1 /*
2 * s_tanf.c - single precision tangent function
3 *
4 * Copyright (c) 2009-2018, Arm Limited.
5 * SPDX-License-Identifier: MIT
6 */
7
8 /*
9 * Source: my own head, and Remez-generated polynomial approximations.
10 */
11
12 #include <math.h>
13 #include "math_private.h"
14 #include <errno.h>
15 #include <fenv.h>
16 #include "rredf.h"
17
18 #ifdef __cplusplus
19 extern "C" {
20 #endif /* __cplusplus */
21
tanf(float x)22 float tanf(float x)
23 {
24 int q;
25
26 /*
27 * Range-reduce x to the range [-pi/4,pi/4].
28 */
29 {
30 /*
31 * I enclose the call to __mathlib_rredf in braces so that
32 * the address-taken-ness of qq does not propagate
33 * throughout the rest of the function, for what that might
34 * be worth.
35 */
36 int qq;
37 x = __mathlib_rredf(x, &qq);
38 q = qq;
39 }
40 if (__builtin_expect(q < 0, 0)) { /* this signals tiny, inf, or NaN */
41 unsigned k = fai(x) << 1;
42 if (k < 0xFF000000) /* tiny */
43 return FLOAT_CHECKDENORM(x);
44 else if (k == 0xFF000000) /* inf */
45 return MATHERR_TANF_INF(x);
46 else /* NaN */
47 return FLOAT_INFNAN(x);
48 }
49
50 /*
51 * We use a direct polynomial approximation for tan(x) on
52 * [-pi/4,pi/4], and then take the negative reciprocal of the
53 * result if we're in an interval surrounding an odd rather than
54 * even multiple of pi/2.
55 *
56 * Coefficients generated by the command
57
58 ./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)'
59
60 */
61 {
62 float x2 = x*x;
63 x += x * (x2 * (
64 3.333294809182307633621540045249152105330074691488121206914336806061620616979305e-01f+x2*(1.334274588580033216191949445078951865160600494428914956688702429547258497367525e-01f+x2*(5.315177279765676178198868818834880279286012428084733419724267810723468887753723e-02f+x2*(2.520300881849204519070372772571624013984546591252791443673871814078418474596388e-02f+x2*(2.051177187082974766686645514206648277055233230110624602600687812103764075834307e-03f+x2*(9.943421494628597182458186353995299429948224864648292162238582752158235742046109e-03f)))))
65 ));
66 if (q & 1)
67 x = -1.0f/x;
68
69 return x;
70 }
71 }
72
73 #ifdef __cplusplus
74 } /* end of extern "C" */
75 #endif /* __cplusplus */
76
77 /* end of s_tanf.c */
78