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

4 files changed, 127 insertions, 8 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 */
diff --git a/lib/msun/ld80/invtrig.h b/lib/msun/ld80/invtrig.h
index 069a408..fe30c01 100644
--- a/lib/msun/ld80/invtrig.h
+++ b/lib/msun/ld80/invtrig.h
@@ -64,10 +64,21 @@
 #define	pio2_lo	atanlo[3]
 #define	pio4_hi	atanhi[1]
 
-extern const long double pS0, pS1, pS2, pS3, pS4, pS5, pS6;
-extern const long double qS1, qS2, qS3, qS4, qS5;
-extern const long double atanhi[], atanlo[], aT[];
-extern const long double pi_lo;
+#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)
@@ -99,3 +110,5 @@ T_odd(long double x)
 	return (aT[1] + x * (aT[3] + x * (aT[5] + x * (aT[7] + x * \
 		(aT[9] + x * aT[11])))));
 }
+
+#endif
diff --git a/lib/msun/src/e_acosl.c b/lib/msun/src/e_acosl.c
index 4e9df52..d33c8fe 100644
--- a/lib/msun/src/e_acosl.c
+++ b/lib/msun/src/e_acosl.c
@@ -27,9 +27,19 @@ __FBSDID("$FreeBSD$");
 #include "math_private.h"
 
 static const long double
-one=  1.00000000000000000000e+00,
+one=  1.00000000000000000000e+00;
+
+#ifdef __i386__
+/* XXX Work around the fact that gcc truncates long double constants on i386 */
+static volatile double
+pi1 =  3.14159265358979311600e+00,	/*  0x1.921fb54442d18p+1  */
+pi2 =  1.22514845490862001043e-16;	/*  0x1.1a80000000000p-53 */
+#define	pi	((long double)pi1 + pi2)
+#else
+static const long double
 pi =  3.14159265358979323846264338327950280e+00L;
-      
+#endif
+
 long double
 acosl(long double x)
 {
diff --git a/lib/msun/src/e_atan2l.c b/lib/msun/src/e_atan2l.c
index 8368bbf..0071a7c 100644
--- a/lib/msun/src/e_atan2l.c
+++ b/lib/msun/src/e_atan2l.c
@@ -30,8 +30,18 @@ __FBSDID("$FreeBSD$");
 static volatile long double
 tiny  = 1.0e-300;
 static const long double
-zero  = 0.0,
-pi = 3.14159265358979323846264338327950280e+00L;
+zero  = 0.0;
+
+#ifdef __i386__
+/* XXX Work around the fact that gcc truncates long double constants on i386 */
+static volatile double
+pi1 =  3.14159265358979311600e+00,	/*  0x1.921fb54442d18p+1  */
+pi2 =  1.22514845490862001043e-16;	/*  0x1.1a80000000000p-53 */
+#define	pi	((long double)pi1 + pi2)
+#else
+static const long double
+pi =  3.14159265358979323846264338327950280e+00L;
+#endif
 
 long double
 atan2l(long double y, long double x)