Fast algorithm for double->string conversion.

src/double.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_DOUBLE_H_
+#define V8_DOUBLE_H_
+
+namespace v8 {
+namespace internal {
+
+// We assume that doubles and uint64_t have the same endianness.
+static uint64_t double_to_uint64(double d) { return bit_cast<uint64_t>(d); }
+static double uint64_to_double(uint64_t d64) { return bit_cast<double>(d64); }
+
+// Helper functions for doubles.
+class Double {
+ public:
+  static const int kSignificandSize = 52;  // Excludes the hidden bit.
+
+  Double() : d64_(0.0) {}
+  explicit Double(double d) : d64_(double_to_uint64(d)) {}
+  explicit Double(uint64_t d64) : d64_(d64) {}
+
+  DiyFp AsDiyFp() const {
+    ASSERT(!IsSpecial());
+    return DiyFp(Significand(), Exponent());
+  }
+
+  DiyFp AsNormalizedDiyFp() const {
+    uint64_t f = Significand();
+    int e = Exponent();
+
+    // The current double could be a denormal.
+    while ((f & kHiddenBit) == 0) {
+      f <<= 1;
+      e--;
+    }
+    // Do the final shifts in one go. Don't forget the hidden bit (the '-1').
+    f <<= DiyFp::kSignificandSize - kSignificandSize - 1;
+    e -= DiyFp::kSignificandSize - kSignificandSize - 1;
+    return DiyFp(f, e);
+  }
+
+  int Exponent() const {
+    if (IsDenormal()) return kDenormalExponent;
+
+    uint64_t d64 = AsUint64();
+    int biased_e = (d64 & kExponentMask) >> kSignificandSize;
+    return biased_e - kExponentBias;
+  }
+
+  uint64_t Significand() const {
+    uint64_t d64 = AsUint64();
+    uint64_t significand = d64 & kSignificandMask;
+    if (!IsDenormal()) {
+      return significand + kHiddenBit;
+    } else {
+      return significand;
+    }
+  }
+
+  // Returns true if the double is a denormal.
+  bool IsDenormal() const {
+    uint64_t d64 = AsUint64();
+    return (d64 & kExponentMask) == 0;
+  }
+
+  // We consider denormals not to be special.
+  // Hence only Infinity and NaN are special.
+  bool IsSpecial() const {
+    uint64_t d64 = AsUint64();
+    return (d64 & kExponentMask) == kExponentMask;
+  }
+
+  // Returns the two boundaries of this.
+  // The bigger boundary (m_plus) is normalized. The lower boundary has the same
+  // exponent as m_plus.
+  void NormalizedBoundaries(DiyFp* out_m_minus, DiyFp* out_m_plus) const {
+    DiyFp v = this->AsDiyFp();
+    bool significand_is_zero = (v.f() == kHiddenBit);
+    DiyFp m_plus = DiyFp::Normalize(DiyFp((v.f() << 1) + 1, v.e() - 1));
+    DiyFp m_minus;
+    if (significand_is_zero && v.e() != kDenormalExponent) {
+      // The boundary is closer. Think of v = 1000e10 and v- = 9999e9.
+      // Then the boundary (== (v - v-)/2) is not just at a distance of 1e9 but
+      // at a distance of 1e8.
+      // The only exception is for the smallest normal: the largest denormal is
+      // at the same distance as its successor.
+      // Note: denormals have the same exponent as the smallest normals.
+      m_minus = DiyFp((v.f() << 2) - 1, v.e() - 2);
+    } else {
+      m_minus = DiyFp((v.f() << 1) - 1, v.e() - 1);
+    }
+    m_minus.set_f(m_minus.f() << (m_minus.e() - m_plus.e()));
+    m_minus.set_e(m_plus.e());
+    *out_m_plus = m_plus;
+    *out_m_minus = m_minus;
+  }
+
+  double value() const { return uint64_to_double(d64_); }
+
+ private:
+  static const int kExponentBias = 0x3FF + kSignificandSize;
+  static const int kDenormalExponent = -kExponentBias + 1;
+  static const uint64_t kExponentMask = V8_2PART_UINT64_C(0x7FF00000, 00000000);
+  static const uint64_t kSignificandMask =
+      V8_2PART_UINT64_C(0x000FFFFF,FFFFFFFF);
+  static const uint64_t kHiddenBit = V8_2PART_UINT64_C(0x00100000, 00000000);
+
+  uint64_t d64_;
+
+  // Returns the double's bit as uint64.
+  uint64_t AsUint64() const {
+    return d64_;
+  }
+};
+
+} }  // namespace v8::internal
+
+#endif  // V8_DOUBLE_H_