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| 1 #include "libm.h" |
| 2 |
| 3 /* atanh(x) = log((1+x)/(1-x))/2 = log1p(2x/(1-x))/2 ~= x + x^3/3 + o(x^5) */ |
| 4 float atanhf(float x) |
| 5 { |
| 6 union {float f; uint32_t i;} u = {.f = x}; |
| 7 unsigned s = u.i >> 31; |
| 8 float_t y; |
| 9 |
| 10 /* |x| */ |
| 11 u.i &= 0x7fffffff; |
| 12 y = u.f; |
| 13 |
| 14 if (u.i < 0x3f800000 - (1<<23)) { |
| 15 if (u.i < 0x3f800000 - (32<<23)) { |
| 16 /* handle underflow */ |
| 17 if (u.i < (1<<23)) |
| 18 FORCE_EVAL((float)(y*y)); |
| 19 } else { |
| 20 /* |x| < 0.5, up to 1.7ulp error */ |
| 21 y = 0.5f*log1pf(2*y + 2*y*y/(1-y)); |
| 22 } |
| 23 } else { |
| 24 /* avoid overflow */ |
| 25 y = 0.5f*log1pf(2*(y/(1-y))); |
| 26 } |
| 27 return s ? -y : y; |
| 28 } |
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