AArch64: Improve codegen SVE log1p helper

Improve codegen by packing coefficients.
4% and 2% improvement in throughput microbenchmark on Neoverse V1, for acosh
and atanh respectively.

Reviewed-by: Wilco Dijkstra  <Wilco.Dijkstra@arm.com>

diff --git a/sysdeps/aarch64/fpu/acosh_sve.c b/sysdeps/aarch64/fpu/acosh_sve.c
index 326b2cca2ec403e07cf0fabbba0e84ba167bd58b..3a84959f0a39b48892ea3911b76ee5a8b81eb269 100644 (file)
--- a/sysdeps/aarch64/fpu/acosh_sve.c
+++ b/sysdeps/aarch64/fpu/acosh_sve.c
@@ -30,10 +30,10 @@ special_case (svfloat64_t x, svfloat64_t y, svbool_t special)
 }
 
 /* SVE approximation for double-precision acosh, based on log1p.
-   The largest observed error is 3.19 ULP in the region where the
+   The largest observed error is 3.14 ULP in the region where the
    argument to log1p falls in the k=0 interval, i.e. x close to 1:
-   SV_NAME_D1 (acosh)(0x1.1e4388d4ca821p+0) got 0x1.ed23399f5137p-2
-                                          want 0x1.ed23399f51373p-2.  */
+   SV_NAME_D1 (acosh)(0x1.1e80ed12f0ad1p+0) got 0x1.ef0cee7c33ce1p-2
+                                          want 0x1.ef0cee7c33ce4p-2.  */
 svfloat64_t SV_NAME_D1 (acosh) (svfloat64_t x, const svbool_t pg)
 {
   /* (ix - One) >= (BigBound - One).  */

diff --git a/sysdeps/aarch64/fpu/atanh_sve.c b/sysdeps/aarch64/fpu/atanh_sve.c
index 16a7cf6aa7ffb74e571bd99a77166f1999d14681..958d69a5f5f7ba29426cbf0a274a78b437fb8c07 100644 (file)
--- a/sysdeps/aarch64/fpu/atanh_sve.c
+++ b/sysdeps/aarch64/fpu/atanh_sve.c
@@ -30,7 +30,7 @@ special_case (svfloat64_t x, svfloat64_t y, svbool_t special)
 }
 
 /* SVE approximation for double-precision atanh, based on log1p.
-   The greatest observed error is 2.81 ULP:
+   The greatest observed error is 3.3 ULP:
    _ZGVsMxv_atanh(0x1.ffae6288b601p-6) got 0x1.ffd8ff31b5019p-6
                                      want 0x1.ffd8ff31b501cp-6.  */
 svfloat64_t SV_NAME_D1 (atanh) (svfloat64_t x, const svbool_t pg)
@@ -42,7 +42,6 @@ svfloat64_t SV_NAME_D1 (atanh) (svfloat64_t x, const svbool_t pg)
   svfloat64_t halfsign = svreinterpret_f64 (svorr_x (pg, sign, Half));
 
   /* It is special if iax >= 1.  */
-//   svbool_t special = svcmpge (pg, iax, One);
   svbool_t special = svacge (pg, x, 1.0);
 
   /* Computation is performed based on the following sequence of equality:

diff --git a/sysdeps/aarch64/fpu/sv_log1p_inline.h b/sysdeps/aarch64/fpu/sv_log1p_inline.h
index 71f88e02debc2387d2d718f199329800f237f803..c2b196f35b275a651acf36ae3d5e6f04414d6e36 100644 (file)
--- a/sysdeps/aarch64/fpu/sv_log1p_inline.h
+++ b/sysdeps/aarch64/fpu/sv_log1p_inline.h
@@ -21,11 +21,12 @@
 #define AARCH64_FPU_SV_LOG1P_INLINE_H
 
 #include "sv_math.h"
-#include "poly_sve_f64.h"
 
 static const struct sv_log1p_data
 {
-  double poly[19], ln2[2];
+  double c0, c2, c4, c6, c8, c10, c12, c14, c16;
+  double c1, c3, c5, c7, c9, c11, c13, c15, c17, c18;
+  double ln2_lo, ln2_hi;
   uint64_t hf_rt2_top;
   uint64_t one_m_hf_rt2_top;
   uint32_t bottom_mask;
@@ -33,15 +34,30 @@ static const struct sv_log1p_data
 } sv_log1p_data = {
   /* Coefficients generated using Remez, deg=20, in [sqrt(2)/2-1, sqrt(2)-1].
    */
-  .poly = { -0x1.ffffffffffffbp-2, 0x1.55555555551a9p-2, -0x1.00000000008e3p-2,
-           0x1.9999999a32797p-3, -0x1.555555552fecfp-3, 0x1.249248e071e5ap-3,
-           -0x1.ffffff8bf8482p-4, 0x1.c71c8f07da57ap-4, -0x1.9999ca4ccb617p-4,
-           0x1.7459ad2e1dfa3p-4, -0x1.554d2680a3ff2p-4, 0x1.3b4c54d487455p-4,
-           -0x1.2548a9ffe80e6p-4, 0x1.0f389a24b2e07p-4, -0x1.eee4db15db335p-5,
-           0x1.e95b494d4a5ddp-5, -0x1.15fdf07cb7c73p-4, 0x1.0310b70800fcfp-4,
-           -0x1.cfa7385bdb37ep-6 },
-  .ln2 = { 0x1.62e42fefa3800p-1, 0x1.ef35793c76730p-45 },
+  .c0 = -0x1.ffffffffffffbp-2,
+  .c1 = 0x1.55555555551a9p-2,
+  .c2 = -0x1.00000000008e3p-2,
+  .c3 = 0x1.9999999a32797p-3,
+  .c4 = -0x1.555555552fecfp-3,
+  .c5 = 0x1.249248e071e5ap-3,
+  .c6 = -0x1.ffffff8bf8482p-4,
+  .c7 = 0x1.c71c8f07da57ap-4,
+  .c8 = -0x1.9999ca4ccb617p-4,
+  .c9 = 0x1.7459ad2e1dfa3p-4,
+  .c10 = -0x1.554d2680a3ff2p-4,
+  .c11 = 0x1.3b4c54d487455p-4,
+  .c12 = -0x1.2548a9ffe80e6p-4,
+  .c13 = 0x1.0f389a24b2e07p-4,
+  .c14 = -0x1.eee4db15db335p-5,
+  .c15 = 0x1.e95b494d4a5ddp-5,
+  .c16 = -0x1.15fdf07cb7c73p-4,
+  .c17 = 0x1.0310b70800fcfp-4,
+  .c18 = -0x1.cfa7385bdb37ep-6,
+  .ln2_lo = 0x1.62e42fefa3800p-1,
+  .ln2_hi = 0x1.ef35793c76730p-45,
+  /* top32(asuint64(sqrt(2)/2)) << 32.  */
   .hf_rt2_top = 0x3fe6a09e00000000,
+  /* (top32(asuint64(1)) - top32(asuint64(sqrt(2)/2))) << 32.  */
   .one_m_hf_rt2_top = 0x00095f6200000000,
   .bottom_mask = 0xffffffff,
   .one_top = 0x3ff
@@ -51,14 +67,14 @@ static inline svfloat64_t
 sv_log1p_inline (svfloat64_t x, const svbool_t pg)
 {
   /* Helper for calculating log(x + 1). Adapted from v_log1p_inline.h, which
-     differs from v_log1p_2u5.c by:
+     differs from advsimd/log1p.c by:
      - No special-case handling - this should be dealt with by the caller.
      - Pairwise Horner polynomial evaluation for improved accuracy.
      - Optionally simulate the shortcut for k=0, used in the scalar routine,
        using svsel, for improved accuracy when the argument to log1p is close
      to 0. This feature is enabled by defining WANT_SV_LOG1P_K0_SHORTCUT as 1
      in the source of the caller before including this file.
-     See sv_log1p_2u1.c for details of the algorithm.  */
+     See sve/log1p.c for details of the algorithm.  */
   const struct sv_log1p_data *d = ptr_barrier (&sv_log1p_data);
   svfloat64_t m = svadd_x (pg, x, 1);
   svuint64_t mi = svreinterpret_u64 (m);
@@ -79,7 +95,7 @@ sv_log1p_inline (svfloat64_t x, const svbool_t pg)
   svfloat64_t cm;
 
 #ifndef WANT_SV_LOG1P_K0_SHORTCUT
-#error                                                                         \
+#error                                                                       \
   "Cannot use sv_log1p_inline.h without specifying whether you need the k0 shortcut for greater accuracy close to 0"
 #elif WANT_SV_LOG1P_K0_SHORTCUT
   /* Shortcut if k is 0 - set correction term to 0 and f to x. The result is
@@ -96,14 +112,46 @@ sv_log1p_inline (svfloat64_t x, const svbool_t pg)
 #endif
 
   /* Approximate log1p(f) on the reduced input using a polynomial.  */
-  svfloat64_t f2 = svmul_x (pg, f, f);
-  svfloat64_t p = sv_pw_horner_18_f64_x (pg, f, f2, d->poly);
+  svfloat64_t f2 = svmul_x (svptrue_b64 (), f, f),
+             f4 = svmul_x (svptrue_b64 (), f2, f2),
+             f8 = svmul_x (svptrue_b64 (), f4, f4),
+             f16 = svmul_x (svptrue_b64 (), f8, f8);
+
+  svfloat64_t c13 = svld1rq (svptrue_b64 (), &d->c1);
+  svfloat64_t c57 = svld1rq (svptrue_b64 (), &d->c5);
+  svfloat64_t c911 = svld1rq (svptrue_b64 (), &d->c9);
+  svfloat64_t c1315 = svld1rq (svptrue_b64 (), &d->c13);
+  svfloat64_t c1718 = svld1rq (svptrue_b64 (), &d->c17);
+
+  /* Order-18 Estrin scheme.  */
+  svfloat64_t p01 = svmla_lane (sv_f64 (d->c0), f, c13, 0);
+  svfloat64_t p23 = svmla_lane (sv_f64 (d->c2), f, c13, 1);
+  svfloat64_t p45 = svmla_lane (sv_f64 (d->c4), f, c57, 0);
+  svfloat64_t p67 = svmla_lane (sv_f64 (d->c6), f, c57, 1);
+
+  svfloat64_t p03 = svmla_x (pg, p01, f2, p23);
+  svfloat64_t p47 = svmla_x (pg, p45, f2, p67);
+  svfloat64_t p07 = svmla_x (pg, p03, f4, p47);
+
+  svfloat64_t p89 = svmla_lane (sv_f64 (d->c8), f, c911, 0);
+  svfloat64_t p1011 = svmla_lane (sv_f64 (d->c10), f, c911, 1);
+  svfloat64_t p1213 = svmla_lane (sv_f64 (d->c12), f, c1315, 0);
+  svfloat64_t p1415 = svmla_lane (sv_f64 (d->c14), f, c1315, 1);
+
+  svfloat64_t p811 = svmla_x (pg, p89, f2, p1011);
+  svfloat64_t p1215 = svmla_x (pg, p1213, f2, p1415);
+  svfloat64_t p815 = svmla_x (pg, p811, f4, p1215);
+
+  svfloat64_t p015 = svmla_x (pg, p07, f8, p815);
+  svfloat64_t p1617 = svmla_lane (sv_f64 (d->c16), f, c1718, 0);
+  svfloat64_t p1618 = svmla_lane (p1617, f2, c1718, 1);
+  svfloat64_t p = svmla_x (pg, p015, f16, p1618);
 
   /* Assemble log1p(x) = k * log2 + log1p(f) + c/m.  */
-  svfloat64_t ylo = svmla_x (pg, cm, k, d->ln2[0]);
-  svfloat64_t yhi = svmla_x (pg, f, k, d->ln2[1]);
+  svfloat64_t ln2_lo_hi = svld1rq (svptrue_b64 (), &d->ln2_lo);
+  svfloat64_t ylo = svmla_lane (cm, k, ln2_lo_hi, 0);
+  svfloat64_t yhi = svmla_lane (f, k, ln2_lo_hi, 1);
 
-  return svmla_x (pg, svadd_x (pg, ylo, yhi), f2, p);
+  return svmad_x (pg, p, f2, svadd_x (pg, ylo, yhi));
 }
-
 #endif