1 files changed, 117 insertions, 0 deletions
diff --git a/math/aarch64/advsimd/cbrtf.c b/math/aarch64/advsimd/cbrtf.c
new file mode 100644
index 000000000000..4e76feb2dd8b
--- /dev/null
+++ b/math/aarch64/advsimd/cbrtf.c
@@ -0,0 +1,117 @@
+/*
+ * Single-precision vector cbrt(x) function.
+ *
+ * Copyright (c) 2022-2024, 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"
+
+const static struct data
+{
+  float32x4_t poly[4], one_third;
+  float table[5];
+} data = {
+  .poly = { /* Very rough approximation of cbrt(x) in [0.5, 1], generated with
+               FPMinimax.  */
+	    V4 (0x1.c14e96p-2), V4 (0x1.dd2d3p-1), V4 (-0x1.08e81ap-1),
+	    V4 (0x1.2c74c2p-3) },
+  .table = { /* table[i] = 2^((i - 2) / 3).  */
+	    0x1.428a3p-1, 0x1.965feap-1, 0x1p0, 0x1.428a3p0, 0x1.965feap0 },
+  .one_third = V4 (0x1.555556p-2f),
+};
+
+#define SignMask v_u32 (0x80000000)
+#define SmallestNormal v_u32 (0x00800000)
+#define Thresh vdup_n_u16 (0x7f00) /* asuint(INFINITY) - SmallestNormal.  */
+#define MantissaMask v_u32 (0x007fffff)
+#define HalfExp v_u32 (0x3f000000)
+
+static float32x4_t VPCS_ATTR NOINLINE
+special_case (float32x4_t x, float32x4_t y, uint16x4_t special)
+{
+  return v_call_f32 (cbrtf, x, y, vmovl_u16 (special));
+}
+
+static inline float32x4_t
+shifted_lookup (const float *table, int32x4_t i)
+{
+  return (float32x4_t){ table[i[0] + 2], table[i[1] + 2], table[i[2] + 2],
+			table[i[3] + 2] };
+}
+
+/* Approximation for vector single-precision cbrt(x) using Newton iteration
+   with initial guess obtained by a low-order polynomial. Greatest error
+   is 1.64 ULP. This is observed for every value where the mantissa is
+   0x1.85a2aa and the exponent is a multiple of 3, for example:
+   _ZGVnN4v_cbrtf(0x1.85a2aap+3) got 0x1.267936p+1
+				want 0x1.267932p+1.  */
+float32x4_t VPCS_ATTR NOINLINE V_NAME_F1 (cbrt) (float32x4_t x)
+{
+  const struct data *d = ptr_barrier (&data);
+  uint32x4_t iax = vreinterpretq_u32_f32 (vabsq_f32 (x));
+
+  /* Subnormal, +/-0 and special values.  */
+  uint16x4_t special = vcge_u16 (vsubhn_u32 (iax, SmallestNormal), Thresh);
+
+  /* Decompose |x| into m * 2^e, where m is in [0.5, 1.0]. This is a vector
+     version of frexpf, which gets subnormal values wrong - these have to be
+     special-cased as a result.  */
+  float32x4_t m = vbslq_f32 (MantissaMask, x, v_f32 (0.5));
+  int32x4_t e
+      = vsubq_s32 (vreinterpretq_s32_u32 (vshrq_n_u32 (iax, 23)), v_s32 (126));
+
+  /* p is a rough approximation for cbrt(m) in [0.5, 1.0]. The better this is,
+     the less accurate the next stage of the algorithm needs to be. An order-4
+     polynomial is enough for one Newton iteration.  */
+  float32x4_t p = v_pairwise_poly_3_f32 (m, vmulq_f32 (m, m), d->poly);
+
+  float32x4_t one_third = d->one_third;
+  float32x4_t two_thirds = vaddq_f32 (one_third, one_third);
+
+  /* One iteration of Newton's method for iteratively approximating cbrt.  */
+  float32x4_t m_by_3 = vmulq_f32 (m, one_third);
+  float32x4_t a
+      = vfmaq_f32 (vdivq_f32 (m_by_3, vmulq_f32 (p, p)), two_thirds, p);
+
+  /* Assemble the result by the following:
+
+     cbrt(x) = cbrt(m) * 2 ^ (e / 3).
+
+     We can get 2 ^ round(e / 3) using ldexp and integer divide, but since e is
+     not necessarily a multiple of 3 we lose some information.
+
+     Let q = 2 ^ round(e / 3), then t = 2 ^ (e / 3) / q.
+
+     Then we know t = 2 ^ (i / 3), where i is the remainder from e / 3, which
+     is an integer in [-2, 2], and can be looked up in the table T. Hence the
+     result is assembled as:
+
+     cbrt(x) = cbrt(m) * t * 2 ^ round(e / 3) * sign.  */
+  float32x4_t ef = vmulq_f32 (vcvtq_f32_s32 (e), one_third);
+  int32x4_t ey = vcvtq_s32_f32 (ef);
+  int32x4_t em3 = vsubq_s32 (e, vmulq_s32 (ey, v_s32 (3)));
+
+  float32x4_t my = shifted_lookup (d->table, em3);
+  my = vmulq_f32 (my, a);
+
+  /* Vector version of ldexpf.  */
+  float32x4_t y
+      = vreinterpretq_f32_s32 (vshlq_n_s32 (vaddq_s32 (ey, v_s32 (127)), 23));
+  y = vmulq_f32 (y, my);
+
+  if (unlikely (v_any_u16h (special)))
+    return special_case (x, vbslq_f32 (SignMask, x, y), special);
+
+  /* Copy sign.  */
+  return vbslq_f32 (SignMask, x, y);
+}
+
+HALF_WIDTH_ALIAS_F1 (cbrt)
+
+TEST_SIG (V, F, 1, cbrt, -10.0, 10.0)
+TEST_ULP (V_NAME_F1 (cbrt), 1.15)
+TEST_SYM_INTERVAL (V_NAME_F1 (cbrt), 0, inf, 1000000)