Add kernel functions for 128-bit long doubles. These could be improved
a bit, but access to a freebsd/sparc64 machine is needed. Submitted by: bde and Steve Kargl <sgk@apl.washington.edu> (earlier version)
This commit is contained in:
David Schultz
parent
de336b0c5e
commit
61f955827d
61
lib/msun/ld128/k_cosl.c
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61
lib/msun/ld128/k_cosl.c
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/* From: @(#)k_cos.c 1.3 95/01/18 */
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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* Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans.
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*
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* Developed at SunSoft, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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#include <sys/cdefs.h>
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__FBSDID("$FreeBSD$");
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/*
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* ld128 version of k_cos.c. See ../src/k_cos.c for most comments.
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*/
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#include "math_private.h"
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/*
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* Domain [-0.7854, 0.7854], range ~[-1.80e-37, 1.79e-37]:
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* |cos(x) - c(x))| < 2**-122.0
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*
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* 113-bit precision requires more care than 64-bit precision, since
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* simple methods give a minimax polynomial with coefficient for x^2
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* that is 1 ulp below 0.5, but we want it to be precisely 0.5. See
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* ../ld80/k_cosl.c for more details.
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*/
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static const double
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one = 1.0;
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static const long double
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C1 = 0.04166666666666666666666666666666658424671L,
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C2 = -0.001388888888888888888888888888863490893732L,
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C3 = 0.00002480158730158730158730158600795304914210L,
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C4 = -0.2755731922398589065255474947078934284324e-6L,
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C5 = 0.2087675698786809897659225313136400793948e-8L,
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C6 = -0.1147074559772972315817149986812031204775e-10L,
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C7 = 0.4779477332386808976875457937252120293400e-13L;
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static const double
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C8 = -0.1561920696721507929516718307820958119868e-15,
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C9 = 0.4110317413744594971475941557607804508039e-18,
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C10 = -0.8896592467191938803288521958313920156409e-21,
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C11 = 0.1601061435794535138244346256065192782581e-23;
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long double
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__kernel_cosl(long double x, long double y)
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{
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long double hz,z,r,w;
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z = x*x;
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r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*(C6+z*(C7+
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z*(C8+z*(C9+z*(C10+z*C11))))))))));
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hz = 0.5*z;
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w = one-hz;
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return w + (((one-w)-hz) + (z*r-x*y));
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}
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59
lib/msun/ld128/k_sinl.c
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59
lib/msun/ld128/k_sinl.c
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/* From: @(#)k_sin.c 1.3 95/01/18 */
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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* Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans.
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*
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* Developed at SunSoft, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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#include <sys/cdefs.h>
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__FBSDID("$FreeBSD$");
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/*
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* ld128 version of k_sin.c. See ../src/k_sin.c for most comments.
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*/
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#include "math_private.h"
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static const double
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half = 0.5;
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/*
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* Domain [-0.7854, 0.7854], range ~[-1.53e-37, 1.659e-37]
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* |sin(x)/x - s(x)| < 2**-122.1
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*
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* See ../ld80/k_cosl.c for more details about the polynomial.
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*/
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static const long double
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S1 = -0.16666666666666666666666666666666666606732416116558L,
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S2 = 0.0083333333333333333333333333333331135404851288270047L,
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S3 = -0.00019841269841269841269841269839935785325638310428717L,
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S4 = 0.27557319223985890652557316053039946268333231205686e-5L,
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S5 = -0.25052108385441718775048214826384312253862930064745e-7L,
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S6 = 0.16059043836821614596571832194524392581082444805729e-9L,
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S7 = -0.76471637318198151807063387954939213287488216303768e-12L,
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S8 = 0.28114572543451292625024967174638477283187397621303e-14L;
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static const double
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S9 = -0.82206352458348947812512122163446202498005154296863e-17,
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S10 = 0.19572940011906109418080609928334380560135358385256e-19,
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S11 = -0.38680813379701966970673724299207480965452616911420e-22,
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S12 = 0.64038150078671872796678569586315881020659912139412e-25;
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long double
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__kernel_sinl(long double x, long double y, int iy)
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{
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long double z,r,v;
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z = x*x;
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v = z*x;
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r = S2+z*(S3+z*(S4+z*(S5+z*(S6+z*(S7+z*(S8+
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z*(S9+z*(S10+z*(S11+z*S12)))))))));
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if(iy==0) return x+v*(S1+z*r);
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else return x-((z*(half*y-v*r)-y)-v*S1);
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}
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119
lib/msun/ld128/k_tanl.c
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119
lib/msun/ld128/k_tanl.c
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@ -0,0 +1,119 @@
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/* From: @(#)k_tan.c 1.5 04/04/22 SMI */
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/*
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* ====================================================
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* Copyright 2004 Sun Microsystems, Inc. All Rights Reserved.
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* Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans.
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*
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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#include <sys/cdefs.h>
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__FBSDID("$FreeBSD$");
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/*
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* ld128 version of k_tan.c. See ../src/k_tan.c for most comments.
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*/
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#include "math.h"
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#include "math_private.h"
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/*
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* Domain [-0.67434, 0.67434], range ~[-3.37e-36, 1.982e-37]
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* |tan(x)/x - t(x)| < 2**-117.8 (XXX should be ~1e-37)
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*
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* See ../ld80/k_cosl.c for more details about the polynomial.
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*/
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static const long double
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T3 = 0x1.5555555555555555555555555553p-2L,
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T5 = 0x1.1111111111111111111111111eb5p-3L,
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T7 = 0x1.ba1ba1ba1ba1ba1ba1ba1b694cd6p-5L,
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T9 = 0x1.664f4882c10f9f32d6bbe09d8bcdp-6L,
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T11 = 0x1.226e355e6c23c8f5b4f5762322eep-7L,
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T13 = 0x1.d6d3d0e157ddfb5fed8e84e27b37p-9L,
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T15 = 0x1.7da36452b75e2b5fce9ee7c2c92ep-10L,
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T17 = 0x1.355824803674477dfcf726649efep-11L,
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T19 = 0x1.f57d7734d1656e0aceb716f614c2p-13L,
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T21 = 0x1.967e18afcb180ed942dfdc518d6cp-14L,
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T23 = 0x1.497d8eea21e95bc7e2aa79b9f2cdp-15L,
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T25 = 0x1.0b132d39f055c81be49eff7afd50p-16L,
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T27 = 0x1.b0f72d33eff7bfa2fbc1059d90b6p-18L,
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T29 = 0x1.5ef2daf21d1113df38d0fbc00267p-19L,
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T31 = 0x1.1c77d6eac0234988cdaa04c96626p-20L,
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T33 = 0x1.cd2a5a292b180e0bdd701057dfe3p-22L,
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T35 = 0x1.75c7357d0298c01a31d0a6f7d518p-23L,
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T37 = 0x1.2f3190f4718a9a520f98f50081fcp-24L,
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pio4 = 0x1.921fb54442d18469898cc51701b8p-1L,
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pio4lo = 0x1.cd129024e088a67cc74020bbea60p-116L;
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static const double
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T39 = 0.000000028443389121318352, /* 0x1e8a7592977938.0p-78 */
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T41 = 0.000000011981013102001973, /* 0x19baa1b1223219.0p-79 */
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T43 = 0.0000000038303578044958070, /* 0x107385dfb24529.0p-80 */
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T45 = 0.0000000034664378216909893, /* 0x1dc6c702a05262.0p-81 */
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T47 = -0.0000000015090641701997785, /* -0x19ecef3569ebb6.0p-82 */
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T49 = 0.0000000029449552300483952, /* 0x194c0668da786a.0p-81 */
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T51 = -0.0000000022006995706097711, /* -0x12e763b8845268.0p-81 */
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T53 = 0.0000000015468200913196612, /* 0x1a92fc98c29554.0p-82 */
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T55 = -0.00000000061311613386849674, /* -0x151106cbc779a9.0p-83 */
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T57 = 1.4912469681508012e-10; /* 0x147edbdba6f43a.0p-85 */
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long double
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__kernel_tanl(long double x, long double y, int iy) {
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long double z, r, v, w, s;
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long double osign;
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int i;
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iy = (iy == 1 ? -1 : 1); /* XXX recover original interface */
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osign = (x >= 0 ? 1.0 : -1.0); /* XXX slow, probably wrong for -0 */
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if (fabsl(x) >= 0.67434) {
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if (x < 0) {
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x = -x;
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y = -y;
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}
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z = pio4 - x;
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w = pio4lo - y;
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x = z + w;
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y = 0.0;
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i = 1;
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} else
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i = 0;
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z = x * x;
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w = z * z;
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r = T5 + w * (T9 + w * (T13 + w * (T17 + w * (T21 +
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w * (T25 + w * (T29 + w * (T33 +
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w * (T37 + w * (T41 + w * (T45 + w * (T49 + w * (T53 +
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w * T57))))))))))));
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v = z * (T7 + w * (T11 + w * (T15 + w * (T19 + w * (T23 +
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w * (T27 + w * (T31 + w * (T35 +
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w * (T39 + w * (T43 + w * (T47 + w * (T51 + w * T55))))))))))));
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s = z * x;
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r = y + z * (s * (r + v) + y);
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r += T3 * s;
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w = x + r;
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if (i == 1) {
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v = (long double) iy;
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return osign *
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(v - 2.0 * (x - (w * w / (w + v) - r)));
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}
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if (iy == 1)
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return w;
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else {
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/*
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* if allow error up to 2 ulp, simply return
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* -1.0 / (x+r) here
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*/
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/* compute -1.0 / (x+r) accurately */
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long double a, t;
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z = w;
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z = z + 0x1p32 - 0x1p32;
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v = r - (z - x); /* z+v = r+x */
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t = a = -1.0 / w; /* a = -1.0/w */
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t = t + 0x1p32 - 0x1p32;
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s = 1.0 + t * z;
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return t + a * (s + t * v);
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}
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}
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