| 1 | /* s_asinhl.c -- long double version of s_asinh.c. |
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| 2 | */ |
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| 3 | |
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| 4 | /* |
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| 5 | * ==================================================== |
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| 6 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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| 7 | * |
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| 8 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
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| 9 | * Permission to use, copy, modify, and distribute this |
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| 10 | * software is freely granted, provided that this notice |
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| 11 | * is preserved. |
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| 12 | * ==================================================== |
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| 13 | */ |
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| 14 | |
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| 15 | #if defined(LIBM_SCCS) && !defined(lint) |
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| 16 | static char rcsid[] = "$NetBSD: $" ; |
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| 17 | #endif |
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| 18 | |
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| 19 | /* asinhl(x) |
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| 20 | * Method : |
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| 21 | * Based on |
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| 22 | * asinhl(x) = signl(x) * logl [ |x| + sqrtl(x*x+1) ] |
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| 23 | * we have |
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| 24 | * asinhl(x) := x if 1+x*x=1, |
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| 25 | * := signl(x)*(logl(x)+ln2)) for large |x|, else |
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| 26 | * := signl(x)*logl(2|x|+1/(|x|+sqrtl(x*x+1))) if|x|>2, else |
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| 27 | * := signl(x)*log1pl(|x| + x^2/(1 + sqrtl(1+x^2))) |
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| 28 | */ |
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| 29 | |
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| 30 | #include <float.h> |
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| 31 | #include <math.h> |
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| 32 | #include <math_private.h> |
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| 33 | #include <math-underflow.h> |
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| 34 | #include <libm-alias-ldouble.h> |
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| 35 | |
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| 36 | static const _Float128 |
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| 37 | one = 1, |
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| 38 | ln2 = L(6.931471805599453094172321214581765681e-1), |
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| 39 | huge = L(1.0e+4900); |
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| 40 | |
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| 41 | _Float128 |
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| 42 | __asinhl (_Float128 x) |
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| 43 | { |
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| 44 | _Float128 t, w; |
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| 45 | int32_t ix, sign; |
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| 46 | ieee854_long_double_shape_type u; |
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| 47 | |
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| 48 | u.value = x; |
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| 49 | sign = u.parts32.w0; |
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| 50 | ix = sign & 0x7fffffff; |
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| 51 | if (ix == 0x7fff0000) |
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| 52 | return x + x; /* x is inf or NaN */ |
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| 53 | if (ix < 0x3fc70000) |
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| 54 | { /* |x| < 2^ -56 */ |
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| 55 | math_check_force_underflow (x); |
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| 56 | if (huge + x > one) |
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| 57 | return x; /* return x inexact except 0 */ |
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| 58 | } |
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| 59 | u.parts32.w0 = ix; |
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| 60 | if (ix > 0x40350000) |
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| 61 | { /* |x| > 2 ^ 54 */ |
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| 62 | w = __ieee754_logl (u.value) + ln2; |
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| 63 | } |
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| 64 | else if (ix >0x40000000) |
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| 65 | { /* 2^ 54 > |x| > 2.0 */ |
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| 66 | t = u.value; |
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| 67 | w = __ieee754_logl (2.0 * t + one / (sqrtl (x * x + one) + t)); |
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| 68 | } |
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| 69 | else |
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| 70 | { /* 2.0 > |x| > 2 ^ -56 */ |
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| 71 | t = x * x; |
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| 72 | w = __log1pl (u.value + t / (one + sqrtl (one + t))); |
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| 73 | } |
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| 74 | if (sign & 0x80000000) |
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| 75 | return -w; |
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| 76 | else |
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| 77 | return w; |
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| 78 | } |
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| 79 | libm_alias_ldouble (__asinh, asinh) |
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| 80 | |
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