1 files changed, 86 insertions, 0 deletions
diff --git a/pl/math/asinh_2u5.c b/pl/math/asinh_2u5.c
new file mode 100644
index 0000000..f167955
--- /dev/null
+++ b/pl/math/asinh_2u5.c
@@ -0,0 +1,86 @@
+/*
+ * Double-precision asinh(x) function
+ *
+ * Copyright (c) 2022-2023, Arm Limited.
+ * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
+ */
+#include "estrin.h"
+#include "math_config.h"
+#include "pl_sig.h"
+#include "pl_test.h"
+
+#define AbsMask 0x7fffffffffffffff
+#define ExpM26 0x3e50000000000000 /* asuint64(0x1.0p-26).  */
+#define One 0x3ff0000000000000	  /* asuint64(1.0).  */
+#define Exp511 0x5fe0000000000000 /* asuint64(0x1.0p511).  */
+#define Ln2 0x1.62e42fefa39efp-1
+
+double
+optr_aor_log_f64 (double);
+
+/* Scalar double-precision asinh implementation. This routine uses different
+   approaches on different intervals:
+
+   |x| < 2^-26: Return x. Function is exact in this region.
+
+   |x| < 1: Use custom order-17 polynomial. This is least accurate close to 1.
+     The largest observed error in this region is 1.47 ULPs:
+     asinh(0x1.fdfcd00cc1e6ap-1) got 0x1.c1d6bf874019bp-1
+				want 0x1.c1d6bf874019cp-1.
+
+   |x| < 2^511: Upper bound of this region is close to sqrt(DBL_MAX). Calculate
+     the result directly using the definition asinh(x) = ln(x + sqrt(x*x + 1)).
+     The largest observed error in this region is 2.03 ULPs:
+     asinh(-0x1.00094e0f39574p+0) got -0x1.c3508eb6a681ep-1
+				 want -0x1.c3508eb6a682p-1.
+
+   |x| >= 2^511: We cannot square x without overflow at a low
+     cost. At very large x, asinh(x) ~= ln(2x). At huge x we cannot
+     even double x without overflow, so calculate this as ln(x) +
+     ln(2). The largest observed error in this region is 0.98 ULPs at many
+     values, for instance:
+     asinh(0x1.5255a4cf10319p+975) got 0x1.52652f4cb26cbp+9
+				  want 0x1.52652f4cb26ccp+9.  */
+double
+asinh (double x)
+{
+  uint64_t ix = asuint64 (x);
+  uint64_t ia = ix & AbsMask;
+  double ax = asdouble (ia);
+  uint64_t sign = ix & ~AbsMask;
+
+  if (ia < ExpM26)
+    {
+      return x;
+    }
+
+  if (ia < One)
+    {
+      double x2 = x * x;
+      double z2 = x2 * x2;
+      double z4 = z2 * z2;
+      double z8 = z4 * z4;
+#define C(i) __asinh_data.poly[i]
+      double p = ESTRIN_17 (x2, z2, z4, z8, z8 * z8, C);
+      double y = fma (p, x2 * ax, ax);
+      return asdouble (asuint64 (y) | sign);
+    }
+
+  if (unlikely (ia >= Exp511))
+    {
+      return asdouble (asuint64 (optr_aor_log_f64 (ax) + Ln2) | sign);
+    }
+
+  return asdouble (asuint64 (optr_aor_log_f64 (ax + sqrt (ax * ax + 1)))
+		   | sign);
+}
+
+PL_SIG (S, D, 1, asinh, -10.0, 10.0)
+PL_TEST_ULP (asinh, 1.54)
+PL_TEST_INTERVAL (asinh, -0x1p-26, 0x1p-26, 50000)
+PL_TEST_INTERVAL (asinh, 0x1p-26, 1.0, 40000)
+PL_TEST_INTERVAL (asinh, -0x1p-26, -1.0, 10000)
+PL_TEST_INTERVAL (asinh, 1.0, 100.0, 40000)
+PL_TEST_INTERVAL (asinh, -1.0, -100.0, 10000)
+PL_TEST_INTERVAL (asinh, 100.0, inf, 50000)
+PL_TEST_INTERVAL (asinh, -100.0, -inf, 10000)