diff options
Diffstat (limited to 'sysdeps/ieee754/ldbl-128ibm/s_expm1l.c')
| -rw-r--r-- | sysdeps/ieee754/ldbl-128ibm/s_expm1l.c | 160 |
1 files changed, 0 insertions, 160 deletions
diff --git a/sysdeps/ieee754/ldbl-128ibm/s_expm1l.c b/sysdeps/ieee754/ldbl-128ibm/s_expm1l.c deleted file mode 100644 index 4908d4e..0000000 --- a/sysdeps/ieee754/ldbl-128ibm/s_expm1l.c +++ /dev/null @@ -1,160 +0,0 @@ -/* 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, write to the Free Software - Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */ - -#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 (2^16384 * (1 - 2^-113)) */ - maxlog = 1.1356523406294143949491931077970764891253E4L, -/* ln 2^-114 */ - minarg = -7.9018778583833765273564461846232128760607E1L, big = 2e307L; - - -long double -__expm1l (long double x) -{ - long double px, qx, xx; - int32_t ix, sign; - ieee854_long_double_shape_type u; - int k; - - /* Detect infinity and NaN. */ - u.value = x; - ix = u.parts32.w0; - sign = ix & 0x80000000; - ix &= 0x7fffffff; - if (ix >= 0x7ff00000) - { - /* Infinity. */ - if (((ix & 0xfffff) | u.parts32.w1 | (u.parts32.w2&0x7fffffff) | u.parts32.w3) == 0) - { - if (sign) - return -1.0L; - else - return x; - } - /* NaN. No invalid exception. */ - return x; - } - - /* expm1(+- 0) = +- 0. */ - if ((ix == 0) && (u.parts32.w1 | (u.parts32.w2&0x7fffffff) | u.parts32.w3) == 0) - return x; - - /* Overflow. */ - if (x > maxlog) - return (big * big); - - /* 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); |