diff options
Diffstat (limited to 'sysdeps/ieee754/ldbl-128/s_log1pl.c')
| -rw-r--r-- | sysdeps/ieee754/ldbl-128/s_log1pl.c | 256 |
1 files changed, 0 insertions, 256 deletions
diff --git a/sysdeps/ieee754/ldbl-128/s_log1pl.c b/sysdeps/ieee754/ldbl-128/s_log1pl.c deleted file mode 100644 index b8b2ffeba1..0000000000 --- a/sysdeps/ieee754/ldbl-128/s_log1pl.c +++ /dev/null @@ -1,256 +0,0 @@ -/* log1pl.c - * - * Relative error logarithm - * Natural logarithm of 1+x, 128-bit 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(w-1)/(w+1), - * - * log(w) = z + z^3 P(z)/Q(z). - * - * - * - * ACCURACY: - * - * Relative error: - * arithmetic domain # trials peak rms - * IEEE -1, 8 100000 1.9e-34 4.3e-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 <float.h> -#include <math.h> -#include <math_private.h> - -/* Coefficients for log(1+x) = x - x^2 / 2 + x^3 P(x)/Q(x) - * 1/sqrt(2) <= 1+x < sqrt(2) - * Theoretical peak relative error = 5.3e-37, - * relative peak error spread = 2.3e-14 - */ -static const _Float128 - P12 = L(1.538612243596254322971797716843006400388E-6), - P11 = L(4.998469661968096229986658302195402690910E-1), - P10 = L(2.321125933898420063925789532045674660756E1), - P9 = L(4.114517881637811823002128927449878962058E2), - P8 = L(3.824952356185897735160588078446136783779E3), - P7 = L(2.128857716871515081352991964243375186031E4), - P6 = L(7.594356839258970405033155585486712125861E4), - P5 = L(1.797628303815655343403735250238293741397E5), - P4 = L(2.854829159639697837788887080758954924001E5), - P3 = L(3.007007295140399532324943111654767187848E5), - P2 = L(2.014652742082537582487669938141683759923E5), - P1 = L(7.771154681358524243729929227226708890930E4), - P0 = L(1.313572404063446165910279910527789794488E4), - /* Q12 = 1.000000000000000000000000000000000000000E0L, */ - Q11 = L(4.839208193348159620282142911143429644326E1), - Q10 = L(9.104928120962988414618126155557301584078E2), - Q9 = L(9.147150349299596453976674231612674085381E3), - Q8 = L(5.605842085972455027590989944010492125825E4), - Q7 = L(2.248234257620569139969141618556349415120E5), - Q6 = L(6.132189329546557743179177159925690841200E5), - Q5 = L(1.158019977462989115839826904108208787040E6), - Q4 = L(1.514882452993549494932585972882995548426E6), - Q3 = L(1.347518538384329112529391120390701166528E6), - Q2 = L(7.777690340007566932935753241556479363645E5), - Q1 = L(2.626900195321832660448791748036714883242E5), - Q0 = L(3.940717212190338497730839731583397586124E4); - -/* 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 = 1.1e-35, - * relative peak error spread 1.1e-9 - */ -static const _Float128 - R5 = L(-8.828896441624934385266096344596648080902E-1), - R4 = L(8.057002716646055371965756206836056074715E1), - R3 = L(-2.024301798136027039250415126250455056397E3), - R2 = L(2.048819892795278657810231591630928516206E4), - R1 = L(-8.977257995689735303686582344659576526998E4), - R0 = L(1.418134209872192732479751274970992665513E5), - /* S6 = 1.000000000000000000000000000000000000000E0L, */ - S5 = L(-1.186359407982897997337150403816839480438E2), - S4 = L(3.998526750980007367835804959888064681098E3), - S3 = L(-5.748542087379434595104154610899551484314E4), - S2 = L(4.001557694070773974936904547424676279307E5), - S1 = L(-1.332535117259762928288745111081235577029E6), - S0 = L(1.701761051846631278975701529965589676574E6); - -/* C1 + C2 = ln 2 */ -static const _Float128 C1 = L(6.93145751953125E-1); -static const _Float128 C2 = L(1.428606820309417232121458176568075500134E-6); - -static const _Float128 sqrth = L(0.7071067811865475244008443621048490392848); -/* ln (2^16384 * (1 - 2^-113)) */ -static const _Float128 zero = 0; - -_Float128 -__log1pl (_Float128 xm1) -{ - _Float128 x, y, z, r, s; - ieee854_long_double_shape_type u; - int32_t hx; - int e; - - /* Test for NaN or infinity input. */ - u.value = xm1; - hx = u.parts32.w0; - if ((hx & 0x7fffffff) >= 0x7fff0000) - return xm1 + fabsl (xm1); - - /* log1p(+- 0) = +- 0. */ - if (((hx & 0x7fffffff) == 0) - && (u.parts32.w1 | u.parts32.w2 | u.parts32.w3) == 0) - return xm1; - - if ((hx & 0x7fffffff) < 0x3f8e0000) - { - math_check_force_underflow (xm1); - if ((int) xm1 == 0) - return xm1; - } - - if (xm1 >= L(0x1p113)) - x = xm1; - else - x = xm1 + 1; - - /* log1p(-1) = -inf */ - if (x <= 0) - { - if (x == 0) - return (-1 / zero); /* log1p(-1) = -inf */ - else - return (zero / (x - x)); - } - - /* Separate mantissa from exponent. */ - - /* Use frexp used so that denormal numbers will be handled properly. */ - x = __frexpl (x, &e); - - /* Logarithm using log(x) = z + z^3 P(z^2)/Q(z^2), - where z = 2(x-1)/x+1). */ - if ((e > 2) || (e < -2)) - { - if (x < sqrth) - { /* 2( 2x-1 )/( 2x+1 ) */ - e -= 1; - z = x - L(0.5); - y = L(0.5) * z + L(0.5); - } - else - { /* 2 (x-1)/(x+1) */ - z = x - L(0.5); - z -= L(0.5); - y = L(0.5) * x + L(0.5); - } - x = z / y; - z = x * x; - r = ((((R5 * z - + R4) * z - + R3) * z - + R2) * z - + R1) * z - + R0; - s = (((((z - + S5) * z - + S4) * z - + S3) * z - + S2) * z - + S1) * z - + S0; - z = x * (z * r / s); - 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 * x - 1; /* 2x - 1 */ - else - x = xm1; - } - else - { - if (e != 0) - x = x - 1; - else - x = xm1; - } - z = x * x; - r = (((((((((((P12 * x - + P11) * x - + P10) * x - + P9) * x - + P8) * x - + P7) * x - + P6) * x - + P5) * x - + P4) * x - + P3) * x - + P2) * x - + P1) * x - + P0; - s = (((((((((((x - + Q11) * x - + Q10) * x - + Q9) * x - + Q8) * x - + Q7) * x - + Q6) * x - + Q5) * x - + Q4) * x - + Q3) * x - + Q2) * x - + Q1) * x - + Q0; - y = x * (z * r / s); - y = y + e * C2; - z = y - L(0.5) * z; - z = z + x; - z = z + e * C1; - return (z); -} |