aarch64: Add vector implementations of expm1 routines

May discard sign of 0 - auto tests for -0 and -0x1p-10000 updated accordingly.

1 files changed, 99 insertions, 0 deletions

diff --git a/sysdeps/aarch64/fpu/expm1_sve.c b/sysdeps/aarch64/fpu/expm1_sve.c
new file mode 100644
index 0000000000..50646aff7c
--- /dev/null
+++ b/sysdeps/aarch64/fpu/expm1_sve.c
@@ -0,0 +1,99 @@
+/* Double-precision SVE expm1
+
+   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"
+
+#define SpecialBound 0x1.62b7d369a5aa9p+9
+#define ExponentBias 0x3ff0000000000000
+
+static const struct data
+{
+  double poly[11];
+  double shift, inv_ln2, special_bound;
+  /* To be loaded in one quad-word.  */
+  double ln2_hi, ln2_lo;
+} data = {
+  /* Generated using fpminimax.  */
+  .poly = { 0x1p-1, 0x1.5555555555559p-3, 0x1.555555555554bp-5,
+            0x1.111111110f663p-7, 0x1.6c16c16c1b5f3p-10, 0x1.a01a01affa35dp-13,
+            0x1.a01a018b4ecbbp-16, 0x1.71ddf82db5bb4p-19, 0x1.27e517fc0d54bp-22,
+            0x1.af5eedae67435p-26, 0x1.1f143d060a28ap-29, },
+
+  .special_bound = SpecialBound,
+  .inv_ln2 = 0x1.71547652b82fep0,
+  .ln2_hi = 0x1.62e42fefa39efp-1,
+  .ln2_lo = 0x1.abc9e3b39803fp-56,
+  .shift = 0x1.8p52,
+};
+
+static svfloat64_t NOINLINE
+special_case (svfloat64_t x, svfloat64_t y, svbool_t pg)
+{
+  return sv_call_f64 (expm1, x, y, pg);
+}
+
+/* Double-precision vector exp(x) - 1 function.
+   The maximum error observed error is 2.18 ULP:
+   _ZGVsMxv_expm1(0x1.634ba0c237d7bp-2) got 0x1.a8b9ea8d66e22p-2
+				       want 0x1.a8b9ea8d66e2p-2.  */
+svfloat64_t SV_NAME_D1 (expm1) (svfloat64_t x, svbool_t pg)
+{
+  const struct data *d = ptr_barrier (&data);
+
+  /* Large, Nan/Inf.  */
+  svbool_t special = svnot_z (pg, svaclt (pg, x, d->special_bound));
+
+  /* Reduce argument to smaller range:
+     Let i = round(x / ln2)
+     and f = x - i * ln2, then f is in [-ln2/2, ln2/2].
+     exp(x) - 1 = 2^i * (expm1(f) + 1) - 1
+     where 2^i is exact because i is an integer.  */
+  svfloat64_t shift = sv_f64 (d->shift);
+  svfloat64_t n = svsub_x (pg, svmla_x (pg, shift, x, d->inv_ln2), shift);
+  svint64_t i = svcvt_s64_x (pg, n);
+  svfloat64_t ln2 = svld1rq (svptrue_b64 (), &d->ln2_hi);
+  svfloat64_t f = svmls_lane (x, n, ln2, 0);
+  f = svmls_lane (f, n, ln2, 1);
+
+  /* Approximate expm1(f) using polynomial.
+     Taylor expansion for expm1(x) has the form:
+	 x + ax^2 + bx^3 + cx^4 ....
+     So we calculate the polynomial P(f) = a + bf + cf^2 + ...
+     and assemble the approximation expm1(f) ~= f + f^2 * P(f).  */
+  svfloat64_t f2 = svmul_x (pg, f, f);
+  svfloat64_t f4 = svmul_x (pg, f2, f2);
+  svfloat64_t f8 = svmul_x (pg, f4, f4);
+  svfloat64_t p
+      = svmla_x (pg, f, f2, sv_estrin_10_f64_x (pg, f, f2, f4, f8, d->poly));
+
+  /* Assemble the result.
+   expm1(x) ~= 2^i * (p + 1) - 1
+   Let t = 2^i.  */
+  svint64_t u = svadd_x (pg, svlsl_x (pg, i, 52), ExponentBias);
+  svfloat64_t t = svreinterpret_f64 (u);
+
+  /* expm1(x) ~= p * t + (t - 1).  */
+  svfloat64_t y = svmla_x (pg, svsub_x (pg, t, 1), p, t);
+
+  if (__glibc_unlikely (svptest_any (pg, special)))
+    return special_case (x, y, special);
+
+  return y;
+}