Fix x86/x86_64 expm1l inaccuracy and exceptions (bugs 13885, 13923).

3 files changed, 68 insertions, 132 deletions

diff --git a/sysdeps/i386/fpu/e_expl.S b/sysdeps/i386/fpu/e_expl.S
index 9adf2a4..bab0a08 100644
--- a/sysdeps/i386/fpu/e_expl.S
+++ b/sysdeps/i386/fpu/e_expl.S
@@ -28,6 +28,10 @@
 # define IEEE754_EXPL __ieee754_exp10l
 # define EXPL_FINITE __exp10l_finite
 # define FLDLOG fldl2t
+#elif defined USE_AS_EXPM1L
+# define IEEE754_EXPL __expm1l
+# undef EXPL_FINITE
+# define FLDLOG fldl2e
 #else
 # define IEEE754_EXPL __ieee754_expl
 # define EXPL_FINITE __expl_finite
@@ -69,6 +73,12 @@ csat:	.byte 0, 0, 0, 0, 0, 0, 0, 0x80, 0x0e, 0x40
 
 	.text
 ENTRY(IEEE754_EXPL)
+#ifdef USE_AS_EXPM1L
+	movzwl	4+8(%esp), %eax
+	xorb	$0x80, %ah	// invert sign bit (now 1 is "positive")
+	cmpl	$0xc006, %eax	// is num positive and exp >= 6 (number is >= 128.0)?
+	jae	HIDDEN_JUMPTARGET (__expl) // (if num is denormal, it is at least >= 64.0)
+#endif
 	fldt	4(%esp)
 /* I added the following ugly construct because expl(+-Inf) resulted
    in NaN.  The ugliness results from the bright minds at Intel.
@@ -78,7 +88,9 @@ ENTRY(IEEE754_EXPL)
 #ifdef PIC
 	LOAD_PIC_REG (cx)
 #endif
+#ifndef USE_AS_EXPM1L
 	movzwl	4+8(%esp), %eax
+#endif
 	andl	$0x7fff, %eax
 	cmpl	$0x400d, %eax
 	jle	3f
@@ -96,7 +108,16 @@ ENTRY(IEEE754_EXPL)
 	andb	$2, %ah
 	jz	3f
 	fchs
-3:	FLDLOG			/* 1  log2(base)      */
+3:
+#ifdef USE_AS_EXPM1L
+	/* Test for +-0 as argument.  */
+	fstsw	%ax
+	movb	$0x45, %dh
+	andb	%ah, %dh
+	cmpb	$0x40, %dh
+	je	2f
+#endif
+	FLDLOG			/* 1  log2(base)      */
 	fmul	%st(1), %st	/* 1  x log2(base)    */
 	frndint			/* 1  i               */
 	fld	%st(1)		/* 2  x               */
@@ -114,17 +135,39 @@ ENTRY(IEEE754_EXPL)
 	fmul	%st(4), %st	/* 4  c1 * x          */
 	faddp	%st, %st(1)	/* 3  f = f + c1 * x  */
 	f2xm1			/* 3 2^(fract(x * log2(base))) - 1 */
+#ifdef USE_AS_EXPM1L
+	fstp	%st(1)		/* 2                  */
+	fscale			/* 2 scale factor is st(1); base^x - 2^i */
+	fxch			/* 2 i                */
+	fld1			/* 3 1.0              */
+	fscale			/* 3 2^i              */
+	fld1			/* 4 1.0              */
+	fsubrp	%st, %st(1)	/* 3 2^i - 1.0        */
+	fstp	%st(1)		/* 2                  */
+	faddp	%st, %st(1)	/* 1 base^x - 1.0     */
+#else
 	fld1			/* 4 1.0              */
 	faddp			/* 3 2^(fract(x * log2(base))) */
 	fstp	%st(1)		/* 2  */
 	fscale			/* 2 scale factor is st(1); base^x */
 	fstp	%st(1)		/* 1  */
+#endif
 	fstp	%st(1)		/* 0  */
 	jmp	2f
 1:	testl	$0x200, %eax	/* Test sign.  */
 	jz	2f		/* If positive, jump.  */
 	fstp	%st
+#ifdef USE_AS_EXPM1L
+	fld1
+	fchs
+#else
 	fldz			/* Set result to 0.  */
+#endif
 2:	ret
 END(IEEE754_EXPL)
+#ifdef USE_AS_EXPM1L
+libm_hidden_def (__expm1l)
+weak_alias (__expm1l, expm1l)
+#else
 strong_alias (IEEE754_EXPL, EXPL_FINITE)
+#endif
diff --git a/sysdeps/i386/fpu/libm-test-ulps b/sysdeps/i386/fpu/libm-test-ulps
index 6323553..cdc26a0 100644
--- a/sysdeps/i386/fpu/libm-test-ulps
+++ b/sysdeps/i386/fpu/libm-test-ulps
@@ -1008,10 +1008,6 @@ Test "cos_upward (9) == -0.9111302618846769883682947111811653112463":
 ildouble: 1
 ldouble: 1
 
-# cosh
-Test "cosh (0.75) == 1.29468328467684468784170818539018176":
-ildouble: 1
-
 # cosh_downward
 Test "cosh_downward (22) == 1792456423.065795780980053377632656584997":
 double: 1
@@ -1899,29 +1895,20 @@ double: 1
 float: 1
 idouble: 1
 ifloat: 1
-ildouble: 4
-ldouble: 4
+ildouble: 2
+ldouble: 2
 Test "sinh_downward (23) == 4872401723.124451299966006944252978187305":
 double: 1
 float: 1
 idouble: 1
 ifloat: 1
+ildouble: 2
+ldouble: 2
 Test "sinh_downward (24) == 13244561064.92173614705070540368454568168":
 float: 1
 ifloat: 1
-ildouble: 5
-ldouble: 5
-
-# sinh_tonearest
-Test "sinh_tonearest (22) == 1792456423.065795780701106568345764104225":
-ildouble: 3
-ldouble: 3
-Test "sinh_tonearest (23) == 4872401723.124451299966006944252978187305":
-ildouble: 1
-ldouble: 1
-Test "sinh_tonearest (24) == 13244561064.92173614705070540368454568168":
-ildouble: 6
-ldouble: 6
+ildouble: 2
+ldouble: 2
 
 # sinh_towardzero
 Test "sinh_towardzero (22) == 1792456423.065795780701106568345764104225":
@@ -1929,31 +1916,31 @@ double: 1
 float: 1
 idouble: 1
 ifloat: 1
-ildouble: 4
-ldouble: 4
+ildouble: 2
+ldouble: 2
 Test "sinh_towardzero (23) == 4872401723.124451299966006944252978187305":
 double: 1
 float: 1
 idouble: 1
 ifloat: 1
+ildouble: 2
+ldouble: 2
 Test "sinh_towardzero (24) == 13244561064.92173614705070540368454568168":
 float: 1
 ifloat: 1
-ildouble: 5
-ldouble: 5
+ildouble: 2
+ldouble: 2
 
 # sinh_upward
 Test "sinh_upward (22) == 1792456423.065795780701106568345764104225":
-ildouble: 16
-ldouble: 16
+ildouble: 1
+ldouble: 1
 Test "sinh_upward (23) == 4872401723.124451299966006944252978187305":
-ildouble: 27
-ldouble: 27
+ildouble: 1
+ldouble: 1
 Test "sinh_upward (24) == 13244561064.92173614705070540368454568168":
 double: 1
 idouble: 1
-ildouble: 7
-ldouble: 7
 
 # tan
 Test "tan (0x1p16383) == 0.422722393732022337800504160054440141575":
@@ -2587,9 +2574,6 @@ ifloat: 1
 ildouble: 1
 ldouble: 1
 
-Function: "cosh":
-ildouble: 1
-
 Function: "cosh_downward":
 double: 1
 float: 1
@@ -2862,26 +2846,22 @@ double: 1
 float: 1
 idouble: 1
 ifloat: 1
-ildouble: 5
-ldouble: 5
-
-Function: "sinh_tonearest":
-ildouble: 6
-ldouble: 6
+ildouble: 2
+ldouble: 2
 
 Function: "sinh_towardzero":
 double: 1
 float: 1
 idouble: 1
 ifloat: 1
-ildouble: 5
-ldouble: 5
+ildouble: 2
+ldouble: 2
 
 Function: "sinh_upward":
 double: 1
 idouble: 1
-ildouble: 27
-ldouble: 27
+ildouble: 1
+ldouble: 1
 
 Function: "tan":
 double: 1
diff --git a/sysdeps/i386/fpu/s_expm1l.S b/sysdeps/i386/fpu/s_expm1l.S
index e91f18b..7fbd99b 100644
--- a/sysdeps/i386/fpu/s_expm1l.S
+++ b/sysdeps/i386/fpu/s_expm1l.S
@@ -1,89 +1,2 @@
-/* ix87 specific implementation of exp(x)-1.
-   Copyright (C) 1996-1997, 2002, 2005, 2008, 2012 Free Software Foundation, Inc.
-   This file is part of the GNU C Library.
-   Contributed by Ulrich Drepper <drepper@cygnus.com>, 1996.
-   Based on code by John C. Bowman <bowman@ipp-garching.mpg.de>.
-   Corrections by H.J. Lu (hjl@gnu.ai.mit.edu), 1997.
-
-   The GNU C Library is free software; you can redistribute it and/or
-   modify it under the terms of the GNU Lesser General Public
-   License as published by the Free Software Foundation; either
-   version 2.1 of the License, or (at your option) any later version.
-
-   The GNU C Library is distributed in the hope that it will be useful,
-   but WITHOUT ANY WARRANTY; without even the implied warranty of
-   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
-   Lesser General Public License for more details.
-
-   You should have received a copy of the GNU Lesser General Public
-   License along with the GNU C Library; if not, see
-   <http://www.gnu.org/licenses/>.  */
-
-	/* Using: e^x - 1 = 2^(x * log2(e)) - 1 */
-
-#include <sysdep.h>
-#include <machine/asm.h>
-
-	.section .rodata
-
-	.align ALIGNARG(4)
-	ASM_TYPE_DIRECTIVE(minus1,@object)
-minus1:	.double -1.0
-	ASM_SIZE_DIRECTIVE(minus1)
-	ASM_TYPE_DIRECTIVE(one,@object)
-one:	.double 1.0
-	ASM_SIZE_DIRECTIVE(one)
-	ASM_TYPE_DIRECTIVE(l2e,@object)
-l2e:	.tfloat 1.442695040888963407359924681002
-	ASM_SIZE_DIRECTIVE(l2e)
-
-#ifdef PIC
-#define MO(op) op##@GOTOFF(%edx)
-#else
-#define MO(op) op
-#endif
-
-	.text
-ENTRY(__expm1l)
-	movzwl	4+8(%esp), %eax	// load sign bit and 15-bit exponent
-	xorb	$0x80, %ah	// invert sign bit (now 1 is "positive")
-	cmpl	$0xc006, %eax	// is num positive and exp >= 6 (number is >= 128.0)?
-	jae	HIDDEN_JUMPTARGET (__expl) // (if num is denormal, it is at least >= 64.0)
-
-	fldt	4(%esp)		// x
-	fxam			// Is NaN or +-Inf?
-	fstsw	%ax
-	movb	$0x45, %ch
-	andb	%ah, %ch
-	cmpb	$0x40, %ch
-	je	3f		// If +-0, jump.
-#ifdef	PIC
-	LOAD_PIC_REG (dx)
-#endif
-	cmpb	$0x05, %ch
-	je	2f		// If +-Inf, jump.
-
-	fldt	MO(l2e)		// log2(e) : x
-	fmulp			// log2(e)*x
-	fld	%st		// log2(e)*x : log2(e)*x
-	frndint			// int(log2(e)*x) : log2(e)*x
-	fsubr	%st, %st(1)	// int(log2(e)*x) : fract(log2(e)*x)
-	fxch			// fract(log2(e)*x) : int(log2(e)*x)
-	f2xm1			// 2^fract(log2(e)*x)-1 : int(log2(e)*x)
-	fscale			// 2^(log2(e)*x)-2^int(log2(e)*x) : int(log2(e)*x)
-	fxch			// int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x)
-	fldl	MO(one)		// 1 : int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x)
-	fscale			// 2^int(log2(e)*x) : int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x)
-	fsubrl	MO(one)		// 1-2^int(log2(e)*x) : int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x)
-	fstp	%st(1)		// 1-2^int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x)
-	fsubrp	%st, %st(1)	// 2^(log2(e)*x)
-	ret
-
-2:	testl	$0x200, %eax	// Test sign.
-	jz	3f		// If positive, jump.
-	fstp	%st
-	fldl	MO(minus1)	// Set result to -1.0.
-3:	ret
-END(__expm1l)
-libm_hidden_def (__expm1l)
-weak_alias (__expm1l, expm1l)
+#define USE_AS_EXPM1L
+#include <e_expl.S>