pl/math: Add vector/SVE log2f

New SVE routine is an SVE port of the Neon algorithm
and is accurate to 2.48 ULPs.

2 files changed, 81 insertions, 0 deletions

diff --git a/pl/math/include/mathlib.h b/pl/math/include/mathlib.h
index 041b407..f05ad03 100644
--- a/pl/math/include/mathlib.h
+++ b/pl/math/include/mathlib.h
@@ -190,6 +190,7 @@ svfloat32_t __sv_logf_x (svfloat32_t, svbool_t);
 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);
 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);
@@ -210,6 +211,7 @@ svfloat32_t _ZGVsMxv_logf (svfloat32_t, svbool_t);
 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);
 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_log2f_2u5.c b/pl/math/sv_log2f_2u5.c
new file mode 100644
index 0000000..6488658
--- /dev/null
+++ b/pl/math/sv_log2f_2u5.c
@@ -0,0 +1,79 @@
+/*
+ * Single-precision vector/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 P(i) __v_log2f_data.poly[i]
+
+#define Ln2 (0x1.62e43p-1f) /* 0x3f317218.  */
+#define Min (0x00800000)
+#define Max (0x7f800000)
+#define Mask (0x007fffff)
+#define Off (0x3f2aaaab) /* 0.666667.  */
+
+static NOINLINE sv_f32_t
+specialcase (sv_f32_t x, sv_f32_t y, svbool_t cmp)
+{
+  return sv_call_f32 (log2f, x, y, cmp);
+}
+
+/* Optimised implementation of SVE log2f, using the same algorithm
+   and polynomial as Neon log2f. Maximum error is 2.48 ULPs:
+   __sv_log2f(0x1.558174p+0) got 0x1.a9be84p-2
+			    want 0x1.a9be8p-2.  */
+sv_f32_t
+__sv_log2f_x (sv_f32_t x, const svbool_t pg)
+{
+  sv_u32_t u = sv_as_u32_f32 (x);
+  svbool_t special
+    = svcmpge_u32 (pg, svsub_n_u32_x (pg, u, Min), sv_u32 (Max - Min));
+
+  /* x = 2^n * (1+r), where 2/3 < 1+r < 4/3.  */
+  u = svsub_n_u32_x (pg, u, Off);
+  sv_f32_t n = sv_to_f32_s32_x (pg, svasr_n_s32_x (pg, sv_as_s32_u32 (u),
+						   23)); /* Sign-extend.  */
+  u = svand_n_u32_x (pg, u, Mask);
+  u = svadd_n_u32_x (pg, u, Off);
+  sv_f32_t r = svsub_n_f32_x (pg, sv_as_f32_u32 (u), 1.0f);
+
+  /* y = log2(1+r) + n.  */
+  sv_f32_t r2 = svmul_f32_x (pg, r, r);
+
+  /* Evaluate polynomial using pairwise Horner scheme.  */
+  sv_f32_t p67 = sv_fma_n_f32_x (pg, P (7), r, sv_f32 (P (6)));
+  sv_f32_t p45 = sv_fma_n_f32_x (pg, P (5), r, sv_f32 (P (4)));
+  sv_f32_t p23 = sv_fma_n_f32_x (pg, P (3), r, sv_f32 (P (2)));
+  sv_f32_t p01 = sv_fma_n_f32_x (pg, P (1), r, sv_f32 (P (0)));
+  sv_f32_t y;
+  y = sv_fma_n_f32_x (pg, P (8), r2, p67);
+  y = sv_fma_f32_x (pg, y, r2, p45);
+  y = sv_fma_f32_x (pg, y, r2, p23);
+  y = sv_fma_f32_x (pg, y, r2, p01);
+  y = sv_fma_f32_x (pg, y, r, n);
+
+  if (unlikely (svptest_any (pg, special)))
+    return specialcase (x, y, special);
+  return y;
+}
+
+PL_ALIAS (__sv_log2f_x, _ZGVsMxv_log2f)
+
+PL_SIG (SV, F, 1, log2, 0.01, 11.1)
+PL_TEST_ULP (__sv_log2f, 1.99)
+PL_TEST_EXPECT_FENV_ALWAYS (__sv_log2f)
+PL_TEST_INTERVAL (__sv_log2f, -0.0, -0x1p126, 4000)
+PL_TEST_INTERVAL (__sv_log2f, 0.0, 0x1p-126, 4000)
+PL_TEST_INTERVAL (__sv_log2f, 0x1p-126, 0x1p-23, 50000)
+PL_TEST_INTERVAL (__sv_log2f, 0x1p-23, 1.0, 50000)
+PL_TEST_INTERVAL (__sv_log2f, 1.0, 100, 50000)
+PL_TEST_INTERVAL (__sv_log2f, 100, inf, 50000)
+
+#endif // SV_SUPPORTED