1 files changed, 96 insertions, 0 deletions
diff --git a/pl/math/v_cbrtf_1u5.c b/pl/math/v_cbrtf_1u5.c
new file mode 100644
index 0000000..62fa375
--- /dev/null
+++ b/pl/math/v_cbrtf_1u5.c
@@ -0,0 +1,96 @@
+/*
+ * Single-precision vector cbrt(x) function.
+ *
+ * Copyright (c) 2022-2023, Arm Limited.
+ * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
+ */
+
+#include "v_math.h"
+#include "mathlib.h"
+#include "pl_sig.h"
+#include "pl_test.h"
+
+#if V_SUPPORTED
+
+#define AbsMask 0x7fffffff
+#define SignMask v_u32 (0x80000000)
+#define TwoThirds v_f32 (0x1.555556p-1f)
+#define SmallestNormal 0x00800000
+#define MantissaMask 0x007fffff
+#define HalfExp 0x3f000000
+
+#define C(i) v_f32 (__cbrtf_data.poly[i])
+#define T(i) v_lookup_f32 (__cbrtf_data.table, i)
+
+static NOINLINE v_f32_t
+specialcase (v_f32_t x, v_f32_t y, v_u32_t special)
+{
+  return v_call_f32 (cbrtf, x, y, special);
+}
+
+/* Approximation for vector single-precision cbrt(x) using Newton iteration with
+   initial guess obtained by a low-order polynomial. Greatest error is 1.5 ULP.
+   This is observed for every value where the mantissa is 0x1.81410e and the
+   exponent is a multiple of 3, for example:
+   __v_cbrtf(0x1.81410ep+30) got 0x1.255d96p+10
+			    want 0x1.255d92p+10.  */
+VPCS_ATTR v_f32_t V_NAME (cbrtf) (v_f32_t x)
+{
+  v_u32_t ix = v_as_u32_f32 (x);
+  v_u32_t iax = ix & AbsMask;
+
+  /* Subnormal, +/-0 and special values.  */
+  v_u32_t special = v_cond_u32 ((iax < SmallestNormal) | (iax >= 0x7f800000));
+
+  /* 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.  */
+  v_f32_t m = v_as_f32_u32 ((iax & MantissaMask) | HalfExp);
+  v_s32_t e = v_as_s32_u32 (iax >> 23) - 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.  */
+  v_f32_t p_01 = v_fma_f32 (C (1), m, C (0));
+  v_f32_t p_23 = v_fma_f32 (C (3), m, C (2));
+  v_f32_t p = v_fma_f32 (m * m, p_23, p_01);
+
+  /* One iteration of Newton's method for iteratively approximating cbrt.  */
+  v_f32_t m_by_3 = m / 3;
+  v_f32_t a = v_fma_f32 (TwoThirds, p, m_by_3 / (p * 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.  */
+
+  v_s32_t ey = e / 3;
+  v_f32_t my = a * T (v_as_u32_s32 (e % 3 + 2));
+
+  /* Vector version of ldexpf.  */
+  v_f32_t y = v_as_f32_u32 ((v_as_u32_s32 (ey + 127) << 23)) * my;
+  /* Copy sign.  */
+  y = v_as_f32_u32 (v_bsl_u32 (SignMask, ix, v_as_u32_f32 (y)));
+
+  if (unlikely (v_any_u32 (special)))
+    return specialcase (x, y, special);
+  return y;
+}
+VPCS_ALIAS
+
+PL_SIG (V, F, 1, cbrt, -10.0, 10.0)
+PL_TEST_ULP (V_NAME (cbrtf), 1.03)
+PL_TEST_EXPECT_FENV_ALWAYS (V_NAME (cbrtf))
+PL_TEST_INTERVAL (V_NAME (cbrtf), 0, inf, 1000000)
+PL_TEST_INTERVAL (V_NAME (cbrtf), -0, -inf, 1000000)
+#endif