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Diffstat (limited to 'src/math/log1pl.c')
| -rw-r--r-- | src/math/log1pl.c | 176 |
1 files changed, 176 insertions, 0 deletions
diff --git a/src/math/log1pl.c b/src/math/log1pl.c new file mode 100644 index 00000000..7aafc5ce --- /dev/null +++ b/src/math/log1pl.c @@ -0,0 +1,176 @@ +/* origin: OpenBSD /usr/src/lib/libm/src/ld80/s_log1pl.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. + */ +/* + * Relative error logarithm + * Natural logarithm of 1+x, long double precision + * + * + * SYNOPSIS: + * + * long double x, y, log1pl(); + * + * y = log1pl( x ); + * + * + * DESCRIPTION: + * + * Returns the base e (2.718...) logarithm of 1+x. + * + * The argument 1+x is separated into its exponent and fractional + * parts. If the exponent is between -1 and +1, the logarithm + * of the fraction is approximated by + * + * log(1+x) = x - 0.5 x^2 + x^3 P(x)/Q(x). + * + * Otherwise, setting z = 2(x-1)/x+1), + * + * log(x) = z + z^3 P(z)/Q(z). + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE -1.0, 9.0 100000 8.2e-20 2.5e-20 + * + * ERROR MESSAGES: + * + * log singularity: x-1 = 0; returns -INFINITY + * log domain: x-1 < 0; returns NAN + */ + +#include "libm.h" + +#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 +long double log1pl(long double x) +{ + return log1p(x); +} +#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 +/* Coefficients for log(1+x) = x - x^2 / 2 + x^3 P(x)/Q(x) + * 1/sqrt(2) <= x < sqrt(2) + * Theoretical peak relative error = 2.32e-20 + */ +static long double P[] = { + 4.5270000862445199635215E-5L, + 4.9854102823193375972212E-1L, + 6.5787325942061044846969E0L, + 2.9911919328553073277375E1L, + 6.0949667980987787057556E1L, + 5.7112963590585538103336E1L, + 2.0039553499201281259648E1L, +}; +static long double Q[] = { +/* 1.0000000000000000000000E0,*/ + 1.5062909083469192043167E1L, + 8.3047565967967209469434E1L, + 2.2176239823732856465394E2L, + 3.0909872225312059774938E2L, + 2.1642788614495947685003E2L, + 6.0118660497603843919306E1L, +}; + +/* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2), + * where z = 2(x-1)/(x+1) + * 1/sqrt(2) <= x < sqrt(2) + * Theoretical peak relative error = 6.16e-22 + */ +static long double R[4] = { + 1.9757429581415468984296E-3L, +-7.1990767473014147232598E-1L, + 1.0777257190312272158094E1L, +-3.5717684488096787370998E1L, +}; +static long double S[4] = { +/* 1.00000000000000000000E0L,*/ +-2.6201045551331104417768E1L, + 1.9361891836232102174846E2L, +-4.2861221385716144629696E2L, +}; +static const long double C1 = 6.9314575195312500000000E-1L; +static const long double C2 = 1.4286068203094172321215E-6L; + +#define SQRTH 0.70710678118654752440L + +long double log1pl(long double xm1) +{ + long double x, y, z; + int e; + + if (isnan(xm1)) + return xm1; + if (xm1 == INFINITY) + return xm1; + if (xm1 == 0.0) + return xm1; + + x = xm1 + 1.0L; + + /* Test for domain errors. */ + if (x <= 0.0L) { + if (x == 0.0L) + return -INFINITY; + return NAN; + } + + /* Separate mantissa from exponent. + Use frexp so that denormal numbers will be handled properly. */ + x = frexpl(x, &e); + + /* logarithm using log(x) = z + z^3 P(z)/Q(z), + where z = 2(x-1)/x+1) */ + if (e > 2 || e < -2) { + if (x < SQRTH) { /* 2(2x-1)/(2x+1) */ + e -= 1; + z = x - 0.5L; + y = 0.5L * z + 0.5L; + } else { /* 2 (x-1)/(x+1) */ + z = x - 0.5L; + z -= 0.5L; + y = 0.5L * x + 0.5L; + } + x = z / y; + z = x*x; + z = x * (z * __polevll(z, R, 3) / __p1evll(z, S, 3)); + z = z + e * C2; + z = z + x; + z = z + e * C1; + return z; + } + + /* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */ + if (x < SQRTH) { + e -= 1; + if (e != 0) + x = 2.0 * x - 1.0L; + else + x = xm1; + } else { + if (e != 0) + x = x - 1.0L; + else + x = xm1; + } + z = x*x; + y = x * (z * __polevll(x, P, 6) / __p1evll(x, Q, 6)); + y = y + e * C2; + z = y - 0.5 * z; + z = z + x; + z = z + e * C1; + return z; +} +#endif |