Author: jgardou Date: Sat Jul 23 18:03:11 2011 New Revision: 52812
URL: http://svn.reactos.org/svn/reactos?rev=52812&view=rev Log: [CRT] - import bessel's function j0, j1, jn, y0, y1, yn from glibc
Added: trunk/reactos/lib/sdk/crt/math/ieee754/ (with props) trunk/reactos/lib/sdk/crt/math/ieee754/ieee754.h (with props) trunk/reactos/lib/sdk/crt/math/ieee754/j0_y0.c (with props) trunk/reactos/lib/sdk/crt/math/ieee754/j1_y1.c (with props) trunk/reactos/lib/sdk/crt/math/ieee754/jn_yn.c (with props) Modified: trunk/reactos/lib/sdk/crt/crt.cmake trunk/reactos/lib/sdk/crt/crt.rbuild trunk/reactos/lib/sdk/crt/math/j0_y0.c trunk/reactos/lib/sdk/crt/math/j1_y1.c trunk/reactos/lib/sdk/crt/math/jn_yn.c
Modified: trunk/reactos/lib/sdk/crt/crt.cmake URL: http://svn.reactos.org/svn/reactos/trunk/reactos/lib/sdk/crt/crt.cmake?rev=5... ============================================================================== --- trunk/reactos/lib/sdk/crt/crt.cmake [iso-8859-1] (original) +++ trunk/reactos/lib/sdk/crt/crt.cmake [iso-8859-1] Sat Jul 23 18:03:11 2011 @@ -45,6 +45,12 @@ math/frexp.c math/huge_val.c math/hypot.c + math/ieee754/j0_y0.c + math/ieee754/j1_y1.c + math/ieee754/jn_yn.c + math/j0_y0.c + math/j1_y1.c + math/jn_yn.c math/ldiv.c math/logf.c math/modf.c
Modified: trunk/reactos/lib/sdk/crt/crt.rbuild URL: http://svn.reactos.org/svn/reactos/trunk/reactos/lib/sdk/crt/crt.rbuild?rev=... ============================================================================== --- trunk/reactos/lib/sdk/crt/crt.rbuild [iso-8859-1] (original) +++ trunk/reactos/lib/sdk/crt/crt.rbuild [iso-8859-1] Sat Jul 23 18:03:11 2011 @@ -144,6 +144,9 @@ <file>frexp.c</file> <file>huge_val.c</file> <file>hypot.c</file> + <file>j0_y0.c</file> + <file>j1_y1.c</file> + <file>jn_yn.c</file> <file>ldiv.c</file> <file>logf.c</file> <file>modf.c</file> @@ -154,6 +157,12 @@ <file>sinh.c</file> <file>tanh.c</file> <file>powl.c</file> + + <directory name="ieee754"> + <file>j0_y0.c</file> + <file>j1_y1.c</file> + <file>jn_yn.c</file> + </directory>
<if property="ARCH" value="i386"> <directory name="i386"> @@ -190,10 +199,6 @@ <file>ldexp.c</file> <file>sqrtf.c</file> </directory> - <!-- FIXME: we don't actually implement these... they recursively call themselves through an alias --> - <!--<file>j0_y0.c</file> - <file>j1_y1.c</file> - <file>jn_yn.c</file>--> </if> <if property="ARCH" value="amd64"> <file>cos.c</file>
Propchange: trunk/reactos/lib/sdk/crt/math/ieee754/ ------------------------------------------------------------------------------ --- bugtraq:logregex (added) +++ bugtraq:logregex Sat Jul 23 18:03:11 2011 @@ -1,0 +1,2 @@ +([Ii]ssue|[Bb]ug)s? #?(\d+)(,? ?#?(\d+))*(,? ?(and |or )?#?(\d+))? +(\d+)
Propchange: trunk/reactos/lib/sdk/crt/math/ieee754/ ------------------------------------------------------------------------------ bugtraq:message = See issue #%BUGID% for more details.
Propchange: trunk/reactos/lib/sdk/crt/math/ieee754/ ------------------------------------------------------------------------------ bugtraq:number = true
Propchange: trunk/reactos/lib/sdk/crt/math/ieee754/ ------------------------------------------------------------------------------ bugtraq:url = http://www.reactos.org/bugzilla/show_bug.cgi?id=%BUGID%
Propchange: trunk/reactos/lib/sdk/crt/math/ieee754/ ------------------------------------------------------------------------------ tsvn:logminsize = 10
Added: trunk/reactos/lib/sdk/crt/math/ieee754/ieee754.h URL: http://svn.reactos.org/svn/reactos/trunk/reactos/lib/sdk/crt/math/ieee754/ie... ============================================================================== --- trunk/reactos/lib/sdk/crt/math/ieee754/ieee754.h (added) +++ trunk/reactos/lib/sdk/crt/math/ieee754/ieee754.h [iso-8859-1] Sat Jul 23 18:03:11 2011 @@ -1,0 +1,54 @@ +#pragma once + +typedef __int32 int32_t; +typedef unsigned __int32 u_int32_t; + +typedef union +{ + double value; + struct + { + u_int32_t lsw; + u_int32_t msw; + } parts; +} ieee_double_shape_type; + +#define EXTRACT_WORDS(ix0,ix1,d) \ +do { \ + ieee_double_shape_type ew_u; \ + ew_u.value = (d); \ + (ix0) = ew_u.parts.msw; \ + (ix1) = ew_u.parts.lsw; \ +} while (0) + +/* Get the more significant 32 bit int from a double. */ + +#define GET_HIGH_WORD(i,d) \ +do { \ + ieee_double_shape_type gh_u; \ + gh_u.value = (d); \ + (i) = gh_u.parts.msw; \ +} while (0) + +#define GET_LOW_WORD(i,d) \ +do { \ + ieee_double_shape_type gl_u; \ + gl_u.value = (d); \ + (i) = gl_u.parts.lsw; \ +} while (0) + +static __inline double __ieee754_sqrt(double x) {return sqrt(x);} +static __inline double __ieee754_log(double x) {return log(x);} +static __inline double __cos(double x) {return cos(x);} +static __inline void __sincos(double x, double *s, double *c) +{ + *s = sin(x); + *c = cos(x); +} + +double __ieee754_j0(double); +double __ieee754_j1(double); +double __ieee754_jn(int, double); +double __ieee754_y0(double); +double __ieee754_y1(double); +double __ieee754_yn(int, double);
Propchange: trunk/reactos/lib/sdk/crt/math/ieee754/ieee754.h ------------------------------------------------------------------------------ svn:eol-style = native
Added: trunk/reactos/lib/sdk/crt/math/ieee754/j0_y0.c URL: http://svn.reactos.org/svn/reactos/trunk/reactos/lib/sdk/crt/math/ieee754/j0... ============================================================================== --- trunk/reactos/lib/sdk/crt/math/ieee754/j0_y0.c (added) +++ trunk/reactos/lib/sdk/crt/math/ieee754/j0_y0.c [iso-8859-1] Sat Jul 23 18:03:11 2011 @@ -1,0 +1,529 @@ +/* @(#)e_j0.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ +/* Modified by Naohiko Shimizu/Tokai University, Japan 1997/08/26, + for performance improvement on pipelined processors. +*/ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_j0.c,v 1.8 1995/05/10 20:45:23 jtc Exp $"; +#endif + +/* __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 "math.h" +#include "ieee754.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] */ +R[] = {0.0, 0.0, 1.56249999999999947958e-02, /* 0x3F8FFFFF, 0xFFFFFFFD */ + -1.89979294238854721751e-04, /* 0xBF28E6A5, 0xB61AC6E9 */ + 1.82954049532700665670e-06, /* 0x3EBEB1D1, 0x0C503919 */ + -4.61832688532103189199e-09}, /* 0xBE33D5E7, 0x73D63FCE */ +S[] = {0.0, 1.56191029464890010492e-02, /* 0x3F8FFCE8, 0x82C8C2A4 */ + 1.16926784663337450260e-04, /* 0x3F1EA6D2, 0xDD57DBF4 */ + 5.13546550207318111446e-07, /* 0x3EA13B54, 0xCE84D5A9 */ + 1.16614003333790000205e-09}; /* 0x3E1408BC, 0xF4745D8F */ + +#ifdef __STDC__ +static const double zero = 0.0; +#else +static double zero = 0.0; +#endif + +#ifdef __STDC__ + double __ieee754_j0(double x) +#else + double __ieee754_j0(x) + double x; +#endif +{ + double z, s,c,ss,cc,r,u,v,r1,r2,s1,s2,z2,z4; + int32_t hx,ix; + + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7ff00000) return one/(x*x); + x = fabs(x); + if(ix >= 0x40000000) { /* |x| >= 2.0 */ + __sincos (x, &s, &c); + 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)/__ieee754_sqrt(x); + else { + u = pzero(x); v = qzero(x); + z = invsqrtpi*(u*cc-v*ss)/__ieee754_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; +#ifdef DO_NOT_USE_THIS + r = z*(R02+z*(R03+z*(R04+z*R05))); + s = one+z*(S01+z*(S02+z*(S03+z*S04))); +#else + r1 = z*R[2]; z2=z*z; + r2 = R[3]+z*R[4]; z4=z2*z2; + r = r1 + z2*r2 + z4*R[5]; + s1 = one+z*S[1]; + s2 = S[2]+z*S[3]; + s = s1 + z2*s2 + z4*S[4]; +#endif + 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 +U[] = {-7.38042951086872317523e-02, /* 0xBFB2E4D6, 0x99CBD01F */ + 1.76666452509181115538e-01, /* 0x3FC69D01, 0x9DE9E3FC */ + -1.38185671945596898896e-02, /* 0xBF8C4CE8, 0xB16CFA97 */ + 3.47453432093683650238e-04, /* 0x3F36C54D, 0x20B29B6B */ + -3.81407053724364161125e-06, /* 0xBECFFEA7, 0x73D25CAD */ + 1.95590137035022920206e-08, /* 0x3E550057, 0x3B4EABD4 */ + -3.98205194132103398453e-11}, /* 0xBDC5E43D, 0x693FB3C8 */ +V[] = {1.27304834834123699328e-02, /* 0x3F8A1270, 0x91C9C71A */ + 7.60068627350353253702e-05, /* 0x3F13ECBB, 0xF578C6C1 */ + 2.59150851840457805467e-07, /* 0x3E91642D, 0x7FF202FD */ + 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,z2,z4,z6,u1,u2,u3,v1,v2; + int32_t hx,ix,lx; + + EXTRACT_WORDS(hx,lx,x); + ix = 0x7fffffff&hx; + /* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0, y0(0) is -inf. */ + if(ix>=0x7ff00000) return one/(x+x*x); + if((ix|lx)==0) return -HUGE_VAL+x; /* -inf and overflow exception. */ + if(hx<0) return zero/(zero*x); + 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. + */ + __sincos (x, &s, &c); + 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)/__ieee754_sqrt(x); + else { + u = pzero(x); v = qzero(x); + z = invsqrtpi*(u*ss+v*cc)/__ieee754_sqrt(x); + } + return z; + } + if(ix<=0x3e400000) { /* x < 2**-27 */ + return(U[0] + tpi*__ieee754_log(x)); + } + z = x*x; +#ifdef DO_NOT_USE_THIS + u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06))))); + v = one+z*(v01+z*(v02+z*(v03+z*v04))); +#else + u1 = U[0]+z*U[1]; z2=z*z; + u2 = U[2]+z*U[3]; z4=z2*z2; + u3 = U[4]+z*U[5]; z6=z4*z2; + u = u1 + z2*u2 + z4*u3 + z6*U[6]; + v1 = one+z*V[0]; + v2 = V[1]+z*V[2]; + v = v1 + z2*v2 + z4*V[3]; +#endif + 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,*q; +#else + double *p,*q; +#endif + double z,r,s,z2,z4,r1,r2,r3,s1,s2,s3; + int32_t ix; + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; + 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); +#ifdef DO_NOT_USE_THIS + 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])))); +#else + r1 = p[0]+z*p[1]; z2=z*z; + r2 = p[2]+z*p[3]; z4=z2*z2; + r3 = p[4]+z*p[5]; + r = r1 + z2*r2 + z4*r3; + s1 = one+z*q[0]; + s2 = q[1]+z*q[2]; + s3 = q[3]+z*q[4]; + s = s1 + z2*s2 + z4*s3; +#endif + 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,*q; +#else + double *p,*q; +#endif + double s,r,z,z2,z4,z6,r1,r2,r3,s1,s2,s3; + int32_t ix; + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; + 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); +#ifdef DO_NOT_USE_THIS + 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]))))); +#else + r1 = p[0]+z*p[1]; z2=z*z; + r2 = p[2]+z*p[3]; z4=z2*z2; + r3 = p[4]+z*p[5]; z6=z4*z2; + r= r1 + z2*r2 + z4*r3; + s1 = one+z*q[0]; + s2 = q[1]+z*q[2]; + s3 = q[3]+z*q[4]; + s = s1 + z2*s2 + z4*s3 +z6*q[5]; +#endif + return (-.125 + r/s)/x; +}
Propchange: trunk/reactos/lib/sdk/crt/math/ieee754/j0_y0.c ------------------------------------------------------------------------------ svn:eol-style = native
Added: trunk/reactos/lib/sdk/crt/math/ieee754/j1_y1.c URL: http://svn.reactos.org/svn/reactos/trunk/reactos/lib/sdk/crt/math/ieee754/j1... ============================================================================== --- trunk/reactos/lib/sdk/crt/math/ieee754/j1_y1.c (added) +++ trunk/reactos/lib/sdk/crt/math/ieee754/j1_y1.c [iso-8859-1] Sat Jul 23 18:03:11 2011 @@ -1,0 +1,530 @@ +/* @(#)e_j1.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ +/* Modified by Naohiko Shimizu/Tokai University, Japan 1997/08/26, + for performance improvement on pipelined processors. +*/ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_j1.c,v 1.8 1995/05/10 20:45:27 jtc Exp $"; +#endif + +/* __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 "math.h" +#include "ieee754.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] */ +R[] = {-6.25000000000000000000e-02, /* 0xBFB00000, 0x00000000 */ + 1.40705666955189706048e-03, /* 0x3F570D9F, 0x98472C61 */ + -1.59955631084035597520e-05, /* 0xBEF0C5C6, 0xBA169668 */ + 4.96727999609584448412e-08}, /* 0x3E6AAAFA, 0x46CA0BD9 */ +S[] = {0.0, 1.91537599538363460805e-02, /* 0x3F939D0B, 0x12637E53 */ + 1.85946785588630915560e-04, /* 0x3F285F56, 0xB9CDF664 */ + 1.17718464042623683263e-06, /* 0x3EB3BFF8, 0x333F8498 */ + 5.04636257076217042715e-09, /* 0x3E35AC88, 0xC97DFF2C */ + 1.23542274426137913908e-11}; /* 0x3DAB2ACF, 0xCFB97ED8 */ + +#ifdef __STDC__ +static const double zero = 0.0; +#else +static double zero = 0.0; +#endif + +#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,r1,r2,s1,s2,s3,z2,z4; + int32_t hx,ix; + + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7ff00000) return one/x; + y = fabs(x); + if(ix >= 0x40000000) { /* |x| >= 2.0 */ + __sincos (y, &s, &c); + 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)/__ieee754_sqrt(y); + else { + u = pone(y); v = qone(y); + z = invsqrtpi*(u*cc-v*ss)/__ieee754_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; +#ifdef DO_NOT_USE_THIS + r = z*(r00+z*(r01+z*(r02+z*r03))); + s = one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05)))); + r *= x; +#else + r1 = z*R[0]; z2=z*z; + r2 = R[1]+z*R[2]; z4=z2*z2; + r = r1 + z2*r2 + z4*R[3]; + r *= x; + s1 = one+z*S[1]; + s2 = S[2]+z*S[3]; + s3 = S[4]+z*S[5]; + s = s1 + z2*s2 + z4*s3; +#endif + 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,u1,u2,v1,v2,v3,z2,z4; + int32_t hx,ix,lx; + + EXTRACT_WORDS(hx,lx,x); + ix = 0x7fffffff&hx; + /* 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 -HUGE_VAL+x; /* -inf and overflow exception. */; + if(hx<0) return zero/(zero*x); + if(ix >= 0x40000000) { /* |x| >= 2.0 */ + __sincos (x, &s, &c); + 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)/__ieee754_sqrt(x); + else { + u = pone(x); v = qone(x); + z = invsqrtpi*(u*ss+v*cc)/__ieee754_sqrt(x); + } + return z; + } + if(ix<=0x3c900000) { /* x < 2**-54 */ + return(-tpi/x); + } + z = x*x; +#ifdef DO_NOT_USE_THIS + 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])))); +#else + u1 = U0[0]+z*U0[1];z2=z*z; + u2 = U0[2]+z*U0[3];z4=z2*z2; + u = u1 + z2*u2 + z4*U0[4]; + v1 = one+z*V0[0]; + v2 = V0[1]+z*V0[2]; + v3 = V0[3]+z*V0[4]; + v = v1 + z2*v2 + z4*v3; +#endif + 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,*q; +#else + double *p,*q; +#endif + double z,r,s,r1,r2,r3,s1,s2,s3,z2,z4; + int32_t ix; + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; + 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); +#ifdef DO_NOT_USE_THIS + 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])))); +#else + r1 = p[0]+z*p[1]; z2=z*z; + r2 = p[2]+z*p[3]; z4=z2*z2; + r3 = p[4]+z*p[5]; + r = r1 + z2*r2 + z4*r3; + s1 = one+z*q[0]; + s2 = q[1]+z*q[2]; + s3 = q[3]+z*q[4]; + s = s1 + z2*s2 + z4*s3; +#endif + 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,*q; +#else + double *p,*q; +#endif + double s,r,z,r1,r2,r3,s1,s2,s3,z2,z4,z6; + int32_t ix; + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; + 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); +#ifdef DO_NOT_USE_THIS + 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]))))); +#else + r1 = p[0]+z*p[1]; z2=z*z; + r2 = p[2]+z*p[3]; z4=z2*z2; + r3 = p[4]+z*p[5]; z6=z4*z2; + r = r1 + z2*r2 + z4*r3; + s1 = one+z*q[0]; + s2 = q[1]+z*q[2]; + s3 = q[3]+z*q[4]; + s = s1 + z2*s2 + z4*s3 + z6*q[5]; +#endif + return (.375 + r/s)/x; +}
Propchange: trunk/reactos/lib/sdk/crt/math/ieee754/j1_y1.c ------------------------------------------------------------------------------ svn:eol-style = native
Added: trunk/reactos/lib/sdk/crt/math/ieee754/jn_yn.c URL: http://svn.reactos.org/svn/reactos/trunk/reactos/lib/sdk/crt/math/ieee754/jn... ============================================================================== --- trunk/reactos/lib/sdk/crt/math/ieee754/jn_yn.c (added) +++ trunk/reactos/lib/sdk/crt/math/ieee754/jn_yn.c [iso-8859-1] Sat Jul 23 18:03:11 2011 @@ -1,0 +1,287 @@ +/* @(#)e_jn.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_jn.c,v 1.9 1995/05/10 20:45:34 jtc Exp $"; +#endif + +/* + * __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 overflow 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 "math.h" +#include "ieee754.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 */ + +#ifdef __STDC__ +static const double zero = 0.00000000000000000000e+00; +#else +static double zero = 0.00000000000000000000e+00; +#endif + +#ifdef __STDC__ + double __ieee754_jn(int n, double x) +#else + double __ieee754_jn(n,x) + int n; double x; +#endif +{ + int32_t i,hx,ix,lx, sgn; + double a, b, temp, 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) + */ + EXTRACT_WORDS(hx,lx,x); + ix = 0x7fffffff&hx; + /* if J(n,NaN) is NaN */ + if((ix|((u_int32_t)(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 + */ + double s; + double c; + __sincos (x, &s, &c); + switch(n&3) { + case 0: temp = c + s; break; + case 1: temp = -c + s; break; + case 2: temp = -c - s; break; + case 3: temp = c - s; break; + } + b = invsqrtpi*temp/__ieee754_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; int32_t 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 +{ + int32_t i,hx,ix,lx; + int32_t sign; + double a, b, temp; + + EXTRACT_WORDS(hx,lx,x); + ix = 0x7fffffff&hx; + /* if Y(n,NaN) is NaN */ + if((ix|((u_int32_t)(lx|-lx))>>31)>0x7ff00000) return x+x; + if((ix|lx)==0) return -HUGE_VAL+x; /* -inf and overflow exception. */; + if(hx<0) return zero/(zero*x); + 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 + */ + double c; + double s; + __sincos (x, &s, &c); + switch(n&3) { + case 0: temp = s - c; break; + case 1: temp = -s - c; break; + case 2: temp = -s + c; break; + case 3: temp = s + c; break; + } + b = invsqrtpi*temp/__ieee754_sqrt(x); + } else { + u_int32_t high; + a = __ieee754_y0(x); + b = __ieee754_y1(x); + /* quit if b is -inf */ + GET_HIGH_WORD(high,b); + for(i=1;i<n&&high!=0xfff00000;i++){ + temp = b; + b = ((double)(i+i)/x)*b - a; + GET_HIGH_WORD(high,b); + a = temp; + } + } + if(sign>0) return b; else return -b; +}
Propchange: trunk/reactos/lib/sdk/crt/math/ieee754/jn_yn.c ------------------------------------------------------------------------------ svn:eol-style = native
Modified: trunk/reactos/lib/sdk/crt/math/j0_y0.c URL: http://svn.reactos.org/svn/reactos/trunk/reactos/lib/sdk/crt/math/j0_y0.c?re... ============================================================================== --- trunk/reactos/lib/sdk/crt/math/j0_y0.c [iso-8859-1] (original) +++ trunk/reactos/lib/sdk/crt/math/j0_y0.c [iso-8859-1] Sat Jul 23 18:03:11 2011 @@ -1,4 +1,6 @@ #include <math.h> +#include <float.h> +#include "ieee754/ieee754.h"
typedef int fpclass_t; fpclass_t _fpclass(double __d); @@ -10,7 +12,7 @@ double _j0(double num) { /* FIXME: errno handling */ - return j0(num); + return __ieee754_j0(num); }
/* @@ -19,8 +21,8 @@ double _y0(double num) { double retval; - if (!isfinite(num)) *_errno() = EDOM; - retval = y0(num); + if (!_finite(num)) *_errno() = EDOM; + retval = __ieee754_y0(num); if (_fpclass(retval) == _FPCLASS_NINF) { *_errno() = EDOM;
Modified: trunk/reactos/lib/sdk/crt/math/j1_y1.c URL: http://svn.reactos.org/svn/reactos/trunk/reactos/lib/sdk/crt/math/j1_y1.c?re... ============================================================================== --- trunk/reactos/lib/sdk/crt/math/j1_y1.c [iso-8859-1] (original) +++ trunk/reactos/lib/sdk/crt/math/j1_y1.c [iso-8859-1] Sat Jul 23 18:03:11 2011 @@ -1,4 +1,6 @@ #include <math.h> +#include <float.h> +#include "ieee754/ieee754.h"
typedef int fpclass_t; fpclass_t _fpclass(double __d); @@ -10,7 +12,7 @@ double _j1(double num) { /* FIXME: errno handling */ - return j1(num); + return __ieee754_j1(num); }
/* @@ -19,8 +21,8 @@ double _y1(double num) { double retval; - if (!isfinite(num)) *_errno() = EDOM; - retval = y1(num); + if (!_finite(num)) *_errno() = EDOM; + retval = __ieee754_y1(num); if (_fpclass(retval) == _FPCLASS_NINF) { *_errno() = EDOM;
Modified: trunk/reactos/lib/sdk/crt/math/jn_yn.c URL: http://svn.reactos.org/svn/reactos/trunk/reactos/lib/sdk/crt/math/jn_yn.c?re... ============================================================================== --- trunk/reactos/lib/sdk/crt/math/jn_yn.c [iso-8859-1] (original) +++ trunk/reactos/lib/sdk/crt/math/jn_yn.c [iso-8859-1] Sat Jul 23 18:03:11 2011 @@ -1,4 +1,6 @@ #include <math.h> +#include <float.h> +#include "ieee754/ieee754.h"
typedef int fpclass_t; fpclass_t _fpclass(double __d); @@ -10,7 +12,7 @@ double _jn(int n, double num) { /* FIXME: errno handling */ - return jn(n, num); + return __ieee754_jn(n, num); }
/* @@ -19,8 +21,8 @@ double _yn(int order, double num) { double retval; - if (!isfinite(num)) *_errno() = EDOM; - retval = yn(order,num); + if (!_finite(num)) *_errno() = EDOM; + retval = __ieee754_yn(order,num); if (_fpclass(retval) == _FPCLASS_NINF) { *_errno() = EDOM;
-
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