1 files changed, 90 insertions, 0 deletions
diff --git a/sysdeps/aarch64/fpu/atan_sve.c b/sysdeps/aarch64/fpu/atan_sve.c
new file mode 100644
index 0000000000..35587ef212
--- /dev/null
+++ b/sysdeps/aarch64/fpu/atan_sve.c
@@ -0,0 +1,90 @@
+/* Double-precision SVE inverse tan
+
+   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 "sv_math.h"
+#include "poly_sve_f64.h"
+
+static const struct data
+{
+  float64_t poly[20];
+  float64_t pi_over_2;
+} data = {
+  /* Coefficients of polynomial P such that atan(x)~x+x*P(x^2) on
+     [2**-1022, 1.0].  */
+  .poly = { -0x1.5555555555555p-2,  0x1.99999999996c1p-3, -0x1.2492492478f88p-3,
+            0x1.c71c71bc3951cp-4,   -0x1.745d160a7e368p-4, 0x1.3b139b6a88ba1p-4,
+            -0x1.11100ee084227p-4,  0x1.e1d0f9696f63bp-5, -0x1.aebfe7b418581p-5,
+            0x1.842dbe9b0d916p-5,   -0x1.5d30140ae5e99p-5, 0x1.338e31eb2fbbcp-5,
+            -0x1.00e6eece7de8p-5,   0x1.860897b29e5efp-6, -0x1.0051381722a59p-6,
+            0x1.14e9dc19a4a4ep-7,  -0x1.d0062b42fe3bfp-9, 0x1.17739e210171ap-10,
+            -0x1.ab24da7be7402p-13, 0x1.358851160a528p-16, },
+  .pi_over_2 = 0x1.921fb54442d18p+0,
+};
+
+/* Useful constants.  */
+#define SignMask (0x8000000000000000)
+
+/* Fast implementation of SVE atan.
+   Based on atan(x) ~ shift + z + z^3 * P(z^2) with reduction to [0,1] using
+   z=1/x and shift = pi/2. Largest errors are close to 1. The maximum observed
+   error is 2.27 ulps:
+   _ZGVsMxv_atan (0x1.0005af27c23e9p+0) got 0x1.9225645bdd7c1p-1
+				       want 0x1.9225645bdd7c3p-1.  */
+svfloat64_t SV_NAME_D1 (atan) (svfloat64_t x, const svbool_t pg)
+{
+  const struct data *d = ptr_barrier (&data);
+
+  /* No need to trigger special case. Small cases, infs and nans
+     are supported by our approximation technique.  */
+  svuint64_t ix = svreinterpret_u64 (x);
+  svuint64_t sign = svand_x (pg, ix, SignMask);
+
+  /* Argument reduction:
+     y := arctan(x) for x < 1
+     y := pi/2 + arctan(-1/x) for x > 1
+     Hence, use z=-1/a if x>=1, otherwise z=a.  */
+  svbool_t red = svacgt (pg, x, 1.0);
+  /* Avoid dependency in abs(x) in division (and comparison).  */
+  svfloat64_t z = svsel (red, svdivr_x (pg, x, 1.0), x);
+  /* Use absolute value only when needed (odd powers of z).  */
+  svfloat64_t az = svabs_x (pg, z);
+  az = svneg_m (az, red, az);
+
+  /* Use split Estrin scheme for P(z^2) with deg(P)=19.  */
+  svfloat64_t z2 = svmul_x (pg, z, z);
+  svfloat64_t x2 = svmul_x (pg, z2, z2);
+  svfloat64_t x4 = svmul_x (pg, x2, x2);
+  svfloat64_t x8 = svmul_x (pg, x4, x4);
+
+  svfloat64_t y
+      = svmla_x (pg, sv_estrin_7_f64_x (pg, z2, x2, x4, d->poly),
+		 sv_estrin_11_f64_x (pg, z2, x2, x4, x8, d->poly + 8), x8);
+
+  /* y = shift + z + z^3 * P(z^2).  */
+  svfloat64_t z3 = svmul_x (pg, z2, az);
+  y = svmla_x (pg, az, z3, y);
+
+  /* Apply shift as indicated by `red` predicate.  */
+  y = svadd_m (red, y, d->pi_over_2);
+
+  /* y = atan(x) if x>0, -atan(-x) otherwise.  */
+  y = svreinterpret_f64 (sveor_x (pg, svreinterpret_u64 (y), sign));
+
+  return y;
+}