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-rw-r--r--lib/mlibc/options/ansi/musl-generic-math/jn.c280
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diff --git a/lib/mlibc/options/ansi/musl-generic-math/jn.c b/lib/mlibc/options/ansi/musl-generic-math/jn.c
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--- a/lib/mlibc/options/ansi/musl-generic-math/jn.c
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-/* origin: FreeBSD /usr/src/lib/msun/src/e_jn.c */
-/*
- * ====================================================
- * 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.
- * ====================================================
- */
-/*
- * jn(n, x), 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 is 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 "libm.h"
-
-static const double invsqrtpi = 5.64189583547756279280e-01; /* 0x3FE20DD7, 0x50429B6D */
-
-double jn(int n, double x)
-{
- uint32_t ix, lx;
- int nm1, i, sign;
- double a, b, temp;
-
- EXTRACT_WORDS(ix, lx, x);
- sign = ix>>31;
- ix &= 0x7fffffff;
-
- if ((ix | (lx|-lx)>>31) > 0x7ff00000) /* nan */
- return x;
-
- /* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x)
- * Thus, J(-n,x) = J(n,-x)
- */
- /* nm1 = |n|-1 is used instead of |n| to handle n==INT_MIN */
- if (n == 0)
- return j0(x);
- if (n < 0) {
- nm1 = -(n+1);
- x = -x;
- sign ^= 1;
- } else
- nm1 = n-1;
- if (nm1 == 0)
- return j1(x);
-
- sign &= n; /* even n: 0, odd n: signbit(x) */
- x = fabs(x);
- if ((ix|lx) == 0 || ix == 0x7ff00000) /* if x is 0 or inf */
- b = 0.0;
- else if (nm1 < 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(nm1&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;
- default:
- case 3: temp = cos(x)+sin(x); break;
- }
- b = invsqrtpi*temp/sqrt(x);
- } else {
- a = j0(x);
- b = j1(x);
- for (i=0; i<nm1; ) {
- i++;
- temp = b;
- b = b*(2.0*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 (nm1 > 32) /* underflow */
- b = 0.0;
- else {
- temp = x*0.5;
- b = temp;
- a = 1.0;
- for (i=2; i<=nm1+1; 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,q0,q1,w,h,z,tmp,nf;
- int k;
-
- nf = nm1 + 1.0;
- w = 2*nf/x;
- h = 2/x;
- z = w+h;
- q0 = w;
- q1 = w*z - 1.0;
- k = 1;
- while (q1 < 1.0e9) {
- k += 1;
- z += h;
- tmp = z*q1 - q0;
- q0 = q1;
- q1 = tmp;
- }
- for (t=0.0, i=k; i>=0; i--)
- t = 1/(2*(i+nf)/x - t);
- a = t;
- b = 1.0;
- /* 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 = nf*log(fabs(w));
- if (tmp < 7.09782712893383973096e+02) {
- for (i=nm1; i>0; i--) {
- temp = b;
- b = b*(2.0*i)/x - a;
- a = temp;
- }
- } else {
- for (i=nm1; i>0; i--) {
- temp = b;
- b = b*(2.0*i)/x - a;
- a = temp;
- /* scale b to avoid spurious overflow */
- if (b > 0x1p500) {
- a /= b;
- t /= b;
- b = 1.0;
- }
- }
- }
- z = j0(x);
- w = j1(x);
- if (fabs(z) >= fabs(w))
- b = t*z/b;
- else
- b = t*w/a;
- }
- }
- return sign ? -b : b;
-}
-
-
-double yn(int n, double x)
-{
- uint32_t ix, lx, ib;
- int nm1, sign, i;
- double a, b, temp;
-
- EXTRACT_WORDS(ix, lx, x);
- sign = ix>>31;
- ix &= 0x7fffffff;
-
- if ((ix | (lx|-lx)>>31) > 0x7ff00000) /* nan */
- return x;
- if (sign && (ix|lx)!=0) /* x < 0 */
- return 0/0.0;
- if (ix == 0x7ff00000)
- return 0.0;
-
- if (n == 0)
- return y0(x);
- if (n < 0) {
- nm1 = -(n+1);
- sign = n&1;
- } else {
- nm1 = n-1;
- sign = 0;
- }
- if (nm1 == 0)
- return sign ? -y1(x) : y1(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(nm1&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;
- default:
- case 3: temp = sin(x)-cos(x); break;
- }
- b = invsqrtpi*temp/sqrt(x);
- } else {
- a = y0(x);
- b = y1(x);
- /* quit if b is -inf */
- GET_HIGH_WORD(ib, b);
- for (i=0; i<nm1 && ib!=0xfff00000; ){
- i++;
- temp = b;
- b = (2.0*i/x)*b - a;
- GET_HIGH_WORD(ib, b);
- a = temp;
- }
- }
- return sign ? -b : b;
-}
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