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annotate libquadmath/math/tanq.c @ 158:494b0b89df80 default tip

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author Shinji KONO <kono@ie.u-ryukyu.ac.jp>
date Mon, 25 May 2020 18:13:55 +0900
parents 1830386684a0
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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1 /* s_tanl.c -- long double version of s_tan.c.
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2 * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz.
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3 */
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4
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5 /* @(#)s_tan.c 5.1 93/09/24 */
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6 /*
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7 * ====================================================
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8 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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9 *
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10 * Developed at SunPro, a Sun Microsystems, Inc. business.
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11 * Permission to use, copy, modify, and distribute this
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12 * software is freely granted, provided that this notice
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13 * is preserved.
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14 * ====================================================
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15 */
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17 /* tanq(x)
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18 * Return tangent function of x.
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19 *
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20 * kernel function:
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21 * __quadmath_kernel_tanq ... tangent function on [-pi/4,pi/4]
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22 * __quadmath_rem_pio2q ... argument reduction routine
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23 *
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24 * Method.
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25 * Let S,C and T denote the sin, cos and tan respectively on
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26 * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
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27 * in [-pi/4 , +pi/4], and let n = k mod 4.
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28 * We have
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29 *
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30 * n sin(x) cos(x) tan(x)
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31 * ----------------------------------------------------------
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32 * 0 S C T
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33 * 1 C -S -1/T
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34 * 2 -S -C T
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35 * 3 -C S -1/T
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36 * ----------------------------------------------------------
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37 *
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38 * Special cases:
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39 * Let trig be any of sin, cos, or tan.
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40 * trig(+-INF) is NaN, with signals;
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41 * trig(NaN) is that NaN;
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42 *
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43 * Accuracy:
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44 * TRIG(x) returns trig(x) nearly rounded
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45 */
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47 #include "quadmath-imp.h"
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49 __float128 tanq(__float128 x)
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50 {
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51 __float128 y[2],z=0;
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52 int64_t n, ix;
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54 /* High word of x. */
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55 GET_FLT128_MSW64(ix,x);
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56
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57 /* |x| ~< pi/4 */
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58 ix &= 0x7fffffffffffffffLL;
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59 if(ix <= 0x3ffe921fb54442d1LL) return __quadmath_kernel_tanq(x,z,1);
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61 /* tanq(Inf or NaN) is NaN */
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62 else if (ix>=0x7fff000000000000LL) {
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63 if (ix == 0x7fff000000000000LL) {
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64 GET_FLT128_LSW64(n,x);
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65 if (n == 0)
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66 errno = EDOM;
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67 }
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68 return x-x; /* NaN */
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69 }
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71 /* argument reduction needed */
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72 else {
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73 n = __quadmath_rem_pio2q(x,y);
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74 return __quadmath_kernel_tanq(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even
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75 -1 -- n odd */
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76 }
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77 }