On i386, gcc truncates long double constants to double precision

at compile time regardless of the dynamic precision, and there's
no way to disable this misfeature at compile time. Hence, it's
impossible to generate the appropriate tables of constants for the
long double inverse trig functions in a straightforward way on i386;
this change hacks around the problem by encoding the underlying bits
in the table.

Note that these functions won't pass the regression test on i386,
even with the FPU set to extended precision, because the regression
test is similarly damaged by gcc. However, the tests all pass when
compiled with a modified version of gcc.

Reported by:  	bde

1 files changed, 86 insertions, 0 deletions

diff --git a/lib/msun/i387/invtrig.c b/lib/msun/i387/invtrig.c
new file mode 100644
index 0000000..fac2d05
--- /dev/null
+++ b/lib/msun/i387/invtrig.c
@@ -0,0 +1,86 @@
+/*-
+ * 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 <sys/cdefs.h>
+__FBSDID("$FreeBSD$");
+
+#include <stdint.h>
+
+#define STRUCT_DECLS
+#include "invtrig.h"
+
+/*
+ * asinl() and acosl()
+ */
+const LONGDOUBLE
+pS0 = { 0xaaaaaaaaaaaaaaa8ULL, 0x3ffcU }, /*  1.66666666666666666631e-01L */
+pS1 = { 0xd5271b6699b48bfaULL, 0xbffdU }, /* -4.16313987993683104320e-01L */
+pS2 = { 0xbcf67ca9e9f669cfULL, 0x3ffdU }, /*  3.69068046323246813704e-01L */
+pS3 = { 0x8b7baa3d15f9830dULL, 0xbffcU }, /* -1.36213932016738603108e-01L */
+pS4 = { 0x92154b093a3bff1cULL, 0x3ff9U }, /*  1.78324189708471965733e-02L */
+pS5 = { 0xe5dd76401964508cULL, 0xbff2U }, /* -2.19216428382605211588e-04L */
+pS6 = { 0xee69c5b0fdb76951ULL, 0xbfedU }, /* -7.10526623669075243183e-06L */
+qS1 = { 0xbcaa2159c01436a0ULL, 0xc000U }, /* -2.94788392796209867269e+00L */
+qS2 = { 0xd17a73d1e1564c29ULL, 0x4000U }, /*  3.27309890266528636716e+00L */
+qS3 = { 0xd767e411c9cf4c2cULL, 0xbfffU }, /* -1.68285799854822427013e+00L */
+qS4 = { 0xc809c0dfb9b0d0b7ULL, 0x3ffdU }, /*  3.90699412641738801874e-01L */
+qS5 = { 0x80c3a2197c8ced57ULL, 0xbffaU }; /* -3.14365703596053263322e-02L */
+
+/*
+ * atanl()
+ */
+const LONGDOUBLE atanhi[] = {
+	{ 0xed63382b0dda7b45ULL, 0x3ffdU }, /*  4.63647609000806116202e-01L */
+	{ 0xc90fdaa22168c235ULL, 0x3ffeU }, /*  7.85398163397448309628e-01L */
+	{ 0xfb985e940fb4d900ULL, 0x3ffeU }, /*  9.82793723247329067960e-01L */
+	{ 0xc90fdaa22168c235ULL, 0x3fffU }, /*  1.57079632679489661926e+00L */
+};
+
+const LONGDOUBLE atanlo[] = {
+	{ 0xdfc88bd978751a07ULL, 0x3fbcU }, /*  1.18469937025062860669e-20L */
+	{ 0xece675d1fc8f8cbbULL, 0xbfbcU }, /* -1.25413940316708300586e-20L */
+	{ 0xf10f5e197793c283ULL, 0x3fbdU }, /*  2.55232234165405176172e-20L */
+	{ 0xece675d1fc8f8cbbULL, 0xbfbdU }, /* -2.50827880633416601173e-20L */
+};
+
+const LONGDOUBLE aT[] = {
+	{ 0xaaaaaaaaaaaaaa9fULL, 0x3ffdU }, /*  3.33333333333333333017e-01L */
+	{ 0xcccccccccccc62bcULL, 0xbffcU }, /* -1.99999999999999632011e-01L */
+	{ 0x9249249248b81e3fULL, 0x3ffcU }, /*  1.42857142857046531280e-01L */
+	{ 0xe38e38e3316f3de5ULL, 0xbffbU }, /* -1.11111111100562372733e-01L */
+	{ 0xba2e8b8dc280726aULL, 0x3ffbU }, /*  9.09090902935647302252e-02L */
+	{ 0x9d89d5b4c6847ec4ULL, 0xbffbU }, /* -7.69230552476207730353e-02L */
+	{ 0x8888461d3099c677ULL, 0x3ffbU }, /*  6.66661718042406260546e-02L */
+	{ 0xf0e8ee0f5328dc29ULL, 0xbffaU }, /* -5.88158892835030888692e-02L */
+	{ 0xd73ea84d24bae54aULL, 0x3ffaU }, /*  5.25499891539726639379e-02L */
+	{ 0xc08fa381dcd9213aULL, 0xbffaU }, /* -4.70119845393155721494e-02L */
+	{ 0xa54a26f4095f2a3aULL, 0x3ffaU }, /*  4.03539201366454414072e-02L */
+	{ 0xeea2d8d059ef3ad6ULL, 0xbff9U }, /* -2.91303858419364158725e-02L */
+	{ 0xcc82292ab894b051ULL, 0x3ff8U }, /*  1.24822046299269234080e-02L */
+};
+
+const LONGDOUBLE
+pi_lo = { 0xece675d1fc8f8cbbULL, 0xbfbeU }; /* -5.01655761266833202345e-20L */