mirror of
https://github.com/jart/cosmopolitan.git
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550b52abf6
- Introduce epoll_pwait() - Rewrite -ftrapv and ffs() libraries in C code - Use more FreeBSD code in math function library - Get significantly more tests passing on qemu-aarch64 - Fix many Musl long double functions that were broken on AARCH64
241 lines
7.3 KiB
C
241 lines
7.3 KiB
C
/*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-│
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│vi: set et ft=c ts=8 tw=8 fenc=utf-8 :vi│
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╚──────────────────────────────────────────────────────────────────────────────╝
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│ │
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│ Musl Libc │
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│ Copyright © 2005-2014 Rich Felker, et al. │
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│ │
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│ Permission is hereby granted, free of charge, to any person obtaining │
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│ a copy of this software and associated documentation files (the │
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│ "Software"), to deal in the Software without restriction, including │
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│ without limitation the rights to use, copy, modify, merge, publish, │
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│ distribute, sublicense, and/or sell copies of the Software, and to │
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│ permit persons to whom the Software is furnished to do so, subject to │
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│ the following conditions: │
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│ │
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│ The above copyright notice and this permission notice shall be │
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│ included in all copies or substantial portions of the Software. │
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│ │
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│ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, │
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│ EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF │
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│ MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. │
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│ IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY │
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│ CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, │
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│ TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE │
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│ SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. │
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│ │
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╚─────────────────────────────────────────────────────────────────────────────*/
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#include "libc/math.h"
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#include "libc/tinymath/complex.internal.h"
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asm(".ident\t\"\\n\\n\
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Double-precision math functions (MIT License)\\n\
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Copyright 2018 ARM Limited\"");
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asm(".include \"libc/disclaimer.inc\"");
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// clang-format off
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/* origin: FreeBSD /usr/src/lib/msun/src/e_jnf.c */
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/*
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* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
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*/
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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/**
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* Returns Bessel function of 𝑥 of first kind of order 𝑛.
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*/
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float jnf(int n, float x)
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{
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uint32_t ix;
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int nm1, sign, i;
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float a, b, temp;
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GET_FLOAT_WORD(ix, x);
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sign = ix>>31;
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ix &= 0x7fffffff;
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if (ix > 0x7f800000) /* nan */
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return x;
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/* J(-n,x) = J(n,-x), use |n|-1 to avoid overflow in -n */
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if (n == 0)
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return j0f(x);
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if (n < 0) {
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nm1 = -(n+1);
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x = -x;
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sign ^= 1;
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} else
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nm1 = n-1;
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if (nm1 == 0)
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return j1f(x);
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sign &= n; /* even n: 0, odd n: signbit(x) */
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x = fabsf(x);
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if (ix == 0 || ix == 0x7f800000) /* if x is 0 or inf */
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b = 0.0f;
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else if (nm1 < x) {
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/* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
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a = j0f(x);
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b = j1f(x);
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for (i=0; i<nm1; ){
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i++;
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temp = b;
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b = b*(2.0f*i/x) - a;
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a = temp;
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}
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} else {
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if (ix < 0x35800000) { /* x < 2**-20 */
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/* x is tiny, return the first Taylor expansion of J(n,x)
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* J(n,x) = 1/n!*(x/2)^n - ...
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*/
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if (nm1 > 8) /* underflow */
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nm1 = 8;
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temp = 0.5f * x;
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b = temp;
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a = 1.0f;
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for (i=2; i<=nm1+1; i++) {
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a *= (float)i; /* a = n! */
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b *= temp; /* b = (x/2)^n */
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}
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b = b/a;
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} else {
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/* use backward recurrence */
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/* x x^2 x^2
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* J(n,x)/J(n-1,x) = ---- ------ ------ .....
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* 2n - 2(n+1) - 2(n+2)
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*
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* 1 1 1
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* (for large x) = ---- ------ ------ .....
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* 2n 2(n+1) 2(n+2)
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* -- - ------ - ------ -
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* x x x
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*
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* Let w = 2n/x and h=2/x, then the above quotient
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* is equal to the continued fraction:
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* 1
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* = -----------------------
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* 1
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* w - -----------------
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* 1
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* w+h - ---------
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* w+2h - ...
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*
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* To determine how many terms needed, let
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* Q(0) = w, Q(1) = w(w+h) - 1,
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* Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
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* When Q(k) > 1e4 good for single
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* When Q(k) > 1e9 good for double
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* When Q(k) > 1e17 good for quadruple
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*/
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/* determine k */
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float t,q0,q1,w,h,z,tmp,nf;
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int k;
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nf = nm1+1.0f;
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w = 2*nf/x;
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h = 2/x;
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z = w+h;
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q0 = w;
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q1 = w*z - 1.0f;
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k = 1;
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while (q1 < 1.0e4f) {
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k += 1;
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z += h;
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tmp = z*q1 - q0;
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q0 = q1;
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q1 = tmp;
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}
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for (t=0.0f, i=k; i>=0; i--)
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t = 1.0f/(2*(i+nf)/x-t);
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a = t;
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b = 1.0f;
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/* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)
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* Hence, if n*(log(2n/x)) > ...
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* single 8.8722839355e+01
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* double 7.09782712893383973096e+02
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* long double 1.1356523406294143949491931077970765006170e+04
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* then recurrent value may overflow and the result is
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* likely underflow to zero
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*/
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tmp = nf*logf(fabsf(w));
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if (tmp < 88.721679688f) {
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for (i=nm1; i>0; i--) {
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temp = b;
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b = 2.0f*i*b/x - a;
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a = temp;
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}
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} else {
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for (i=nm1; i>0; i--){
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temp = b;
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b = 2.0f*i*b/x - a;
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a = temp;
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/* scale b to avoid spurious overflow */
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if (b > 0x1p60f) {
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a /= b;
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t /= b;
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b = 1.0f;
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}
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}
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}
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z = j0f(x);
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w = j1f(x);
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if (fabsf(z) >= fabsf(w))
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b = t*z/b;
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else
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b = t*w/a;
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}
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}
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return sign ? -b : b;
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}
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/**
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* Returns Bessel function of 𝑥 of second kind of order 𝑛.
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*/
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float ynf(int n, float x)
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{
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uint32_t ix, ib;
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int nm1, sign, i;
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float a, b, temp;
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GET_FLOAT_WORD(ix, x);
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sign = ix>>31;
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ix &= 0x7fffffff;
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if (ix > 0x7f800000) /* nan */
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return x;
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if (sign && ix != 0) /* x < 0 */
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return 0/0.0f;
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if (ix == 0x7f800000)
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return 0.0f;
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if (n == 0)
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return y0f(x);
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if (n < 0) {
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nm1 = -(n+1);
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sign = n&1;
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} else {
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nm1 = n-1;
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sign = 0;
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}
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if (nm1 == 0)
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return sign ? -y1f(x) : y1f(x);
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a = y0f(x);
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b = y1f(x);
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/* quit if b is -inf */
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GET_FLOAT_WORD(ib,b);
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for (i = 0; i < nm1 && ib != 0xff800000; ) {
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i++;
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temp = b;
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b = (2.0f*i/x)*b - a;
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GET_FLOAT_WORD(ib, b);
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a = temp;
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}
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return sign ? -b : b;
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}
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