amath  1.8.5
Simple command line calculator
sinh.c
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1 /*-
2  * Copyright (c) 2014-2018 Carsten Sonne Larsen <cs@innolan.net>
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40 
41 /**
42  * @file sinh.c
43  * @brief Hyperbolic sine function
44  */
45 
46 #include "prim.h"
47 
48 #if __GNUC__ > 2
49 #pragma GCC diagnostic ignored "-Wstrict-aliasing"
50 #endif
51 
52 static const double
53  one = 1.0,
54  shuge = 1.0e307;
55 
56 /**
57  * @brief Hyperbolic sine function
58  * @details
59  * <pre>
60  * Method
61  * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
62  * 1. Replace x by |x| (sinh(-x) = -sinh(x)).
63  * 2.
64  * E + E/(E+1)
65  * 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x)
66  * 2
67  *
68  * 22 <= x <= lnovft : sinh(x) := exp(x)/2
69  * lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2)
70  * ln2ovft < x : sinh(x) := x*shuge (overflow)
71  *
72  * Special cases
73  * sinh(x) is |x| if x is +INF, -INF, or NaN.
74  * only sinh(0)=0 is exact for finite x.
75  * </pre>
76  */
77 double sinh(double x)
78 {
79  double t, w, h;
80  int32_t ix, jx;
81  uint32_t lx;
82 
83  // High word of |x|
84  GET_HIGH_WORD(jx, x);
85  ix = jx & 0x7FFFFFFF;
86 
87  // x is INF or NaN
88  if (ix >= 0x7FF00000)
89  {
90  return NAN;
91  }
92 
93  h = 0.5;
94  if (jx < 0)
95  h = -h;
96  /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
97  if (ix < 0x40360000)
98  { /* |x|<22 */
99  if (ix < 0x3E300000) /* |x|<2**-28 */
100  if (shuge + x > one)
101  return x; /* sinh(tiny) = tiny with inexact */
102  t = expm1(fabs(x));
103  if (ix < 0x3FF00000)
104  return h * (2.0 * t - t * t / (t + one));
105  return h * (t + t / (t + one));
106  }
107 
108  /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
109  if (ix < 0x40862E42)
110  return h * exp(fabs(x));
111 
112  /* |x| in [log(maxdouble), overflowthresold] */
113  lx = *((((*(uint32_t *)&one) >> 29)) + (uint32_t *)&x);
114  if (ix < 0x408633CE || ((ix == 0x408633CE) && (lx <= (uint32_t)0X8FB9F87D)))
115  {
116  w = exp(0.5 * fabs(x));
117  t = h * w;
118  return t * w;
119  }
120 
121  /* |x| > overflowthresold, sinh(x) overflow */
122  return x * shuge;
123 }
static const double one
Definition: sinh.c:53
#define GET_HIGH_WORD(i, d)
Get the more significant 32 bit int from a double.
Definition: prim.h:167
double expm1(double x)
Definition: expm1.c:153
double sinh(double x)
Hyperbolic sine function.
Definition: sinh.c:77
#define NAN
Definition: mathr.h:53
static const double shuge
Definition: sinh.c:54
double fabs(double x)
Returns the absolute value of x.
Definition: fabs.c:51
double exp(double x)
Returns the exponential of x.
Definition: exp.c:138