709482e+02, /* 0x40850EEB, 0xC031EE3E */ - 3.38015286679526343505e+03, /* 0x40AA684E, 0x448E7C9A */ - 5.54772909720722782367e+03, /* 0x40B5ABBA, 0xA61D54A6 */ - 1.90311919338810798763e+03, /* 0x409DBC7A, 0x0DD4DF4B */ - -1.35201191444307340817e+02, /* 0xC060E670, 0x290A311F */ -}; - -#ifdef __STDC__ -static const double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ -#else -static double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ -#endif - -1.78381727510958865572e-07, /* 0xBE87F126, 0x44C626D2 */ - -1.02517042607985553460e-01, /* 0xBFBA3E8E, 0x9148B010 */ - -2.75220568278187460720e+00, /* 0xC0060484, 0x69BB4EDA */ - -1.96636162643703720221e+01, /* 0xC033A9E2, 0xC168907F */ - -4.23253133372830490089e+01, /* 0xC04529A3, 0xDE104AAA */ - -2.13719211703704061733e+01, /* 0xC0355F36, 0x39CF6E52 */ -}; -#ifdef __STDC__ -static const double qs2[6] = { -#else -static double qs2[6] = { -#endif - 2.95333629060523854548e+01, /* 0x403D888A, 0x78AE64FF */ - 2.52981549982190529136e+02, /* 0x406F9F68, 0xDB821CBA */ - 7.57502834868645436472e+02, /* 0x4087AC05, 0xCE49A0F7 */ - 7.39393205320467245656e+02, /* 0x40871B25, 0x48D4C029 */ - 1.55949003336666123687e+02, /* 0x40637E5E, 0x3C3ED8D4 */ - -4.95949898822628210127e+00, /* 0xC013D686, 0xE71BE86B */ -}; - -#ifdef __STDC__ - static double qone(double x) -#else - static double qone(x) - double x; -#endif -{ -#ifdef __STDC__ - const double *p=(void*)0,*q=(void*)0; -#else - double *p,*q; -#endif - double s,r,z; - int ix; - ix = 0x7fffffff&__HI(x); - if(ix>=0x40200000) {p = qr8; q= qs8;} - else if(ix>=0x40122E8B){p = qr5; q= qs5;} - else if(ix>=0x4006DB6D){p = qr3; q= qs3;} - else if(ix>=0x40000000){p = qr2; q= qs2;} - z = one/(x*x); - r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); - s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); - return (.375 + r/s)/x; -}
--- a/src/share/native/java/lang/fdlibm/src/e_jn.c Thu Aug 04 08:53:16 2011 -0700 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,285 +0,0 @@ - -/* - * Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved. - * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. - * - * This code is free software; you can redistribute it and/or modify it - * under the terms of the GNU General Public License version 2 only, as - * published by the Free Software Foundation. Oracle designates this - * particular file as subject to the "Classpath" exception as provided - * by Oracle in the LICENSE file that accompanied this code. - * - * This code is distributed in the hope that it will be useful, but WITHOUT - * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or - * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License - * version 2 for more details (a copy is included in the LICENSE file that - * accompanied this code). - * - * You should have received a copy of the GNU General Public License version - * 2 along with this work; if not, write to the Free Software Foundation, - * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. - * - * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA - * or visit www.oracle.com if you need additional information or have any - * questions. - */ - -/* - * __ieee754_jn(n, x), __ieee754_yn(n, x) - * floating point Bessel's function of the 1st and 2nd kind - * of order n - * - * Special cases: - * y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal; - * y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal. - * Note 2. About jn(n,x), yn(n,x) - * For n=0, j0(x) is called, - * for n=1, j1(x) is called, - * for n<x, forward recursion us used starting - * from values of j0(x) and j1(x). - * for n>x, a continued fraction approximation to - * j(n,x)/j(n-1,x) is evaluated and then backward - * recursion is used starting from a supposed value - * for j(n,x). The resulting value of j(0,x) is - * compared with the actual value to correct the - * supposed value of j(n,x). - * - * yn(n,x) is similar in all respects, except - * that forward recursion is used for all - * values of n>1. - * - */ - -#include "fdlibm.h" - -#ifdef __STDC__ -static const double -#else -static double -#endif -invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ -two = 2.00000000000000000000e+00, /* 0x40000000, 0x00000000 */ -one = 1.00000000000000000000e+00; /* 0x3FF00000, 0x00000000 */ - -static double zero = 0.00000000000000000000e+00; - -#ifdef __STDC__ - double __ieee754_jn(int n, double x) -#else - double __ieee754_jn(n,x) - int n; double x; -#endif -{ - int i,hx,ix,lx, sgn; - double a, b, temp = 0, di; - double z, w; - - /* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x) - * Thus, J(-n,x) = J(n,-x) - */ - hx = __HI(x); - ix = 0x7fffffff&hx; - lx = __LO(x); - /* if J(n,NaN) is NaN */ - if((ix|((unsigned)(lx|-lx))>>31)>0x7ff00000) return x+x; - if(n<0){ - n = -n; - x = -x; - hx ^= 0x80000000; - } - if(n==0) return(__ieee754_j0(x)); - if(n==1) return(__ieee754_j1(x)); - sgn = (n&1)&(hx>>31); /* even n -- 0, odd n -- sign(x) */ - x = fabs(x); - if((ix|lx)==0||ix>=0x7ff00000) /* if x is 0 or inf */ - b = zero; - else if((double)n<=x) { - /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */ - if(ix>=0x52D00000) { /* x > 2**302 */ - /* (x >> n**2) - * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi) - * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi) - * Let s=sin(x), c=cos(x), - * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then - * - * n sin(xn)*sqt2 cos(xn)*sqt2 - * ---------------------------------- - * 0 s-c c+s - * 1 -s-c -c+s - * 2 -s+c -c-s - * 3 s+c c-s - */ - switch(n&3) { - case 0: temp = cos(x)+sin(x); break; - case 1: temp = -cos(x)+sin(x); break; - case 2: temp = -cos(x)-sin(x); break; - case 3: temp = cos(x)-sin(x); break; - } - b = invsqrtpi*temp/sqrt(x); - } else { - a = __ieee754_j0(x); - b = __ieee754_j1(x); - for(i=1;i<n;i++){ - temp = b; - b = b*((double)(i+i)/x) - a; /* avoid underflow */ - a = temp; - } - } - } else { - if(ix<0x3e100000) { /* x < 2**-29 */ - /* x is tiny, return the first Taylor expansion of J(n,x) - * J(n,x) = 1/n!*(x/2)^n - ... - */ - if(n>33) /* underflow */ - b = zero; - else { - temp = x*0.5; b = temp; - for (a=one,i=2;i<=n;i++) { - a *= (double)i; /* a = n! */ - b *= temp; /* b = (x/2)^n */ - } - b = b/a; - } - } else { - /* use backward recurrence */ - /* x x^2 x^2 - * J(n,x)/J(n-1,x) = ---- ------ ------ ..... - * 2n - 2(n+1) - 2(n+2) - * - * 1 1 1 - * (for large x) = ---- ------ ------ ..... - * 2n 2(n+1) 2(n+2) - * -- - ------ - ------ - - * x x x - * - * Let w = 2n/x and h=2/x, then the above quotient - * is equal to the continued fraction: - * 1 - * = ----------------------- - * 1 - * w - ----------------- - * 1 - * w+h - --------- - * w+2h - ... - * - * To determine how many terms needed, let - * Q(0) = w, Q(1) = w(w+h) - 1, - * Q(k) = (w+k*h)*Q(k-1) - Q(k-2), - * When Q(k) > 1e4 good for single - * When Q(k) > 1e9 good for double - * When Q(k) > 1e17 good for quadruple - */ - /* determine k */ - double t,v; - double q0,q1,h,tmp; int k,m; - w = (n+n)/(double)x; h = 2.0/(double)x; - q0 = w; z = w+h; q1 = w*z - 1.0; k=1; - while(q1<1.0e9) { - k += 1; z += h; - tmp = z*q1 - q0; - q0 = q1; - q1 = tmp; - } - m = n+n; - for(t=zero, i = 2*(n+k); i>=m; i -= 2) t = one/(i/x-t); - a = t; - b = one; - /* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n) - * Hence, if n*(log(2n/x)) > ... - * single 8.8722839355e+01 - * double 7.09782712893383973096e+02 - * long double 1.1356523406294143949491931077970765006170e+04 - * then recurrent value may overflow and the result is - * likely underflow to zero - */ - tmp = n; - v = two/x; - tmp = tmp*__ieee754_log(fabs(v*tmp)); - if(tmp<7.09782712893383973096e+02) { - for(i=n-1,di=(double)(i+i);i>0;i--){ - temp = b; - b *= di; - b = b/x - a; - a = temp; - di -= two; - } - } else { - for(i=n-1,di=(double)(i+i);i>0;i--){ - temp = b; - b *= di; - b = b/x - a; - a = temp; - di -= two; - /* scale b to avoid spurious overflow */ - if(b>1e100) { - a /= b; - t /= b; - b = one; - } - } - } - b = (t*__ieee754_j0(x)/b); - } - } - if(sgn==1) return -b; else return b; -} - -#ifdef __STDC__ - double __ieee754_yn(int n, double x) -#else - double __ieee754_yn(n,x) - int n; double x; -#endif -{ - int i,hx,ix,lx; - int sign; - double a, b, temp = 0; - - hx = __HI(x); - ix = 0x7fffffff&hx; - lx = __LO(x); - /* if Y(n,NaN) is NaN */ - if((ix|((unsigned)(lx|-lx))>>31)>0x7ff00000) return x+x; - if((ix|lx)==0) return -one/zero; - if(hx<0) return zero/zero; - sign = 1; - if(n<0){ - n = -n; - sign = 1 - ((n&1)<<1); - } - if(n==0) return(__ieee754_y0(x)); - if(n==1) return(sign*__ieee754_y1(x)); - if(ix==0x7ff00000) return zero; - if(ix>=0x52D00000) { /* x > 2**302 */ - /* (x >> n**2) - * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi) - * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi) - * Let s=sin(x), c=cos(x), - * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then - * - * n sin(xn)*sqt2 cos(xn)*sqt2 - * ---------------------------------- - * 0 s-c c+s - * 1 -s-c -c+s - * 2 -s+c -c-s - * 3 s+c c-s - */ - switch(n&3) { - case 0: temp = sin(x)-cos(x); break; - case 1: temp = -sin(x)-cos(x); break; - case 2: temp = -sin(x)+cos(x); break; - case 3: temp = sin(x)+cos(x); break; - } - b = invsqrtpi*temp/sqrt(x); - } else { - a = __ieee754_y0(x); - b = __ieee754_y1(x); - /* quit if b is -inf */ - for(i=1;i<n&&(__HI(b) != 0xfff00000);i++){ - temp = b; - b = ((double)(i+i)/x)*b - a; - a = temp; - } - } - if(sign>0) return b; else return -b; -}
--- a/src/share/native/java/lang/fdlibm/src/e_lgamma.c Thu Aug 04 08:53:16 2011 -0700 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,45 +0,0 @@ - -/* - * Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved. - * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. - * - * This code is free software; you can redistribute it and/or modify it - * under the terms of the GNU General Public License version 2 only, as - * published by the Free Software Foundation. Oracle designates this - * particular file as subject to the "Classpath" exception as provided - * by Oracle in the LICENSE file that accompanied this code. - * - * This code is distributed in the hope that it will be useful, but WITHOUT - * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or - * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License - * version 2 for more details (a copy is included in the LICENSE file that - * accompanied this code). - * - * You should have received a copy of the GNU General Public License version - * 2 along with this work; if not, write to the Free Software Foundation, - * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. - * - * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA - * or visit www.oracle.com if you need additional information or have any - * questions. - */ - -/* __ieee754_lgamma(x) - * Return the logarithm of the Gamma function of x. - * - * Method: call __ieee754_lgamma_r - */ - -#include "fdlibm.h" - -extern int signgam; - -#ifdef __STDC__ - double __ieee754_lgamma(double x) -#else - double __ieee754_lgamma(x) - double x; -#endif -{ - return __ieee754_lgamma_r(x,&signgam); -}
--- a/src/share/native/java/lang/fdlibm/src/e_lgamma_r.c Thu Aug 04 08:53:16 2011 -0700 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,316 +0,0 @@ - -/* - * Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved. - * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. - * - * This code is free software; you can redistribute it and/or modify it - * under the terms of the GNU General Public License version 2 only, as - * published by the Free Software Foundation. Oracle designates this - * particular file as subject to the "Classpath" exception as provided - * by Oracle in the LICENSE file that accompanied this code. - * - * This code is distributed in the hope that it will be useful, but WITHOUT - * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or - * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License - * version 2 for more details (a copy is included in the LICENSE file that - * accompanied this code). - * - * You should have received a copy of the GNU General Public License version - * 2 along with this work; if not, write to the Free Software Foundation, - * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. - * - * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA - * or visit www.oracle.com if you need additional information or have any - * questions. - */ - -/* __ieee754_lgamma_r(x, signgamp) - * Reentrant version of the logarithm of the Gamma function - * with user provide pointer for the sign of Gamma(x). - * - * Method: - * 1. Argument Reduction for 0 < x <= 8 - * Since gamma(1+s)=s*gamma(s), for x in [0,8], we may - * reduce x to a number in [1.5,2.5] by - * lgamma(1+s) = log(s) + lgamma(s) - * for example, - * lgamma(7.3) = log(6.3) + lgamma(6.3) - * = log(6.3*5.3) + lgamma(5.3) - * = log(6.3*5.3*4.3*3.3*2.3) + lgamma(2.3) - * 2. Polynomial approximation of lgamma around its - * minimun ymin=1.461632144968362245 to maintain monotonicity. - * On [ymin-0.23, ymin+0.27] (i.e., [1.23164,1.73163]), use - * Let z = x-ymin; - * lgamma(x) = -1.214862905358496078218 + z^2*poly(z) - * where - * poly(z) is a 14 degree polynomial. - * 2. Rational approximation in the primary interval [2,3] - * We use the following approximation: - * s = x-2.0; - * lgamma(x) = 0.5*s + s*P(s)/Q(s) - * with accuracy - * |P/Q - (lgamma(x)-0.5s)| < 2**-61.71 - * Our algorithms are based on the following observation - * - * zeta(2)-1 2 zeta(3)-1 3 - * lgamma(2+s) = s*(1-Euler) + --------- * s - --------- * s + ... - * 2 3 - * - * where Euler = 0.5771... is the Euler constant, which is very - * close to 0.5. - * - * 3. For x>=8, we have - * lgamma(x)~(x-0.5)log(x)-x+0.5*log(2pi)+1/(12x)-1/(360x**3)+.... - * (better formula: - * lgamma(x)~(x-0.5)*(log(x)-1)-.5*(log(2pi)-1) + ...) - * Let z = 1/x, then we approximation - * f(z) = lgamma(x) - (x-0.5)(log(x)-1) - * by - * 3 5 11 - * w = w0 + w1*z + w2*z + w3*z + ... + w6*z - * where - * |w - f(z)| < 2**-58.74 - * - * 4. For negative x, since (G is gamma function) - * -x*G(-x)*G(x) = pi/sin(pi*x), - * we have - * G(x) = pi/(sin(pi*x)*(-x)*G(-x)) - * since G(-x) is positive, sign(G(x)) = sign(sin(pi*x)) for x<0 - * Hence, for x<0, signgam = sign(sin(pi*x)) and - * lgamma(x) = log(|Gamma(x)|) - * = log(pi/(|x*sin(pi*x)|)) - lgamma(-x); - * Note: one should avoid compute pi*(-x) directly in the - * computation of sin(pi*(-x)). - * - * 5. Special Cases - * lgamma(2+s) ~ s*(1-Euler) for tiny s - * lgamma(1)=lgamma(2)=0 - * lgamma(x) ~ -log(x) for tiny x - * lgamma(0) = lgamma(inf) = inf - * lgamma(-integer) = +-inf - * - */ - -#include "fdlibm.h" - -#ifdef __STDC__ -static const double -#else -static double -#endif -two52= 4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */ -half= 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ -one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ -pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */ -a0 = 7.72156649015328655494e-02, /* 0x3FB3C467, 0xE37DB0C8 */ -a1 = 3.22467033424113591611e-01, /* 0x3FD4A34C, 0xC4A60FAD */ -a2 = 6.73523010531292681824e-02, /* 0x3FB13E00, 0x1A5562A7 */ -a3 = 2.05808084325167332806e-02, /* 0x3F951322, 0xAC92547B */ -a4 = 7.38555086081402883957e-03, /* 0x3F7E404F, 0xB68FEFE8 */ -a5 = 2.89051383673415629091e-03, /* 0x3F67ADD8, 0xCCB7926B */ -a6 = 1.19270763183362067845e-03, /* 0x3F538A94, 0x116F3F5D */ -a7 = 5.10069792153511336608e-04, /* 0x3F40B6C6, 0x89B99C00 */ -a8 = 2.20862790713908385557e-04, /* 0x3F2CF2EC, 0xED10E54D */ -a9 = 1.08011567247583939954e-04, /* 0x3F1C5088, 0x987DFB07 */ -a10 = 2.52144565451257326939e-05, /* 0x3EFA7074, 0x428CFA52 */ -a11 = 4.48640949618915160150e-05, /* 0x3F07858E, 0x90A45837 */ -tc = 1.46163214496836224576e+00, /* 0x3FF762D8, 0x6356BE3F */ -tf = -1.21486290535849611461e-01, /* 0xBFBF19B9, 0xBCC38A42 */ -/* tt = -(tail of tf) */ -tt = -3.63867699703950536541e-18, /* 0xBC50C7CA, 0xA48A971F */ -t0 = 4.83836122723810047042e-01, /* 0x3FDEF72B, 0xC8EE38A2 */ -t1 = -1.47587722994593911752e-01, /* 0xBFC2E427, 0x8DC6C509 */ -t2 = 6.46249402391333854778e-02, /* 0x3FB08B42, 0x94D5419B */ -t3 = -3.27885410759859649565e-02, /* 0xBFA0C9A8, 0xDF35B713 */ -t4 = 1.79706750811820387126e-02, /* 0x3F9266E7, 0x970AF9EC */ -t5 = -1.03142241298341437450e-02, /* 0xBF851F9F, 0xBA91EC6A */ -t6 = 6.10053870246291332635e-03, /* 0x3F78FCE0, 0xE370E344 */ -t7 = -3.68452016781138256760e-03, /* 0xBF6E2EFF, 0xB3E914D7 */ -t8 = 2.25964780900612472250e-03, /* 0x3F6282D3, 0x2E15C915 */ -t9 = -1.40346469989232843813e-03, /* 0xBF56FE8E, 0xBF2D1AF1 */ -t10 = 8.81081882437654011382e-04, /* 0x3F4CDF0C, 0xEF61A8E9 */ -t11 = -5.38595305356740546715e-04, /* 0xBF41A610, 0x9C73E0EC */ -t12 = 3.15632070903625950361e-04, /* 0x3F34AF6D, 0x6C0EBBF7 */ -t13 = -3.12754168375120860518e-04, /* 0xBF347F24, 0xECC38C38 */ -t14 = 3.35529192635519073543e-04, /* 0x3F35FD3E, 0xE8C2D3F4 */ -u0 = -7.72156649015328655494e-02, /* 0xBFB3C467, 0xE37DB0C8 */ -u1 = 6.32827064025093366517e-01, /* 0x3FE4401E, 0x8B005DFF */ -u2 = 1.45492250137234768737e+00, /* 0x3FF7475C, 0xD119BD6F */ -u3 = 9.77717527963372745603e-01, /* 0x3FEF4976, 0x44EA8450 */ -u4 = 2.28963728064692451092e-01, /* 0x3FCD4EAE, 0xF6010924 */ -u5 = 1.33810918536787660377e-02, /* 0x3F8B678B, 0xBF2BAB09 */ -v1 = 2.45597793713041134822e+00, /* 0x4003A5D7, 0xC2BD619C */ -v2 = 2.12848976379893395361e+00, /* 0x40010725, 0xA42B18F5 */ -v3 = 7.69285150456672783825e-01, /* 0x3FE89DFB, 0xE45050AF */ -v4 = 1.04222645593369134254e-01, /* 0x3FBAAE55, 0xD6537C88 */ -v5 = 3.21709242282423911810e-03, /* 0x3F6A5ABB, 0x57D0CF61 */ -s0 = -7.72156649015328655494e-02, /* 0xBFB3C467, 0xE37DB0C8 */ -s1 = 2.14982415960608852501e-01, /* 0x3FCB848B, 0x36E20878 */ -s2 = 3.25778796408930981787e-01, /* 0x3FD4D98F, 0x4F139F59 */ -s3 = 1.46350472652464452805e-01, /* 0x3FC2BB9C, 0xBEE5F2F7 */ -s4 = 2.66422703033638609560e-02, /* 0x3F9B481C, 0x7E939961 */ -s5 = 1.84028451407337715652e-03, /* 0x3F5E26B6, 0x7368F239 */ -s6 = 3.19475326584100867617e-05, /* 0x3F00BFEC, 0xDD17E945 */ -r1 = 1.39200533467621045958e+00, /* 0x3FF645A7, 0x62C4AB74 */ -r2 = 7.21935547567138069525e-01, /* 0x3FE71A18, 0x93D3DCDC */ -r3 = 1.71933865632803078993e-01, /* 0x3FC601ED, 0xCCFBDF27 */ -r4 = 1.86459191715652901344e-02, /* 0x3F9317EA, 0x742ED475 */ -r5 = 7.77942496381893596434e-04, /* 0x3F497DDA, 0xCA41A95B */ -r6 = 7.32668430744625636189e-06, /* 0x3EDEBAF7, 0xA5B38140 */ -w0 = 4.18938533204672725052e-01, /* 0x3FDACFE3, 0x90C97D69 */ -w1 = 8.33333333333329678849e-02, /* 0x3FB55555, 0x5555553B */ -w2 = -2.77777777728775536470e-03, /* 0xBF66C16C, 0x16B02E5C */ -w3 = 7.93650558643019558500e-04, /* 0x3F4A019F, 0x98CF38B6 */ -w4 = -5.95187557450339963135e-04, /* 0xBF4380CB, 0x8C0FE741 */ -w5 = 8.36339918996282139126e-04, /* 0x3F4B67BA, 0x4CDAD5D1 */ -w6 = -1.63092934096575273989e-03; /* 0xBF5AB89D, 0x0B9E43E4 */ - -static double zero= 0.00000000000000000000e+00; - -#ifdef __STDC__ - static double sin_pi(double x) -#else - static double sin_pi(x) - double x; -#endif -{ - double y,z; - int n,ix; - - ix = 0x7fffffff&__HI(x); - - if(ix<0x3fd00000) return __kernel_sin(pi*x,zero,0); - y = -x; /* x is assume negative */ - - /* - * argument reduction, make sure inexact flag not raised if input - * is an integer - */ - z = floor(y); - if(z!=y) { /* inexact anyway */ - y *= 0.5; - y = 2.0*(y - floor(y)); /* y = |x| mod 2.0 */ - n = (int) (y*4.0); - } else { - if(ix>=0x43400000) { - y = zero; n = 0; /* y must be even */ - } else { - if(ix<0x43300000) z = y+two52; /* exact */ - n = __LO(z)&1; /* lower word of z */ - y = n; - n<<= 2; - } - } - switch (n) { - case 0: y = __kernel_sin(pi*y,zero,0); break; - case 1: - case 2: y = __kernel_cos(pi*(0.5-y),zero); break; - case 3: - case 4: y = __kernel_sin(pi*(one-y),zero,0); break; - case 5: - case 6: y = -__kernel_cos(pi*(y-1.5),zero); break; - default: y = __kernel_sin(pi*(y-2.0),zero,0); break; - } - return -y; -} - - -#ifdef __STDC__ - double __ieee754_lgamma_r(double x, int *signgamp) -#else - double __ieee754_lgamma_r(x,signgamp) - double x; int *signgamp; -#endif -{ - double t,y,z,nadj=0,p,p1,p2,p3,q,r,w; - int i,hx,lx,ix; - - hx = __HI(x); - lx = __LO(x); - - /* purge off +-inf, NaN, +-0, and negative arguments */ - *signgamp = 1; - ix = hx&0x7fffffff; - if(ix>=0x7ff00000) return x*x; - if((ix|lx)==0) return one/zero; - if(ix<0x3b900000) { /* |x|<2**-70, return -log(|x|) */ - if(hx<0) { - *signgamp = -1; - return -__ieee754_log(-x); - } else return -__ieee754_log(x); - } - if(hx<0) { - if(ix>=0x43300000) /* |x|>=2**52, must be -integer */ - return one/zero; - t = sin_pi(x); - if(t==zero) return one/zero; /* -integer */ - nadj = __ieee754_log(pi/fabs(t*x)); - if(t<zero) *signgamp = -1; - x = -x; - } - - /* purge off 1 and 2 */ - if((((ix-0x3ff00000)|lx)==0)||(((ix-0x40000000)|lx)==0)) r = 0; - /* for x < 2.0 */ - else if(ix<0x40000000) { - if(ix<=0x3feccccc) { /* lgamma(x) = lgamma(x+1)-log(x) */ - r = -__ieee754_log(x); - if(ix>=0x3FE76944) {y = one-x; i= 0;} - else if(ix>=0x3FCDA661) {y= x-(tc-one); i=1;} - else {y = x; i=2;} - } else { - r = zero; - if(ix>=0x3FFBB4C3) {y=2.0-x;i=0;} /* [1.7316,2] */ - else if(ix>=0x3FF3B4C4) {y=x-tc;i=1;} /* [1.23,1.73] */ - else {y=x-one;i=2;} - } - switch(i) { - case 0: - z = y*y; - p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10)))); - p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11))))); - p = y*p1+p2; - r += (p-0.5*y); break; - case 1: - z = y*y; - w = z*y; - p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */ - p2 = t1+w*(t4+w*(t7+w*(t10+w*t13))); - p3 = t2+w*(t5+w*(t8+w*(t11+w*t14))); - p = z*p1-(tt-w*(p2+y*p3)); - r += (tf + p); break; - case 2: - p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5))))); - p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5)))); - r += (-0.5*y + p1/p2); - } - } - else if(ix<0x40200000) { /* x < 8.0 */ - i = (int)x; - t = zero; - y = x-(double)i; - p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6)))))); - q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6))))); - r = half*y+p/q; - z = one; /* lgamma(1+s) = log(s) + lgamma(s) */ - switch(i) { - case 7: z *= (y+6.0); /* FALLTHRU */ - case 6: z *= (y+5.0); /* FALLTHRU */ - case 5: z *= (y+4.0); /* FALLTHRU */ - case 4: z *= (y+3.0); /* FALLTHRU */ - case 3: z *= (y+2.0); /* FALLTHRU */ - r += __ieee754_log(z); break; - } - /* 8.0 <= x < 2**58 */ - } else if (ix < 0x43900000) { - t = __ieee754_log(x); - z = one/x; - y = z*z; - w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6))))); - r = (x-half)*(t-one)+w; - } else - /* 2**58 <= x <= inf */ - r = x*(__ieee754_log(x)-one); - if(hx<0) r = nadj - r; - return r; -}
--- a/src/share/native/java/lang/fdlibm/src/s_asinh.c Thu Aug 04 08:53:16 2011 -0700 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,74 +0,0 @@ - -/* - * Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved. - * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. - * - * This code is free software; you can redistribute it and/or modify it - * under the terms of the GNU General Public License version 2 only, as - * published by the Free Software Foundation. Oracle designates this - * particular file as subject to the "Classpath" exception as provided - * by Oracle in the LICENSE file that accompanied this code. - * - * This code is distributed in the hope that it will be useful, but WITHOUT - * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or - * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License - * version 2 for more details (a copy is included in the LICENSE file that - * accompanied this code). - * - * You should have received a copy of the GNU General Public License version - * 2 along with this work; if not, write to the Free Software Foundation, - * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. - * - * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA - * or visit www.oracle.com if you need additional information or have any - * questions. - */ - -/* asinh(x) - * Method : - * Based on - * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ] - * we have - * asinh(x) := x if 1+x*x=1, - * := sign(x)*(log(x)+ln2)) for large |x|, else - * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else - * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2))) - */ - -#include "fdlibm.h" - -#ifdef __STDC__ -static const double -#else -static double -#endif -one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ -ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ -huge= 1.00000000000000000000e+300; - -#ifdef __STDC__ - double asinh(double x) -#else - double asinh(x) - double x; -#endif -{ - double t,w; - int hx,ix; - hx = __HI(x); - ix = hx&0x7fffffff; - if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */ - if(ix< 0x3e300000) { /* |x|<2**-28 */ - if(huge+x>one) return x; /* return x inexact except 0 */ - } - if(ix>0x41b00000) { /* |x| > 2**28 */ - w = __ieee754_log(fabs(x))+ln2; - } else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */ - t = fabs(x); - w = __ieee754_log(2.0*t+one/(sqrt(x*x+one)+t)); - } else { /* 2.0 > |x| > 2**-28 */ - t = x*x; - w =log1p(fabs(x)+t/(one+sqrt(one+t))); - } - if(hx>0) return w; else return -w; -}
--- a/src/share/native/java/lang/fdlibm/src/s_erf.c Thu Aug 04 08:53:16 2011 -0700 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,323 +0,0 @@ - -/* - * Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved. - * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. - * - * This code is free software; you can redistribute it and/or modify it - * under the terms of the GNU General Public License version 2 only, as - * published by the Free Software Foundation. Oracle designates this - * particular file as subject to the "Classpath" exception as provided - * by Oracle in the LICENSE file that accompanied this code. - * - * This code is distributed in the hope that it will be useful, but WITHOUT - * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or - * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License - * version 2 for more details (a copy is included in the LICENSE file that - * accompanied this code). - * - * You should have received a copy of the GNU General Public License version - * 2 along with this work; if not, write to the Free Software Foundation, - * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. - * - * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA - * or visit www.oracle.com if you need additional information or have any - * questions. - */ - -/* 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 - */ - - -#include "fdlibm.h" - -#ifdef __STDC__ -static const double -#else -static double -#endif -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 */ -pp0 = 1.28379167095512558561e-01, /* 0x3FC06EBA, 0x8214DB68 */ -pp1 = -3.25042107247001499370e-01, /* 0xBFD4CD7D, 0x691CB913 */ -pp2 = -2.84817495755985104766e-02, /* 0xBF9D2A51, 0xDBD7194F */ -pp3 = -5.77027029648944159157e-03, /* 0xBF77A291, 0x236668E4 */ -pp4 = -2.37630166566501626084e-05, /* 0xBEF8EAD6, 0x120016AC */ -qq1 = 3.97917223959155352819e-01, /* 0x3FD97779, 0xCDDADC09 */ -qq2 = 6.50222499887672944485e-02, /* 0x3FB0A54C, 0x5536CEBA */ -qq3 = 5.08130628187576562776e-03, /* 0x3F74D022, 0xC4D36B0F */ -qq4 = 1.32494738004321644526e-04, /* 0x3F215DC9, 0x221C1A10 */ -qq5 = -3.96022827877536812320e-06, /* 0xBED09C43, 0x42A26120 */ -/* - * Coefficients for approximation to erf in [0.84375,1.25] - */ -pa0 = -2.36211856075265944077e-03, /* 0xBF6359B8, 0xBEF77538 */ -pa1 = 4.14856118683748331666e-01, /* 0x3FDA8D00, 0xAD92B34D */ -pa2 = -3.72207876035701323847e-01, /* 0xBFD7D240, 0xFBB8C3F1 */ -pa3 = 3.18346619901161753674e-01, /* 0x3FD45FCA, 0x805120E4 */ -pa4 = -1.10894694282396677476e-01, /* 0xBFBC6398, 0x3D3E28EC */ -pa5 = 3.54783043256182359371e-02, /* 0x3FA22A36, 0x599795EB */ -pa6 = -2.16637559486879084300e-03, /* 0xBF61BF38, 0x0A96073F */ -qa1 = 1.06420880400844228286e-01, /* 0x3FBB3E66, 0x18EEE323 */ -qa2 = 5.40397917702171048937e-01, /* 0x3FE14AF0, 0x92EB6F33 */ -qa3 = 7.18286544141962662868e-02, /* 0x3FB2635C, 0xD99FE9A7 */ -qa4 = 1.26171219808761642112e-01, /* 0x3FC02660, 0xE763351F */ -qa5 = 1.36370839120290507362e-02, /* 0x3F8BEDC2, 0x6B51DD1C */ -qa6 = 1.19844998467991074170e-02, /* 0x3F888B54, 0x5735151D */ -/* - * Coefficients for approximation to erfc in [1.25,1/0.35] - */ -ra0 = -9.86494403484714822705e-03, /* 0xBF843412, 0x600D6435 */ -ra1 = -6.93858572707181764372e-01, /* 0xBFE63416, 0xE4BA7360 */ -ra2 = -1.05586262253232909814e+01, /* 0xC0251E04, 0x41B0E726 */ -ra3 = -6.23753324503260060396e+01, /* 0xC04F300A, 0xE4CBA38D */ -ra4 = -1.62396669462573470355e+02, /* 0xC0644CB1, 0x84282266 */ -ra5 = -1.84605092906711035994e+02, /* 0xC067135C, 0xEBCCABB2 */ -ra6 = -8.12874355063065934246e+01, /* 0xC0545265, 0x57E4D2F2 */ -ra7 = -9.81432934416914548592e+00, /* 0xC023A0EF, 0xC69AC25C */ -sa1 = 1.96512716674392571292e+01, /* 0x4033A6B9, 0xBD707687 */ -sa2 = 1.37657754143519042600e+02, /* 0x4061350C, 0x526AE721 */ -sa3 = 4.34565877475229228821e+02, /* 0x407B290D, 0xD58A1A71 */ -sa4 = 6.45387271733267880336e+02, /* 0x40842B19, 0x21EC2868 */ -sa5 = 4.29008140027567833386e+02, /* 0x407AD021, 0x57700314 */ -sa6 = 1.08635005541779435134e+02, /* 0x405B28A3, 0xEE48AE2C */ -sa7 = 6.57024977031928170135e+00, /* 0x401A47EF, 0x8E484A93 */ -sa8 = -6.04244152148580987438e-02, /* 0xBFAEEFF2, 0xEE749A62 */ -/* - * Coefficients for approximation to erfc in [1/.35,28] - */ -rb0 = -9.86494292470009928597e-03, /* 0xBF843412, 0x39E86F4A */ -rb1 = -7.99283237680523006574e-01, /* 0xBFE993BA, 0x70C285DE */ -rb2 = -1.77579549177547519889e+01, /* 0xC031C209, 0x555F995A */ -rb3 = -1.60636384855821916062e+02, /* 0xC064145D, 0x43C5ED98 */ -rb4 = -6.37566443368389627722e+02, /* 0xC083EC88, 0x1375F228 */ -rb5 = -1.02509513161107724954e+03, /* 0xC0900461, 0x6A2E5992 */ -rb6 = -4.83519191608651397019e+02, /* 0xC07E384E, 0x9BDC383F */ -sb1 = 3.03380607434824582924e+01, /* 0x403E568B, 0x261D5190 */ -sb2 = 3.25792512996573918826e+02, /* 0x40745CAE, 0x221B9F0A */ -sb3 = 1.53672958608443695994e+03, /* 0x409802EB, 0x189D5118 */ -sb4 = 3.19985821950859553908e+03, /* 0x40A8FFB7, 0x688C246A */ -sb5 = 2.55305040643316442583e+03, /* 0x40A3F219, 0xCEDF3BE6 */ -sb6 = 4.74528541206955367215e+02, /* 0x407DA874, 0xE79FE763 */ -sb7 = -2.24409524465858183362e+01; /* 0xC03670E2, 0x42712D62 */ - -#ifdef __STDC__ - double erf(double x) -#else - double erf(x) - double x; -#endif -{ - int hx,ix,i; - double R,S,P,Q,s,y,z,r; - hx = __HI(x); - ix = hx&0x7fffffff; - if(ix>=0x7ff00000) { /* erf(nan)=nan */ - 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) - 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; - __LO(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; -} - -#ifdef __STDC__ - double erfc(double x) -#else - double erfc(x) - double x; -#endif -{ - int hx,ix; - double R,S,P,Q,s,y,z,r; - hx = __HI(x); - ix = hx&0x7fffffff; - if(ix>=0x7ff00000) { /* erfc(nan)=nan */ - /* 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; - __LO(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; - } -}
--- a/src/share/native/java/lang/fdlibm/src/w_acosh.c Thu Aug 04 08:53:16 2011 -0700 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,51 +0,0 @@ - -/* - * Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved. - * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. - * - * This code is free software; you can redistribute it and/or modify it - * under the terms of the GNU General Public License version 2 only, as - * published by the Free Software Foundation. Oracle designates this - * particular file as subject to the "Classpath" exception as provided - * by Oracle in the LICENSE file that accompanied this code. - * - * This code is distributed in the hope that it will be useful, but WITHOUT - * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or - * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License - * version 2 for more details (a copy is included in the LICENSE file that - * accompanied this code). - * - * You should have received a copy of the GNU General Public License version - * 2 along with this work; if not, write to the Free Software Foundation, - * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. - * - * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA - * or visit www.oracle.com if you need additional information or have any - * questions. - */ - -/* - * wrapper acosh(x) - */ - -#include "fdlibm.h" - -#ifdef __STDC__ - double acosh(double x) /* wrapper acosh */ -#else - double acosh(x) /* wrapper acosh */ - double x; -#endif -{ -#ifdef _IEEE_LIBM - return __ieee754_acosh(x); -#else - double z; - z = __ieee754_acosh(x); - if(_LIB_VERSION == _IEEE_ || isnan(x)) return z; - if(x<1.0) { - return __kernel_standard(x,x,29); /* acosh(x<1) */ - } else - return z; -#endif -}
--- a/src/share/native/java/lang/fdlibm/src/w_gamma.c Thu Aug 04 08:53:16 2011 -0700 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,58 +0,0 @@ - -/* - * Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved. - * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. - * - * This code is free software; you can redistribute it and/or modify it - * under the terms of the GNU General Public License version 2 only, as - * published by the Free Software Foundation. Oracle designates this - * particular file as subject to the "Classpath" exception as provided - * by Oracle in the LICENSE file that accompanied this code. - * - * This code is distributed in the hope that it will be useful, but WITHOUT - * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or - * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License - * version 2 for more details (a copy is included in the LICENSE file that - * accompanied this code). - * - * You should have received a copy of the GNU General Public License version - * 2 along with this work; if not, write to the Free Software Foundation, - * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. - * - * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA - * or visit www.oracle.com if you need additional information or have any - * questions. - */ - -/* double gamma(double x) - * Return the logarithm of the Gamma function of x. - * - * Method: call gamma_r - */ - -#include "fdlibm.h" - -extern int signgam; - -#ifdef __STDC__ - double gamma(double x) -#else - double gamma(x) - double x; -#endif -{ -#ifdef _IEEE_LIBM - return __ieee754_gamma_r(x,&signgam); -#else - double y; - y = __ieee754_gamma_r(x,&signgam); - if(_LIB_VERSION == _IEEE_) return y; - if(!finite(y)&&finite(x)) { - if(floor(x)==x&&x<=0.0) - return __kernel_standard(x,x,41); /* gamma pole */ - else - return __kernel_standard(x,x,40); /* gamma overflow */ - } else - return y; -#endif -}
--- a/src/share/native/java/lang/fdlibm/src/w_gamma_r.c Thu Aug 04 08:53:16 2011 -0700 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,55 +0,0 @@ - -/* - * Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved. - * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. - * - * This code is free software; you can redistribute it and/or modify it - * under the terms of the GNU General Public License version 2 only, as - * published by the Free Software Foundation. Oracle designates this - * particular file as subject to the "Classpath" exception as provided - * by Oracle in the LICENSE file that accompanied this code. - * - * This code is distributed in the hope that it will be useful, but WITHOUT - * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or - * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License - * version 2 for more details (a copy is included in the LICENSE file that - * accompanied this code). - * - * You should have received a copy of the GNU General Public License version - * 2 along with this work; if not, write to the Free Software Foundation, - * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. - * - * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA - * or visit www.oracle.com if you need additional information or have any - * questions. - */ - -/* - * wrapper double gamma_r(double x, int *signgamp) - */ - -#include "fdlibm.h" - - -#ifdef __STDC__ - double gamma_r(double x, int *signgamp) /* wrapper lgamma_r */ -#else - double gamma_r(x,signgamp) /* wrapper lgamma_r */ - double x; int *signgamp; -#endif -{ -#ifdef _IEEE_LIBM - return __ieee754_gamma_r(x,signgamp); -#else - double y; - y = __ieee754_gamma_r(x,signgamp); - if(_LIB_VERSION == _IEEE_) return y; - if(!finite(y)&&finite(x)) { - if(floor(x)==x&&x<=0.0) - return __kernel_standard(x,x,41); /* gamma pole */ - else - return __kernel_standard(x,x,40); /* gamma overflow */ - } else - return y; -#endif -}
--- a/src/share/native/java/lang/fdlibm/src/w_j0.c Thu Aug 04 08:53:16 2011 -0700 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,78 +0,0 @@ - -/* - * Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved. - * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. - * - * This code is free software; you can redistribute it and/or modify it - * under the terms of the GNU General Public License version 2 only, as - * published by the Free Software Foundation. Oracle designates this - * particular file as subject to the "Classpath" exception as provided - * by Oracle in the LICENSE file that accompanied this code. - * - * This code is distributed in the hope that it will be useful, but WITHOUT - * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or - * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License - * version 2 for more details (a copy is included in the LICENSE file that - * accompanied this code). - * - * You should have received a copy of the GNU General Public License version - * 2 along with this work; if not, write to the Free Software Foundation, - * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. - * - * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA - * or visit www.oracle.com if you need additional information or have any - * questions. - */ - -/* - * wrapper j0(double x), y0(double x) - */ - -#include "fdlibm.h" - -#ifdef __STDC__ - double j0(double x) /* wrapper j0 */ -#else - double j0(x) /* wrapper j0 */ - double x; -#endif -{ -#ifdef _IEEE_LIBM - return __ieee754_j0(x); -#else - double z = __ieee754_j0(x); - if(_LIB_VERSION == _IEEE_ || isnan(x)) return z; - if(fabs(x)>X_TLOSS) { - return __kernel_standard(x,x,34); /* j0(|x|>X_TLOSS) */ - } else - return z; -#endif -} - -#ifdef __STDC__ - double y0(double x) /* wrapper y0 */ -#else - double y0(x) /* wrapper y0 */ - double x; -#endif -{ -#ifdef _IEEE_LIBM - return __ieee754_y0(x); -#else - double z; - z = __ieee754_y0(x); - if(_LIB_VERSION == _IEEE_ || isnan(x) ) return z; - if(x <= 0.0){ - if(x==0.0) - /* d= -one/(x-x); */ - return __kernel_standard(x,x,8); - else - /* d = zero/(x-x); */ - return __kernel_standard(x,x,9); - } - if(x>X_TLOSS) { - return __kernel_standard(x,x,35); /* y0(x>X_TLOSS) */ - } else - return z; -#endif -}
--- a/src/share/native/java/lang/fdlibm/src/w_j1.c Thu Aug 04 08:53:16 2011 -0700 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,79 +0,0 @@ - -/* - * Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved. - * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. - * - * This code is free software; you can redistribute it and/or modify it - * under the terms of the GNU General Public License version 2 only, as - * published by the Free Software Foundation. Oracle designates this - * particular file as subject to the "Classpath" exception as provided - * by Oracle in the LICENSE file that accompanied this code. - * - * This code is distributed in the hope that it will be useful, but WITHOUT - * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or - * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License - * version 2 for more details (a copy is included in the LICENSE file that - * accompanied this code). - * - * You should have received a copy of the GNU General Public License version - * 2 along with this work; if not, write to the Free Software Foundation, - * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. - * - * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA - * or visit www.oracle.com if you need additional information or have any - * questions. - */ - -/* - * wrapper of j1,y1 - */ - -#include "fdlibm.h" - -#ifdef __STDC__ - double j1(double x) /* wrapper j1 */ -#else - double j1(x) /* wrapper j1 */ - double x; -#endif -{ -#ifdef _IEEE_LIBM - return __ieee754_j1(x); -#else - double z; - z = __ieee754_j1(x); - if(_LIB_VERSION == _IEEE_ || isnan(x) ) return z; - if(fabs(x)>X_TLOSS) { - return __kernel_standard(x,x,36); /* j1(|x|>X_TLOSS) */ - } else - return z; -#endif -} - -#ifdef __STDC__ - double y1(double x) /* wrapper y1 */ -#else - double y1(x) /* wrapper y1 */ - double x; -#endif -{ -#ifdef _IEEE_LIBM - return __ieee754_y1(x); -#else - double z; - z = __ieee754_y1(x); - if(_LIB_VERSION == _IEEE_ || isnan(x) ) return z; - if(x <= 0.0){ - if(x==0.0) - /* d= -one/(x-x); */ - return __kernel_standard(x,x,10); - else - /* d = zero/(x-x); */ - return __kernel_standard(x,x,11); - } - if(x>X_TLOSS) { - return __kernel_standard(x,x,37); /* y1(x>X_TLOSS) */ - } else - return z; -#endif -}
--- a/src/share/native/java/lang/fdlibm/src/w_jn.c Thu Aug 04 08:53:16 2011 -0700 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,101 +0,0 @@ - -/* - * Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved. - * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. - * - * This code is free software; you can redistribute it and/or modify it - * under the terms of the GNU General Public License version 2 only, as - * published by the Free Software Foundation. Oracle designates this - * particular file as subject to the "Classpath" exception as provided - * by Oracle in the LICENSE file that accompanied this code. - * - * This code is distributed in the hope that it will be useful, but WITHOUT - * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or - * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License - * version 2 for more details (a copy is included in the LICENSE file that - * accompanied this code). - * - * You should have received a copy of the GNU General Public License version - * 2 along with this work; if not, write to the Free Software Foundation, - * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. - * - * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA - * or visit www.oracle.com if you need additional information or have any - * questions. - */ - -/* - * wrapper jn(int n, double x), yn(int n, double x) - * floating point Bessel's function of the 1st and 2nd kind - * of order n - * - * Special cases: - * y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal; - * y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal. - * Note 2. About jn(n,x), yn(n,x) - * For n=0, j0(x) is called, - * for n=1, j1(x) is called, - * for n<x, forward recursion us used starting - * from values of j0(x) and j1(x). - * for n>x, a continued fraction approximation to - * j(n,x)/j(n-1,x) is evaluated and then backward - * recursion is used starting from a supposed value - * for j(n,x). The resulting value of j(0,x) is - * compared with the actual value to correct the - * supposed value of j(n,x). - * - * yn(n,x) is similar in all respects, except - * that forward recursion is used for all - * values of n>1. - * - */ - -#include "fdlibm.h" - -#ifdef __STDC__ - double jn(int n, double x) /* wrapper jn */ -#else - double jn(n,x) /* wrapper jn */ - double x; int n; -#endif -{ -#ifdef _IEEE_LIBM - return __ieee754_jn(n,x); -#else - double z; - z = __ieee754_jn(n,x); - if(_LIB_VERSION == _IEEE_ || isnan(x) ) return z; - if(fabs(x)>X_TLOSS) { - return __kernel_standard((double)n,x,38); /* jn(|x|>X_TLOSS,n) */ - } else - return z; -#endif -} - -#ifdef __STDC__ - double yn(int n, double x) /* wrapper yn */ -#else - double yn(n,x) /* wrapper yn */ - double x; int n; -#endif -{ -#ifdef _IEEE_LIBM - return __ieee754_yn(n,x); -#else - double z; - z = __ieee754_yn(n,x); - if(_LIB_VERSION == _IEEE_ || isnan(x) ) return z; - if(x <= 0.0){ - if(x==0.0) - /* d= -one/(x-x); */ - return __kernel_standard((double)n,x,12); - else - /* d = zero/(x-x); */ - return __kernel_standard((double)n,x,13); - } - if(x>X_TLOSS) { - return __kernel_standard((double)n,x,39); /* yn(x>X_TLOSS,n) */ - } else - return z; -#endif -}
--- a/src/share/native/java/lang/fdlibm/src/w_lgamma.c Thu Aug 04 08:53:16 2011 -0700 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,58 +0,0 @@ - -/* - * Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved. - * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. - * - * This code is free software; you can redistribute it and/or modify it - * under the terms of the GNU General Public License version 2 only, as - * published by the Free Software Foundation. Oracle designates this - * particular file as subject to the "Classpath" exception as provided - * by Oracle in the LICENSE file that accompanied this code. - * - * This code is distributed in the hope that it will be useful, but WITHOUT - * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or - * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License - * version 2 for more details (a copy is included in the LICENSE file that - * accompanied this code). - * - * You should have received a copy of the GNU General Public License version - * 2 along with this work; if not, write to the Free Software Foundation, - * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. - * - * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA - * or visit www.oracle.com if you need additional information or have any - * questions. - */ - -/* double lgamma(double x) - * Return the logarithm of the Gamma function of x. - * - * Method: call __ieee754_lgamma_r - */ - -#include "fdlibm.h" - -extern int signgam; - -#ifdef __STDC__ - double lgamma(double x) -#else - double lgamma(x) - double x; -#endif -{ -#ifdef _IEEE_LIBM - return __ieee754_lgamma_r(x,&signgam); -#else - double y; - y = __ieee754_lgamma_r(x,&signgam); - if(_LIB_VERSION == _IEEE_) return y; - if(!finite(y)&&finite(x)) { - if(floor(x)==x&&x<=0.0) - return __kernel_standard(x,x,15); /* lgamma pole */ - else - return __kernel_standard(x,x,14); /* lgamma overflow */ - } else - return y; -#endif -}
--- a/src/share/native/java/lang/fdlibm/src/w_lgamma_r.c Thu Aug 04 08:53:16 2011 -0700 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,55 +0,0 @@ - -/* - * Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved. - * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. - * - * This code is free software; you can redistribute it and/or modify it - * under the terms of the GNU General Public License version 2 only, as - * published by the Free Software Foundation. Oracle designates this - * particular file as subject to the "Classpath" exception as provided - * by Oracle in the LICENSE file that accompanied this code. - * - * This code is distributed in the hope that it will be useful, but WITHOUT - * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or - * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License - * version 2 for more details (a copy is included in the LICENSE file that - * accompanied this code). - * - * You should have received a copy of the GNU General Public License version - * 2 along with this work; if not, write to the Free Software Foundation, - * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. - * - * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA - * or visit www.oracle.com if you need additional information or have any - * questions. - */ - -/* - * wrapper double lgamma_r(double x, int *signgamp) - */ - -#include "fdlibm.h" - - -#ifdef __STDC__ - double lgamma_r(double x, int *signgamp) /* wrapper lgamma_r */ -#else - double lgamma_r(x,signgamp) /* wrapper lgamma_r */ - double x; int *signgamp; -#endif -{ -#ifdef _IEEE_LIBM - return __ieee754_lgamma_r(x,signgamp); -#else - double y; - y = __ieee754_lgamma_r(x,signgamp); - if(_LIB_VERSION == _IEEE_) return y; - if(!finite(y)&&finite(x)) { - if(floor(x)==x&&x<=0.0) - return __kernel_standard(x,x,15); /* lgamma pole */ - else - return __kernel_standard(x,x,14); /* lgamma overflow */ - } else - return y; -#endif -}