1 files changed, 100 insertions, 0 deletions
diff --git a/pl/math/acos_2u.c b/pl/math/acos_2u.c
new file mode 100644
index 000000000000..9ec6894f1d81
--- /dev/null
+++ b/pl/math/acos_2u.c
@@ -0,0 +1,100 @@
+/*
+ * Double-precision acos(x) function.
+ *
+ * Copyright (c) 2023, Arm Limited.
+ * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
+ */
+
+#include "math_config.h"
+#include "poly_scalar_f64.h"
+#include "pl_sig.h"
+#include "pl_test.h"
+
+#define AbsMask (0x7fffffffffffffff)
+#define Half (0x3fe0000000000000)
+#define One (0x3ff0000000000000)
+#define PiOver2 (0x1.921fb54442d18p+0)
+#define Pi (0x1.921fb54442d18p+1)
+#define Small (0x3c90000000000000) /* 2^-53.  */
+#define Small16 (0x3c90)
+#define QNaN (0x7ff8)
+
+/* Fast implementation of double-precision acos(x) based on polynomial
+   approximation of double-precision asin(x).
+
+   For x < Small, approximate acos(x) by pi/2 - x. Small = 2^-53 for correct
+   rounding.
+
+   For |x| in [Small, 0.5], use the trigonometric identity
+
+     acos(x) = pi/2 - asin(x)
+
+   and use an order 11 polynomial P such that the final approximation of asin is
+   an odd polynomial: asin(x) ~ x + x^3 * P(x^2).
+
+   The largest observed error in this region is 1.18 ulps,
+   acos(0x1.fbab0a7c460f6p-2) got 0x1.0d54d1985c068p+0
+			     want 0x1.0d54d1985c069p+0.
+
+   For |x| in [0.5, 1.0], use the following development of acos(x) near x = 1
+
+     acos(x) ~ pi/2 - 2 * sqrt(z) (1 + z * P(z))
+
+   where z = (1-x)/2, z is near 0 when x approaches 1, and P contributes to the
+   approximation of asin near 0.
+
+   The largest observed error in this region is 1.52 ulps,
+   acos(0x1.23d362722f591p-1) got 0x1.edbbedf8a7d6ep-1
+			     want 0x1.edbbedf8a7d6cp-1.
+
+   For x in [-1.0, -0.5], use this other identity to deduce the negative inputs
+   from their absolute value: acos(x) = pi - acos(-x).  */
+double
+acos (double x)
+{
+  uint64_t ix = asuint64 (x);
+  uint64_t ia = ix & AbsMask;
+  uint64_t ia16 = ia >> 48;
+  double ax = asdouble (ia);
+  uint64_t sign = ix & ~AbsMask;
+
+  /* Special values and invalid range.  */
+  if (unlikely (ia16 == QNaN))
+    return x;
+  if (ia > One)
+    return __math_invalid (x);
+  if (ia16 < Small16)
+    return PiOver2 - x;
+
+  /* Evaluate polynomial Q(|x|) = z + z * z2 * P(z2) with
+     z2 = x ^ 2         and z = |x|     , if |x| < 0.5
+     z2 = (1 - |x|) / 2 and z = sqrt(z2), if |x| >= 0.5.  */
+  double z2 = ax < 0.5 ? x * x : fma (-0.5, ax, 0.5);
+  double z = ax < 0.5 ? ax : sqrt (z2);
+
+  /* Use a single polynomial approximation P for both intervals.  */
+  double z4 = z2 * z2;
+  double z8 = z4 * z4;
+  double z16 = z8 * z8;
+  double p = estrin_11_f64 (z2, z4, z8, z16, __asin_poly);
+
+  /* Finalize polynomial: z + z * z2 * P(z2).  */
+  p = fma (z * z2, p, z);
+
+  /* acos(|x|) = pi/2 - sign(x) * Q(|x|), for |x| < 0.5
+	       = pi - 2 Q(|x|), for -1.0 < x <= -0.5
+	       = 2 Q(|x|)     , for -0.5 < x < 0.0.  */
+  if (ax < 0.5)
+    return PiOver2 - asdouble (asuint64 (p) | sign);
+
+  return (x <= -0.5) ? fma (-2.0, p, Pi) : 2.0 * p;
+}
+
+PL_SIG (S, D, 1, acos, -1.0, 1.0)
+PL_TEST_ULP (acos, 1.02)
+PL_TEST_INTERVAL (acos, 0, Small, 5000)
+PL_TEST_INTERVAL (acos, Small, 0.5, 50000)
+PL_TEST_INTERVAL (acos, 0.5, 1.0, 50000)
+PL_TEST_INTERVAL (acos, 1.0, 0x1p11, 50000)
+PL_TEST_INTERVAL (acos, 0x1p11, inf, 20000)
+PL_TEST_INTERVAL (acos, -0, -inf, 20000)