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      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 /*
     16  * See e_sinh.c for complete comments.
     17  *
     18  * Converted to long double by Bruce D. Evans.
     19  */
     20 
     21 #include "namespace.h"
     22 
     23 __weak_alias(sinhl, _sinhl)
     24 
     25 #include <float.h>
     26 
     27 #ifdef __HAVE_LONG_DOUBLE
     28 
     29 #include "math.h"
     30 #include "math_private.h"
     31 #if LDBL_MANT_DIG == 64
     32 #include "../ld80/k_expl.h"
     33 #elif LDBL_MANT_DIG == 113
     34 #include "../ld128/k_expl.h"
     35 #else
     36 #error "Unsupported long double format"
     37 #endif
     38 
     39 #if LDBL_MAX_EXP != 0x4000
     40 /* We also require the usual expsign encoding. */
     41 #error "Unsupported long double format"
     42 #endif
     43 
     44 #define	BIAS	(LDBL_MAX_EXP - 1)
     45 
     46 static const long double shuge = 0x1p16383L;
     47 #if LDBL_MANT_DIG == 64
     48 /*
     49  * Domain [-1, 1], range ~[-6.6749e-22, 6.6749e-22]:
     50  * |sinh(x)/x - s(x)| < 2**-70.3
     51  */
     52 static const union ieee_ext_u
     53 S3u = LD80C(0xaaaaaaaaaaaaaaaa, -3,  1.66666666666666666658e-1L);
     54 #define	S3	S3u.extu_ld
     55 static const double
     56 S5  =  8.3333333333333332e-3,		/*  0x11111111111111.0p-59 */
     57 S7  =  1.9841269841270074e-4,		/*  0x1a01a01a01a070.0p-65 */
     58 S9  =  2.7557319223873889e-6,		/*  0x171de3a5565fe6.0p-71 */
     59 S11 =  2.5052108406704084e-8,		/*  0x1ae6456857530f.0p-78 */
     60 S13 =  1.6059042748655297e-10,		/*  0x161245fa910697.0p-85 */
     61 S15 =  7.6470006914396920e-13,		/*  0x1ae7ce4eff2792.0p-93 */
     62 S17 =  2.8346142308424267e-15;		/*  0x19882ce789ffc6.0p-101 */
     63 #elif LDBL_MANT_DIG == 113
     64 /*
     65  * Domain [-1, 1], range ~[-2.9673e-36, 2.9673e-36]:
     66  * |sinh(x)/x - s(x)| < 2**-118.0
     67  */
     68 static const long double
     69 S3  =  1.66666666666666666666666666666666033e-1L,	/*  0x1555555555555555555555555553b.0p-115L */
     70 S5  =  8.33333333333333333333333333337643193e-3L,	/*  0x111111111111111111111111180f5.0p-119L */
     71 S7  =  1.98412698412698412698412697391263199e-4L,	/*  0x1a01a01a01a01a01a01a0176aad11.0p-125L */
     72 S9  =  2.75573192239858906525574406205464218e-6L,	/*  0x171de3a556c7338faac243aaa9592.0p-131L */
     73 S11 =  2.50521083854417187749675637460977997e-8L,	/*  0x1ae64567f544e38fe59b3380d7413.0p-138L */
     74 S13 =  1.60590438368216146368737762431552702e-10L,	/*  0x16124613a86d098059c7620850fc2.0p-145L */
     75 S15 =  7.64716373181980539786802470969096440e-13L,	/*  0x1ae7f3e733b814193af09ce723043.0p-153L */
     76 S17 =  2.81145725434775409870584280722701574e-15L;	/*  0x1952c77030c36898c3fd0b6dfc562.0p-161L */
     77 static const double
     78 S19=  8.2206352435411005e-18,		/*  0x12f49b4662b86d.0p-109 */
     79 S21=  1.9572943931418891e-20,		/*  0x171b8f2fab9628.0p-118 */
     80 S23 =  3.8679983530666939e-23,		/*  0x17617002b73afc.0p-127 */
     81 S25 =  6.5067867911512749e-26;		/*  0x1423352626048a.0p-136 */
     82 #else
     83 #error "Unsupported long double format"
     84 #endif /* LDBL_MANT_DIG == 64 */
     85 
     86 /* log(2**16385 - 0.5) rounded up: */
     87 static const float
     88 o_threshold =  1.13572168e4;		/*  0xb174de.0p-10 */
     89 
     90 long double
     91 sinhl(long double x)
     92 {
     93 	long double hi,lo,x2;
     94 #if LDBL_MANT_DIG == 113
     95 	double dx2;
     96 #endif
     97 	double s;
     98 	int16_t ix,jx;
     99 
    100 	GET_LDBL_EXPSIGN(jx,x);
    101 	ix = jx&0x7fff;
    102 
    103     /* x is INF or NaN */
    104 	if(ix>=0x7fff) return x+x;
    105 
    106 	ENTERI();
    107 
    108 	s = 1;
    109 	if (jx<0) s = -1;
    110 
    111     /* |x| < 64, return x, s(x), or accurate s*(exp(|x|)/2-1/exp(|x|)/2) */
    112 	if (ix<0x4005) {		/* |x|<64 */
    113 	    if (ix<BIAS-(LDBL_MANT_DIG+1)/2) 	/* |x|<TINY */
    114 		if(shuge+x>1) RETURNI(x);  /* sinh(tiny) = tiny with inexact */
    115 	    if (ix<0x3fff) {		/* |x|<1 */
    116 		x2 = x*x;
    117 #if LDBL_MANT_DIG == 64
    118 		long double x4 = x2*x2;
    119 		RETURNI(((S17*x2 + S15)*x4 + (S13*x2 + S11))*(x2*x*x4*x4) +
    120 		    ((S9*x2 + S7)*x2 + S5)*(x2*x*x2) + S3*(x2*x) + x);
    121 #elif LDBL_MANT_DIG == 113
    122 		dx2 = x2;
    123 		RETURNI(((((((((((S25*dx2 + S23)*dx2 +
    124 		    S21)*x2 + S19)*x2 +
    125 		    S17)*x2 + S15)*x2 + S13)*x2 + S11)*x2 + S9)*x2 + S7)*x2 +
    126 		    S5)* (x2*x*x2) +
    127 		    S3*(x2*x) + x);
    128 #endif
    129 	    }
    130 	    k_hexpl(fabsl(x), &hi, &lo);
    131 	    RETURNI(s*(lo - 0.25/(hi + lo) + hi));
    132 	}
    133 
    134     /* |x| in [64, o_threshold], return correctly-overflowing s*exp(|x|)/2 */
    135 	if (fabsl(x) <= o_threshold)
    136 	    RETURNI(s*hexpl(fabsl(x)));
    137 
    138     /* |x| > o_threshold, sinh(x) overflow */
    139 	return x*shuge;
    140 }
    141 #else
    142 
    143 #include "math.h"
    144 
    145 long double
    146 sinhl(long double x)
    147 {
    148 	return sinh(x);
    149 }
    150 
    151 #endif
    152