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/*
* s_tanf.c - single precision tangent function
*
* Copyright (c) 2009-2018, Arm Limited.
* SPDX-License-Identifier: MIT
*/
/*
* Source: my own head, and Remez-generated polynomial approximations.
*/
#include <math.h>
#include "math_private.h"
#include <errno.h>
#include <fenv.h>
#include "rredf.h"
#ifdef __cplusplus
extern "C" {
#endif /* __cplusplus */
float tanf(float x)
{
int q;
/*
* Range-reduce x to the range [-pi/4,pi/4].
*/
{
/*
* I enclose the call to __mathlib_rredf in braces so that
* the address-taken-ness of qq does not propagate
* throughout the rest of the function, for what that might
* be worth.
*/
int qq;
x = __mathlib_rredf(x, &qq);
q = qq;
}
if (__builtin_expect(q < 0, 0)) { /* this signals tiny, inf, or NaN */
unsigned k = fai(x) << 1;
if (k < 0xFF000000) /* tiny */
return FLOAT_CHECKDENORM(x);
else if (k == 0xFF000000) /* inf */
return MATHERR_TANF_INF(x);
else /* NaN */
return FLOAT_INFNAN(x);
}
/*
* We use a direct polynomial approximation for tan(x) on
* [-pi/4,pi/4], and then take the negative reciprocal of the
* result if we're in an interval surrounding an odd rather than
* even multiple of pi/2.
*
* Coefficients generated by the command
./auxiliary/remez.jl --variable=x2 --suffix=f -- '0' '(pi/BigFloat(4))^2' 5 0 'x==0 ? 1/BigFloat(3) : (tan(sqrt(x))-sqrt(x))/sqrt(x^3)' 'sqrt(x^3)'
*/
{
float x2 = x*x;
x += x * (x2 * (
3.333294809182307633621540045249152105330074691488121206914336806061620616979305e-01f+x2*(1.334274588580033216191949445078951865160600494428914956688702429547258497367525e-01f+x2*(5.315177279765676178198868818834880279286012428084733419724267810723468887753723e-02f+x2*(2.520300881849204519070372772571624013984546591252791443673871814078418474596388e-02f+x2*(2.051177187082974766686645514206648277055233230110624602600687812103764075834307e-03f+x2*(9.943421494628597182458186353995299429948224864648292162238582752158235742046109e-03f)))))
));
if (q & 1)
x = -1.0f/x;
return x;
}
}
#ifdef __cplusplus
} /* end of extern "C" */
#endif /* __cplusplus */
/* end of s_tanf.c */
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