如何使用双浮点数? [英] How to use double-float?

问题描述

我正在努力尝试弄清楚如何告诉Lisp我想使用double-float值.假设我有:

I am struggling a little trying to figure out how to tell Lisp that I want to use double-float values. Suppose I have:

(let ((x 1)) (format t "~A~%" (/ x 3.0)))

哪个给:

0.33333334

如果我想使用浮点数，可以尝试以下方法:

If I want to use double-float, I tried this:

(let ((x 1)) (declare (type double-float x)) (format t "~A~%" (/ x 3.0)))
0.33333334

因此结果不是双精度浮点数.但是，我可以像这样强制双浮动:

So the result is not a double-float. I can, however, force double-float like this:

(let ((x 1)) (format t "~A~%" (/ x 3.0d0)))
0.3333333333333333d0

现在我得到一个双浮点结果.

And now I get a double-float result.

所以我的问题是:如果我要定义一种形式或函数，希望算术运算为双精度浮点数，该如何确定呢?我已经阅读了许多有关使用declare，proclaim等的在线资源，但是还无法将其应用于获得我想要的结果.我不敢相信我知道如何在这种情况下利用它们，即使它们是正确的使用机制.

So my question is: if I'm defining a form or function in which I want arithmetic to be in double-float, how do I establish that? I've read lots of online resources on using declare, proclaim, etc, but haven't been able to apply it to getting the result I'm after. I'm not convinced I know how to utilize these in this context, or even if they are the correct mechanism to use.

如果我尝试执行long-float或不是默认值的其他任何操作，也会出现相同的问题.

Same question would apply if I were trying to do long-float or anything else that isn't the default.

推荐答案

如果要使用特殊的float格式进行计算，则必须告诉它.通常，如果您将双精度浮点数相除，则结果将是双精度浮点数.如果您有常量，则需要这样表示.

If you want to compute with a special float format you have to tell it. Usually if you divide double-floats, the result will be a double float. If you have constants, you need to denote them as such.

Common Lisp标准说:数值函数的结果是该函数的所有浮点参数中最大格式的浮点数..

The Common Lisp standard says: The result of a numerical function is a float of the largest format among all the floating-point arguments to the function..

以下内容的解释取决于几件事.这取决于阅读器阅读数字的方式.对于整数，可以指定基数.对于浮点数，取决于默认的浮点格式.

The interpretation of the following depends on a few things. It depends on how the reader reads numbers. For integers the base can be specified. For floats it depends on the default float format.

(let ((x 1)) (format t "~A~%" (/ x 3.0)))

让我们看看 *read-default-float-format* 会如何影响它:

Let's see how *read-default-float-format* affects it:

CL-USER 9 > *read-default-float-format*
SINGLE-FLOAT

CL-USER 10 > (let ((x 1)) (format t "~A~%" (/ x 3.0)))
0.33333334
NIL

CL-USER 11 > (setf *read-default-float-format* 'double-float)
DOUBLE-FLOAT

CL-USER 12 > (let ((x 1)) (format t "~A~%" (/ x 3.0)))
0.3333333333333333
NIL

还请注意，您可以使用指数标记:

Also note that you can specify the type for literal numbers by using an exponent marker:

• d =双浮点
• e = *read-default-float-format*
的浮点数
• f =单浮点
• l =浮空
• s =浮空

• d = double-float
• e = float of *read-default-float-format*
• f = single-float
• l = long-float
• s = short-float

示例:

CL-USER 15 > (setf *read-default-float-format* 'single-float)
SINGLE-FLOAT

CL-USER 16 > (let ((x 1)) (format t "~A~%" (/ x 3.0d0)))
0.3333333333333333D0
NIL

您还可以强制编号为某种类型.函数 COERCE 明确指出了您所指的类型:

You can also coerce numbers to a certain type. The function COERCE makes it explicit which type you mean:

CL-USER 17 > (let ((x 1))
               (format t "~A~%" (/ (coerce x 'double-float) 3.0)))
0.3333333333333333D0
NIL

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