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| 2 | /* @(#)s_asinh.c 5.1 93/09/24 */ |
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| 3 | /* |
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| 4 | * ==================================================== |
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| 5 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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| 6 | * |
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| 7 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
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| 8 | * Permission to use, copy, modify, and distribute this |
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| 9 | * software is freely granted, provided that this notice |
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| 10 | * is preserved. |
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| 11 | * ==================================================== |
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| 12 | */ |
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| 13 | |
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| 14 | /* |
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| 15 | FUNCTION |
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| 16 | <<asinh>>, <<asinhf>>---inverse hyperbolic sine |
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| 17 | |
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| 18 | INDEX |
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| 19 | asinh |
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| 20 | INDEX |
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| 21 | asinhf |
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| 22 | |
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| 23 | SYNOPSIS |
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| 24 | #include <math.h> |
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| 25 | double asinh(double <[x]>); |
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| 26 | float asinhf(float <[x]>); |
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| 27 | |
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| 28 | DESCRIPTION |
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| 29 | <<asinh>> calculates the inverse hyperbolic sine of <[x]>. |
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| 30 | <<asinh>> is defined as |
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| 31 | @ifnottex |
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| 32 | . sgn(<[x]>) * log(abs(<[x]>) + sqrt(1+<[x]>*<[x]>)) |
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| 33 | @end ifnottex |
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| 34 | @tex |
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| 35 | $$sign(x) \times ln\Bigl(|x| + \sqrt{1+x^2}\Bigr)$$ |
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| 36 | @end tex |
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| 37 | |
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| 38 | <<asinhf>> is identical, other than taking and returning floats. |
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| 39 | |
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| 40 | RETURNS |
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| 41 | <<asinh>> and <<asinhf>> return the calculated value. |
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| 42 | |
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| 43 | PORTABILITY |
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| 44 | Neither <<asinh>> nor <<asinhf>> are ANSI C. |
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| 45 | |
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| 46 | */ |
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| 47 | |
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| 48 | /* asinh(x) |
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| 49 | * Method : |
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| 50 | * Based on |
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| 51 | * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ] |
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| 52 | * we have |
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| 53 | * asinh(x) := x if 1+x*x=1, |
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| 54 | * := sign(x)*(log(x)+ln2)) for large |x|, else |
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| 55 | * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else |
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| 56 | * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2))) |
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| 57 | */ |
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| 58 | |
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| 59 | #include "fdlibm.h" |
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| 60 | |
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| 61 | #ifndef _DOUBLE_IS_32BITS |
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| 62 | |
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| 63 | #ifdef __STDC__ |
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| 64 | static const double |
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| 65 | #else |
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| 66 | static double |
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| 67 | #endif |
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| 68 | one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ |
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| 69 | ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ |
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| 70 | huge= 1.00000000000000000000e+300; |
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| 71 | |
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| 72 | #ifdef __STDC__ |
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| 73 | double asinh(double x) |
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| 74 | #else |
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| 75 | double asinh(x) |
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| 76 | double x; |
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| 77 | #endif |
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| 78 | { |
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| 79 | double t,w; |
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| 80 | __int32_t hx,ix; |
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| 81 | GET_HIGH_WORD(hx,x); |
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| 82 | ix = hx&0x7fffffff; |
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| 83 | if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */ |
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| 84 | if(ix< 0x3e300000) { /* |x|<2**-28 */ |
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| 85 | if(huge+x>one) return x; /* return x inexact except 0 */ |
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| 86 | } |
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| 87 | if(ix>0x41b00000) { /* |x| > 2**28 */ |
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| 88 | w = __ieee754_log(fabs(x))+ln2; |
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| 89 | } else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */ |
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| 90 | t = fabs(x); |
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| 91 | w = __ieee754_log(2.0*t+one/(__ieee754_sqrt(x*x+one)+t)); |
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| 92 | } else { /* 2.0 > |x| > 2**-28 */ |
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| 93 | t = x*x; |
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| 94 | w =log1p(fabs(x)+t/(one+__ieee754_sqrt(one+t))); |
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| 95 | } |
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| 96 | if(hx>0) return w; else return -w; |
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| 97 | } |
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| 98 | |
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| 99 | #endif /* _DOUBLE_IS_32BITS */ |
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