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Implement round half to even

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This commit is contained in:
Victor Zverovich
2019-10-13 19:59:09 -07:00
parent 599e0aef45
commit 36d1390e67
3 changed files with 24 additions and 19 deletions
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36
include/fmt/format-inl.h
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@@ -946,20 +946,20 @@ template <int GRISU_VERSION> struct grisu_shortest_handler {
}
};
// Formats v using a variation of the Fixed-Precision Positive Floating-Point
// Printout ((FPP)^2) algorithm by Steele & White:
// Formats value using a variation of the Fixed-Precision Positive
// Floating-Point Printout ((FPP)^2) algorithm by Steele & White:
// http://kurtstephens.com/files/p372-steele.pdf.
template <typename Double>
FMT_FUNC void fallback_format(Double v, buffer<char>& buf, int& exp10) {
fp fp_value(v);
FMT_FUNC void fallback_format(Double value, buffer<char>& buf, int& exp10) {
fp fp_value(value);
// Shift to account for unequal gaps when lower boundary is 2 times closer.
// TODO: handle denormals
int shift = 0; //fp_value.f == 1 ? 1 : 0;
bigint numerator; // 2 * R in (FPP)^2.
bigint denominator; // 2 * S in (FPP)^2.
bigint lower; // (M^- in (FPP)^2).
int shift = 0; // fp_value.f == 1 ? 1 : 0;
bigint numerator; // 2 * R in (FPP)^2.
bigint denominator; // 2 * S in (FPP)^2.
bigint lower; // (M^- in (FPP)^2).
bigint upper_store;
bigint *upper = nullptr; // (M^+ in (FPP)^2).
bigint* upper = nullptr; // (M^+ in (FPP)^2).
// Shift numerator and denominator by an extra bit to make lower and upper
// which are normally half ulp integers. This eliminates multiplication by 2
// during later computations.
@@ -998,27 +998,29 @@ FMT_FUNC void fallback_format(Double v, buffer<char>& buf, int& exp10) {
}
}
if (!upper) upper = &lower;
// Invariant: fp_value == (numerator / denominator) * pow(10, exp10).
// Invariant: value == (numerator / denominator) * pow(10, exp10).
bool even = (fp_value.f & 1) == 0;
int num_digits = 0;
char* data = buf.data();
for (;;) {
int digit = numerator.divmod_assign(denominator);
bool low = compare(numerator, lower) - even < 0; // numerator <[=] lower.
bool high = add_compare(numerator, *upper, denominator) + even >
0; // numerator + upper >[=] pow10.
// numerator + upper >[=] pow10:
bool high = add_compare(numerator, *upper, denominator) + even > 0;
data[num_digits++] = static_cast<char>('0' + digit);
if (low || high) {
if (!low) {
++digit;
++data[num_digits - 1];
} else if (high) {
// TODO: round up if 2 * numerator >= denominator
int result = add_compare(numerator, numerator, denominator);
// Round half to even.
if (result > 0 || (result == 0 && (digit % 2) != 0))
++data[num_digits - 1];
}
data[num_digits++] = static_cast<char>('0' + digit);
buf.resize(num_digits);
exp10 -= num_digits -1;
exp10 -= num_digits - 1;
return;
}
data[num_digits++] = static_cast<char>('0' + digit);
numerator *= 10;
lower *= 10;
if (upper != &lower) *upper *= 10;