newlib/libm/ld/e_sinhl.c

   1 /* from: FreeBSD: head/lib/msun/src/e_sinhl.c XXX */
   2
   3 /*
   4  * ====================================================
   5  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   6  *
   7  * Developed at SunPro, a Sun Microsystems, Inc. business.
   8  * Permission to use, copy, modify, and distribute this
   9  * software is freely granted, provided that this notice
  10  * is preserved.
  11  * ====================================================
  12  */
  13
  14 #include <sys/cdefs.h>
  15 __FBSDID("$FreeBSD$");
  16
  17 /*
  18  * See e_sinh.c for complete comments.
  19  *
  20  * Converted to long double by Bruce D. Evans.
  21  */
  22
  23 #include <float.h>
  24 #ifdef __i386__
  25 #include <ieeefp.h>
  26 #endif
  27
  28 #include "fpmath.h"
  29 #include "math.h"
  30 #include "math_private.h"
  31 #include "k_expl.h"
  32
  33 #if LDBL_MAX_EXP != 0x4000
  34 /* We also require the usual expsign encoding. */
  35 #error "Unsupported long double format"
  36 #endif
  37
  38 #define BIAS    (LDBL_MAX_EXP - 1)
  39
  40 static const long double shuge = 0x1p16383L;
  41 #if LDBL_MANT_DIG == 64
  42 /*
  43  * Domain [-1, 1], range ~[-6.6749e-22, 6.6749e-22]:
  44  * |sinh(x)/x - s(x)| < 2**-70.3
  45  */
  46 static const union IEEEl2bits
  47 S3u = LD80C(0xaaaaaaaaaaaaaaaa, -3,  1.66666666666666666658e-1L);
  48 #define S3      S3u.e
  49 static const double
  50 S5  =  8.3333333333333332e-3,           /*  0x11111111111111.0p-59 */
  51 S7  =  1.9841269841270074e-4,           /*  0x1a01a01a01a070.0p-65 */
  52 S9  =  2.7557319223873889e-6,           /*  0x171de3a5565fe6.0p-71 */
  53 S11 =  2.5052108406704084e-8,           /*  0x1ae6456857530f.0p-78 */
  54 S13 =  1.6059042748655297e-10,          /*  0x161245fa910697.0p-85 */
  55 S15 =  7.6470006914396920e-13,          /*  0x1ae7ce4eff2792.0p-93 */
  56 S17 =  2.8346142308424267e-15;          /*  0x19882ce789ffc6.0p-101 */
  57 #elif LDBL_MANT_DIG == 113
  58 /*
  59  * Domain [-1, 1], range ~[-2.9673e-36, 2.9673e-36]:
  60  * |sinh(x)/x - s(x)| < 2**-118.0
  61  */
  62 static const long double
  63 S3  =  1.66666666666666666666666666666666033e-1L,       /*  0x1555555555555555555555555553b.0p-115L */
  64 S5  =  8.33333333333333333333333333337643193e-3L,       /*  0x111111111111111111111111180f5.0p-119L */
  65 S7  =  1.98412698412698412698412697391263199e-4L,       /*  0x1a01a01a01a01a01a01a0176aad11.0p-125L */
  66 S9  =  2.75573192239858906525574406205464218e-6L,       /*  0x171de3a556c7338faac243aaa9592.0p-131L */
  67 S11 =  2.50521083854417187749675637460977997e-8L,       /*  0x1ae64567f544e38fe59b3380d7413.0p-138L */
  68 S13 =  1.60590438368216146368737762431552702e-10L,      /*  0x16124613a86d098059c7620850fc2.0p-145L */
  69 S15 =  7.64716373181980539786802470969096440e-13L,      /*  0x1ae7f3e733b814193af09ce723043.0p-153L */
  70 S17 =  2.81145725434775409870584280722701574e-15L;      /*  0x1952c77030c36898c3fd0b6dfc562.0p-161L */
  71 static const double
  72 S19=  8.2206352435411005e-18,           /*  0x12f49b4662b86d.0p-109 */
  73 S21=  1.9572943931418891e-20,           /*  0x171b8f2fab9628.0p-118 */
  74 S23 =  3.8679983530666939e-23,          /*  0x17617002b73afc.0p-127 */
  75 S25 =  6.5067867911512749e-26;          /*  0x1423352626048a.0p-136 */
  76 #else
  77 #error "Unsupported long double format"
  78 #endif /* LDBL_MANT_DIG == 64 */
  79
  80 /* log(2**16385 - 0.5) rounded up: */
  81 static const float
  82 o_threshold =  1.13572168e4;            /*  0xb174de.0p-10 */
  83
  84 long double
  85 sinhl(long double x)
  86 {
  87         long double hi,lo,x2,x4;
  88 #if LDBL_MANT_DIG == 113
  89         double dx2;
  90 #endif
  91         double s;
  92         int16_t ix,jx;
  93
  94         GET_LDBL_EXPSIGN(jx,x);
  95         ix = jx&0x7fff;
  96
  97     /* x is INF or NaN */
  98         if(ix>=0x7fff) return x+x;
  99
 100         ENTERI();
 101
 102         s = 1;
 103         if (jx<0) s = -1;
 104
 105     /* |x| < 64, return x, s(x), or accurate s*(exp(|x|)/2-1/exp(|x|)/2) */
 106         if (ix<0x4005) {                /* |x|<64 */
 107             if (ix<BIAS-(LDBL_MANT_DIG+1)/2)    /* |x|<TINY */
 108                 if(shuge+x>1) RETURNI(x);  /* sinh(tiny) = tiny with inexact */
 109             if (ix<0x3fff) {            /* |x|<1 */
 110                 x2 = x*x;
 111 #if LDBL_MANT_DIG == 64
 112                 x4 = x2*x2;
 113                 RETURNI(((S17*x2 + S15)*x4 + (S13*x2 + S11))*(x2*x*x4*x4) +
 114                     ((S9*x2 + S7)*x2 + S5)*(x2*x*x2) + S3*(x2*x) + x);
 115 #elif LDBL_MANT_DIG == 113
 116                 dx2 = x2;
 117                 RETURNI(((((((((((S25*dx2 + S23)*dx2 +
 118                     S21)*x2 + S19)*x2 +
 119                     S17)*x2 + S15)*x2 + S13)*x2 + S11)*x2 + S9)*x2 + S7)*x2 +
 120                     S5)* (x2*x*x2) +
 121                     S3*(x2*x) + x);
 122 #endif
 123             }
 124             k_hexpl(fabsl(x), &hi, &lo);
 125             RETURNI(s*(lo - 0.25/(hi + lo) + hi));
 126         }
 127
 128     /* |x| in [64, o_threshold], return correctly-overflowing s*exp(|x|)/2 */
 129         if (fabsl(x) <= o_threshold)
 130             RETURNI(s*hexpl(fabsl(x)));
 131
 132     /* |x| > o_threshold, sinh(x) overflow */
 133         return x*shuge;
 134 }