## 从1970开始将秒转换为日期的数学，反之亦然。？内容来源于 Stack Overflow，并遵循CC BY-SA 3.0许可协议进行翻译与使用

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1. days_from_civil:

// Returns number of days since civil 1970-01-01.  Negative values indicate
//    days prior to 1970-01-01.
// Preconditions:  y-m-d represents a date in the civil (Gregorian) calendar
//                 m is in [1, 12]
//                 d is in [1, last_day_of_month(y, m)]
//                 y is "approximately" in
//                   [numeric_limits<Int>::min()/366, numeric_limits<Int>::max()/366]
//                 Exact range of validity is:
//                 [civil_from_days(numeric_limits<Int>::min()),
//                  civil_from_days(numeric_limits<Int>::max()-719468)]
template <class Int>
constexpr
Int
days_from_civil(Int y, unsigned m, unsigned d) noexcept
{
static_assert(std::numeric_limits<unsigned>::digits >= 18,
"This algorithm has not been ported to a 16 bit unsigned integer");
static_assert(std::numeric_limits<Int>::digits >= 20,
"This algorithm has not been ported to a 16 bit signed integer");
y -= m <= 2;
const Int era = (y >= 0 ? y : y-399) / 400;
const unsigned yoe = static_cast<unsigned>(y - era * 400);      // [0, 399]
const unsigned doy = (153*(m + (m > 2 ? -3 : 9)) + 2)/5 + d-1;  // [0, 365]
const unsigned doe = yoe * 365 + yoe/4 - yoe/100 + doy;         // [0, 146096]
return era * 146097 + static_cast<Int>(doe) - 719468;
}

2. civil_from_days:

// Returns year/month/day triple in civil calendar
// Preconditions:  z is number of days since 1970-01-01 and is in the range:
//                   [numeric_limits<Int>::min(), numeric_limits<Int>::max()-719468].
template <class Int>
constexpr
std::tuple<Int, unsigned, unsigned>
civil_from_days(Int z) noexcept
{
static_assert(std::numeric_limits<unsigned>::digits >= 18,
"This algorithm has not been ported to a 16 bit unsigned integer");
static_assert(std::numeric_limits<Int>::digits >= 20,
"This algorithm has not been ported to a 16 bit signed integer");
z += 719468;
const Int era = (z >= 0 ? z : z - 146096) / 146097;
const unsigned doe = static_cast<unsigned>(z - era * 146097);          // [0, 146096]
const unsigned yoe = (doe - doe/1460 + doe/36524 - doe/146096) / 365;  // [0, 399]
const Int y = static_cast<Int>(yoe) + era * 400;
const unsigned doy = doe - (365*yoe + yoe/4 - yoe/100);                // [0, 365]
const unsigned mp = (5*doy + 2)/153;                                   // [0, 11]
const unsigned d = doy - (153*mp+2)/5 + 1;                             // [1, 31]
const unsigned m = mp + (mp < 10 ? 3 : -9);                            // [1, 12]
return std::tuple<Int, unsigned, unsigned>(y + (m <= 2), m, d);
}

3. weekday_from_days:

// Returns day of week in civil calendar [0, 6] -> [Sun, Sat]
// Preconditions:  z is number of days since 1970-01-01 and is in the range:
//                   [numeric_limits<Int>::min(), numeric_limits<Int>::max()-4].
template <class Int>
constexpr
unsigned
weekday_from_days(Int z) noexcept
{
return static_cast<unsigned>(z >= -4 ? (z+4) % 7 : (z+5) % 7 + 6);
}

#include <iostream>

int
main()
{
int64_t z = days_from_civil(2015LL, 8, 22);
int64_t ns = z*86400*1000000000;
std::cout << ns << '\n';
const char* weekdays[] = {"Sun", "Mon", "Tue", "Wed", "Thu", "Fri", "Sat"};
unsigned wd = weekday_from_days(z);
int64_t y;
unsigned m, d;
std::tie(y, m, d) = civil_from_days(ns/86400/1000000000);
std::cout << y << '-' << m << '-' << d << ' ' << weekdays[wd] << '\n';
}

1440201600000000000
2015-8-22 Sat

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