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annotate libquadmath/math/tanhq.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
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1 /* s_tanhl.c -- long double version of s_tanh.c.
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2 * Conversion to long double by Ulrich Drepper,
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3 * Cygnus Support, drepper@cygnus.com.
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4 */
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5
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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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16
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17 /* Changes for 128-bit long double contributed by
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18 Stephen L. Moshier <moshier@na-net.ornl.gov> */
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19
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20 /* tanhq(x)
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21 * Return the Hyperbolic Tangent of x
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22 *
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23 * Method :
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24 * x -x
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25 * e - e
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26 * 0. tanhq(x) is defined to be -----------
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27 * x -x
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28 * e + e
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29 * 1. reduce x to non-negative by tanhq(-x) = -tanhq(x).
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30 * 2. 0 <= x <= 2**-57 : tanhq(x) := x*(one+x)
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31 * -t
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32 * 2**-57 < x <= 1 : tanhq(x) := -----; t = expm1q(-2x)
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33 * t + 2
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34 * 2
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35 * 1 <= x <= 40.0 : tanhq(x) := 1- ----- ; t=expm1q(2x)
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36 * t + 2
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37 * 40.0 < x <= INF : tanhq(x) := 1.
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38 *
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39 * Special cases:
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40 * tanhq(NaN) is NaN;
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41 * only tanhq(0)=0 is exact for finite argument.
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42 */
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43
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44 #include "quadmath-imp.h"
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45
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46 static const __float128 one = 1.0, two = 2.0, tiny = 1.0e-4900Q;
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47
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48 __float128
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49 tanhq (__float128 x)
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50 {
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51 __float128 t, z;
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52 uint32_t jx, ix;
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53 ieee854_float128 u;
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54
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55 /* Words of |x|. */
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56 u.value = x;
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57 jx = u.words32.w0;
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58 ix = jx & 0x7fffffff;
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59 /* x is INF or NaN */
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60 if (ix >= 0x7fff0000)
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61 {
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62 /* for NaN it's not important which branch: tanhq(NaN) = NaN */
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63 if (jx & 0x80000000)
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64 return one / x - one; /* tanhq(-inf)= -1; */
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65 else
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66 return one / x + one; /* tanhq(+inf)=+1 */
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67 }
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68
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69 /* |x| < 40 */
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70 if (ix < 0x40044000)
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71 {
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72 if (u.value == 0)
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73 return x; /* x == +- 0 */
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74 if (ix < 0x3fc60000) /* |x| < 2^-57 */
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75 {
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76 math_check_force_underflow (x);
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77 return x * (one + tiny); /* tanh(small) = small */
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78 }
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79 u.words32.w0 = ix; /* Absolute value of x. */
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80 if (ix >= 0x3fff0000)
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81 { /* |x| >= 1 */
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82 t = expm1q (two * u.value);
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83 z = one - two / (t + two);
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84 }
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85 else
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86 {
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87 t = expm1q (-two * u.value);
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88 z = -t / (t + two);
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89 }
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90 /* |x| > 40, return +-1 */
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91 }
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92 else
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93 {
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94 z = one - tiny; /* raised inexact flag */
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95 }
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96 return (jx & 0x80000000) ? -z : z;
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97 }