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| 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 |
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