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      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 	double dx2;
     90 	uint16_t ix;
     91 
     92 	GET_LDBL_EXPSIGN(ix,x);
     93 	ix &= 0x7fff;
     94 
     95     /* x is INF or NaN */
     96 	if(ix>=0x7fff) return x*x;
     97 
     98 	ENTERI();
     99 
    100     /* |x| < 1, return 1 or c(x) */
    101 	if(ix<0x3fff) {
    102 	    if (ix<BIAS-(LDBL_MANT_DIG+1)/2) 	/* |x| < TINY */
    103 		RETURNI(1+tiny);	/* cosh(tiny) = 1(+) with inexact */
    104 	    x2 = x*x;
    105 #if LDBL_MANT_DIG == 64
    106 	    x4 = x2*x2;
    107 	    RETURNI(((C16*x2 + C14)*x4 + (C12*x2 + C10))*(x4*x4*x2) +
    108 		((C8*x2 + C6)*x2 + C4)*x4 + C2*x2 + 1);
    109 #elif LDBL_MANT_DIG == 113
    110 	    dx2 = x2;
    111 	    RETURNI((((((((((((C26*dx2 + C24)*dx2 + C22)*dx2 +
    112 		C20)*x2 + C18)*x2 +
    113 		C16)*x2 + C14)*x2 + C12)*x2 + C10)*x2 + C8)*x2 + C6)*x2 +
    114 		C4)*(x2*x2) + C2*x2 + 1);
    115 #endif
    116 	}
    117 
    118     /* |x| in [1, 64), return accurate exp(|x|)/2+1/exp(|x|)/2 */
    119 	if (ix < 0x4005) {
    120 	    k_hexpl(fabsl(x), &hi, &lo);
    121 	    RETURNI(lo + 0.25/(hi + lo) + hi);
    122 	}
    123 
    124     /* |x| in [64, o_threshold], return correctly-overflowing exp(|x|)/2 */
    125 	if (fabsl(x) <= o_threshold)
    126 	    RETURNI(hexpl(fabsl(x)));
    127 
    128     /* |x| > o_threshold, cosh(x) overflow */
    129 	RETURNI(huge*huge);
    130 }
    131