Fast algorithm for double->string conversion.

src/diy_fp.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_DIY_FP_H_
+#define V8_DIY_FP_H_
+
+namespace v8 {
+namespace internal {
+
+// Implements a 64bit significand/int exponent Floating Point number.
+// Only the minus and multiply operations are implemented. Both operations have
+// severe limitations. But we don't need more.
+// DiyFp are not designed to contain special doubles (NaN and Infinity).
+class DiyFp {
+ public:
+  static const int kSignificandSize = 64;
+
+  DiyFp() : f_(0), e_(0) {}
+  DiyFp(uint64_t f, int e) : f_(f), e_(e) {}
+
+  // this = this - other.
+  // The exponents of both numbers must be the same and this must be bigger
+  // than other. The result will not be normalized.
+  void Subtract(const DiyFp& other) {
+    ASSERT(e_ == other.e_);
+    ASSERT(f_ >= other.f_);
+    f_ -= other.f_;
+  }
+
+  // returns a - b.
+  // The exponents of both numbers must be the same and this must be bigger
+  // than other. The result will not be normalized.
+  static DiyFp Minus(const DiyFp& a, const DiyFp& b) {
+    DiyFp result = a;
+    result.Subtract(b);
+    return result;
+  }
+
+
+  // this = this * other.
+  void Multiply(const DiyFp& other) {
+    // Simply "emulates" a 128 bit multiplication.
+    // However: the resulting number only contains 64 bits. The last 64 bits
+    // are only used for rounding the first 64 bits.

[Lasse Reichstein, 2010/02/22 11:31:36]

Which bits are first and last? Do you mean low and high/most or least
signficant?

[Florian Loitsch, 2010/02/22 15:52:53]

Done.

[floitsch, 2012/04/10 15:54:34]

Done.

+    const uint64_t kM32 = 0xFFFFFFFF;

[Lasse Reichstein, 2010/02/22 11:31:36]

Put a "u" on the end of the literal to make it unsigned.

[Florian Loitsch, 2010/02/22 15:52:53]

Done.

[floitsch, 2012/04/10 15:54:34]

Done.

+    uint64_t a = f_ >> 32;
+    uint64_t b = f_ & kM32;
+    uint64_t c = other.f_ >> 32;
+    uint64_t d = other.f_ & kM32;
+    uint64_t ac = a * c;
+    uint64_t bc = b * c;
+    uint64_t ad = a * d;
+    uint64_t bd = b * d;
+    uint64_t tmp = (bd >> 32) + (ad & kM32) + (bc & kM32);
+    tmp += 1U << 31;  // round
+    uint64_t result_f = ac + (ad >> 32) + (bc >> 32) + (tmp >> 32);
+    e_ += other.e_ + 64;
+    f_ = result_f;
+  }
+
+  // returns a * b;
+  static DiyFp Times(const DiyFp& a, const DiyFp& b) {
+    DiyFp result = a;
+    result.Multiply(b);
+    return result;
+  }
+
+  void Normalize() {
+    ASSERT(f_ != 0);
+    uint64_t f = f_;
+    int e = e_;
+
+    // This method is mainly called for normalizing boundaries. In general
+    // boundaries need to be shifted by 10 bits. We thus optimize for this case.
+    const uint64_t k10MSBits = V8_2PART_UINT64_C(0xFFC00000,00000000);
+    while ((f & k10MSBits) == 0) {
+      f <<= 10;
+      e -= 10;
+    }
+    while ((f & kUint64MSB) == 0) {
+      f <<= 1;
+      e--;
+    }
+    f_ = f;
+    e_ = e;
+  }
+
+  static DiyFp Normalize(const DiyFp& a) {
+    DiyFp result = a;
+    result.Normalize();
+    return result;
+  }
+
+  uint64_t f() const { return f_; }
+  int e() const { return e_; }
+
+  void set_f(uint64_t new_value) { f_ = new_value; }
+  void set_e(int new_value) { e_ = new_value; }
+
+ private:
+  static const uint64_t kUint64MSB = V8_2PART_UINT64_C(0x80000000,00000000);
+
+  uint64_t f_;
+  int e_;
+};
+
+} }  // namespace v8::internal
+
+#endif  // V8_DIY_FP_H_