`ball_float` API

安定性

bare/decorated interval 構築、relation、forward arithmetic、context、flags は 0.7.1 API です。reverse operation と tightness 保証は契約外です。

このページは 0.7.1 基準における @ball_float.BallFloat、 @ball_float.Decoration、@ball_float.BallFloatDecorated を説明します。

意味

BallFloat は次の包絡を表します。

center +/- radius

現在の実装ではこれを BinFloat の下界・上界として保持し、できるだけ狭い区間よりも、包絡を絶対に落とさないことを優先します。

構築

BallFloat::new
BallFloat::exact
BallFloat::from_bounds
BallFloat::from_coefficient
BallFloat::from_int
BallFloat::from_float
BallFloat::from_double

from_coefficient は非負の @bin_float.BinCoeff と独立した negative? 符号を受け取ります。二進 stack の BigInt constructor は廃止され、Decimal の BigInt 境界は維持されます。

制約:

中心値は有限でなければなりません。
半径は有限かつ非負でなければなりません。
exact、from_float、from_double は非有限入力で abort します。

補足:

中心値の再量子化で生じる変位は半径へ加えられ、包絡が縮まないようにします。
半径の量子化は常に外向きに丸められます。

アクセサと区間形状

lower_bound
upper_bound
center
radius
precision
classify
sign
is_bounded
is_entire
contains_zero
normalized
with_precision

補足:

center() と radius() は非有界区間では abort します。
包絡が負値と正値の両方をまたぐと sign() は Sign::Zero を返します。
classify() は非有界区間に対して Infinity を返します。

関係と比較

contains
overlaps
separated_from
definitely_lt
definitely_le
definitely_gt
maybe_eq

補足:

これらは enclosure relation であり、scalar の全順序を装いません。

算術と checked capability の挙動

add
sub
mul
div
abs
neg
pow_interval
sin_interval
cos_interval
tan_interval

対応演算子:

+
-
*
/
単項 -

checked 挙動メモ:

checked division は分母包絡が 0 を含むと whole-real enclosure へ広がることがあります。
checked integer power は enclosure の正しさを保ち、零交差を含む逆冪でも同じ whole-real fallback を使います。
BallFloat は scalar CompareChecked を実装しません。
一般の冪は IEEE 1788 の非負底定義域に従い、負底の整数冪は引き続き pown が担います。
このパッケージは双曲・逆三角関数、微積分、行列、複素 ball、特殊関数をまだ公開しません。

Decorated interval

BallFloatDecorated は BallFloat と同じ ball_float パッケージに属します。利用側が import するのは Luna-Flow/floating/ball_float だけであり、独立した Luna-Flow/floating/decorated_ball_float パッケージはありません。bare interval、decorated interval、context、IEEE 1788 の集合意味論は一つのパッケージ境界を共有します。

Decoration は弱い順に Ill、Trv、Def、Dac、Com です。 BallFloatDecorated は underlying BallFloat、decoration、独立した NaI 状態を保持します。

BallFloatDecorated::new は bare interval を包みます。
BallFloatDecorated::nai は NaI を構築します。NaI は Ill ですが Empty ではありません。
interval、decoration、is_nai で三つの状態を観測できます。
Empty は Trv に正規化され、non-common interval の Com は Dac に下がります。
演算結果は入力と演算自身の最も弱い decoration を取るため、評価中に等級が上がることはありません。
部分定義域、0 除算の可能性、三角関数の極では演算等級が Trv に下がります。
数値演算は NaI を伝播し、NaI を含む Boolean relation は false、 overlap_state は Undefined を返します。

decorated 型は集合演算、relation、算術、cancellation、初等関数、FMA、整数冪、極値、context 操作を公開し、+、-、*、/、Show に対応します。

Trait 面

Context と status

BallContext は端点を directed rounding し、BallFlags は inexact、overflow、underflow を返します。set semantics は変わりません。

BallFloat は現在次を実装します。

@def.Floating
@arithmetic.Contains
@arithmetic.Overlaps
@arithmetic.DefinitelyLt
@arithmetic.DefinitelyLe
@arithmetic.MaybeEq
@arithmetic.DivChecked
@arithmetic.PowNatChecked
@arithmetic.PowIntChecked
Eq、Add、Sub、Mul、Div、Neg、Show

完全な公開インターフェース

次の snapshot は 0.7.1 の完全な生成 package interface です。公開宣言が名前と signature の基準で、前の説明は挙動別に整理しています。

moonbit

// Generated using `moon info`, DON'T EDIT IT
package "Luna-Flow/floating/ball_float"

import {
  "Luna-Flow/arithmetic",
  "Luna-Flow/floating/bin_float",
  "Luna-Flow/floating/def",
  "moonbitlang/core/debug",
}

// Values

// Errors

// Types and methods
pub struct BallContext {
  // private fields
}
pub fn BallContext::binary32() -> Self
pub fn BallContext::binary64() -> Self
pub fn BallContext::e_max(Self) -> Int
pub fn BallContext::e_min(Self) -> Int
pub fn BallContext::new(precision? : Int, e_min? : Int, e_max? : Int) -> Self
pub fn BallContext::precision(Self) -> Int
pub fn BallContext::try_new(precision? : Int, e_min? : Int, e_max? : Int) -> Result[Self, @arithmetic.ArithmeticError]

pub struct BallFlags {
  inexact : Bool
  overflow : Bool
  underflow : Bool
} derive(Eq)
pub fn BallFlags::combine(Self, Self) -> Self
pub fn BallFlags::inexact(Self) -> Bool
pub fn BallFlags::new() -> Self
pub fn BallFlags::overflow(Self) -> Bool
pub fn BallFlags::underflow(Self) -> Bool

pub struct BallFloat {
  // private fields
} derive(Eq, @debug.Debug)
pub fn BallFloat::abs(Self) -> Self
pub fn BallFloat::acos_interval(Self) -> Self
pub fn BallFloat::acosh_interval(Self) -> Self
pub fn BallFloat::add(Self, Self) -> Self
pub fn BallFloat::add_ctx(Self, Self, BallContext) -> (Self, BallFlags)
pub fn BallFloat::apply_ctx(Self, BallContext) -> (Self, BallFlags)
pub fn BallFloat::asin_interval(Self) -> Self
pub fn BallFloat::asinh_interval(Self) -> Self
pub fn BallFloat::atan2_interval(Self, Self) -> Self
pub fn BallFloat::atan_interval(Self) -> Self
pub fn BallFloat::atanh_interval(Self) -> Self
pub fn BallFloat::cancel_minus(Self, Self) -> Self
pub fn BallFloat::cancel_plus(Self, Self) -> Self
pub fn BallFloat::center(Self) -> @bin_float.BinFloat
pub fn BallFloat::classify(Self) -> @arithmetic.FpClass
pub fn BallFloat::contains(Self, @bin_float.BinFloat) -> Bool
pub fn BallFloat::contains_zero(Self) -> Bool
pub fn BallFloat::convex_hull(Self, Self) -> Self
pub fn BallFloat::cos_interval(Self) -> Self
pub fn BallFloat::cosh_interval(Self) -> Self
pub fn BallFloat::cospi_interval(Self) -> Self
pub fn BallFloat::definitely_gt(Self, Self) -> Bool
pub fn BallFloat::definitely_le(Self, Self) -> Bool
pub fn BallFloat::definitely_lt(Self, Self) -> Bool
pub fn BallFloat::disjoint(Self, Self) -> Bool
pub fn BallFloat::div(Self, Self) -> Self
pub fn BallFloat::div_ctx(Self, Self, BallContext) -> (Self, BallFlags)
pub fn BallFloat::empty(precision? : Int) -> Self
pub fn BallFloat::exact(@bin_float.BinFloat, precision? : Int) -> Self
pub fn BallFloat::exp10_interval(Self) -> Self
pub fn BallFloat::exp2_interval(Self) -> Self
pub fn BallFloat::exp_ctx(Self, BallContext) -> (Self, BallFlags)
pub fn BallFloat::exp_interval(Self) -> Self
pub fn BallFloat::expm1_interval(Self) -> Self
pub fn BallFloat::fma(Self, Self, Self) -> Self
pub fn BallFloat::from_bounds(@bin_float.BinFloat, @bin_float.BinFloat, precision? : Int) -> Self
pub fn BallFloat::from_coefficient(@bin_float.BinCoeff, precision? : Int, negative? : Bool) -> Self
pub fn BallFloat::from_double(Double, precision? : Int) -> Self
pub fn BallFloat::from_float(Float, precision? : Int) -> Self
pub fn BallFloat::from_int(Int, precision? : Int) -> Self
pub fn BallFloat::hypot(Self, Self) -> Self
pub fn BallFloat::interior(Self, Self) -> Bool
pub fn BallFloat::intersection(Self, Self) -> Self
pub fn BallFloat::is_bounded(Self) -> Bool
pub fn BallFloat::is_common_interval(Self) -> Bool
pub fn BallFloat::is_empty(Self) -> Bool
pub fn BallFloat::is_entire(Self) -> Bool
pub fn BallFloat::is_singleton(Self) -> Bool
pub fn BallFloat::less(Self, Self) -> Bool
pub fn BallFloat::ln_ctx(Self, BallContext) -> (Self, BallFlags)
pub fn BallFloat::ln_interval(Self) -> Self
pub fn BallFloat::log10_interval(Self) -> Self
pub fn BallFloat::log1p_interval(Self) -> Self
pub fn BallFloat::log2_interval(Self) -> Self
pub fn BallFloat::lower_bound(Self) -> @bin_float.BinFloat
pub fn BallFloat::magnitude(Self) -> @bin_float.BinFloat
pub fn BallFloat::maximum(Self, Self) -> Self
pub fn BallFloat::maybe_eq(Self, Self) -> Bool
pub fn BallFloat::midpoint(Self) -> @bin_float.BinFloat
pub fn BallFloat::midpoint_ctx(Self, BallContext) -> (@bin_float.BinFloat, BallFlags)
pub fn BallFloat::mignitude(Self) -> @bin_float.BinFloat
pub fn BallFloat::minimum(Self, Self) -> Self
pub fn BallFloat::mul(Self, Self) -> Self
pub fn BallFloat::mul_ctx(Self, Self, BallContext) -> (Self, BallFlags)
pub fn BallFloat::neg(Self) -> Self
pub fn BallFloat::new(@bin_float.BinFloat, @bin_float.BinFloat, precision? : Int) -> Self
pub fn BallFloat::normalized(Self) -> Self
pub fn BallFloat::overlap_state(Self, Self) -> OverlapState
pub fn BallFloat::overlaps(Self, Self) -> Bool
pub fn BallFloat::pow_interval(Self, Self) -> Self
pub fn BallFloat::pown(Self, Int) -> Self
pub fn BallFloat::precedes(Self, Self) -> Bool
pub fn BallFloat::precision(Self) -> Int
pub fn BallFloat::radius(Self) -> @bin_float.BinFloat
pub fn BallFloat::radius_extended(Self) -> @bin_float.BinFloat
pub fn BallFloat::reciprocal(Self) -> Self
pub fn BallFloat::rootn(Self, Int) -> Self
pub fn BallFloat::separated_from(Self, Self) -> Bool
pub fn BallFloat::set_equal(Self, Self) -> Bool
pub fn BallFloat::sign(Self) -> @def.Sign
pub fn BallFloat::sin_interval(Self) -> Self
pub fn BallFloat::sinh_interval(Self) -> Self
pub fn BallFloat::sinpi_interval(Self) -> Self
pub fn BallFloat::sqrt_interval(Self) -> Self
pub fn BallFloat::square(Self) -> Self
pub fn BallFloat::strictly_less(Self, Self) -> Bool
pub fn BallFloat::strictly_precedes(Self, Self) -> Bool
pub fn BallFloat::sub(Self, Self) -> Self
pub fn BallFloat::sub_ctx(Self, Self, BallContext) -> (Self, BallFlags)
pub fn BallFloat::subset(Self, Self) -> Bool
pub fn BallFloat::tan_interval(Self) -> Self
pub fn BallFloat::tanh_interval(Self) -> Self
pub fn BallFloat::tanpi_interval(Self) -> Self
pub fn BallFloat::try_acos_interval(Self) -> Result[Self, @arithmetic.ArithmeticError]
pub fn BallFloat::try_acosh_interval(Self) -> Result[Self, @arithmetic.ArithmeticError]
pub fn BallFloat::try_asin_interval(Self) -> Result[Self, @arithmetic.ArithmeticError]
pub fn BallFloat::try_asinh_interval(Self) -> Result[Self, @arithmetic.ArithmeticError]
pub fn BallFloat::try_atan2_interval(Self, Self) -> Result[Self, @arithmetic.ArithmeticError]
pub fn BallFloat::try_atan_interval(Self) -> Result[Self, @arithmetic.ArithmeticError]
pub fn BallFloat::try_atanh_interval(Self) -> Result[Self, @arithmetic.ArithmeticError]
pub fn BallFloat::try_cos_interval(Self) -> Result[Self, @arithmetic.ArithmeticError]
pub fn BallFloat::try_cosh_interval(Self) -> Result[Self, @arithmetic.ArithmeticError]
pub fn BallFloat::try_cospi_interval(Self) -> Result[Self, @arithmetic.ArithmeticError]
pub fn BallFloat::try_exact(@bin_float.BinFloat, precision? : Int) -> Result[Self, @arithmetic.ArithmeticError]
pub fn BallFloat::try_exp10_interval(Self) -> Result[Self, @arithmetic.ArithmeticError]
pub fn BallFloat::try_exp2_interval(Self) -> Result[Self, @arithmetic.ArithmeticError]
pub fn BallFloat::try_exp_interval(Self) -> Result[Self, @arithmetic.ArithmeticError]
pub fn BallFloat::try_expm1_interval(Self) -> Result[Self, @arithmetic.ArithmeticError]
pub fn BallFloat::try_from_bounds(@bin_float.BinFloat, @bin_float.BinFloat, precision? : Int) -> Result[Self, @arithmetic.ArithmeticError]
pub fn BallFloat::try_from_double(Double, precision? : Int) -> Result[Self, @arithmetic.ArithmeticError]
pub fn BallFloat::try_from_float(Float, precision? : Int) -> Result[Self, @arithmetic.ArithmeticError]
pub fn BallFloat::try_hypot(Self, Self) -> Result[Self, @arithmetic.ArithmeticError]
pub fn BallFloat::try_ln_interval(Self) -> Result[Self, @arithmetic.ArithmeticError]
pub fn BallFloat::try_log10_interval(Self) -> Result[Self, @arithmetic.ArithmeticError]
pub fn BallFloat::try_log1p_interval(Self) -> Result[Self, @arithmetic.ArithmeticError]
pub fn BallFloat::try_log2_interval(Self) -> Result[Self, @arithmetic.ArithmeticError]
pub fn BallFloat::try_pow_interval(Self, Self) -> Result[Self, @arithmetic.ArithmeticError]
pub fn BallFloat::try_rootn(Self, Int) -> Result[Self, @arithmetic.ArithmeticError]
pub fn BallFloat::try_sin_interval(Self) -> Result[Self, @arithmetic.ArithmeticError]
pub fn BallFloat::try_sinh_interval(Self) -> Result[Self, @arithmetic.ArithmeticError]
pub fn BallFloat::try_sinpi_interval(Self) -> Result[Self, @arithmetic.ArithmeticError]
pub fn BallFloat::try_tan_interval(Self) -> Result[Self, @arithmetic.ArithmeticError]
pub fn BallFloat::try_tanh_interval(Self) -> Result[Self, @arithmetic.ArithmeticError]
pub fn BallFloat::try_tanpi_interval(Self) -> Result[Self, @arithmetic.ArithmeticError]
pub fn BallFloat::upper_bound(Self) -> @bin_float.BinFloat
pub fn BallFloat::whole(precision? : Int) -> Self
pub fn BallFloat::width(Self) -> @bin_float.BinFloat
pub fn BallFloat::with_precision(Self, Int, @arithmetic.RoundingMode) -> Self
pub impl @arithmetic.Contains for BallFloat
pub impl @arithmetic.DefinitelyLe for BallFloat
pub impl @arithmetic.DefinitelyLt for BallFloat
pub impl @arithmetic.DivChecked for BallFloat
pub impl @arithmetic.MaybeEq for BallFloat
pub impl @arithmetic.Overlaps for BallFloat
pub impl @arithmetic.PowIntChecked for BallFloat
pub impl @arithmetic.PowNatChecked for BallFloat
pub impl @def.Floating for BallFloat
pub impl Add for BallFloat
pub impl Div for BallFloat
pub impl Mul for BallFloat
pub impl Neg for BallFloat
pub impl Show for BallFloat
pub impl Sub for BallFloat

pub struct BallFloatDecorated {
  // private fields
} derive(Eq)
pub fn BallFloatDecorated::abs(Self) -> Self
pub fn BallFloatDecorated::acos_interval(Self) -> Self
pub fn BallFloatDecorated::acosh_interval(Self) -> Self
pub fn BallFloatDecorated::add(Self, Self) -> Self
pub fn BallFloatDecorated::apply_ctx(Self, BallContext) -> (Self, BallFlags)
pub fn BallFloatDecorated::asin_interval(Self) -> Self
pub fn BallFloatDecorated::asinh_interval(Self) -> Self
pub fn BallFloatDecorated::atan2_interval(Self, Self) -> Self
pub fn BallFloatDecorated::atan_interval(Self) -> Self
pub fn BallFloatDecorated::atanh_interval(Self) -> Self
pub fn BallFloatDecorated::cancel_minus(Self, Self) -> Self
pub fn BallFloatDecorated::cancel_plus(Self, Self) -> Self
pub fn BallFloatDecorated::contains(Self, @bin_float.BinFloat) -> Bool
pub fn BallFloatDecorated::convex_hull(Self, Self) -> Self
pub fn BallFloatDecorated::cos_interval(Self) -> Self
pub fn BallFloatDecorated::cosh_interval(Self) -> Self
pub fn BallFloatDecorated::cospi_interval(Self) -> Self
pub fn BallFloatDecorated::decoration(Self) -> Decoration
pub fn BallFloatDecorated::disjoint(Self, Self) -> Bool
pub fn BallFloatDecorated::div(Self, Self) -> Self
pub fn BallFloatDecorated::exp10_interval(Self) -> Self
pub fn BallFloatDecorated::exp2_interval(Self) -> Self
pub fn BallFloatDecorated::exp_interval(Self) -> Self
pub fn BallFloatDecorated::expm1_interval(Self) -> Self
pub fn BallFloatDecorated::fma(Self, Self, Self) -> Self
pub fn BallFloatDecorated::hypot(Self, Self) -> Self
pub fn BallFloatDecorated::interior(Self, Self) -> Bool
pub fn BallFloatDecorated::intersection(Self, Self) -> Self
pub fn BallFloatDecorated::interval(Self) -> BallFloat
pub fn BallFloatDecorated::is_common_interval(Self) -> Bool
pub fn BallFloatDecorated::is_empty(Self) -> Bool
pub fn BallFloatDecorated::is_entire(Self) -> Bool
pub fn BallFloatDecorated::is_nai(Self) -> Bool
pub fn BallFloatDecorated::is_singleton(Self) -> Bool
pub fn BallFloatDecorated::less(Self, Self) -> Bool
pub fn BallFloatDecorated::ln_interval(Self) -> Self
pub fn BallFloatDecorated::log10_interval(Self) -> Self
pub fn BallFloatDecorated::log1p_interval(Self) -> Self
pub fn BallFloatDecorated::log2_interval(Self) -> Self
pub fn BallFloatDecorated::maximum(Self, Self) -> Self
pub fn BallFloatDecorated::minimum(Self, Self) -> Self
pub fn BallFloatDecorated::mul(Self, Self) -> Self
pub fn BallFloatDecorated::nai(precision? : Int) -> Self
pub fn BallFloatDecorated::neg(Self) -> Self
pub fn BallFloatDecorated::new(BallFloat, decoration? : Decoration) -> Self
pub fn BallFloatDecorated::overlap_state(Self, Self) -> OverlapState
pub fn BallFloatDecorated::pos(Self) -> Self
pub fn BallFloatDecorated::pow_interval(Self, Self) -> Self
pub fn BallFloatDecorated::pown(Self, Int) -> Self
pub fn BallFloatDecorated::precedes(Self, Self) -> Bool
pub fn BallFloatDecorated::reciprocal(Self) -> Self
pub fn BallFloatDecorated::rootn(Self, Int) -> Self
pub fn BallFloatDecorated::set_equal(Self, Self) -> Bool
pub fn BallFloatDecorated::sin_interval(Self) -> Self
pub fn BallFloatDecorated::sinh_interval(Self) -> Self
pub fn BallFloatDecorated::sinpi_interval(Self) -> Self
pub fn BallFloatDecorated::sqrt_interval(Self) -> Self
pub fn BallFloatDecorated::square(Self) -> Self
pub fn BallFloatDecorated::strictly_less(Self, Self) -> Bool
pub fn BallFloatDecorated::strictly_precedes(Self, Self) -> Bool
pub fn BallFloatDecorated::sub(Self, Self) -> Self
pub fn BallFloatDecorated::subset(Self, Self) -> Bool
pub fn BallFloatDecorated::tan_interval(Self) -> Self
pub fn BallFloatDecorated::tanh_interval(Self) -> Self
pub fn BallFloatDecorated::tanpi_interval(Self) -> Self
pub impl Add for BallFloatDecorated
pub impl Div for BallFloatDecorated
pub impl Mul for BallFloatDecorated
pub impl Show for BallFloatDecorated
pub impl Sub for BallFloatDecorated

pub(all) enum Decoration {
  Ill
  Trv
  Def
  Dac
  Com
} derive(Eq, @debug.Debug)
pub impl Show for Decoration

pub(all) enum OverlapState {
  Undefined
  BothEmpty
  FirstEmpty
  SecondEmpty
  Before
  Meets
  OverlapsState
  Starts
  ContainedBy
  Finishes
  EqualIntervals
  After
  MetBy
  OverlappedBy
  StartedBy
  ContainsInterval
  FinishedBy
} derive(Eq, @debug.Debug)

// Type aliases

// Traits

Bench

Cli

Frontend

Internal

Bench

Cli

Frontend

Internal

Bench

Cli

Frontend

Internal

Backends

Immut

Mutable

Backends

Immut

Mutable

Backends

Immut

Mutable

`ball_float` API

安定性

意味

構築

アクセサと区間形状

関係と比較

算術と checked capability の挙動

Decorated interval

Trait 面

Context と status

完全な公開インターフェース

Bench

Cli

Internal

Bench

Cli

Internal

Bench

Cli

Internal

ball_float API ​

安定性 ​

意味 ​

構築 ​

アクセサと区間形状 ​

関係と比較 ​

算術と checked capability の挙動 ​

Decorated interval ​

Trait 面 ​

Context と status ​

完全な公開インターフェース ​

`ball_float` API

安定性

意味

構築

アクセサと区間形状

関係と比較

算術と checked capability の挙動

Decorated interval

Trait 面

Context と status

完全な公開インターフェース