我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）。子程序代码是
!
! 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
适用于中等大小的值。但是，如果我使用n = 100和k = 55，我得到以下
61448471214136179596720592959.998
小数部分显然是错误的，因为组合总是整数。主程序是
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
BTW：kind = 16是我机器上的四倍精度。
由于
答案 0 :(得分：1)
根据您使用的整数的大小，可能有便携式方法在您的系统上使用扩展精度整数。标准模块ISO_FORTRAN_ENV应该定义许多整数种类（INT8，INT16，INT32，INT64等）。从Fortran 2008开始，它们包含在数组INTEGER_KINDS中，但目前这种实现看起来很不稳定。
如果你仍然没有空间，你有两个选择：根据你的精确度重新设计你的问题，或寻找扩展或任意精度的数学库。令人高兴的是，LBNL在http://crd-legacy.lbl.gov/~dhbailey/mpdist/
下列出了一些此类库<强> 更新
selected_int_kind是创建扩展精度值的替代动态方法，但您仍需要知道编译器接受哪些“类型”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
通过稍加修改，程序在同一系统上使用ifort生成以下内容：
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
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建议的那样，使用selected_int_type可以获得一些额外的精度，但它会因硬件和编译器的不同而有所不同，根据问题可能会给出足够的精度。