+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.
+
2001-05-14 Roland McGrath <roland@frob.com>
* csu/Makefile ($(objpfx)g$(start-installed-name)): Turn this into a
+++ /dev/null
-/*
- * 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)
--- /dev/null
+/*
+ * 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;
+}
projects / platform / upstream / glibc.git / commitdiff