diff options
Diffstat (limited to 'libc-top-half/musl/src/math/jnf.c')
| -rw-r--r-- | libc-top-half/musl/src/math/jnf.c | 202 |
1 files changed, 202 insertions, 0 deletions
diff --git a/libc-top-half/musl/src/math/jnf.c b/libc-top-half/musl/src/math/jnf.c new file mode 100644 index 0000000..f63c062 --- /dev/null +++ b/libc-top-half/musl/src/math/jnf.c @@ -0,0 +1,202 @@ +/* origin: FreeBSD /usr/src/lib/msun/src/e_jnf.c */ +/* + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ +/* + * ==================================================== + * 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. + * ==================================================== + */ + +#define _GNU_SOURCE +#include "libm.h" + +float jnf(int n, float x) +{ + uint32_t ix; + int nm1, sign, i; + float a, b, temp; + + GET_FLOAT_WORD(ix, x); + sign = ix>>31; + ix &= 0x7fffffff; + if (ix > 0x7f800000) /* nan */ + return x; + + /* J(-n,x) = J(n,-x), use |n|-1 to avoid overflow in -n */ + if (n == 0) + return j0f(x); + if (n < 0) { + nm1 = -(n+1); + x = -x; + sign ^= 1; + } else + nm1 = n-1; + if (nm1 == 0) + return j1f(x); + + sign &= n; /* even n: 0, odd n: signbit(x) */ + x = fabsf(x); + if (ix == 0 || ix == 0x7f800000) /* if x is 0 or inf */ + b = 0.0f; + else if (nm1 < x) { + /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */ + a = j0f(x); + b = j1f(x); + for (i=0; i<nm1; ){ + i++; + temp = b; + b = b*(2.0f*i/x) - a; + a = temp; + } + } else { + if (ix < 0x35800000) { /* x < 2**-20 */ + /* x is tiny, return the first Taylor expansion of J(n,x) + * J(n,x) = 1/n!*(x/2)^n - ... + */ + if (nm1 > 8) /* underflow */ + nm1 = 8; + temp = 0.5f * x; + b = temp; + a = 1.0f; + for (i=2; i<=nm1+1; i++) { + a *= (float)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 */ + float t,q0,q1,w,h,z,tmp,nf; + int k; + + nf = nm1+1.0f; + w = 2*nf/x; + h = 2/x; + z = w+h; + q0 = w; + q1 = w*z - 1.0f; + k = 1; + while (q1 < 1.0e4f) { + k += 1; + z += h; + tmp = z*q1 - q0; + q0 = q1; + q1 = tmp; + } + for (t=0.0f, i=k; i>=0; i--) + t = 1.0f/(2*(i+nf)/x-t); + a = t; + b = 1.0f; + /* 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*logf(fabsf(w)); + if (tmp < 88.721679688f) { + for (i=nm1; i>0; i--) { + temp = b; + b = 2.0f*i*b/x - a; + a = temp; + } + } else { + for (i=nm1; i>0; i--){ + temp = b; + b = 2.0f*i*b/x - a; + a = temp; + /* scale b to avoid spurious overflow */ + if (b > 0x1p60f) { + a /= b; + t /= b; + b = 1.0f; + } + } + } + z = j0f(x); + w = j1f(x); + if (fabsf(z) >= fabsf(w)) + b = t*z/b; + else + b = t*w/a; + } + } + return sign ? -b : b; +} + +float ynf(int n, float x) +{ + uint32_t ix, ib; + int nm1, sign, i; + float a, b, temp; + + GET_FLOAT_WORD(ix, x); + sign = ix>>31; + ix &= 0x7fffffff; + if (ix > 0x7f800000) /* nan */ + return x; + if (sign && ix != 0) /* x < 0 */ + return 0/0.0f; + if (ix == 0x7f800000) + return 0.0f; + + if (n == 0) + return y0f(x); + if (n < 0) { + nm1 = -(n+1); + sign = n&1; + } else { + nm1 = n-1; + sign = 0; + } + if (nm1 == 0) + return sign ? -y1f(x) : y1f(x); + + a = y0f(x); + b = y1f(x); + /* quit if b is -inf */ + GET_FLOAT_WORD(ib,b); + for (i = 0; i < nm1 && ib != 0xff800000; ) { + i++; + temp = b; + b = (2.0f*i/x)*b - a; + GET_FLOAT_WORD(ib, b); + a = temp; + } + return sign ? -b : b; +} |