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, 269 insertions, 0 deletions

diff --git a/src/math/powf.c b/src/math/powf.c
new file mode 100644
index 00000000..e322ff28
--- /dev/null
+++ b/src/math/powf.c
@@ -0,0 +1,269 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_powf.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.
+ * ====================================================
+ */
+
+#include "libm.h"
+
+static const float
+bp[]   = {1.0, 1.5,},
+dp_h[] = { 0.0, 5.84960938e-01,}, /* 0x3f15c000 */
+dp_l[] = { 0.0, 1.56322085e-06,}, /* 0x35d1cfdc */
+zero   =  0.0,
+one    =  1.0,
+two    =  2.0,
+two24  =  16777216.0,  /* 0x4b800000 */
+huge   =  1.0e30,
+tiny   =  1.0e-30,
+/* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
+L1 =  6.0000002384e-01, /* 0x3f19999a */
+L2 =  4.2857143283e-01, /* 0x3edb6db7 */
+L3 =  3.3333334327e-01, /* 0x3eaaaaab */
+L4 =  2.7272811532e-01, /* 0x3e8ba305 */
+L5 =  2.3066075146e-01, /* 0x3e6c3255 */
+L6 =  2.0697501302e-01, /* 0x3e53f142 */
+P1 =  1.6666667163e-01, /* 0x3e2aaaab */
+P2 = -2.7777778450e-03, /* 0xbb360b61 */
+P3 =  6.6137559770e-05, /* 0x388ab355 */
+P4 = -1.6533901999e-06, /* 0xb5ddea0e */
+P5 =  4.1381369442e-08, /* 0x3331bb4c */
+lg2     =  6.9314718246e-01, /* 0x3f317218 */
+lg2_h   =  6.93145752e-01,   /* 0x3f317200 */
+lg2_l   =  1.42860654e-06,   /* 0x35bfbe8c */
+ovt     =  4.2995665694e-08, /* -(128-log2(ovfl+.5ulp)) */
+cp      =  9.6179670095e-01, /* 0x3f76384f =2/(3ln2) */
+cp_h    =  9.6191406250e-01, /* 0x3f764000 =12b cp */
+cp_l    = -1.1736857402e-04, /* 0xb8f623c6 =tail of cp_h */
+ivln2   =  1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */
+ivln2_h =  1.4426879883e+00, /* 0x3fb8aa00 =16b 1/ln2*/
+ivln2_l =  7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/
+
+float powf(float x, float y)
+{
+	float z,ax,z_h,z_l,p_h,p_l;
+	float y1,t1,t2,r,s,sn,t,u,v,w;
+	int32_t i,j,k,yisint,n;
+	int32_t hx,hy,ix,iy,is;
+
+	GET_FLOAT_WORD(hx, x);
+	GET_FLOAT_WORD(hy, y);
+	ix = hx & 0x7fffffff;
+	iy = hy & 0x7fffffff;
+
+	/* y == zero: x**0 = 1 */
+	if (iy == 0)
+		return one;
+
+	/* x == 1: 1**y = 1, even if y is NaN */
+	if (hx == 0x3f800000)
+		return one;
+
+	/* y != zero: result is NaN if either arg is NaN */
+	if (ix > 0x7f800000 || iy > 0x7f800000)
+		return (x+0.0F) + (y+0.0F);
+
+	/* 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 >= 0x4b800000)
+			yisint = 2; /* even integer y */
+		else if (iy >= 0x3f800000) {
+			k = (iy>>23) - 0x7f;         /* exponent */
+			j = iy>>(23-k);
+			if ((j<<(23-k)) == iy)
+				yisint = 2 - (j & 1);
+		}
+	}
+
+	/* special value of y */
+	if (iy == 0x7f800000) {  /* y is +-inf */
+		if (ix == 0x3f800000)      /* (-1)**+-inf is 1 */
+			return one;
+		else if (ix > 0x3f800000)  /* (|x|>1)**+-inf = inf,0 */
+			return hy >= 0 ? y : zero;
+		else                       /* (|x|<1)**+-inf = 0,inf */
+			return hy < 0 ? -y : zero;
+	}
+	if (iy == 0x3f800000) {  /* y is +-1 */
+		if (hy < 0)
+			return one/x;
+		return x;
+	}
+	if (hy == 0x40000000)    /* y is 2 */
+		return x*x;
+	if (hy == 0x3f000000) {  /* y is  0.5 */
+		if (hx >= 0)     /* x >= +0 */
+			return sqrtf(x);
+	}
+
+	ax = fabsf(x);
+	/* special value of x */
+	if (ix == 0x7f800000 || ix == 0 || ix == 0x3f800000) { /* x is +-0,+-inf,+-1 */
+		z = ax;
+		if (hy < 0)  /* z = (1/|x|) */
+			z = one/z;
+		if (hx < 0) {
+			if (((ix-0x3f800000)|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;
+	}
+
+	n = ((uint32_t)hx>>31) - 1;
+
+	/* (x<0)**(non-int) is NaN */
+	if ((n|yisint) == 0)
+		return (x-x)/(x-x);
+
+	sn = one; /* s (sign of result -ve**odd) = -1 else = 1 */
+	if ((n|(yisint-1)) == 0)  /* (-ve)**(odd int) */
+		sn = -one;
+
+	/* |y| is huge */
+	if (iy > 0x4d000000) { /* if |y| > 2**27 */
+		/* over/underflow if x is not close to one */
+		if (ix < 0x3f7ffff8)
+			return hy < 0 ? sn*huge*huge : sn*tiny*tiny;
+		if (ix > 0x3f800007)
+			return hy > 0 ? sn*huge*huge : sn*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 - 1;     /* t has 20 trailing zeros */
+		w = (t*t)*((float)0.5-t*((float)0.333333333333-t*(float)0.25));
+		u = ivln2_h*t;  /* ivln2_h has 16 sig. bits */
+		v = t*ivln2_l - w*ivln2;
+		t1 = u + v;
+		GET_FLOAT_WORD(is, t1);
+		SET_FLOAT_WORD(t1, is & 0xfffff000);
+		t2 = v - (t1-u);
+	} else {
+		float s2,s_h,s_l,t_h,t_l;
+		n = 0;
+		/* take care subnormal number */
+		if (ix < 0x00800000) {
+			ax *= two24;
+			n -= 24;
+			GET_FLOAT_WORD(ix, ax);
+		}
+		n += ((ix)>>23) - 0x7f;
+		j = ix & 0x007fffff;
+		/* determine interval */
+		ix = j | 0x3f800000;     /* normalize ix */
+		if (j <= 0x1cc471)       /* |x|<sqrt(3/2) */
+			k = 0;
+		else if (j < 0x5db3d7)   /* |x|<sqrt(3)   */
+			k = 1;
+		else {
+			k = 0;
+			n += 1;
+			ix -= 0x00800000;
+		}
+		SET_FLOAT_WORD(ax, ix);
+
+		/* compute s = 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]);
+		s = u*v;
+		s_h = s;
+		GET_FLOAT_WORD(is, s_h);
+		SET_FLOAT_WORD(s_h, is & 0xfffff000);
+		/* t_h=ax+bp[k] High */
+		is = ((ix>>1) & 0xfffff000) | 0x20000000;
+		SET_FLOAT_WORD(t_h, is + 0x00400000 + (k<<21));
+		t_l = ax - (t_h - bp[k]);
+		s_l = v*((u - s_h*t_h) - s_h*t_l);
+		/* compute log(ax) */
+		s2 = s*s;
+		r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
+		r += s_l*(s_h+s);
+		s2 = s_h*s_h;
+		t_h = (float)3.0 + s2 + r;
+		GET_FLOAT_WORD(is, t_h);
+		SET_FLOAT_WORD(t_h, is & 0xfffff000);
+		t_l = r - ((t_h - (float)3.0) - s2);
+		/* u+v = s*(1+...) */
+		u = s_h*t_h;
+		v = s_l*t_h + t_l*s;
+		/* 2/(3log2)*(s+...) */
+		p_h = u + v;
+		GET_FLOAT_WORD(is, p_h);
+		SET_FLOAT_WORD(p_h, is & 0xfffff000);
+		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) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
+		t = (float)n;
+		t1 = (((z_h + z_l) + dp_h[k]) + t);
+		GET_FLOAT_WORD(is, t1);
+		SET_FLOAT_WORD(t1, is & 0xfffff000);
+		t2 = z_l - (((t1 - t) - dp_h[k]) - z_h);
+	}
+
+	/* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
+	GET_FLOAT_WORD(is, y);
+	SET_FLOAT_WORD(y1, is & 0xfffff000);
+	p_l = (y-y1)*t1 + y*t2;
+	p_h = y1*t1;
+	z = p_l + p_h;
+	GET_FLOAT_WORD(j, z);
+	if (j > 0x43000000)          /* if z > 128 */
+		return sn*huge*huge;  /* overflow */
+	else if (j == 0x43000000) {  /* if z == 128 */
+		if (p_l + ovt > z - p_h)
+			return sn*huge*huge;  /* overflow */
+	} else if ((j&0x7fffffff) > 0x43160000)  /* z < -150 */ // FIXME: check should be  (uint32_t)j > 0xc3160000
+		return sn*tiny*tiny;  /* underflow */
+	else if (j == 0xc3160000) {  /* z == -150 */
+		if (p_l <= z-p_h)
+			return sn*tiny*tiny;  /* underflow */
+	}
+	/*
+	 * compute 2**(p_h+p_l)
+	 */
+	i = j & 0x7fffffff;
+	k = (i>>23) - 0x7f;
+	n = 0;
+	if (i > 0x3f000000) {   /* if |z| > 0.5, set n = [z+0.5] */
+		n = j + (0x00800000>>(k+1));
+		k = ((n&0x7fffffff)>>23) - 0x7f;  /* new k for n */
+		SET_FLOAT_WORD(t, n & ~(0x007fffff>>k));
+		n = ((n&0x007fffff)|0x00800000)>>(23-k);
+		if (j < 0)
+			n = -n;
+		p_h -= t;
+	}
+	t = p_l + p_h;
+	GET_FLOAT_WORD(is, t);
+	SET_FLOAT_WORD(t, is & 0xffff8000);
+	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_FLOAT_WORD(j, z);
+	j += n<<23;
+	if ((j>>23) <= 0)  /* subnormal output */
+		z = scalbnf(z, n);
+	else
+		SET_FLOAT_WORD(z, j);
+	return sn*z;
+}