Index: fusl/src/math/atanh.c |
diff --git a/fusl/src/math/atanh.c b/fusl/src/math/atanh.c |
new file mode 100644 |
index 0000000000000000000000000000000000000000..63a035d7063ae2d5df2c31728e10e5d471209c79 |
--- /dev/null |
+++ b/fusl/src/math/atanh.c |
@@ -0,0 +1,29 @@ |
+#include "libm.h" |
+ |
+/* atanh(x) = log((1+x)/(1-x))/2 = log1p(2x/(1-x))/2 ~= x + x^3/3 + o(x^5) */ |
+double atanh(double x) |
+{ |
+ union {double f; uint64_t i;} u = {.f = x}; |
+ unsigned e = u.i >> 52 & 0x7ff; |
+ unsigned s = u.i >> 63; |
+ double_t y; |
+ |
+ /* |x| */ |
+ u.i &= (uint64_t)-1/2; |
+ y = u.f; |
+ |
+ if (e < 0x3ff - 1) { |
+ if (e < 0x3ff - 32) { |
+ /* handle underflow */ |
+ if (e == 0) |
+ FORCE_EVAL((float)y); |
+ } else { |
+ /* |x| < 0.5, up to 1.7ulp error */ |
+ y = 0.5*log1p(2*y + 2*y*y/(1-y)); |
+ } |
+ } else { |
+ /* avoid overflow */ |
+ y = 0.5*log1p(2*(y/(1-y))); |
+ } |
+ return s ? -y : y; |
+} |