overby.me
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1/*
2 * by Ian Ollmann
3 *
4 * based on fdlibm cosh by Sun Microsystems, with improvements for efficiency and proper flag setting on i386.
5 *
6 * Copyright (C) 2005 by Apple Computer, Inc. All rights reserved.
7 */
8
9
10
11#include "math.h"
12#include "math_private.h"
13
14long double coshl( long double x )
15{
16 static const long double overflow = 0x1.62e9bb80635d81d4p+13L; //ln(LDBL_MAX) + ln(2.0)
17 static const long double ln2 = 0.693147180559945309417232121458176568L; //ln(2)
18 long double fabsx = __builtin_fabsl( x );
19 long double t, w;
20
21 if( x != x ) return x + x;
22
23 if( fabsx < __builtin_infl() )
24 {
25 if( fabsx < 0.5L * ln2 )
26 {
27 if( fabsx > 0x1.0p-1000L ) //avoid underflow, save time
28 fabsx = expm1l( fabsx );
29 w = 1.0L + fabsx;
30 if( fabsx < 0x1.0p-67L )
31 return w;
32 return 1.0L + (fabsx*fabsx)/(w+w);
33 }
34
35 if( fabsx < 22.L )
36 {
37 t = expl( fabsx );
38 return 0.5L * t + 0.5L/t;
39 }
40
41 if( fabsx < overflow )
42 {
43 w = expl( 0.5L * fabsx );
44 t = 0.5L * w;
45 return t * w;
46 }
47
48 return fabsx * 0x1.0p16383L;
49 }
50
51 //Nan or Inf result
52 return fabsx + fabsx;
53}