1 files changed, 78 insertions, 0 deletions
diff --git a/pl/math/asinhf_3u5.c b/pl/math/asinhf_3u5.c
new file mode 100644
index 0000000..2b2c55d
--- /dev/null
+++ b/pl/math/asinhf_3u5.c
@@ -0,0 +1,78 @@
+/*
+ * Single-precision asinh(x) function.
+ *
+ * Copyright (c) 2022-2023, Arm Limited.
+ * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
+ */
+
+#include "estrinf.h"
+#include "math_config.h"
+#include "pl_sig.h"
+#include "pl_test.h"
+
+#define AbsMask (0x7fffffff)
+#define SqrtFltMax (0x1.749e96p+10f)
+#define Ln2 (0x1.62e4p-1f)
+#define One (0x3f8)
+#define ExpM12 (0x398)
+
+#define C(i) __asinhf_data.coeffs[i]
+
+float
+optr_aor_log_f32 (float);
+
+/* asinhf approximation using a variety of approaches on different intervals:
+
+   |x| < 2^-12: Return x. Function is exactly rounded in this region.
+
+   |x| < 1.0: Use custom order-8 polynomial. The largest observed
+     error in this region is 1.3ulps:
+     asinhf(0x1.f0f74cp-1) got 0x1.b88de4p-1 want 0x1.b88de2p-1.
+
+   |x| <= SqrtFltMax: Calculate the result directly using the
+     definition of asinh(x) = ln(x + sqrt(x*x + 1)). The largest
+     observed error in this region is 1.99ulps.
+     asinhf(0x1.00e358p+0) got 0x1.c4849ep-1 want 0x1.c484a2p-1.
+
+   |x| > SqrtFltMax: 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). This largest observed error in this region is 3.39ulps.
+     asinhf(0x1.749e9ep+10) got 0x1.fffff8p+2 want 0x1.fffffep+2.  */
+float
+asinhf (float x)
+{
+  uint32_t ix = asuint (x);
+  uint32_t ia = ix & AbsMask;
+  uint32_t ia12 = ia >> 20;
+  float ax = asfloat (ia);
+  uint32_t sign = ix & ~AbsMask;
+
+  if (unlikely (ia12 < ExpM12 || ia == 0x7f800000))
+    return x;
+
+  if (unlikely (ia12 >= 0x7f8))
+    return __math_invalidf (x);
+
+  if (ia12 < One)
+    {
+      float x2 = ax * ax;
+      float p = ESTRIN_7 (ax, x2, x2 * x2, C);
+      float y = fmaf (x2, p, ax);
+      return asfloat (asuint (y) | sign);
+    }
+
+  if (unlikely (ax > SqrtFltMax))
+    {
+      return asfloat (asuint (optr_aor_log_f32 (ax) + Ln2) | sign);
+    }
+
+  return asfloat (asuint (optr_aor_log_f32 (ax + sqrtf (ax * ax + 1))) | sign);
+}
+
+PL_SIG (S, F, 1, asinh, -10.0, 10.0)
+PL_TEST_ULP (asinhf, 2.9)
+PL_TEST_INTERVAL (asinhf, 0, 0x1p-12, 5000)
+PL_TEST_INTERVAL (asinhf, 0x1p-12, 1.0, 50000)
+PL_TEST_INTERVAL (asinhf, 1.0, 0x1p11, 50000)
+PL_TEST_INTERVAL (asinhf, 0x1p11, 0x1p127, 20000)