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Make stopping condition configurable in grisu
This commit is contained in:
Victor Zverovich
parent
a44238f2ef
commit
5b0006476a
@ -445,26 +445,21 @@ FMT_FUNC fp get_cached_power(int min_exponent, int& pow10_exponent) {
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return fp(data::POW10_SIGNIFICANDS[index], data::POW10_EXPONENTS[index]);
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}
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FMT_FUNC bool grisu2_round(char* buf, int& size, int max_digits, uint64_t delta,
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uint64_t remainder, uint64_t exp, uint64_t diff,
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int& exp10) {
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FMT_FUNC bool grisu2_round(char* buf, int& size, uint64_t delta,
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uint64_t remainder, uint64_t exp, uint64_t diff) {
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while (
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remainder < diff && delta - remainder >= exp &&
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(remainder + exp < diff || diff - remainder > remainder + exp - diff)) {
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--buf[size - 1];
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remainder += exp;
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}
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if (size > max_digits) {
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--size;
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++exp10;
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if (buf[size] >= '5') return false;
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}
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return true;
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}
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// Generates output using Grisu2 digit-gen algorithm.
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FMT_FUNC int grisu2_gen_digits(char* buf, fp upper, int& exp, uint64_t delta,
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const fp& diff, int max_digits) {
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template <typename Stop>
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int grisu2_gen_digits(char* buf, fp upper, uint64_t error_ulp, int& exp,
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Stop stop) {
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fp one(1ull << -upper.e, upper.e);
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// The integral part of scaled upper (p1 in Grisu) = upper / one. It cannot be
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// zero because it contains a product of two 64-bit numbers with MSB set (due
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@ -529,33 +524,55 @@ FMT_FUNC int grisu2_gen_digits(char* buf, fp upper, int& exp, uint64_t delta,
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--exp;
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uint64_t remainder =
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(static_cast<uint64_t>(integral) << -one.e) + fractional;
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if (remainder <= delta || size > max_digits) {
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return grisu2_round(buf, size, max_digits, delta, remainder,
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data::POWERS_OF_10_64[exp] << -one.e, diff.f, exp)
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? size
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: -1;
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}
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if (stop(buf, size, remainder, one, error_ulp, exp, true)) return size;
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} while (exp > 0);
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// Generate digits for the fractional part.
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for (;;) {
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fractional *= 10;
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delta *= 10;
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error_ulp *= 10;
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char digit = static_cast<char>(fractional >> -one.e);
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buf[size++] = static_cast<char>('0' + digit);
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fractional &= one.f - 1;
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--exp;
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if (fractional < delta || size > max_digits) {
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return grisu2_round(buf, size, max_digits, delta, fractional, one.f,
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diff.f * data::POWERS_OF_10_64[-exp], exp)
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? size
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: -1;
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}
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if (stop(buf, size, fractional, one, error_ulp, exp, false)) return size;
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}
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}
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// Stopping condition for the fixed precision.
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struct fixed_stop {
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int precision;
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bool operator()(char* buf, int size, uint64_t remainder, fp,
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uint64_t error_ulp, int&, bool) {
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if (size != precision) return false;
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// TODO: pass correct arguments to round
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if (!grisu2_round(buf, size, error_ulp, remainder, 0, 0)) {
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size = -1;
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}
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return true;
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}
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};
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// Stopping condition for the shortest representation.
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struct shortest_stop {
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fp diff; // wp_w in Grisu.
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bool operator()(char* buf, int size, uint64_t remainder, fp one,
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uint64_t error_ulp, int& exp, bool integral) {
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if (remainder > error_ulp) return false;
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if (!grisu2_round(
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buf, size, error_ulp, remainder,
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integral ? data::POWERS_OF_10_64[exp] << -one.e : one.f,
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integral ? diff.f : diff.f * data::POWERS_OF_10_64[-exp])) {
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size = -1;
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}
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return true;
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}
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};
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template <typename Double>
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FMT_FUNC typename std::enable_if<sizeof(Double) == sizeof(uint64_t), bool>::type
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grisu2_format(Double value, buffer& buf, core_format_specs, int& exp) {
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grisu2_format(Double value, buffer& buf, core_format_specs specs, int& exp) {
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FMT_ASSERT(value >= 0, "value is negative");
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if (value <= 0) { // <= instead of == to silence a warning.
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buf.push_back('0');
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@ -564,29 +581,38 @@ grisu2_format(Double value, buffer& buf, core_format_specs, int& exp) {
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}
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fp fp_value(value);
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fp lower, upper; // w^- and w^+ in the Grisu paper.
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fp_value.compute_boundaries(lower, upper);
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// Find a cached power of 10 close to 1 / upper and use it to scale upper.
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const int min_exp = -60; // alpha in Grisu.
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int cached_exp = 0; // K in Grisu.
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auto cached_pow = get_cached_power( // \tilde{c}_{-k} in Grisu.
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min_exp - (upper.e + fp::significand_size), cached_exp);
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cached_exp = -cached_exp;
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upper = upper * cached_pow; // \tilde{M}^+ in Grisu.
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--upper.f; // \tilde{M}^+ - 1 ulp -> M^+_{\downarrow}.
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assert(min_exp <= upper.e && upper.e <= -32);
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fp_value.normalize();
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fp scaled_value = fp_value * cached_pow;
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lower = lower * cached_pow; // \tilde{M}^- in Grisu.
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++lower.f; // \tilde{M}^- + 1 ulp -> M^-_{\uparrow}.
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uint64_t delta = upper.f - lower.f;
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fp diff = upper - scaled_value; // wp_w in Grisu.
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const int max_digits = 20;
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int size = grisu2_gen_digits(buf.data(), upper, exp, delta, diff, max_digits);
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if (size < 0) return false;
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buf.resize(to_unsigned(size));
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exp += cached_exp;
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const int min_exp = -60; // alpha in Grisu.
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int cached_exp10 = 0; // K in Grisu.
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if (specs.precision != -1) {
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if (specs.precision > 17) return false;
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fp_value.normalize();
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auto cached_pow = get_cached_power(
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min_exp - (fp_value.e + fp::significand_size), cached_exp10);
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fp_value = fp_value * cached_pow;
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int size = grisu2_gen_digits(buf.data(), fp_value, 1, exp,
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fixed_stop{specs.precision});
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if (size < 0) return false;
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buf.resize(to_unsigned(size));
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} else {
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fp lower, upper; // w^- and w^+ in the Grisu paper.
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fp_value.compute_boundaries(lower, upper);
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// Find a cached power of 10 such that multiplying upper by it will bring
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// the exponent in the range [min_exp, -32].
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auto cached_pow = get_cached_power( // \tilde{c}_{-k} in Grisu.
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min_exp - (upper.e + fp::significand_size), cached_exp10);
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upper = upper * cached_pow; // \tilde{M}^+ in Grisu.
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--upper.f; // \tilde{M}^+ - 1 ulp -> M^+_{\downarrow}.
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assert(min_exp <= upper.e && upper.e <= -32);
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fp_value.normalize();
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fp_value = fp_value * cached_pow;
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lower = lower * cached_pow; // \tilde{M}^- in Grisu.
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++lower.f; // \tilde{M}^- + 1 ulp -> M^-_{\uparrow}.
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int size = grisu2_gen_digits(buf.data(), upper, upper.f - lower.f, exp,
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shortest_stop{upper - fp_value});
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if (size < 0) return false;
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buf.resize(to_unsigned(size));
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}
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exp -= cached_exp10;
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return true;
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}
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