Fast algorithm for double->string conversion.

src/cached_powers.h

+// Copyright 2010 the V8 project authors. All rights reserved.
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are
+// met:
+//
+//     * Redistributions of source code must retain the above copyright
+//       notice, this list of conditions and the following disclaimer.
+//     * 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.
+//     * Neither the name of Google Inc. nor the names of its
+//       contributors may be used to endorse or promote products derived
+//       from this software without specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+// "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 THE COPYRIGHT
+// OWNER OR CONTRIBUTORS 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.
+
+#ifndef V8_CACHED_POWERS_H_
+#define V8_CACHED_POWERS_H_
+
+#include "diy_fp.h"
+
+namespace v8 {
+namespace internal {
+
+struct CachedPower {
+  uint64_t significand;
+  int16_t binary_exponent;
+  int16_t decimal_exponent;
+};
+
+// The following defines implement the interface between this file and the
+// generated 'powers_ten.h'.
+// GRISU_CACHE_NAME(1) contains all possible cached powers.
+// GRISU_CACHE_NAME(i) contains GRISU_CACHE_NAME(1) where only every 'i'th
+// element is kept. More formally GRISU_CACHE_NAME(i) contains the elements j*i
+// with 0 <= j < k with k such that j*k < the size of GRISU_CACHE_NAME(1).
+// The higher 'i' is the fewer elements we use.
+// Given that there are less elements, the exponent-distance between two
+// elements in the cache grows. The variable GRISU_CACHE_MAX_DISTANCE(i) stores
+// the maximum distance between two elements.
+#define GRISU_CACHE_STRUCT CachedPower
+#define GRISU_CACHE_NAME(i) kCachedPowers##i
+#define GRISU_CACHE_MAX_DISTANCE(i) kCachedPowersMaxDistance##i
+#define GRISU_CACHE_OFFSET kCachedPowerOffset
+#define GRISU_UINT64_C V8_2PART_UINT64_C
+// The following include imports the precompiled cached powers.
+#include "powers_ten.h"  // NOLINT
+
+static const double kD_1_LOG2_10 = 0.30102999566398114;  //  1 / lg(10)
+
+// We can't use a function since we reference variables depending on the 'i'.
+// This way the compiler is able to see at compile time that only one
+// cache-array variable is used and thus can remove all the others.
+#define COMPUTE_FOR_CACHE(i) \
+  if (!found && (gamma - alpha + 1 >= GRISU_CACHE_MAX_DISTANCE(i))) {   \
+    int kQ = DiyFp::kSignificandSize;                                   \
+    int k = ceiling((alpha - e + kQ - 1) * kD_1_LOG2_10);               \
+    int index = (GRISU_CACHE_OFFSET + k - 1) / i + 1;                   \
+    cached_power = GRISU_CACHE_NAME(i)[index];                          \
+    found = true;                                                       \
+  }                                                                     \
+
+static void GetCachedPower(int e, int alpha, int gamma, int* mk, DiyFp* c_mk) {
+  // The following if statement should be optimized by the compiler so that only
+  // one array is referenced and the others are not included in the object file.
+  bool found = false;
+  CachedPower cached_power;
+  COMPUTE_FOR_CACHE(20);
+  COMPUTE_FOR_CACHE(19);
+  COMPUTE_FOR_CACHE(18);
+  COMPUTE_FOR_CACHE(17);
+  COMPUTE_FOR_CACHE(16);
+  COMPUTE_FOR_CACHE(15);
+  COMPUTE_FOR_CACHE(14);
+  COMPUTE_FOR_CACHE(13);
+  COMPUTE_FOR_CACHE(12);
+  COMPUTE_FOR_CACHE(11);
+  COMPUTE_FOR_CACHE(10);
+  COMPUTE_FOR_CACHE(9);
+  COMPUTE_FOR_CACHE(8);
+  COMPUTE_FOR_CACHE(7);
+  COMPUTE_FOR_CACHE(6);
+  COMPUTE_FOR_CACHE(5);
+  COMPUTE_FOR_CACHE(4);
+  COMPUTE_FOR_CACHE(3);
+  COMPUTE_FOR_CACHE(2);
+  COMPUTE_FOR_CACHE(1);
+  if (!found) {
+    UNIMPLEMENTED();
+    // Silence compiler warnings.
+    cached_power.significand = 0;
+    cached_power.binary_exponent = 0;
+    cached_power.decimal_exponent = 0;
+  }
+  *c_mk = DiyFp(cached_power.significand, cached_power.binary_exponent);
+  *mk = cached_power.decimal_exponent;
+  ASSERT((alpha <= c_mk->e() + e) && (c_mk->e() + e <= gamma));
+}
+#undef GRISU_REDUCTION
+#undef GRISU_CACHE_STRUCT
+#undef GRISU_CACHE_NAME
+#undef GRISU_CACHE_MAX_DISTANCE
+#undef GRISU_CACHE_OFFSET
+#undef GRISU_UINT64_C
+
+} }  // namespace v8::internal
+
+#endif  // V8_CACHED_POWERS_H_