1 files changed, 66 insertions, 0 deletions
diff --git a/pl/math/acosh_3u.c b/pl/math/acosh_3u.c
new file mode 100644
index 0000000..4e2cb67
--- /dev/null
+++ b/pl/math/acosh_3u.c
@@ -0,0 +1,66 @@
+/*
+ * Double-precision acosh(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 Ln2 (0x1.62e42fefa39efp-1)
+#define MinusZero (0x8000000000000000)
+#define SquareLim (0x5fe0000000000000) /* asuint64(0x1.0p511).  */
+#define Two (0x4000000000000000)       /* asuint64(2.0).  */
+
+double
+optr_aor_log_f64 (double);
+
+double
+log1p (double);
+
+/* acosh approximation using a variety of approaches on different intervals:
+
+   acosh(x) = ln(x + sqrt(x * x - 1)).
+
+   x >= 2^511: We cannot square x without overflow. For huge x, sqrt(x*x - 1) is
+   close enough to x that we can calculate the result by ln(2x) == ln(x) +
+   ln(2). The greatest observed error in this region is 0.98 ULP:
+   acosh(0x1.1b9bf42923d1dp+853) got 0x1.28066a11a7c7fp+9
+				want 0x1.28066a11a7c8p+9.
+
+   x > 2: Calculate the result directly using definition of acosh(x). Greatest
+   observed error in this region is 1.33 ULP:
+   acosh(0x1.1e45d14bfcfa2p+1) got 0x1.71a06f50c34b5p+0
+			      want 0x1.71a06f50c34b6p+0.
+
+   0 <= x <= 2: Calculate the result using log1p. For x < 1, acosh(x) is
+   undefined. For 1 <= x <= 2, the largest observed error is 2.69 ULP:
+   acosh(0x1.073528248093p+0) got 0x1.e4d9bd20684f3p-3
+			     want 0x1.e4d9bd20684f6p-3.  */
+double
+acosh (double x)
+{
+  uint64_t ix = asuint64 (x);
+
+  if (unlikely (ix >= MinusZero))
+    return __math_invalid (x);
+
+  if (unlikely (ix >= SquareLim))
+    return optr_aor_log_f64 (x) + Ln2;
+
+  if (ix >= Two)
+    return optr_aor_log_f64 (x + sqrt (x * x - 1));
+
+  double xm1 = x - 1;
+  return log1p (xm1 + sqrt (2 * xm1 + xm1 * xm1));
+}
+
+PL_SIG (S, D, 1, acosh, 1.0, 10.0)
+PL_TEST_ULP (acosh, 2.19)
+PL_TEST_INTERVAL (acosh, 0, 1, 10000)
+PL_TEST_INTERVAL (acosh, 1, 2, 100000)
+PL_TEST_INTERVAL (acosh, 2, 0x1p511, 100000)
+PL_TEST_INTERVAL (acosh, 0x1p511, inf, 100000)
+PL_TEST_INTERVAL (acosh, -0, -inf, 10000)