1 files changed, 73 insertions, 0 deletions
diff --git a/pl/math/atan_2u5.c b/pl/math/atan_2u5.c
new file mode 100644
index 0000000..ee47701
--- /dev/null
+++ b/pl/math/atan_2u5.c
@@ -0,0 +1,73 @@
+/*
+ * Double-precision atan(x) function.
+ *
+ * Copyright (c) 2022-2023, Arm Limited.
+ * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
+ */
+
+#include "pl_sig.h"
+#include "pl_test.h"
+#include "atan_common.h"
+
+#define AbsMask 0x7fffffffffffffff
+#define PiOver2 0x1.921fb54442d18p+0
+#define TinyBound 0x3e1 /* top12(asuint64(0x1p-30)).  */
+#define BigBound 0x434	/* top12(asuint64(0x1p53)).  */
+#define OneTop 0x3ff
+
+/* Fast implementation of double-precision atan.
+   Based on atan(x) ~ shift + z + z^3 * P(z^2) with reduction to [0,1] using
+   z=1/x and shift = pi/2. Maximum observed error is 2.27 ulps:
+   atan(0x1.0005af27c23e9p+0) got 0x1.9225645bdd7c1p-1
+			     want 0x1.9225645bdd7c3p-1.  */
+double
+atan (double x)
+{
+  uint64_t ix = asuint64 (x);
+  uint64_t sign = ix & ~AbsMask;
+  uint64_t ia = ix & AbsMask;
+  uint32_t ia12 = ia >> 52;
+
+  if (unlikely (ia12 >= BigBound || ia12 < TinyBound))
+    {
+      if (ia12 < TinyBound)
+	/* Avoid underflow by returning x.  */
+	return x;
+      if (ia > 0x7ff0000000000000)
+	/* Propagate NaN.  */
+	return __math_invalid (x);
+      /* atan(x) rounds to PiOver2 for large x.  */
+      return asdouble (asuint64 (PiOver2) ^ sign);
+    }
+
+  double z, az, shift;
+  if (ia12 >= OneTop)
+    {
+      /* For x > 1, use atan(x) = pi / 2 + atan(-1 / x).  */
+      z = -1.0 / x;
+      shift = PiOver2;
+      /* Use absolute value only when needed (odd powers of z).  */
+      az = -fabs (z);
+    }
+  else
+    {
+      /* For x < 1, approximate atan(x) directly.  */
+      z = x;
+      shift = 0;
+      az = asdouble (ia);
+    }
+
+  /* Calculate polynomial, shift + z + z^3 * P(z^2).  */
+  double y = eval_poly (z, az, shift);
+  /* Copy sign.  */
+  return asdouble (asuint64 (y) ^ sign);
+}
+
+PL_SIG (S, D, 1, atan, -10.0, 10.0)
+PL_TEST_ULP (atan, 1.78)
+PL_TEST_INTERVAL (atan, 0, 0x1p-30, 10000)
+PL_TEST_INTERVAL (atan, -0, -0x1p-30, 1000)
+PL_TEST_INTERVAL (atan, 0x1p-30, 0x1p53, 900000)
+PL_TEST_INTERVAL (atan, -0x1p-30, -0x1p53, 90000)
+PL_TEST_INTERVAL (atan, 0x1p53, inf, 10000)
+PL_TEST_INTERVAL (atan, -0x1p53, -inf, 1000)