aarch64/fpu: Add vector variants of erfc

Reviewed-by: Szabolcs Nagy <szabolcs.nagy@arm.com>

1 files changed, 113 insertions, 0 deletions

diff --git a/sysdeps/aarch64/fpu/erfcf_sve.c b/sysdeps/aarch64/fpu/erfcf_sve.c
new file mode 100644
index 0000000000..48d1677eb4
--- /dev/null
+++ b/sysdeps/aarch64/fpu/erfcf_sve.c
@@ -0,0 +1,113 @@
+/* Single-precision vector (SVE) erfc function
+
+   Copyright (C) 2024 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 "sv_math.h"
+
+static const struct data
+{
+  uint32_t off_idx, off_arr;
+  float max, shift;
+  float third, two_thirds, two_over_fifteen, two_over_five, tenth;
+} data = {
+  /* Set an offset so the range of the index used for lookup is 644, and it can
+     be clamped using a saturated add.  */
+  .off_idx = 0xb7fffd7b, /* 0xffffffff - asuint(shift) - 644.  */
+  .off_arr = 0xfffffd7b, /* 0xffffffff - 644.  */
+  .max = 10.0625f,	 /* 644/64.  */
+  .shift = 0x1p17f,
+  .third = 0x1.555556p-2f,
+  .two_thirds = 0x1.555556p-1f,
+  .two_over_fifteen = 0x1.111112p-3f,
+  .two_over_five = -0x1.99999ap-2f,
+  .tenth = -0x1.99999ap-4f,
+};
+
+#define SignMask 0x80000000
+#define TableScale 0x28000000 /* 0x1p-47.  */
+
+/* Optimized single-precision vector erfcf(x).
+   Approximation based on series expansion near x rounded to
+   nearest multiple of 1/64.
+   Let d = x - r, and scale = 2 / sqrt(pi) * exp(-r^2). For x near r,
+
+   erfc(x) ~ erfc(r) - scale * d * poly(r, d), with
+
+   poly(r, d) = 1 - r d + (2/3 r^2 - 1/3) d^2 - r (1/3 r^2 - 1/2) d^3
+		+ (2/15 r^4 - 2/5 r^2 + 1/10) d^4
+
+   Values of erfc(r) and scale are read from lookup tables. Stored values
+   are scaled to avoid hitting the subnormal range.
+
+   Note that for x < 0, erfc(x) = 2.0 - erfc(-x).
+
+   Maximum error: 1.63 ULP (~1.0 ULP for x < 0.0).
+   _ZGVsMxv_erfcf(0x1.1dbf7ap+3) got 0x1.f51212p-120
+				want 0x1.f51216p-120.  */
+svfloat32_t SV_NAME_F1 (erfc) (svfloat32_t x, const svbool_t pg)
+{
+  const struct data *dat = ptr_barrier (&data);
+
+  svfloat32_t a = svabs_x (pg, x);
+
+  /* Clamp input at |x| <= 10.0 + 4/64.  */
+  a = svmin_x (pg, a, dat->max);
+
+  /* Reduce x to the nearest multiple of 1/64.  */
+  svfloat32_t shift = sv_f32 (dat->shift);
+  svfloat32_t z = svadd_x (pg, a, shift);
+
+  /* Saturate index for the NaN case.  */
+  svuint32_t i = svqadd (svreinterpret_u32 (z), dat->off_idx);
+
+  /* Lookup erfc(r) and 2/sqrt(pi)*exp(-r^2) in tables.  */
+  i = svmul_x (pg, i, 2);
+  const float32_t *p = &__erfcf_data.tab[0].erfc - 2 * dat->off_arr;
+  svfloat32_t erfcr = svld1_gather_index (pg, p, i);
+  svfloat32_t scale = svld1_gather_index (pg, p + 1, i);
+
+  /* erfc(x) ~ erfc(r) - scale * d * poly(r, d).  */
+  svfloat32_t r = svsub_x (pg, z, shift);
+  svfloat32_t d = svsub_x (pg, a, r);
+  svfloat32_t d2 = svmul_x (pg, d, d);
+  svfloat32_t r2 = svmul_x (pg, r, r);
+
+  svfloat32_t coeffs = svld1rq (svptrue_b32 (), &dat->third);
+  svfloat32_t third = svdup_lane (coeffs, 0);
+
+  svfloat32_t p1 = r;
+  svfloat32_t p2 = svmls_lane (third, r2, coeffs, 1);
+  svfloat32_t p3 = svmul_x (pg, r, svmla_lane (sv_f32 (-0.5), r2, coeffs, 0));
+  svfloat32_t p4 = svmla_lane (sv_f32 (dat->two_over_five), r2, coeffs, 2);
+  p4 = svmls_x (pg, sv_f32 (dat->tenth), r2, p4);
+
+  svfloat32_t y = svmla_x (pg, p3, d, p4);
+  y = svmla_x (pg, p2, d, y);
+  y = svmla_x (pg, p1, d, y);
+
+  /* Solves the |x| = inf/nan case.  */
+  y = svmls_x (pg, erfcr, scale, svmls_x (pg, d, d2, y));
+
+  /* Offset equals 2.0f if sign, else 0.0f.  */
+  svuint32_t sign = svand_x (pg, svreinterpret_u32 (x), SignMask);
+  svfloat32_t off = svreinterpret_f32 (svlsr_x (pg, sign, 1));
+  /* Handle sign and scale back in a single fma.  */
+  svfloat32_t fac = svreinterpret_f32 (svorr_x (pg, sign, TableScale));
+
+  return svmla_x (pg, off, fac, y);
+}