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Diffstat (limited to 'src/math/expl.c')
-rw-r--r-- | src/math/expl.c | 127 |
1 files changed, 127 insertions, 0 deletions
diff --git a/src/math/expl.c b/src/math/expl.c new file mode 100644 index 00000000..898cf1a5 --- /dev/null +++ b/src/math/expl.c @@ -0,0 +1,127 @@ +/* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_expl.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, long double precision + * + * + * SYNOPSIS: + * + * long double x, y, expl(); + * + * y = expl( x ); + * + * + * DESCRIPTION: + * + * Returns e (2.71828...) raised to the x power. + * + * Range reduction is accomplished by separating the argument + * into an integer k and fraction f such that + * + * x k f + * e = 2 e. + * + * A Pade' form of degree 2/3 is used to approximate exp(f) - 1 + * in the basic range [-0.5 ln 2, 0.5 ln 2]. + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE +-10000 50000 1.12e-19 2.81e-20 + * + * + * Error amplification in the exponential function can be + * a serious matter. The error propagation involves + * exp( X(1+delta) ) = exp(X) ( 1 + X*delta + ... ), + * which shows that a 1 lsb error in representing X produces + * a relative error of X times 1 lsb in the function. + * While the routine gives an accurate result for arguments + * that are exactly represented by a long double precision + * computer number, the result contains amplified roundoff + * error for large arguments not exactly represented. + * + * + * ERROR MESSAGES: + * + * message condition value returned + * exp underflow x < MINLOG 0.0 + * exp overflow x > MAXLOG MAXNUM + * + */ + +#include "libm.h" + +#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 +long double expl(long double x) +{ + return exp(x); +} +#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 + +static long double P[3] = { + 1.2617719307481059087798E-4L, + 3.0299440770744196129956E-2L, + 9.9999999999999999991025E-1L, +}; +static long double Q[4] = { + 3.0019850513866445504159E-6L, + 2.5244834034968410419224E-3L, + 2.2726554820815502876593E-1L, + 2.0000000000000000000897E0L, +}; +static const long double +C1 = 6.9314575195312500000000E-1L, +C2 = 1.4286068203094172321215E-6L, +MAXLOGL = 1.1356523406294143949492E4L, +MINLOGL = -1.13994985314888605586758E4L, +LOG2EL = 1.4426950408889634073599E0L; + +long double expl(long double x) +{ + long double px, xx; + int n; + + if (isnan(x)) + return x; + if (x > MAXLOGL) + return INFINITY; + if (x < MINLOGL) + return 0.0L; + + /* Express e**x = e**g 2**n + * = e**g e**(n loge(2)) + * = e**(g + n loge(2)) + */ + px = floorl(LOG2EL * x + 0.5L); /* floor() truncates toward -infinity. */ + n = px; + x -= px * C1; + x -= px * C2; + + /* rational approximation for exponential + * of the fractional part: + * e**x = 1 + 2x P(x**2)/(Q(x**2) - P(x**2)) + */ + xx = x * x; + px = x * __polevll(xx, P, 2); + x = px/(__polevll(xx, Q, 3) - px); + x = 1.0L + ldexpl(x, 1); + x = ldexpl(x, n); + return x; +} +#endif |