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, 109 insertions, 0 deletions

diff --git a/src/math/__invtrigl.h b/src/math/__invtrigl.h
new file mode 100644
index 00000000..c3ad3c49
--- /dev/null
+++ b/src/math/__invtrigl.h
@@ -0,0 +1,109 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/ld80/invtrig.h */
+/*-
+ * Copyright (c) 2008 David Schultz <das@FreeBSD.ORG>
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+#include "libm.h"
+
+#if LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
+
+#define BIAS            (LDBL_MAX_EXP - 1)
+#define MANH_SIZE       LDBL_MANH_SIZE
+
+/* Approximation thresholds. */
+#define ASIN_LINEAR     (BIAS - 32)     /* 2**-32 */
+#define ACOS_CONST      (BIAS - 65)     /* 2**-65 */
+#define ATAN_CONST      (BIAS + 65)     /* 2**65 */
+#define ATAN_LINEAR     (BIAS - 32)     /* 2**-32 */
+
+/* 0.95 */
+#define THRESH  ((0xe666666666666666ULL>>(64-(MANH_SIZE-1)))|LDBL_NBIT)
+
+/* Constants shared by the long double inverse trig functions. */
+#define pS0     __pS0
+#define pS1     __pS1
+#define pS2     __pS2
+#define pS3     __pS3
+#define pS4     __pS4
+#define pS5     __pS5
+#define pS6     __pS6
+#define qS1     __qS1
+#define qS2     __qS2
+#define qS3     __qS3
+#define qS4     __qS4
+#define qS5     __qS5
+#define atanhi  __atanhi
+#define atanlo  __atanlo
+#define aT      __aT
+#define pi_lo   __pi_lo
+
+#define pio2_hi atanhi[3]
+#define pio2_lo atanlo[3]
+#define pio4_hi atanhi[1]
+
+#ifdef STRUCT_DECLS
+typedef struct longdouble {
+	uint64_t mant;
+	uint16_t expsign;
+} LONGDOUBLE;
+#else
+typedef long double LONGDOUBLE;
+#endif
+
+extern const LONGDOUBLE pS0, pS1, pS2, pS3, pS4, pS5, pS6;
+extern const LONGDOUBLE qS1, qS2, qS3, qS4, qS5;
+extern const LONGDOUBLE atanhi[], atanlo[], aT[];
+extern const LONGDOUBLE pi_lo;
+
+#ifndef STRUCT_DECLS
+static inline long double
+P(long double x)
+{
+	return (x * (pS0 + x * (pS1 + x * (pS2 + x * (pS3 + x * \
+		(pS4 + x * (pS5 + x * pS6)))))));
+}
+
+static inline long double
+Q(long double x)
+{
+	return (1.0 + x * (qS1 + x * (qS2 + x * (qS3 + x * (qS4 + x * qS5)))));
+}
+
+static inline long double
+T_even(long double x)
+{
+	return (aT[0] + x * (aT[2] + x * (aT[4] + x * (aT[6] + x * \
+		(aT[8] + x * (aT[10] + x * aT[12]))))));
+}
+
+static inline long double
+T_odd(long double x)
+{
+	return (aT[1] + x * (aT[3] + x * (aT[5] + x * (aT[7] + x * \
+		(aT[9] + x * aT[11])))));
+}
+#endif
+
+#endif