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411 lines
13 KiB
C++
411 lines
13 KiB
C++
#pragma once
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// Based on https://github.com/amdn/itoa and combined with our optimizations
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//
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//=== itoa.h - Fast integer to ascii conversion --*- C++ -*-//
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//
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// The MIT License (MIT)
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// Copyright (c) 2016 Arturo Martin-de-Nicolas
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//
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// Permission is hereby granted, free of charge, to any person obtaining a copy
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// of this software and associated documentation files (the "Software"), to deal
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// in the Software without restriction, including without limitation the rights
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// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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// copies of the Software, and to permit persons to whom the Software is
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// furnished to do so, subject to the following conditions:
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//
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// The above copyright notice and this permission notice shall be included
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// in all copies or substantial portions of the Software.
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//
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// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
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// SOFTWARE.
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//===----------------------------------------------------------------------===//
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#include <cstdint>
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#include <cstddef>
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#include <cstring>
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#include <type_traits>
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#include "likely.h"
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using int128_t = __int128;
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using uint128_t = unsigned __int128;
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namespace impl
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{
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template <typename T>
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static constexpr T pow10(size_t x)
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{
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return x ? 10 * pow10<T>(x - 1) : 1;
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}
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// Division by a power of 10 is implemented using a multiplicative inverse.
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// This strength reduction is also done by optimizing compilers, but
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// presently the fastest results are produced by using the values
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// for the multiplication and the shift as given by the algorithm
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// described by Agner Fog in "Optimizing Subroutines in Assembly Language"
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//
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// http://www.agner.org/optimize/optimizing_assembly.pdf
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//
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// "Integer division by a constant (all processors)
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// A floating point number can be divided by a constant by multiplying
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// with the reciprocal. If we want to do the same with integers, we have
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// to scale the reciprocal by 2n and then shift the product to the right
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// by n. There are various algorithms for finding a suitable value of n
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// and compensating for rounding errors. The algorithm described below
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// was invented by Terje Mathisen, Norway, and not published elsewhere."
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/// Division by constant is performed by:
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/// 1. Adding 1 if needed;
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/// 2. Multiplying by another constant;
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/// 3. Shifting right by another constant.
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template <typename UInt, bool add_, UInt multiplier_, unsigned shift_>
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struct Division
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{
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static constexpr bool add{add_};
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static constexpr UInt multiplier{multiplier_};
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static constexpr unsigned shift{shift_};
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};
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/// Select a type with appropriate number of bytes from the list of types.
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/// First parameter is the number of bytes requested. Then goes a list of types with 1, 2, 4, ... number of bytes.
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/// Example: SelectType<4, uint8_t, uint16_t, uint32_t, uint64_t> will select uint32_t.
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template <size_t N, typename T, typename... Ts>
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struct SelectType
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{
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using Result = typename SelectType<N / 2, Ts...>::Result;
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};
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template <typename T, typename... Ts>
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struct SelectType<1, T, Ts...>
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{
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using Result = T;
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};
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/// Division by 10^N where N is the size of the type.
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template <size_t N>
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using DivisionBy10PowN = typename SelectType
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<
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N,
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Division<uint8_t, 0, 205U, 11>, /// divide by 10
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Division<uint16_t, 1, 41943U, 22>, /// divide by 100
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Division<uint32_t, 0, 3518437209U, 45>, /// divide by 10000
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Division<uint64_t, 0, 12379400392853802749ULL, 90> /// divide by 100000000
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>::Result;
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template <size_t N>
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using UnsignedOfSize = typename SelectType
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<
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N,
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uint8_t,
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uint16_t,
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uint32_t,
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uint64_t,
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uint128_t
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>::Result;
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/// Holds the result of dividing an unsigned N-byte variable by 10^N resulting in
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template <size_t N>
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struct QuotientAndRemainder
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{
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UnsignedOfSize<N> quotient; // quotient with fewer than 2*N decimal digits
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UnsignedOfSize<N / 2> remainder; // remainder with at most N decimal digits
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};
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template <size_t N>
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QuotientAndRemainder<N> static inline split(UnsignedOfSize<N> value)
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{
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constexpr DivisionBy10PowN<N> division;
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UnsignedOfSize<N> quotient = (division.multiplier * (UnsignedOfSize<2 * N>(value) + division.add)) >> division.shift;
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UnsignedOfSize<N / 2> remainder = value - quotient * pow10<UnsignedOfSize<N / 2>>(N);
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return {quotient, remainder};
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}
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static inline char * outDigit(char * p, uint8_t value)
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{
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*p = '0' + value;
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++p;
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return p;
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}
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// Using a lookup table to convert binary numbers from 0 to 99
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// into ascii characters as described by Andrei Alexandrescu in
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// https://www.facebook.com/notes/facebook-engineering/three-optimization-tips-for-c/10151361643253920/
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static const char digits[201] = "00010203040506070809"
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"10111213141516171819"
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"20212223242526272829"
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"30313233343536373839"
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"40414243444546474849"
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"50515253545556575859"
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"60616263646566676869"
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"70717273747576777879"
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"80818283848586878889"
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"90919293949596979899";
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static inline char * outTwoDigits(char * p, uint8_t value)
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{
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memcpy(p, &digits[value * 2], 2);
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p += 2;
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return p;
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}
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namespace convert
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{
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template <typename UInt, size_t N = sizeof(UInt)> static char * head(char * p, UInt u);
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template <typename UInt, size_t N = sizeof(UInt)> static char * tail(char * p, UInt u);
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//===----------------------------------------------------------===//
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// head: find most significant digit, skip leading zeros
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//===----------------------------------------------------------===//
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// "x" contains quotient and remainder after division by 10^N
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// quotient is less than 10^N
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template <size_t N>
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static inline char * head(char * p, QuotientAndRemainder<N> x)
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{
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p = head(p, UnsignedOfSize<N / 2>(x.quotient));
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p = tail(p, x.remainder);
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return p;
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}
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// "u" is less than 10^2*N
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template <typename UInt, size_t N>
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static inline char * head(char * p, UInt u)
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{
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return u < pow10<UnsignedOfSize<N>>(N)
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? head(p, UnsignedOfSize<N / 2>(u))
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: head<N>(p, split<N>(u));
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}
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// recursion base case, selected when "u" is one byte
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template <>
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inline char * head<UnsignedOfSize<1>, 1>(char * p, UnsignedOfSize<1> u)
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{
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return u < 10
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? outDigit(p, u)
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: outTwoDigits(p, u);
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}
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//===----------------------------------------------------------===//
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// tail: produce all digits including leading zeros
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//===----------------------------------------------------------===//
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// recursive step, "u" is less than 10^2*N
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template <typename UInt, size_t N>
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static inline char * tail(char * p, UInt u)
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{
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QuotientAndRemainder<N> x = split<N>(u);
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p = tail(p, UnsignedOfSize<N / 2>(x.quotient));
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p = tail(p, x.remainder);
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return p;
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}
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// recursion base case, selected when "u" is one byte
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template <>
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inline char * tail<UnsignedOfSize<1>, 1>(char * p, UnsignedOfSize<1> u)
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{
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return outTwoDigits(p, u);
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}
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//===----------------------------------------------------------===//
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// large values are >= 10^2*N
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// where x contains quotient and remainder after division by 10^N
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//===----------------------------------------------------------===//
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template <size_t N>
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static inline char * large(char * p, QuotientAndRemainder<N> x)
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{
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QuotientAndRemainder<N> y = split<N>(x.quotient);
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p = head(p, UnsignedOfSize<N / 2>(y.quotient));
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p = tail(p, y.remainder);
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p = tail(p, x.remainder);
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return p;
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}
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//===----------------------------------------------------------===//
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// handle values of "u" that might be >= 10^2*N
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// where N is the size of "u" in bytes
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//===----------------------------------------------------------===//
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template <typename UInt, size_t N = sizeof(UInt)>
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static inline char * uitoa(char * p, UInt u)
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{
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if (u < pow10<UnsignedOfSize<N>>(N))
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return head(p, UnsignedOfSize<N / 2>(u));
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QuotientAndRemainder<N> x = split<N>(u);
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return u < pow10<UnsignedOfSize<N>>(2 * N)
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? head<N>(p, x)
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: large<N>(p, x);
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}
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// selected when "u" is one byte
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template <>
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inline char * uitoa<UnsignedOfSize<1>, 1>(char * p, UnsignedOfSize<1> u)
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{
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if (u < 10)
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return outDigit(p, u);
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else if (u < 100)
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return outTwoDigits(p, u);
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else
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{
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p = outDigit(p, u / 100);
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p = outTwoDigits(p, u % 100);
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return p;
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}
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}
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//===----------------------------------------------------------===//
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// handle unsigned and signed integral operands
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//===----------------------------------------------------------===//
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// itoa: handle unsigned integral operands (selected by SFINAE)
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template <typename U, std::enable_if_t<!std::is_signed_v<U> && std::is_integral_v<U>> * = nullptr>
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static inline char * itoa(U u, char * p)
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{
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return convert::uitoa(p, u);
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}
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// itoa: handle signed integral operands (selected by SFINAE)
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template <typename I, size_t N = sizeof(I), std::enable_if_t<std::is_signed_v<I> && std::is_integral_v<I>> * = nullptr>
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static inline char * itoa(I i, char * p)
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{
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// Need "mask" to be filled with a copy of the sign bit.
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// If "i" is a negative value, then the result of "operator >>"
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// is implementation-defined, though usually it is an arithmetic
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// right shift that replicates the sign bit.
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// Use a conditional expression to be portable,
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// a good optimizing compiler generates an arithmetic right shift
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// and avoids the conditional branch.
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UnsignedOfSize<N> mask = i < 0 ? ~UnsignedOfSize<N>(0) : 0;
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// Now get the absolute value of "i" and cast to unsigned type UnsignedOfSize<N>.
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// Cannot use std::abs() because the result is undefined
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// in 2's complement systems for the most-negative value.
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// Want to avoid conditional branch for performance reasons since
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// CPU branch prediction will be ineffective when negative values
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// occur randomly.
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// Let "u" be "i" cast to unsigned type UnsignedOfSize<N>.
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// Subtract "u" from 2*u if "i" is positive or 0 if "i" is negative.
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// This yields the absolute value with the desired type without
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// using a conditional branch and without invoking undefined or
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// implementation defined behavior:
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UnsignedOfSize<N> u = ((2 * UnsignedOfSize<N>(i)) & ~mask) - UnsignedOfSize<N>(i);
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// Unconditionally store a minus sign when producing digits
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// in a forward direction and increment the pointer only if
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// the value is in fact negative.
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// This avoids a conditional branch and is safe because we will
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// always produce at least one digit and it will overwrite the
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// minus sign when the value is not negative.
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*p = '-';
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p += (mask & 1);
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p = convert::uitoa(p, u);
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return p;
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}
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}
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static inline int digits10(uint128_t x)
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{
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if (x < 10ULL)
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return 1;
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if (x < 100ULL)
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return 2;
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if (x < 1000ULL)
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return 3;
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if (x < 1000000000000ULL)
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{
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if (x < 100000000ULL)
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{
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if (x < 1000000ULL)
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{
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if (x < 10000ULL)
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return 4;
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else
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return 5 + (x >= 100000ULL);
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}
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return 7 + (x >= 10000000ULL);
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}
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if (x < 10000000000ULL)
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return 9 + (x >= 1000000000ULL);
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return 11 + (x >= 100000000000ULL);
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}
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return 12 + digits10(x / 1000000000000ULL);
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}
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static inline char * writeUIntText(uint128_t x, char * p)
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{
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int len = digits10(x);
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auto pp = p + len;
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while (x >= 100)
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{
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const auto i = x % 100;
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x /= 100;
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pp -= 2;
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outTwoDigits(pp, i);
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}
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if (x < 10)
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*p = '0' + x;
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else
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outTwoDigits(p, x);
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return p + len;
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}
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static inline char * writeLeadingMinus(char * pos)
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{
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*pos = '-';
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return pos + 1;
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}
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static inline char * writeSIntText(int128_t x, char * pos)
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{
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static const int128_t min_int128 = int128_t(0x8000000000000000ll) << 64;
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if (unlikely(x == min_int128))
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{
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memcpy(pos, "-170141183460469231731687303715884105728", 40);
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return pos + 40;
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}
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if (x < 0)
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{
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x = -x;
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pos = writeLeadingMinus(pos);
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}
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return writeUIntText(static_cast<uint128_t>(x), pos);
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}
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}
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template <typename I>
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char * itoa(I i, char * p)
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{
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return impl::convert::itoa(i, p);
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}
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template <>
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inline char * itoa<uint128_t>(uint128_t i, char * p)
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{
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return impl::writeUIntText(i, p);
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}
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template <>
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inline char * itoa<int128_t>(int128_t i, char * p)
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{
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return impl::writeSIntText(i, p);
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}
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