fortran 中 COMPLEX 的存储是否保证为两个 REAL? [英] Is the storage of COMPLEX in fortran guaranteed to be two REALs?

问题描述

许多 FFT 算法利用复数存储在数组中的实部和虚部交替.通过创建一个 COMPLEX 数组并将其传递给 FFT 例程，是否可以保证它可以转换为具有交替实部和虚部的 REAL 数组(大小为两倍)?

Many FFT algorithms take advantage of complex numbers stored with alternating real and imaginary part in the array. By creating a COMPLEX array and passing it to a FFT routine, is it guaranteed that it can be cast to a REAL array (of twice the size) with alternating real and imaginary components?

    subroutine fft (data, n, isign)
      dimension data(2*n)

      do 1 i=1,2*n,2
        data(i) = ..
        data(i+1) = ..
 1    continue
    return
    end

    ...
    complex s(n)
    call fft (s, n, 1)
    ...

(顺便说一句，维度数据(2*n)和说它是真实的一样吗?)

(and, btw, is dimension data(2*n) the same as saying it is a REAL?)

推荐答案

我之所以写这个答案，是因为经验告诉我，一旦我写出这样的答案，一位真正的 Fortran 专家就会涌入纠正我.

I'm only writing this answer because experience has taught me that as soon as I do write this sort of answer one of the real Fortran experts hereabouts piles in to correct me.

我认为当前的标准及其任何前身都没有明确声明 complex 将被实现为两个相邻的内存 reals.但是，我认为这种实现是标准定义equivalence 和common 的必然结果.我想我从来没有遇到过一个 complex 没有被实现为一对 reals 的实现.

I don't think that the current standard, nor any of its predecessors, states explicitly that a complex is to be implemented as two neighbouring-in-memory reals. However, I think that this implementation is a necessary consequence of the standard's definitions of equivalence and of common. I don't think I have ever encountered an implementation in which a complex was not implemented as a pair of reals.

标准确实保证，尽管一个 complex 可以转换成一对 reals.所以，给定一些定义:

The standard does guarantee, though that a complex can be converted into a pair of reals. So, given some definitions:

complex :: z
complex, dimension(4) :: zarr
real :: r1, r2
real, dimension(8) :: rarr

以下将满足您的期望

r1 = real(z)
r2 = aimag(z)

这两个功能都是基本的，这里有一个皱纹:

Both those functions are elemental and here comes a wrinkle:

real(zarr)

返回一个 4 元素的实数数组，就像

returns a 4-element array of reals, as does

aimag(zarr)

同时

[real(zarr), aimag(zarr)]

是一个 8 元素实数数组，其中 zarr 的实数部分后跟复数部分.也许

is an 8-element array of reals with the real parts of zarr followed by the complex parts. Perhaps

rarr(1:8:2) = real(zarr)
rarr(2:8:2) = aimag(zarr)

对你来说没问题.不过，我不确定有什么更简洁的方法.

will be OK for you. I'm not sure of any neater way to do this though.

亚历山大不是唯一一个能够引用标准的人！他引用的部分让我想知道非默认复杂标量.所以我继续阅读，我认为他指向我们的部分的第 6 段是密切相关的

Alexander's not the only one able to quote the standard ! The part he quotes left me wondering about non-default complex scalars. So I read on, and I think that para 6 of the section he points us towards is germane

项目 (1)-(5) 中未指定的任何类型的非指针标量对象占用单个未指定的存储单元，每个存储单元都不同case 和每组类型参数的值，那是不同的第(4)项的未指定存储单元，

a nonpointer scalar object of any type not specified in items (1)-(5) occupies a single unspecified storage unit that is different for each case and each set of type parameter values, and that is different from the unspecified storage units of item (4),

我认为这对这里的任何答案都没有任何影响.

I don't think that this has any impact at all on any of the answers here.

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