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47ad14d789
Finally remove all mpa related files, headers, declarations, probes, unused tables and update makefiles. Reviewed-By: Paul Zimmermann <Paul.Zimmermann@inria.fr>
329 lines
9.3 KiB
C
329 lines
9.3 KiB
C
/*
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* IBM Accurate Mathematical Library
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* written by International Business Machines Corp.
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* Copyright (C) 2001-2021 Free Software Foundation, Inc.
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU Lesser General Public License as published by
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* the Free Software Foundation; either version 2.1 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU Lesser General Public License for more details.
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*
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* You should have received a copy of the GNU Lesser General Public License
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* along with this program; if not, see <https://www.gnu.org/licenses/>.
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*/
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/****************************************************************************/
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/* */
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/* MODULE_NAME:usncs.c */
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/* */
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/* FUNCTIONS: usin */
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/* ucos */
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/* FILES NEEDED: dla.h endian.h mpa.h mydefs.h usncs.h */
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/* branred.c sincos.tbl */
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/* */
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/* An ultimate sin and cos routine. Given an IEEE double machine number x */
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/* it computes sin(x) or cos(x) with ~0.55 ULP. */
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/* Assumption: Machine arithmetic operations are performed in */
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/* round to nearest mode of IEEE 754 standard. */
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/* */
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/****************************************************************************/
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#include <errno.h>
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#include <float.h>
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#include "endian.h"
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#include "mydefs.h"
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#include "usncs.h"
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#include <math.h>
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#include <math_private.h>
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#include <fenv_private.h>
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#include <math-underflow.h>
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#include <libm-alias-double.h>
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#include <fenv.h>
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/* Helper macros to compute sin of the input values. */
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#define POLYNOMIAL2(xx) ((((s5 * (xx) + s4) * (xx) + s3) * (xx) + s2) * (xx))
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#define POLYNOMIAL(xx) (POLYNOMIAL2 (xx) + s1)
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/* The computed polynomial is a variation of the Taylor series expansion for
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sin(a):
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a - a^3/3! + a^5/5! - a^7/7! + a^9/9! + (1 - a^2) * da / 2
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The constants s1, s2, s3, etc. are pre-computed values of 1/3!, 1/5! and so
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on. The result is returned to LHS. */
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#define TAYLOR_SIN(xx, a, da) \
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({ \
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double t = ((POLYNOMIAL (xx) * (a) - 0.5 * (da)) * (xx) + (da)); \
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double res = (a) + t; \
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res; \
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})
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#define SINCOS_TABLE_LOOKUP(u, sn, ssn, cs, ccs) \
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({ \
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int4 k = u.i[LOW_HALF] << 2; \
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sn = __sincostab.x[k]; \
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ssn = __sincostab.x[k + 1]; \
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cs = __sincostab.x[k + 2]; \
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ccs = __sincostab.x[k + 3]; \
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})
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#ifndef SECTION
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# define SECTION
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#endif
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extern const union
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{
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int4 i[880];
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double x[440];
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} __sincostab attribute_hidden;
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static const double
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sn3 = -1.66666666666664880952546298448555E-01,
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sn5 = 8.33333214285722277379541354343671E-03,
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cs2 = 4.99999999999999999999950396842453E-01,
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cs4 = -4.16666666666664434524222570944589E-02,
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cs6 = 1.38888874007937613028114285595617E-03;
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int __branred (double x, double *a, double *aa);
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/* Given a number partitioned into X and DX, this function computes the cosine
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of the number by combining the sin and cos of X (as computed by a variation
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of the Taylor series) with the values looked up from the sin/cos table to
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get the result. */
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static __always_inline double
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do_cos (double x, double dx)
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{
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mynumber u;
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if (x < 0)
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dx = -dx;
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u.x = big + fabs (x);
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x = fabs (x) - (u.x - big) + dx;
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double xx, s, sn, ssn, c, cs, ccs, cor;
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xx = x * x;
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s = x + x * xx * (sn3 + xx * sn5);
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c = xx * (cs2 + xx * (cs4 + xx * cs6));
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SINCOS_TABLE_LOOKUP (u, sn, ssn, cs, ccs);
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cor = (ccs - s * ssn - cs * c) - sn * s;
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return cs + cor;
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}
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/* Given a number partitioned into X and DX, this function computes the sine of
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the number by combining the sin and cos of X (as computed by a variation of
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the Taylor series) with the values looked up from the sin/cos table to get
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the result. */
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static __always_inline double
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do_sin (double x, double dx)
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{
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double xold = x;
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/* Max ULP is 0.501 if |x| < 0.126, otherwise ULP is 0.518. */
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if (fabs (x) < 0.126)
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return TAYLOR_SIN (x * x, x, dx);
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mynumber u;
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if (x <= 0)
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dx = -dx;
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u.x = big + fabs (x);
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x = fabs (x) - (u.x - big);
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double xx, s, sn, ssn, c, cs, ccs, cor;
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xx = x * x;
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s = x + (dx + x * xx * (sn3 + xx * sn5));
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c = x * dx + xx * (cs2 + xx * (cs4 + xx * cs6));
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SINCOS_TABLE_LOOKUP (u, sn, ssn, cs, ccs);
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cor = (ssn + s * ccs - sn * c) + cs * s;
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return copysign (sn + cor, xold);
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}
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/* Reduce range of x to within PI/2 with abs (x) < 105414350. The high part
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is written to *a, the low part to *da. Range reduction is accurate to 136
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bits so that when x is large and *a very close to zero, all 53 bits of *a
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are correct. */
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static __always_inline int4
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reduce_sincos (double x, double *a, double *da)
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{
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mynumber v;
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double t = (x * hpinv + toint);
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double xn = t - toint;
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v.x = t;
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double y = (x - xn * mp1) - xn * mp2;
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int4 n = v.i[LOW_HALF] & 3;
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double b, db, t1, t2;
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t1 = xn * pp3;
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t2 = y - t1;
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db = (y - t2) - t1;
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t1 = xn * pp4;
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b = t2 - t1;
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db += (t2 - b) - t1;
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*a = b;
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*da = db;
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return n;
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}
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/* Compute sin or cos (A + DA) for the given quadrant N. */
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static __always_inline double
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do_sincos (double a, double da, int4 n)
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{
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double retval;
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if (n & 1)
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/* Max ULP is 0.513. */
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retval = do_cos (a, da);
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else
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/* Max ULP is 0.501 if xx < 0.01588, otherwise ULP is 0.518. */
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retval = do_sin (a, da);
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return (n & 2) ? -retval : retval;
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}
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/*******************************************************************/
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/* An ultimate sin routine. Given an IEEE double machine number x */
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/* it computes the rounded value of sin(x). */
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/*******************************************************************/
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#ifndef IN_SINCOS
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double
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SECTION
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__sin (double x)
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{
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double t, a, da;
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mynumber u;
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int4 k, m, n;
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double retval = 0;
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SET_RESTORE_ROUND_53BIT (FE_TONEAREST);
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u.x = x;
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m = u.i[HIGH_HALF];
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k = 0x7fffffff & m; /* no sign */
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if (k < 0x3e500000) /* if x->0 =>sin(x)=x */
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{
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math_check_force_underflow (x);
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retval = x;
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}
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/*--------------------------- 2^-26<|x|< 0.855469---------------------- */
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else if (k < 0x3feb6000)
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{
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/* Max ULP is 0.548. */
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retval = do_sin (x, 0);
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} /* else if (k < 0x3feb6000) */
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/*----------------------- 0.855469 <|x|<2.426265 ----------------------*/
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else if (k < 0x400368fd)
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{
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t = hp0 - fabs (x);
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/* Max ULP is 0.51. */
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retval = copysign (do_cos (t, hp1), x);
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} /* else if (k < 0x400368fd) */
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/*-------------------------- 2.426265<|x|< 105414350 ----------------------*/
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else if (k < 0x419921FB)
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{
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n = reduce_sincos (x, &a, &da);
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retval = do_sincos (a, da, n);
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} /* else if (k < 0x419921FB ) */
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/* --------------------105414350 <|x| <2^1024------------------------------*/
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else if (k < 0x7ff00000)
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{
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n = __branred (x, &a, &da);
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retval = do_sincos (a, da, n);
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}
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/*--------------------- |x| > 2^1024 ----------------------------------*/
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else
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{
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if (k == 0x7ff00000 && u.i[LOW_HALF] == 0)
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__set_errno (EDOM);
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retval = x / x;
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}
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return retval;
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}
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/*******************************************************************/
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/* An ultimate cos routine. Given an IEEE double machine number x */
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/* it computes the rounded value of cos(x). */
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/*******************************************************************/
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double
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SECTION
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__cos (double x)
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{
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double y, a, da;
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mynumber u;
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int4 k, m, n;
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double retval = 0;
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SET_RESTORE_ROUND_53BIT (FE_TONEAREST);
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u.x = x;
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m = u.i[HIGH_HALF];
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k = 0x7fffffff & m;
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/* |x|<2^-27 => cos(x)=1 */
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if (k < 0x3e400000)
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retval = 1.0;
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else if (k < 0x3feb6000)
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{ /* 2^-27 < |x| < 0.855469 */
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/* Max ULP is 0.51. */
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retval = do_cos (x, 0);
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} /* else if (k < 0x3feb6000) */
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else if (k < 0x400368fd)
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{ /* 0.855469 <|x|<2.426265 */ ;
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y = hp0 - fabs (x);
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a = y + hp1;
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da = (y - a) + hp1;
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/* Max ULP is 0.501 if xx < 0.01588 or 0.518 otherwise.
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Range reduction uses 106 bits here which is sufficient. */
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retval = do_sin (a, da);
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} /* else if (k < 0x400368fd) */
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else if (k < 0x419921FB)
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{ /* 2.426265<|x|< 105414350 */
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n = reduce_sincos (x, &a, &da);
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retval = do_sincos (a, da, n + 1);
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} /* else if (k < 0x419921FB ) */
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/* 105414350 <|x| <2^1024 */
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else if (k < 0x7ff00000)
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{
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n = __branred (x, &a, &da);
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retval = do_sincos (a, da, n + 1);
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}
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else
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{
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if (k == 0x7ff00000 && u.i[LOW_HALF] == 0)
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__set_errno (EDOM);
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retval = x / x; /* |x| > 2^1024 */
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}
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return retval;
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}
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#ifndef __cos
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libm_alias_double (__cos, cos)
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#endif
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#ifndef __sin
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libm_alias_double (__sin, sin)
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#endif
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#endif
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