Index: fusl/src/math/asinh.c |
diff --git a/fusl/src/math/asinh.c b/fusl/src/math/asinh.c |
new file mode 100644 |
index 0000000000000000000000000000000000000000..0829f228ef9d2540578c6512736c107b25c2bc06 |
--- /dev/null |
+++ b/fusl/src/math/asinh.c |
@@ -0,0 +1,28 @@ |
+#include "libm.h" |
+ |
+/* asinh(x) = sign(x)*log(|x|+sqrt(x*x+1)) ~= x - x^3/6 + o(x^5) */ |
+double asinh(double x) |
+{ |
+ union {double f; uint64_t i;} u = {.f = x}; |
+ unsigned e = u.i >> 52 & 0x7ff; |
+ unsigned s = u.i >> 63; |
+ |
+ /* |x| */ |
+ u.i &= (uint64_t)-1/2; |
+ x = u.f; |
+ |
+ if (e >= 0x3ff + 26) { |
+ /* |x| >= 0x1p26 or inf or nan */ |
+ x = log(x) + 0.693147180559945309417232121458176568; |
+ } else if (e >= 0x3ff + 1) { |
+ /* |x| >= 2 */ |
+ x = log(2*x + 1/(sqrt(x*x+1)+x)); |
+ } else if (e >= 0x3ff - 26) { |
+ /* |x| >= 0x1p-26, up to 1.6ulp error in [0.125,0.5] */ |
+ x = log1p(x + x*x/(sqrt(x*x+1)+1)); |
+ } else { |
+ /* |x| < 0x1p-26, raise inexact if x != 0 */ |
+ FORCE_EVAL(x + 0x1p120f); |
+ } |
+ return s ? -x : x; |
+} |