| Index: fusl/src/math/expm1l.c
|
| diff --git a/fusl/src/math/expm1l.c b/fusl/src/math/expm1l.c
|
| new file mode 100644
|
| index 0000000000000000000000000000000000000000..d17150785282f9ce2e566de629b0061cd8848207
|
| --- /dev/null
|
| +++ b/fusl/src/math/expm1l.c
|
| @@ -0,0 +1,123 @@
|
| +/* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_expm1l.c */
|
| +/*
|
| + * 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.
|
| + */
|
| +/*
|
| + * Exponential function, minus 1
|
| + * Long double precision
|
| + *
|
| + *
|
| + * SYNOPSIS:
|
| + *
|
| + * long double x, y, expm1l();
|
| + *
|
| + * y = expm1l( x );
|
| + *
|
| + *
|
| + * DESCRIPTION:
|
| + *
|
| + * Returns e (2.71828...) raised to the x power, minus 1.
|
| + *
|
| + * 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 -45,+maxarg 200,000 1.2e-19 2.5e-20
|
| + */
|
| +
|
| +#include "libm.h"
|
| +
|
| +#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
|
| +long double expm1l(long double x)
|
| +{
|
| + return expm1(x);
|
| +}
|
| +#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
|
| +
|
| +/* 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 = 3.4e-22 */
|
| +static const long double
|
| +P0 = -1.586135578666346600772998894928250240826E4L,
|
| +P1 = 2.642771505685952966904660652518429479531E3L,
|
| +P2 = -3.423199068835684263987132888286791620673E2L,
|
| +P3 = 1.800826371455042224581246202420972737840E1L,
|
| +P4 = -5.238523121205561042771939008061958820811E-1L,
|
| +Q0 = -9.516813471998079611319047060563358064497E4L,
|
| +Q1 = 3.964866271411091674556850458227710004570E4L,
|
| +Q2 = -7.207678383830091850230366618190187434796E3L,
|
| +Q3 = 7.206038318724600171970199625081491823079E2L,
|
| +Q4 = -4.002027679107076077238836622982900945173E1L,
|
| +/* Q5 = 1.000000000000000000000000000000000000000E0 */
|
| +/* C1 + C2 = ln 2 */
|
| +C1 = 6.93145751953125E-1L,
|
| +C2 = 1.428606820309417232121458176568075500134E-6L,
|
| +/* ln 2^-65 */
|
| +minarg = -4.5054566736396445112120088E1L,
|
| +/* ln 2^16384 */
|
| +maxarg = 1.1356523406294143949492E4L;
|
| +
|
| +long double expm1l(long double x)
|
| +{
|
| + long double px, qx, xx;
|
| + int k;
|
| +
|
| + if (isnan(x))
|
| + return x;
|
| + if (x > maxarg)
|
| + return x*0x1p16383L; /* overflow, unless x==inf */
|
| + if (x == 0.0)
|
| + return x;
|
| + if (x < minarg)
|
| + return -1.0;
|
| +
|
| + xx = C1 + C2;
|
| + /* Express x = ln 2 (k + remainder), remainder not exceeding 1/2. */
|
| + px = floorl(0.5 + x / xx);
|
| + k = px;
|
| + /* remainder times ln 2 */
|
| + x -= px * C1;
|
| + x -= px * C2;
|
| +
|
| + /* Approximate exp(remainder ln 2).*/
|
| + px = (((( P4 * x + P3) * x + P2) * x + P1) * x + P0) * x;
|
| + qx = (((( 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 = scalbnl(1.0, k);
|
| + x = px * qx + (px - 1.0);
|
| + return x;
|
| +}
|
| +#elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384
|
| +// TODO: broken implementation to make things compile
|
| +long double expm1l(long double x)
|
| +{
|
| + return expm1(x);
|
| +}
|
| +#endif
|
|
|