1 files changed, 63 insertions, 0 deletions
diff --git a/pl/math/acoshf_2u8.c b/pl/math/acoshf_2u8.c
new file mode 100644
index 0000000..c9cded7
--- /dev/null
+++ b/pl/math/acoshf_2u8.c
@@ -0,0 +1,63 @@
+/*
+ * Single-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 (0x1.62e4p-1f)
+#define MinusZero 0x80000000
+#define SquareLim 0x5f800000 /* asuint(0x1p64).  */
+#define Two 0x40000000
+
+/* Single-precision log from math/.  */
+float
+optr_aor_log_f32 (float);
+
+/* Single-precision log(1+x) from pl/math.  */
+float
+log1pf (float);
+
+/* acoshf approximation using a variety of approaches on different intervals:
+
+   x >= 2^64: 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 error in the region is 0.94 ULP:
+   acoshf(0x1.15f706p+92) got 0x1.022e14p+6 want 0x1.022e16p+6.
+
+   x > 2: Calculate the result directly using definition of asinh(x) = ln(x +
+   sqrt(x*x - 1)). Greatest error in this region is 1.30 ULP:
+   acoshf(0x1.249d8p+1) got 0x1.77e1aep+0 want 0x1.77e1bp+0.
+
+   0 <= x <= 2: Calculate the result using log1p. For x < 1, acosh(x) is
+   undefined. For 1 <= x <= 2, the greatest error is 2.78 ULP:
+   acoshf(0x1.07887p+0) got 0x1.ef9e9cp-3 want 0x1.ef9ea2p-3.  */
+float
+acoshf (float x)
+{
+  uint32_t ix = asuint (x);
+
+  if (unlikely (ix >= MinusZero))
+    return __math_invalidf (x);
+
+  if (unlikely (ix >= SquareLim))
+    return optr_aor_log_f32 (x) + Ln2;
+
+  if (ix > Two)
+    return optr_aor_log_f32 (x + sqrtf (x * x - 1));
+
+  float xm1 = x - 1;
+  return log1pf (xm1 + sqrtf (2 * xm1 + xm1 * xm1));
+}
+
+PL_SIG (S, F, 1, acosh, 1.0, 10.0)
+PL_TEST_ULP (acoshf, 2.30)
+PL_TEST_INTERVAL (acoshf, 0, 1, 100)
+PL_TEST_INTERVAL (acoshf, 1, 2, 10000)
+PL_TEST_INTERVAL (acoshf, 2, 0x1p64, 100000)
+PL_TEST_INTERVAL (acoshf, 0x1p64, inf, 100000)
+PL_TEST_INTERVAL (acoshf, -0, -inf, 10000)