1 files changed, 66 insertions, 0 deletions
diff --git a/pl/math/sinh_3u.c b/pl/math/sinh_3u.c
new file mode 100644
index 0000000..f534815
--- /dev/null
+++ b/pl/math/sinh_3u.c
@@ -0,0 +1,66 @@
+/*
+ * Double-precision sinh(x) function.
+ *
+ * Copyright (c) 2022-2023, Arm Limited.
+ * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
+ */
+
+#include "math_config.h"
+#include "pl_sig.h"
+#include "pl_test.h"
+
+#define AbsMask 0x7fffffffffffffff
+#define Half 0x3fe0000000000000
+#define OFlowBound                                                             \
+  0x40862e42fefa39f0 /* 0x1.62e42fefa39fp+9, above which using expm1 results   \
+			in NaN.  */
+
+double
+__exp_dd (double, double);
+
+/* Approximation for double-precision sinh(x) using expm1.
+   sinh(x) = (exp(x) - exp(-x)) / 2.
+   The greatest observed error is 2.57 ULP:
+   __v_sinh(0x1.9fb1d49d1d58bp-2) got 0x1.ab34e59d678dcp-2
+				 want 0x1.ab34e59d678d9p-2.  */
+double
+sinh (double x)
+{
+  uint64_t ix = asuint64 (x);
+  uint64_t iax = ix & AbsMask;
+  double ax = asdouble (iax);
+  uint64_t sign = ix & ~AbsMask;
+  double halfsign = asdouble (Half | sign);
+
+  if (unlikely (iax >= OFlowBound))
+    {
+      /* Special values and overflow.  */
+      if (unlikely (iax > 0x7ff0000000000000))
+	return __math_invalidf (x);
+      /* expm1 overflows a little before sinh. We have to fill this
+	 gap by using a different algorithm, in this case we use a
+	 double-precision exp helper. For large x sinh(x) is dominated
+	 by exp(x), however we cannot compute exp without overflow
+	 either. We use the identity: exp(a) = (exp(a / 2)) ^ 2
+	 to compute sinh(x) ~= (exp(|x| / 2)) ^ 2 / 2    for x > 0
+			    ~= (exp(|x| / 2)) ^ 2 / -2   for x < 0.  */
+      double e = __exp_dd (ax / 2, 0);
+      return (e * halfsign) * e;
+    }
+
+  /* Use expm1f to retain acceptable precision for small numbers.
+     Let t = e^(|x|) - 1.  */
+  double t = expm1 (ax);
+  /* Then sinh(x) = (t + t / (t + 1)) / 2   for x > 0
+		    (t + t / (t + 1)) / -2  for x < 0.  */
+  return (t + t / (t + 1)) * halfsign;
+}
+
+PL_SIG (S, D, 1, sinh, -10.0, 10.0)
+PL_TEST_ULP (sinh, 2.08)
+PL_TEST_INTERVAL (sinh, 0, 0x1p-51, 100)
+PL_TEST_INTERVAL (sinh, -0, -0x1p-51, 100)
+PL_TEST_INTERVAL (sinh, 0x1p-51, 0x1.62e42fefa39fp+9, 100000)
+PL_TEST_INTERVAL (sinh, -0x1p-51, -0x1.62e42fefa39fp+9, 100000)
+PL_TEST_INTERVAL (sinh, 0x1.62e42fefa39fp+9, inf, 1000)
+PL_TEST_INTERVAL (sinh, -0x1.62e42fefa39fp+9, -inf, 1000)