Fix exp10 inaccuracy and exceptions (bugs 13884, 13914).

8 files changed, 212 insertions, 55 deletions

diff --git a/sysdeps/i386/fpu/e_exp10l.S b/sysdeps/i386/fpu/e_exp10l.S
index 04ec800..d843e2b 100644
--- a/sysdeps/i386/fpu/e_exp10l.S
+++ b/sysdeps/i386/fpu/e_exp10l.S
@@ -1,39 +1,2 @@
-/*
- * Written by Ulrich Drepper <drepper@cygnus.com>.
- */
-
-#include <machine/asm.h>
-
-/* 10^x = 2^(x * log2l(10)) */
-ENTRY(__ieee754_exp10l)
-	fldt	4(%esp)
-/* I added the following ugly construct because expl(+-Inf) resulted
-   in NaN.  The ugliness results from the bright minds at Intel.
-   For the i686 the code can be written better.
-   -- drepper@cygnus.com.  */
-	fxam				/* Is NaN or +-Inf?  */
-	fstsw	%ax
-	movb	$0x45, %dh
-	andb	%ah, %dh
-	cmpb	$0x05, %dh
-	je	1f			/* Is +-Inf, jump.  */
-	fldl2t
-	fmulp				/* x * log2(10) */
-	fld	%st
-	frndint				/* int(x * log2(10)) */
-	fsubr	%st,%st(1)		/* fract(x * log2(10)) */
-	fxch
-	f2xm1				/* 2^(fract(x * log2(10))) - 1 */
-	fld1
-	faddp				/* 2^(fract(x * log2(10))) */
-	fscale				/* e^x */
-	fstp	%st(1)
-	ret
-
-1:	testl	$0x200, %eax		/* Test sign.  */
-	jz	2f			/* If positive, jump.  */
-	fstp	%st
-	fldz				/* Set result to 0.  */
-2:	ret
-END (__ieee754_exp10l)
-strong_alias (__ieee754_exp10l, __exp10l_finite)
+#define USE_AS_EXP10L
+#include <e_expl.S>
diff --git a/sysdeps/i386/fpu/e_expl.S b/sysdeps/i386/fpu/e_expl.S
index 45c4d07..9adf2a4 100644
--- a/sysdeps/i386/fpu/e_expl.S
+++ b/sysdeps/i386/fpu/e_expl.S
@@ -24,9 +24,29 @@
 
 #include <machine/asm.h>
 
+#ifdef USE_AS_EXP10L
+# define IEEE754_EXPL __ieee754_exp10l
+# define EXPL_FINITE __exp10l_finite
+# define FLDLOG fldl2t
+#else
+# define IEEE754_EXPL __ieee754_expl
+# define EXPL_FINITE __expl_finite
+# define FLDLOG fldl2e
+#endif
+
 	.section .rodata.cst16,"aM",@progbits,16
 
 	.p2align 4
+#ifdef USE_AS_EXP10L
+	ASM_TYPE_DIRECTIVE(c0,@object)
+c0:	.byte 0, 0, 0, 0, 0, 0, 0x9a, 0xd4, 0x00, 0x40
+	.byte 0, 0, 0, 0, 0, 0
+	ASM_SIZE_DIRECTIVE(c0)
+	ASM_TYPE_DIRECTIVE(c1,@object)
+c1:	.byte 0x58, 0x92, 0xfc, 0x15, 0x37, 0x9a, 0x97, 0xf0, 0xef, 0x3f
+	.byte 0, 0, 0, 0, 0, 0
+	ASM_SIZE_DIRECTIVE(c1)
+#else
 	ASM_TYPE_DIRECTIVE(c0,@object)
 c0:	.byte 0, 0, 0, 0, 0, 0, 0xaa, 0xb8, 0xff, 0x3f
 	.byte 0, 0, 0, 0, 0, 0
@@ -35,6 +55,7 @@ c0:	.byte 0, 0, 0, 0, 0, 0, 0xaa, 0xb8, 0xff, 0x3f
 c1:	.byte 0x20, 0xfa, 0xee, 0xc2, 0x5f, 0x70, 0xa5, 0xec, 0xed, 0x3f
 	.byte 0, 0, 0, 0, 0, 0
 	ASM_SIZE_DIRECTIVE(c1)
+#endif
 	ASM_TYPE_DIRECTIVE(csat,@object)
 csat:	.byte 0, 0, 0, 0, 0, 0, 0, 0x80, 0x0e, 0x40
 	.byte 0, 0, 0, 0, 0, 0
@@ -47,7 +68,7 @@ csat:	.byte 0, 0, 0, 0, 0, 0, 0, 0x80, 0x0e, 0x40
 #endif
 
 	.text
-ENTRY(__ieee754_expl)
+ENTRY(IEEE754_EXPL)
 	fldt	4(%esp)
 /* I added the following ugly construct because expl(+-Inf) resulted
    in NaN.  The ugliness results from the bright minds at Intel.
@@ -75,8 +96,8 @@ ENTRY(__ieee754_expl)
 	andb	$2, %ah
 	jz	3f
 	fchs
-3:	fldl2e			/* 1  log2(e)         */
-	fmul	%st(1), %st	/* 1  x log2(e)       */
+3:	FLDLOG			/* 1  log2(base)      */
+	fmul	%st(1), %st	/* 1  x log2(base)    */
 	frndint			/* 1  i               */
 	fld	%st(1)		/* 2  x               */
 	frndint			/* 2  xi              */
@@ -92,11 +113,11 @@ ENTRY(__ieee754_expl)
 	fldt	MO(c1)		/* 4                  */
 	fmul	%st(4), %st	/* 4  c1 * x          */
 	faddp	%st, %st(1)	/* 3  f = f + c1 * x  */
-	f2xm1			/* 3 2^(fract(x * log2(e))) - 1 */
+	f2xm1			/* 3 2^(fract(x * log2(base))) - 1 */
 	fld1			/* 4 1.0              */
-	faddp			/* 3 2^(fract(x * log2(e))) */
+	faddp			/* 3 2^(fract(x * log2(base))) */
 	fstp	%st(1)		/* 2  */
-	fscale			/* 2 scale factor is st(1); e^x */
+	fscale			/* 2 scale factor is st(1); base^x */
 	fstp	%st(1)		/* 1  */
 	fstp	%st(1)		/* 0  */
 	jmp	2f
@@ -105,5 +126,5 @@ ENTRY(__ieee754_expl)
 	fstp	%st
 	fldz			/* Set result to 0.  */
 2:	ret
-END(__ieee754_expl)
-strong_alias (__ieee754_expl, __expl_finite)
+END(IEEE754_EXPL)
+strong_alias (IEEE754_EXPL, EXPL_FINITE)
diff --git a/sysdeps/ieee754/dbl-64/e_exp10.c b/sysdeps/ieee754/dbl-64/e_exp10.c
new file mode 100644
index 0000000..eeb63a6
--- /dev/null
+++ b/sysdeps/ieee754/dbl-64/e_exp10.c
@@ -0,0 +1,48 @@
+/* Copyright (C) 2012 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   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/>.  */
+
+#include <math.h>
+#include <math_private.h>
+#include <float.h>
+
+static const double log10_high = 0x2.4d7637p0;
+static const double log10_low = 0x7.6aaa2b05ba95cp-28;
+
+double
+__ieee754_exp10 (double arg)
+{
+  int32_t lx;
+  double arg_high, arg_low;
+  double exp_high, exp_low;
+
+  if (!__finite (arg))
+    return __ieee754_exp (arg);
+  if (arg < DBL_MIN_10_EXP - DBL_DIG - 10)
+    return DBL_MIN * DBL_MIN;
+  else if (arg > DBL_MAX_10_EXP + 1)
+    return DBL_MAX * DBL_MAX;
+
+  GET_LOW_WORD (lx, arg);
+  lx &= 0xf8000000;
+  arg_high = arg;
+  SET_LOW_WORD (arg_high, lx);
+  arg_low = arg - arg_high;
+  exp_high = arg_high * log10_high;
+  exp_low = arg_high * log10_low + arg_low * M_LN10;
+  return __ieee754_exp (exp_high) * __ieee754_exp (exp_low);
+}
+strong_alias (__ieee754_exp10, __exp10_finite)
diff --git a/sysdeps/ieee754/ldbl-128/e_exp10l.c b/sysdeps/ieee754/ldbl-128/e_exp10l.c
new file mode 100644
index 0000000..503c1de
--- /dev/null
+++ b/sysdeps/ieee754/ldbl-128/e_exp10l.c
@@ -0,0 +1,47 @@
+/* Copyright (C) 2012 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   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/>.  */
+
+#include <math.h>
+#include <math_private.h>
+#include <float.h>
+
+static const long double log10_high = 0x2.4d763776aaa2bp0L;
+static const long double log10_low = 0x5.ba95b58ae0b4c28a38a3fb3e7698p-60L;
+
+long double
+__ieee754_exp10l (long double arg)
+{
+  ieee854_long_double_shape_type u;
+  long double arg_high, arg_low;
+  long double exp_high, exp_low;
+
+  if (!__finitel (arg))
+    return __ieee754_expl (arg);
+  if (arg < LDBL_MIN_10_EXP - LDBL_DIG - 10)
+    return LDBL_MIN * LDBL_MIN;
+  else if (arg > LDBL_MAX_10_EXP + 1)
+    return LDBL_MAX * LDBL_MAX;
+
+  u.value = arg;
+  u.parts64.lsw &= 0xfe00000000000000LL;
+  arg_high = u.value;
+  arg_low = arg - arg_high;
+  exp_high = arg_high * log10_high;
+  exp_low = arg_high * log10_low + arg_low * M_LN10l;
+  return __ieee754_expl (exp_high) * __ieee754_expl (exp_low);
+}
+strong_alias (__ieee754_exp10l, __exp10l_finite)
diff --git a/sysdeps/ieee754/ldbl-128ibm/e_exp10l.c b/sysdeps/ieee754/ldbl-128ibm/e_exp10l.c
new file mode 100644
index 0000000..b19e6c7
--- /dev/null
+++ b/sysdeps/ieee754/ldbl-128ibm/e_exp10l.c
@@ -0,0 +1,46 @@
+/* Copyright (C) 2012 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   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/>.  */
+
+#include <math.h>
+#include <math_private.h>
+#include <float.h>
+
+static const long double log10_high = 0x2.4d763776aaa2cp0L;
+static const long double log10_low = -0xf.a456a4a751f4b3d75c75c04c18p-56L;
+
+long double
+__ieee754_exp10l (long double arg)
+{
+  union ibm_extended_long_double u;
+  long double arg_high, arg_low;
+  long double exp_high, exp_low;
+
+  if (!__finitel (arg))
+    return __ieee754_expl (arg);
+  if (arg < LDBL_MIN_10_EXP - LDBL_DIG - 10)
+    return LDBL_MIN * LDBL_MIN;
+  else if (arg > LDBL_MAX_10_EXP + 1)
+    return LDBL_MAX * LDBL_MAX;
+
+  u.d = arg;
+  arg_high = u.dd[0];
+  arg_low = u.dd[1];
+  exp_high = arg_high * log10_high;
+  exp_low = arg_high * log10_low + arg_low * M_LN10l;
+  return __ieee754_expl (exp_high) * __ieee754_expl (exp_low);
+}
+strong_alias (__ieee754_exp10l, __exp10l_finite)
diff --git a/sysdeps/x86_64/fpu/e_exp10l.S b/sysdeps/x86_64/fpu/e_exp10l.S
new file mode 100644
index 0000000..d843e2b
--- /dev/null
+++ b/sysdeps/x86_64/fpu/e_exp10l.S
@@ -0,0 +1,2 @@
+#define USE_AS_EXP10L
+#include <e_expl.S>
diff --git a/sysdeps/x86_64/fpu/e_expl.S b/sysdeps/x86_64/fpu/e_expl.S
index d497b28..fd613f9 100644
--- a/sysdeps/x86_64/fpu/e_expl.S
+++ b/sysdeps/x86_64/fpu/e_expl.S
@@ -24,9 +24,29 @@
 
 #include <machine/asm.h>
 
+#ifdef USE_AS_EXP10L
+# define IEEE754_EXPL __ieee754_exp10l
+# define EXPL_FINITE __exp10l_finite
+# define FLDLOG fldl2t
+#else
+# define IEEE754_EXPL __ieee754_expl
+# define EXPL_FINITE __expl_finite
+# define FLDLOG fldl2e
+#endif
+
 	.section .rodata.cst16,"aM",@progbits,16
 
 	.p2align 4
+#ifdef USE_AS_EXP10L
+	ASM_TYPE_DIRECTIVE(c0,@object)
+c0:	.byte 0, 0, 0, 0, 0, 0, 0x9a, 0xd4, 0x00, 0x40
+	.byte 0, 0, 0, 0, 0, 0
+	ASM_SIZE_DIRECTIVE(c0)
+	ASM_TYPE_DIRECTIVE(c1,@object)
+c1:	.byte 0x58, 0x92, 0xfc, 0x15, 0x37, 0x9a, 0x97, 0xf0, 0xef, 0x3f
+	.byte 0, 0, 0, 0, 0, 0
+	ASM_SIZE_DIRECTIVE(c1)
+#else
 	ASM_TYPE_DIRECTIVE(c0,@object)
 c0:	.byte 0, 0, 0, 0, 0, 0, 0xaa, 0xb8, 0xff, 0x3f
 	.byte 0, 0, 0, 0, 0, 0
@@ -35,6 +55,7 @@ c0:	.byte 0, 0, 0, 0, 0, 0, 0xaa, 0xb8, 0xff, 0x3f
 c1:	.byte 0x20, 0xfa, 0xee, 0xc2, 0x5f, 0x70, 0xa5, 0xec, 0xed, 0x3f
 	.byte 0, 0, 0, 0, 0, 0
 	ASM_SIZE_DIRECTIVE(c1)
+#endif
 	ASM_TYPE_DIRECTIVE(csat,@object)
 csat:	.byte 0, 0, 0, 0, 0, 0, 0, 0x80, 0x0e, 0x40
 	.byte 0, 0, 0, 0, 0, 0
@@ -47,7 +68,7 @@ csat:	.byte 0, 0, 0, 0, 0, 0, 0, 0x80, 0x0e, 0x40
 #endif
 
 	.text
-ENTRY(__ieee754_expl)
+ENTRY(IEEE754_EXPL)
 	fldt	8(%rsp)
 /* I added the following ugly construct because expl(+-Inf) resulted
    in NaN.  The ugliness results from the bright minds at Intel.
@@ -72,8 +93,8 @@ ENTRY(__ieee754_expl)
 	andb	$2, %ah
 	jz	3f
 	fchs
-3:	fldl2e			/* 1  log2(e)         */
-	fmul	%st(1), %st	/* 1  x log2(e)       */
+3:	FLDLOG			/* 1  log2(base)      */
+	fmul	%st(1), %st	/* 1  x log2(base)    */
 	frndint			/* 1  i               */
 	fld	%st(1)		/* 2  x               */
 	frndint			/* 2  xi              */
@@ -89,11 +110,11 @@ ENTRY(__ieee754_expl)
 	fldt	MO(c1)		/* 4                  */
 	fmul	%st(4), %st	/* 4  c1 * x          */
 	faddp	%st, %st(1)	/* 3  f = f + c1 * x  */
-	f2xm1			/* 3 2^(fract(x * log2(e))) - 1 */
+	f2xm1			/* 3 2^(fract(x * log2(base))) - 1 */
 	fld1			/* 4 1.0              */
-	faddp			/* 3 2^(fract(x * log2(e))) */
+	faddp			/* 3 2^(fract(x * log2(base))) */
 	fstp	%st(1)		/* 2  */
-	fscale			/* 2 scale factor is st(1); e^x */
+	fscale			/* 2 scale factor is st(1); base^x */
 	fstp	%st(1)		/* 1  */
 	fstp	%st(1)		/* 0  */
 	jmp	2f
@@ -102,5 +123,5 @@ ENTRY(__ieee754_expl)
 	fstp	%st
 	fldz			/* Set result to 0.  */
 2:	ret
-END(__ieee754_expl)
-strong_alias (__ieee754_expl, __expl_finite)
+END(IEEE754_EXPL)
+strong_alias (IEEE754_EXPL, EXPL_FINITE)
diff --git a/sysdeps/x86_64/fpu/libm-test-ulps b/sysdeps/x86_64/fpu/libm-test-ulps
index 70b091f..f33c07f 100644
--- a/sysdeps/x86_64/fpu/libm-test-ulps
+++ b/sysdeps/x86_64/fpu/libm-test-ulps
@@ -1287,6 +1287,12 @@ idouble: 2
 ifloat: 1
 ildouble: 1
 ldouble: 1
+Test "exp10 (-305) == 1.0e-305":
+double: 1
+idouble: 1
+Test "exp10 (-36) == 1.0e-36":
+double: 1
+idouble: 1
 Test "exp10 (0.75) == 5.62341325190349080394951039776481231":
 double: 1
 float: 1
@@ -1301,6 +1307,9 @@ idouble: 6
 ifloat: 2
 ildouble: 8
 ldouble: 8
+Test "exp10 (36) == 1.0e36":
+double: 1
+idouble: 1
 
 # exp_downward
 Test "exp_downward (1) == e":