Szabolcs NagyandRich Felker
f4e4632abf
This is in preparation for the aarch64 port only to have the long double math symbols available on ld128 platforms. The implementations should be fixed up later once we have proper tests for these functions. Added bigendian handling for ld128 bit manipulations too.
124 lines
3.6 KiB
C
124 lines
3.6 KiB
C
/* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_expm1l.c */
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/*
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* Copyright (c) 2008 Stephen L. Moshier <[email protected]>
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*
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* Permission to use, copy, modify, and distribute this software for any
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* purpose with or without fee is hereby granted, provided that the above
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* copyright notice and this permission notice appear in all copies.
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*
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* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
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* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
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* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
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* ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
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* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
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* ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
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* OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
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*/
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/*
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* Exponential function, minus 1
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* Long double precision
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*
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*
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* SYNOPSIS:
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*
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* long double x, y, expm1l();
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*
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* y = expm1l( x );
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*
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*
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* DESCRIPTION:
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*
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* Returns e (2.71828...) raised to the x power, minus 1.
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*
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* Range reduction is accomplished by separating the argument
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* into an integer k and fraction f such that
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*
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* x k f
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* e = 2 e.
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*
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* An expansion x + .5 x^2 + x^3 R(x) approximates exp(f) - 1
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* in the basic range [-0.5 ln 2, 0.5 ln 2].
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*
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*
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* ACCURACY:
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*
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* Relative error:
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* arithmetic domain # trials peak rms
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* IEEE -45,+maxarg 200,000 1.2e-19 2.5e-20
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*/
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#include "libm.h"
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#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
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long double expm1l(long double x)
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{
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return expm1(x);
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}
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#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
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/* exp(x) - 1 = x + 0.5 x^2 + x^3 P(x)/Q(x)
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-.5 ln 2 < x < .5 ln 2
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Theoretical peak relative error = 3.4e-22 */
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static const long double
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P0 = -1.586135578666346600772998894928250240826E4L,
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P1 = 2.642771505685952966904660652518429479531E3L,
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P2 = -3.423199068835684263987132888286791620673E2L,
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P3 = 1.800826371455042224581246202420972737840E1L,
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P4 = -5.238523121205561042771939008061958820811E-1L,
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Q0 = -9.516813471998079611319047060563358064497E4L,
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Q1 = 3.964866271411091674556850458227710004570E4L,
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Q2 = -7.207678383830091850230366618190187434796E3L,
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Q3 = 7.206038318724600171970199625081491823079E2L,
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Q4 = -4.002027679107076077238836622982900945173E1L,
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/* Q5 = 1.000000000000000000000000000000000000000E0 */
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/* C1 + C2 = ln 2 */
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C1 = 6.93145751953125E-1L,
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C2 = 1.428606820309417232121458176568075500134E-6L,
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/* ln 2^-65 */
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minarg = -4.5054566736396445112120088E1L,
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/* ln 2^16384 */
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maxarg = 1.1356523406294143949492E4L;
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long double expm1l(long double x)
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{
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long double px, qx, xx;
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int k;
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if (isnan(x))
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return x;
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if (x > maxarg)
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return x*0x1p16383L; /* overflow, unless x==inf */
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if (x == 0.0)
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return x;
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if (x < minarg)
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return -1.0;
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xx = C1 + C2;
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/* Express x = ln 2 (k + remainder), remainder not exceeding 1/2. */
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px = floorl(0.5 + x / xx);
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k = px;
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/* remainder times ln 2 */
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x -= px * C1;
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x -= px * C2;
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/* Approximate exp(remainder ln 2).*/
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px = (((( P4 * x + P3) * x + P2) * x + P1) * x + P0) * x;
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qx = (((( x + Q4) * x + Q3) * x + Q2) * x + Q1) * x + Q0;
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xx = x * x;
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qx = x + (0.5 * xx + xx * px / qx);
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/* exp(x) = exp(k ln 2) exp(remainder ln 2) = 2^k exp(remainder ln 2).
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We have qx = exp(remainder ln 2) - 1, so
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exp(x) - 1 = 2^k (qx + 1) - 1 = 2^k qx + 2^k - 1. */
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px = scalbnl(1.0, k);
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x = px * qx + (px - 1.0);
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return x;
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}
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#elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384
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// TODO: broken implementation to make things compile
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long double expm1l(long double x)
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{
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return expm1(x);
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}
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#endif
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