1 files changed, 82 insertions, 0 deletions
diff --git a/pl/math/tanh_3u.c b/pl/math/tanh_3u.c
new file mode 100644
index 0000000..46d9fb3
--- /dev/null
+++ b/pl/math/tanh_3u.c
@@ -0,0 +1,82 @@
+/*
+ * Double-precision tanh(x) function.
+ *
+ * Copyright (c) 2023, Arm Limited.
+ * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
+ */
+#include "math_config.h"
+#include "estrin.h"
+#include "pl_sig.h"
+#include "pl_test.h"
+
+#define AbsMask 0x7fffffffffffffff
+#define InvLn2 0x1.71547652b82fep0
+#define Ln2hi 0x1.62e42fefa39efp-1
+#define Ln2lo 0x1.abc9e3b39803fp-56
+#define Shift 0x1.8p52
+#define C(i) __expm1_poly[i]
+
+#define BoringBound 0x403241bf835f9d5f /* asuint64 (0x1.241bf835f9d5fp+4).  */
+#define TinyBound 0x3e40000000000000   /* asuint64 (0x1p-27).  */
+#define One 0x3ff0000000000000
+
+static inline double
+expm1_inline (double x)
+{
+  /* Helper routine for calculating exp(x) - 1. Copied from expm1_2u5.c, with
+     several simplifications:
+     - No special-case handling for tiny or special values.
+     - Simpler combination of p and t in final stage of the algorithm.
+     - Use shift-and-add instead of ldexp to calculate t.  */
+
+  /* Reduce argument: f in [-ln2/2, ln2/2], i is exact.  */
+  double j = fma (InvLn2, x, Shift) - Shift;
+  int64_t i = j;
+  double f = fma (j, -Ln2hi, x);
+  f = fma (j, -Ln2lo, f);
+
+  /* Approximate expm1(f) using polynomial.  */
+  double f2 = f * f;
+  double f4 = f2 * f2;
+  double p = fma (f2, ESTRIN_10 (f, f2, f4, f4 * f4, C), f);
+
+  /* t = 2 ^ i.  */
+  double t = asdouble ((uint64_t) (i + 1023) << 52);
+  /* expm1(x) = p * t + (t - 1).  */
+  return fma (p, t, t - 1);
+}
+
+/* Approximation for double-precision tanh(x), using a simplified version of
+   expm1. The greatest observed error is 2.75 ULP:
+   tanh(-0x1.c143c3a44e087p-3) got -0x1.ba31ba4691ab7p-3
+			      want -0x1.ba31ba4691ab4p-3.  */
+double
+tanh (double x)
+{
+  uint64_t ix = asuint64 (x);
+  uint64_t ia = ix & AbsMask;
+  uint64_t sign = ix & ~AbsMask;
+
+  if (unlikely (ia > BoringBound))
+    {
+      if (ia > 0x7ff0000000000000)
+	return __math_invalid (x);
+      return asdouble (One | sign);
+    }
+
+  if (unlikely (ia < TinyBound))
+    return x;
+
+  /* tanh(x) = (e^2x - 1) / (e^2x + 1).  */
+  double q = expm1_inline (2 * x);
+  return q / (q + 2);
+}
+
+PL_SIG (S, D, 1, tanh, -10.0, 10.0)
+PL_TEST_ULP (tanh, 2.26)
+PL_TEST_INTERVAL (tanh, 0, TinyBound, 1000)
+PL_TEST_INTERVAL (tanh, -0, -TinyBound, 1000)
+PL_TEST_INTERVAL (tanh, TinyBound, BoringBound, 100000)
+PL_TEST_INTERVAL (tanh, -TinyBound, -BoringBound, 100000)
+PL_TEST_INTERVAL (tanh, BoringBound, inf, 1000)
+PL_TEST_INTERVAL (tanh, -BoringBound, -inf, 1000)