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Implement Grisu2 digit generation

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This commit is contained in:
Victor Zverovich
2018-08-25 16:08:32 -07:00
parent 569ac91e0b
commit f0d0a1ebd7
3 changed files with 95 additions and 33 deletions
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79
include/fmt/format-inl.h
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@@ -275,11 +275,16 @@ const char basic_data<T>::DIGITS[] =
template <typename T>
const uint32_t basic_data<T>::POWERS_OF_10_32[] = {
1, FMT_POWERS_OF_10(1)
};
template <typename T>
const uint32_t basic_data<T>::ZERO_OR_POWERS_OF_10_32[] = {
0, FMT_POWERS_OF_10(1)
};
template <typename T>
const uint64_t basic_data<T>::POWERS_OF_10_64[] = {
const uint64_t basic_data<T>::ZERO_OR_POWERS_OF_10_64[] = {
0,
FMT_POWERS_OF_10(1),
FMT_POWERS_OF_10(1000000000ull),
@@ -361,6 +366,78 @@ FMT_FUNC fp get_cached_power(int min_exponent, int &pow10_exponent) {
pow10_exponent = first_dec_exp + index * dec_exp_step;
return fp(data::POW10_SIGNIFICANDS[index], data::POW10_EXPONENTS[index]);
}
// Generates output using Grisu2 digit-gen algorithm.
FMT_FUNC void grisu2_gen_digits(
const fp &scaled_value, const fp &scaled_upper, uint64_t delta,
char *buffer, size_t &size, int &dec_exp) {
internal::fp one(1ull << -scaled_upper.e, scaled_upper.e);
uint32_t hi = static_cast<uint32_t>(scaled_upper.f >> -one.e); // p1 in Grisu
uint64_t lo = scaled_upper.f & (one.f - 1); // p2 in Grisu
size = 0;
auto kappa = count_digits(hi); // TODO: more descriptive name
while (kappa > 0) {
uint32_t digit = 0;
// This optimization by miloyip reduces the number of integer divisions by
// one per iteration.
switch (kappa) {
case 10: digit = hi / 1000000000; hi %= 1000000000; break;
case 9: digit = hi / 100000000; hi %= 100000000; break;
case 8: digit = hi / 10000000; hi %= 10000000; break;
case 7: digit = hi / 1000000; hi %= 1000000; break;
case 6: digit = hi / 100000; hi %= 100000; break;
case 5: digit = hi / 10000; hi %= 10000; break;
case 4: digit = hi / 1000; hi %= 1000; break;
case 3: digit = hi / 100; hi %= 100; break;
case 2: digit = hi / 10; hi %= 10; break;
case 1: digit = hi; hi = 0; break;
default:
FMT_ASSERT(false, "invalid number of digits");
}
if (digit != 0 || size != 0)
buffer[size++] = '0' + static_cast<char>(digit);
--kappa;
uint64_t remainder = (static_cast<uint64_t>(hi) << -one.e) + lo;
if (remainder <= delta) {
dec_exp += kappa;
// TODO: use scaled_value
(void)scaled_value;
return;
}
}
for (;;) {
lo *= 10;
delta *= 10;
char digit = static_cast<char>(lo >> -one.e);
if (digit != 0 || size != 0)
buffer[size++] = '0' + digit;
lo &= one.f - 1;
--kappa;
if (lo < delta) {
dec_exp += kappa;
return;
}
}
}
FMT_FUNC void grisu2_format(double value, char *buffer, size_t &size) {
fp fp_value(value);
fp lower, upper;
fp_value.compute_boundaries(lower, upper);
// Find a cached power of 10 close to 1 / upper.
int dec_exp = 0; // K in Grisu paper.
const int min_exp = -60;
auto dec_pow = get_cached_power(
min_exp - (upper.e + fp::significand_size), dec_exp);
fp_value.normalize();
fp scaled_value = fp_value * dec_pow;
fp scaled_lower = lower * dec_pow;
fp scaled_upper = upper * dec_pow;
++scaled_lower.f; // +1 ulp
--scaled_upper.f; // -1 ulp
uint64_t delta = scaled_upper.f - scaled_lower.f;
grisu2_gen_digits(scaled_value, scaled_upper, delta, buffer, size, dec_exp);
}
} // namespace internal
#if FMT_USE_WINDOWS_H