Rounding- Модуль
- std.
decimal → - Получатель
- Неприменимо
- Минимальное число аргументов
- 0
- Максимальное число аргументов
- 0
Declaration and parameters
СсылкаДоступность
Включено по умолчанию · Не определено
Import std.decimal in language mode 5.21.
The current compiler selects std/decimal.tpz for this language mode. Availability in other released editions and inclusion in each installed distribution are Pending.
Получатель
Ограничения параметров
For a requested scale s, rounding selects a multiple of ten raised to negative s. A value already on that grid is unchanged in every rounding mode.
The requested scale must be an int from 0 through 4294967295 inclusive. A negative value or a value above that range raises TPZ5001 during execution. Scale is never clamped or interpreted as digits to the left of the decimal point.
When the requested scale is at least the canonical scale, round returns the same value. Otherwise it chooses a grid value according to the supplied mode and normalizes the result.
RoundingMode.Down() chooses the greatest grid value no greater than the input. It rounds toward negative infinity, including at a midpoint.
RoundingMode.Up() chooses the least grid value no smaller than the input. It rounds toward positive infinity, including at a midpoint.
RoundingMode.TowardZero() chooses the grid value with smaller absolute magnitude when the input is between two grid values. RoundingMode.AwayFromZero() chooses the one with larger absolute magnitude. These directions also apply at midpoints.
RoundingMode.HalfUp() chooses the nearer grid value. At an exact midpoint it chooses the value with greater absolute magnitude for either sign.
RoundingMode.HalfEven() chooses the nearer grid value. At an exact midpoint it chooses the value whose integer coefficient on the requested grid is even. Determine parity before canonical trailing zeros are removed.
Omitting the mode selects RoundingMode.HalfEven(). The default is independent of host settings and applies equally to positive and negative values.
A carry may reduce the canonical scale. A rounded zero has scale zero and no negative sign. Rounding does not pad the result to the requested scale.
Each RoundingMode spelling constructs a distinct zero payload enum variant and uses parentheses. The modes are immutable values that callers may store and pass to both round and div.
Связанное правило · Choose a decimal grid and a rounding direction →Результат
The declared result type is Rounding.
Эффекты
Ошибки
Result and effects
СсылкаAt an exact midpoint choose the even integer coefficient on the requested grid before normalization. This is the default mode for round and div.
Why
СсылкаEven midpoint selection is deterministic without consistently favoring a magnitude direction.
Resolved contracts
СсылкаRelated entries
СсылкаChoose a decimal grid and a rounding direction
СсылкаChoose a decimal grid and a rounding direction
For a requested scale s, rounding selects a multiple of ten raised to negative s. A value already on that grid is unchanged in every rounding mode.
The requested scale must be an int from 0 through 4294967295 inclusive. A negative value or a value above that range raises TPZ5001 during execution. Scale is never clamped or interpreted as digits to the left of the decimal point.
When the requested scale is at least the canonical scale, round returns the same value. Otherwise it chooses a grid value according to the supplied mode and normalizes the result.
RoundingMode.Down() chooses the greatest grid value no greater than the input. It rounds toward negative infinity, including at a midpoint.
RoundingMode.Up() chooses the least grid value no smaller than the input. It rounds toward positive infinity, including at a midpoint.
RoundingMode.TowardZero() chooses the grid value with smaller absolute magnitude when the input is between two grid values. RoundingMode.AwayFromZero() chooses the one with larger absolute magnitude. These directions also apply at midpoints.
RoundingMode.HalfUp() chooses the nearer grid value. At an exact midpoint it chooses the value with greater absolute magnitude for either sign.
RoundingMode.HalfEven() chooses the nearer grid value. At an exact midpoint it chooses the value whose integer coefficient on the requested grid is even. Determine parity before canonical trailing zeros are removed.
Omitting the mode selects RoundingMode.HalfEven(). The default is independent of host settings and applies equally to positive and negative values.
A carry may reduce the canonical scale. A rounded zero has scale zero and no negative sign. Rounding does not pad the result to the requested scale.
Each RoundingMode spelling constructs a distinct zero payload enum variant and uses parentheses. The modes are immutable values that callers may store and pass to both round and div.
Причина
A decimal grid states which precision the caller needs. Nearest rounding, an upper or lower bound, and movement toward or away from zero express different numeric intentions. Their results can agree for some inputs without making their meanings interchangeable. HalfEven gives exact ties a stable rule without consistently favoring one magnitude direction.
Resolve positive and negative ties in every rounding mode
Ссылкаimport std.decimal { Decimal, RoundingMode }import std.testimport std.iofunction read(text: string) -> Decimal {let parsed: Option<Decimal> = Decimal.parse(text)let value: Decimal = test.assertSome(parsed)return value}function rounded(text: string, mode: RoundingMode) -> string {let value: Decimal = read(text)return value.round(0, mode).toString()}let modes: Array<RoundingMode> = [RoundingMode.Down(), RoundingMode.Up(), RoundingMode.TowardZero(), RoundingMode.AwayFromZero(), RoundingMode.HalfUp(), RoundingMode.HalfEven()]for mode in (modes) {let a = rounded("2.5", mode)let b = rounded("3.5", mode)let c = rounded("-2.5", mode)let d = rounded("-3.5", mode)io.writeLine("{a} {b} {c} {d}")}
2 3 -3 -4
3 4 -2 -3
2 3 -2 -3
3 4 -3 -4
3 4 -3 -4
2 4 -2 -4
Ожидаемый результат
Ожидаемый результат
Выполнение завершается. Код завершения 0.
2 3 -3 -43 4 -2 -32 3 -2 -33 4 -3 -43 4 -3 -42 4 -2 -4
Distinguish directed rounding from nearest rounding
Ссылкаimport std.decimal { Decimal, RoundingMode }import std.testimport std.iofunction read(text: string) -> Decimal {let parsed: Option<Decimal> = Decimal.parse(text)let value: Decimal = test.assertSome(parsed)return value}function rounded(text: string, mode: RoundingMode) -> string {let value: Decimal = read(text)return value.round(0, mode).toString()}let modes: Array<RoundingMode> = [RoundingMode.Down(), RoundingMode.Up(), RoundingMode.TowardZero(), RoundingMode.AwayFromZero(), RoundingMode.HalfUp(), RoundingMode.HalfEven()]for mode in (modes) {let a = rounded("2.1", mode)let b = rounded("2.9", mode)let c = rounded("-2.1", mode)let d = rounded("-2.9", mode)io.writeLine("{a} {b} {c} {d}")}
2 2 -3 -3
3 3 -2 -2
2 2 -2 -2
3 3 -3 -3
2 3 -2 -3
2 3 -2 -3
Ожидаемый результат
Ожидаемый результат
Выполнение завершается. Код завершения 0.
2 2 -3 -33 3 -2 -22 2 -2 -23 3 -3 -32 3 -2 -32 3 -2 -3
Apply the default mode and normalize a carry or zero
Ссылкаimport std.decimal { Decimal }import std.testimport std.iofunction read(text: string) -> Decimal {let parsed: Option<Decimal> = Decimal.parse(text)let value: Decimal = test.assertSome(parsed)return value}let value: Decimal = read("1.245")io.writeLine(value.round(2).toString())io.writeLine(read("1.255").round(2).toString())io.writeLine(value.round(5).toString())let carry: Decimal = read("9.995").round(2)let zero: Decimal = read("-0.004").round(2)io.writeLine("{carry.toString()} {carry.scale()}")io.writeLine("{zero.toString()} {zero.scale()}")io.writeLine(value.toString())
1.24
1.26
1.245
10 0
0 0
1.245
Ожидаемый результат
Ожидаемый результат
Выполнение завершается. Код завершения 0.
1.241.261.24510 00 01.245
Accept the largest scale without adding stored zeros
Ссылкаimport std.decimal { Decimal }import std.testimport std.iolet one: Decimal = (1).toDecimal()let zero: Decimal = (0).toDecimal()let same: Decimal = one.round(4294967295)let sameZero: Decimal = zero.round(4294967295)io.writeLine("{same.toString()} {same.scale()}")io.writeLine("{sameZero.toString()} {sameZero.scale()}")
1 0
0 0
Ожидаемый результат
Ожидаемый результат
Выполнение завершается. Код завершения 0.
1 00 0
Reject a rounding scale outside the valid range
Ссылкаimport std.decimal { Decimal }import std.iolet value: Decimal = (1).toDecimal()value.round(-1)io.writeLine("after")
Нет стандартного вывода.Ожидаемый результат
Ожидаемый результат
Этап отклонения run. Ненулевой код завершения.
stdlib-decimal-scale at
main.tpz:4:1
Reject a rounding scale outside the valid range
Ссылкаimport std.decimal { Decimal }import std.iolet value: Decimal = (1).toDecimal()value.round(4294967296)io.writeLine("after")
Нет стандартного вывода.Ожидаемый результат
Ожидаемый результат
Этап отклонения run. Ненулевой код завершения.
stdlib-decimal-scale at
main.tpz:4:1