aarch64: Add vector implementations of exp10 routines

Double-precision routines either reuse the exp table (AdvSIMD) or use
SVE FEXPA intruction.

1 files changed, 127 insertions, 0 deletions

diff --git a/sysdeps/aarch64/fpu/exp10_sve.c b/sysdeps/aarch64/fpu/exp10_sve.c
new file mode 100644
index 0000000000..a8cef7b692
--- /dev/null
+++ b/sysdeps/aarch64/fpu/exp10_sve.c
@@ -0,0 +1,127 @@
+/* Double-precision vector (SVE) exp10 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 "sv_math.h"
+#include "poly_sve_f64.h"
+
+#define SpecialBound 307.0 /* floor (log10 (2^1023)).  */
+
+static const struct data
+{
+  double poly[5];
+  double shift, log10_2, log2_10_hi, log2_10_lo, scale_thres, special_bound;
+} data = {
+  /* Coefficients generated using Remez algorithm.
+     rel error: 0x1.9fcb9b3p-60
+     abs error: 0x1.a20d9598p-60 in [ -log10(2)/128, log10(2)/128 ]
+     max ulp err 0.52 +0.5.  */
+  .poly = { 0x1.26bb1bbb55516p1, 0x1.53524c73cd32ap1, 0x1.0470591daeafbp1,
+	    0x1.2bd77b1361ef6p0, 0x1.142b5d54e9621p-1 },
+  /* 1.5*2^46+1023. This value is further explained below.  */
+  .shift = 0x1.800000000ffc0p+46,
+  .log10_2 = 0x1.a934f0979a371p1,     /* 1/log2(10).  */
+  .log2_10_hi = 0x1.34413509f79ffp-2, /* log2(10).  */
+  .log2_10_lo = -0x1.9dc1da994fd21p-59,
+  .scale_thres = 1280.0,
+  .special_bound = SpecialBound,
+};
+
+#define SpecialOffset 0x6000000000000000 /* 0x1p513.  */
+/* SpecialBias1 + SpecialBias1 = asuint(1.0).  */
+#define SpecialBias1 0x7000000000000000 /* 0x1p769.  */
+#define SpecialBias2 0x3010000000000000 /* 0x1p-254.  */
+
+/* Update of both special and non-special cases, if any special case is
+   detected.  */
+static inline svfloat64_t
+special_case (svbool_t pg, svfloat64_t s, svfloat64_t y, svfloat64_t n,
+	      const struct data *d)
+{
+  /* s=2^n may overflow, break it up into s=s1*s2,
+     such that exp = s + s*y can be computed as s1*(s2+s2*y)
+     and s1*s1 overflows only if n>0.  */
+
+  /* If n<=0 then set b to 0x6, 0 otherwise.  */
+  svbool_t p_sign = svcmple (pg, n, 0.0); /* n <= 0.  */
+  svuint64_t b = svdup_u64_z (p_sign, SpecialOffset);
+
+  /* Set s1 to generate overflow depending on sign of exponent n.  */
+  svfloat64_t s1 = svreinterpret_f64 (svsubr_x (pg, b, SpecialBias1));
+  /* Offset s to avoid overflow in final result if n is below threshold.  */
+  svfloat64_t s2 = svreinterpret_f64 (
+      svadd_x (pg, svsub_x (pg, svreinterpret_u64 (s), SpecialBias2), b));
+
+  /* |n| > 1280 => 2^(n) overflows.  */
+  svbool_t p_cmp = svacgt (pg, n, d->scale_thres);
+
+  svfloat64_t r1 = svmul_x (pg, s1, s1);
+  svfloat64_t r2 = svmla_x (pg, s2, s2, y);
+  svfloat64_t r0 = svmul_x (pg, r2, s1);
+
+  return svsel (p_cmp, r1, r0);
+}
+
+/* Fast vector implementation of exp10 using FEXPA instruction.
+   Maximum measured error is 1.02 ulp.
+   SV_NAME_D1 (exp10)(-0x1.2862fec805e58p+2) got 0x1.885a89551d782p-16
+					    want 0x1.885a89551d781p-16.  */
+svfloat64_t SV_NAME_D1 (exp10) (svfloat64_t x, svbool_t pg)
+{
+  const struct data *d = ptr_barrier (&data);
+  svbool_t no_big_scale = svacle (pg, x, d->special_bound);
+  svbool_t special = svnot_z (pg, no_big_scale);
+
+  /* n = round(x/(log10(2)/N)).  */
+  svfloat64_t shift = sv_f64 (d->shift);
+  svfloat64_t z = svmla_x (pg, shift, x, d->log10_2);
+  svfloat64_t n = svsub_x (pg, z, shift);
+
+  /* r = x - n*log10(2)/N.  */
+  svfloat64_t log2_10 = svld1rq (svptrue_b64 (), &d->log2_10_hi);
+  svfloat64_t r = x;
+  r = svmls_lane (r, n, log2_10, 0);
+  r = svmls_lane (r, n, log2_10, 1);
+
+  /* scale = 2^(n/N), computed using FEXPA. FEXPA does not propagate NaNs, so
+     for consistent NaN handling we have to manually propagate them. This
+     comes at significant performance cost.  */
+  svuint64_t u = svreinterpret_u64 (z);
+  svfloat64_t scale = svexpa (u);
+
+  /* Approximate exp10(r) using polynomial.  */
+  svfloat64_t r2 = svmul_x (pg, r, r);
+  svfloat64_t y = svmla_x (pg, svmul_x (pg, r, d->poly[0]), r2,
+			   sv_pairwise_poly_3_f64_x (pg, r, r2, d->poly + 1));
+
+  /* Assemble result as exp10(x) = 2^n * exp10(r).  If |x| > SpecialBound
+     multiplication may overflow, so use special case routine.  */
+  if (__glibc_unlikely (svptest_any (pg, special)))
+    {
+      /* FEXPA zeroes the sign bit, however the sign is meaningful to the
+	 special case function so needs to be copied.
+	 e = sign bit of u << 46.  */
+      svuint64_t e = svand_x (pg, svlsl_x (pg, u, 46), 0x8000000000000000);
+      /* Copy sign to scale.  */
+      scale = svreinterpret_f64 (svadd_x (pg, e, svreinterpret_u64 (scale)));
+      return special_case (pg, scale, y, n, d);
+    }
+
+  /* No special case.  */
+  return svmla_x (pg, scale, scale, y);
+}