1 files changed, 91 insertions, 0 deletions
diff --git a/pl/math/tanhf_2u6.c b/pl/math/tanhf_2u6.c
new file mode 100644
index 0000000..76e54a4
--- /dev/null
+++ b/pl/math/tanhf_2u6.c
@@ -0,0 +1,91 @@
+/*
+ * Single-precision tanh(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 BoringBound                                                            \
+  0x41102cb3 /* 0x1.205966p+3, above which tanhf rounds to 1 (or -1 for        \
+		negative).  */
+#define AbsMask 0x7fffffff
+#define One 0x3f800000
+
+#define Shift (0x1.8p23f)
+#define InvLn2 (0x1.715476p+0f)
+#define Ln2hi (0x1.62e4p-1f)
+#define Ln2lo (0x1.7f7d1cp-20f)
+
+#define C(i) __expm1f_poly[i]
+
+static inline float
+expm1f_inline (float x)
+{
+  /* Helper routine for calculating exp(x) - 1.
+     Copied from expm1f_1u6.c, with several simplifications:
+     - No special-case handling for tiny or special values, instead return early
+       from the main routine.
+     - No special handling for large values:
+       - No early return for infinity.
+       - Simpler combination of p and t in final stage of algorithm.
+       - |i| < 27, so can calculate t by simpler shift-and-add, instead of
+	 ldexpf (same as vector algorithm).  */
+
+  /* Reduce argument: f in [-ln2/2, ln2/2], i is exact.  */
+  float j = fmaf (InvLn2, x, Shift) - Shift;
+  int32_t i = j;
+  float f = fmaf (j, -Ln2hi, x);
+  f = fmaf (j, -Ln2lo, f);
+
+  /* Approximate expm1(f) with polynomial P, expm1(f) ~= f + f^2 * P(f).
+     Uses Estrin scheme, where the main expm1f routine uses Horner.  */
+  float f2 = f * f;
+  float p_01 = fmaf (f, C (1), C (0));
+  float p_23 = fmaf (f, C (3), C (2));
+  float p = fmaf (f2, p_23, p_01);
+  p = fmaf (f2 * f2, C (4), p);
+  p = fmaf (f2, p, f);
+
+  /* t = 2^i.  */
+  float t = asfloat ((uint32_t) (i + 127) << 23);
+  /* expm1(x) ~= p * t + (t - 1).  */
+  return fmaf (p, t, t - 1);
+}
+
+/* Approximation for single-precision tanh(x), using a simplified version of
+   expm1f. The maximum error is 2.58 ULP:
+   tanhf(0x1.fa5eep-5) got 0x1.f9ba02p-5
+		      want 0x1.f9ba08p-5.  */
+float
+tanhf (float x)
+{
+  uint32_t ix = asuint (x);
+  uint32_t iax = ix & AbsMask;
+  uint32_t sign = ix & ~AbsMask;
+
+  if (unlikely (iax > BoringBound))
+    {
+      if (iax > 0x7f800000)
+	return __math_invalidf (x);
+      return asfloat (One | sign);
+    }
+
+  if (unlikely (iax < 0x34000000))
+    return x;
+
+  /* tanh(x) = (e^2x - 1) / (e^2x + 1).  */
+  float q = expm1f_inline (2 * x);
+  return q / (q + 2);
+}
+
+PL_SIG (S, F, 1, tanh, -10.0, 10.0)
+PL_TEST_ULP (tanhf, 2.09)
+PL_TEST_INTERVAL (tanhf, 0, 0x1p-23, 1000)
+PL_TEST_INTERVAL (tanhf, -0, -0x1p-23, 1000)
+PL_TEST_INTERVAL (tanhf, 0x1p-23, 0x1.205966p+3, 100000)
+PL_TEST_INTERVAL (tanhf, -0x1p-23, -0x1.205966p+3, 100000)
+PL_TEST_INTERVAL (tanhf, 0x1.205966p+3, inf, 100)
+PL_TEST_INTERVAL (tanhf, -0x1.205966p+3, -inf, 100)