Fast double-to-ascii conversion.

src/grisu3.cc

 // 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
@@ skipping 56 matching lines @@
   // Generates w's digits. The result is the shortest in the interval low-high.
   // All DiyFp are assumed to be imprecise and this function takes this
   // imprecision into account. If the function cannot compute the best
   // representation (due to the imprecision) then false is returned.
   static bool DigitGen_m60_m32(DiyFp low, DiyFp w, DiyFp high,
                                char* buffer, int* length, int* kappa);
 };
 
 
 template<int alpha, int gamma>
-bool Grisu3<alpha, gamma>::grisu3(
-    double v, char* buffer, int* length, int* decimal_exponent) {
+bool Grisu3<alpha, gamma>::grisu3(double v,
+                                  char* buffer,
+                                  int* length,
+                                  int* decimal_exponent) {
   DiyFp w = Double(v).AsNormalizedDiyFp();
   // boundary_minus and boundary_plus are the boundaries between v and its
   // neighbors. Any number strictly between boundary_minus and boundary_plus
   // will round to v when read as double.
   // Grisu3 will never output representations that lie exactly on a boundary.
   DiyFp boundary_minus, boundary_plus;
   Double(v).NormalizedBoundaries(&boundary_minus, &boundary_plus);
   ASSERT(boundary_plus.e() == w.e());
   DiyFp ten_mk;  // Cached power of ten: 10^-k
   int mk;        // -k
@@ skipping 51 matching lines @@
 //     * buffer contains the shortest possible decimal digit-sequence
 //       such that LOW < buffer * 10^kappa < HIGH, where LOW and HIGH are the
 //       correct values of low and high (without their error).
 //     * if more than one decimal representation gives the minimal number of
 //       decimal digits then the one closest to W (where W is the correct value
 //       of w) is chosen.
 // Remark: this procedure takes into account the imprecision of its input
 //   numbers. If the precision is not enough to guarantee all the postconditions
 //   then false is returned. This usually happens rarely (~0.5%).
 template<int alpha, int gamma>
-bool Grisu3<alpha, gamma>::DigitGen(
-    DiyFp low, DiyFp w, DiyFp high, char* buffer, int* len, int* kappa) {
+bool Grisu3<alpha, gamma>::DigitGen(DiyFp low,
+                                    DiyFp w,
+                                    DiyFp high,
+                                    char* buffer,
+                                    int* len,
+                                    int* kappa) {
   ASSERT(low.e() == w.e() && w.e() == high.e());
   ASSERT(low.f() + 1 <= high.f() - 1);
   ASSERT(alpha <= w.e() && w.e() <= gamma);
   // The following tests use alpha and gamma to avoid unnecessary dynamic tests.
   if ((alpha >= -60 && gamma <= -32) ||  // -60 <= w.e() <= -32
       (alpha <= -32 && gamma >= -60 &&   // Alpha/gamma overlaps -60/-32 region.
        -60 <= w.e() && w.e() <= -32)) {
     return DigitGen_m60_m32(low, w, high, buffer, len, kappa);
   } else {
     // A simple adaption of the special case -60/-32 would allow greater ranges
     // of alpha/gamma and thus reduce the number of precomputed cached powers of
     // ten.
     UNIMPLEMENTED();
     return false;
   }
 }
 
 static const uint32_t kTen4 = 10000;
 static const uint32_t kTen5 = 100000;
 static const uint32_t kTen6 = 1000000;
 static const uint32_t kTen7 = 10000000;
 static const uint32_t kTen8 = 100000000;
 static const uint32_t kTen9 = 1000000000;
 
 // Returns the biggest power of ten that is <= than the given number. We
 // furthermore receive the maximum number of bits 'number' has.
 // If number_bits == 0 then 0^-1 is returned
 // The number of bits must be <= 32.
-static void BiggestPowerTen(uint32_t number, int number_bits,
-                            uint32_t* power, int* exponent) {
+static void BiggestPowerTen(uint32_t number,
+                            int number_bits,
+                            uint32_t* power,
+                            int* exponent) {
   switch (number_bits) {
     case 32:
     case 31:
     case 30:
       if (kTen9 <= number) {
         *power = kTen9;
         *exponent = 9;
         break;
       }  // else fallthrough
     case 29:
@@ skipping 95 matching lines @@
 // Printing w's integral part is easy (simply print 0x1234 in decimal).
 // In order to print its fraction we repeatedly multiply the fraction by 10 and
 // get each digit. Example the first digit after the comma would be computed by
 //   (0x567890abcdef * 10) >> 48. -> 3
 // The whole thing becomes slightly more complicated because we want to stop
 // once we have enough digits. That is, once the digits inside the buffer
 // represent 'w' we can stop. Everything inside the interval low - high
 // represents w. However we have to pay attention to low, high and w's
 // imprecision.
 template<int alpha, int gamma>
-bool Grisu3<alpha, gamma>::DigitGen_m60_m32(
-    DiyFp low, DiyFp w, DiyFp high, char* buffer, int* length, int* kappa) {
+bool Grisu3<alpha, gamma>::DigitGen_m60_m32(DiyFp low,
+                                            DiyFp w,
+                                            DiyFp high,
+                                            char* buffer,
+                                            int* length,
+                                            int* kappa) {
   // low, w and high are imprecise, but by less than one ulp (unit in the last
   // place).
   // If we remove (resp. add) 1 ulp from low (resp. high) we are certain that
   // the new numbers are outside of the interval we want the final
   // representation to lie in.
   // Inversely adding (resp. removing) 1 ulp from low (resp. high) would yield
   // numbers that are certain to lie in the interval. We will use this fact
   // later on.
   // We will now start by generating the digits within the uncertain
   // interval. Later we will weed out representations that lie outside the safe
   // interval and thus _might_ lie outside the correct interval.
   uint64_t unit = 1;
   DiyFp too_low = DiyFp(low.f() - unit, low.e());
   DiyFp too_high = DiyFp(high.f() + unit, high.e());
   // too_low and too_high are guaranteed to lie outside the interval we want the
   // generated number in.
   DiyFp unsafe_interval = DiyFp::Minus(too_high, too_low);
   // We now cut the input number into two parts: the integral digits and the
   // fractionals. We will not write any decimal separator though, but adapt
   // kappa instead.
   // Reminder: we are currently computing the digits (stored inside the buffer)
   // such that:   too_low < buffer * 10^kappa < too_high
   // We use too_high for the digit_generation and stop as soon as possible.
   // If we stop early we effectively round down.
   DiyFp one = DiyFp(static_cast<uint64_t>(1) << -w.e(), w.e());
-  uint32_t integrals = too_high.f() >> -one.e();        // Division by one.
-  uint64_t fractionals = too_high.f() & (one.f() - 1);  // Modulo by one.
+  // Division by one is a shift.
+  uint32_t integrals = static_cast<uint32_t>(too_high.f() >> -one.e());
+  // Modulo by one is an and.
+  uint64_t fractionals = too_high.f() & (one.f() - 1);
   uint32_t divider;
   int divider_exponent;
   BiggestPowerTen(integrals, DiyFp::kSignificandSize - (-one.e()),
                   &divider, &divider_exponent);
   *kappa = divider_exponent + 1;
   *length = 0;
   // Loop invariant: buffer = too_high / 10^kappa  (integer division)
   // The invariant holds for the first iteration: kappa has been initialized
   // with the divider exponent + 1. And the divider is the biggest power of ten
-  // that fits into the bits that had been reserved for the integrals.
+  // that is smaller than integrals.
   while (*kappa > 0) {
     int digit = integrals / divider;
     buffer[*length] = '0' + digit;
     (*length)++;
     integrals %= divider;
     (*kappa)--;
     // Note that kappa now equals the exponent of the divider and that the
     // invariant thus holds again.
     uint64_t rest =
         (static_cast<uint64_t>(integrals) << -one.e()) + fractionals;
@@ skipping 23 matching lines @@
   //      and we have again fractionals.e == one.e which allows us to divide
   //           fractionals.f() by one.f()
   // We simply combine the *= 10 and the >>= 1.
   while (true) {
     fractionals *= 5;
     unit *= 5;
     unsafe_interval.set_f(unsafe_interval.f() * 5);
     unsafe_interval.set_e(unsafe_interval.e() + 1);  // Will be optimized out.
     one.set_f(one.f() >> 1);
     one.set_e(one.e() + 1);
-    int digit = fractionals >> -one.e();  // Integer division by one.
+    // Integer division by one.
+    int digit = static_cast<int>(fractionals >> -one.e());
     buffer[*length] = '0' + digit;
     (*length)++;
     fractionals &= one.f() - 1;  // Modulo by one.
     (*kappa)--;
     if (fractionals < unsafe_interval.f()) {
       return RoundWeed(buffer, *length, DiyFp::Minus(too_high, w).f() * unit,
                        unsafe_interval.f(), fractionals, one.f(), unit);
     }
   }
 }
 
 
 // Rounds the given generated digits in the buffer and weeds out generated
 // digits that are not in the safe interval, or where we cannot find a rounded
 // representation.
 // Input: * buffer containing the digits of too_high / 10^kappa
 //        * the buffer's length
 //        * distance_too_high_w == (too_high - w).f() * unit
 //        * unsafe_interval == (too_high - too_low).f() * unit
 //        * rest = (too_high - buffer * 10^kappa).f() * unit
 //        * ten_kappa = 10^kappa * unit
 //        * unit = the common multiplier
 // Output: returns true on success.
 //    Modifies the generated digits in the buffer to approach (round towards) w.
 template<int alpha, int gamma>
-bool Grisu3<alpha, gamma>::RoundWeed(
-    char* buffer, int length, uint64_t distance_too_high_w,
-    uint64_t unsafe_interval, uint64_t rest, uint64_t ten_kappa,
-    uint64_t unit) {
+bool Grisu3<alpha, gamma>::RoundWeed(char* buffer,
+                                     int length,
+                                     uint64_t distance_too_high_w,
+                                     uint64_t unsafe_interval,
+                                     uint64_t rest,
+                                     uint64_t ten_kappa,
+                                     uint64_t unit) {
   uint64_t small_distance = distance_too_high_w - unit;
   uint64_t big_distance = distance_too_high_w + unit;
   // Let w- = too_high - big_distance, and
   //     w+ = too_high - small_distance.
   // Note: w- < w < w+
   //
   // The real w (* unit) must lie somewhere inside the interval
   // ]w-; w+[ (often written as "(w-; w+)")
 
   // Basically the buffer currently contains a number in the unsafe interval
@@ skipping 30 matching lines @@
 
   // Weeding test.
   //   The safe interval is [too_low + 2 ulp; too_high - 2 ulp]
   //   Since too_low = too_high - unsafe_interval this is equivalent too
   //      [too_high - unsafe_interval + 4 ulp; too_high - 2 ulp]
   //   Conceptually we have: rest ~= too_high - buffer
   return (2 * unit <= rest) && (rest <= unsafe_interval - 4 * unit);
 }
 
 
-bool grisu3(double v,
-            char* buffer, int* sign, int* length, int* decimal_point) {
+bool grisu3(double v, char* buffer, int* sign, int* length, int* point) {
   ASSERT(v != 0);
   ASSERT(!Double(v).IsSpecial());
 
   if (v < 0) {
     v = -v;
     *sign = 1;
   } else {
     *sign = 0;
   }
   int decimal_exponent;
   bool result = Grisu3<-60, -32>::grisu3(v, buffer, length, &decimal_exponent);
-  *decimal_point = *length + decimal_exponent;
+  *point = *length + decimal_exponent;
   buffer[*length] = '\0';
   return result;
 }
 
 } }  // namespace v8::internal