1 files changed, 86 insertions, 0 deletions
diff --git a/pl/math/atanh_3u.c b/pl/math/atanh_3u.c
new file mode 100644
index 0000000..a168cd5
--- /dev/null
+++ b/pl/math/atanh_3u.c
@@ -0,0 +1,86 @@
+/*
+ * Double-precision atanh(x) function.
+ *
+ * Copyright (c) 2022-2023, 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 Half 0x3fe0000000000000
+#define One 0x3ff0000000000000
+#define Ln2Hi 0x1.62e42fefa3800p-1
+#define Ln2Lo 0x1.ef35793c76730p-45
+#define OneMHfRt2Top                                                           \
+  0x00095f62 /* top32(asuint64(1)) - top32(asuint64(sqrt(2)/2)).  */
+#define OneTop12 0x3ff
+#define HfRt2Top 0x3fe6a09e /* top32(asuint64(sqrt(2)/2)).  */
+#define BottomMask 0xffffffff
+#define C(i) __log1p_data.coeffs[i]
+
+static inline double
+log1p_inline (double x)
+{
+  /* Helper for calculating log(1 + x) using order-18 polynomial on a reduced
+     interval. Copied from log1p_2u.c, with no special-case handling. See that
+     file for details of the algorithm.  */
+  double m = x + 1;
+  uint64_t mi = asuint64 (m);
+
+  /* Decompose x + 1 into (f + 1) * 2^k, with k chosen such that f is in
+     [sqrt(2)/2, sqrt(2)].  */
+  uint32_t u = (mi >> 32) + OneMHfRt2Top;
+  int32_t k = (int32_t) (u >> 20) - OneTop12;
+  uint32_t utop = (u & 0x000fffff) + HfRt2Top;
+  uint64_t u_red = ((uint64_t) utop << 32) | (mi & BottomMask);
+  double f = asdouble (u_red) - 1;
+
+  /* Correction term for round-off in f.  */
+  double cm = (x - (m - 1)) / m;
+
+  /* Approximate log1p(f) with polynomial.  */
+  double f2 = f * f;
+  double f4 = f2 * f2;
+  double f8 = f4 * f4;
+  double p = fma (f, ESTRIN_18 (f, f2, f4, f8, f8 * f8, C) * f, f);
+
+  /* Recombine log1p(x) = k*log2 + log1p(f) + c/m.  */
+  double kd = k;
+  double y = fma (Ln2Lo, kd, cm);
+  return y + fma (Ln2Hi, kd, p);
+}
+
+/* Approximation for double-precision inverse tanh(x), using a simplified
+   version of log1p. Greatest observed error is 3.00 ULP:
+   atanh(0x1.e58f3c108d714p-4) got 0x1.e7da77672a647p-4
+			      want 0x1.e7da77672a64ap-4.  */
+double
+atanh (double x)
+{
+  uint64_t ix = asuint64 (x);
+  uint64_t sign = ix & ~AbsMask;
+  uint64_t ia = ix & AbsMask;
+
+  if (unlikely (ia == One))
+    return __math_divzero (sign >> 32);
+
+  if (unlikely (ia > One))
+    return __math_invalid (x);
+
+  double halfsign = asdouble (Half | sign);
+  double ax = asdouble (ia);
+  return halfsign * log1p_inline ((2 * ax) / (1 - ax));
+}
+
+PL_SIG (S, D, 1, atanh, -1.0, 1.0)
+PL_TEST_ULP (atanh, 3.00)
+PL_TEST_INTERVAL (atanh, 0, 0x1p-23, 10000)
+PL_TEST_INTERVAL (atanh, -0, -0x1p-23, 10000)
+PL_TEST_INTERVAL (atanh, 0x1p-23, 1, 90000)
+PL_TEST_INTERVAL (atanh, -0x1p-23, -1, 90000)
+PL_TEST_INTERVAL (atanh, 1, inf, 100)
+PL_TEST_INTERVAL (atanh, -1, -inf, 100)