mirror of
https://git.planet-casio.com/Lephenixnoir/OpenLibm.git
synced 2024-12-28 20:43:41 +01:00
7e5585aaca
This is a bit more consistent with the naming of the other header files (openlibm_complex.h and openlibm_fenv.h). Re-add an openlibm.h header that includes all of the public headers as a shorthand. Fix up all of the source files to include <openlibm_math.h> instead of <openlibm.h>. While there, fix ordering of the includes.
162 lines
4.4 KiB
C
162 lines
4.4 KiB
C
/* $OpenBSD: s_expm1l.c,v 1.1 2011/07/06 00:02:42 martynas Exp $ */
|
|
|
|
/*
|
|
* Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
|
|
*
|
|
* Permission to use, copy, modify, and distribute this software for any
|
|
* purpose with or without fee is hereby granted, provided that the above
|
|
* copyright notice and this permission notice appear in all copies.
|
|
*
|
|
* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
|
|
* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
|
|
* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
|
|
* ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
|
|
* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
|
|
* ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
|
|
* OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
|
|
*/
|
|
|
|
/* 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
|
|
*
|
|
*/
|
|
|
|
#include <errno.h>
|
|
#include <openlibm_math.h>
|
|
|
|
#include "math_private.h"
|
|
|
|
/* 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 */
|
|
|
|
static const long double
|
|
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 */
|
|
minarg = -7.9018778583833765273564461846232128760607E1L, big = 1e4932L;
|
|
|
|
|
|
long double
|
|
expm1l(long double x)
|
|
{
|
|
long double px, qx, xx;
|
|
int32_t ix, sign;
|
|
ieee_quad_shape_type u;
|
|
int k;
|
|
|
|
/* Detect infinity and NaN. */
|
|
u.value = x;
|
|
ix = u.parts32.mswhi;
|
|
sign = ix & 0x80000000;
|
|
ix &= 0x7fffffff;
|
|
if (ix >= 0x7fff0000)
|
|
{
|
|
/* Infinity. */
|
|
if (((ix & 0xffff) | u.parts32.mswlo | u.parts32.lswhi |
|
|
u.parts32.lswlo) == 0)
|
|
{
|
|
if (sign)
|
|
return -1.0L;
|
|
else
|
|
return x;
|
|
}
|
|
/* NaN. No invalid exception. */
|
|
return x;
|
|
}
|
|
|
|
/* expm1(+- 0) = +- 0. */
|
|
if ((ix == 0) && (u.parts32.mswlo | u.parts32.lswhi | u.parts32.lswlo) == 0)
|
|
return x;
|
|
|
|
/* Overflow. */
|
|
if (x > maxlog)
|
|
return (big * big);
|
|
|
|
/* Minimum value. */
|
|
if (x < minarg)
|
|
return (4.0/big - 1.0L);
|
|
|
|
/* 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. */
|
|
|
|
px = ldexpl (1.0L, k);
|
|
x = px * qx + (px - 1.0);
|
|
return x;
|
|
}
|