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This chapter contains the following topics:
Table 9-1 lists the intrinsic data types provided by Compaq Fortran, the storage required, and valid numeric ranges.
| Data Type | Bytes | Description |
|---|---|---|
|
BYTE
(INTEGER*1) |
1 (8 bits) | A BYTE declaration is a signed integer data type equivalent to INTEGER*1 or INTEGER (KIND=1). |
| INTEGER | 1, 2, 4, or 8 | Signed integer whose size is controlled by a kind type parameter or, if a kind type parameter (or size specifier) is omitted, certain f90 or fort command options (see Section 9.2.1). |
|
INTEGER (KIND=1)
INTEGER*1 |
1 (8 bits) | Signed integer value from --128 to 127 (--2**7 to 2**7--1). Unsigned values from 0 to 255 (2**8-1) 1. |
|
INTEGER (KIND=2)
INTEGER*2 |
2 (16 bits) | Signed integer value from --32,768 to 32,767 (--2**15 to 2**15--1). Unsigned values from 0 to 65535 (2**16-1) 1. |
|
INTEGER (KIND=4)
INTEGER*4 |
4 (32 bits) | Signed integer value from --2,147,483,648 to 2,147,483,647 (--2**31 to 2**31--1). Unsigned values from 0 to 4,294,967,295 (2**32-1) 1. |
|
INTEGER (KIND=8)
INTEGER*8 |
8 (64 bits) | Signed integer value from --9,223,372,036,854,775,808 to 9,223,372,036,854,775,807 (--2**63 to 2**63--1). |
| LOGICAL | 1, 2, 4, or 8 | Logical value whose size is controlled by a kind type parameter or, if a kind type parameter (or size specifier) is omitted, certain f90 command options (see Section 9.3). |
|
LOGICAL (KIND=1)
LOGICAL*1 |
1 (8 bits) | Logical values .TRUE. or .FALSE. 2 |
|
LOGICAL (KIND=2)
LOGICAL*2 |
2 (16 bits) | Logical values .TRUE. or .FALSE. 2 |
|
LOGICAL (KIND=4)
LOGICAL*4 |
4 (32 bits) | Logical values .TRUE. or .FALSE. 2 |
|
LOGICAL (KIND=8)
LOGICAL*8 |
8 (64 bits) | Logical values .TRUE. or .FALSE. 2 |
| REAL | 4, 8, or 16 | Real floating-point numbers whose size is controlled by a kind type parameter or, if a kind type parameter (or size specifier) is omitted, certain f90 command options (see Section 9.4.1). |
|
REAL (KIND=4)
REAL*4 |
4 (32 bits) | Single-precision real floating-point values in IEEE S_float format ranging from 1.17549435E--38 to 3.40282347E38. Values between 1.17549429E--38 and 1.40129846E--45 are denormalized 3. You cannot write a constant for a denormalized number. |
|
DOUBLE PRECISION
REAL (KIND=8) REAL*8 |
8 (64 bits) | Double-precision real floating-point values in IEEE T_float format ranging from 2.2250738585072013D-308 to 1.7976931348623158D308. Values between 2.2250738585072008D--308 and 4.94065645841246544D--324 are denormalized 3. You cannot write a constant for a denormalized number. |
|
REAL (KIND=16)
REAL*16 |
16 (128 bits) | Extended-precision real floating-point values in Compaq IEEE style X_float format ranging from 6.4751751194380251109244389582276465524996Q-4966 to 1.189731495357231765085759326628007016196477Q4932. |
| COMPLEX | 8, 16, or 32 | Complex floating-point numbers whose size is controlled by a kind type parameter or, if a kind type parameter (or size specifier) is omitted, the f90 command options described in Section 9.4.1. |
|
COMPLEX (KIND=4)
COMPLEX*8 |
8 (64 bits) | Single-precision complex floating-point values in a pair of IEEE S_float format parts: real and imaginary. The real and imaginary parts range from 1.17549435E--38 to 3.40282347E38. Values between 1.17549429E--38 and 1.40129846E--45 are denormalized 3. You cannot write a constant for a denormalized number. |
|
DOUBLE COMPLEX
COMPLEX (KIND=8) COMPLEX*16 |
16 (128 bits) | Double-precision complex floating-point values in a pair of IEEE T_float format parts: real and imaginary. The real and imaginary parts each range from 2.2250738585072013D-308 to 1.7976931348623158D308. Values between 2.2250738585072008D--308 and 4.94065645841246544D--324 are denormalized 3. You cannot write a constant for a denormalized number. |
|
COMPLEX (KIND=16)
COMPLEX*32 |
32 (256 bits) | Extended-precision complex floating-point values in a pair of Compaq IEEE style X_float format parts: real and imaginary. The real and imaginary parts each range from 6.4751751194380251109244389582276465524996Q-4966 to 1.189731495357231765085759326628007016196477Q4932. |
| CHARACTER | 1 byte (8 bits) per character | Character data represented by character code convention. Character declarations can be in the form CHARACTER(LEN= n), CHARACTER( n), or CHARACTER* n, where n is the number of bytes or n can be (*) to indicate passed-length format. |
| HOLLERITH | 1 byte (8 bits) per Hollerith character | Hollerith constants. |
In addition to the intrinsic numeric data types, you can also define
nondecimal (binary, octal, or hexadecimal) constants as explained in
the Compaq Fortran Language Reference Manual.
9.2 Integer Data Representations
Integer data lengths can be one, two, four, or eight bytes in length.
Integer data is signed with the sign bit being 0 (zero) for positive numbers and 1 for negative numbers.
To improve performance, avoid using 2-byte or 1-byte integer
declarations (see Chapter 5).
9.2.1 Integer Declarations and f90/fort Compiler Options
The default size used for an INTEGER data declaration without a kind parameter is INTEGER (KIND=4) (same as INTEGER*4), unless you do one of the following:
Intrinsic INTEGER (KIND=1) or INTEGER*1 signed values range from --128 to 127 and are stored in a two's complement representation. For example:
+22 = 16(hex) -7 = F9(hex) |
INTEGER (KIND=1) or INTEGER*1 values are stored in one byte, as shown in Figure 9-1.
Figure 9-1 INTEGER (KIND=1) or INTEGER*1 Representation
Intrinsic INTEGER (KIND=2) or INTEGER*2 signed values range from --32,768 to 32,767 and are stored in a two's complement representation. For example:
+22 = 0016(hex) -7 = FFF9(hex) |
INTEGER (KIND=2) or INTEGER*2 values are stored in two contiguous bytes, as shown in Figure 9-2.
Figure 9-2 INTEGER (KIND=2) or INTEGER*2 Representation
Intrinsic INTEGER (KIND=4) or INTEGER*4 signed values range from --2,147,483,648 to 2,147,483,647 and are stored in a two's complement representation. INTEGER (KIND=4) or INTEGER*4 values are stored in four contiguous bytes, as shown in Figure 9-3.
Figure 9-3 INTEGER (KIND=4) or INTEGER*4 Representation
Intrinsic INTEGER (KIND=8) or INTEGER*8 signed values range from --9,223,372,036,854,775,808 to 9,223,372,036,854,775,807 and are stored in a two's complement representation. INTEGER*8 or INTEGER (KIND=8) values are stored in eight contiguous bytes, as shown in Figure 9-4.
Figure 9-4 INTEGER (KIND=8) or INTEGER*8 Representation
Logical data can be one, two, four, or eight bytes in length.
The default size used for a LOGICAL data declaration without a kind parameter (or size specifier) is LOGICAL (KIND=4) (same as LOGICAL*4), unless you do one of the following:
To improve default performance, avoid using 2-byte or 1-byte logical declarations (see Chapter 5).
Intrinsic LOGICAL*1 or LOGICAL (KIND=1) values are stored in a single byte.
Logical (intrinsic) values can also be stored in the following sizes of contiguous bytes starting on an arbitrary byte boundary:
The low-order bit determines whether the logical value is true or false. Logical variables can also be interpreted as integer data (an extension to the Fortran 95/90 standards). For example, in addition to having logical values .TRUE. and .FALSE., LOGICAL*1 data can also have values in the range --128 to 127.
LOGICAL*1, LOGICAL*2, LOGICAL*4, and LOGICAL*8 data representations appear in Figure 9-5.
Figure 9-5 LOGICAL Representations
Floating-point numbers are stored on Compaq Tru64 UNIX systems in standard IEEE little endian floating-point notation, as follows:
COMPLEX numbers use a pair of little endian REAL values to denote the real and imaginary parts of the data, as follows:
All floating-point formats represent fractions in sign-magnitude notation, with the binary radix point to the right of the most-significant bit. Fractions are assumed to be normalized, and therefore the most-significant bit is not stored. This is called hidden bit normalization. The hidden bit is assumed to be 1 unless the exponent is 0. If the exponent equals 0, then the value represented is denormalized (subnormal) or plus or minus 0 (zero).
For an explanation of the representation of NaN, Infinity, and related
IEEE exceptional values on Alpha systems, see Section 9.4.8.
9.4.1 REAL and COMPLEX Declarations and f90/fort Compiler Options
The default sizes for REAL and COMPLEX data declarations are as follows:
To control the size of all REAL or COMPLEX declarations without a kind parameter, use the f90 command -real_size nn , -r8 , or -r16 (see Section 3.78).
You can explicitly declare the length of a REAL or a COMPLEX declaration using a kind parameter or specify DOUBLE PRECISION or DOUBLE COMPLEX. To control the size of all DOUBLE PRECISION and DOUBLE COMPLEX declarations, use the f90 command -double_size nn (see Section 3.78).
Intrinsic REAL kinds are 4 (single precision), 8 (double precision),
and 16 (extended precision). Intrinsic COMPLEX kinds are also 4 (single
precision), 8 (double precision), and 16 (extended precision), such as
REAL (KIND=4) for single-precision floating-point data. To obtain the
kind of a variable, use the KIND intrinsic function. You can also use a
size specifier, such as REAL*4, but be aware this is an extension to
the Fortran 95/90 standards.
9.4.2 REAL (KIND=4) or REAL*4 Representation
Intrinsic REAL (KIND=4) or REAL*4 (single precision REAL) data occupies four contiguous bytes stored in IEEE S_float format. Bits are labeled from the right, 0 through 31, as shown in Figure 9-6.
Figure 9-6 REAL (KIND=4) or REAL*4 Representation
The form of REAL (KIND=4) or REAL*4 data is sign magnitude, with:
The value of data is in the approximate range: 1.17549435E--38 (normalized) to 3.40282347E38. The IEEE denormalized limit is 1.40129846E--45.
The precision is approximately one part in 2**23, typically seven
decimal digits.
9.4.3 REAL (KIND=8) or REAL*8 Representation
Intrinsic REAL (KIND=8) or REAL*8 (same as DOUBLE PRECISION) data occupies eight contiguous bytes stored in IEEE T_float format. Bits are labeled from the right, 0 through 63, as shown in Figure 9-7.
Figure 9-7 REAL (KIND=8) or REAL*8 Representation
The form of REAL (KIND=8) or REAL*8 data is sign magnitude, with:
The value of data is in the approximate range: 2.2250738585072013D-308 (normalized) to 1.7976931348623158D308. The IEEE denormalized limit is 4.94065645841246544D-324.
The precision is approximately one part in 2**52, typically 15 decimal
digits.
9.4.4 REAL (KIND=16) or REAL*16 Representation
Intrinsic REAL (KIND=16) or REAL*16 (extended precision) data occupies 16 contiguous bytes stored in Compaq IEEE style X_float format. Bits are labeled from the right, 0 through 127, as shown in Figure 9-8.
Figure 9-8 REAL (KIND=16) or REAL*16 Representation
The form of REAL*16 data is sign magnitude, with:
The value of data is in the approximate range: 6.4751751194380251109244389582276465524996Q-4966 to 1.189731495357231765085759326628007016196477Q4932.
Unlike other floating-point formats, there is little if any performance penalty from using denormalized extended-precision numbers. This is because accessing denormalized REAL (KIND=16) numbers does not result in an arithmetic trap (the extended-precision format is emulated in software). The smallest normalized number is 3.362103143112093506262677817321753Q-4932.
The precision is approximately one part in 2**112 or typically 33
decimal digits.
9.4.5 COMPLEX (KIND=4) or COMPLEX*8 Representation
Intrinsic COMPLEX (KIND=4) or COMPLEX*8 (single-precision COMPLEX) data is eight contiguous bytes containing a pair of REAL (KIND=4) or REAL*4 values stored in IEEE S_float format.
The low-order four bytes contain REAL (KIND=4) data that represents the real part of the complex number. The high-order four bytes contain REAL (KIND=4) data that represents the imaginary part of the complex number, as shown in Figure 9-9.
Figure 9-9 COMPLEX (KIND=4) or COMPLEX*8 Representation
The limits and underflow characteristics for REAL (KIND=4) or REAL*4
apply to the two separate real and imaginary parts of a COMPLEX
(KIND=4) or COMPLEX*8 number. Like REAL (KIND=4) numbers, the sign bit
representation is 0 (zero) for positive numbers and 1 for negative
numbers.
9.4.6 COMPLEX (KIND=8) or COMPLEX*16 Representation
Intrinsic COMPLEX (KIND=8) or COMPLEX*16 (same as DOUBLE COMPLEX) data is 16 contiguous bytes containing a pair of REAL*8 values stored in IEEE T_float format.
The low-order eight bytes contain REAL (KIND=8) data that represents the real part of the complex data. The high-order eight bytes contain REAL (KIND=8) data that represents the imaginary part of the complex data, as shown in Figure 9-10.
Figure 9-10 COMPLEX (KIND=8) or COMPLEX*16 Representation
The limits and underflow characteristics for REAL (KIND=8) apply to the
two separate real and imaginary parts of a COMPLEX (KIND=8) or
COMPLEX*16 number. Like REAL (KIND=8) numbers, the sign bit
representation is 0 (zero) for positive numbers and 1 for negative
numbers.
9.4.7 COMPLEX (KIND=16) or COMPLEX*32 Representation
Intrinsic COMPLEX (KIND=16) or COMPLEX*32 (extended precision) data is 32 contiguous bytes containing a pair of REAL*16 values stored in Compaq IEEE style X_float.
The low-order 16 bytes contain REAL (KIND=16) data that represents the real part of the complex data. The high-order 16 bytes contain REAL (KIND=16) data that represents the imaginary part of the complex data, as shown in Figure 9-11.
Figure 9-11 COMPLEX (KIND=16) or COMPLEX*32 Representation
The limits and underflow characteristics for REAL (KIND=16) apply to the two separate real and imaginary parts of a COMPLEX (KIND=16) or COMPLEX*32 number. Like REAL (KIND=16) numbers, the sign bit representation is 0 (zero) for positive numbers and 1 for negative numbers.
Exceptional values usually result from a computation and include plus infinity, minus infinity, NaN, and denormalized numbers.
Floating-point numbers can be one of the following:
A NaN or infinity value might result from a calculation that contains a divide by zero, overflow, or invalid data.
A denormalized number occurs when the result of a calculation falls within the denormalized range for that data type (subnormal value).
To control floating-point exception handling at run time for the main program, use the appropriate -fpen option. The callable for_set_fpe routine allows further control for subprogram use or conditional use during program execution.
If an exceptional value is used in a calculation, an unrecoverable exception can occur unless you specify the appropriate -fpen option or use the for_set_fpe routine. Denormalized numbers can be processed as is, set equal to zero with program continuation or a program stop, and generate warning messages (see Section 3.44).
Table 9-2 lists the hexadecimal (hex) values of the IEEE exceptional floating-point numbers for S_float (single precision), T_float (double precision), and X_float (extended precision) formats.
| Exceptional Number | Hex Value |
|---|---|
| S_float Representation | |
| Infinity (+) | Z ' 7F800000 ' |
| Infinity (--) | Z ' FF800000 ' |
| Zero (+0) | Z ' 00000000 ' |
| Zero (--0) | Z ' 80000000 ' |
| Quiet NaN (+) | From Z ' 7FC00000 ' to Z ' 7FFFFFFF ' |
| Quiet NaN (--) | From Z ' FFC00000 ' to Z ' FFFFFFFF ' |
| Signaling NaN (+) | From Z ' 7F800001 ' to Z ' 7FBFFFFF ' |
| Signaling NaN (--) | From Z ' FF800001 ' to Z ' FFBFFFFF ' |
| T_float Representation | |
| Infinity (+) | Z ' 7FF0000000000000 ' |
| Infinity (--) | Z ' FFF0000000000000 ' |
| Zero (+0) | Z ' 0000000000000000 ' |
| Zero (-0) | Z ' 8000000000000000 ' |
| Quiet NaN (+) | From Z ' 7FF8000000000000 ' to Z ' 7FFFFFFFFFFFFFFF ' |
| Quiet NaN (--) | From Z ' FFF8000000000000 ' to Z ' FFFFFFFFFFFFFFFF ' |
| Signaling NaN (+) | From Z ' 7FF0000000000001 ' to Z ' 7FF7FFFFFFFFFFFF ' |
| Signaling NaN (--) | From Z ' FFF0000000000001 ' to Z ' FFF7FFFFFFFFFFFF ' |
| X_float Representation | |
| Infinity (+) | Z ' 7FFF0000000000000000000000000000 ' |
| Infinity (--) | Z ' FFFF0000000000000000000000000000 ' |
| Zero (+0) | Z ' 000000000000000000000000000000000 ' |
| Zero (--0) | Z ' 800000000000000000000000000000000 ' |
| Quiet NaN (+) | From Z ' 7FFF80000000000000000000000000000 ' to Z ' 7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF ' |
| Quiet NaN (--) | From Z ' FFFF80000000000000000000000000000 ' to Z ' FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF ' |
| Signaling NaN (+) | From Z ' 7FFF00000000000000000000000000001 ' to Z ' 7FFF7FFFFFFFFFFFFFFFFFFFFFFFFFFFF ' |
| Signaling NaN (--) | From Z ' FFFF00000000000000000000000000001 ' to Z ' FFFF7FFFFFFFFFFFFFFFFFFFFFFFFFFFF ' |
Compaq Fortran supports IEEE exception handling, allowing you to test for infinity by using a comparison of floating-point data (such as generating positive infinity by using a calculation like x=1.0/0 and comparing x to the calculated number).
The appropriate f90 command -fpen options or calling the for_set_fpe routine with appropriate arguments allows program continuation when a calculation results in a divide by zero, overflow, or invalid data arithmetic exception, generating an exceptional value (a NaN or Infinity (+ or --)).
To test for a NaN when Compaq Fortran allows continuation for arithmetic exceptions, you can use the ISNAN intrinsic function.
For example, you might use the following code to test a DOUBLE PRECISION (REAL (KIND=8)) value:
DOUBLE PRECISION A, B, F
A = 0.
B = 0.
! Perform calculations with variables A and B
.
.
.
! f contains the value to check against a particular NaN
F = A / B
IF (ISNAN(F)) THEN
WRITE (6,*) '--> Variable F contains a NaN value <--'
ENDIF
! Inform user that f has the hardware quiet NaN value
! Perform calculations with variable F (or stop program early)
END PROGRAM
|
This program might be compiled with -fpe2 or -fpe4 to allow:
% f90 -fpe2 isnan.for % a.out forrtl: error: floating invalid --> Variable F contains a NaN value <-- forrtl: info: 1 floating invalid traps |
The FP_CLASS intrinsic function is also available to check for exceptional values (see the Compaq Fortran Language Reference Manual and the file /usr/include/fordef.f ).
A character string is a contiguous sequence of bytes in memory, as shown in Figure 9-12.
Figure 9-12 CHARACTER Data Representation
A character string is specified by two attributes: the address A of the first byte of the string, and the length L of the string in bytes. The length L of a string is in the range 1 through 65,535.
Hollerith constants are stored internally, one character per byte. When Hollerith constants contain the ASCII representation of characters, they resemble the storage of character data (see Figure 9-12).
When Hollerith constants store numeric data, they usually have a length of one, two, four, or eight bytes and resemble the corresponding numeric data type.
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