Update.

2001-05-15  Andreas Jaeger  <aj@suse.de>

	* sysdeps/ieee754/ldbl-128/s_expm1l.c: New file, contributed by
	Stephen L Moshier <moshier@mediaone.net>.

	* sysdeps/i386/fpu/libm-test-ulps: Adjust for change.

	* math/libm-test.inc: Add comment with ToDo.

	* sysdeps/i386/fpu/e_expl.c: Rewritten to C and using a more
	accurate algorithm.  Patch by Stephen L Moshier <moshier@mediaone.net>.

	* sysdeps/i386/fpu/e_expl.S: Removed.

3 files changed, 85 insertions, 53 deletions

diff --git a/sysdeps/i386/fpu/e_expl.S b/sysdeps/i386/fpu/e_expl.S
deleted file mode 100644
index 2bcdf58c58..0000000000
--- a/sysdeps/i386/fpu/e_expl.S
+++ /dev/null
@@ -1,43 +0,0 @@
-/*
- * Written by J.T. Conklin <jtc@netbsd.org>.
- * Public domain.
- *
- * Adapted for `long double' by Ulrich Drepper <drepper@cygnus.com>.
- */
-
-#include <machine/asm.h>
-
-RCSID("$NetBSD: $")
-
-/* e^x = 2^(x * log2l(e)) */
-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.
-   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.  */
-	fldl2e
-	fmulp				/* x * log2(e) */
-	fld	%st
-	frndint				/* int(x * log2(e)) */
-	fsubr	%st,%st(1)		/* fract(x * log2(e)) */
-	fxch
-	f2xm1				/* 2^(fract(x * log2(e))) - 1 */
-	fld1
-	faddp				/* 2^(fract(x * log2(e))) */
-	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_expl)
diff --git a/sysdeps/i386/fpu/e_expl.c b/sysdeps/i386/fpu/e_expl.c
new file mode 100644
index 0000000000..d9c6476e11
--- /dev/null
+++ b/sysdeps/i386/fpu/e_expl.c
@@ -0,0 +1,75 @@
+/*
+ * Written by J.T. Conklin <jtc@netbsd.org>.
+ * Public domain.
+ *
+ * Adapted for `long double' by Ulrich Drepper <drepper@cygnus.com>.
+ */
+
+/*
+ * The 8087 method for the exponential function is to calculate
+ *   exp(x) = 2^(x log2(e))
+ * after separating integer and fractional parts
+ *   x log2(e) = i + f, |f| <= .5
+ * 2^i is immediate but f needs to be precise for long double accuracy.
+ * Suppress range reduction error in computing f by the following.
+ * Separate x into integer and fractional parts
+ *   x = xi + xf, |xf| <= .5
+ * Separate log2(e) into the sum of an exact number c0 and small part c1.
+ *   c0 + c1 = log2(e) to extra precision
+ * Then
+ *   f = (c0 xi - i) + c0 xf + c1 x
+ * where c0 xi is exact and so also is (c0 xi - i).
+ * -- moshier@na-net.ornl.gov
+ */
+
+static long double c0 = 1.44268798828125L;
+static long double c1 = 7.05260771340735992468e-6L;
+
+long double
+__ieee754_expl (long double x)
+{
+  long double res, t;
+
+/* 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.  */
+  asm ("fxam\n\t"		/* Is NaN or +-Inf?  */
+       "fstsw	%%ax\n\t"
+       "movb	$0x45, %%dh\n\t"
+       "andb	%%ah, %%dh\n\t"
+       "cmpb	$0x05, %%dh\n\t"
+       "je	1f\n\t"		/* Is +-Inf, jump.    */
+       "fldl2e\n\t"             /* 1  log2(e)         */
+       "fmul %%st(1),%%st\n\t"  /* 1  x log2(e)       */
+       "frndint\n\t"            /* 1  i               */
+       "fld %%st(1)\n\t"        /* 2  x               */
+       "frndint\n\t"            /* 2  xi              */
+       "fld %%st(1)\n\t"        /* 3  i               */
+       "fldt c0\n\t"            /* 4  c0              */
+       "fld %%st(2)\n\t"        /* 5  xi              */
+       "fmul %%st(1),%%st\n\t"  /* 5  c0 xi           */
+       "fsubp %%st,%%st(2)\n\t" /* 4  f = c0 xi  - i  */
+       "fld %%st(4)\n\t"        /* 5  x               */
+       "fsub %%st(3),%%st\n\t"  /* 5  xf = x - xi     */
+       "fmulp %%st,%%st(1)\n\t" /* 4  c0 xf           */
+       "faddp %%st,%%st(1)\n\t" /* 3  f = f + c0 xf   */
+       "fldt c1\n\t"            /* 4                  */
+       "fmul %%st(4),%%st\n\t"  /* 4  c1 * x          */
+       "faddp %%st,%%st(1)\n\t" /* 3  f = f + c1 * x  */
+       "f2xm1\n\t"		/* 3 2^(fract(x * log2(e))) - 1 */
+       "fld1\n\t"               /* 4 1.0              */
+       "faddp\n\t"		/* 3 2^(fract(x * log2(e))) */
+       "fstp	%%st(1)\n\t"    /* 2  */
+       "fscale\n\t"	        /* 2 scale factor is st(1); e^x */
+       "fstp	%%st(1)\n\t"    /* 1  */
+       "fstp	%%st(1)\n\t"    /* 0  */
+       "jmp 2f\n\t"
+       "1:\ttestl	$0x200, %%eax\n\t"	/* Test sign.  */
+       "jz	2f\n\t"		/* If positive, jump.  */
+       "fstp	%%st\n\t"
+       "fldz\n\t"		/* Set result to 0.  */
+       "2:\t\n"
+       : "=t" (res) : "0" (x) : "ax", "dx");
+  return res;
+}
diff --git a/sysdeps/i386/fpu/libm-test-ulps b/sysdeps/i386/fpu/libm-test-ulps
index 7c60eea593..82d167cd18 100644
--- a/sysdeps/i386/fpu/libm-test-ulps
+++ b/sysdeps/i386/fpu/libm-test-ulps
@@ -484,13 +484,13 @@ ldouble: 128
 
 # ctan
 Test "Real part of: ctan (-2 - 3 i) == 0.0037640256415042482 - 1.0032386273536098014 i":
-ildouble: 437
-ldouble: 437
+ildouble: 439
+ldouble: 439
 Test "Imaginary part of: ctan (-2 - 3 i) == 0.0037640256415042482 - 1.0032386273536098014 i":
 float: 1
 ifloat: 1
-ildouble: 1
-ldouble: 1
+ildouble: 2
+ldouble: 2
 Test "Real part of: ctan (0.7 + 1.2 i) == 0.1720734197630349001 + 0.9544807059989405538 i":
 double: 1
 float: 1
@@ -506,13 +506,13 @@ ldouble: 367
 
 # ctanh
 Test "Real part of: ctanh (-2 - 3 i) == -0.9653858790221331242 + 0.0098843750383224937 i":
-ildouble: 2
-ldouble: 2
+ildouble: 5
+ldouble: 5
 Test "Imaginary part of: ctanh (-2 - 3 i) == -0.9653858790221331242 + 0.0098843750383224937 i":
 float: 1
 ifloat: 1
-ildouble: 23
-ldouble: 23
+ildouble: 25
+ldouble: 25
 Test "Real part of: ctanh (0 + pi/4 i) == 0.0 + 1.0 i":
 Test "Imaginary part of: ctanh (0 + pi/4 i) == 0.0 + 1.0 i":
 float: 1
@@ -551,8 +551,8 @@ double: 24
 float: 12
 idouble: 24
 ifloat: 12
-ldouble: 4
-ildouble: 4
+ldouble: 12
+ildouble: 12
 Test "erfc (9) == 0.41370317465138102381e-36":
 ldouble: 36
 ildouble: 36