Haskell 范围和浮点数 [英] Haskell ranges and floats

问题描述

为什么浮点数和整数和字符的 Haskell 范围表示法的行为不同?

Why is the behavior of the Haskell range notation different for floats than for integers and chars?

Prelude> [1, 3 .. 10] :: [Int]
[1,3,5,7,9] 
Prelude> [1, 3 .. 10] :: [Float]
[1.0,3.0,5.0,7.0,9.0,11.0]
Prelude> ['a', 'c' .. 'f']
"ace"

如果最后一个元素接近上限我会理解，但这显然不是舍入问题.

I would understand it if the last element was close to the upper bound, but this is obviously not a rounding issue.

推荐答案

语法 [e1, e2 .. e3] 真的是 enumFromThenTo e1 e2 e3 的语法糖，它是 Enum 类型类中的一个函数.

The syntax [e1, e2 .. e3] is really syntactic sugar for enumFromThenTo e1 e2 e3, which is a function in the Enum typeclass.

Haskell 标准 定义其语义如下:

对于 Int 和 Integer 类型，枚举函数具有以下含义:

For the types Int and Integer, the enumeration functions have the following meaning:

• 序列enumFrom e1是列表[e1,e1 + 1,e1 + 2,…].
• 序列enumFromThen e1 e2是列表[e1,e1 + i,e1 + 2i,…]，其中增量 i 是 e2 - e1.增量可能为零或消极的.如果增量为零，则所有列表元素都是一样.
• 序列enumFromTo e1 e3是列表[e1,e1 + 1,e1 + 2,…e3].如果 e1 > 则列表为空e3.
• 序列 enumFromThenTo e1 e2 e3 是列表 [e1,e1 + i,e1 +2i,…e3]，其中增量 i 为 e2 - e1.如果增量是正数或零，列表在下一个元素为时终止大于e3；如果 e1 > 则列表为空e3.如果增量是负数，当下一个元素小于时列表终止e3;如果 e1 < 则列表为空e3.

• The sequence enumFrom e1 is the list [e1,e1 + 1,e1 + 2,…].
• The sequence enumFromThen e1 e2 is the list [e1,e1 + i,e1 + 2i,…], where the increment, i, is e2 − e1. The increment may be zero or negative. If the increment is zero, all the list elements are the same.
• The sequence enumFromTo e1 e3 is the list [e1,e1 + 1,e1 + 2,…e3]. The list is empty if e1 > e3.
• The sequence enumFromThenTo e1 e2 e3 is the list [e1,e1 + i,e1 + 2i,…e3], where the increment, i, is e2 − e1. If the increment is positive or zero, the list terminates when the next element would be greater than e3; the list is empty if e1 > e3. If the increment is negative, the list terminates when the next element would be less than e3; the list is empty if e1 < e3.

这几乎是您所期望的，但是 Float 和 Double 实例的定义不同:

This is pretty much what you'd expect, but the Float and Double instances are defined differently:

对于 Float 和 Double，enumFrom 系列的语义由上述 Int 的规则给出, 除了当元素变得大于 e3 + i∕2 为正增量 i 或当它们变得小于 e3 + i∕2 时列表终止 表示否定的i.

For Float and Double, the semantics of the enumFrom family is given by the rules for Int above, except that the list terminates when the elements become greater than e3 + i∕2 for positive increment i, or when they become less than e3 + i∕2 for negative i.

我不太确定这样做的理由是什么，所以我可以给你的唯一答案是，它是这样的，因为它在标准中是这样定义的.

I'm not really sure what the justification for this is, so the only answer I can give you is that it is that way because it's defined that way in the standard.

您可以通过使用整数枚举并随后转换为 Float 来解决此问题.

You can work around this by enumerating using integers and converting to Float afterward.

Prelude> map fromIntegral [1, 3 .. 10] :: [Float]
[1.0,3.0,5.0,7.0,9.0]

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