mirror of
https://sourceware.org/git/glibc.git
synced 2024-11-16 01:50:11 +00:00
154 lines
4.7 KiB
C
154 lines
4.7 KiB
C
/*
|
|
* ====================================================
|
|
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
|
*
|
|
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
|
* Permission to use, copy, modify, and distribute this
|
|
* software is freely granted, provided that this notice
|
|
* is preserved.
|
|
* ====================================================
|
|
*/
|
|
|
|
/*
|
|
Long double expansions are
|
|
Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov>
|
|
and are incorporated herein by permission of the author. The author
|
|
reserves the right to distribute this material elsewhere under different
|
|
copying permissions. These modifications are distributed here under
|
|
the following terms:
|
|
|
|
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/>. */
|
|
|
|
/* __kernel_tanl( x, y, k )
|
|
* kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854
|
|
* Input x is assumed to be bounded by ~pi/4 in magnitude.
|
|
* Input y is the tail of x.
|
|
* Input k indicates whether tan (if k=1) or
|
|
* -1/tan (if k= -1) is returned.
|
|
*
|
|
* Algorithm
|
|
* 1. Since tan(-x) = -tan(x), we need only to consider positive x.
|
|
* 2. if x < 2^-57, return x with inexact if x!=0.
|
|
* 3. tan(x) is approximated by a rational form x + x^3 / 3 + x^5 R(x^2)
|
|
* on [0,0.67433].
|
|
*
|
|
* Note: tan(x+y) = tan(x) + tan'(x)*y
|
|
* ~ tan(x) + (1+x*x)*y
|
|
* Therefore, for better accuracy in computing tan(x+y), let
|
|
* r = x^3 * R(x^2)
|
|
* then
|
|
* tan(x+y) = x + (x^3 / 3 + (x^2 *(r+y)+y))
|
|
*
|
|
* 4. For x in [0.67433,pi/4], let y = pi/4 - x, then
|
|
* tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y))
|
|
* = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y)))
|
|
*/
|
|
|
|
#include <math.h>
|
|
#include <math_private.h>
|
|
static const long double
|
|
one = 1.0L,
|
|
pio4hi = 7.8539816339744830961566084581987569936977E-1L,
|
|
pio4lo = 2.1679525325309452561992610065108379921906E-35L,
|
|
|
|
/* tan x = x + x^3 / 3 + x^5 T(x^2)/U(x^2)
|
|
0 <= x <= 0.6743316650390625
|
|
Peak relative error 8.0e-36 */
|
|
TH = 3.333333333333333333333333333333333333333E-1L,
|
|
T0 = -1.813014711743583437742363284336855889393E7L,
|
|
T1 = 1.320767960008972224312740075083259247618E6L,
|
|
T2 = -2.626775478255838182468651821863299023956E4L,
|
|
T3 = 1.764573356488504935415411383687150199315E2L,
|
|
T4 = -3.333267763822178690794678978979803526092E-1L,
|
|
|
|
U0 = -1.359761033807687578306772463253710042010E8L,
|
|
U1 = 6.494370630656893175666729313065113194784E7L,
|
|
U2 = -4.180787672237927475505536849168729386782E6L,
|
|
U3 = 8.031643765106170040139966622980914621521E4L,
|
|
U4 = -5.323131271912475695157127875560667378597E2L;
|
|
/* 1.000000000000000000000000000000000000000E0 */
|
|
|
|
|
|
long double
|
|
__kernel_tanl (long double x, long double y, int iy)
|
|
{
|
|
long double z, r, v, w, s;
|
|
int32_t ix, sign;
|
|
ieee854_long_double_shape_type u, u1;
|
|
|
|
u.value = x;
|
|
ix = u.parts32.w0 & 0x7fffffff;
|
|
if (ix < 0x3fc60000) /* x < 2**-57 */
|
|
{
|
|
if ((int) x == 0)
|
|
{ /* generate inexact */
|
|
if ((ix | u.parts32.w1 | u.parts32.w2 | u.parts32.w3
|
|
| (iy + 1)) == 0)
|
|
return one / fabs (x);
|
|
else
|
|
return (iy == 1) ? x : -one / x;
|
|
}
|
|
}
|
|
if (ix >= 0x3ffe5942) /* |x| >= 0.6743316650390625 */
|
|
{
|
|
if ((u.parts32.w0 & 0x80000000) != 0)
|
|
{
|
|
x = -x;
|
|
y = -y;
|
|
sign = -1;
|
|
}
|
|
else
|
|
sign = 1;
|
|
z = pio4hi - x;
|
|
w = pio4lo - y;
|
|
x = z + w;
|
|
y = 0.0;
|
|
}
|
|
z = x * x;
|
|
r = T0 + z * (T1 + z * (T2 + z * (T3 + z * T4)));
|
|
v = U0 + z * (U1 + z * (U2 + z * (U3 + z * (U4 + z))));
|
|
r = r / v;
|
|
|
|
s = z * x;
|
|
r = y + z * (s * r + y);
|
|
r += TH * s;
|
|
w = x + r;
|
|
if (ix >= 0x3ffe5942)
|
|
{
|
|
v = (long double) iy;
|
|
w = (v - 2.0 * (x - (w * w / (w + v) - r)));
|
|
if (sign < 0)
|
|
w = -w;
|
|
return w;
|
|
}
|
|
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 */
|
|
u1.value = w;
|
|
u1.parts32.w2 = 0;
|
|
u1.parts32.w3 = 0;
|
|
v = r - (u1.value - x); /* u1+v = r+x */
|
|
z = -1.0 / w;
|
|
u.value = z;
|
|
u.parts32.w2 = 0;
|
|
u.parts32.w3 = 0;
|
|
s = 1.0 + u.value * u1.value;
|
|
return u.value + z * (s + u.value * v);
|
|
}
|
|
}
|