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, 326 insertions, 0 deletions

diff --git a/src/math/pow.c b/src/math/pow.c
new file mode 100644
index 00000000..f843645d
--- /dev/null
+++ b/src/math/pow.c
@@ -0,0 +1,326 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_pow.c */
+/*
+ * ====================================================
+ * 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 except 1) ** NAN is NAN,  1 ** NAN is 1
+ *      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 1
+ *      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 "libm.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-017, /* -(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;
+
+	/* x == 1: 1**y = 1, even if y is NaN */
+	if (hx == 0x3ff00000 && lx == 0)
+		return one;
+
+	/* y != zero: result is NaN if either arg is NaN */
+	if (ix > 0x7ff00000 || (ix == 0x7ff00000 && lx != 0) ||
+	    iy > 0x7ff00000 || (iy == 0x7ff00000 && ly != 0))
+		return (x+0.0)+(y+0.0); // FIXME: 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)  /* (-1)**+-inf is 1 */
+				return one;
+			else if (ix >= 0x3ff00000) /* (|x|>1)**+-inf = inf,0 */
+				return hy >= 0 ? y : zero;
+			else                       /* (|x|<1)**+-inf = 0,inf */
+				return hy < 0 ? -y : zero;
+		}
+		if (iy == 0x3ff00000) {  /* y is +-1 */
+			if (hy < 0)
+				return one/x;
+			return x;
+		}
+		if (hy == 0x40000000)    /* y is 2 */
+			return x*x;
+		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) { /* x is +-0,+-inf,+-1 */
+			z = ax;
+			if (hy < 0)   /* z = (1/|x|) */
+				z = one/z;
+			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)      /* |x|<sqrt(3/2) */
+			k = 0;
+		else if (j < 0xBB67A)  /* |x|<sqrt(3)   */
+			k = 1;
+		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 */
+		if (p_l + ovt > z - p_h)
+			return s*huge*huge;         /* overflow */
+	} else if ((j&0x7fffffff) >= 0x4090cc00) {  /* z <= -1075 */  // FIXME: instead of abs(j) use unsigned j
+		if (((j-0xc090cc00)|i) != 0)        /* z < -1075 */
+			return s*tiny*tiny;         /* underflow */
+		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)  /* subnormal output */
+		z = scalbn(z,n);
+	else
+		SET_HIGH_WORD(z, j);
+	return s*z;
+}