mirror of
https://sourceware.org/git/glibc.git
synced 2024-11-25 14:30:06 +00:00
329 lines
9.3 KiB
C
329 lines
9.3 KiB
C
/*
|
|
* IBM Accurate Mathematical Library
|
|
* written by International Business Machines Corp.
|
|
* Copyright (C) 2001-2024 Free Software Foundation, Inc.
|
|
*
|
|
* This program 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 program 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 program; if not, see <https://www.gnu.org/licenses/>.
|
|
*/
|
|
/****************************************************************************/
|
|
/* */
|
|
/* MODULE_NAME:usncs.c */
|
|
/* */
|
|
/* FUNCTIONS: usin */
|
|
/* ucos */
|
|
/* FILES NEEDED: dla.h endian.h mpa.h mydefs.h usncs.h */
|
|
/* branred.c sincos.tbl */
|
|
/* */
|
|
/* An ultimate sin and cos routine. Given an IEEE double machine number x */
|
|
/* it computes sin(x) or cos(x) with ~0.55 ULP. */
|
|
/* Assumption: Machine arithmetic operations are performed in */
|
|
/* round to nearest mode of IEEE 754 standard. */
|
|
/* */
|
|
/****************************************************************************/
|
|
|
|
|
|
#include <errno.h>
|
|
#include <float.h>
|
|
#include "endian.h"
|
|
#include "mydefs.h"
|
|
#include "usncs.h"
|
|
#include <math.h>
|
|
#include <math_private.h>
|
|
#include <fenv_private.h>
|
|
#include <math-underflow.h>
|
|
#include <libm-alias-double.h>
|
|
#include <fenv.h>
|
|
|
|
/* Helper macros to compute sin of the input values. */
|
|
#define POLYNOMIAL2(xx) ((((s5 * (xx) + s4) * (xx) + s3) * (xx) + s2) * (xx))
|
|
|
|
#define POLYNOMIAL(xx) (POLYNOMIAL2 (xx) + s1)
|
|
|
|
/* The computed polynomial is a variation of the Taylor series expansion for
|
|
sin(x):
|
|
|
|
x - x^3/3! + x^5/5! - x^7/7! + x^9/9! - dx*x^2/2 + dx
|
|
|
|
The constants s1, s2, s3, etc. are pre-computed values of 1/3!, 1/5! and so
|
|
on. The result is returned to LHS. */
|
|
#define TAYLOR_SIN(xx, x, dx) \
|
|
({ \
|
|
double t = ((POLYNOMIAL (xx) * (x) - 0.5 * (dx)) * (xx) + (dx)); \
|
|
double res = (x) + t; \
|
|
res; \
|
|
})
|
|
|
|
#define SINCOS_TABLE_LOOKUP(u, sn, ssn, cs, ccs) \
|
|
({ \
|
|
int4 k = u.i[LOW_HALF] << 2; \
|
|
sn = __sincostab.x[k]; \
|
|
ssn = __sincostab.x[k + 1]; \
|
|
cs = __sincostab.x[k + 2]; \
|
|
ccs = __sincostab.x[k + 3]; \
|
|
})
|
|
|
|
#ifndef SECTION
|
|
# define SECTION
|
|
#endif
|
|
|
|
extern const union
|
|
{
|
|
int4 i[880];
|
|
double x[440];
|
|
} __sincostab attribute_hidden;
|
|
|
|
static const double
|
|
sn3 = -1.66666666666664880952546298448555E-01,
|
|
sn5 = 8.33333214285722277379541354343671E-03,
|
|
cs2 = 4.99999999999999999999950396842453E-01,
|
|
cs4 = -4.16666666666664434524222570944589E-02,
|
|
cs6 = 1.38888874007937613028114285595617E-03;
|
|
|
|
int __branred (double x, double *a, double *aa);
|
|
|
|
/* Given a number partitioned into X and DX, this function computes the cosine
|
|
of the number by combining the sin and cos of X (as computed by a variation
|
|
of the Taylor series) with the values looked up from the sin/cos table to
|
|
get the result. */
|
|
static __always_inline double
|
|
do_cos (double x, double dx)
|
|
{
|
|
mynumber u;
|
|
|
|
if (x < 0)
|
|
dx = -dx;
|
|
|
|
u.x = big + fabs (x);
|
|
x = fabs (x) - (u.x - big) + dx;
|
|
|
|
double xx, s, sn, ssn, c, cs, ccs, cor;
|
|
xx = x * x;
|
|
s = x + x * xx * (sn3 + xx * sn5);
|
|
c = xx * (cs2 + xx * (cs4 + xx * cs6));
|
|
SINCOS_TABLE_LOOKUP (u, sn, ssn, cs, ccs);
|
|
cor = (ccs - s * ssn - cs * c) - sn * s;
|
|
return cs + cor;
|
|
}
|
|
|
|
/* Given a number partitioned into X and DX, this function computes the sine of
|
|
the number by combining the sin and cos of X (as computed by a variation of
|
|
the Taylor series) with the values looked up from the sin/cos table to get
|
|
the result. */
|
|
static __always_inline double
|
|
do_sin (double x, double dx)
|
|
{
|
|
double xold = x;
|
|
/* Max ULP is 0.501 if |x| < 0.126, otherwise ULP is 0.518. */
|
|
if (fabs (x) < 0.126)
|
|
return TAYLOR_SIN (x * x, x, dx);
|
|
|
|
mynumber u;
|
|
|
|
if (x <= 0)
|
|
dx = -dx;
|
|
u.x = big + fabs (x);
|
|
x = fabs (x) - (u.x - big);
|
|
|
|
double xx, s, sn, ssn, c, cs, ccs, cor;
|
|
xx = x * x;
|
|
s = x + (dx + x * xx * (sn3 + xx * sn5));
|
|
c = x * dx + xx * (cs2 + xx * (cs4 + xx * cs6));
|
|
SINCOS_TABLE_LOOKUP (u, sn, ssn, cs, ccs);
|
|
cor = (ssn + s * ccs - sn * c) + cs * s;
|
|
return copysign (sn + cor, xold);
|
|
}
|
|
|
|
/* Reduce range of x to within PI/2 with abs (x) < 105414350. The high part
|
|
is written to *a, the low part to *da. Range reduction is accurate to 136
|
|
bits so that when x is large and *a very close to zero, all 53 bits of *a
|
|
are correct. */
|
|
static __always_inline int4
|
|
reduce_sincos (double x, double *a, double *da)
|
|
{
|
|
mynumber v;
|
|
|
|
double t = (x * hpinv + toint);
|
|
double xn = t - toint;
|
|
v.x = t;
|
|
double y = (x - xn * mp1) - xn * mp2;
|
|
int4 n = v.i[LOW_HALF] & 3;
|
|
|
|
double b, db, t1, t2;
|
|
t1 = xn * pp3;
|
|
t2 = y - t1;
|
|
db = (y - t2) - t1;
|
|
|
|
t1 = xn * pp4;
|
|
b = t2 - t1;
|
|
db += (t2 - b) - t1;
|
|
|
|
*a = b;
|
|
*da = db;
|
|
return n;
|
|
}
|
|
|
|
/* Compute sin or cos (A + DA) for the given quadrant N. */
|
|
static __always_inline double
|
|
do_sincos (double a, double da, int4 n)
|
|
{
|
|
double retval;
|
|
|
|
if (n & 1)
|
|
/* Max ULP is 0.513. */
|
|
retval = do_cos (a, da);
|
|
else
|
|
/* Max ULP is 0.501 if xx < 0.01588, otherwise ULP is 0.518. */
|
|
retval = do_sin (a, da);
|
|
|
|
return (n & 2) ? -retval : retval;
|
|
}
|
|
|
|
|
|
/*******************************************************************/
|
|
/* An ultimate sin routine. Given an IEEE double machine number x */
|
|
/* it computes the rounded value of sin(x). */
|
|
/*******************************************************************/
|
|
#ifndef IN_SINCOS
|
|
double
|
|
SECTION
|
|
__sin (double x)
|
|
{
|
|
double t, a, da;
|
|
mynumber u;
|
|
int4 k, m, n;
|
|
double retval = 0;
|
|
|
|
SET_RESTORE_ROUND_53BIT (FE_TONEAREST);
|
|
|
|
u.x = x;
|
|
m = u.i[HIGH_HALF];
|
|
k = 0x7fffffff & m; /* no sign */
|
|
if (k < 0x3e500000) /* if x->0 =>sin(x)=x */
|
|
{
|
|
math_check_force_underflow (x);
|
|
retval = x;
|
|
}
|
|
/*--------------------------- 2^-26<|x|< 0.855469---------------------- */
|
|
else if (k < 0x3feb6000)
|
|
{
|
|
/* Max ULP is 0.548. */
|
|
retval = do_sin (x, 0);
|
|
} /* else if (k < 0x3feb6000) */
|
|
|
|
/*----------------------- 0.855469 <|x|<2.426265 ----------------------*/
|
|
else if (k < 0x400368fd)
|
|
{
|
|
t = hp0 - fabs (x);
|
|
/* Max ULP is 0.51. */
|
|
retval = copysign (do_cos (t, hp1), x);
|
|
} /* else if (k < 0x400368fd) */
|
|
|
|
/*-------------------------- 2.426265<|x|< 105414350 ----------------------*/
|
|
else if (k < 0x419921FB)
|
|
{
|
|
n = reduce_sincos (x, &a, &da);
|
|
retval = do_sincos (a, da, n);
|
|
} /* else if (k < 0x419921FB ) */
|
|
|
|
/* --------------------105414350 <|x| <2^1024------------------------------*/
|
|
else if (k < 0x7ff00000)
|
|
{
|
|
n = __branred (x, &a, &da);
|
|
retval = do_sincos (a, da, n);
|
|
}
|
|
/*--------------------- |x| > 2^1024 ----------------------------------*/
|
|
else
|
|
{
|
|
if (k == 0x7ff00000 && u.i[LOW_HALF] == 0)
|
|
__set_errno (EDOM);
|
|
retval = x / x;
|
|
}
|
|
|
|
return retval;
|
|
}
|
|
|
|
|
|
/*******************************************************************/
|
|
/* An ultimate cos routine. Given an IEEE double machine number x */
|
|
/* it computes the rounded value of cos(x). */
|
|
/*******************************************************************/
|
|
|
|
double
|
|
SECTION
|
|
__cos (double x)
|
|
{
|
|
double y, a, da;
|
|
mynumber u;
|
|
int4 k, m, n;
|
|
|
|
double retval = 0;
|
|
|
|
SET_RESTORE_ROUND_53BIT (FE_TONEAREST);
|
|
|
|
u.x = x;
|
|
m = u.i[HIGH_HALF];
|
|
k = 0x7fffffff & m;
|
|
|
|
/* |x|<2^-27 => cos(x)=1 */
|
|
if (k < 0x3e400000)
|
|
retval = 1.0;
|
|
|
|
else if (k < 0x3feb6000)
|
|
{ /* 2^-27 < |x| < 0.855469 */
|
|
/* Max ULP is 0.51. */
|
|
retval = do_cos (x, 0);
|
|
} /* else if (k < 0x3feb6000) */
|
|
|
|
else if (k < 0x400368fd)
|
|
{ /* 0.855469 <|x|<2.426265 */ ;
|
|
y = hp0 - fabs (x);
|
|
a = y + hp1;
|
|
da = (y - a) + hp1;
|
|
/* Max ULP is 0.501 if xx < 0.01588 or 0.518 otherwise.
|
|
Range reduction uses 106 bits here which is sufficient. */
|
|
retval = do_sin (a, da);
|
|
} /* else if (k < 0x400368fd) */
|
|
|
|
else if (k < 0x419921FB)
|
|
{ /* 2.426265<|x|< 105414350 */
|
|
n = reduce_sincos (x, &a, &da);
|
|
retval = do_sincos (a, da, n + 1);
|
|
} /* else if (k < 0x419921FB ) */
|
|
|
|
/* 105414350 <|x| <2^1024 */
|
|
else if (k < 0x7ff00000)
|
|
{
|
|
n = __branred (x, &a, &da);
|
|
retval = do_sincos (a, da, n + 1);
|
|
}
|
|
|
|
else
|
|
{
|
|
if (k == 0x7ff00000 && u.i[LOW_HALF] == 0)
|
|
__set_errno (EDOM);
|
|
retval = x / x; /* |x| > 2^1024 */
|
|
}
|
|
|
|
return retval;
|
|
}
|
|
|
|
#ifndef __cos
|
|
libm_alias_double (__cos, cos)
|
|
#endif
|
|
#ifndef __sin
|
|
libm_alias_double (__sin, sin)
|
|
#endif
|
|
|
|
#endif
|