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AK: Replace linear exponentiation by binary in MinimalBigInt

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This further optimizes floating point parsing (specifically with a large
amount of digits). The commit shaves additional 20% of the run time for
750-digit numbers. No performance degradation is noticeable for small
numbers.
This commit is contained in:
Dan Klishch 2023-02-09 21:05:45 +03:00 • committed by Andreas Kling
parent 80517b5a70
commit 4653b38808
Notes: sideshowbarker 2024-07-16 22:14:49 +09:00
1 changed files with 122 additions and 41 deletions
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163
AK/FloatingPointStringConversions.cpp
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@ -1529,50 +1529,131 @@ public:
void multiply_with_power_of_5(u32 exponent)
{
// FIXME: We might be able to store a bigger power of 5 but this would
// require a wide multiply, so perhaps using u4096 would be
// better to get wide multiply and not duplicate logic.
static constexpr Array<u64, 28> power_of_5 = {
1ul,
5ul,
25ul,
125ul,
625ul,
3125ul,
15625ul,
78125ul,
390625ul,
1953125ul,
9765625ul,
48828125ul,
244140625ul,
1220703125ul,
6103515625ul,
30517578125ul,
152587890625ul,
762939453125ul,
3814697265625ul,
19073486328125ul,
95367431640625ul,
476837158203125ul,
2384185791015625ul,
11920928955078125ul,
59604644775390625ul,
298023223876953125ul,
1490116119384765625ul,
7450580596923828125ul,
};
// FIXME: Using UFixedBigInt here does not feel right. We need to nicely (without
// reinterpret_cast and ifs) convert u64 to NativeWord (if NativeWord == u32)
// and one of UFixedBigInt constructors happens to do this exact job.
//
// To calculate this lookup table, we compute 5 ** (2 ** i) for all i \in [0; 10], split
// numbers into 64-bit words and concatenate the results, writing corresponding sizes to
// `sizes` array in `power_of_5` lambda.
static constexpr UFixedBigInt<82 * 64> power_of_5_coefficients = { {
5ull,
25ull,
625ull,
390625ull,
152587890625ull,
3273344365508751233ull,
1262ull,
7942358959831785217ull,
16807427164405733357ull,
1593091ull,
279109966635548161ull,
2554917779393558781ull,
14124656261812188652ull,
11976055582626787546ull,
2537941837315ull,
13750482914757213185ull,
1302999927698857842ull,
14936872543252795590ull,
2788415840139466767ull,
2095640732773017264ull,
7205570348933370714ull,
7348167152523113408ull,
9285516396840364274ull,
6907659600622710236ull,
349175ull,
8643096425819600897ull,
6743743997439985372ull,
14059704609098336919ull,
10729359125898331411ull,
4933048501514368705ull,
12258131603170554683ull,
2172371001088594721ull,
13569903330219142946ull,
13809142207969578845ull,
16716360519037769646ull,
9631256923806107285ull,
12866941232305103710ull,
1397931361048440292ull,
7619627737732970332ull,
12725409486282665900ull,
11703051443360963910ull,
9947078370803086083ull,
13966287901448440471ull,
121923442132ull,
17679772531488845825ull,
2216509366347768155ull,
1568689219195129479ull,
5511594616325588277ull,
1067709417009240089ull,
9070650952098657518ull,
11515285870634858015ull,
2539561553659505564ull,
17604889300961091799ull,
14511540856854204724ull,
12099083339557485471ull,
7115240299237943815ull,
313979240050606788ull,
10004784664717172195ull,
15570268847930131473ull,
10359715202835930803ull,
17685054012115162812ull,
13183273382855797757ull,
7743260039872919062ull,
9284593436392572926ull,
11105921222066415013ull,
18198799323400703846ull,
16314988383739458320ull,
4387527177871570570ull,
8476708682254672590ull,
4925096874831034057ull,
14075687868072027455ull,
112866656203221926ull,
9852830467773230418ull,
25755239915196746ull,
2201493076310172510ull,
8342165458688466438ull,
13954006576066379050ull,
15193819059903295636ull,
12565616718911389531ull,
3815854855847885129ull,
15696762163583540628ull,
805ull,
} };
static constexpr u32 max_step = power_of_5.size() - 1;
static constexpr u64 max_power = power_of_5[max_step];
// power_of_5[i] = 5 ** (2 ** i)
static constexpr auto power_of_5 = [&] {
constexpr size_t powers_count = 11;
while (exponent >= max_step) {
multiply_with_small(max_power);
exponent -= max_step;
Array<UnsignedStorageReadonlySpan, powers_count> result;
Array<size_t, powers_count> sizes = { 1, 1, 1, 1, 1, 2, 3, 5, 10, 19, 38 };
size_t offset = 0;
for (size_t i = 0; i < powers_count; ++i) {
if constexpr (SameAs<NativeWord, u32>)
sizes[i] *= 2;
result[i] = UnsignedStorageReadonlySpan(power_of_5_coefficients.span().slice(offset, sizes[i]));
offset += sizes[i];
}
return result;
}();
VERIFY(exponent < (1 << power_of_5.size()));
// Binary exponentiation
for (size_t i = 0; i < power_of_5.size(); ++i) {
if (exponent >> i & 1) {
if (power_of_5[i].size() == 1) {
multiply_with_small(power_of_5[i][0]);
} else {
auto copy = *this;
StorageOperations::baseline_mul(copy.get_storage(), power_of_5[i],
get_storage(m_used_length + power_of_5[i].size()), g_null_allocator);
trim_last_word_if_zero();
}
}
}
if (exponent > 0)
multiply_with_small(power_of_5[exponent]);
}
void multiply_with_power_of_2(u32 exponent)