1 files changed, 131 insertions, 0 deletions
diff --git a/pl/math/v_tanf_3u5.c b/pl/math/v_tanf_3u5.c
new file mode 100644
index 0000000..828466b
--- /dev/null
+++ b/pl/math/v_tanf_3u5.c
@@ -0,0 +1,131 @@
+/*
+ * Single-precision vector tan(x) function.
+ *
+ * Copyright (c) 2021-2023, Arm Limited.
+ * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
+ */
+
+#include "v_math.h"
+#include "estrinf.h"
+#include "pl_sig.h"
+#include "pl_test.h"
+
+#if V_SUPPORTED
+
+/* Constants.  */
+#define NegPio2_1 (v_f32 (-0x1.921fb6p+0f))
+#define NegPio2_2 (v_f32 (0x1.777a5cp-25f))
+#define NegPio2_3 (v_f32 (0x1.ee59dap-50f))
+#define InvPio2 (v_f32 (0x1.45f306p-1f))
+#define RangeVal (0x47000000)  /* asuint32(0x1p15f).  */
+#define TinyBound (0x30000000) /* asuint32 (0x1p-31).  */
+#define Shift (v_f32 (0x1.8p+23f))
+#define AbsMask (v_u32 (0x7fffffff))
+
+#define poly(i) v_f32 (__tanf_poly_data.poly_tan[i])
+
+/* Special cases (fall back to scalar calls).  */
+VPCS_ATTR
+NOINLINE static v_f32_t
+specialcase (v_f32_t x, v_f32_t y, v_u32_t cmp)
+{
+  return v_call_f32 (tanf, x, y, cmp);
+}
+
+/* Use a full Estrin scheme to evaluate polynomial.  */
+static inline v_f32_t
+eval_poly (v_f32_t z)
+{
+  v_f32_t z2 = z * z;
+#if WANT_SIMD_EXCEPT
+  /* Tiny z (<= 0x1p-31) will underflow when calculating z^4. If fp exceptions
+     are to be triggered correctly, sidestep this by fixing such lanes to 0.  */
+  v_u32_t will_uflow = v_cond_u32 ((v_as_u32_f32 (z) & AbsMask) <= TinyBound);
+  if (unlikely (v_any_u32 (will_uflow)))
+    z2 = v_sel_f32 (will_uflow, v_f32 (0), z2);
+#endif
+  v_f32_t z4 = z2 * z2;
+  return ESTRIN_5 (z, z2, z4, poly);
+}
+
+/* Fast implementation of Neon tanf.
+   Maximum error is 3.45 ULP:
+   __v_tanf(-0x1.e5f0cap+13) got 0x1.ff9856p-1
+			    want 0x1.ff9850p-1.  */
+VPCS_ATTR
+v_f32_t V_NAME (tanf) (v_f32_t x)
+{
+  v_f32_t special_arg = x;
+  v_u32_t ix = v_as_u32_f32 (x);
+  v_u32_t iax = ix & AbsMask;
+
+  /* iax >= RangeVal means x, if not inf or NaN, is too large to perform fast
+     regression.  */
+#if WANT_SIMD_EXCEPT
+  /* If fp exceptions are to be triggered correctly, also special-case tiny
+     input, as this will load to overflow later. Fix any special lanes to 1 to
+     prevent any exceptions being triggered.  */
+  v_u32_t special = v_cond_u32 (iax - TinyBound >= RangeVal - TinyBound);
+  if (unlikely (v_any_u32 (special)))
+    x = v_sel_f32 (special, v_f32 (1.0f), x);
+#else
+  /* Otherwise, special-case large and special values.  */
+  v_u32_t special = v_cond_u32 (iax >= RangeVal);
+#endif
+
+  /* n = rint(x/(pi/2)).  */
+  v_f32_t q = v_fma_f32 (InvPio2, x, Shift);
+  v_f32_t n = q - Shift;
+  /* n is representable as a signed integer, simply convert it.  */
+  v_s32_t in = v_round_s32 (n);
+  /* Determine if x lives in an interval, where |tan(x)| grows to infinity.  */
+  v_s32_t alt = in & 1;
+  v_u32_t pred_alt = (alt != 0);
+
+  /* r = x - n * (pi/2)  (range reduction into -pi./4 .. pi/4).  */
+  v_f32_t r;
+  r = v_fma_f32 (NegPio2_1, n, x);
+  r = v_fma_f32 (NegPio2_2, n, r);
+  r = v_fma_f32 (NegPio2_3, n, r);
+
+  /* If x lives in an interval, where |tan(x)|
+     - is finite, then use a polynomial approximation of the form
+       tan(r) ~ r + r^3 * P(r^2) = r + r * r^2 * P(r^2).
+     - grows to infinity then use symmetries of tangent and the identity
+       tan(r) = cotan(pi/2 - r) to express tan(x) as 1/tan(-r). Finally, use
+       the same polynomial approximation of tan as above.  */
+
+  /* Perform additional reduction if required.  */
+  v_f32_t z = v_sel_f32 (pred_alt, -r, r);
+
+  /* Evaluate polynomial approximation of tangent on [-pi/4, pi/4].  */
+  v_f32_t z2 = r * r;
+  v_f32_t p = eval_poly (z2);
+  v_f32_t y = v_fma_f32 (z * z2, p, z);
+
+  /* Compute reciprocal and apply if required.  */
+  v_f32_t inv_y = v_div_f32 (v_f32 (1.0f), y);
+  y = v_sel_f32 (pred_alt, inv_y, y);
+
+  /* Fast reduction does not handle the x = -0.0 case well,
+     therefore it is fixed here.  */
+  y = v_sel_f32 (x == v_f32 (-0.0), x, y);
+
+  if (unlikely (v_any_u32 (special)))
+    return specialcase (special_arg, y, special);
+  return y;
+}
+VPCS_ALIAS
+
+PL_SIG (V, F, 1, tan, -3.1, 3.1)
+PL_TEST_ULP (V_NAME (tanf), 2.96)
+PL_TEST_EXPECT_FENV (V_NAME (tanf), WANT_SIMD_EXCEPT)
+PL_TEST_INTERVAL (V_NAME (tanf), -0.0, -0x1p126, 100)
+PL_TEST_INTERVAL (V_NAME (tanf), 0x1p-149, 0x1p-126, 4000)
+PL_TEST_INTERVAL (V_NAME (tanf), 0x1p-126, 0x1p-23, 50000)
+PL_TEST_INTERVAL (V_NAME (tanf), 0x1p-23, 0.7, 50000)
+PL_TEST_INTERVAL (V_NAME (tanf), 0.7, 1.5, 50000)
+PL_TEST_INTERVAL (V_NAME (tanf), 1.5, 100, 50000)
+PL_TEST_INTERVAL (V_NAME (tanf), 100, 0x1p17, 50000)
+PL_TEST_INTERVAL (V_NAME (tanf), 0x1p17, inf, 50000)
+#endif