Audit ULP limits in runulp.sh

We have not been consistent in using the pre- or post-rounding ULP
estimate here. We now use the pre-rounding value. There are also a
handful of inaccuracies which are probably due to running ULP against
different versions of GLIBC. A few routines have been updated because
of this - going forward we will compare against GLIBC 2.31. The bounds
in runulp have mostly been tightened.

1 files changed, 89 insertions, 0 deletions

diff --git a/pl/math/v_log2_3u.c b/pl/math/v_log2_3u.c
new file mode 100644
index 0000000..d34d0e8
--- /dev/null
+++ b/pl/math/v_log2_3u.c
@@ -0,0 +1,89 @@
+/*
+ * Double-precision vector log2 function.
+ *
+ * Copyright (c) 2022, Arm Limited.
+ * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
+ */
+
+#include "include/mathlib.h"
+#include "v_math.h"
+#if V_SUPPORTED
+
+#define InvLn2 v_f64 (0x1.71547652b82fep0)
+#define N (1 << V_LOG2_TABLE_BITS)
+#define OFF v_u64 (0x3fe6900900000000)
+#define P(i) v_f64 (__v_log2_data.poly[i])
+
+struct entry
+{
+  v_f64_t invc;
+  v_f64_t log2c;
+};
+
+static inline struct entry
+lookup (v_u64_t i)
+{
+  struct entry e;
+#ifdef SCALAR
+  e.invc = __v_log2_data.tab[i].invc;
+  e.log2c = __v_log2_data.tab[i].log2c;
+#else
+  e.invc[0] = __v_log2_data.tab[i[0]].invc;
+  e.log2c[0] = __v_log2_data.tab[i[0]].log2c;
+  e.invc[1] = __v_log2_data.tab[i[1]].invc;
+  e.log2c[1] = __v_log2_data.tab[i[1]].log2c;
+#endif
+  return e;
+}
+
+VPCS_ATTR
+NOINLINE static v_f64_t
+specialcase (v_f64_t x, v_f64_t y, v_u64_t cmp)
+{
+  return v_call_f64 (log2, x, y, 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(0x1.0b5572f05bc9dp+0) got 0x1.fffc917a7a52dp-5
+				  want 0x1.fffc917a7a53p-5.  */
+VPCS_ATTR
+v_f64_t V_NAME (log2) (v_f64_t x)
+{
+  v_u64_t ix = v_as_u64_f64 (x);
+  v_u64_t top = ix >> 48;
+  v_u64_t special
+    = v_cond_u64 (top - v_u64 (0x0010) >= v_u64 (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.  */
+  v_u64_t tmp = ix - OFF;
+  v_u64_t i = (tmp >> (52 - V_LOG2_TABLE_BITS)) % N;
+  v_s64_t k = v_as_s64_u64 (tmp) >> 52; /* arithmetic shift.  */
+  v_u64_t iz = ix - (tmp & v_u64 (0xfffULL << 52));
+  v_f64_t z = v_as_f64_u64 (iz);
+  struct entry e = lookup (i);
+
+  /* log2(x) = log1p(z/c-1)/log(2) + log2(c) + k.  */
+
+  v_f64_t r = v_fma_f64 (z, e.invc, v_f64 (-1.0));
+  v_f64_t kd = v_to_f64_s64 (k);
+  v_f64_t w = v_fma_f64 (r, InvLn2, e.log2c);
+
+  v_f64_t r2 = r * r;
+  v_f64_t p_45 = v_fma_f64 (P (5), r, P (4));
+  v_f64_t p_23 = v_fma_f64 (P (3), r, P (2));
+  v_f64_t p_01 = v_fma_f64 (P (1), r, P (0));
+  v_f64_t y = v_fma_f64 (r2, p_45, p_23);
+  y = v_fma_f64 (r2, y, p_01);
+  y = v_fma_f64 (r2, y, kd + w);
+
+  if (unlikely (v_any_u64 (special)))
+    return specialcase (x, y, special);
+  return y;
+}
+VPCS_ALIAS
+
+#endif