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, 300 deletions

diff --git a/src/math/e_pow.c b/src/math/e_pow.c
deleted file mode 100644
index aad24287..00000000
--- a/src/math/e_pow.c
+++ /dev/null
@@ -1,300 +0,0 @@
-/* @(#)e_pow.c 1.5 04/04/22 SMI */
-/*
- * ====================================================
- * Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved.
- *
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice 
- * is preserved.
- * ====================================================
- */
-
-/* pow(x,y) return x**y
- *
- *                    n
- * Method:  Let x =  2   * (1+f)
- *      1. Compute and return log2(x) in two pieces:
- *              log2(x) = w1 + w2,
- *         where w1 has 53-24 = 29 bit trailing zeros.
- *      2. Perform y*log2(x) = n+y' by simulating muti-precision 
- *         arithmetic, where |y'|<=0.5.
- *      3. Return x**y = 2**n*exp(y'*log2)
- *
- * Special cases:
- *      1.  (anything) ** 0  is 1
- *      2.  (anything) ** 1  is itself
- *      3.  (anything) ** NAN is NAN
- *      4.  NAN ** (anything except 0) is NAN
- *      5.  +-(|x| > 1) **  +INF is +INF
- *      6.  +-(|x| > 1) **  -INF is +0
- *      7.  +-(|x| < 1) **  +INF is +0
- *      8.  +-(|x| < 1) **  -INF is +INF
- *      9.  +-1         ** +-INF is NAN
- *      10. +0 ** (+anything except 0, NAN)               is +0
- *      11. -0 ** (+anything except 0, NAN, odd integer)  is +0
- *      12. +0 ** (-anything except 0, NAN)               is +INF
- *      13. -0 ** (-anything except 0, NAN, odd integer)  is +INF
- *      14. -0 ** (odd integer) = -( +0 ** (odd integer) )
- *      15. +INF ** (+anything except 0,NAN) is +INF
- *      16. +INF ** (-anything except 0,NAN) is +0
- *      17. -INF ** (anything)  = -0 ** (-anything)
- *      18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)
- *      19. (-anything except 0 and inf) ** (non-integer) is NAN
- *
- * Accuracy:
- *      pow(x,y) returns x**y nearly rounded. In particular
- *                      pow(integer,integer)
- *      always returns the correct integer provided it is 
- *      representable.
- *
- * Constants :
- * The hexadecimal values are the intended ones for the following 
- * constants. The decimal values may be used, provided that the 
- * compiler will convert from decimal to binary accurately enough 
- * to produce the hexadecimal values shown.
- */
-
-#include <math.h>
-#include "math_private.h"
-
-static const double
-bp[] = {1.0, 1.5,},
-dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */
-dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */
-zero    =  0.0,
-one     =  1.0,
-two     =  2.0,
-two53   =  9007199254740992.0,  /* 0x43400000, 0x00000000 */
-huge    =  1.0e300,
-tiny    =  1.0e-300,
-        /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
-L1  =  5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */
-L2  =  4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */
-L3  =  3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */
-L4  =  2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */
-L5  =  2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */
-L6  =  2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */
-P1   =  1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
-P2   = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
-P3   =  6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
-P4   = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
-P5   =  4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */
-lg2  =  6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
-lg2_h  =  6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */
-lg2_l  = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */
-ovt =  8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */
-cp    =  9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */
-cp_h  =  9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */
-cp_l  = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/
-ivln2    =  1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */
-ivln2_h  =  1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/
-ivln2_l  =  1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/
-
-double
-pow(double x, double y)
-{
-        double z,ax,z_h,z_l,p_h,p_l;
-        double y1,t1,t2,r,s,t,u,v,w;
-        int32_t i,j,k,yisint,n;
-        int32_t hx,hy,ix,iy;
-        uint32_t lx,ly;
-
-        EXTRACT_WORDS(hx,lx,x);
-        EXTRACT_WORDS(hy,ly,y);
-        ix = hx&0x7fffffff;  iy = hy&0x7fffffff;
-
-    /* y==zero: x**0 = 1 */
-        if((iy|ly)==0) return one;      
-
-    /* +-NaN return x+y */
-        if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) ||
-           iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0))) 
-                return x+y;     
-
-    /* determine if y is an odd int when x < 0
-     * yisint = 0       ... y is not an integer
-     * yisint = 1       ... y is an odd int
-     * yisint = 2       ... y is an even int
-     */
-        yisint  = 0;
-        if(hx<0) {      
-            if(iy>=0x43400000) yisint = 2; /* even integer y */
-            else if(iy>=0x3ff00000) {
-                k = (iy>>20)-0x3ff;        /* exponent */
-                if(k>20) {
-                    j = ly>>(52-k);
-                    if((j<<(52-k))==ly) yisint = 2-(j&1);
-                } else if(ly==0) {
-                    j = iy>>(20-k);
-                    if((j<<(20-k))==iy) yisint = 2-(j&1);
-                }
-            }           
-        } 
-
-    /* special value of y */
-        if(ly==0) {     
-            if (iy==0x7ff00000) {       /* y is +-inf */
-                if(((ix-0x3ff00000)|lx)==0)
-                    return  y - y;      /* inf**+-1 is NaN */
-                else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */
-                    return (hy>=0)? y: zero;
-                else                    /* (|x|<1)**-,+inf = inf,0 */
-                    return (hy<0)?-y: zero;
-            } 
-            if(iy==0x3ff00000) {        /* y is  +-1 */
-                if(hy<0) return one/x; else return x;
-            }
-            if(hy==0x40000000) return x*x; /* y is  2 */
-            if(hy==0x3fe00000) {        /* y is  0.5 */
-                if(hx>=0)       /* x >= +0 */
-                return sqrt(x); 
-            }
-        }
-
-        ax   = fabs(x);
-    /* special value of x */
-        if(lx==0) {
-            if(ix==0x7ff00000||ix==0||ix==0x3ff00000){
-                z = ax;                 /*x is +-0,+-inf,+-1*/
-                if(hy<0) z = one/z;     /* z = (1/|x|) */
-                if(hx<0) {
-                    if(((ix-0x3ff00000)|yisint)==0) {
-                        z = (z-z)/(z-z); /* (-1)**non-int is NaN */
-                    } else if(yisint==1) 
-                        z = -z;         /* (x<0)**odd = -(|x|**odd) */
-                }
-                return z;
-            }
-        }
-    
-    /* CYGNUS LOCAL + fdlibm-5.3 fix: This used to be
-        n = (hx>>31)+1;
-       but ANSI C says a right shift of a signed negative quantity is
-       implementation defined.  */
-        n = ((uint32_t)hx>>31)-1;
-
-    /* (x<0)**(non-int) is NaN */
-        if((n|yisint)==0) return (x-x)/(x-x);
-
-        s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
-        if((n|(yisint-1))==0) s = -one;/* (-ve)**(odd int) */
-
-    /* |y| is huge */
-        if(iy>0x41e00000) { /* if |y| > 2**31 */
-            if(iy>0x43f00000){  /* if |y| > 2**64, must o/uflow */
-                if(ix<=0x3fefffff) return (hy<0)? huge*huge:tiny*tiny;
-                if(ix>=0x3ff00000) return (hy>0)? huge*huge:tiny*tiny;
-            }
-        /* over/underflow if x is not close to one */
-            if(ix<0x3fefffff) return (hy<0)? s*huge*huge:s*tiny*tiny;
-            if(ix>0x3ff00000) return (hy>0)? s*huge*huge:s*tiny*tiny;
-        /* now |1-x| is tiny <= 2**-20, suffice to compute 
-           log(x) by x-x^2/2+x^3/3-x^4/4 */
-            t = ax-one;         /* t has 20 trailing zeros */
-            w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25));
-            u = ivln2_h*t;      /* ivln2_h has 21 sig. bits */
-            v = t*ivln2_l-w*ivln2;
-            t1 = u+v;
-            SET_LOW_WORD(t1,0);
-            t2 = v-(t1-u);
-        } else {
-            double ss,s2,s_h,s_l,t_h,t_l;
-            n = 0;
-        /* take care subnormal number */
-            if(ix<0x00100000)
-                {ax *= two53; n -= 53; GET_HIGH_WORD(ix,ax); }
-            n  += ((ix)>>20)-0x3ff;
-            j  = ix&0x000fffff;
-        /* determine interval */
-            ix = j|0x3ff00000;          /* normalize ix */
-            if(j<=0x3988E) k=0;         /* |x|<sqrt(3/2) */
-            else if(j<0xBB67A) k=1;     /* |x|<sqrt(3)   */
-            else {k=0;n+=1;ix -= 0x00100000;}
-            SET_HIGH_WORD(ax,ix);
-
-        /* compute ss = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
-            u = ax-bp[k];               /* bp[0]=1.0, bp[1]=1.5 */
-            v = one/(ax+bp[k]);
-            ss = u*v;
-            s_h = ss;
-            SET_LOW_WORD(s_h,0);
-        /* t_h=ax+bp[k] High */
-            t_h = zero;
-            SET_HIGH_WORD(t_h,((ix>>1)|0x20000000)+0x00080000+(k<<18));
-            t_l = ax - (t_h-bp[k]);
-            s_l = v*((u-s_h*t_h)-s_h*t_l);
-        /* compute log(ax) */
-            s2 = ss*ss;
-            r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
-            r += s_l*(s_h+ss);
-            s2  = s_h*s_h;
-            t_h = 3.0+s2+r;
-            SET_LOW_WORD(t_h,0);
-            t_l = r-((t_h-3.0)-s2);
-        /* u+v = ss*(1+...) */
-            u = s_h*t_h;
-            v = s_l*t_h+t_l*ss;
-        /* 2/(3log2)*(ss+...) */
-            p_h = u+v;
-            SET_LOW_WORD(p_h,0);
-            p_l = v-(p_h-u);
-            z_h = cp_h*p_h;             /* cp_h+cp_l = 2/(3*log2) */
-            z_l = cp_l*p_h+p_l*cp+dp_l[k];
-        /* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */
-            t = (double)n;
-            t1 = (((z_h+z_l)+dp_h[k])+t);
-            SET_LOW_WORD(t1,0);
-            t2 = z_l-(((t1-t)-dp_h[k])-z_h);
-        }
-
-    /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
-        y1  = y;
-        SET_LOW_WORD(y1,0);
-        p_l = (y-y1)*t1+y*t2;
-        p_h = y1*t1;
-        z = p_l+p_h;
-        EXTRACT_WORDS(j,i,z);
-        if (j>=0x40900000) {                            /* z >= 1024 */
-            if(((j-0x40900000)|i)!=0)                   /* if z > 1024 */
-                return s*huge*huge;                     /* overflow */
-            else {
-                if(p_l+ovt>z-p_h) return s*huge*huge;   /* overflow */
-            }
-        } else if((j&0x7fffffff)>=0x4090cc00 ) {        /* z <= -1075 */
-            if(((j-0xc090cc00)|i)!=0)           /* z < -1075 */
-                return s*tiny*tiny;             /* underflow */
-            else {
-                if(p_l<=z-p_h) return s*tiny*tiny;      /* underflow */
-            }
-        }
-    /*
-     * compute 2**(p_h+p_l)
-     */
-        i = j&0x7fffffff;
-        k = (i>>20)-0x3ff;
-        n = 0;
-        if(i>0x3fe00000) {              /* if |z| > 0.5, set n = [z+0.5] */
-            n = j+(0x00100000>>(k+1));
-            k = ((n&0x7fffffff)>>20)-0x3ff;     /* new k for n */
-            t = zero;
-            SET_HIGH_WORD(t,n&~(0x000fffff>>k));
-            n = ((n&0x000fffff)|0x00100000)>>(20-k);
-            if(j<0) n = -n;
-            p_h -= t;
-        } 
-        t = p_l+p_h;
-        SET_LOW_WORD(t,0);
-        u = t*lg2_h;
-        v = (p_l-(t-p_h))*lg2+t*lg2_l;
-        z = u+v;
-        w = v-(z-u);
-        t  = z*z;
-        t1  = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
-        r  = (z*t1)/(t1-two)-(w+z*w);
-        z  = one-(r-z);
-        GET_HIGH_WORD(j,z);
-        j += (n<<20);
-        if((j>>20)<=0) z = scalbn(z,n); /* subnormal output */
-        else SET_HIGH_WORD(z,j);
-        return s*z;
-}