diff options
author | Ian Moffett <ian@osmora.org> | 2024-03-07 17:28:52 -0500 |
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committer | Ian Moffett <ian@osmora.org> | 2024-03-07 18:24:51 -0500 |
commit | f5e48e94a2f4d4bbd6e5628c7f2afafc6dbcc459 (patch) | |
tree | 93b156621dc0303816b37f60ba88051b702d92f6 /lib/mlibc/options/ansi/musl-generic-math/jn.c | |
parent | bd5969fc876a10b18613302db7087ef3c40f18e1 (diff) |
build: Build mlibc + add distclean target
Signed-off-by: Ian Moffett <ian@osmora.org>
Diffstat (limited to 'lib/mlibc/options/ansi/musl-generic-math/jn.c')
-rw-r--r-- | lib/mlibc/options/ansi/musl-generic-math/jn.c | 280 |
1 files changed, 0 insertions, 280 deletions
diff --git a/lib/mlibc/options/ansi/musl-generic-math/jn.c b/lib/mlibc/options/ansi/musl-generic-math/jn.c deleted file mode 100644 index 4878a54..0000000 --- a/lib/mlibc/options/ansi/musl-generic-math/jn.c +++ /dev/null @@ -1,280 +0,0 @@ -/* 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; -} |