1 2 /* @(#)s_asinh.c 5.1 93/09/24 */ 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 /* 15 FUNCTION 16 <<asinh>>, <<asinhf>>---inverse hyperbolic sine 17 18 INDEX 19 asinh 20 INDEX 21 asinhf 22 23 ANSI_SYNOPSIS 24 #include <math.h> 25 double asinh(double <[x]>); 26 float asinhf(float <[x]>); 27 28 TRAD_SYNOPSIS 29 #include <math.h> 30 double asinh(<[x]>) 31 double <[x]>; 32 33 float asinhf(<[x]>) 34 float <[x]>; 35 36 DESCRIPTION 37 <<asinh>> calculates the inverse hyperbolic sine of <[x]>. 38 <<asinh>> is defined as 39 @ifnottex 40 . sgn(<[x]>) * log(abs(<[x]>) + sqrt(1+<[x]>*<[x]>)) 41 @end ifnottex 42 @tex 43 $$sign(x) \times ln\Bigl(|x| + \sqrt{1+x^2}\Bigr)$$ 44 @end tex 45 46 <<asinhf>> is identical, other than taking and returning floats. 47 48 RETURNS 49 <<asinh>> and <<asinhf>> return the calculated value. 50 51 PORTABILITY 52 Neither <<asinh>> nor <<asinhf>> are ANSI C. 53 54 */ 55 56 /* asinh(x) 57 * Method : 58 * Based on 59 * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ] 60 * we have 61 * asinh(x) := x if 1+x*x=1, 62 * := sign(x)*(log(x)+ln2)) for large |x|, else 63 * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else 64 * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2))) 65 */ 66 67 #include "fdlibm.h" 68 69 #ifndef _DOUBLE_IS_32BITS 70 71 #ifdef __STDC__ 72 static const double 73 #else 74 static double 75 #endif 76 one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ 77 ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ 78 huge= 1.00000000000000000000e+300; 79 80 #ifdef __STDC__ asinh(double x)81 double asinh(double x) 82 #else 83 double asinh(x) 84 double x; 85 #endif 86 { 87 double t,w; 88 __int32_t hx,ix; 89 GET_HIGH_WORD(hx,x); 90 ix = hx&0x7fffffff; 91 if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */ 92 if(ix< 0x3e300000) { /* |x|<2**-28 */ 93 if(huge+x>one) return x; /* return x inexact except 0 */ 94 } 95 if(ix>0x41b00000) { /* |x| > 2**28 */ 96 w = __ieee754_log(fabs(x))+ln2; 97 } else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */ 98 t = fabs(x); 99 w = __ieee754_log(2.0*t+one/(__ieee754_sqrt(x*x+one)+t)); 100 } else { /* 2.0 > |x| > 2**-28 */ 101 t = x*x; 102 w =log1p(fabs(x)+t/(one+__ieee754_sqrt(one+t))); 103 } 104 if(hx>0) return w; else return -w; 105 } 106 107 #endif /* _DOUBLE_IS_32BITS */ 108