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, 150 insertions, 0 deletions

diff --git a/src/math/__rem_pio2l.h b/src/math/__rem_pio2l.h
new file mode 100644
index 00000000..37f3bd28
--- /dev/null
+++ b/src/math/__rem_pio2l.h
@@ -0,0 +1,150 @@
+/* origin: FreeBSD /usr/src/lib/msun/ld80/e_rem_pio2.c */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans.
+ *
+ * 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.
+ * ====================================================
+ *
+ * Optimized by Bruce D. Evans.
+ */
+#include "libm.h"
+#if LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
+/* ld80 version of __rem_pio2(x,y)
+ *
+ * return the remainder of x rem pi/2 in y[0]+y[1]
+ * use __rem_pio2_large() for large x
+ */
+
+#define BIAS    (LDBL_MAX_EXP - 1)
+
+/*
+ * invpio2:  64 bits of 2/pi
+ * pio2_1:   first  39 bits of pi/2
+ * pio2_1t:  pi/2 - pio2_1
+ * pio2_2:   second 39 bits of pi/2
+ * pio2_2t:  pi/2 - (pio2_1+pio2_2)
+ * pio2_3:   third  39 bits of pi/2
+ * pio2_3t:  pi/2 - (pio2_1+pio2_2+pio2_3)
+ */
+static const double
+zero   =  0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
+two24  =  1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
+pio2_1 =  1.57079632679597125389e+00, /* 0x3FF921FB, 0x54444000 */
+pio2_2 = -1.07463465549783099519e-12, /* -0x12e7b967674000.0p-92 */
+pio2_3 =  6.36831716351370313614e-25; /*  0x18a2e037074000.0p-133 */
+
+// FIXME: this should be verified (maybe old gcc specific hack)
+//#if defined(__amd64__) || defined(__i386__)
+/* Long double constants are slow on these arches, and broken on i386. */
+static const volatile double
+invpio2hi =  6.3661977236758138e-01,    /*  0x145f306dc9c883.0p-53 */
+invpio2lo = -3.9356538861223811e-17,    /* -0x16b00000000000.0p-107 */
+pio2_1thi = -1.0746346554971943e-12,    /* -0x12e7b9676733af.0p-92 */
+pio2_1tlo =  8.8451028997905949e-29,    /*  0x1c080000000000.0p-146 */
+pio2_2thi =  6.3683171635109499e-25,    /*  0x18a2e03707344a.0p-133 */
+pio2_2tlo =  2.3183081793789774e-41,    /*  0x10280000000000.0p-187 */
+pio2_3thi = -2.7529965190440717e-37,    /* -0x176b7ed8fbbacc.0p-174 */
+pio2_3tlo = -4.2006647512740502e-54;    /* -0x19c00000000000.0p-230 */
+#define invpio2 ((long double)invpio2hi + invpio2lo)
+#define pio2_1t ((long double)pio2_1thi + pio2_1tlo)
+#define pio2_2t ((long double)pio2_2thi + pio2_2tlo)
+#define pio2_3t ((long double)pio2_3thi + pio2_3tlo)
+//#else
+#if 0
+static const long double
+invpio2 =  6.36619772367581343076e-01L, /*  0xa2f9836e4e44152a.0p-64 */
+pio2_1t = -1.07463465549719416346e-12L, /* -0x973dcb3b399d747f.0p-103 */
+pio2_2t =  6.36831716351095013979e-25L, /*  0xc51701b839a25205.0p-144 */
+pio2_3t = -2.75299651904407171810e-37L; /* -0xbb5bf6c7ddd660ce.0p-185 */
+#endif
+
+static inline int __rem_pio2l(long double x, long double *y)
+{
+	union IEEEl2bits u,u1;
+	long double z,w,t,r,fn;
+	double tx[3],ty[2];
+	int e0,ex,i,j,nx,n;
+	int16_t expsign;
+
+	u.e = x;
+	expsign = u.xbits.expsign;
+	ex = expsign & 0x7fff;
+	if (ex < BIAS + 25 || (ex == BIAS + 25 && u.bits.manh < 0xc90fdaa2)) {
+		union IEEEl2bits u2;
+		int ex1;
+
+		/* |x| ~< 2^25*(pi/2), medium size */
+		/* Use a specialized rint() to get fn.  Assume round-to-nearest. */
+		fn = x*invpio2 + 0x1.8p63;
+		fn = fn - 0x1.8p63;
+// FIXME
+//#ifdef HAVE_EFFICIENT_IRINT
+//		n = irint(fn);
+//#else
+		n = fn;
+//#endif
+		r = x-fn*pio2_1;
+		w = fn*pio2_1t;    /* 1st round good to 102 bit */
+		j = ex;
+		y[0] = r-w;
+		u2.e = y[0];
+		ex1 = u2.xbits.expsign & 0x7fff;
+		i = j-ex1;
+		if (i > 22) {  /* 2nd iteration needed, good to 141 */
+			t = r;
+			w = fn*pio2_2;
+			r = t-w;
+			w = fn*pio2_2t-((t-r)-w);
+			y[0] = r-w;
+			u2.e = y[0];
+			ex1 = u2.xbits.expsign & 0x7fff;
+			i = j-ex1;
+			if (i > 61) {  /* 3rd iteration need, 180 bits acc */
+				t = r; /* will cover all possible cases */
+				w = fn*pio2_3;
+				r = t-w;
+				w = fn*pio2_3t-((t-r)-w);
+				y[0] = r-w;
+			}
+		}
+		y[1] = (r - y[0]) - w;
+		return n;
+	}
+	/*
+	 * all other (large) arguments
+	 */
+	if (ex == 0x7fff) {                /* x is inf or NaN */
+		y[0] = y[1] = x - x;
+		return 0;
+	}
+	/* set z = scalbn(|x|,ilogb(x)-23) */
+	u1.e = x;
+	e0 = ex - BIAS - 23;            /* e0 = ilogb(|x|)-23; */
+	u1.xbits.expsign = ex - e0;
+	z = u1.e;
+	for (i=0; i<2; i++) {
+		tx[i] = (double)(int32_t)z;
+		z     = (z-tx[i])*two24;
+	}
+	tx[2] = z;
+	nx = 3;
+	while (tx[nx-1] == zero)
+		nx--;     /* skip zero term */
+	n = __rem_pio2_large(tx,ty,e0,nx,2);
+	r = (long double)ty[0] + ty[1];
+	w = ty[1] - (r - ty[0]);
+	if (expsign < 0) {
+		y[0] = -r;
+		y[1] = -w;
+		return -n;
+	}
+	y[0] = r;
+	y[1] = w;
+	return n;
+}
+#endif