Fortran 简明教程
Fortran - Numbers
Fortran 中的数字由三种固有数据类型表示 −
Numbers in Fortran are represented by three intrinsic data types −
-
Integer type
-
Real type
-
Complex type
Integer Type
整型只能保存整数值。以下示例提取了一个普通四字节整数中可以保存的最大值 −
The integer types can hold only integer values. The following example extracts the largest value that could be hold in a usual four byte integer −
program testingInt
implicit none
integer :: largeval
print *, huge(largeval)
end program testingInt当您编译并执行以上程序时，将生成以下结果——
When you compile and execute the above program it produces the following result −
2147483647请注意， huge() 函数给出特定整数数据类型可以保存的最大数字。您还可以使用 kind 说明符指定字节数。以下示例对此进行了说明 -
Please note that the huge() function gives the largest number that can be held by the specific integer data type. You can also specify the number of bytes using the kind specifier. The following example demonstrates this −
program testingInt
implicit none
!two byte integer
integer(kind = 2) :: shortval
!four byte integer
integer(kind = 4) :: longval
!eight byte integer
integer(kind = 8) :: verylongval
!sixteen byte integer
integer(kind = 16) :: veryverylongval
!default integer
integer :: defval
print *, huge(shortval)
print *, huge(longval)
print *, huge(verylongval)
print *, huge(veryverylongval)
print *, huge(defval)
end program testingInt当您编译并执行以上程序时，将生成以下结果——
When you compile and execute the above program it produces the following result −
32767
2147483647
9223372036854775807
170141183460469231731687303715884105727
2147483647Real Type
它存储浮点数，例如 2.0、3.1415、-100.876 等。
It stores the floating point numbers, such as 2.0, 3.1415, -100.876, etc.
传统上有两种不同的 @ {s0} 类型：默认实数类型和 @ {s1} 类型。
Traditionally there were two different real types : the default real type and double precision type.
但是，Fortran 90/95 通过我们稍后将研究的 @ {s2} 说明符提供了对实数和整数数据类型精度的更多控制。
However, Fortran 90/95 provides more control over the precision of real and integer data types through the kind specifier, which we will study shortly.
以下示例展示了 real 数据类型的使用方法——
The following example shows the use of real data type −
program division
implicit none
! Define real variables
real :: p, q, realRes
! Define integer variables
integer :: i, j, intRes
! Assigning values
p = 2.0
q = 3.0
i = 2
j = 3
! floating point division
realRes = p/q
intRes = i/j
print *, realRes
print *, intRes
end program division当您编译并执行以上程序时，将生成以下结果——
When you compile and execute the above program it produces the following result −
0.666666687
0Complex Type
这用于存储复数。复数有两个部分：实部和虚部。两个连续的数值存储单元存储这两个部分。
This is used for storing complex numbers. A complex number has two parts : the real part and the imaginary part. Two consecutive numeric storage units store these two parts.
例如，复数 (3.0, -5.0) 等于 3.0 – 5.0i
For example, the complex number (3.0, -5.0) is equal to 3.0 – 5.0i
通用函数 @ {s3} 创建一个复数。它产生一个实部和虚部均为单精度的结果，而不管输入参数的类型如何。
The generic function cmplx() creates a complex number. It produces a result who’s real and imaginary parts are single precision, irrespective of the type of the input arguments.
program createComplex
implicit none
integer :: i = 10
real :: x = 5.17
print *, cmplx(i, x)
end program createComplex当您编译并执行以上程序时，将生成以下结果——
When you compile and execute the above program it produces the following result −
(10.0000000, 5.17000008)以下程序演示复数算术 −
The following program demonstrates complex number arithmetic −
program ComplexArithmatic
implicit none
complex, parameter :: i = (0, 1) ! sqrt(-1)
complex :: x, y, z
x = (7, 8);
y = (5, -7)
write(*,*) i * x * y
z = x + y
print *, "z = x + y = ", z
z = x - y
print *, "z = x - y = ", z
z = x * y
print *, "z = x * y = ", z
z = x / y
print *, "z = x / y = ", z
end program ComplexArithmatic当您编译并执行以上程序时，将生成以下结果——
When you compile and execute the above program it produces the following result −
(9.00000000, 91.0000000)
z = x + y = (12.0000000, 1.00000000)
z = x - y = (2.00000000, 15.0000000)
z = x * y = (91.0000000, -9.00000000)
z = x / y = (-0.283783793, 1.20270276)The Range, Precision and Size of Numbers
整数范围、浮点数的精度和大小取决于分配给特定数据类型的位数。
The range on integer numbers, the precision and the size of floating point numbers depends on the number of bits allocated to the specific data type.
下表显示了整数的位数和范围 −
The following table displays the number of bits and range for integers −
Number of bits |
Maximum value |
Reason |
64 |
9,223,372,036,854,774,807 |
(2**63)–1 |
32 |
2,147,483,647 |
(2**31)–1 |
下表显示了实数的位数、最小值和最大值以及精度。
The following table displays the number of bits, smallest and largest value, and the precision for real numbers.
Number of bits |
Largest value |
Smallest value |
Precision |
64 |
0.8E+308 |
0.5E–308 |
15–18 |
32 |
1.7E+38 |
0.3E–38 |
6-9 |
以下示例展示了这一点 −
The following examples demonstrate this −
program rangePrecision
implicit none
real:: x, y, z
x = 1.5e+40
y = 3.73e+40
z = x * y
print *, z
end program rangePrecision当您编译并执行以上程序时，将生成以下结果——
When you compile and execute the above program it produces the following result −
x = 1.5e+40
1
Error : Real constant overflows its kind at (1)
main.f95:5.12:
y = 3.73e+40
1
Error : Real constant overflows its kind at (1)现在让我们使用一个较小的数字 −
Now let us use a smaller number −
program rangePrecision
implicit none
real:: x, y, z
x = 1.5e+20
y = 3.73e+20
z = x * y
print *, z
z = x/y
print *, z
end program rangePrecision当您编译并执行以上程序时，将生成以下结果——
When you compile and execute the above program it produces the following result −
Infinity
0.402144760现在让我们观测下溢 −
Now let’s watch underflow −
program rangePrecision
implicit none
real:: x, y, z
x = 1.5e-30
y = 3.73e-60
z = x * y
print *, z
z = x/y
print *, z
end program rangePrecision当您编译并执行以上程序时，将生成以下结果——
When you compile and execute the above program it produces the following result −
y = 3.73e-60
1
Warning : Real constant underflows its kind at (1)
Executing the program....
$demo
0.00000000E+00
InfinityThe Kind Specifier
在科学编程中，人们经常需要了解正在完成工作的硬件平台的数据范围和精度。
In scientific programming, one often needs to know the range and precision of data of the hardware platform on which the work is being done.
固有函数 @ {s4} 允许您在运行程序之前查询硬件数据表示的详细信息。
The intrinsic function kind() allows you to query the details of the hardware’s data representations before running a program.
program kindCheck
implicit none
integer :: i
real :: r
complex :: cp
print *,' Integer ', kind(i)
print *,' Real ', kind(r)
print *,' Complex ', kind(cp)
end program kindCheck当您编译并执行以上程序时，将生成以下结果——
When you compile and execute the above program it produces the following result −
Integer 4
Real 4
Complex 4您还可以检查所有数据类型的种类 −
You can also check the kind of all data types −
program checkKind
implicit none
integer :: i
real :: r
character :: c
logical :: lg
complex :: cp
print *,' Integer ', kind(i)
print *,' Real ', kind(r)
print *,' Complex ', kind(cp)
print *,' Character ', kind(c)
print *,' Logical ', kind(lg)
end program checkKind当您编译并执行以上程序时，将生成以下结果——
When you compile and execute the above program it produces the following result −
Integer 4
Real 4
Complex 4
Character 1
Logical 4