2001-05-15 07:57:46 +00:00
|
|
|
/* expm1l.c
|
|
|
|
*
|
|
|
|
* Exponential function, minus 1
|
|
|
|
* 128-bit long double precision
|
|
|
|
*
|
|
|
|
*
|
|
|
|
*
|
|
|
|
* SYNOPSIS:
|
|
|
|
*
|
|
|
|
* long double x, y, expm1l();
|
|
|
|
*
|
|
|
|
* y = expm1l( x );
|
|
|
|
*
|
|
|
|
*
|
|
|
|
*
|
|
|
|
* DESCRIPTION:
|
|
|
|
*
|
|
|
|
* Returns e (2.71828...) raised to the x power, minus one.
|
|
|
|
*
|
|
|
|
* Range reduction is accomplished by separating the argument
|
|
|
|
* into an integer k and fraction f such that
|
|
|
|
*
|
|
|
|
* x k f
|
|
|
|
* e = 2 e.
|
|
|
|
*
|
|
|
|
* An expansion x + .5 x^2 + x^3 R(x) approximates exp(f) - 1
|
|
|
|
* in the basic range [-0.5 ln 2, 0.5 ln 2].
|
|
|
|
*
|
|
|
|
*
|
|
|
|
* ACCURACY:
|
|
|
|
*
|
|
|
|
* Relative error:
|
|
|
|
* arithmetic domain # trials peak rms
|
|
|
|
* IEEE -79,+MAXLOG 100,000 1.7e-34 4.5e-35
|
|
|
|
*
|
|
|
|
*/
|
|
|
|
|
2013-06-05 20:44:03 +00:00
|
|
|
/* Copyright 2001 by Stephen L. Moshier
|
2002-08-26 22:40:48 +00:00
|
|
|
|
|
|
|
This 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.
|
|
|
|
|
|
|
|
This 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
|
2012-02-09 23:18:22 +00:00
|
|
|
License along with this library; if not, see
|
|
|
|
<http://www.gnu.org/licenses/>. */
|
2002-08-26 22:40:48 +00:00
|
|
|
|
2001-05-15 07:57:46 +00:00
|
|
|
|
|
|
|
|
2009-05-29 19:00:22 +00:00
|
|
|
#include <errno.h>
|
2012-03-09 19:29:16 +00:00
|
|
|
#include <math.h>
|
|
|
|
#include <math_private.h>
|
2001-05-15 07:57:46 +00:00
|
|
|
|
|
|
|
/* exp(x) - 1 = x + 0.5 x^2 + x^3 P(x)/Q(x)
|
|
|
|
-.5 ln 2 < x < .5 ln 2
|
|
|
|
Theoretical peak relative error = 8.1e-36 */
|
|
|
|
|
2001-10-14 22:33:08 +00:00
|
|
|
static const long double
|
2001-05-15 07:57:46 +00:00
|
|
|
P0 = 2.943520915569954073888921213330863757240E8L,
|
|
|
|
P1 = -5.722847283900608941516165725053359168840E7L,
|
|
|
|
P2 = 8.944630806357575461578107295909719817253E6L,
|
|
|
|
P3 = -7.212432713558031519943281748462837065308E5L,
|
|
|
|
P4 = 4.578962475841642634225390068461943438441E4L,
|
|
|
|
P5 = -1.716772506388927649032068540558788106762E3L,
|
|
|
|
P6 = 4.401308817383362136048032038528753151144E1L,
|
|
|
|
P7 = -4.888737542888633647784737721812546636240E-1L,
|
|
|
|
Q0 = 1.766112549341972444333352727998584753865E9L,
|
|
|
|
Q1 = -7.848989743695296475743081255027098295771E8L,
|
|
|
|
Q2 = 1.615869009634292424463780387327037251069E8L,
|
|
|
|
Q3 = -2.019684072836541751428967854947019415698E7L,
|
|
|
|
Q4 = 1.682912729190313538934190635536631941751E6L,
|
|
|
|
Q5 = -9.615511549171441430850103489315371768998E4L,
|
|
|
|
Q6 = 3.697714952261803935521187272204485251835E3L,
|
|
|
|
Q7 = -8.802340681794263968892934703309274564037E1L,
|
|
|
|
/* Q8 = 1.000000000000000000000000000000000000000E0 */
|
|
|
|
/* C1 + C2 = ln 2 */
|
|
|
|
|
|
|
|
C1 = 6.93145751953125E-1L,
|
|
|
|
C2 = 1.428606820309417232121458176568075500134E-6L,
|
|
|
|
/* ln (2^16384 * (1 - 2^-113)) */
|
|
|
|
maxlog = 1.1356523406294143949491931077970764891253E4L,
|
|
|
|
/* ln 2^-114 */
|
2010-01-17 01:55:37 +00:00
|
|
|
minarg = -7.9018778583833765273564461846232128760607E1L, big = 1e4932L;
|
2001-05-15 07:57:46 +00:00
|
|
|
|
|
|
|
|
|
|
|
long double
|
|
|
|
__expm1l (long double x)
|
|
|
|
{
|
|
|
|
long double px, qx, xx;
|
|
|
|
int32_t ix, sign;
|
|
|
|
ieee854_long_double_shape_type u;
|
|
|
|
int k;
|
|
|
|
|
|
|
|
/* Detect infinity and NaN. */
|
|
|
|
u.value = x;
|
|
|
|
ix = u.parts32.w0;
|
|
|
|
sign = ix & 0x80000000;
|
|
|
|
ix &= 0x7fffffff;
|
2012-03-13 07:31:48 +00:00
|
|
|
if (!sign && ix >= 0x40060000)
|
|
|
|
{
|
|
|
|
/* If num is positive and exp >= 6 use plain exp. */
|
|
|
|
return __expl (x);
|
|
|
|
}
|
2001-05-15 07:57:46 +00:00
|
|
|
if (ix >= 0x7fff0000)
|
|
|
|
{
|
|
|
|
/* Infinity. */
|
|
|
|
if (((ix & 0xffff) | u.parts32.w1 | u.parts32.w2 | u.parts32.w3) == 0)
|
|
|
|
{
|
|
|
|
if (sign)
|
|
|
|
return -1.0L;
|
|
|
|
else
|
|
|
|
return x;
|
|
|
|
}
|
2001-07-23 08:54:31 +00:00
|
|
|
/* NaN. No invalid exception. */
|
|
|
|
return x;
|
2001-05-15 07:57:46 +00:00
|
|
|
}
|
|
|
|
|
2001-07-23 08:54:31 +00:00
|
|
|
/* expm1(+- 0) = +- 0. */
|
|
|
|
if ((ix == 0) && (u.parts32.w1 | u.parts32.w2 | u.parts32.w3) == 0)
|
|
|
|
return x;
|
2001-10-14 22:33:08 +00:00
|
|
|
|
2001-07-23 08:54:31 +00:00
|
|
|
/* Overflow. */
|
|
|
|
if (x > maxlog)
|
2009-05-29 19:00:22 +00:00
|
|
|
{
|
|
|
|
__set_errno (ERANGE);
|
|
|
|
return (big * big);
|
|
|
|
}
|
2001-10-14 22:33:08 +00:00
|
|
|
|
2001-07-23 08:54:31 +00:00
|
|
|
/* Minimum value. */
|
|
|
|
if (x < minarg)
|
|
|
|
return (4.0/big - 1.0L);
|
|
|
|
|
2001-05-15 07:57:46 +00:00
|
|
|
/* Express x = ln 2 (k + remainder), remainder not exceeding 1/2. */
|
|
|
|
xx = C1 + C2; /* ln 2. */
|
|
|
|
px = __floorl (0.5 + x / xx);
|
|
|
|
k = px;
|
|
|
|
/* remainder times ln 2 */
|
|
|
|
x -= px * C1;
|
|
|
|
x -= px * C2;
|
|
|
|
|
|
|
|
/* Approximate exp(remainder ln 2). */
|
|
|
|
px = (((((((P7 * x
|
|
|
|
+ P6) * x
|
|
|
|
+ P5) * x + P4) * x + P3) * x + P2) * x + P1) * x + P0) * x;
|
|
|
|
|
|
|
|
qx = (((((((x
|
|
|
|
+ Q7) * x
|
|
|
|
+ Q6) * x + Q5) * x + Q4) * x + Q3) * x + Q2) * x + Q1) * x + Q0;
|
|
|
|
|
|
|
|
xx = x * x;
|
|
|
|
qx = x + (0.5 * xx + xx * px / qx);
|
|
|
|
|
|
|
|
/* exp(x) = exp(k ln 2) exp(remainder ln 2) = 2^k exp(remainder ln 2).
|
|
|
|
|
|
|
|
We have qx = exp(remainder ln 2) - 1, so
|
|
|
|
exp(x) - 1 = 2^k (qx + 1) - 1
|
|
|
|
= 2^k qx + 2^k - 1. */
|
|
|
|
|
2008-05-10 23:36:40 +00:00
|
|
|
px = __ldexpl (1.0L, k);
|
2001-05-15 07:57:46 +00:00
|
|
|
x = px * qx + (px - 1.0);
|
|
|
|
return x;
|
|
|
|
}
|
Update.
2002-09-09 Jakub Jelinek <jakub@redhat.com>
* include/math.h (__finite_internal, __finitef_internal,
__finitel_internal, __isinf_internal, __isnan_internal): Remove.
(isfinite): Remove.
(__finite, __isinf, __isnan, __finitef, __isinff, __isnanf, __finitel,
__isinfl, __isnanl): Add hidden_proto.
(__fpclassify, __fpclassifyf, __fpclassifyl, __expm1l): Add
libm_hidden_proto.
* math/Makefile (libm-calls): Add s_isinf and s_isnan.
* stdio-common/printf_fp.c (__printf_fp): Remove INTUSE from
__is{inf,nan} calls.
* stdio-common/printf_size.c (printf_size): Likewise.
* sysdeps/generic/printf_fphex.c (__printf_fphex): Likewise.
* sysdeps/generic/s_ldexp.c (__ldexp): Likewise.
* sysdeps/generic/s_ldexpf.c (__ldexpf): Likewise.
* sysdeps/generic/s_ldexpl.c (__ldexpl): Likewise.
* sysdeps/generic/s_expm1l.c (__expm1l): Add libm_hidden_def.
* sysdeps/i386/fpu/s_finite.S (__finite_internal): Remove alias.
(__finite): Add hidden_def.
* sysdeps/i386/fpu/s_finitef.S (__finitef_internal): Remove alias.
(__finitef): Add hidden_def.
* sysdeps/i386/fpu/s_finitel.S (__finitel_internal): Remove alias.
(__finitel): Add hidden_def.
* sysdeps/i386/fpu/s_isinfl.c (__isinfl): Remove INTDEF. Add
hidden_def.
* sysdeps/i386/fpu/s_isnanl.c (__isnanl): Likewise.
* sysdeps/i386/fpu/s_fpclassifyl.c (__fpclassifyl): Add
libm_hidden_def.
* sysdeps/i386/fpu/s_expm1l.S (__expm1l): Likewise.
* sysdeps/ieee754/dbl-64/s_finite.c (__finite): Remove INTDEF. Add
hidden_def.
* sysdeps/ieee754/dbl-64/s_isinf.c (__isinf): Likewise.
(__isinfl): Remove INTDEF.
* sysdeps/ieee754/dbl-64/s_isnan.c (__isnan): Remove INTDEF. Add
hidden_def.
(__isnanl): Remove INTDEF.
* sysdeps/ieee754/dbl-64/s_fpclassify.c (__fpclassify): Add
libm_hidden_def.
* sysdeps/ieee754/dbl-64/e_lgamma_r.c (sin_pi): Use __sin and __cos
instead of sin and cos.
* sysdeps/ieee754/flt-32/s_finitef.c (__finitef): Remove INTDEF.
Add hidden_def.
* sysdeps/ieee754/flt-32/s_isinff.c (__isinff): Likewise.
* sysdeps/ieee754/flt-32/s_isnanf.c (__isnanf): Likewise.
* sysdeps/ieee754/flt-32/s_fpclassifyf.c (__fpclassifyf): Add
libm_hidden_def.
* sysdeps/ieee754/ldbl-128/s_finitel.c (__finitel): Remove INTDEF.
Add hidden_def.
* sysdeps/ieee754/ldbl-128/s_isinfl.c (__isinfl): Likewise.
* sysdeps/ieee754/ldbl-128/s_isnanl.c (__isnanl): Likewise.
* sysdeps/ieee754/ldbl-128/s_fpclassifyl.c (__fpclassifyl): Add
libm_hidden_def.
* sysdeps/ieee754/ldbl-128/s_expm1l.c (__expm1l): Add
libm_hidden_def.
* sysdeps/ieee754/ldbl-96/s_finitel.c (__finitel): Remove INTDEF.
Add hidden_def.
* sysdeps/ieee754/ldbl-96/s_isinfl.c (__isinfl): Likewise.
* sysdeps/ieee754/ldbl-96/s_isnanl.c (__isnanl): Likewise.
* sysdeps/ieee754/ldbl-96/s_fpclassifyl.c (__fpclassifyl): Add
libm_hidden_def.
* sysdeps/ia64/fpu/s_finite.S (__finite_internal, __finitef_internal,
__finitel_internal): Remove aliases.
(__finite, __finitef, __finitel): Add hidden_def.
* sysdeps/ia64/fpu/s_isnan.S (__isnan_internal, __isnanf_internal,
__isnanl_internal): Remove aliases.
(__isnan, __isnanf, __isnanl): Add hidden_def.
* sysdeps/ia64/fpu/s_isinf.S (__isinf_internal, __isinff_internal,
__isinfl_internal): Remove aliases.
(__isinf, __isinff, __isinfl): Add hidden_def.
* sysdeps/ia64/fpu/s_fpclassify.S (__fpclassify, __fpclassifyf,
__fpclassifyl): Add libm_hidden_def.
* sysdeps/ia64/fpu/s_expm1l.S (__expm1l): Likewise.
* sysdeps/m68k/s_isinfl.c (__isinfl): Remove INTDEF. Add hidden_def.
* sysdeps/m68k/fpu/s_isinf.c (INTDEFX): Remove.
(hidden_defx): Define and use.
* sysdeps/m68k/fpu/s_fpclassifyl.c (__fpclassifyl): Add
libm_hidden_def.
* sysdeps/m68k/fpu/s_expm1l.c (__expm1l): Likewise.
* sysdeps/m68k/s_isnanl.c (__isnanl): Add hidden_def.
* sysdeps/powerpc/fpu/s_isnan.c (__isnan, __isnanf, __isnanl):
Remove INTDEF.
(__isnan, __isnanf): Add hidden_def.
* sysdeps/x86_64/fpu/s_finitel.S (__finitel_internal): Remove alias.
(__finitel): Add libm_hidden_def.
* sysdeps/x86_64/fpu/s_expm1l.S (__expm1l): Likewise.
* include/fenv.h (feraiseexcept, fesetenv): Add libm_hidden_proto.
* sysdeps/alpha/fpu/fesetenv.c (fesetenv): Add libm_hidden_ver.
* sysdeps/alpha/fpu/fraiseexcpt.c (feraiseexcept): Likewise.
* sysdeps/arm/fpu/fesetenv.c (fesetenv): Likewise.
* sysdeps/arm/fpu/fraiseexcpt.c (feraiseexcept): Likewise.
* sysdeps/generic/fesetenv.c (fesetenv): Likewise.
* sysdeps/generic/fraiseexcpt.c (feraiseexcept): Likewise.
* sysdeps/i386/fpu/fesetenv.c (fesetenv): Likewise.
* sysdeps/i386/fpu/fraiseexcpt.c (feraiseexcept): Likewise.
* sysdeps/m68k/fpu/fesetenv.c (fesetenv): Likewise.
* sysdeps/m68k/fpu/fraiseexcpt.c (feraiseexcept): Likewise.
* sysdeps/mips/fpu/fesetenv.c (fesetenv): Likewise.
* sysdeps/mips/fpu/fraiseexcpt.c (feraiseexcept): Likewise.
* sysdeps/powerpc/fpu/fesetenv.c (fesetenv): Likewise.
* sysdeps/powerpc/fpu/fraiseexcpt.c (feraiseexcept): Likewise.
* sysdeps/sparc/fpu/fesetenv.c (fesetenv): Likewise.
* sysdeps/sparc/fpu/fraiseexcpt.c (feraiseexcept): Likewise.
* sysdeps/hppa/fpu/fesetenv.c (fesetenv): Add libm_hidden_def.
* sysdeps/hppa/fpu/fraiseexcpt.c (feraiseexcept): Likewise.
* sysdeps/ia64/fpu/fesetenv.c (fesetenv): Likewise.
* sysdeps/ia64/fpu/fraiseexcpt.c (feraiseexcept): Likewise.
* sysdeps/sh/sh4/fpu/fesetenv.c (fesetenv): Likewise.
* sysdeps/sh/sh4/fpu/fraiseexcpt.c (feraiseexcept): Likewise.
* sysdeps/s390/fpu/fesetenv.c (fesetenv): Likewise.
* sysdeps/s390/fpu/fraiseexcpt.c (feraiseexcept): Likewise.
* sysdeps/x86_64/fpu/fesetenv.c (fesetenv): Likewise.
* sysdeps/x86_64/fpu/fraiseexcpt.c (feraiseexcept): Likewise.
2002-09-10 01:40:26 +00:00
|
|
|
libm_hidden_def (__expm1l)
|
2001-05-15 07:57:46 +00:00
|
|
|
weak_alias (__expm1l, expm1l)
|