pl/math: Add vector/SVE log2

The new SVE implementation is a direct port of Neon log2, and is
accurate to 2.58 ULPs.
Update error threshold and comments for Neon log2 too, new
approximate argmax but same threshold.

3 files changed, 91 insertions, 4 deletions

diff --git a/pl/math/include/mathlib.h b/pl/math/include/mathlib.h
index f05ad03..67c3c9d 100644
--- a/pl/math/include/mathlib.h
+++ b/pl/math/include/mathlib.h
@@ -191,6 +191,7 @@ svfloat64_t __sv_log_x (svfloat64_t, svbool_t);
 svfloat32_t __sv_log10f_x (svfloat32_t, svbool_t);
 svfloat64_t __sv_log10_x (svfloat64_t, svbool_t);
 svfloat32_t __sv_log2f_x (svfloat32_t, svbool_t);
+svfloat64_t __sv_log2_x (svfloat64_t, svbool_t);
 svfloat32_t __sv_powif_x (svfloat32_t, svint32_t, svbool_t);
 svfloat64_t __sv_powi_x (svfloat64_t, svint64_t, svbool_t);
 svfloat32_t __sv_sinf_x (svfloat32_t, svbool_t);
@@ -212,6 +213,7 @@ svfloat64_t _ZGVsMxv_log (svfloat64_t, svbool_t);
 svfloat32_t _ZGVsMxv_log10f (svfloat32_t, svbool_t);
 svfloat64_t _ZGVsMxv_log10 (svfloat64_t, svbool_t);
 svfloat32_t _ZGVsMxv_log2f (svfloat32_t, svbool_t);
+svfloat64_t _ZGVsMxv_log2 (svfloat64_t, svbool_t);
 svfloat32_t _ZGVsMxvv_powi(svfloat32_t, svint32_t, svbool_t);
 svfloat64_t _ZGVsMxvv_powk(svfloat64_t, svint64_t, svbool_t);
 svfloat32_t _ZGVsMxv_sinf (svfloat32_t, svbool_t);
diff --git a/pl/math/sv_log2_3u.c b/pl/math/sv_log2_3u.c
new file mode 100644
index 0000000..d66a474
--- /dev/null
+++ b/pl/math/sv_log2_3u.c
@@ -0,0 +1,85 @@
+/*
+ * Double-precision SVE log2 function.
+ *
+ * Copyright (c) 2022, Arm Limited.
+ * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
+ */
+
+#include "sv_math.h"
+#include "pl_sig.h"
+#include "pl_test.h"
+
+#if SV_SUPPORTED
+
+#define InvLn2 sv_f64 (0x1.71547652b82fep0)
+#define N (1 << V_LOG2_TABLE_BITS)
+#define OFF 0x3fe6900900000000
+#define P(i) sv_f64 (__v_log2_data.poly[i])
+
+NOINLINE static sv_f64_t
+specialcase (sv_f64_t x, sv_f64_t y, const svbool_t cmp)
+{
+  return sv_call_f64 (log2, x, y, cmp);
+}
+
+/* Double-precision SVE log2 routine. Implements the same algorithm as vector
+   log10, with coefficients and table entries scaled in extended precision.
+   The maximum observed error is 2.58 ULP:
+   __v_log2(0x1.0b556b093869bp+0) got 0x1.fffb34198d9dap-5
+				 want 0x1.fffb34198d9ddp-5.  */
+sv_f64_t
+__sv_log2_x (sv_f64_t x, const svbool_t pg)
+{
+  sv_u64_t ix = sv_as_u64_f64 (x);
+  sv_u64_t top = svlsr_n_u64_x (pg, ix, 48);
+
+  svbool_t special
+    = svcmpge_n_u64 (pg, svsub_n_u64_x (pg, top, 0x0010), 0x7ff0 - 0x0010);
+
+  /* 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.  */
+  sv_u64_t tmp = svsub_n_u64_x (pg, ix, OFF);
+  sv_u64_t i
+    = sv_mod_n_u64_x (pg, svlsr_n_u64_x (pg, tmp, 52 - V_LOG2_TABLE_BITS), N);
+  sv_f64_t k
+    = sv_to_f64_s64_x (pg, svasr_n_s64_x (pg, sv_as_s64_u64 (tmp), 52));
+  sv_f64_t z = sv_as_f64_u64 (
+    svsub_u64_x (pg, ix, svand_n_u64_x (pg, tmp, 0xfffULL << 52)));
+
+  sv_u64_t idx = svmul_n_u64_x (pg, i, 2);
+  sv_f64_t invc = sv_lookup_f64_x (pg, &__v_log2_data.tab[0].invc, idx);
+  sv_f64_t log2c = sv_lookup_f64_x (pg, &__v_log2_data.tab[0].log2c, idx);
+
+  /* log2(x) = log1p(z/c-1)/log(2) + log2(c) + k.  */
+
+  sv_f64_t r = sv_fma_f64_x (pg, z, invc, sv_f64 (-1.0));
+  sv_f64_t w = sv_fma_f64_x (pg, r, InvLn2, log2c);
+
+  sv_f64_t r2 = svmul_f64_x (pg, r, r);
+  sv_f64_t p_23 = sv_fma_f64_x (pg, P (3), r, P (2));
+  sv_f64_t p_01 = sv_fma_f64_x (pg, P (1), r, P (0));
+  sv_f64_t y = sv_fma_f64_x (pg, P (4), r2, p_23);
+  y = sv_fma_f64_x (pg, y, r2, p_01);
+  y = sv_fma_f64_x (pg, y, r2, svadd_f64_x (pg, k, w));
+
+  if (unlikely (svptest_any (pg, special)))
+    {
+      return specialcase (x, y, special);
+    }
+  return y;
+}
+
+PL_ALIAS (__sv_log2_x, _ZGVsMxv_log2)
+
+PL_SIG (SV, D, 1, log2, 0.01, 11.1)
+PL_TEST_ULP (__sv_log2, 2.09)
+PL_TEST_EXPECT_FENV_ALWAYS (__sv_log2)
+PL_TEST_INTERVAL (__sv_log2, -0.0, -0x1p126, 1000)
+PL_TEST_INTERVAL (__sv_log2, 0.0, 0x1p-126, 4000)
+PL_TEST_INTERVAL (__sv_log2, 0x1p-126, 0x1p-23, 50000)
+PL_TEST_INTERVAL (__sv_log2, 0x1p-23, 1.0, 50000)
+PL_TEST_INTERVAL (__sv_log2, 1.0, 100, 50000)
+PL_TEST_INTERVAL (__sv_log2, 100, inf, 50000)
+
+#endif
diff --git a/pl/math/v_log2_3u.c b/pl/math/v_log2_3u.c
index e0a854f..5b9bdd8 100644
--- a/pl/math/v_log2_3u.c
+++ b/pl/math/v_log2_3u.c
@@ -48,9 +48,9 @@ specialcase (v_f64_t x, v_f64_t y, v_u64_t cmp)
 
 /* Double-precision vector log2 routine. Implements the same algorithm as vector
    log10, with coefficients and table entries scaled in extended precision.
-   The maximum observed error is 2.59 ULP:
-   __v_log2(0x1.0b555054a9bd1p+0) got 0x1.fff6977bdced3p-5
-				 want 0x1.fff6977bdced6p-5.  */
+   The maximum observed error is 2.58 ULP:
+   __v_log2(0x1.0b556b093869bp+0) got 0x1.fffb34198d9dap-5
+				 want 0x1.fffb34198d9ddp-5.  */
 VPCS_ATTR
 v_f64_t V_NAME (log2) (v_f64_t x)
 {
@@ -89,7 +89,7 @@ v_f64_t V_NAME (log2) (v_f64_t x)
 VPCS_ALIAS
 
 PL_SIG (V, D, 1, log2, 0.01, 11.1)
-PL_TEST_ULP (V_NAME (log2), 2.10)
+PL_TEST_ULP (V_NAME (log2), 2.09)
 PL_TEST_EXPECT_FENV_ALWAYS (V_NAME (log2))
 PL_TEST_INTERVAL (V_NAME (log2), -0.0, -0x1p126, 100)
 PL_TEST_INTERVAL (V_NAME (log2), 0x1p-149, 0x1p-126, 4000)