newlib/libm/ld/e_coshl.c

   1 /* from: FreeBSD: head/lib/msun/src/e_coshl.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_cosh.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 volatile long double huge = 0x1p10000L, tiny = 0x1p-10000L;
  41 #if LDBL_MANT_DIG == 64
  42 /*
  43  * Domain [-1, 1], range ~[-1.8211e-21, 1.8211e-21]:
  44  * |cosh(x) - c(x)| < 2**-68.8
  45  */
  46 static const union IEEEl2bits
  47 C4u = LD80C(0xaaaaaaaaaaaaac78, -5,  4.16666666666666682297e-2L);
  48 #define C4      C4u.e
  49 static const double
  50 C2  =  0.5,
  51 C6  =  1.3888888888888616e-3,           /*  0x16c16c16c16b99.0p-62 */
  52 C8  =  2.4801587301767953e-5,           /*  0x1a01a01a027061.0p-68 */
  53 C10 =  2.7557319163300398e-7,           /*  0x127e4fb6c9b55f.0p-74 */
  54 C12 =  2.0876768371393075e-9,           /*  0x11eed99406a3f4.0p-81 */
  55 C14 =  1.1469537039374480e-11,          /*  0x1938c67cd18c48.0p-89 */
  56 C16 =  4.8473490896852041e-14;          /*  0x1b49c429701e45.0p-97 */
  57 #elif LDBL_MANT_DIG == 113
  58 /*
  59  * Domain [-1, 1], range ~[-2.3194e-37, 2.3194e-37]:
  60  * |cosh(x) - c(x)| < 2**-121.69
  61  */
  62 static const long double
  63 C4  =  4.16666666666666666666666666666666225e-2L,       /*  0x1555555555555555555555555554e.0p-117L */
  64 C6  =  1.38888888888888888888888888889434831e-3L,       /*  0x16c16c16c16c16c16c16c16c1dd7a.0p-122L */
  65 C8  =  2.48015873015873015873015871870962089e-5L,       /*  0x1a01a01a01a01a01a01a017af2756.0p-128L */
  66 C10 =  2.75573192239858906525574318600800201e-7L,       /*  0x127e4fb7789f5c72ef01c8a040640.0p-134L */
  67 C12 =  2.08767569878680989791444691755468269e-9L,       /*  0x11eed8eff8d897b543d0679607399.0p-141L */
  68 C14=  1.14707455977297247387801189650495351e-11L,       /*  0x193974a8c07c9d24ae169a7fa9b54.0p-149L */
  69 C16 =  4.77947733238737883626416876486279985e-14L;      /*  0x1ae7f3e733b814d4e1b90f5727fe4.0p-157L */
  70 static const double
  71 C2  =  0.5,
  72 C18 =  1.5619206968597871e-16,          /*  0x16827863b9900b.0p-105 */
  73 C20 =  4.1103176218528049e-19,          /*  0x1e542ba3d3c269.0p-114 */
  74 C22 =  8.8967926401641701e-22,          /*  0x10ce399542a014.0p-122 */
  75 C24 =  1.6116681626523904e-24,          /*  0x1f2c981d1f0cb7.0p-132 */
  76 C26 =  2.5022374732804632e-27;          /*  0x18c7ecf8b2c4a0.0p-141 */
  77 #else
  78 #error "Unsupported long double format"
  79 #endif /* LDBL_MANT_DIG == 64 */
  80
  81 /* log(2**16385 - 0.5) rounded up: */
  82 static const float
  83 o_threshold =  1.13572168e4;            /*  0xb174de.0p-10 */
  84
  85 long double
  86 coshl(long double x)
  87 {
  88         long double hi,lo,x2,x4;
  89 #if LDBL_MANT_DIG == 113
  90         double dx2;
  91 #endif
  92         uint16_t ix;
  93
  94         GET_LDBL_EXPSIGN(ix,x);
  95         ix &= 0x7fff;
  96
  97     /* x is INF or NaN */
  98         if(ix>=0x7fff) return x*x;
  99
 100         ENTERI();
 101
 102     /* |x| < 1, return 1 or c(x) */
 103         if(ix<0x3fff) {
 104             if (ix<BIAS-(LDBL_MANT_DIG+1)/2)    /* |x| < TINY */
 105                 RETURNI(1+tiny);        /* cosh(tiny) = 1(+) with inexact */
 106             x2 = x*x;
 107 #if LDBL_MANT_DIG == 64
 108             x4 = x2*x2;
 109             RETURNI(((C16*x2 + C14)*x4 + (C12*x2 + C10))*(x4*x4*x2) +
 110                 ((C8*x2 + C6)*x2 + C4)*x4 + C2*x2 + 1);
 111 #elif LDBL_MANT_DIG == 113
 112             dx2 = x2;
 113             RETURNI((((((((((((C26*dx2 + C24)*dx2 + C22)*dx2 +
 114                 C20)*x2 + C18)*x2 +
 115                 C16)*x2 + C14)*x2 + C12)*x2 + C10)*x2 + C8)*x2 + C6)*x2 +
 116                 C4)*(x2*x2) + C2*x2 + 1);
 117 #endif
 118         }
 119
 120     /* |x| in [1, 64), return accurate exp(|x|)/2+1/exp(|x|)/2 */
 121         if (ix < 0x4005) {
 122             k_hexpl(fabsl(x), &hi, &lo);
 123             RETURNI(lo + 0.25/(hi + lo) + hi);
 124         }
 125
 126     /* |x| in [64, o_threshold], return correctly-overflowing exp(|x|)/2 */
 127         if (fabsl(x) <= o_threshold)
 128             RETURNI(hexpl(fabsl(x)));
 129
 130     /* |x| > o_threshold, cosh(x) overflow */
 131         RETURNI(huge*huge);
 132 }