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Diffstat (limited to 'REORG.TODO/sysdeps/ieee754/ldbl-128/s_log1pl.c')
| -rw-r--r-- | REORG.TODO/sysdeps/ieee754/ldbl-128/s_log1pl.c | 256 |
1 files changed, 256 insertions, 0 deletions
diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_log1pl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_log1pl.c new file mode 100644 index 0000000000..b8b2ffeba1 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_log1pl.c @@ -0,0 +1,256 @@ +/* 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); +} |