Rounding- 수신자
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Declaration and parameters
링크사용 조건
기본 포함 · 미정
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.
수신자
매개변수 제약
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.
관련 규칙 · Choose a decimal grid and a rounding direction →결과
The declared result type is Rounding.
효과
실패
Result and effects
링크At an exact midpoint choose the even integer coefficient on the requested grid before normalization. This is the default mode for round and div.
Why
링크Even midpoint selection is deterministic without consistently favoring a magnitude direction.
Resolved contracts
링크Related entries
링크Choose a decimal grid and a rounding direction
링크Choose 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.
이유
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
링크import 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
기대 결과
기대 결과
실행을 마칩니다. 종료 코드 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
링크import 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
기대 결과
기대 결과
실행을 마칩니다. 종료 코드 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
링크import 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
기대 결과
기대 결과
실행을 마칩니다. 종료 코드 0.
1.241.261.24510 00 01.245
Accept the largest scale without adding stored zeros
링크import 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
기대 결과
기대 결과
실행을 마칩니다. 종료 코드 0.
1 00 0
Reject a rounding scale outside the valid range
링크import std.decimal { Decimal }import std.iolet value: Decimal = (1).toDecimal()value.round(-1)io.writeLine("after")
표준 출력 없음.기대 결과
Reject a rounding scale outside the valid range
링크import std.decimal { Decimal }import std.iolet value: Decimal = (1).toDecimal()value.round(4294967296)io.writeLine("after")
표준 출력 없음.