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Simplify integer checks

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This commit is contained in:
Junekey Jeon 2022-01-12 16:41:32 -08:00 committed by Victor Zverovich
parent 1882a7a2c1
commit 35a468ed38
1 changed files with 92 additions and 51 deletions
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135
include/fmt/format-inl.h
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@ -864,26 +864,27 @@ inline uint64_t umul128_upper64(uint64_t x, uint64_t y) FMT_NOEXCEPT {
#endif #endif
} }
// Computes upper 64 bits of multiplication of a 64-bit unsigned integer and a // Computes upper 128 bits of multiplication of a 64-bit unsigned integer and a
// 128-bit unsigned integer. // 128-bit unsigned integer.
inline uint64_t umul192_upper64(uint64_t x, uint128_wrapper y) FMT_NOEXCEPT { inline uint128_wrapper umul192_upper128(uint64_t x,
uint128_wrapper g0 = umul128(x, y.high()); uint128_wrapper y) FMT_NOEXCEPT {
g0 += umul128_upper64(x, y.low()); uint128_wrapper r = umul128(x, y.high());
return g0.high(); r += umul128_upper64(x, y.low());
return r;
} }
// Computes upper 32 bits of multiplication of a 32-bit unsigned integer and a // Computes upper 64 bits of multiplication of a 32-bit unsigned integer and a
// 64-bit unsigned integer. // 64-bit unsigned integer.
inline uint32_t umul96_upper32(uint32_t x, uint64_t y) FMT_NOEXCEPT { inline uint64_t umul96_upper64(uint32_t x, uint64_t y) FMT_NOEXCEPT {
return static_cast<uint32_t>(umul128_upper64(x, y)); return umul128_upper64(uint64_t(x) << 32, y);
} }
// Computes middle 64 bits of multiplication of a 64-bit unsigned integer and a // Computes lower 128 bits of multiplication of a 64-bit unsigned integer and a
// 128-bit unsigned integer. // 128-bit unsigned integer.
inline uint64_t umul192_middle64(uint64_t x, uint128_wrapper y) FMT_NOEXCEPT { inline uint64_t umul192_lower128(uint64_t x, uint128_wrapper y) FMT_NOEXCEPT {
uint64_t g01 = x * y.high(); uint64_t high = x * y.high();
uint64_t g10 = umul128_upper64(x, y.low()); uint128_wrapper high_low = umul128(x, y.low());
return g01 + g10; return {high + high_low.high(), high_low.low()};
} }
// Computes lower 64 bits of multiplication of a 32-bit unsigned integer and a // Computes lower 64 bits of multiplication of a 32-bit unsigned integer and a
@ -1071,9 +1072,20 @@ template <> struct cache_accessor<float> {
return pow10_significands[k - float_info<float>::min_k]; return pow10_significands[k - float_info<float>::min_k];
} }
static carrier_uint compute_mul(carrier_uint u, struct compute_mul_result {
const cache_entry_type& cache) FMT_NOEXCEPT { carrier_uint result;
return umul96_upper32(u, cache); bool is_integer;
};
struct compute_mul_parity_result {
bool parity;
bool is_integer;
};
static compute_mul_result compute_mul(
carrier_uint u, const cache_entry_type& cache) FMT_NOEXCEPT {
auto r = umul96_upper64(u, cache);
return {static_cast<carrier_uint>(r >> 32),
static_cast<carrier_uint>(r) == 0};
} }
static uint32_t compute_delta(const cache_entry_type& cache, static uint32_t compute_delta(const cache_entry_type& cache,
@ -1081,13 +1093,15 @@ template <> struct cache_accessor<float> {
return static_cast<uint32_t>(cache >> (64 - 1 - beta_minus_1)); return static_cast<uint32_t>(cache >> (64 - 1 - beta_minus_1));
} }
static bool compute_mul_parity(carrier_uint two_f, static compute_mul_parity_result compute_mul_parity(
const cache_entry_type& cache, carrier_uint two_f, const cache_entry_type& cache,
int beta_minus_1) FMT_NOEXCEPT { int beta_minus_1) FMT_NOEXCEPT {
FMT_ASSERT(beta_minus_1 >= 1, ""); FMT_ASSERT(beta_minus_1 >= 1, "");
FMT_ASSERT(beta_minus_1 < 64, ""); FMT_ASSERT(beta_minus_1 < 64, "");
return ((umul96_lower64(two_f, cache) >> (64 - beta_minus_1)) & 1) != 0; auto r = umul96_lower64(two_f, cache);
return {((r >> (64 - beta_minus_1)) & 1) != 0,
static_cast<uint32_t>(r >> (32 - beta_minus_1)) == 0};
} }
static carrier_uint compute_left_endpoint_for_shorter_interval_case( static carrier_uint compute_left_endpoint_for_shorter_interval_case(
@ -1838,9 +1852,19 @@ template <> struct cache_accessor<double> {
#endif #endif
} }
static carrier_uint compute_mul(carrier_uint u, struct compute_mul_result {
const cache_entry_type& cache) FMT_NOEXCEPT { carrier_uint result;
return umul192_upper64(u, cache); bool is_integer;
};
struct compute_mul_parity_result {
bool parity;
bool is_integer;
};
static compute_mul_result compute_mul(
carrier_uint u, const cache_entry_type& cache) FMT_NOEXCEPT {
auto r = umul192_upper128(u, cache);
return {r.high(), r.low() == 0};
} }
static uint32_t compute_delta(cache_entry_type const& cache, static uint32_t compute_delta(cache_entry_type const& cache,
@ -1848,13 +1872,16 @@ template <> struct cache_accessor<double> {
return static_cast<uint32_t>(cache.high() >> (64 - 1 - beta_minus_1)); return static_cast<uint32_t>(cache.high() >> (64 - 1 - beta_minus_1));
} }
static bool compute_mul_parity(carrier_uint two_f, static compute_mul_parity_result compute_mul_parity(
const cache_entry_type& cache, carrier_uint two_f, const cache_entry_type& cache,
int beta_minus_1) FMT_NOEXCEPT { int beta_minus_1) FMT_NOEXCEPT {
FMT_ASSERT(beta_minus_1 >= 1, ""); FMT_ASSERT(beta_minus_1 >= 1, "");
FMT_ASSERT(beta_minus_1 < 64, ""); FMT_ASSERT(beta_minus_1 < 64, "");
return ((umul192_middle64(two_f, cache) >> (64 - beta_minus_1)) & 1) != 0; auto r = umul192_lower128(two_f, cache);
return {
((r.high() >> (64 - beta_minus_1)) & 1) != 0,
((r.high() << beta_minus_1) | (r.low() >> (64 - beta_minus_1))) == 0};
} }
static carrier_uint compute_left_endpoint_for_shorter_interval_case( static carrier_uint compute_left_endpoint_for_shorter_interval_case(
@ -2114,39 +2141,50 @@ template <typename T> decimal_fp<T> to_decimal(T x) FMT_NOEXCEPT {
// 10^kappa <= deltai < 10^(kappa + 1) // 10^kappa <= deltai < 10^(kappa + 1)
const uint32_t deltai = cache_accessor<T>::compute_delta(cache, beta_minus_1); const uint32_t deltai = cache_accessor<T>::compute_delta(cache, beta_minus_1);
const carrier_uint two_fc = significand << 1; const carrier_uint two_fc = significand << 1;
const carrier_uint two_fr = two_fc | 1; const typename cache_accessor<T>::compute_mul_result z_mul =
const carrier_uint zi = cache_accessor<T>::compute_mul((two_fc | 1) << beta_minus_1, cache);
cache_accessor<T>::compute_mul(two_fr << beta_minus_1, cache);
// Step 2: Try larger divisor; remove trailing zeros if necessary. // Step 2: Try larger divisor; remove trailing zeros if necessary.
// Using an upper bound on zi, we might be able to optimize the division // Using an upper bound on zi, we might be able to optimize the division
// better than the compiler; we are computing zi / big_divisor here. // better than the compiler; we are computing zi / big_divisor here.
decimal_fp<T> ret_value; decimal_fp<T> ret_value;
ret_value.significand = divide_by_10_to_kappa_plus_1(zi); ret_value.significand = divide_by_10_to_kappa_plus_1(z_mul.result);
uint32_t r = static_cast<uint32_t>(zi - float_info<T>::big_divisor * const uint32_t r = static_cast<uint32_t>(
ret_value.significand); z_mul.result - float_info<T>::big_divisor * ret_value.significand);
if (r > deltai) { if (r > deltai) {
goto small_divisor_case_label; goto small_divisor_case_label;
} else if (r < deltai) { } else if (r < deltai) {
// Exclude the right endpoint if necessary. // Exclude the right endpoint if necessary.
if (r == 0 && !include_right_endpoint && if (r == 0 && z_mul.is_integer && !include_right_endpoint) {
is_endpoint_integer<T>(two_fr, exponent, minus_k)) {
--ret_value.significand; --ret_value.significand;
r = float_info<T>::big_divisor; r = float_info<T>::big_divisor;
goto small_divisor_case_label; goto small_divisor_case_label;
} }
} else { } else {
// r == deltai; compare fractional parts // r == deltai; compare fractional parts.
// Check conditions in the order different from the paper
// to take advantage of short-circuiting.
const carrier_uint two_fl = two_fc - 1; const carrier_uint two_fl = two_fc - 1;
if ((!include_left_endpoint ||
!is_endpoint_integer<T>(two_fl, exponent, minus_k)) && if (!include_left_endpoint ||
!cache_accessor<T>::compute_mul_parity(two_fl, cache, beta_minus_1)) { exponent < float_info<T>::case_fc_pm_half_lower_threshold ||
exponent > float_info<T>::divisibility_check_by_5_threshold) {
// If the left endpoint is not included, the condition for
// success is z^(f) < delta^(f) (odd parity).
// Otherwise, the inequalities on exponent ensure that
// x is not an integer, so if z^(f) >= delta^(f) (even parity), we in fact
// have strict inequality.
if (!cache_accessor<T>::compute_mul_parity(two_fl, cache, beta_minus_1)
.parity) {
goto small_divisor_case_label; goto small_divisor_case_label;
} }
} else {
const typename cache_accessor<T>::compute_mul_parity_result x_mul = =
compute_mul_parity(two_fl, cache, beta_minus_1);
if (!x_mul.parity && !x_mul.is_integer) {
goto small_divisor_case_label;
}
}
} }
ret_value.exponent = minus_k + float_info<T>::kappa + 1; ret_value.exponent = minus_k + float_info<T>::kappa + 1;
@ -2160,37 +2198,40 @@ small_divisor_case_label:
ret_value.significand *= 10; ret_value.significand *= 10;
ret_value.exponent = minus_k + float_info<T>::kappa; ret_value.exponent = minus_k + float_info<T>::kappa;
auto dist = r - (deltai / 2) + (float_info<T>::small_divisor / 2); uint32_t dist = r - (deltai / 2) + (float_info<T>::small_divisor / 2);
bool const approx_y_parity = ((dist ^ (small_divisor / 2)) & 1) != 0; const bool approx_y_parity =
((dist ^ (float_info<T>::small_divisor / 2)) & 1) != 0;
// Is dist divisible by 10^kappa? // Is dist divisible by 10^kappa?
bool divisible_by_10_to_the_kappa = const bool divisible_by_small_divisor =
check_divisibility_and_divide_by_pow10<float_info<T>::kappa>(dist); check_divisibility_and_divide_by_pow10<float_info<T>::kappa>(dist);
// Add dist / 10^kappa to the significand. // Add dist / 10^kappa to the significand.
ret_value.significand += dist; ret_value.significand += dist;
if (divisible_by_10_to_the_kappa) { if (divisible_by_small_divisor) {
// Check z^(f) >= epsilon^(f). // Check z^(f) >= epsilon^(f).
// We have either yi == zi - epsiloni or yi == (zi - epsiloni) - 1, // We have either yi == zi - epsiloni or yi == (zi - epsiloni) - 1,
// where yi == zi - epsiloni if and only if z^(f) >= epsilon^(f) // where yi == zi - epsiloni if and only if z^(f) >= epsilon^(f)
// Since there are only 2 possibilities, we only need to care about the // Since there are only 2 possibilities, we only need to care about the
// parity. Also, zi and r should have the same parity since the divisor // parity. Also, zi and r should have the same parity since the divisor
// is an even number. // is an even number.
if (cache_accessor<T>::compute_mul_parity(two_fc, cache, beta_minus_1) != const typename cache_accessor<T>::compute_mul_parity_result y_mul = =
approx_y_parity) { compute_mul_parity(two_fc, cache, beta_minus_1);
if (y_mul.parity != approx_y_parity) {
--ret_value.significand; --ret_value.significand;
} else { } else {
// If z^(f) >= epsilon^(f), we might have a tie // If z^(f) >= epsilon^(f), we might have a tie
// when z^(f) == epsilon^(f), or equivalently, when y is an integer // when z^(f) == epsilon^(f), or equivalently, when y is an integer
if (is_center_integer<T>(two_fc, exponent, minus_k)) { if (y_mul.is_integer) {
ret_value.significand = ret_value.significand % 2 == 0 ret_value.significand = ret_value.significand % 2 == 0
? ret_value.significand ? ret_value.significand
: ret_value.significand - 1; : ret_value.significand - 1;
} }
} }
return ret_value; return ret_value;
} }
} // namespace dragonbox } // namespace dragonbox
// Formats a floating-point number using a variation of the Fixed-Precision // Formats a floating-point number using a variation of the Fixed-Precision