| 1 | #include "libm.h" |
| 2 | |
| 3 | #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 |
| 4 | long double atanhl(long double x) |
| 5 | { |
| 6 | return atanh(x); |
| 7 | } |
| 8 | #elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384 |
| 9 | /* atanh(x) = log((1+x)/(1-x))/2 = log1p(2x/(1-x))/2 ~= x + x^3/3 + o(x^5) */ |
| 10 | long double atanhl(long double x) |
| 11 | { |
| 12 | union ldshape u = {x}; |
| 13 | unsigned e = u.i.se & 0x7fff; |
| 14 | unsigned s = u.i.se >> 15; |
| 15 | |
| 16 | /* |x| */ |
| 17 | u.i.se = e; |
| 18 | x = u.f; |
| 19 | |
| 20 | if (e < 0x3ff - 1) { |
| 21 | if (e < 0x3ff - LDBL_MANT_DIG/2) { |
| 22 | /* handle underflow */ |
| 23 | if (e == 0) |
| 24 | FORCE_EVAL((float)x); |
| 25 | } else { |
| 26 | /* |x| < 0.5, up to 1.7ulp error */ |
| 27 | x = 0.5*log1pl(2*x + 2*x*x/(1-x)); |
| 28 | } |
| 29 | } else { |
| 30 | /* avoid overflow */ |
| 31 | x = 0.5*log1pl(2*(x/(1-x))); |
| 32 | } |
| 33 | return s ? -x : x; |
| 34 | } |
| 35 | #endif |