Initial import

libc/math/sinh.c

@@ -0,0 +1,39 @@
+#include "libc/math/libm.h"
+
+/* sinh(x) = (exp(x) - 1/exp(x))/2
+ *         = (exp(x)-1 + (exp(x)-1)/exp(x))/2
+ *         = x + x^3/6 + o(x^5)
+ */
+double sinh(double x)
+{
+	union {double f; uint64_t i;} u = {.f = x};
+	uint32_t w;
+	double t, h, absx;
+
+	h = 0.5;
+	if (u.i >> 63)
+		h = -h;
+	/* |x| */
+	u.i &= (uint64_t)-1/2;
+	absx = u.f;
+	w = u.i >> 32;
+
+	/* |x| < log(DBL_MAX) */
+	if (w < 0x40862e42) {
+		t = expm1(absx);
+		if (w < 0x3ff00000) {
+			if (w < 0x3ff00000 - (26<<20))
+				/* note: inexact and underflow are raised by expm1 */
+				/* note: this branch avoids spurious underflow */
+				return x;
+			return h*(2*t - t*t/(t+1));
+		}
+		/* note: |x|>log(0x1p26)+eps could be just h*exp(x) */
+		return h*(t + t/(t+1));
+	}
+
+	/* |x| > log(DBL_MAX) or nan */
+	/* note: the result is stored to handle overflow */
+	t = 2*h*__expo2(absx);
+	return t;
+}