New log implementation

The new implementations are provided under !__OBSOLETE_MATH, it uses
ISO C99 code.  With default settings the worst case error in nearest
rounding mode is 0.519 ULP with inlined fma and fma contraction.  It uses
a 2 KB lookup table, on aarch64 .text+.rodata size of libm.a is increased
by 1703 bytes.  The w_log.c wrapper is disabled since error handling is
inline in the new code.

New __HAVE_FAST_FMA and __HAVE_FAST_FMA_DEFAULT feature macros were
added to enable selecting between the code path that uses fma and the
one that does not.  Targets supposed to set __HAVE_FAST_FMA_DEFAULT
if they have single instruction fma and the compiler can actually
inline it (gcc has __FP_FAST_FMA macro but that does not guarantee
inlining with -fno-builtin-fma).

Improvements on Cortex-A72:
latency: 1.9x
thruput: 2.3x

1 files changed, 175 insertions, 0 deletions

diff --git a/newlib/libm/common/log.c b/newlib/libm/common/log.c
new file mode 100644
index 000000000..32752f55c
--- /dev/null
+++ b/newlib/libm/common/log.c
@@ -0,0 +1,175 @@
+/* Double-precision log(x) function.
+   Copyright (c) 2018 Arm Ltd.  All rights reserved.
+
+   SPDX-License-Identifier: BSD-3-Clause
+
+   Redistribution and use in source and binary forms, with or without
+   modification, are permitted provided that the following conditions
+   are met:
+   1. Redistributions of source code must retain the above copyright
+      notice, this list of conditions and the following disclaimer.
+   2. Redistributions in binary form must reproduce the above copyright
+      notice, this list of conditions and the following disclaimer in the
+      documentation and/or other materials provided with the distribution.
+   3. The name of the company may not be used to endorse or promote
+      products derived from this software without specific prior written
+      permission.
+
+   THIS SOFTWARE IS PROVIDED BY Arm LTD ``AS IS AND ANY EXPRESS OR IMPLIED
+   WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
+   MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+   IN NO EVENT SHALL Arm LTD BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+   SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
+   TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+   PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+   LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+   NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+   SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
+
+#include "fdlibm.h"
+#if !__OBSOLETE_MATH
+
+#include <math.h>
+#include <stdint.h>
+#include "math_config.h"
+
+#define T __log_data.tab
+#define T2 __log_data.tab2
+#define B __log_data.poly1
+#define A __log_data.poly
+#define Ln2hi __log_data.ln2hi
+#define Ln2lo __log_data.ln2lo
+#define N (1 << LOG_TABLE_BITS)
+#define OFF 0x3fe6000000000000
+
+static inline uint32_t
+top16 (double x)
+{
+  return asuint64 (x) >> 48;
+}
+
+double
+log (double x)
+{
+  /* double_t for better performance on targets with FLT_EVAL_METHOD==2.  */
+  double_t w, z, r, r2, r3, y, invc, logc, kd, hi, lo;
+  uint64_t ix, iz, tmp;
+  uint32_t top;
+  int k, i;
+
+  ix = asuint64 (x);
+  top = top16 (x);
+
+#if LOG_POLY1_ORDER == 10 || LOG_POLY1_ORDER == 11
+# define LO asuint64 (1.0 - 0x1p-5)
+# define HI asuint64 (1.0 + 0x1.1p-5)
+#elif LOG_POLY1_ORDER == 12
+# define LO asuint64 (1.0 - 0x1p-4)
+# define HI asuint64 (1.0 + 0x1.09p-4)
+#endif
+  if (unlikely (ix - LO < HI - LO))
+    {
+      /* Handle close to 1.0 inputs separately.  */
+      /* Fix sign of zero with downward rounding when x==1.  */
+      if (WANT_ROUNDING && unlikely (ix == asuint64 (1.0)))
+	return 0;
+      r = x - 1.0;
+      r2 = r*r;
+      r3 = r*r2;
+#if LOG_POLY1_ORDER == 10
+      /* Worst-case error is around 0.516 ULP.  */
+      y = r3*(B[1] + r*B[2] + r2*B[3]
+	      + r3*(B[4] + r*B[5] + r2*B[6] + r3*(B[7] + r*B[8])));
+      w = B[0]*r2; /* B[0] == -0.5.  */
+      hi = r + w;
+      y += r - hi + w;
+      y += hi;
+#elif LOG_POLY1_ORDER == 11
+      /* Worst-case error is around 0.516 ULP.  */
+      y = r3*(B[1] + r*B[2]
+	      + r2*(B[3] + r*B[4] + r2*B[5]
+		    + r3*(B[6] + r*B[7] + r2*B[8] + r3*B[9])));
+      w = B[0]*r2; /* B[0] == -0.5.  */
+      hi = r + w;
+      y += r - hi + w;
+      y += hi;
+#elif LOG_POLY1_ORDER == 12
+      y = r3*(B[1] + r*B[2] + r2*B[3]
+	      + r3*(B[4] + r*B[5] + r2*B[6]
+		    + r3*(B[7] + r*B[8] + r2*B[9] + r3*B[10])));
+# if N <= 64
+      /* Worst-case error is around 0.532 ULP.  */
+      w = B[0]*r2; /* B[0] == -0.5.  */
+      hi = r + w;
+      y += r - hi + w;
+      y += hi;
+# else
+      /* Worst-case error is around 0.507 ULP.  */
+      w = r*0x1p27;
+      double_t rhi = r + w - w;
+      double_t rlo = r - rhi;
+      w = rhi*rhi*B[0]; /* B[0] == -0.5.  */
+      hi = r + w;
+      lo = r - hi + w;
+      lo += B[0]*rlo*(rhi + r);
+      y += lo;
+      y += hi;
+# endif
+#endif
+      return y;
+    }
+  if (unlikely (top - 0x0010 >= 0x7ff0 - 0x0010))
+    {
+      /* x < 0x1p-1022 or inf or nan.  */
+      if (ix * 2 == 0)
+	return __math_divzero (1);
+      if (ix == asuint64 (INFINITY)) /* log(inf) == inf.  */
+	return x;
+      if ((top & 0x8000) || (top & 0x7ff0) == 0x7ff0)
+	return __math_invalid (x);
+      /* x is subnormal, normalize it.  */
+      ix = asuint64 (x * 0x1p52);
+      ix -= 52ULL << 52;
+    }
+
+  /* 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.  */
+  tmp = ix - OFF;
+  i = (tmp >> (52 - LOG_TABLE_BITS)) % N;
+  k = (int64_t) tmp >> 52; /* arithmetic shift */
+  iz = ix - (tmp & 0xfffULL << 52);
+  invc = T[i].invc;
+  logc = T[i].logc;
+  z = asdouble (iz);
+
+  /* log(x) = log1p(z/c-1) + log(c) + k*Ln2.  */
+  /* r ~= z/c - 1, |r| < 1/(2*N).  */
+#if __HAVE_FAST_FMA
+  /* rounding error: 0x1p-55/N.  */
+  r = fma (z, invc, -1.0);
+#else
+  /* rounding error: 0x1p-55/N + 0x1p-66.  */
+  r = (z - T2[i].chi - T2[i].clo)*invc;
+#endif
+  kd = (double_t) k;
+
+  /* hi + lo = r + log(c) + k*Ln2.  */
+  w = kd*Ln2hi + logc;
+  hi = w + r;
+  lo = w - hi + r + kd*Ln2lo;
+
+  /* log(x) = lo + (log1p(r) - r) + hi.  */
+  r2 = r * r; /* rounding error: 0x1p-54/N^2.  */
+  /* Worst case error if |y| > 0x1p-5:
+     0.5 + 4.13/N + abs-poly-error*2^57 ULP (+ 0.002 ULP without fma)
+     Worst case error if |y| > 0x1p-4:
+     0.5 + 2.06/N + abs-poly-error*2^56 ULP (+ 0.001 ULP without fma).  */
+#if LOG_POLY_ORDER == 6
+  y = lo + r2*A[0] + r*r2*(A[1] + r*A[2] + r2*(A[3] + r*A[4])) + hi;
+#elif LOG_POLY_ORDER == 7
+  y = lo + r2*(A[0] + r*A[1] + r2*(A[2] + r*A[3]) + r2*r2*(A[4] + r*A[5])) + hi;
+#endif
+  return y;
+}
+#endif