1 files changed, 109 insertions, 0 deletions
diff --git a/math/aarch64/advsimd/atanf.c b/math/aarch64/advsimd/atanf.c
new file mode 100644
index 000000000000..61927c9b261a
--- /dev/null
+++ b/math/aarch64/advsimd/atanf.c
@@ -0,0 +1,109 @@
+/*
+ * Single-precision vector atan(x) function.
+ *
+ * Copyright (c) 2021-2024, Arm Limited.
+ * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
+ */
+
+#include "v_math.h"
+#include "test_sig.h"
+#include "test_defs.h"
+#include "v_poly_f32.h"
+
+static const struct data
+{
+  float32x4_t poly[8];
+  float32x4_t pi_over_2;
+} data = {
+  /* Coefficients of polynomial P such that atan(x)~x+x*P(x^2) on
+     [2**-128, 1.0].
+     Generated using fpminimax between FLT_MIN and 1.  */
+  .poly = { V4 (-0x1.55555p-2f), V4 (0x1.99935ep-3f), V4 (-0x1.24051ep-3f),
+	    V4 (0x1.bd7368p-4f), V4 (-0x1.491f0ep-4f), V4 (0x1.93a2c0p-5f),
+	    V4 (-0x1.4c3c60p-6f), V4 (0x1.01fd88p-8f) },
+  .pi_over_2 = V4 (0x1.921fb6p+0f),
+};
+
+#define SignMask v_u32 (0x80000000)
+
+#define P(i) d->poly[i]
+
+#define TinyBound 0x30800000 /* asuint(0x1p-30).  */
+#define BigBound 0x4e800000  /* asuint(0x1p30).  */
+
+#if WANT_SIMD_EXCEPT
+static float32x4_t VPCS_ATTR NOINLINE
+special_case (float32x4_t x, float32x4_t y, uint32x4_t special)
+{
+  return v_call_f32 (atanf, x, y, special);
+}
+#endif
+
+/* Fast implementation of vector atanf 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 2.9ulps:
+   _ZGVnN4v_atanf (0x1.0468f6p+0) got 0x1.967f06p-1 want 0x1.967fp-1.  */
+float32x4_t VPCS_ATTR NOINLINE V_NAME_F1 (atan) (float32x4_t x)
+{
+  const struct data *d = ptr_barrier (&data);
+
+  /* Small cases, infs and nans are supported by our approximation technique,
+     but do not set fenv flags correctly. Only trigger special case if we need
+     fenv.  */
+  uint32x4_t ix = vreinterpretq_u32_f32 (x);
+  uint32x4_t sign = vandq_u32 (ix, SignMask);
+
+#if WANT_SIMD_EXCEPT
+  uint32x4_t ia = vandq_u32 (ix, v_u32 (0x7ff00000));
+  uint32x4_t special = vcgtq_u32 (vsubq_u32 (ia, v_u32 (TinyBound)),
+				  v_u32 (BigBound - TinyBound));
+  /* If any lane is special, fall back to the scalar routine for all lanes.  */
+  if (unlikely (v_any_u32 (special)))
+    return special_case (x, x, v_u32 (-1));
+#endif
+
+  /* Argument reduction:
+     y := arctan(x) for x < 1
+     y := pi/2 + arctan(-1/x) for x > 1
+     Hence, use z=-1/a if x>=1, otherwise z=a.  */
+  uint32x4_t red = vcagtq_f32 (x, v_f32 (1.0));
+  /* Avoid dependency in abs(x) in division (and comparison).  */
+  float32x4_t z = vbslq_f32 (red, vdivq_f32 (v_f32 (1.0f), x), x);
+  float32x4_t shift = vreinterpretq_f32_u32 (
+      vandq_u32 (red, vreinterpretq_u32_f32 (d->pi_over_2)));
+  /* Use absolute value only when needed (odd powers of z).  */
+  float32x4_t az = vbslq_f32 (
+      SignMask, vreinterpretq_f32_u32 (vandq_u32 (SignMask, red)), z);
+
+  /* Calculate the polynomial approximation.
+     Use 2-level Estrin scheme for P(z^2) with deg(P)=7. However,
+     a standard implementation using z8 creates spurious underflow
+     in the very last fma (when z^8 is small enough).
+     Therefore, we split the last fma into a mul and an fma.
+     Horner and single-level Estrin have higher errors that exceed
+     threshold.  */
+  float32x4_t z2 = vmulq_f32 (z, z);
+  float32x4_t z4 = vmulq_f32 (z2, z2);
+
+  float32x4_t y = vfmaq_f32 (
+      v_pairwise_poly_3_f32 (z2, z4, d->poly), z4,
+      vmulq_f32 (z4, v_pairwise_poly_3_f32 (z2, z4, d->poly + 4)));
+
+  /* y = shift + z * P(z^2).  */
+  y = vaddq_f32 (vfmaq_f32 (az, y, vmulq_f32 (z2, az)), shift);
+
+  /* y = atan(x) if x>0, -atan(-x) otherwise.  */
+  y = vreinterpretq_f32_u32 (veorq_u32 (vreinterpretq_u32_f32 (y), sign));
+
+  return y;
+}
+
+HALF_WIDTH_ALIAS_F1 (atan)
+
+TEST_SIG (V, F, 1, atan, -10.0, 10.0)
+TEST_ULP (V_NAME_F1 (atan), 2.5)
+TEST_DISABLE_FENV_IF_NOT (V_NAME_F1 (atan), WANT_SIMD_EXCEPT)
+TEST_SYM_INTERVAL (V_NAME_F1 (atan), 0, 0x1p-30, 5000)
+TEST_SYM_INTERVAL (V_NAME_F1 (atan), 0x1p-30, 1, 40000)
+TEST_SYM_INTERVAL (V_NAME_F1 (atan), 1, 0x1p30, 40000)
+TEST_SYM_INTERVAL (V_NAME_F1 (atan), 0x1p30, inf, 1000)