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authorUlrich Drepper <drepper@redhat.com>1998-02-13 17:54:15 +0000
committerUlrich Drepper <drepper@redhat.com>1998-02-13 17:54:15 +0000
commitdc30f461575342ffeb6c0f2d5931493c1c3a91c0 (patch)
tree99243511beca706f0743fe2316854c5a30709f17 /sysdeps/libm-ieee754/e_expf.c
parente15867921d8f3b75deb0d91628cf9a323709ea9f (diff)
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Update.
1998-02-13 17:39 Ulrich Drepper <drepper@cygnus.com> * elf/Makefile: Don't use --version-script parameter to link ld.so unconditionally. 1998-01-02 04:19 Geoff Keating <geoffk@ozemail.com.au> * math/Makefile: Add t_exp. * math/libm-test.c: Tighten accuracy bounds for exp(), correct constants. * math/test-reduce.c: Remove temporarily, it seems to be broken. * sysdeps/libm-ieee754/e_exp.c: Use accurate table method. * sysdeps/libm-ieee754/e_expf.c: Use table & double precision for better accuracy. * sysdeps/libm-ieee754/s_exp2.c: Use better polynomial; correct algorithm for very large/very small arguments. * sysdeps/libm-ieee754/s_exp2f.c: Use slightly better polynomial; correct algorithm for very large/very small arguments; adjust for new table. * sysdeps/libm-ieee754/t_exp.c: New file. * sysdeps/libm-ieee754/t_exp2f.h: Use table with smaller deltas. * sysdeps/unix/sysv/linux/powerpc/dl-sysdep.c: Put 'strange test' back, with comment that explains what breaks when you remove it :-(. * localedata/xfrm-test.c: Avoid integer overflow. * stdlib/strfmon.c: char is unsigned, sometimes. *sysdeps/powerpc * sysdeps/powerpc/Makefile: Remove quad float support. * sysdeps/powerpc/q_*.c: Remove, they will become an add-on. * sysdeps/powerpc/quad_float.h: Likewise. * sysdeps/powerpc/test-arith.c: Likewise. * sysdeps/powerpc/test-arithf.c: Likewise. * sysdeps/generic/s_exp2.c: Remove, we have this implemented now. * sysdeps/generic/s_exp2f.c: Likewise. * sysdeps/powerpc/bits/mathinline.h: Use underscores around __asm__, don't try anything if _SOFT_FLOAT. 1997-12-31 Andreas Schwab <schwab@issan.informatik.uni-dortmund.de> * locale/C-ctype.c (_nl_C_LC_CTYPE_class32): Undo last change. * locale/programs/ld-ctype.c (CHAR_CLASS32_TRANS): Likewise. * wctype/wctype.c: Likewise. * wctype/wctype.h (_ISwxxx): Renamed from _ISxxx, all uses changed. They are incompatible with the _ISxxx values from <ctype.h> on little endian machines. (_ISwbit) [__BYTE_ORDER == __LITTLE_ENDIAN]: Correctly transform bit number. This fixes the real bug and restores the integrity of the ctype locale file. * wctype/wcfuncs.c: Change all _ISxxx to _ISwxxx. * wctype/wcfuncs_l.c: Likewise. * wctype/wcextra.c: Likewise. * wctype/wctype_l.c [__BYTE_ORDER == __LITTLE_ENDIAN]: Use correct byte swapping. 1998-02-09 Andreas Schwab <schwab@issan.informatik.uni-dortmund.de> * sysdeps/unix/sysv/linux/sparc/sparc32/sysdep.S (errno): Put it into .bss segment instead of .common, so that aliases on it work. * sysdeps/unix/sysv/linux/i386/sysdep.S (errno): Add .type and .size directives, put into .bss segment instead of initializing it to 4. 1998-02-12 08:00 H.J. Lu <hjl@gnu.org> * libc.map (gnu_get_libc_release, gnu_get_libc_version): Added. * version.c (__gnu_get_libc_release, __gnu_get_libc_version): New functions. Make names without __ weak aliases. (__libc_release, __libc_version): Make them static. * include/gnu/libc-version.h: New file. * Makefile (headers): Add gnu/libc-version.h. 1998-02-13 Ulrich Drepper <drepper@cygnus.com> * stdlib/stdlib.h (struct drand48_data): Leave X to user macros and use x for member name. Reported by Daniel Lyddy <daniell@cs.berkeley.edu>. * stdlib/drand48.c: Change according to member name change. * stdlib/drand48_r.c: Likewise. * stdlib/lcong48_r.c: Likewise. * stdlib/lrand48.c: Likewise. * stdlib/lrand48_r.c: Likewise. * stdlib/mrand48.c: Likewise. * stdlib/mrand48_r.c: Likewise. * stdlib/seed48.c: Likewise. * stdlib/seed48_r.c: Likewise. * stdlib/srand48_r.c: Likewise. 1998-02-11 Andreas Jaeger <aj@arthur.rhein-neckar.de> * nss/test-netdb.c: Add some more test cases. 1998-02-13 11:39 Ulrich Drepper <drepper@cygnus.com> * libio/iovsscanf.c: Undo last change modifying errno. 1998-02-12 Andreas Schwab <schwab@issan.informatik.uni-dortmund.de> * stdio-common/vfscanf.c: Never try to read another character after EOF. Don't decrement read_in after EOF, it wasn't incremented in the first place. (NEXT_WIDE_CHAR): Set First, not first. 1998-02-06 07:48 H.J. Lu <hjl@gnu.org> * db/Makefile ($(inst_libdir)/libndbm.a, $(inst_libdir)/libndbm.so): New targets. * db2/Makefile: Likewise. 1998-02-12 08:20 H.J. Lu <hjl@gnu.org> * sysdeps/gnu/errlist.awk (sys_errlist, sys_nerr): Create weak aliases if HAVE_ELF or PIC or DO_VERSIONING is not defined. 1998-02-12 Andreas Schwab <schwab@issan.informatik.uni-dortmund.de> * sysdeps/generic/_G_config.h: Define _G_wchar_t, for C++ <streambuf.h>. * sysdeps/unix/sysv/linux/_G_config.h: Likewise. 1998-02-11 Andreas Schwab <schwab@issan.informatik.uni-dortmund.de> * sysdeps/unix/make-syscalls.sh: Fix sed pattern when dealing with versioned symbols. 1998-02-13 08:14 H.J. Lu <hjl@gnu.org> * libc.map (_dl_global_scope, _dl_lookup_symbol_skip, _dl_lookup_versioned_symbol, _dl_lookup_versioned_symbol_skip): Added for libdl.so. * elf/rtld.map: New file. Needed to define the GLIBC_2.* * manual/socket.texi (Host Address Functions): Clarify description * sysdeps/unix/sysv/linux/alpha/bits/time.h (struct timeval):
Diffstat (limited to 'sysdeps/libm-ieee754/e_expf.c')
-rw-r--r--sysdeps/libm-ieee754/e_expf.c241
1 files changed, 147 insertions, 94 deletions
diff --git a/sysdeps/libm-ieee754/e_expf.c b/sysdeps/libm-ieee754/e_expf.c
index fbf2691bf9..08103aa271 100644
--- a/sysdeps/libm-ieee754/e_expf.c
+++ b/sysdeps/libm-ieee754/e_expf.c
@@ -1,104 +1,157 @@
-/* e_expf.c -- float version of e_exp.c.
- * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
- */
-
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
-
-#if defined(LIBM_SCCS) && !defined(lint)
-static char rcsid[] = "$NetBSD: e_expf.c,v 1.6 1996/04/08 15:43:43 phil Exp $";
-#endif
+/* Single-precision floating point e^x.
+ Copyright (C) 1997, 1998 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+ Contributed by Geoffrey Keating <geoffk@ozemail.com.au>
-#include "math.h"
-#include "math_private.h"
+ The GNU C Library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Library General Public License as
+ published by the Free Software Foundation; either version 2 of the
+ License, or (at your option) any later version.
-static const float huge = 1.0e+30;
+ 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
+ Library General Public License for more details.
-#ifdef __STDC__
-static const float
-#else
-static float
-#endif
-one = 1.0,
-halF[2] = {0.5,-0.5,},
-twom100 = 7.8886090522e-31, /* 2**-100=0x0d800000 */
-o_threshold= 8.8721679688e+01, /* 0x42b17180 */
-u_threshold= -1.0397208405e+02, /* 0xc2cff1b5 */
-ln2HI[2] ={ 6.9313812256e-01, /* 0x3f317180 */
- -6.9313812256e-01,}, /* 0xbf317180 */
-ln2LO[2] ={ 9.0580006145e-06, /* 0x3717f7d1 */
- -9.0580006145e-06,}, /* 0xb717f7d1 */
-invln2 = 1.4426950216e+00, /* 0x3fb8aa3b */
-P1 = 1.6666667163e-01, /* 0x3e2aaaab */
-P2 = -2.7777778450e-03, /* 0xbb360b61 */
-P3 = 6.6137559770e-05, /* 0x388ab355 */
-P4 = -1.6533901999e-06, /* 0xb5ddea0e */
-P5 = 4.1381369442e-08; /* 0x3331bb4c */
-
-#ifdef __STDC__
- float __ieee754_expf(float x) /* default IEEE double exp */
-#else
- float __ieee754_expf(x) /* default IEEE double exp */
- float x;
+ You should have received a copy of the GNU Library General Public
+ License along with the GNU C Library; see the file COPYING.LIB. If not,
+ write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
+ Boston, MA 02111-1307, USA. */
+
+/* How this works:
+
+ The input value, x, is written as
+
+ x = n * ln(2) + t/512 + delta[t] + x;
+
+ where:
+ - n is an integer, 127 >= n >= -150;
+ - t is an integer, 177 >= t >= -177
+ - delta is based on a table entry, delta[t] < 2^-28
+ - x is whatever is left, |x| < 2^-10
+
+ Then e^x is approximated as
+
+ e^x = 2^n ( e^(t/512 + delta[t])
+ + ( e^(t/512 + delta[t])
+ * ( p(x + delta[t] + n * ln(2)) - delta ) ) )
+
+ where
+ - p(x) is a polynomial approximating e(x)-1;
+ - e^(t/512 + delta[t]) is obtained from a table.
+
+ The table used is the same one as for the double precision version;
+ since we have the table, we might as well use it.
+
+ It turns out to be faster to do calculations in double precision than
+ to perform an 'accurate table method' expf, because of the range reduction
+ overhead (compare exp2f).
+ */
+#ifndef _GNU_SOURCE
+#define _GNU_SOURCE
#endif
+#include <float.h>
+#include <ieee754.h>
+#include <math.h>
+#include <fenv.h>
+#include <inttypes.h>
+#include <math_private.h>
+
+extern const float __exp_deltatable[178];
+extern const double __exp_atable[355] /* __attribute__((mode(DF))) */;
+
+static const volatile float TWOM100 = 7.88860905e-31;
+static const volatile float TWO127 = 1.7014118346e+38;
+
+float
+__ieee754_expf (float x)
{
- float y,hi,lo,c,t;
- int32_t k,xsb;
- u_int32_t hx;
-
- GET_FLOAT_WORD(hx,x);
- xsb = (hx>>31)&1; /* sign bit of x */
- hx &= 0x7fffffff; /* high word of |x| */
-
- /* filter out non-finite argument */
- if(hx >= 0x42b17218) { /* if |x|>=88.721... */
- if(hx>0x7f800000)
- return x+x; /* NaN */
- if(hx==0x7f800000)
- return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */
- if(x > o_threshold) return huge*huge; /* overflow */
- if(x < u_threshold) return twom100*twom100; /* underflow */
- }
+ static const uint32_t a_minf = 0xff800000;
+ static const float himark = 88.72283935546875;
+ static const float lomark = -103.972084045410;
+ /* Check for usual case. */
+ if (isless (x, himark) && isgreater (x, lomark))
+ {
+ static const float TWO43 = 8796093022208.0;
+ static const float TWO23 = 8388608.0;
+ /* 1/ln(2). */
+#undef M_1_LN2
+ static const float M_1_LN2 = 1.44269502163f;
+ /* ln(2) */
+#undef M_LN2
+ static const double M_LN2 = .6931471805599452862;
+
+ int tval;
+ double x22, t, result, dx;
+ float n, delta;
+ union ieee754_double ex2_u;
+ fenv_t oldenv;
+
+ feholdexcept (&oldenv);
+ fesetround (FE_TONEAREST);
- /* argument reduction */
- if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
- if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */
- hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
- } else {
- k = invln2*x+halF[xsb];
- t = k;
- hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */
- lo = t*ln2LO[0];
- }
- x = hi - lo;
+ /* Calculate n. */
+ if (x >= 0)
+ {
+ n = x * M_1_LN2 + TWO23;
+ n -= TWO23;
}
- else if(hx < 0x31800000) { /* when |x|<2**-28 */
- if(huge+x>one) return one+x;/* trigger inexact */
+ else
+ {
+ n = x * M_1_LN2 - TWO23;
+ n += TWO23;
}
- else k = 0;
-
- /* x is now in primary range */
- t = x*x;
- c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
- if(k==0) return one-((x*c)/(c-(float)2.0)-x);
- else y = one-((lo-(x*c)/((float)2.0-c))-hi);
- if(k >= -125) {
- u_int32_t hy;
- GET_FLOAT_WORD(hy,y);
- SET_FLOAT_WORD(y,hy+(k<<23)); /* add k to y's exponent */
- return y;
- } else {
- u_int32_t hy;
- GET_FLOAT_WORD(hy,y);
- SET_FLOAT_WORD(y,hy+((k+100)<<23)); /* add k to y's exponent */
- return y*twom100;
+ dx = x - n*M_LN2;
+ if (dx >= 0)
+ {
+ /* Calculate t/512. */
+ t = dx + TWO43;
+ t -= TWO43;
+ dx -= t;
+
+ /* Compute tval = t. */
+ tval = (int) (t * 512.0);
+
+ delta = - __exp_deltatable[tval];
}
+ else
+ {
+ /* As above, but x is negative. */
+ t = dx - TWO43;
+ t += TWO43;
+ dx -= t;
+
+ tval = (int) (t * 512.0);
+
+ delta = __exp_deltatable[-tval];
+ }
+
+ /* Compute ex2 = 2^n e^(t/512+delta[t]). */
+ ex2_u.d = __exp_atable[tval+177];
+ ex2_u.ieee.exponent += (int) n;
+
+ /* Approximate e^(dx+delta) - 1, using a second-degree polynomial,
+ with maximum error in [-2^-10-2^-28,2^-10+2^-28]
+ less than 5e-11. */
+ x22 = (0.5000000496709180453 * dx + 1.0000001192102037084) * dx + delta;
+
+ /* Return result. */
+ fesetenv (&oldenv);
+
+ result = x22 * ex2_u.d + ex2_u.d;
+ return (float) result;
+ }
+ /* Exceptional cases: */
+ else if (isless (x, himark))
+ {
+ if (x == *(const float *) &a_minf)
+ /* e^-inf == 0, with no error. */
+ return 0;
+ else
+ /* Underflow */
+ return TWOM100 * TWOM100;
+ }
+ else
+ /* Return x, if x is a NaN or Inf; or overflow, otherwise. */
+ return TWO127*x;
}