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, 123 insertions, 0 deletions

diff --git a/src/math/atan.c b/src/math/atan.c
new file mode 100644
index 00000000..d31782c2
--- /dev/null
+++ b/src/math/atan.c
@@ -0,0 +1,123 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/s_atan.c */
+/*
+ * ====================================================
+ * 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.
+ * ====================================================
+ */
+/* atan(x)
+ * Method
+ *   1. Reduce x to positive by atan(x) = -atan(-x).
+ *   2. According to the integer k=4t+0.25 chopped, t=x, the argument
+ *      is further reduced to one of the following intervals and the
+ *      arctangent of t is evaluated by the corresponding formula:
+ *
+ *      [0,7/16]      atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
+ *      [7/16,11/16]  atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
+ *      [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
+ *      [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
+ *      [39/16,INF]   atan(x) = atan(INF) + atan( -1/t )
+ *
+ * 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 atanhi[] = {
+  4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
+  7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
+  9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
+  1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
+};
+
+static const double atanlo[] = {
+  2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
+  3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
+  1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
+  6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
+};
+
+static const double aT[] = {
+  3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
+ -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
+  1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
+ -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
+  9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
+ -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
+  6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
+ -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
+  4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
+ -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
+  1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
+};
+
+static const double
+one = 1.0,
+huge = 1.0e300;
+
+double atan(double x)
+{
+	double w,s1,s2,z;
+	int32_t ix,hx,id;
+
+	GET_HIGH_WORD(hx, x);
+	ix = hx & 0x7fffffff;
+	if (ix >= 0x44100000) {   /* if |x| >= 2^66 */
+		uint32_t low;
+
+		GET_LOW_WORD(low, x);
+		if (ix > 0x7ff00000 ||
+		    (ix == 0x7ff00000 && low != 0))  /* NaN */
+			return x+x;
+		if (hx > 0)
+			return  atanhi[3] + *(volatile double *)&atanlo[3];
+		else
+			return -atanhi[3] - *(volatile double *)&atanlo[3];
+	}
+	if (ix < 0x3fdc0000) {    /* |x| < 0.4375 */
+		if (ix < 0x3e400000) {  /* |x| < 2^-27 */
+			/* raise inexact */
+			if (huge+x > one)
+				return x;
+		}
+		id = -1;
+	} else {
+		x = fabs(x);
+		if (ix < 0x3ff30000) {  /* |x| < 1.1875 */
+			if (ix < 0x3fe60000) {  /*  7/16 <= |x| < 11/16 */
+				id = 0;
+				x = (2.0*x-one)/(2.0+x);
+			} else {                /* 11/16 <= |x| < 19/16 */
+				id = 1;
+				x = (x-one)/(x+one);
+			}
+		} else {
+			if (ix < 0x40038000) {  /* |x| < 2.4375 */
+				id = 2;
+				x = (x-1.5)/(one+1.5*x);
+			} else {                /* 2.4375 <= |x| < 2^66 */
+				id = 3;
+				x = -1.0/x;
+			}
+		}
+	}
+	/* end of argument reduction */
+	z = x*x;
+	w = z*z;
+	/* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
+	s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
+	s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
+	if (id < 0)
+		return x - x*(s1+s2);
+	z = atanhi[id] - (x*(s1+s2) - atanlo[id] - x);
+	return hx < 0 ? -z : z;
+}