math: long double trigonometric cleanup (cosl, sinl, sincosl, tanl)

ld128 support was added to internal kernel functions (__cosl, __sinl,
__tanl, __rem_pio2l) from freebsd (not tested, but should be a good
start for when ld128 arch arrives)

__rem_pio2l had some code cleanup, the freebsd ld128 code seems to
gather the results of a large reduction with precision loss (fixed
the bug but a todo comment was added for later investigation)

the old copyright was removed from the non-kernel wrapper functions
(cosl, sinl, sincosl, tanl) since these are trivial and the interesting
parts and comments had been already rewritten.

1 files changed, 14 insertions, 56 deletions

diff --git a/src/math/cosl.c b/src/math/cosl.c
index 0794d284..79c41c77 100644
--- a/src/math/cosl.c
+++ b/src/math/cosl.c
@@ -1,34 +1,3 @@
-/* origin: FreeBSD /usr/src/lib/msun/src/s_cosl.c */
-/*-
- * Copyright (c) 2007 Steven G. Kargl
- * 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 unmodified, 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 ``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 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.
- */
-/*
- * Limited testing on pseudorandom numbers drawn within [-2e8:4e8] shows
- * an accuracy of <= 0.7412 ULP.
- */
-
 #include "libm.h"
 
 #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
@@ -38,44 +7,33 @@ long double cosl(long double x) {
 #elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
 long double cosl(long double x)
 {
-	union IEEEl2bits z;
+	union ldshape u = {x};
 	unsigned n;
-	long double y[2];
-	long double hi, lo;
-
-	z.e = x;
-	z.bits.sign = 0;
+	long double y[2], hi, lo;
 
-	/* If x = NaN or Inf, then cos(x) = NaN. */
-	if (z.bits.exp == 0x7fff)
-		return (x - x) / (x - x);
-
-	/* |x| < (double)pi/4 */
-	if (z.e < M_PI_4) {
-		/* |x| < 0x1p-64 */
-		if (z.bits.exp < 0x3fff - 64)
+	u.i.se &= 0x7fff;
+	if (u.i.se == 0x7fff)
+		return x - x;
+	x = u.f;
+	if (x < M_PI_4) {
+		if (u.i.se < 0x3fff - LDBL_MANT_DIG)
 			/* raise inexact if x!=0 */
 			return 1.0 + x;
-		return __cosl(z.e, 0);
+		return __cosl(x, 0);
 	}
-
 	n = __rem_pio2l(x, y);
 	hi = y[0];
 	lo = y[1];
 	switch (n & 3) {
 	case 0:
-		hi = __cosl(hi, lo);
-		break;
+		return __cosl(hi, lo);
 	case 1:
-		hi = -__sinl(hi, lo, 1);
-		break;
+		return -__sinl(hi, lo, 1);
 	case 2:
-		hi = -__cosl(hi, lo);
-		break;
+		return -__cosl(hi, lo);
 	case 3:
-		hi = __sinl(hi, lo, 1);
-		break;
+	default:
+		return __sinl(hi, lo, 1);
 	}
-	return hi;
 }
 #endif