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Diffstat (limited to 'sysdeps/ieee754/ldbl-128ibm/e_log2l.c')
| -rw-r--r-- | sysdeps/ieee754/ldbl-128ibm/e_log2l.c | 250 |
1 files changed, 0 insertions, 250 deletions
diff --git a/sysdeps/ieee754/ldbl-128ibm/e_log2l.c b/sysdeps/ieee754/ldbl-128ibm/e_log2l.c deleted file mode 100644 index fe8a8e1d6c..0000000000 --- a/sysdeps/ieee754/ldbl-128ibm/e_log2l.c +++ /dev/null @@ -1,250 +0,0 @@ -/* log2l.c - * Base 2 logarithm, 128-bit long double precision - * - * - * - * SYNOPSIS: - * - * long double x, y, log2l(); - * - * y = log2l( x ); - * - * - * - * DESCRIPTION: - * - * Returns the base 2 logarithm of x. - * - * The argument is separated into its exponent and fractional - * parts. If the exponent is between -1 and +1, the (natural) - * 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 0.5, 2.0 100,000 2.6e-34 4.9e-35 - * IEEE exp(+-10000) 100,000 9.6e-35 4.0e-35 - * - * In the tests over the interval exp(+-10000), the logarithms - * of the random arguments were uniformly distributed over - * [-10000, +10000]. - * - */ - -/* - Cephes Math Library Release 2.2: January, 1991 - Copyright 1984, 1991 by Stephen L. Moshier - Adapted for glibc November, 2001 - - 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" - -/* Coefficients for ln(1+x) = x - x**2/2 + x**3 P(x)/Q(x) - * 1/sqrt(2) <= x < sqrt(2) - * Theoretical peak relative error = 5.3e-37, - * relative peak error spread = 2.3e-14 - */ -static const long double P[13] = -{ - 1.313572404063446165910279910527789794488E4L, - 7.771154681358524243729929227226708890930E4L, - 2.014652742082537582487669938141683759923E5L, - 3.007007295140399532324943111654767187848E5L, - 2.854829159639697837788887080758954924001E5L, - 1.797628303815655343403735250238293741397E5L, - 7.594356839258970405033155585486712125861E4L, - 2.128857716871515081352991964243375186031E4L, - 3.824952356185897735160588078446136783779E3L, - 4.114517881637811823002128927449878962058E2L, - 2.321125933898420063925789532045674660756E1L, - 4.998469661968096229986658302195402690910E-1L, - 1.538612243596254322971797716843006400388E-6L -}; -static const long double Q[12] = -{ - 3.940717212190338497730839731583397586124E4L, - 2.626900195321832660448791748036714883242E5L, - 7.777690340007566932935753241556479363645E5L, - 1.347518538384329112529391120390701166528E6L, - 1.514882452993549494932585972882995548426E6L, - 1.158019977462989115839826904108208787040E6L, - 6.132189329546557743179177159925690841200E5L, - 2.248234257620569139969141618556349415120E5L, - 5.605842085972455027590989944010492125825E4L, - 9.147150349299596453976674231612674085381E3L, - 9.104928120962988414618126155557301584078E2L, - 4.839208193348159620282142911143429644326E1L -/* 1.000000000000000000000000000000000000000E0L, */ -}; - -/* 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 long double R[6] = -{ - 1.418134209872192732479751274970992665513E5L, - -8.977257995689735303686582344659576526998E4L, - 2.048819892795278657810231591630928516206E4L, - -2.024301798136027039250415126250455056397E3L, - 8.057002716646055371965756206836056074715E1L, - -8.828896441624934385266096344596648080902E-1L -}; -static const long double S[6] = -{ - 1.701761051846631278975701529965589676574E6L, - -1.332535117259762928288745111081235577029E6L, - 4.001557694070773974936904547424676279307E5L, - -5.748542087379434595104154610899551484314E4L, - 3.998526750980007367835804959888064681098E3L, - -1.186359407982897997337150403816839480438E2L -/* 1.000000000000000000000000000000000000000E0L, */ -}; - -static const long double -/* log2(e) - 1 */ -LOG2EA = 4.4269504088896340735992468100189213742664595E-1L, -/* sqrt(2)/2 */ -SQRTH = 7.071067811865475244008443621048490392848359E-1L; - - -/* Evaluate P[n] x^n + P[n-1] x^(n-1) + ... + P[0] */ - -static long double -neval (long double x, const long double *p, int n) -{ - long double y; - - p += n; - y = *p--; - do - { - y = y * x + *p--; - } - while (--n > 0); - return y; -} - - -/* Evaluate x^n+1 + P[n] x^(n) + P[n-1] x^(n-1) + ... + P[0] */ - -static long double -deval (long double x, const long double *p, int n) -{ - long double y; - - p += n; - y = x + *p--; - do - { - y = y * x + *p--; - } - while (--n > 0); - return y; -} - - - -long double -__ieee754_log2l (x) - long double x; -{ - long double z; - long double y; - int e; - int64_t hx, lx; - -/* Test for domain */ - GET_LDOUBLE_WORDS64 (hx, lx, x); - if (((hx & 0x7fffffffffffffffLL) | (lx & 0x7fffffffffffffffLL)) == 0) - return (-1.0L / (x - x)); - if (hx < 0) - return (x - x) / (x - x); - if (hx >= 0x7ff0000000000000LL) - return (x + x); - -/* separate mantissa from exponent */ - -/* Note, frexp is used 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; - y = x * (z * neval (z, R, 5) / deval (z, S, 5)); - goto done; - } - - -/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */ - - if (x < SQRTH) - { - e -= 1; - x = 2.0 * x - 1.0L; /* 2x - 1 */ - } - else - { - x = x - 1.0L; - } - z = x * x; - y = x * (z * neval (x, P, 12) / deval (x, Q, 11)); - y = y - 0.5 * z; - -done: - -/* Multiply log of fraction by log2(e) - * and base 2 exponent by 1 - */ - z = y * LOG2EA; - z += x * LOG2EA; - z += y; - z += x; - z += e; - return (z); -} |