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| author | Bob Jamison <ishmalius@gmail.com> | 2006-01-16 09:50:17 +0000 |
|---|---|---|
| committer | ishmal <ishmal@users.sourceforge.net> | 2006-01-16 09:50:17 +0000 |
| commit | 2d00762bebfb3257161115add4805a57aef25bde (patch) | |
| tree | 2e5dfe871d77655fd43912917160602c9ec83e3c /src/extension/script/js/fdlibm/e_jn.c | |
| parent | * src/svg/Makefile_insert: Updated to reflect a previous header (diff) | |
| download | inkscape-2d00762bebfb3257161115add4805a57aef25bde.tar.gz inkscape-2d00762bebfb3257161115add4805a57aef25bde.zip | |
Remove duplicate Javascript tree. This dupe was probably an artifact of the migration.
(bzr r3)
Diffstat (limited to 'src/extension/script/js/fdlibm/e_jn.c')
| -rw-r--r-- | src/extension/script/js/fdlibm/e_jn.c | 315 |
1 files changed, 0 insertions, 315 deletions
diff --git a/src/extension/script/js/fdlibm/e_jn.c b/src/extension/script/js/fdlibm/e_jn.c deleted file mode 100644 index 2b61b4439..000000000 --- a/src/extension/script/js/fdlibm/e_jn.c +++ /dev/null @@ -1,315 +0,0 @@ -/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*- - * - * ***** BEGIN LICENSE BLOCK ***** - * Version: MPL 1.1/GPL 2.0/LGPL 2.1 - * - * The contents of this file are subject to the Mozilla Public License Version - * 1.1 (the "License"); you may not use this file except in compliance with - * the License. You may obtain a copy of the License at - * http://www.mozilla.org/MPL/ - * - * Software distributed under the License is distributed on an "AS IS" basis, - * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License - * for the specific language governing rights and limitations under the - * License. - * - * The Original Code is Mozilla Communicator client code, released - * March 31, 1998. - * - * The Initial Developer of the Original Code is - * Sun Microsystems, Inc. - * Portions created by the Initial Developer are Copyright (C) 1998 - * the Initial Developer. All Rights Reserved. - * - * Contributor(s): - * - * Alternatively, the contents of this file may be used under the terms of - * either of the GNU General Public License Version 2 or later (the "GPL"), - * or the GNU Lesser General Public License Version 2.1 or later (the "LGPL"), - * in which case the provisions of the GPL or the LGPL are applicable instead - * of those above. If you wish to allow use of your version of this file only - * under the terms of either the GPL or the LGPL, and not to allow others to - * use your version of this file under the terms of the MPL, indicate your - * decision by deleting the provisions above and replace them with the notice - * and other provisions required by the GPL or the LGPL. If you do not delete - * the provisions above, a recipient may use your version of this file under - * the terms of any one of the MPL, the GPL or the LGPL. - * - * ***** END LICENSE BLOCK ***** */ - -/* @(#)e_jn.c 1.4 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* - * __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 -{ - fd_twoints u; - int 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) - */ - u.d = x; - hx = __HI(u); - ix = 0x7fffffff&hx; - lx = __LO(u); - /* 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 = fd_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 = fd_cos(x)+fd_sin(x); break; - case 1: temp = -fd_cos(x)+fd_sin(x); break; - case 2: temp = -fd_cos(x)-fd_sin(x); break; - case 3: temp = fd_cos(x)-fd_sin(x); break; - } - b = invsqrtpi*temp/fd_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(fd_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 -{ - fd_twoints u; - int i,hx,ix,lx; - int sign; - double a, b, temp; - - u.d = x; - hx = __HI(u); - ix = 0x7fffffff&hx; - lx = __LO(u); - /* 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 = fd_sin(x)-fd_cos(x); break; - case 1: temp = -fd_sin(x)-fd_cos(x); break; - case 2: temp = -fd_sin(x)+fd_cos(x); break; - case 3: temp = fd_sin(x)+fd_cos(x); break; - } - b = invsqrtpi*temp/fd_sqrt(x); - } else { - a = __ieee754_y0(x); - b = __ieee754_y1(x); - /* quit if b is -inf */ - u.d = b; - for(i=1;i<n&&(__HI(u) != 0xfff00000);i++){ - temp = b; - b = ((double)(i+i)/x)*b - a; - a = temp; - } - } - if(sign>0) return b; else return -b; -} |
