aarch64: Add vector implementations of tan routines

This includes some utility headers for evaluating polynomials using
various schemes.

1 files changed, 129 insertions, 0 deletions

diff --git a/sysdeps/aarch64/fpu/tanf_advsimd.c b/sysdeps/aarch64/fpu/tanf_advsimd.c
new file mode 100644
index 0000000000..4c8a7f740e
--- /dev/null
+++ b/sysdeps/aarch64/fpu/tanf_advsimd.c
@@ -0,0 +1,129 @@
+/* Single-precision vector (Advanced SIMD) tan function
+
+   Copyright (C) 2023 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   <https://www.gnu.org/licenses/>.  */
+
+#include "v_math.h"
+#include "poly_advsimd_f32.h"
+
+static const struct data
+{
+  float32x4_t poly[6];
+  float32x4_t neg_half_pi_1, neg_half_pi_2, neg_half_pi_3, two_over_pi, shift;
+#if !WANT_SIMD_EXCEPT
+  float32x4_t range_val;
+#endif
+} data = {
+  /* Coefficients generated using FPMinimax.  */
+  .poly = { V4 (0x1.55555p-2f), V4 (0x1.11166p-3f), V4 (0x1.b88a78p-5f),
+	    V4 (0x1.7b5756p-6f), V4 (0x1.4ef4cep-8f), V4 (0x1.0e1e74p-7f) },
+  .neg_half_pi_1 = V4 (-0x1.921fb6p+0f),
+  .neg_half_pi_2 = V4 (0x1.777a5cp-25f),
+  .neg_half_pi_3 = V4 (0x1.ee59dap-50f),
+  .two_over_pi = V4 (0x1.45f306p-1f),
+  .shift = V4 (0x1.8p+23f),
+#if !WANT_SIMD_EXCEPT
+  .range_val = V4 (0x1p15f),
+#endif
+};
+
+#define RangeVal v_u32 (0x47000000)  /* asuint32(0x1p15f).  */
+#define TinyBound v_u32 (0x30000000) /* asuint32 (0x1p-31f).  */
+#define Thresh v_u32 (0x16000000)    /* asuint32(RangeVal) - TinyBound.  */
+
+/* Special cases (fall back to scalar calls).  */
+static float32x4_t VPCS_ATTR NOINLINE
+special_case (float32x4_t x, float32x4_t y, uint32x4_t cmp)
+{
+  return v_call_f32 (tanf, x, y, cmp);
+}
+
+/* Use a full Estrin scheme to evaluate polynomial.  */
+static inline float32x4_t
+eval_poly (float32x4_t z, const struct data *d)
+{
+  float32x4_t z2 = vmulq_f32 (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.  */
+  uint32x4_t will_uflow
+    = vcleq_u32 (vreinterpretq_u32_f32 (vabsq_f32 (z)), TinyBound);
+  if (__glibc_unlikely (v_any_u32 (will_uflow)))
+    z2 = vbslq_f32 (will_uflow, v_f32 (0), z2);
+#endif
+  float32x4_t z4 = vmulq_f32 (z2, z2);
+  return v_estrin_5_f32 (z, z2, z4, d->poly);
+}
+
+/* Fast implementation of AdvSIMD tanf.
+   Maximum error is 3.45 ULP:
+   __v_tanf(-0x1.e5f0cap+13) got 0x1.ff9856p-1
+			    want 0x1.ff9850p-1.  */
+float32x4_t VPCS_ATTR V_NAME_F1 (tan) (float32x4_t x)
+{
+  const struct data *d = ptr_barrier (&data);
+  float32x4_t special_arg = x;
+
+  /* iax >= RangeVal means x, if not inf or NaN, is too large to perform fast
+     regression.  */
+#if WANT_SIMD_EXCEPT
+  uint32x4_t iax = vreinterpretq_u32_f32 (vabsq_f32 (x));
+  /* 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.  */
+  uint32x4_t special = vcgeq_u32 (vsubq_u32 (iax, TinyBound), Thresh);
+  if (__glibc_unlikely (v_any_u32 (special)))
+    x = vbslq_f32 (special, v_f32 (1.0f), x);
+#else
+  /* Otherwise, special-case large and special values.  */
+  uint32x4_t special = vcageq_f32 (x, d->range_val);
+#endif
+
+  /* n = rint(x/(pi/2)).  */
+  float32x4_t q = vfmaq_f32 (d->shift, d->two_over_pi, x);
+  float32x4_t n = vsubq_f32 (q, d->shift);
+  /* Determine if x lives in an interval, where |tan(x)| grows to infinity.  */
+  uint32x4_t pred_alt = vtstq_u32 (vreinterpretq_u32_f32 (q), v_u32 (1));
+
+  /* r = x - n * (pi/2)  (range reduction into -pi./4 .. pi/4).  */
+  float32x4_t r;
+  r = vfmaq_f32 (x, d->neg_half_pi_1, n);
+  r = vfmaq_f32 (r, d->neg_half_pi_2, n);
+  r = vfmaq_f32 (r, d->neg_half_pi_3, n);
+
+  /* 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.  */
+
+  /* Invert sign of r if odd quadrant.  */
+  float32x4_t z = vmulq_f32 (r, vbslq_f32 (pred_alt, v_f32 (-1), v_f32 (1)));
+
+  /* Evaluate polynomial approximation of tangent on [-pi/4, pi/4].  */
+  float32x4_t z2 = vmulq_f32 (r, r);
+  float32x4_t p = eval_poly (z2, d);
+  float32x4_t y = vfmaq_f32 (z, vmulq_f32 (z, z2), p);
+
+  /* Compute reciprocal and apply if required.  */
+  float32x4_t inv_y = vdivq_f32 (v_f32 (1.0f), y);
+
+  if (__glibc_unlikely (v_any_u32 (special)))
+    return special_case (special_arg, vbslq_f32 (pred_alt, inv_y, y), special);
+  return vbslq_f32 (pred_alt, inv_y, y);
+}