mirror of
https://github.com/RGBCube/serenity
synced 2025-10-31 02:42:44 +00:00
3d4afe7614
I've wasted a silly amount of time in the past fretting over which of these words to use. Let's just choose one and use it everywhere. :^)
732 lines
23 KiB
C++
732 lines
23 KiB
C++
/*
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* Copyright (c) 2020, Itamar S. <itamar8910@gmail.com>
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*
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* SPDX-License-Identifier: BSD-2-Clause
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*/
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#include "UnsignedBigInteger.h"
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#include <AK/StringBuilder.h>
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namespace Crypto {
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UnsignedBigInteger::UnsignedBigInteger(const u8* ptr, size_t length)
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{
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m_words.resize_and_keep_capacity((length + sizeof(u32) - 1) / sizeof(u32));
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size_t in = length, out = 0;
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while (in >= sizeof(u32)) {
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in -= sizeof(u32);
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u32 word = ((u32)ptr[in] << 24) | ((u32)ptr[in + 1] << 16) | ((u32)ptr[in + 2] << 8) | (u32)ptr[in + 3];
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m_words[out++] = word;
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}
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if (in > 0) {
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u32 word = 0;
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for (size_t i = 0; i < in; i++) {
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word <<= 8;
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word |= (u32)ptr[i];
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}
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m_words[out++] = word;
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}
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}
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UnsignedBigInteger UnsignedBigInteger::create_invalid()
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{
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UnsignedBigInteger invalid(0);
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invalid.invalidate();
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return invalid;
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}
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size_t UnsignedBigInteger::export_data(Bytes data, bool remove_leading_zeros) const
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{
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size_t word_count = trimmed_length();
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size_t out = 0;
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if (word_count > 0) {
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ssize_t leading_zeros = -1;
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if (remove_leading_zeros) {
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u32 word = m_words[word_count - 1];
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for (size_t i = 0; i < sizeof(u32); i++) {
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u8 byte = (u8)(word >> ((sizeof(u32) - i - 1) * 8));
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data[out++] = byte;
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if (leading_zeros < 0 && byte != 0)
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leading_zeros = (int)i;
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}
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}
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for (size_t i = word_count - (remove_leading_zeros ? 1 : 0); i > 0; i--) {
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auto word = m_words[i - 1];
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data[out++] = (u8)(word >> 24);
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data[out++] = (u8)(word >> 16);
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data[out++] = (u8)(word >> 8);
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data[out++] = (u8)word;
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}
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if (leading_zeros > 0)
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out -= leading_zeros;
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}
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return out;
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}
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UnsignedBigInteger UnsignedBigInteger::from_base10(const String& str)
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{
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UnsignedBigInteger result;
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UnsignedBigInteger ten { 10 };
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for (auto& c : str) {
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result = result.multiplied_by(ten).plus(c - '0');
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}
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return result;
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}
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String UnsignedBigInteger::to_base10() const
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{
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if (*this == UnsignedBigInteger { 0 })
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return "0";
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StringBuilder builder;
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UnsignedBigInteger temp(*this);
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UnsignedBigInteger quotient;
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UnsignedBigInteger remainder;
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while (temp != UnsignedBigInteger { 0 }) {
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divide_u16_without_allocation(temp, 10, quotient, remainder);
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VERIFY(remainder.words()[0] < 10);
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builder.append(static_cast<char>(remainder.words()[0] + '0'));
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temp.set_to(quotient);
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}
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auto reversed_string = builder.to_string();
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builder.clear();
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for (int i = reversed_string.length() - 1; i >= 0; --i) {
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builder.append(reversed_string[i]);
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}
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return builder.to_string();
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}
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void UnsignedBigInteger::set_to_0()
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{
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m_words.clear_with_capacity();
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m_is_invalid = false;
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m_cached_trimmed_length = {};
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}
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void UnsignedBigInteger::set_to(u32 other)
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{
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m_is_invalid = false;
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m_words.resize_and_keep_capacity(1);
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m_words[0] = other;
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m_cached_trimmed_length = {};
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}
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void UnsignedBigInteger::set_to(const UnsignedBigInteger& other)
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{
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m_is_invalid = other.m_is_invalid;
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m_words.resize_and_keep_capacity(other.m_words.size());
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__builtin_memcpy(m_words.data(), other.m_words.data(), other.m_words.size() * sizeof(u32));
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m_cached_trimmed_length = {};
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}
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size_t UnsignedBigInteger::trimmed_length() const
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{
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if (!m_cached_trimmed_length.has_value()) {
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size_t num_leading_zeroes = 0;
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for (int i = length() - 1; i >= 0; --i, ++num_leading_zeroes) {
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if (m_words[i] != 0)
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break;
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}
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m_cached_trimmed_length = length() - num_leading_zeroes;
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}
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return m_cached_trimmed_length.value();
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}
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void UnsignedBigInteger::clamp_to_trimmed_length()
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{
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auto length = trimmed_length();
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if (m_words.size() > length)
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m_words.resize(length);
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}
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FLATTEN UnsignedBigInteger UnsignedBigInteger::plus(const UnsignedBigInteger& other) const
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{
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UnsignedBigInteger result;
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add_without_allocation(*this, other, result);
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return result;
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}
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FLATTEN UnsignedBigInteger UnsignedBigInteger::minus(const UnsignedBigInteger& other) const
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{
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UnsignedBigInteger result;
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subtract_without_allocation(*this, other, result);
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return result;
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}
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FLATTEN UnsignedBigInteger UnsignedBigInteger::bitwise_or(const UnsignedBigInteger& other) const
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{
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UnsignedBigInteger result;
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bitwise_or_without_allocation(*this, other, result);
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return result;
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}
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FLATTEN UnsignedBigInteger UnsignedBigInteger::bitwise_and(const UnsignedBigInteger& other) const
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{
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UnsignedBigInteger result;
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bitwise_and_without_allocation(*this, other, result);
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return result;
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}
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FLATTEN UnsignedBigInteger UnsignedBigInteger::bitwise_xor(const UnsignedBigInteger& other) const
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{
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UnsignedBigInteger result;
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bitwise_xor_without_allocation(*this, other, result);
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return result;
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}
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FLATTEN UnsignedBigInteger UnsignedBigInteger::bitwise_not() const
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{
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UnsignedBigInteger result;
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bitwise_not_without_allocation(*this, result);
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return result;
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}
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FLATTEN UnsignedBigInteger UnsignedBigInteger::shift_left(size_t num_bits) const
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{
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UnsignedBigInteger output;
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UnsignedBigInteger temp_result;
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UnsignedBigInteger temp_plus;
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shift_left_without_allocation(*this, num_bits, temp_result, temp_plus, output);
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return output;
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}
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FLATTEN UnsignedBigInteger UnsignedBigInteger::multiplied_by(const UnsignedBigInteger& other) const
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{
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UnsignedBigInteger result;
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UnsignedBigInteger temp_shift_result;
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UnsignedBigInteger temp_shift_plus;
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UnsignedBigInteger temp_shift;
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UnsignedBigInteger temp_plus;
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multiply_without_allocation(*this, other, temp_shift_result, temp_shift_plus, temp_shift, temp_plus, result);
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return result;
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}
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FLATTEN UnsignedDivisionResult UnsignedBigInteger::divided_by(const UnsignedBigInteger& divisor) const
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{
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UnsignedBigInteger quotient;
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UnsignedBigInteger remainder;
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// If we actually have a u16-compatible divisor, short-circuit to the
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// less computationally-intensive "divide_u16_without_allocation" method.
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if (divisor.trimmed_length() == 1 && divisor.m_words[0] < (1 << 16)) {
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divide_u16_without_allocation(*this, divisor.m_words[0], quotient, remainder);
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return UnsignedDivisionResult { quotient, remainder };
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}
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UnsignedBigInteger temp_shift_result;
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UnsignedBigInteger temp_shift_plus;
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UnsignedBigInteger temp_shift;
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UnsignedBigInteger temp_minus;
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divide_without_allocation(*this, divisor, temp_shift_result, temp_shift_plus, temp_shift, temp_minus, quotient, remainder);
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return UnsignedDivisionResult { quotient, remainder };
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}
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void UnsignedBigInteger::set_bit_inplace(size_t bit_index)
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{
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const size_t word_index = bit_index / UnsignedBigInteger::BITS_IN_WORD;
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const size_t inner_word_index = bit_index % UnsignedBigInteger::BITS_IN_WORD;
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m_words.ensure_capacity(word_index);
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for (size_t i = length(); i <= word_index; ++i) {
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m_words.unchecked_append(0);
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}
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m_words[word_index] |= (1 << inner_word_index);
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m_cached_trimmed_length = {};
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}
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bool UnsignedBigInteger::operator==(const UnsignedBigInteger& other) const
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{
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if (is_invalid() != other.is_invalid())
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return false;
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auto length = trimmed_length();
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if (length != other.trimmed_length())
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return false;
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return !__builtin_memcmp(m_words.data(), other.words().data(), length * (BITS_IN_WORD / 8));
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}
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bool UnsignedBigInteger::operator!=(const UnsignedBigInteger& other) const
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{
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return !(*this == other);
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}
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bool UnsignedBigInteger::operator<(const UnsignedBigInteger& other) const
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{
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auto length = trimmed_length();
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auto other_length = other.trimmed_length();
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if (length < other_length) {
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return true;
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}
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if (length > other_length) {
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return false;
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}
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if (length == 0) {
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return false;
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}
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for (int i = length - 1; i >= 0; --i) {
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if (m_words[i] == other.m_words[i])
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continue;
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return m_words[i] < other.m_words[i];
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}
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return false;
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}
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/**
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* Complexity: O(N) where N is the number of words in the larger number
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*/
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void UnsignedBigInteger::add_without_allocation(
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const UnsignedBigInteger& left,
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const UnsignedBigInteger& right,
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UnsignedBigInteger& output)
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{
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const UnsignedBigInteger* const longer = (left.length() > right.length()) ? &left : &right;
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const UnsignedBigInteger* const shorter = (longer == &right) ? &left : &right;
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u8 carry = 0;
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output.set_to_0();
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output.m_words.resize_and_keep_capacity(longer->length());
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for (size_t i = 0; i < shorter->length(); ++i) {
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u32 word_addition_result = shorter->m_words[i] + longer->m_words[i];
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u8 carry_out = 0;
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// if there was a carry, the result will be smaller than any of the operands
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if (word_addition_result + carry < shorter->m_words[i]) {
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carry_out = 1;
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}
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if (carry) {
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word_addition_result++;
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}
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carry = carry_out;
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output.m_words[i] = word_addition_result;
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}
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for (size_t i = shorter->length(); i < longer->length(); ++i) {
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u32 word_addition_result = longer->m_words[i] + carry;
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carry = 0;
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if (word_addition_result < longer->m_words[i]) {
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carry = 1;
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}
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output.m_words[i] = word_addition_result;
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}
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if (carry) {
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output.m_words.append(carry);
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}
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}
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/**
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* Complexity: O(N) where N is the number of words in the larger number
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*/
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void UnsignedBigInteger::subtract_without_allocation(
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const UnsignedBigInteger& left,
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const UnsignedBigInteger& right,
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UnsignedBigInteger& output)
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{
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if (left < right) {
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output.invalidate();
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return;
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}
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u8 borrow = 0;
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auto own_length = left.length();
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auto other_length = right.length();
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output.set_to_0();
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output.m_words.resize_and_keep_capacity(own_length);
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for (size_t i = 0; i < own_length; ++i) {
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u32 other_word = (i < other_length) ? right.m_words[i] : 0;
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i64 temp = static_cast<i64>(left.m_words[i]) - static_cast<i64>(other_word) - static_cast<i64>(borrow);
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// If temp < 0, we had an underflow
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borrow = (temp >= 0) ? 0 : 1;
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if (temp < 0) {
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temp += (UINT32_MAX + 1);
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}
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output.m_words[i] = temp;
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}
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// This assertion should not fail, because we verified that *this>=other at the beginning of the function
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VERIFY(borrow == 0);
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}
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/**
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* Complexity: O(N) where N is the number of words in the shorter value
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* Method:
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* Apply <op> word-wise until words in the shorter value are used up
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* then copy the rest of the words verbatim from the longer value.
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*/
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FLATTEN void UnsignedBigInteger::bitwise_or_without_allocation(
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const UnsignedBigInteger& left,
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const UnsignedBigInteger& right,
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UnsignedBigInteger& output)
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{
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// If either of the BigInts are invalid, the output is just the other one.
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if (left.is_invalid()) {
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output.set_to(right);
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return;
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}
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if (right.is_invalid()) {
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output.set_to(left);
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return;
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}
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const UnsignedBigInteger *shorter, *longer;
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if (left.length() < right.length()) {
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shorter = &left;
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longer = &right;
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} else {
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shorter = &right;
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longer = &left;
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}
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output.m_words.resize_and_keep_capacity(longer->length());
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size_t longer_offset = longer->length() - shorter->length();
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for (size_t i = 0; i < shorter->length(); ++i)
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output.m_words[i] = longer->words()[i] | shorter->words()[i];
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__builtin_memcpy(output.m_words.data() + shorter->length(), longer->words().data() + shorter->length(), sizeof(u32) * longer_offset);
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}
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/**
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* Complexity: O(N) where N is the number of words in the shorter value
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* Method:
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* Apply 'and' word-wise until words in the shorter value are used up
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* and zero the rest.
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*/
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FLATTEN void UnsignedBigInteger::bitwise_and_without_allocation(
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const UnsignedBigInteger& left,
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const UnsignedBigInteger& right,
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UnsignedBigInteger& output)
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{
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// If either of the BigInts are invalid, the output is just the other one.
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if (left.is_invalid()) {
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output.set_to(right);
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return;
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}
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if (right.is_invalid()) {
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output.set_to(left);
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return;
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}
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const UnsignedBigInteger *shorter, *longer;
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if (left.length() < right.length()) {
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shorter = &left;
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longer = &right;
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} else {
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shorter = &right;
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longer = &left;
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}
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output.m_words.resize_and_keep_capacity(longer->length());
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size_t longer_offset = longer->length() - shorter->length();
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for (size_t i = 0; i < shorter->length(); ++i)
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output.m_words[i] = longer->words()[i] & shorter->words()[i];
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__builtin_memset(output.m_words.data() + shorter->length(), 0, sizeof(u32) * longer_offset);
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}
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/**
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* Complexity: O(N) where N is the number of words in the shorter value
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* Method:
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* Apply 'xor' word-wise until words in the shorter value are used up
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* and copy the rest.
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*/
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FLATTEN void UnsignedBigInteger::bitwise_xor_without_allocation(
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const UnsignedBigInteger& left,
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const UnsignedBigInteger& right,
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UnsignedBigInteger& output)
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{
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// If either of the BigInts are invalid, the output is just the other one.
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if (left.is_invalid()) {
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output.set_to(right);
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return;
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}
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if (right.is_invalid()) {
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output.set_to(left);
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return;
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}
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const UnsignedBigInteger *shorter, *longer;
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if (left.length() < right.length()) {
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shorter = &left;
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longer = &right;
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} else {
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shorter = &right;
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longer = &left;
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}
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output.m_words.resize_and_keep_capacity(longer->length());
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size_t longer_offset = longer->length() - shorter->length();
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for (size_t i = 0; i < shorter->length(); ++i)
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output.m_words[i] = longer->words()[i] ^ shorter->words()[i];
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__builtin_memcpy(output.m_words.data() + shorter->length(), longer->words().data() + shorter->length(), sizeof(u32) * longer_offset);
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}
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/**
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* Complexity: O(N) where N is the number of words
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*/
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FLATTEN void UnsignedBigInteger::bitwise_not_without_allocation(
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const UnsignedBigInteger& right,
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UnsignedBigInteger& output)
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{
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// If the value is invalid, the output value is invalid as well.
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if (right.is_invalid()) {
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output.invalidate();
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return;
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}
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if (right.length() == 0) {
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output.set_to_0();
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return;
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}
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output.m_words.resize_and_keep_capacity(right.length());
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if (right.length() > 1) {
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for (size_t i = 0; i < right.length() - 1; ++i)
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output.m_words[i] = ~right.words()[i];
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}
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auto last_word_index = right.length() - 1;
|
|
auto last_word = right.words()[last_word_index];
|
|
|
|
output.m_words[last_word_index] = ((u32)0xffffffffffffffff >> __builtin_clz(last_word)) & ~last_word;
|
|
}
|
|
|
|
/**
|
|
* Complexity : O(N + num_bits % 8) where N is the number of words in the number
|
|
* Shift method :
|
|
* Start by shifting by whole words in num_bits (by putting missing words at the start),
|
|
* then shift the number's words two by two by the remaining amount of bits.
|
|
*/
|
|
FLATTEN void UnsignedBigInteger::shift_left_without_allocation(
|
|
const UnsignedBigInteger& number,
|
|
size_t num_bits,
|
|
UnsignedBigInteger& temp_result,
|
|
UnsignedBigInteger& temp_plus,
|
|
UnsignedBigInteger& output)
|
|
{
|
|
// We can only do shift operations on individual words
|
|
// where the shift amount is <= size of word (32).
|
|
// But we do know how to shift by a multiple of word size (e.g 64=32*2)
|
|
// So we first shift the result by how many whole words fit in 'num_bits'
|
|
shift_left_by_n_words(number, num_bits / UnsignedBigInteger::BITS_IN_WORD, temp_result);
|
|
|
|
output.set_to(temp_result);
|
|
|
|
// And now we shift by the leftover amount of bits
|
|
num_bits %= UnsignedBigInteger::BITS_IN_WORD;
|
|
|
|
if (num_bits == 0) {
|
|
return;
|
|
}
|
|
|
|
for (size_t i = 0; i < temp_result.length(); ++i) {
|
|
u32 current_word_of_temp_result = shift_left_get_one_word(temp_result, num_bits, i);
|
|
output.m_words[i] = current_word_of_temp_result;
|
|
}
|
|
|
|
// Shifting the last word can produce a carry
|
|
u32 carry_word = shift_left_get_one_word(temp_result, num_bits, temp_result.length());
|
|
if (carry_word != 0) {
|
|
|
|
// output += (carry_word << temp_result.length())
|
|
// FIXME : Using temp_plus this way to transform carry_word into a bigint is not
|
|
// efficient nor pretty. Maybe we should have an "add_with_shift" method ?
|
|
temp_plus.set_to_0();
|
|
temp_plus.m_words.append(carry_word);
|
|
shift_left_by_n_words(temp_plus, temp_result.length(), temp_result);
|
|
add_without_allocation(output, temp_result, temp_plus);
|
|
output.set_to(temp_plus);
|
|
}
|
|
}
|
|
|
|
/**
|
|
* Complexity: O(N^2) where N is the number of words in the larger number
|
|
* Multiplication method:
|
|
* An integer is equal to the sum of the powers of two
|
|
* according to the indices of its 'on' bits.
|
|
* So to multiple x*y, we go over each '1' bit in x (say the i'th bit),
|
|
* and add y<<i to the result.
|
|
*/
|
|
FLATTEN void UnsignedBigInteger::multiply_without_allocation(
|
|
const UnsignedBigInteger& left,
|
|
const UnsignedBigInteger& right,
|
|
UnsignedBigInteger& temp_shift_result,
|
|
UnsignedBigInteger& temp_shift_plus,
|
|
UnsignedBigInteger& temp_shift,
|
|
UnsignedBigInteger& temp_plus,
|
|
UnsignedBigInteger& output)
|
|
{
|
|
output.set_to_0();
|
|
|
|
// iterate all bits
|
|
for (size_t word_index = 0; word_index < left.length(); ++word_index) {
|
|
for (size_t bit_index = 0; bit_index < UnsignedBigInteger::BITS_IN_WORD; ++bit_index) {
|
|
// If the bit is off - skip over it
|
|
if (!(left.m_words[word_index] & (1 << bit_index)))
|
|
continue;
|
|
|
|
const size_t shift_amount = word_index * UnsignedBigInteger::BITS_IN_WORD + bit_index;
|
|
|
|
// output += (right << shift_amount);
|
|
shift_left_without_allocation(right, shift_amount, temp_shift_result, temp_shift_plus, temp_shift);
|
|
add_without_allocation(output, temp_shift, temp_plus);
|
|
output.set_to(temp_plus);
|
|
}
|
|
}
|
|
}
|
|
|
|
/**
|
|
* Complexity: O(N^2) where N is the number of words in the larger number
|
|
* Division method:
|
|
* We loop over the bits of the divisor, attempting to subtract divisor<<i from the dividend.
|
|
* If the result is non-negative, it means that divisor*2^i "fits" in the dividend,
|
|
* so we set the ith bit in the quotient and reduce divisor<<i from the dividend.
|
|
* When we're done, what's left from the dividend is the remainder.
|
|
*/
|
|
FLATTEN void UnsignedBigInteger::divide_without_allocation(
|
|
const UnsignedBigInteger& numerator,
|
|
const UnsignedBigInteger& denominator,
|
|
UnsignedBigInteger& temp_shift_result,
|
|
UnsignedBigInteger& temp_shift_plus,
|
|
UnsignedBigInteger& temp_shift,
|
|
UnsignedBigInteger& temp_minus,
|
|
UnsignedBigInteger& quotient,
|
|
UnsignedBigInteger& remainder)
|
|
{
|
|
quotient.set_to_0();
|
|
remainder.set_to(numerator);
|
|
|
|
// iterate all bits
|
|
for (int word_index = numerator.trimmed_length() - 1; word_index >= 0; --word_index) {
|
|
for (int bit_index = UnsignedBigInteger::BITS_IN_WORD - 1; bit_index >= 0; --bit_index) {
|
|
const size_t shift_amount = word_index * UnsignedBigInteger::BITS_IN_WORD + bit_index;
|
|
shift_left_without_allocation(denominator, shift_amount, temp_shift_result, temp_shift_plus, temp_shift);
|
|
|
|
subtract_without_allocation(remainder, temp_shift, temp_minus);
|
|
if (!temp_minus.is_invalid()) {
|
|
remainder.set_to(temp_minus);
|
|
quotient.set_bit_inplace(shift_amount);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
/**
|
|
* Complexity : O(N) where N is the number of digits in the numerator
|
|
* Division method :
|
|
* Starting from the most significant one, for each half-word of the numerator, combine it
|
|
* with the existing remainder if any, divide the combined number as a u32 operation and
|
|
* update the quotient / remainder as needed.
|
|
*/
|
|
FLATTEN void UnsignedBigInteger::divide_u16_without_allocation(
|
|
const UnsignedBigInteger& numerator,
|
|
u32 denominator,
|
|
UnsignedBigInteger& quotient,
|
|
UnsignedBigInteger& remainder)
|
|
{
|
|
VERIFY(denominator < (1 << 16));
|
|
u32 remainder_word = 0;
|
|
auto numerator_length = numerator.trimmed_length();
|
|
quotient.set_to_0();
|
|
quotient.m_words.resize(numerator_length);
|
|
for (int word_index = numerator_length - 1; word_index >= 0; --word_index) {
|
|
auto word_high = numerator.m_words[word_index] >> 16;
|
|
auto word_low = numerator.m_words[word_index] & ((1 << 16) - 1);
|
|
|
|
auto number_to_divide_high = (remainder_word << 16) | word_high;
|
|
auto quotient_high = number_to_divide_high / denominator;
|
|
remainder_word = number_to_divide_high % denominator;
|
|
|
|
auto number_to_divide_low = remainder_word << 16 | word_low;
|
|
auto quotient_low = number_to_divide_low / denominator;
|
|
remainder_word = number_to_divide_low % denominator;
|
|
|
|
quotient.m_words[word_index] = (quotient_high << 16) | quotient_low;
|
|
}
|
|
remainder.set_to(remainder_word);
|
|
}
|
|
|
|
ALWAYS_INLINE void UnsignedBigInteger::shift_left_by_n_words(
|
|
const UnsignedBigInteger& number,
|
|
const size_t number_of_words,
|
|
UnsignedBigInteger& output)
|
|
{
|
|
// shifting left by N words means just inserting N zeroes to the beginning of the words vector
|
|
output.set_to_0();
|
|
output.m_words.resize_and_keep_capacity(number_of_words + number.length());
|
|
|
|
__builtin_memset(output.m_words.data(), 0, number_of_words * sizeof(unsigned));
|
|
__builtin_memcpy(&output.m_words.data()[number_of_words], number.m_words.data(), number.m_words.size() * sizeof(unsigned));
|
|
}
|
|
|
|
/**
|
|
* Returns the word at a requested index in the result of a shift operation
|
|
*/
|
|
ALWAYS_INLINE u32 UnsignedBigInteger::shift_left_get_one_word(
|
|
const UnsignedBigInteger& number,
|
|
const size_t num_bits,
|
|
const size_t result_word_index)
|
|
{
|
|
// "<= length()" (rather than length() - 1) is intentional,
|
|
// The result inedx of length() is used when calculating the carry word
|
|
VERIFY(result_word_index <= number.length());
|
|
VERIFY(num_bits <= UnsignedBigInteger::BITS_IN_WORD);
|
|
u32 result = 0;
|
|
|
|
// we need to check for "num_bits != 0" since shifting right by 32 is apparently undefined behaviour!
|
|
if (result_word_index > 0 && num_bits != 0) {
|
|
result += number.m_words[result_word_index - 1] >> (UnsignedBigInteger::BITS_IN_WORD - num_bits);
|
|
}
|
|
if (result_word_index < number.length() && num_bits < 32) {
|
|
result += number.m_words[result_word_index] << num_bits;
|
|
}
|
|
return result;
|
|
}
|
|
}
|
|
|
|
void AK::Formatter<Crypto::UnsignedBigInteger>::format(FormatBuilder& fmtbuilder, const Crypto::UnsignedBigInteger& value)
|
|
{
|
|
if (value.is_invalid())
|
|
return Formatter<StringView>::format(fmtbuilder, "invalid");
|
|
|
|
StringBuilder builder;
|
|
for (int i = value.length() - 1; i >= 0; --i)
|
|
builder.appendff("{}|", value.words()[i]);
|
|
|
|
return Formatter<StringView>::format(fmtbuilder, builder.string_view());
|
|
}
|