61f955827d
a bit, but access to a freebsd/sparc64 machine is needed. Submitted by: bde and Steve Kargl <sgk@apl.washington.edu> (earlier version)
120 lines
3.6 KiB
C
120 lines
3.6 KiB
C
/* From: @(#)k_tan.c 1.5 04/04/22 SMI */
|
|
|
|
/*
|
|
* ====================================================
|
|
* Copyright 2004 Sun Microsystems, Inc. All Rights Reserved.
|
|
* Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans.
|
|
*
|
|
* Permission to use, copy, modify, and distribute this
|
|
* software is freely granted, provided that this notice
|
|
* is preserved.
|
|
* ====================================================
|
|
*/
|
|
|
|
#include <sys/cdefs.h>
|
|
__FBSDID("$FreeBSD$");
|
|
|
|
/*
|
|
* ld128 version of k_tan.c. See ../src/k_tan.c for most comments.
|
|
*/
|
|
|
|
#include "math.h"
|
|
#include "math_private.h"
|
|
|
|
/*
|
|
* Domain [-0.67434, 0.67434], range ~[-3.37e-36, 1.982e-37]
|
|
* |tan(x)/x - t(x)| < 2**-117.8 (XXX should be ~1e-37)
|
|
*
|
|
* See ../ld80/k_cosl.c for more details about the polynomial.
|
|
*/
|
|
static const long double
|
|
T3 = 0x1.5555555555555555555555555553p-2L,
|
|
T5 = 0x1.1111111111111111111111111eb5p-3L,
|
|
T7 = 0x1.ba1ba1ba1ba1ba1ba1ba1b694cd6p-5L,
|
|
T9 = 0x1.664f4882c10f9f32d6bbe09d8bcdp-6L,
|
|
T11 = 0x1.226e355e6c23c8f5b4f5762322eep-7L,
|
|
T13 = 0x1.d6d3d0e157ddfb5fed8e84e27b37p-9L,
|
|
T15 = 0x1.7da36452b75e2b5fce9ee7c2c92ep-10L,
|
|
T17 = 0x1.355824803674477dfcf726649efep-11L,
|
|
T19 = 0x1.f57d7734d1656e0aceb716f614c2p-13L,
|
|
T21 = 0x1.967e18afcb180ed942dfdc518d6cp-14L,
|
|
T23 = 0x1.497d8eea21e95bc7e2aa79b9f2cdp-15L,
|
|
T25 = 0x1.0b132d39f055c81be49eff7afd50p-16L,
|
|
T27 = 0x1.b0f72d33eff7bfa2fbc1059d90b6p-18L,
|
|
T29 = 0x1.5ef2daf21d1113df38d0fbc00267p-19L,
|
|
T31 = 0x1.1c77d6eac0234988cdaa04c96626p-20L,
|
|
T33 = 0x1.cd2a5a292b180e0bdd701057dfe3p-22L,
|
|
T35 = 0x1.75c7357d0298c01a31d0a6f7d518p-23L,
|
|
T37 = 0x1.2f3190f4718a9a520f98f50081fcp-24L,
|
|
pio4 = 0x1.921fb54442d18469898cc51701b8p-1L,
|
|
pio4lo = 0x1.cd129024e088a67cc74020bbea60p-116L;
|
|
|
|
static const double
|
|
T39 = 0.000000028443389121318352, /* 0x1e8a7592977938.0p-78 */
|
|
T41 = 0.000000011981013102001973, /* 0x19baa1b1223219.0p-79 */
|
|
T43 = 0.0000000038303578044958070, /* 0x107385dfb24529.0p-80 */
|
|
T45 = 0.0000000034664378216909893, /* 0x1dc6c702a05262.0p-81 */
|
|
T47 = -0.0000000015090641701997785, /* -0x19ecef3569ebb6.0p-82 */
|
|
T49 = 0.0000000029449552300483952, /* 0x194c0668da786a.0p-81 */
|
|
T51 = -0.0000000022006995706097711, /* -0x12e763b8845268.0p-81 */
|
|
T53 = 0.0000000015468200913196612, /* 0x1a92fc98c29554.0p-82 */
|
|
T55 = -0.00000000061311613386849674, /* -0x151106cbc779a9.0p-83 */
|
|
T57 = 1.4912469681508012e-10; /* 0x147edbdba6f43a.0p-85 */
|
|
|
|
long double
|
|
__kernel_tanl(long double x, long double y, int iy) {
|
|
long double z, r, v, w, s;
|
|
long double osign;
|
|
int i;
|
|
|
|
iy = (iy == 1 ? -1 : 1); /* XXX recover original interface */
|
|
osign = (x >= 0 ? 1.0 : -1.0); /* XXX slow, probably wrong for -0 */
|
|
if (fabsl(x) >= 0.67434) {
|
|
if (x < 0) {
|
|
x = -x;
|
|
y = -y;
|
|
}
|
|
z = pio4 - x;
|
|
w = pio4lo - y;
|
|
x = z + w;
|
|
y = 0.0;
|
|
i = 1;
|
|
} else
|
|
i = 0;
|
|
z = x * x;
|
|
w = z * z;
|
|
r = T5 + w * (T9 + w * (T13 + w * (T17 + w * (T21 +
|
|
w * (T25 + w * (T29 + w * (T33 +
|
|
w * (T37 + w * (T41 + w * (T45 + w * (T49 + w * (T53 +
|
|
w * T57))))))))))));
|
|
v = z * (T7 + w * (T11 + w * (T15 + w * (T19 + w * (T23 +
|
|
w * (T27 + w * (T31 + w * (T35 +
|
|
w * (T39 + w * (T43 + w * (T47 + w * (T51 + w * T55))))))))))));
|
|
s = z * x;
|
|
r = y + z * (s * (r + v) + y);
|
|
r += T3 * s;
|
|
w = x + r;
|
|
if (i == 1) {
|
|
v = (long double) iy;
|
|
return osign *
|
|
(v - 2.0 * (x - (w * w / (w + v) - r)));
|
|
}
|
|
if (iy == 1)
|
|
return w;
|
|
else {
|
|
/*
|
|
* if allow error up to 2 ulp, simply return
|
|
* -1.0 / (x+r) here
|
|
*/
|
|
/* compute -1.0 / (x+r) accurately */
|
|
long double a, t;
|
|
z = w;
|
|
z = z + 0x1p32 - 0x1p32;
|
|
v = r - (z - x); /* z+v = r+x */
|
|
t = a = -1.0 / w; /* a = -1.0/w */
|
|
t = t + 0x1p32 - 0x1p32;
|
|
s = 1.0 + t * z;
|
|
return t + a * (s + t * v);
|
|
}
|
|
}
|