/*
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* s_sincosf.c - single precision sine and cosine functions
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*
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* Copyright (c) 2009-2018, Arm Limited.
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* SPDX-License-Identifier: MIT
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*/
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/*
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* Source: my own head, and Remez-generated polynomial approximations.
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*/
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#include <fenv.h>
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#include <math.h>
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#include <errno.h>
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#include "rredf.h"
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#include "math_private.h"
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#ifdef __cplusplus
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extern "C" {
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#endif /* __cplusplus */
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#ifndef COSINE
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#define FUNCNAME sinf
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#define SOFTFP_FUNCNAME __softfp_sinf
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#define DO_SIN (!(q & 1))
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#define NEGATE_SIN ((q & 2))
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#define NEGATE_COS ((q & 2))
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#define TRIVIAL_RESULT(x) FLOAT_CHECKDENORM(x)
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#define ERR_INF MATHERR_SINF_INF
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#else
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#define FUNCNAME cosf
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#define SOFTFP_FUNCNAME __softfp_cosf
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#define DO_SIN (q & 1)
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#define NEGATE_SIN (!(q & 2))
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#define NEGATE_COS ((q & 2))
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#define TRIVIAL_RESULT(x) 1.0f
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#define ERR_INF MATHERR_COSF_INF
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#endif
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float FUNCNAME(float x)
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{
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int q;
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/*
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* Range-reduce x to the range [-pi/4,pi/4].
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*/
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{
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/*
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* I enclose the call to __mathlib_rredf in braces so that
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* the address-taken-ness of qq does not propagate
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* throughout the rest of the function, for what that might
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* be worth.
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*/
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int qq;
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x = __mathlib_rredf(x, &qq);
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q = qq;
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}
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if (__builtin_expect(q < 0, 0)) { /* this signals tiny, inf, or NaN */
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unsigned k = fai(x) << 1;
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if (k < 0xFF000000) /* tiny */
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return TRIVIAL_RESULT(x);
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else if (k == 0xFF000000) /* inf */
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return ERR_INF(x);
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else /* NaN */
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return FLOAT_INFNAN(x);
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}
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/*
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* Depending on the quadrant we were in, we may have to compute
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* a sine-like function (f(0)=0) or a cosine-like one (f(0)=1),
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* and we may have to negate it.
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*/
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if (DO_SIN) {
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float x2 = x*x;
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/*
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* Coefficients generated by the command
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./auxiliary/remez.jl --variable=x2 --suffix=f -- '0' 'atan(BigFloat(1))^2' 2 0 'x==0 ? -1/BigFloat(6) : (x->(sin(x)-x)/x^3)(sqrt(x))' 'sqrt(x^3)'
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*/
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x += x * (x2 * (
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-1.666665066929417292436220415142244613956015227491999719404711781344783392564922e-01f+x2*(8.331978663157089651408875887703995477889496917296385733254577121461421466427772e-03f+x2*(-1.949563623766929906511886482584265500187314705496861877317774185883215997931494e-04f))
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));
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if (NEGATE_SIN)
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x = -x;
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return x;
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} else {
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float x2 = x*x;
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/*
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* Coefficients generated by the command
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./auxiliary/remez.jl --variable=x2 --suffix=f -- '0' 'atan(BigFloat(1))^2' 2 0 'x==0 ? -1/BigFloat(6) : (x->(cos(x)-1)/x^2)(sqrt(x))' 'x'
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*/
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x = 1.0f + x2*(
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-4.999989478137016757327030935768632852012781143541026304540837816323349768666875e-01f+x2*(4.165629457842617238353362092016541041535652603456375154392942188742496860024377e-02f+x2*(-1.35978231111049428748566568960423202948250988565693107969571193763372093404347e-03f))
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);
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if (NEGATE_COS)
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x = -x;
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return x;
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}
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}
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#ifdef __cplusplus
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} /* end of extern "C" */
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#endif /* __cplusplus */
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/* end of sincosf.c */
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