pl/math: Add vector/Neon acoshf

New routine uses inlined log1pf helper, and is accurate to 3.1 ULP
(2.8 ULP if fp exceptions are enabled).

4 files changed, 90 insertions, 0 deletions

diff --git a/pl/math/include/mathlib.h b/pl/math/include/mathlib.h
index 43c5ebc..dc2cef8 100644
--- a/pl/math/include/mathlib.h
+++ b/pl/math/include/mathlib.h
@@ -39,6 +39,7 @@ double log1p (double);
 double sinh (double);
 double tanh (double);
 
+float __s_acoshf (float);
 float __s_asinhf (float);
 float __s_atanf (float);
 float __s_atan2f (float, float);
@@ -82,6 +83,7 @@ typedef __attribute__((__neon_vector_type__(2))) double __f64x2_t;
 #endif
 
 /* Vector functions following the base PCS.  */
+__f32x4_t __v_acoshf (__f32x4_t);
 __f32x4_t __v_asinhf (__f32x4_t);
 __f64x2_t __v_asinh (__f64x2_t);
 __f32x4_t __v_atanf (__f32x4_t);
@@ -116,6 +118,7 @@ __f64x2_t __v_tanh (__f64x2_t);
 #define __vpcs __attribute__((__aarch64_vector_pcs__))
 
 /* Vector functions following the vector PCS.  */
+__vpcs __f32x4_t __vn_acoshf (__f32x4_t);
 __vpcs __f32x4_t __vn_asinhf (__f32x4_t);
 __vpcs __f64x2_t __vn_asinh (__f64x2_t);
 __vpcs __f32x4_t __vn_atanf (__f32x4_t);
@@ -147,6 +150,7 @@ __vpcs __f32x4_t __vn_tanhf (__f32x4_t);
 __vpcs __f64x2_t __vn_tanh (__f64x2_t);
 
 /* Vector functions following the vector PCS using ABI names.  */
+__vpcs __f32x4_t _ZGVnN4v_acoshf (__f32x4_t);
 __vpcs __f32x4_t _ZGVnN4v_asinhf (__f32x4_t);
 __vpcs __f64x2_t _ZGVnN2v_asinh (__f64x2_t);
 __vpcs __f32x4_t _ZGVnN4v_atanf (__f32x4_t);
diff --git a/pl/math/s_acoshf_3u1.c b/pl/math/s_acoshf_3u1.c
new file mode 100644
index 0000000..3740666
--- /dev/null
+++ b/pl/math/s_acoshf_3u1.c
@@ -0,0 +1,6 @@
+/*
+ * Copyright (c) 2023, Arm Limited.
+ * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
+ */
+#define SCALAR 1
+#include "v_acoshf_3u1.c"
diff --git a/pl/math/v_acoshf_3u1.c b/pl/math/v_acoshf_3u1.c
new file mode 100644
index 0000000..2b5aff5
--- /dev/null
+++ b/pl/math/v_acoshf_3u1.c
@@ -0,0 +1,68 @@
+/*
+ * Single-precision vector acosh(x) function.
+ * Copyright (c) 2023, Arm Limited.
+ * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
+ */
+
+#include "v_math.h"
+#include "pl_sig.h"
+#include "pl_test.h"
+
+#define SignMask 0x80000000
+#define One 0x3f800000
+#define SquareLim 0x5f800000 /* asuint(0x1p64).  */
+
+#if V_SUPPORTED
+
+#include "v_log1pf_inline.h"
+
+static NOINLINE VPCS_ATTR v_f32_t
+special_case (v_f32_t x, v_f32_t y, v_u32_t special)
+{
+  return v_call_f32 (acoshf, x, y, special);
+}
+
+/* Vector approximation for single-precision acosh, based on log1p. Maximum
+   error depends on WANT_SIMD_EXCEPT. With SIMD fp exceptions enabled, it
+   is 2.78 ULP:
+   __v_acoshf(0x1.07887p+0) got 0x1.ef9e9cp-3
+			   want 0x1.ef9ea2p-3.
+   With exceptions disabled, we can compute u with a shorter dependency chain,
+   which gives maximum error of 3.07 ULP:
+  __v_acoshf(0x1.01f83ep+0) got 0x1.fbc7fap-4
+			   want 0x1.fbc7f4p-4.  */
+
+VPCS_ATTR v_f32_t V_NAME (acoshf) (v_f32_t x)
+{
+  v_u32_t ix = v_as_u32_f32 (x);
+  v_u32_t special = v_cond_u32 ((ix - One) >= (SquareLim - One));
+
+#if WANT_SIMD_EXCEPT
+  /* Mask special lanes with 1 to side-step spurious invalid or overflow. Use
+     only xm1 to calculate u, as operating on x will trigger invalid for NaN. */
+  v_f32_t xm1 = v_sel_f32 (special, v_f32 (1), x - 1);
+  v_f32_t u = v_fma_f32 (xm1, xm1, 2 * xm1);
+#else
+  v_f32_t xm1 = x - 1;
+  v_f32_t u = xm1 * (x + 1.0f);
+#endif
+  v_f32_t y = log1pf_inline (xm1 + v_sqrt_f32 (u));
+
+  if (unlikely (v_any_u32 (special)))
+    return special_case (x, y, special);
+  return y;
+}
+VPCS_ALIAS
+
+PL_SIG (V, F, 1, acosh, 1.0, 10.0)
+#if WANT_SIMD_EXCEPT
+PL_TEST_ULP (V_NAME (acoshf), 2.29)
+#else
+PL_TEST_ULP (V_NAME (acoshf), 2.58)
+#endif
+PL_TEST_EXPECT_FENV (V_NAME (acoshf), WANT_SIMD_EXCEPT)
+PL_TEST_INTERVAL (V_NAME (acoshf), 0, 1, 500)
+PL_TEST_INTERVAL (V_NAME (acoshf), 1, SquareLim, 100000)
+PL_TEST_INTERVAL (V_NAME (acoshf), SquareLim, inf, 1000)
+PL_TEST_INTERVAL (V_NAME (acoshf), -0, -inf, 1000)
+#endif
diff --git a/pl/math/vn_acoshf_3u1.c b/pl/math/vn_acoshf_3u1.c
new file mode 100644
index 0000000..8c5f106
--- /dev/null
+++ b/pl/math/vn_acoshf_3u1.c
@@ -0,0 +1,12 @@
+/*
+ * AdvSIMD vector PCS variant of __v_acoshf.
+ *
+ * Copyright (c) 2023, Arm Limited.
+ * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
+ */
+#include "include/mathlib.h"
+#ifdef __vpcs
+#define VPCS 1
+#define VPCS_ALIAS PL_ALIAS (__vn_acoshf, _ZGVnN4v_acoshf)
+#include "v_acoshf_3u1.c"
+#endif