AArch64: Improve codegen for SVE logs

Reduce memory access by using lanewise MLA and moving constants to struct
and reduce number of MOVPRFXs.
Update maximum ULP error for double log_sve from 1 to 2.
Speedup on Neoverse V1 for log (3%), log2 (5%), and log10 (4%).

4 files changed, 114 insertions, 47 deletions

diff --git a/sysdeps/aarch64/fpu/log10_sve.c b/sysdeps/aarch64/fpu/log10_sve.c
index 80572e1..35283a5 100644
--- a/sysdeps/aarch64/fpu/log10_sve.c
+++ b/sysdeps/aarch64/fpu/log10_sve.c
@@ -23,28 +23,49 @@
 #define Min 0x0010000000000000
 #define Max 0x7ff0000000000000
 #define Thres 0x7fe0000000000000 /* Max - Min.  */
-#define Off 0x3fe6900900000000
 #define N (1 << V_LOG10_TABLE_BITS)
 
+static const struct data
+{
+  double c0, c2;
+  double c1, c3;
+  double invln10, log10_2;
+  double c4;
+  uint64_t off;
+} data = {
+  .c0 = -0x1.bcb7b1526e506p-3,
+  .c1 = 0x1.287a7636be1d1p-3,
+  .c2 = -0x1.bcb7b158af938p-4,
+  .c3 = 0x1.63c78734e6d07p-4,
+  .c4 = -0x1.287461742fee4p-4,
+  .invln10 = 0x1.bcb7b1526e50ep-2,
+  .log10_2 = 0x1.34413509f79ffp-2,
+  .off = 0x3fe6900900000000,
+};
+
 static svfloat64_t NOINLINE
-special_case (svfloat64_t x, svfloat64_t y, svbool_t special)
+special_case (svfloat64_t hi, svuint64_t tmp, svfloat64_t y, svfloat64_t r2,
+	      svbool_t special, const struct data *d)
 {
-  return sv_call_f64 (log10, x, y, special);
+  svfloat64_t x = svreinterpret_f64 (svadd_x (svptrue_b64 (), tmp, d->off));
+  return sv_call_f64 (log10, x, svmla_x (svptrue_b64 (), hi, r2, y), special);
 }
 
-/* SVE log10 algorithm.
+/* Double-precision SVE log10 routine.
    Maximum measured error is 2.46 ulps.
    SV_NAME_D1 (log10)(0x1.131956cd4b627p+0) got 0x1.fffbdf6eaa669p-6
 					   want 0x1.fffbdf6eaa667p-6.  */
 svfloat64_t SV_NAME_D1 (log10) (svfloat64_t x, const svbool_t pg)
 {
+  const struct data *d = ptr_barrier (&data);
+
   svuint64_t ix = svreinterpret_u64 (x);
   svbool_t special = svcmpge (pg, svsub_x (pg, ix, Min), Thres);
 
   /* x = 2^k z; where z is in range [Off,2*Off) and exact.
      The range is split into N subintervals.
      The ith subinterval contains z and c is near its center.  */
-  svuint64_t tmp = svsub_x (pg, ix, Off);
+  svuint64_t tmp = svsub_x (pg, ix, d->off);
   svuint64_t i = svlsr_x (pg, tmp, 51 - V_LOG10_TABLE_BITS);
   i = svand_x (pg, i, (N - 1) << 1);
   svfloat64_t k = svcvt_f64_x (pg, svasr_x (pg, svreinterpret_s64 (tmp), 52));
@@ -62,15 +83,19 @@ svfloat64_t SV_NAME_D1 (log10) (svfloat64_t x, const svbool_t pg)
   svfloat64_t r = svmad_x (pg, invc, z, -1.0);
 
   /* hi = log(c) + k*log(2).  */
-  svfloat64_t w = svmla_x (pg, logc, r, __v_log10_data.invln10);
-  svfloat64_t hi = svmla_x (pg, w, k, __v_log10_data.log10_2);
+  svfloat64_t invln10_log10_2 = svld1rq_f64 (svptrue_b64 (), &d->invln10);
+  svfloat64_t w = svmla_lane_f64 (logc, r, invln10_log10_2, 0);
+  svfloat64_t hi = svmla_lane_f64 (w, k, invln10_log10_2, 1);
 
   /* y = r2*(A0 + r*A1 + r2*(A2 + r*A3 + r2*A4)) + hi.  */
-  svfloat64_t r2 = svmul_x (pg, r, r);
-  svfloat64_t y = sv_pw_horner_4_f64_x (pg, r, r2, __v_log10_data.poly);
+  svfloat64_t odd_coeffs = svld1rq_f64 (svptrue_b64 (), &d->c1);
+  svfloat64_t r2 = svmul_x (svptrue_b64 (), r, r);
+  svfloat64_t y = svmla_lane_f64 (sv_f64 (d->c2), r, odd_coeffs, 1);
+  svfloat64_t p = svmla_lane_f64 (sv_f64 (d->c0), r, odd_coeffs, 0);
+  y = svmla_x (pg, y, r2, d->c4);
+  y = svmla_x (pg, p, r2, y);
 
   if (__glibc_unlikely (svptest_any (pg, special)))
-    return special_case (x, svmla_x (svnot_z (pg, special), hi, r2, y),
-			 special);
+    return special_case (hi, tmp, y, r2, special, d);
   return svmla_x (pg, hi, r2, y);
 }
diff --git a/sysdeps/aarch64/fpu/log2_sve.c b/sysdeps/aarch64/fpu/log2_sve.c
index 7e0b575..e05dc4e 100644
--- a/sysdeps/aarch64/fpu/log2_sve.c
+++ b/sysdeps/aarch64/fpu/log2_sve.c
@@ -21,15 +21,32 @@
 #include "poly_sve_f64.h"
 
 #define N (1 << V_LOG2_TABLE_BITS)
-#define Off 0x3fe6900900000000
 #define Max (0x7ff0000000000000)
 #define Min (0x0010000000000000)
 #define Thresh (0x7fe0000000000000) /* Max - Min.  */
 
+static const struct data
+{
+  double c0, c2;
+  double c1, c3;
+  double invln2, c4;
+  uint64_t off;
+} data = {
+  .c0 = -0x1.71547652b83p-1,
+  .c1 = 0x1.ec709dc340953p-2,
+  .c2 = -0x1.71547651c8f35p-2,
+  .c3 = 0x1.2777ebe12dda5p-2,
+  .c4 = -0x1.ec738d616fe26p-3,
+  .invln2 = 0x1.71547652b82fep0,
+  .off = 0x3fe6900900000000,
+};
+
 static svfloat64_t NOINLINE
-special_case (svfloat64_t x, svfloat64_t y, svbool_t cmp)
+special_case (svfloat64_t w, svuint64_t tmp, svfloat64_t y, svfloat64_t r2,
+	      svbool_t special, const struct data *d)
 {
-  return sv_call_f64 (log2, x, y, cmp);
+  svfloat64_t x = svreinterpret_f64 (svadd_x (svptrue_b64 (), tmp, d->off));
+  return sv_call_f64 (log2, x, svmla_x (svptrue_b64 (), w, r2, y), special);
 }
 
 /* Double-precision SVE log2 routine.
@@ -40,13 +57,15 @@ special_case (svfloat64_t x, svfloat64_t y, svbool_t cmp)
 					  want 0x1.fffb34198d9ddp-5.  */
 svfloat64_t SV_NAME_D1 (log2) (svfloat64_t x, const svbool_t pg)
 {
+  const struct data *d = ptr_barrier (&data);
+
   svuint64_t ix = svreinterpret_u64 (x);
   svbool_t special = svcmpge (pg, svsub_x (pg, ix, Min), Thresh);
 
   /* x = 2^k z; where z is in range [Off,2*Off) and exact.
      The range is split into N subintervals.
      The ith subinterval contains z and c is near its center.  */
-  svuint64_t tmp = svsub_x (pg, ix, Off);
+  svuint64_t tmp = svsub_x (pg, ix, d->off);
   svuint64_t i = svlsr_x (pg, tmp, 51 - V_LOG2_TABLE_BITS);
   i = svand_x (pg, i, (N - 1) << 1);
   svfloat64_t k = svcvt_f64_x (pg, svasr_x (pg, svreinterpret_s64 (tmp), 52));
@@ -59,15 +78,19 @@ svfloat64_t SV_NAME_D1 (log2) (svfloat64_t x, const svbool_t pg)
 
   /* log2(x) = log1p(z/c-1)/log(2) + log2(c) + k.  */
 
+  svfloat64_t invln2_and_c4 = svld1rq_f64 (svptrue_b64 (), &d->invln2);
   svfloat64_t r = svmad_x (pg, invc, z, -1.0);
-  svfloat64_t w = svmla_x (pg, log2c, r, __v_log2_data.invln2);
-
-  svfloat64_t r2 = svmul_x (pg, r, r);
-  svfloat64_t y = sv_pw_horner_4_f64_x (pg, r, r2, __v_log2_data.poly);
+  svfloat64_t w = svmla_lane_f64 (log2c, r, invln2_and_c4, 0);
   w = svadd_x (pg, k, w);
 
+  svfloat64_t odd_coeffs = svld1rq_f64 (svptrue_b64 (), &d->c1);
+  svfloat64_t r2 = svmul_x (svptrue_b64 (), r, r);
+  svfloat64_t y = svmla_lane_f64 (sv_f64 (d->c2), r, odd_coeffs, 1);
+  svfloat64_t p = svmla_lane_f64 (sv_f64 (d->c0), r, odd_coeffs, 0);
+  y = svmla_lane_f64 (y, r2, invln2_and_c4, 1);
+  y = svmla_x (pg, p, r2, y);
+
   if (__glibc_unlikely (svptest_any (pg, special)))
-    return special_case (x, svmla_x (svnot_z (pg, special), w, r2, y),
-			 special);
+    return special_case (w, tmp, y, r2, special, d);
   return svmla_x (pg, w, r2, y);
 }
diff --git a/sysdeps/aarch64/fpu/log_sve.c b/sysdeps/aarch64/fpu/log_sve.c
index 48b4bd0..dcf84e8 100644
--- a/sysdeps/aarch64/fpu/log_sve.c
+++ b/sysdeps/aarch64/fpu/log_sve.c
@@ -19,39 +19,54 @@
 
 #include "sv_math.h"
 
-#define P(i) sv_f64 (__v_log_data.poly[i])
 #define N (1 << V_LOG_TABLE_BITS)
-#define Off (0x3fe6900900000000)
-#define MaxTop (0x7ff)
-#define MinTop (0x001)
-#define ThreshTop (0x7fe) /* MaxTop - MinTop.  */
+#define Max (0x7ff0000000000000)
+#define Min (0x0010000000000000)
+#define Thresh (0x7fe0000000000000) /* Max - Min.  */
+
+static const struct data
+{
+  double c0, c2;
+  double c1, c3;
+  double ln2, c4;
+  uint64_t off;
+} data = {
+  .c0 = -0x1.ffffffffffff7p-2,
+  .c1 = 0x1.55555555170d4p-2,
+  .c2 = -0x1.0000000399c27p-2,
+  .c3 = 0x1.999b2e90e94cap-3,
+  .c4 = -0x1.554e550bd501ep-3,
+  .ln2 = 0x1.62e42fefa39efp-1,
+  .off = 0x3fe6900900000000,
+};
 
 static svfloat64_t NOINLINE
-special_case (svfloat64_t x, svfloat64_t y, svbool_t cmp)
+special_case (svfloat64_t hi, svuint64_t tmp, svfloat64_t y, svfloat64_t r2,
+	      svbool_t special, const struct data *d)
 {
-  return sv_call_f64 (log, x, y, cmp);
+  svfloat64_t x = svreinterpret_f64 (svadd_x (svptrue_b64 (), tmp, d->off));
+  return sv_call_f64 (log, x, svmla_x (svptrue_b64 (), hi, r2, y), special);
 }
 
-/* SVE port of AdvSIMD log algorithm.
-   Maximum measured error is 2.17 ulp:
-   SV_NAME_D1 (log)(0x1.a6129884398a3p+0) got 0x1.ffffff1cca043p-2
-					 want 0x1.ffffff1cca045p-2.  */
+/* Double-precision SVE log routine.
+   Maximum measured error is 2.64 ulp:
+   SV_NAME_D1 (log)(0x1.95e54bc91a5e2p+184) got 0x1.fffffffe88cacp+6
+					   want 0x1.fffffffe88cafp+6.  */
 svfloat64_t SV_NAME_D1 (log) (svfloat64_t x, const svbool_t pg)
 {
+  const struct data *d = ptr_barrier (&data);
+
   svuint64_t ix = svreinterpret_u64 (x);
-  svuint64_t top = svlsr_x (pg, ix, 52);
-  svbool_t cmp = svcmpge (pg, svsub_x (pg, top, MinTop), sv_u64 (ThreshTop));
+  svbool_t special = svcmpge (pg, svsub_x (pg, ix, Min), Thresh);
 
   /* x = 2^k z; where z is in range [Off,2*Off) and exact.
      The range is split into N subintervals.
      The ith subinterval contains z and c is near its center.  */
-  svuint64_t tmp = svsub_x (pg, ix, Off);
+  svuint64_t tmp = svsub_x (pg, ix, d->off);
   /* Calculate table index = (tmp >> (52 - V_LOG_TABLE_BITS)) % N.
      The actual value of i is double this due to table layout.  */
   svuint64_t i
       = svand_x (pg, svlsr_x (pg, tmp, (51 - V_LOG_TABLE_BITS)), (N - 1) << 1);
-  svint64_t k
-      = svasr_x (pg, svreinterpret_s64 (tmp), 52); /* Arithmetic shift.  */
   svuint64_t iz = svsub_x (pg, ix, svand_x (pg, tmp, 0xfffULL << 52));
   svfloat64_t z = svreinterpret_f64 (iz);
   /* Lookup in 2 global lists (length N).  */
@@ -59,18 +74,22 @@ svfloat64_t SV_NAME_D1 (log) (svfloat64_t x, const svbool_t pg)
   svfloat64_t logc = svld1_gather_index (pg, &__v_log_data.table[0].logc, i);
 
   /* log(x) = log1p(z/c-1) + log(c) + k*Ln2.  */
-  svfloat64_t r = svmad_x (pg, invc, z, -1);
-  svfloat64_t kd = svcvt_f64_x (pg, k);
+  svfloat64_t kd = svcvt_f64_x (pg, svasr_x (pg, svreinterpret_s64 (tmp), 52));
   /* hi = r + log(c) + k*Ln2.  */
-  svfloat64_t hi = svmla_x (pg, svadd_x (pg, logc, r), kd, __v_log_data.ln2);
+  svfloat64_t ln2_and_c4 = svld1rq_f64 (svptrue_b64 (), &d->ln2);
+  svfloat64_t r = svmad_x (pg, invc, z, -1);
+  svfloat64_t hi = svmla_lane_f64 (logc, kd, ln2_and_c4, 0);
+  hi = svadd_x (pg, r, hi);
+
   /* y = r2*(A0 + r*A1 + r2*(A2 + r*A3 + r2*A4)) + hi.  */
-  svfloat64_t r2 = svmul_x (pg, r, r);
-  svfloat64_t y = svmla_x (pg, P (2), r, P (3));
-  svfloat64_t p = svmla_x (pg, P (0), r, P (1));
-  y = svmla_x (pg, y, r2, P (4));
+  svfloat64_t odd_coeffs = svld1rq_f64 (svptrue_b64 (), &d->c1);
+  svfloat64_t r2 = svmul_x (svptrue_b64 (), r, r);
+  svfloat64_t y = svmla_lane_f64 (sv_f64 (d->c2), r, odd_coeffs, 1);
+  svfloat64_t p = svmla_lane_f64 (sv_f64 (d->c0), r, odd_coeffs, 0);
+  y = svmla_lane_f64 (y, r2, ln2_and_c4, 1);
   y = svmla_x (pg, p, r2, y);
 
-  if (__glibc_unlikely (svptest_any (pg, cmp)))
-    return special_case (x, svmla_x (svnot_z (pg, cmp), hi, r2, y), cmp);
+  if (__glibc_unlikely (svptest_any (pg, special)))
+    return special_case (hi, tmp, y, r2, special, d);
   return svmla_x (pg, hi, r2, y);
 }
diff --git a/sysdeps/aarch64/libm-test-ulps b/sysdeps/aarch64/libm-test-ulps
index 61a7eb9..24a31b1 100644
--- a/sysdeps/aarch64/libm-test-ulps
+++ b/sysdeps/aarch64/libm-test-ulps
@@ -1494,7 +1494,7 @@ float: 2
 ldouble: 1
 
 Function: "log_sve":
-double: 1
+double: 2
 float: 3
 
 Function: "log_towardzero":