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Diffstat (limited to 'REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_expm1l.c')
-rw-r--r-- | REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_expm1l.c | 152 |
1 files changed, 152 insertions, 0 deletions
diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_expm1l.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_expm1l.c new file mode 100644 index 0000000000..42d57c6eec --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/s_expm1l.c @@ -0,0 +1,152 @@ +/* expm1l.c + * + * Exponential function, minus 1 + * 128-bit long double precision + * + * + * + * SYNOPSIS: + * + * long double x, y, expm1l(); + * + * y = expm1l( x ); + * + * + * + * DESCRIPTION: + * + * Returns e (2.71828...) raised to the x power, minus one. + * + * 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 -79,+MAXLOG 100,000 1.7e-34 4.5e-35 + * + */ + +/* Copyright 2001 by Stephen L. Moshier + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <errno.h> +#include <math.h> +#include <math_private.h> +#include <math_ldbl_opt.h> + +/* 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 = 8.1e-36 */ + +static const long double + P0 = 2.943520915569954073888921213330863757240E8L, + P1 = -5.722847283900608941516165725053359168840E7L, + P2 = 8.944630806357575461578107295909719817253E6L, + P3 = -7.212432713558031519943281748462837065308E5L, + P4 = 4.578962475841642634225390068461943438441E4L, + P5 = -1.716772506388927649032068540558788106762E3L, + P6 = 4.401308817383362136048032038528753151144E1L, + P7 = -4.888737542888633647784737721812546636240E-1L, + Q0 = 1.766112549341972444333352727998584753865E9L, + Q1 = -7.848989743695296475743081255027098295771E8L, + Q2 = 1.615869009634292424463780387327037251069E8L, + Q3 = -2.019684072836541751428967854947019415698E7L, + Q4 = 1.682912729190313538934190635536631941751E6L, + Q5 = -9.615511549171441430850103489315371768998E4L, + Q6 = 3.697714952261803935521187272204485251835E3L, + Q7 = -8.802340681794263968892934703309274564037E1L, + /* Q8 = 1.000000000000000000000000000000000000000E0 */ +/* C1 + C2 = ln 2 */ + + C1 = 6.93145751953125E-1L, + C2 = 1.428606820309417232121458176568075500134E-6L, +/* ln 2^-114 */ + minarg = -7.9018778583833765273564461846232128760607E1L, big = 1e290L; + + +long double +__expm1l (long double x) +{ + long double px, qx, xx; + int32_t ix, lx, sign; + int k; + double xhi; + + /* Detect infinity and NaN. */ + xhi = ldbl_high (x); + EXTRACT_WORDS (ix, lx, xhi); + sign = ix & 0x80000000; + ix &= 0x7fffffff; + if (!sign && ix >= 0x40600000) + return __expl (x); + if (ix >= 0x7ff00000) + { + /* Infinity (which must be negative infinity). */ + if (((ix - 0x7ff00000) | lx) == 0) + return -1.0L; + /* NaN. Invalid exception if signaling. */ + return x + x; + } + + /* expm1(+- 0) = +- 0. */ + if ((ix | lx) == 0) + return x; + + /* Minimum value. */ + if (x < minarg) + return (4.0/big - 1.0L); + + /* Express x = ln 2 (k + remainder), remainder not exceeding 1/2. */ + xx = C1 + C2; /* ln 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 = (((((((P7 * x + + P6) * x + + P5) * x + P4) * x + P3) * x + P2) * x + P1) * x + P0) * x; + + qx = (((((((x + + Q7) * x + + Q6) * x + Q5) * 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 = __ldexpl (1.0L, k); + x = px * qx + (px - 1.0); + return x; +} +libm_hidden_def (__expm1l) +long_double_symbol (libm, __expm1l, expm1l); |