first commit of the new libm!

thanks to the hard work of Szabolcs Nagy (nsz), identifying the best
(from correctness and license standpoint) implementations from freebsd
and openbsd and cleaning them up! musl should now fully support c99
float and long double math functions, and has near-complete complex
math support. tgmath should also work (fully on gcc-compatible
compilers, and mostly on any c99 compiler).

based largely on commit 0376d44a890fea261506f1fc63833e7a686dca19 from
nsz's libm git repo, with some additions (dummy versions of a few
missing long double complex functions, etc.) by me.

various cleanups still need to be made, including re-adding (if
they're correct) some asm functions that were dropped.

1 files changed, 0 insertions, 109 deletions

diff --git a/src/math/e_asin.c b/src/math/e_asin.c
deleted file mode 100644
index 4bf162a1..00000000
--- a/src/math/e_asin.c
+++ /dev/null
@@ -1,109 +0,0 @@
-
-/* @(#)e_asin.c 1.3 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.
- * ====================================================
- */
-
-/* asin(x)
- * Method :                  
- *      Since  asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
- *      we approximate asin(x) on [0,0.5] by
- *              asin(x) = x + x*x^2*R(x^2)
- *      where
- *              R(x^2) is a rational approximation of (asin(x)-x)/x^3 
- *      and its remez error is bounded by
- *              |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75)
- *
- *      For x in [0.5,1]
- *              asin(x) = pi/2-2*asin(sqrt((1-x)/2))
- *      Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2;
- *      then for x>0.98
- *              asin(x) = pi/2 - 2*(s+s*z*R(z))
- *                      = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo)
- *      For x<=0.98, let pio4_hi = pio2_hi/2, then
- *              f = hi part of s;
- *              c = sqrt(z) - f = (z-f*f)/(s+f)         ...f+c=sqrt(z)
- *      and
- *              asin(x) = pi/2 - 2*(s+s*z*R(z))
- *                      = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo)
- *                      = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c))
- *
- * Special cases:
- *      if x is NaN, return x itself;
- *      if |x|>1, return NaN with invalid signal.
- *
- */
-
-
-#include <math.h>
-#include "math_private.h"
-
-static const double
-one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
-huge =  1.000e+300,
-pio2_hi =  1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
-pio2_lo =  6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
-pio4_hi =  7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */
-        /* coefficient for R(x^2) */
-pS0 =  1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
-pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
-pS2 =  2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
-pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
-pS4 =  7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
-pS5 =  3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
-qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
-qS2 =  2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
-qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
-qS4 =  7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
-
-double
-asin(double x)
-{
-        double t=0.0,w,p,q,c,r,s;
-        int32_t hx,ix;
-        GET_HIGH_WORD(hx,x);
-        ix = hx&0x7fffffff;
-        if(ix>= 0x3ff00000) {           /* |x|>= 1 */
-            uint32_t lx;
-            GET_LOW_WORD(lx,x);
-            if(((ix-0x3ff00000)|lx)==0)
-                    /* asin(1)=+-pi/2 with inexact */
-                return x*pio2_hi+x*pio2_lo;     
-            return (x-x)/(x-x);         /* asin(|x|>1) is NaN */   
-        } else if (ix<0x3fe00000) {     /* |x|<0.5 */
-            if(ix<0x3e400000) {         /* if |x| < 2**-27 */
-                if(huge+x>one) return x;/* return x with inexact if x!=0*/
-            } else 
-                t = x*x;
-                p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
-                q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
-                w = p/q;
-                return x+x*w;
-        }
-        /* 1> |x|>= 0.5 */
-        w = one-fabs(x);
-        t = w*0.5;
-        p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
-        q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
-        s = sqrt(t);
-        if(ix>=0x3FEF3333) {    /* if |x| > 0.975 */
-            w = p/q;
-            t = pio2_hi-(2.0*(s+s*w)-pio2_lo);
-        } else {
-            w  = s;
-            SET_LOW_WORD(w,0);
-            c  = (t-w*w)/(s+w);
-            r  = p/q;
-            p  = 2.0*s*r-(pio2_lo-2.0*c);
-            q  = pio4_hi-2.0*w;
-            t  = pio4_hi-(p-q);
-        }    
-        if(hx>0) return t; else return -t;    
-}