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Transcendental functions for 'long double', from Paolo Bonzini.
author Bruno Haible <bruno@clisp.org>
date Tue, 18 Feb 2003 17:05:23 +0000
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children b09c3f1225b6
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4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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1 /* s_cosl.c -- long double version of s_sin.c.
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2 * Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz.
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3 */
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4
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5 /*
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6 * ====================================================
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7 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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8 *
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9 * Developed at SunPro, a Sun Microsystems, Inc. business.
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10 * Permission to use, copy, modify, and distribute this
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11 * software is freely granted, provided that this notice
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12 * is preserved.
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13 * ====================================================
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14 */
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15
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16 /* sinl(x)
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17 * Return sine function of x.
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18 *
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19 * kernel function:
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20 * __kernel_sinl ... sine function on [-pi/4,pi/4]
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21 * __kernel_cosl ... cose function on [-pi/4,pi/4]
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22 * __ieee754_rem_pio2l ... 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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46
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47 #include <math.h>
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48
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49 #include "mathl.h"
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50
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51 #include "trigl.h"
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52 #ifdef HAVE_SINL
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53 #include "trigl.c"
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54 #include "sincosl.c"
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55 #endif
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56
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57 long double cosl(long double x)
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58 {
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59 long double y[2],z=0.0L;
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60 int n;
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61
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62 /* |x| ~< pi/4 */
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63 if(x >= -0.7853981633974483096156608458198757210492 &&
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64 x <= 0.7853981633974483096156608458198757210492)
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65 return kernel_cosl(x, z);
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66
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67 /* sinl(Inf or NaN) is NaN, sinl(0) is 0 */
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68 else if ((x + x == x && x != 0.0) || x != x)
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69 return x-x; /* NaN */
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70
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71 /* argument reduction needed */
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72 else {
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73 n = ieee754_rem_pio2l(x,y);
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74 switch(n&3) {
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75 case 0: return kernel_cosl(y[0],y[1]);
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76 case 1: return -kernel_sinl(y[0],y[1],1);
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77 case 2: return -kernel_cosl(y[0],y[1]);
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78 default:
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79 return kernel_sinl(y[0],y[1],1);
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80 }
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81 }
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82 }
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83
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84 #if 0
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85 int
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86 main ()
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87 {
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88 printf ("%.16Lg\n", cosl(0.7853981633974483096156608458198757210492));
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89 printf ("%.16Lg\n", cosl(0.7853981633974483096156608458198757210492 *29));
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90 printf ("%.16Lg\n", cosl(0.7853981633974483096156608458198757210492 *2));
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91 printf ("%.16Lg\n", cosl(0.7853981633974483096156608458198757210492 *30));
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92 printf ("%.16Lg\n", cosl(0.7853981633974483096156608458198757210492 *4));
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93 printf ("%.16Lg\n", cosl(0.7853981633974483096156608458198757210492 *32));
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94 printf ("%.16Lg\n", cosl(0.7853981633974483096156608458198757210492 *2/3));
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95 printf ("%.16Lg\n", cosl(0.7853981633974483096156608458198757210492 *4/3));
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96 }
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97 #endif