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annotate libquadmath/math/acoshq.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 /* e_acoshl.c -- long double version of e_acosh.c.
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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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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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Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
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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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16 /* acoshq(x)
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17 * Method :
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18 * Based on
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19 * acoshl(x) = logq [ x + sqrtq(x*x-1) ]
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20 * we have
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21 * acoshl(x) := logq(x)+ln2, if x is large; else
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22 * acoshl(x) := logq(2x-1/(sqrtq(x*x-1)+x)) if x>2; else
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23 * acoshl(x) := log1pq(t+sqrtq(2.0*t+t*t)); where t=x-1.
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24 *
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25 * Special cases:
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26 * acoshl(x) is NaN with signal if x<1.
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27 * acoshl(NaN) is NaN without signal.
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28 */
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29
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30 #include "quadmath-imp.h"
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32 static const __float128
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33 one = 1.0,
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34 ln2 = 0.6931471805599453094172321214581766Q;
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35
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36 __float128
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37 acoshq(__float128 x)
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38 {
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39 __float128 t;
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40 uint64_t lx;
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41 int64_t hx;
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42 GET_FLT128_WORDS64(hx,lx,x);
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43 if(hx<0x3fff000000000000LL) { /* x < 1 */
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44 return (x-x)/(x-x);
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45 } else if(hx >=0x4035000000000000LL) { /* x > 2**54 */
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46 if(hx >=0x7fff000000000000LL) { /* x is inf of NaN */
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47 return x+x;
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48 } else
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49 return logq(x)+ln2; /* acoshl(huge)=logq(2x) */
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50 } else if(((hx-0x3fff000000000000LL)|lx)==0) {
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51 return 0; /* acosh(1) = 0 */
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52 } else if (hx > 0x4000000000000000LL) { /* 2**28 > x > 2 */
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53 t=x*x;
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54 return logq(2*x-one/(x+sqrtq(t-one)));
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55 } else { /* 1<x<2 */
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56 t = x-one;
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57 return log1pq(t+sqrtq(2*t+t*t));
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58 }
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59 }