FORTRAN 95大数除法的精度

我编写了一个子程序来计算二项式系数（n选择k），它将用于n的大值和k的中等值（因此接近给定n的最大值）。子程序代码为

!
!   Subroutine to calculate combinatoric term (n choose x)
!
subroutine COMBO(m,y,combin)
implicit none
integer m,y,b1,b2,maxx,minn
real (kind=16) combin,temp1,temp2
temp1 = real(1,16)
temp2 = real(1,16)
maxx = MAX(y,m-y)
minn = MIN(y,m-y)
do b1 = maxx+1,m
temp1 = temp1*real(b1,16)
enddo
do b2 = 1,minn
temp2 = temp2*real(b2,16)
enddo
combin = temp1/temp2
end subroutine COMBO

这适用于较大的值。然而，如果我使用n=100和k=55，我会得到以下结果

61448471214136179596720592959.998

小数部分显然是错误的，因为组合总是整数。主要节目是

program chkint
implicit none
integer i,j,n,k
real (kind=16) cmb

print*,"what is n?"
read*,n
print*,"what is k?"
read*,k

call combo(n,k,cmb)
print*,cmb

end

顺便说一句：kind=16是我机器上的四精度

---

谢谢

根据您使用的整数的大小，可能有在您的系统上使用扩展精度整数的便携式方法。标准模块ISO_FORTRAN_ENV应该定义一些整数类型（INT8、INT16、INT32、INT64等），从FORTRAN 2008开始，这些类型包含在数组整数类型中，但目前这种类型的实现似乎参差不齐

如果你仍然没有足够的空间，你有两个选择：重新设计你的问题，使其在你的精度范围内工作，或者寻找一个扩展的或任意精度的数学库。令人高兴的是，LBNL在下面列出了许多这样的库

更新：

selected\u int\u kind

是创建扩展精度值的另一种动态方法，但您仍然需要知道编译器接受哪些“kind”值。例如：

program kind_int
    use iso_fortran_env, only: output_unit, INT8, INT16, INT32, INT64!, &
!        INTEGER_KINDS

    implicit none

    integer :: i

1   format(A)
2   format('Kind name = ', A5, T20, 'kind value = ',I2,                &
        T40, 'maximum = ', I19)
3   format('Available kind values: ', I2, *(', ', I2))
    continue

    write(output_unit, 1) 'Maximum value of supported integer kinds:'
    write(output_unit, 2) 'INT8 ', INT8,  huge(1_INT8)
    write(output_unit, 2) 'INT16', INT16, huge(1_INT16)
    write(output_unit, 2) 'INT32', INT32, huge(1_INT32)
    write(output_unit, 2) 'INT64', INT64, huge(1_INT64)
    write(output_unit, 2) '16   ', 16, huge(selected_int_kind(16))
    write(output_unit, 2) '32   ', 32, huge(selected_int_kind(32))

!    write(output_unit, 3) INTEGER_KINDS

    stop
end program kind_int

在linux64系统上使用gfortran提供以下内容：

Maximum value of supported integer kinds:
Kind name = INT8   kind value =  1     maximum =                                      127
Kind name = INT16  kind value =  2     maximum =                                    32767
Kind name = INT32  kind value =  4     maximum =                               2147483647
Kind name = INT64  kind value =  8     maximum =                      9223372036854775807
Kind name = ik32   kind value = 16     maximum =  170141183460469231731687303715884105727
Kind name = ikxx   kind value = 16     maximum =  170141183460469231731687303715884105727

Selected int kind value =  1           kind value =    1
Selected int kind value =  2           kind value =    1
Selected int kind value =  3           kind value =    2
Selected int kind value =  4           kind value =    2
Selected int kind value =  5           kind value =    4
Selected int kind value =  6           kind value =    4
Selected int kind value =  7           kind value =    4
Selected int kind value =  8           kind value =    4
Selected int kind value =  9           kind value =    4
Selected int kind value = 10           kind value =    8
Selected int kind value = 11           kind value =    8
Selected int kind value = 12           kind value =    8
Selected int kind value = 13           kind value =    8
Selected int kind value = 14           kind value =    8
Selected int kind value = 15           kind value =    8
Selected int kind value = 16           kind value =    8
Selected int kind value = 17           kind value =    8
Selected int kind value = 18           kind value =    8
Selected int kind value = 19           kind value =   16
Selected int kind value = 20           kind value =   16
Selected int kind value = 21           kind value =   16
Selected int kind value = 22           kind value =   16
Selected int kind value = 23           kind value =   16
Selected int kind value = 24           kind value =   16
Selected int kind value = 25           kind value =   16
Selected int kind value = 26           kind value =   16
Selected int kind value = 27           kind value =   16
Selected int kind value = 28           kind value =   16
Selected int kind value = 29           kind value =   16
Selected int kind value = 30           kind value =   16
Selected int kind value = 31           kind value =   16
Selected int kind value = 32           kind value =   16
Selected int kind value = 33           kind value =   16
Selected int kind value = 34           kind value =   16
Selected int kind value = 35           kind value =   16
Selected int kind value = 36           kind value =   16
Selected int kind value = 37           kind value =   16
Selected int kind value = 38           kind value =   16
Selected int kind value = 39           kind value =   -1

稍作修改后，程序在同一系统上使用ifort生成以下结果：

Maximum value of supported integer kinds:
Kind name = INT8   kind value =  1     maximum =                                      127
Kind name = INT16  kind value =  2     maximum =                                    32767
Kind name = INT32  kind value =  4     maximum =                               2147483647
Kind name = INT64  kind value =  8     maximum =                      9223372036854775807

Selected int kind value =  1           kind value =    1
Selected int kind value =  2           kind value =    1
Selected int kind value =  3           kind value =    2
Selected int kind value =  4           kind value =    2
Selected int kind value =  5           kind value =    4
Selected int kind value =  6           kind value =    4
Selected int kind value =  7           kind value =    4
Selected int kind value =  8           kind value =    4
Selected int kind value =  9           kind value =    4
Selected int kind value = 10           kind value =    8
Selected int kind value = 11           kind value =    8
Selected int kind value = 12           kind value =    8
Selected int kind value = 13           kind value =    8
Selected int kind value = 14           kind value =    8
Selected int kind value = 15           kind value =    8
Selected int kind value = 16           kind value =    8
Selected int kind value = 17           kind value =    8
Selected int kind value = 18           kind value =    8
Selected int kind value = 19           kind value =   -1

---

正如Vladimir F所建议的，您可以通过使用

selected\u int\u type

获得一些额外的精度，但它会随着硬件和编译器的不同而有所不同，根据问题的不同，可能会给您提供足够的精度。

您使用的编译器是什么？我得到了

61448471214136179596720592960.0000

这是一个预期的答案。小数出现是因为

cmb

是实的。您得到的是由于浮点计算而导致的错误。谢谢您的回答。我使用的是Absolft FORTRAN 95。如果我将cmb声明为整数，则它根本不起作用。有什么我可以做的错误，由于浮点计算？我没有它，使用英特尔的。它还可能取决于x86或x64 OS/CPU。如果您有x64编译器和系统-为什么不使用

selected\u int\u kind（32）

如果您关心精确的数字精度，请不要使用不可移植的

kind=16

，以指定四倍精度，而是使用许多其他可移植方式。它已经在这里重复了一百万次。即使

real*16

在我看来也更好，但最好是使用具有工作精度的命名常量，这很容易更改。在这种情况下，请尝试使用Cheery建议的最大整数类型。我大体上同意你的看法，但在这种情况下需要

int128

，并且它不是由ISO_FORTRAN_ENV定义的，尽管128位整数实际上在某些编译器中可用。这就是为什么我更喜欢注释中已经建议的

selected_int_kind

，而不是这个问题的ISO_FORTRAN_ENV kind常量。这种方法的一个问题是，您需要知道哪些种类值可以作为

selected_int_kind

的参数；我会通过更新我的回答来澄清这一点什么？您只需提供所需的位数，如果您得到它，则为。很简单，只需数一数问题中的数字。也许，也许不是。看上面，当然！它不是动态的，它是完全静态的！关键是你可能会从中得到可用的类型，但是你肯定不会从

iso\u fortran\u env

命名常量中得到它（还有其他方法）。我从来没有说过你可以保证从

选定的类型中获得所需的类型，这就是为什么我在前面的评论中写道，你需要看看你是否可以获得它，以及为什么我在第一篇评论中写道它在某些编译器中可用。