## 9.2.3 Bit Functions

Integer data types are represented internally in binary twos complement notation. Bit positions in the binary representation are numbered from right (least significant bit) to left (most significant bit); the rightmost bit position is numbered 0.

The intrinsic functions IAND, IOR, IEOR, and NOT operate on all of the bits of their argument (or arguments). Bit 0 of the result comes from applying the specified logical operation to bit 0 of the argument. Bit 1 of the result comes from applying the specified logical operation to bit 1 of the argument, and so on for all of the bits of the result.

The functions ISHFT and ISHFTC shift binary patterns.

The functions IBSET, IBCLR, BTEST, and IBITS and the subroutine MVBITS operate on bit fields.

A bit field is a contiguous group of bits within a binary pattern. Bit fields are specified by a starting bit position and a length. A bit field must be entirely contained in its source operand.

For example, the integer 47 is represented by the following:

Binary pattern: | 0...0101111
Bit position: | n...6543210
| Where n is the number of bit positions in the numeric storage unit.

You can refer to the bit field contained in bits 3 through 6 by specifying a starting position of 3 and a length of 4.

Negative integers are represented in twos complement notation. For example, the integer -47 is represented by the following:

Binary pattern: | 1...1010001
Bit position: | n...6543210
| Where n is the number of bit positions in the numeric storage unit.

The value of bit position n is as follows:

       1 for a negative number
       0 for a non-negative number

All the high-order bits in the pattern from the last significant bit of the value up to bit n are the same as bit n.

IBITS and MVBITS operate on general bit fields. Both the starting position of a bit field and its length are arguments to these intrinsics. IBSET, IBCLR, and BTEST operate on 1-bit fields. They do not require a length argument.

For IBSET, IBCLR, and BTEST, the bit position range is as follows:

- 0 to 63 for INTEGER(8) and LOGICAL(8)
- 0 to 31 for INTEGER(4) and LOGICAL(4)
- 0 to 15 for INTEGER(2) and LOGICAL(2)
- 0 to 7 for BYTE, INTEGER(1), and LOGICAL(1)

For IBITS, the bit position can be any number. The length range is 0 to 63 on Alpha and ia64 processors; 0 to 31 on ia32 processors.

The following example demonstrates IBSET, IBCLR, and BTEST:

    I = 4
    J = IBSET (I,5)
    PRINT *, 'J = ',J
    K = IBCLR (J,2)
    PRINT *, 'K = ',K
    PRINT *, 'Bit 2 of K is ',BTEST(K,2)
    END

The results are: J = 36, K = 32, and Bit 2 of K is F.

For optimum selection of performance and memory requirements, Compaq Fortran provides the following integer data types:

Data Type | Storage Required (in bytes)
--- | ---
INTEGER(1) | 1
INTEGER(2) | 2
INTEGER(4) | 4
INTEGER(8) | 8

The bit manipulation functions each have a generic form that operates on all of these integer types and a specific form for each type.

When you specify the intrinsic functions that refer to bit positions or that shift binary patterns within a storage unit, be careful that you do not create a value that is outside the range of integers representable by the data type. If you shift by an amount greater than or equal to the size of the object you're shifting, the result is 0.

Consider the following:

    INTEGER(2) I,J
    I = 1
    J = 17
    I = ISHFT(I,J)

The variables I and J have INTEGER(2) type. Therefore, the generic function ISHFT maps to the specific function IISHFT, which returns an INTEGER(2) result. INTEGER(2) results must be in the range -32768 to 32767, but the value 1, shifted left 17 positions, yields the binary pattern 1 followed by 17 zeros, which represents the integer 131072. In this case, the result in I is 0.

The previous example would be valid if I was INTEGER(4), because ISHFT would then map to the specific function JISHFT, which returns an INTEGER(4) value.

If ISHFT is called with a constant first argument, the result will either be the default integer size or the smallest integer size that can contain the first argument, whichever is larger.

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