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Diffstat (limited to 'lib/msun/src/s_tanhl.c')
| -rw-r--r-- | lib/msun/src/s_tanhl.c | 172 |
1 files changed, 172 insertions, 0 deletions
diff --git a/lib/msun/src/s_tanhl.c b/lib/msun/src/s_tanhl.c new file mode 100644 index 0000000..886158b --- /dev/null +++ b/lib/msun/src/s_tanhl.c @@ -0,0 +1,172 @@ +/* from: FreeBSD: head/lib/msun/src/s_tanhl.c XXX */ + +/* @(#)s_tanh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include <sys/cdefs.h> +__FBSDID("$FreeBSD$"); + +/* + * See s_tanh.c for complete comments. + * + * Converted to long double by Bruce D. Evans. + */ + +#include <float.h> +#ifdef __i386__ +#include <ieeefp.h> +#endif + +#include "math.h" +#include "math_private.h" +#include "fpmath.h" +#include "k_expl.h" + +#if LDBL_MAX_EXP != 0x4000 +/* We also require the usual expsign encoding. */ +#error "Unsupported long double format" +#endif + +#define BIAS (LDBL_MAX_EXP - 1) + +static const volatile double tiny = 1.0e-300; +static const double one = 1.0; +#if LDBL_MANT_DIG == 64 +/* + * Domain [-0.25, 0.25], range ~[-1.6304e-22, 1.6304e-22]: + * |tanh(x)/x - t(x)| < 2**-72.3 + */ +static const union IEEEl2bits +T3u = LD80C(0xaaaaaaaaaaaaaa9f, -2, -3.33333333333333333017e-1L); +#define T3 T3u.e +static const double +T5 = 1.3333333333333314e-1, /* 0x1111111111110a.0p-55 */ +T7 = -5.3968253968210485e-2, /* -0x1ba1ba1ba1a1a1.0p-57 */ +T9 = 2.1869488531393817e-2, /* 0x1664f488172022.0p-58 */ +T11 = -8.8632352345964591e-3, /* -0x1226e34bc138d5.0p-59 */ +T13 = 3.5921169709993771e-3, /* 0x1d6d371d3e400f.0p-61 */ +T15 = -1.4555786415756001e-3, /* -0x17d923aa63814d.0p-62 */ +T17 = 5.8645267876296793e-4, /* 0x13378589b85aa7.0p-63 */ +T19 = -2.1121033571392224e-4; /* -0x1baf0af80c4090.0p-65 */ +#elif LDBL_MANT_DIG == 113 +/* + * Domain [-0.25, 0.25], range ~[-2.4211e-37, 2.4211e-37]: + * |tanh(x)/x - t(x)| < 2**121.6 + */ +static const long double +T3 = -3.33333333333333333333333333333332980e-1L, /* -0x1555555555555555555555555554e.0p-114L */ +T5 = 1.33333333333333333333333333332707260e-1L, /* 0x1111111111111111111111110ab7b.0p-115L */ +T7 = -5.39682539682539682539682535723482314e-2L, /* -0x1ba1ba1ba1ba1ba1ba1ba17b5fc98.0p-117L */ +T9 = 2.18694885361552028218693591149061717e-2L, /* 0x1664f4882c10f9f32d6b1a12a25e5.0p-118L */ +T11 = -8.86323552990219656883762347736381851e-3L, /* -0x1226e355e6c23c8f5a5a0f386cb4d.0p-119L */ +T13 = 3.59212803657248101358314398220822722e-3L, /* 0x1d6d3d0e157ddfb403ad3637442c6.0p-121L */ +T15 = -1.45583438705131796512568010348874662e-3L; /* -0x17da36452b75e150c44cc34253b34.0p-122L */ +static const double +T17 = 5.9002744094556621e-4, /* 0x1355824803668e.0p-63 */ +T19 = -2.3912911424260516e-4, /* -0x1f57d7734c8dde.0p-65 */ +T21 = 9.6915379535512898e-5, /* 0x1967e18ad6a6ca.0p-66 */ +T23 = -3.9278322983156353e-5, /* -0x1497d8e6b75729.0p-67 */ +T25 = 1.5918887220143869e-5, /* 0x10b1319998cafa.0p-68 */ +T27 = -6.4514295231630956e-6, /* -0x1b0f2b71b218eb.0p-70 */ +T29 = 2.6120754043964365e-6, /* 0x15e963a3cf3a39.0p-71 */ +T31 = -1.0407567231003314e-6, /* -0x1176041e656869.0p-72 */ +T33 = 3.4744117554063574e-7; /* 0x1750fe732cab9c.0p-74 */ +#endif /* LDBL_MANT_DIG == 64 */ + +static inline long double +divl(long double a, long double b, long double c, long double d, + long double e, long double f) +{ + long double inv, r; + float fr, fw; + + _2sumF(a, c); + b = b + c; + _2sumF(d, f); + e = e + f; + + inv = 1 / (d + e); + + r = (a + b) * inv; + fr = r; + r = fr; + + fw = d + e; + e = d - fw + e; + d = fw; + + r = r + (a - d * r + b - e * r) * inv; + + return r; +} + +long double +tanhl(long double x) +{ + long double hi,lo,s,x2,x4,z; + double dx2; + int16_t jx,ix; + + GET_LDBL_EXPSIGN(jx,x); + ix = jx&0x7fff; + + /* x is INF or NaN */ + if(ix>=0x7fff) { + if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */ + else return one/x-one; /* tanh(NaN) = NaN */ + } + + ENTERI(); + + /* |x| < 40 */ + if (ix < 0x4004 || fabsl(x) < 40) { /* |x|<40 */ + if (__predict_false(ix<BIAS-(LDBL_MANT_DIG+1)/2)) { /* |x|<TINY */ + /* tanh(+-0) = +0; tanh(tiny) = tiny(-+) with inexact: */ + return (x == 0 ? x : (0x1p200 * x - x) * 0x1p-200); + } + if (ix<0x3ffd) { /* |x|<0.25 */ + x2 = x*x; +#if LDBL_MANT_DIG == 64 + x4 = x2*x2; + RETURNI(((T19*x2 + T17)*x4 + (T15*x2 + T13))*(x2*x*x2*x4*x4) + + ((T11*x2 + T9)*x4 + (T7*x2 + T5))*(x2*x*x2) + + T3*(x2*x) + x); +#elif LDBL_MANT_DIG == 113 + dx2 = x2; +#if 0 + RETURNI(((((((((((((((T33*dx2 + T31)*dx2 + T29)*dx2 + T27)*dx2 + + T25)*x2 + T23)*x2 + T21)*x2 + T19)*x2 + T17)*x2 + + T15)*x2 + T13)*x2 + T11)*x2 + T9)*x2 + T7)*x2 + T5)* + (x2*x*x2) + + T3*(x2*x) + x); +#else + long double q = ((((((((((((((T33*dx2 + T31)*dx2 + T29)*dx2 + T27)*dx2 + + T25)*x2 + T23)*x2 + T21)*x2 + T19)*x2 + T17)*x2 + + T15)*x2 + T13)*x2 + T11)*x2 + T9)*x2 + T7)*x2 + T5)* + (x2*x*x2); + RETURNI(q + T3*(x2*x) + x); +#endif +#endif + } + k_hexpl(2*fabsl(x), &hi, &lo); + if (ix<0x4001 && fabsl(x) < 1.5) /* |x|<1.5 */ + z = divl(hi, lo, -0.5, hi, lo, 0.5); + else + z = one - one/(lo+0.5+hi); + /* |x| >= 40, return +-1 */ + } else { + z = one - tiny; /* raise inexact flag */ + } + s = 1; + if (jx<0) s = -1; + RETURNI(s*z); +} |
