| /* 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: head/lib/msun/src/s_tanhl.c 306527 2016-09-30 20:20:07Z emaste $"); |
| |
| /* |
| * 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; |
| #if LDBL_MANT_DIG == 113 |
| double dx2; |
| #endif |
| 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); |
| } |