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1 #include "libm.h" | 1 #include "libm.h" |
2 | 2 |
3 /* atanh(x) = log((1+x)/(1-x))/2 = log1p(2x/(1-x))/2 ~= x + x^3/3 + o(x^5) */ | 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) | 4 float atanhf(float x) { |
5 { | 5 union { |
6 » union {float f; uint32_t i;} u = {.f = x}; | 6 float f; |
7 » unsigned s = u.i >> 31; | 7 uint32_t i; |
8 » float_t y; | 8 } u = {.f = x}; |
| 9 unsigned s = u.i >> 31; |
| 10 float_t y; |
9 | 11 |
10 » /* |x| */ | 12 /* |x| */ |
11 » u.i &= 0x7fffffff; | 13 u.i &= 0x7fffffff; |
12 » y = u.f; | 14 y = u.f; |
13 | 15 |
14 » if (u.i < 0x3f800000 - (1<<23)) { | 16 if (u.i < 0x3f800000 - (1 << 23)) { |
15 » » if (u.i < 0x3f800000 - (32<<23)) { | 17 if (u.i < 0x3f800000 - (32 << 23)) { |
16 » » » /* handle underflow */ | 18 /* handle underflow */ |
17 » » » if (u.i < (1<<23)) | 19 if (u.i < (1 << 23)) |
18 » » » » FORCE_EVAL((float)(y*y)); | 20 FORCE_EVAL((float)(y * y)); |
19 » » } else { | 21 } else { |
20 » » » /* |x| < 0.5, up to 1.7ulp error */ | 22 /* |x| < 0.5, up to 1.7ulp error */ |
21 » » » y = 0.5f*log1pf(2*y + 2*y*y/(1-y)); | 23 y = 0.5f * log1pf(2 * y + 2 * y * y / (1 - y)); |
22 » » } | 24 } |
23 » } else { | 25 } else { |
24 » » /* avoid overflow */ | 26 /* avoid overflow */ |
25 » » y = 0.5f*log1pf(2*(y/(1-y))); | 27 y = 0.5f * log1pf(2 * (y / (1 - y))); |
26 » } | 28 } |
27 » return s ? -y : y; | 29 return s ? -y : y; |
28 } | 30 } |
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