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, 176 insertions, 0 deletions

diff --git a/src/math/__rem_pio2.c b/src/math/__rem_pio2.c
new file mode 100644
index 00000000..a7d779e0
--- /dev/null
+++ b/src/math/__rem_pio2.c
@@ -0,0 +1,176 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_rem_pio2.c */
+/*
+ * ====================================================
+ * 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.
+ * ====================================================
+ *
+ * Optimized by Bruce D. Evans.
+ */
+/* __rem_pio2(x,y)
+ *
+ * return the remainder of x rem pi/2 in y[0]+y[1]
+ * use __rem_pio2_large() for large x
+ */
+
+#include "libm.h"
+
+/*
+ * invpio2:  53 bits of 2/pi
+ * pio2_1:   first  33 bit of pi/2
+ * pio2_1t:  pi/2 - pio2_1
+ * pio2_2:   second 33 bit of pi/2
+ * pio2_2t:  pi/2 - (pio2_1+pio2_2)
+ * pio2_3:   third  33 bit 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 */
+invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
+pio2_1  = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
+pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
+pio2_2  = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
+pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
+pio2_3  = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
+pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
+
+/* caller must handle the case when reduction is not needed: |x| ~<= pi/4 */
+int __rem_pio2(double x, double *y)
+{
+	double z,w,t,r,fn;
+	double tx[3],ty[2];
+	int32_t e0,i,j,nx,n,ix,hx;
+	uint32_t low;
+
+	GET_HIGH_WORD(hx,x);
+	ix = hx & 0x7fffffff;
+	if (ix <= 0x400f6a7a) {  /* |x| ~<= 5pi/4 */
+		if ((ix & 0xfffff) == 0x921fb)  /* |x| ~= pi/2 or 2pi/2 */
+			goto medium;  /* cancellation -- use medium case */
+		if (ix <= 0x4002d97c) {  /* |x| ~<= 3pi/4 */
+			if (hx > 0) {
+				z = x - pio2_1;  /* one round good to 85 bits */
+				y[0] = z - pio2_1t;
+				y[1] = (z-y[0]) - pio2_1t;
+				return 1;
+			} else {
+				z = x + pio2_1;
+				y[0] = z + pio2_1t;
+				y[1] = (z-y[0]) + pio2_1t;
+				return -1;
+			}
+		} else {
+			if (hx > 0) {
+				z = x - 2*pio2_1;
+				y[0] = z - 2*pio2_1t;
+				y[1] = (z-y[0]) - 2*pio2_1t;
+				return 2;
+			} else {
+				z = x + 2*pio2_1;
+				y[0] = z + 2*pio2_1t;
+				y[1] = (z-y[0]) + 2*pio2_1t;
+				return -2;
+			}
+		}
+	}
+	if (ix <= 0x401c463b) {  /* |x| ~<= 9pi/4 */
+		if (ix <= 0x4015fdbc) {  /* |x| ~<= 7pi/4 */
+			if (ix == 0x4012d97c)  /* |x| ~= 3pi/2 */
+				goto medium;
+			if (hx > 0) {
+				z = x - 3*pio2_1;
+				y[0] = z - 3*pio2_1t;
+				y[1] = (z-y[0]) - 3*pio2_1t;
+				return 3;
+			} else {
+				z = x + 3*pio2_1;
+				y[0] = z + 3*pio2_1t;
+				y[1] = (z-y[0]) + 3*pio2_1t;
+				return -3;
+			}
+		} else {
+			if (ix == 0x401921fb)  /* |x| ~= 4pi/2 */
+				goto medium;
+			if (hx > 0) {
+				z = x - 4*pio2_1;
+				y[0] = z - 4*pio2_1t;
+				y[1] = (z-y[0]) - 4*pio2_1t;
+				return 4;
+			} else {
+				z = x + 4*pio2_1;
+				y[0] = z + 4*pio2_1t;
+				y[1] = (z-y[0]) + 4*pio2_1t;
+				return -4;
+			}
+		}
+	}
+	if (ix < 0x413921fb) {  /* |x| ~< 2^20*(pi/2), medium size */
+		uint32_t high;
+medium:
+		/* Use a specialized rint() to get fn.  Assume round-to-nearest. */
+		STRICT_ASSIGN(double, fn, x*invpio2 + 0x1.8p52);
+		fn = fn - 0x1.8p52;
+// FIXME
+#ifdef HAVE_EFFICIENT_IRINT
+		n = irint(fn);
+#else
+		n = (int32_t)fn;
+#endif
+		r = x - fn*pio2_1;
+		w = fn*pio2_1t;  /* 1st round, good to 85 bits */
+		j = ix>>20;
+		y[0] = r - w;
+		GET_HIGH_WORD(high,y[0]);
+		i = j - ((high>>20)&0x7ff);
+		if (i > 16) {  /* 2nd round, good to 118 bits */
+			t = r;
+			w = fn*pio2_2;
+			r = t - w;
+			w = fn*pio2_2t - ((t-r)-w);
+			y[0] = r - w;
+			GET_HIGH_WORD(high,y[0]);
+			i = j - ((high>>20)&0x7ff);
+			if (i > 49) {  /* 3rd round, good to 151 bits, covers all cases */
+				t = r;
+				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 (ix >= 0x7ff00000) {  /* x is inf or NaN */
+		y[0] = y[1] = x - x;
+		return 0;
+	}
+	/* set z = scalbn(|x|,ilogb(x)-23) */
+	GET_LOW_WORD(low,x);
+	e0 = (ix>>20) - 1046;  /* e0 = ilogb(z)-23; */
+	INSERT_WORDS(z, ix - ((int32_t)(e0<<20)), low);
+	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,1);
+	if (hx < 0) {
+		y[0] = -ty[0];
+		y[1] = -ty[1];
+		return -n;
+	}
+	y[0] = ty[0];
+	y[1] = ty[1];
+	return n;
+}