GCC Code Coverage Report
Directory: ./ Exec Total Coverage
File: lib/libm/src/ld80/s_expm1l.c Lines: 0 25 0.0 %
Date: 2017-11-13 Branches: 0 6 0.0 %

Line Branch Exec Source
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/*	$OpenBSD: s_expm1l.c,v 1.3 2016/09/12 19:47:03 guenther Exp $	*/
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/*
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 * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
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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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/*							expm1l.c
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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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 *
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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,+MAXLOG   200,000     1.2e-19     2.5e-20
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 *
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 * ERROR MESSAGES:
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 *
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 *   message         condition      value returned
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 * expm1l overflow   x > MAXLOG         MAXNUM
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 *
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 */
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#include <math.h>
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static const long double MAXLOGL = 1.1356523406294143949492E4L;
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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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static const long double huge = 0x1p10000L;
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long double
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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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/* Overflow.  */
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if (x > MAXLOGL)
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  return (huge*huge);	/* overflow */
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if (x == 0.0)
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  return x;
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/* Minimum value.  */
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if (x < minarg)
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  return -1.0L;
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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
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	 + P3) * x
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	+ P2) * x
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       + P1) * x
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      + P0) * x;
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qx = (((( x
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	 + Q4) * x
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	+ Q3) * x
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       + Q2) * x
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      + Q1) * x
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     + 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 = ldexpl(1.0L, 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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DEF_STD(expm1l);