Chapter 6 Intrinsic Functions

This chapter tabulates and explains the set of intrinsic functions that are part of Sun FORTRAN 77. (For information about Fortran library routines, see the Fortran Library Reference.)

Intrinsic functions that are Sun extensions of the ANSI FORTRAN 77 standard are marked with @.

Intrinsic functions have generic and specific names when they accept arguments of more than one data type. In general, the generic name returns a value with the same data type as its argument. However, there are exceptions such as the type conversion functions (Table 6-2) and the inquiry functions (Table 6-7). The function may also be called by one of its specific names to handle a specific argument data type.

With functions that work on more than one data item (e.g. sign(a1,a2) ), all the data arguments must be the same type.

In the following tables, the FORTRAN 77 intrinsic functions are listed by:

• Intrinsic Function -description of what the function does

• Definition - a mathematical definition

• No. of Args. - number of arguments the function accepts

• Generic Name - the function's generic name

• Specific Names - the function's specific names

• Argument Type - data type associated with each specific name

• Function Type - data type returned for specific argument data type

---

Note -

Compiler options -dbl, -i2, -r8, and -xtypemap change the default sizes of variables and have an effect on intrinsic references. See "Remarks", and the discussion of default sizes and alignment in "Size and Alignment of Data Types ".

---

Arithmetic and Mathematical Functions

This section details arithmetic, type conversion, trigonometric, and other functions. "a" stands for a function's single argument, "a1" and "a2" for the first and second arguments of a two argument function, and "ar" and "ai" for the real and imaginary parts of a function's complex argument.

Note that REAL*16 and COMPLEX*32 are SPARC only.

Arithmetic

Table 6-1 Arithmetic Functions

Intrinsic Function	Definition	No. of  Args.	Generic  Name	Specific  Names	Argument  Type	Function Type
Absolute value  See Note (6).	|a| =    (ar**2+ai**2)**.5	1	ABS	IABS ABS DABS CABS QABS @ ZABS @ CDABS @ CQABS @	INTEGER REAL DOUBLE COMPLEX REAL*16 DOUBLE COMPLEX DOUBLE COMPLEX COMPLEX*32	INTEGER REAL DOUBLE REAL REAL*16 DOUBLE DOUBLE REAL*16
Truncation  See Note (1).	int(a)	1	AINT	AINT DINT QINT @	REAL DOUBLE REAL*16	REAL DOUBLE REAL*16
Nearest whole number	int(a+.5) if a 0­­­­  int(a-.5) if a < 0	1	ANINT	ANINT DNINT QNINT @	REAL DOUBLE REAL*16	REAL DOUBLE REAL*16
Nearest integer	int(a+.5) if a 0  int(a-.5) if a < 0	1	NINT	NINT IDNINT IQNINT @	REAL DOUBLE REAL*16	INTEGER INTEGER INTEGER
Remainder  See Note (1).	a1-int(a1/a2)*a2	2	MOD	MOD AMOD DMOD QMOD @	INTEGER REAL DOUBLE REAL*16	INTEGER REAL DOUBLE REAL*16
Transfer of sign	|a1| if a2 0  -|a1| if a2 < 0	2	SIGN	ISIGN SIGN DSIGN QSIGN @	INTEGER REAL DOUBLE REAL*16	INTEGER REAL DOUBLE REAL*16
Positive difference	a1-a2 if a1 > a2  0 if a1 £ a2	2	DIM	IDIM DIM DDIM QDIM @	INTEGER REAL DOUBLE REAL*16	INTEGER REAL DOUBLE REAL*16
Double and quad products	a1 * a2	2	-	DPROD QPROD @	REAL DOUBLE	DOUBLE REAL*16
Choosing largest value	max(a1, a2, ...)	2	MAX	MAX0 AMAX1 DMAX1 QMAX1 @	INTEGER REAL DOUBLE REAL*16	INTEGER REAL DOUBLE REAL*16
			AMAX0	AMAX0	INTEGER	REAL
			MAX1	MAX1	REAL	INTEGER
Choosing smallest value	min(a1, a2, ...)	2	MIN	MIN0 AMIN1 DMIN1 QMIN1 @	INTEGER REAL DOUBLE REAL*16	INTEGER REAL DOUBLE REAL*16
			AMIN0	AMIN0	INTEGER	REAL
			MIN1	MIN1	REAL	INTEGER

Type Conversion

Table 6-2 Type Conversion Functions

Conversion to	No. of Args	Generic Name	Specific   Names	Argument Type	Function Type
INTEGER See Note (1).	1	INT	- INT IFIX IDINT - - - IQINT @	INTEGER REAL REAL DOUBLE COMPLEX COMPLEX*16 COMPLEX*32 REAL*16	INTEGER INTEGER INTEGER INTEGER INTEGER INTEGER INTEGER INTEGER
REAL See Note (2).	1	REAL	REAL FLOAT - SNGL SNGLQ @ - - -	INTEGER INTEGER REAL DOUBLE REAL*16 COMPLEX COMPLEX*16 COMPLEX*32	REAL REAL REAL REAL REAL REAL REAL REAL
DOUBLE See Note (3).	1	DBLE	DBLE DFLOAT DREAL @ DBLEQ @ - - - -	INTEGER INTEGER REAL DOUBLE REAL*16 COMPLEX COMPLEX*16 COMPLEX*32	DOUBLE PRECISION DOUBLE PRECISION DOUBLE PRECISION DOUBLE PRECISION DOUBLE PRECISION DOUBLE PRECISION DOUBLE PRECISION DOUBLE PRECISION
REAL*16 See Note (3').	1	QREAL@ QEXT @	QREAL @ QFLOAT @ - QEXT @ QEXTD @ - - - -	INTEGER INTEGER REAL INTEGER DOUBLE REAL*16 COMPLEX COMPLEX*16 COMPLEX*32	REAL*16 REAL*16 REAL*16 REAL*16 REAL*16 REAL*16 REAL*16 REAL*16 REAL*16
COMPLEX See Notes (4) and (8).	1 or 2	CMPLX	- - - - - - -	INTEGER REAL DOUBLE REAL*16 COMPLEX COMPLEX*16 COMPLEX*32	COMPLEX COMPLEX COMPLEX COMPLEX COMPLEX COMPLEX COMPLEX
DOUBLE COMPLEX See Note (8).	1 or 2	DCMPLX@	- - - - - - -	INTEGER REAL DOUBLE REAL*16 COMPLEX COMPLEX*16 COMPLEX*32	DOUBLE COMPLEX DOUBLE COMPLEX DOUBLE COMPLEX DOUBLE COMPLEX DOUBLE COMPLEX DOUBLE COMPLEX DOUBLE COMPLEX
COMPLEX*32 See Note (8).	1 or 2	QCMPLX@	- - - - - - -	INTEGER REAL DOUBLE REAL*16 COMPLEX COMPLEX*16 COMPLEX*32	COMPLEX*32 COMPLEX*32 COMPLEX*32 COMPLEX*32 COMPLEX*32 COMPLEX*32 COMPLEX*32
INTEGER See Note (5).	1	- -	ICHAR IACHAR @	CHARACTER	INTEGER
CHARACTER See Note (5).	1	- -	CHAR ACHAR @	INTEGER	CHARACTER

On an ASCII machine, including Sun systems:

• ACHAR is a nonstandard synonym for CHAR

• IACHAR is a nonstandard synonym for ICHAR

On a non-ASCII machine, ACHAR and IACHAR were intended to provide a way to deal directly with ASCII.

Trigonometric Functions

Table 6-3 Trigonometric Functions

Intrinsic Function	Definition	Args	Generic Name	Specific   Names	Argument Type	Function Type
Sine  See Note (7).	sin(a)	1	SIN	SIN DSIN QSIN @ CSIN ZSIN @ CDSIN @ CQSIN @	REAL DOUBLE REAL*16 COMPLEX DOUBLE COMPLEX DOUBLE COMPLEX COMPLEX*32	REAL DOUBLE REAL*16 COMPLEX DOUBLE COMPLEX DOUBLE COMPLEX COMPLEX*32
Sine (degrees)  See Note (7).	sin(a)	1	SIND @	SIND @ DSIND @ QSIND @	REAL DOUBLE REAL*16	REAL DOUBLE REAL*16
Cosine  See Note (7).	cos(a)	1	COS	COS DCOS QCOS @ CCOS ZCOS @ CDCOS @ CQCOS @	REAL DOUBLE REAL*16 COMPLEX DOUBLE COMPLEX DOUBLE COMPLEX COMPLEX*32	REAL DOUBLE REAL*16 COMPLEX DOUBLE COMPLEX DOUBLE COMPLEX COMPLEX*32
Cosine (degrees)  See Note (7).	cos(a)	1	COSD @	COSD @ DCOSD @ QCOSD @	REAL DOUBLE REAL*16	REAL DOUBLE REAL*16
Tangent  See Note (7).	tan(a)	1	TAN	TAN DTAN QTAN @	REAL DOUBLE REAL*16	REAL DOUBLE REAL*16
Tangent (degrees)  See Note (7).	tan(a)	1	TAND @	TAND @ DTAND @ QTAND @	REAL DOUBLE REAL*16	REAL DOUBLE REAL*16
Arcsine  See Note (7).	arcsin(a)	1	ASIN	ASIN DASIN QASIN @	REAL DOUBLE REAL*16	REAL DOUBLE REAL*16
Arcsine (degrees)  See Note (7).	arcsin(a)	1	ASIND @	ASIND @ DASIND @ QASIND @	REAL DOUBLE REAL*16	REAL DOUBLE REAL*16
Arccosine  See Note (7).	arccos(a)	1	ACOS	ACOS DACOS QACOS @	REAL DOUBLE REAL*16	REAL DOUBLE REAL*16
Arccosine (degrees)  See Note (7).	arccos(a)	1	ACOSD @	ACOSD @ DACOSD @ QACOSD @	REAL DOUBLE REAL*16	REAL DOUBLE REAL*16
Arctangent  See Note (7).	arctan(a)	1	ATAN	ATAN DATAN QATAN @	REAL DOUBLE REAL*16	REAL DOUBLE REAL*16
	arctan  (a1/a2)	2	ATAN2	ATAN2 DATAN2 QATAN2 @	REAL DOUBLE REAL*16	REAL DOUBLE REAL*16
Arctangent (degrees)  See Note (7).	arctan(a)	1	ATAND @	ATAND @ DATAND @ QATAND @	REAL DOUBLE REAL*16	REAL DOUBLE REAL*16
	arctan  (a1/a2)	2	ATAN2D@	ATAN2D @ DATAN2D @ QATAN2D @	REAL DOUBLE REAL*16	REAL DOUBLE REAL*16
Hyperbolic Sine  See Note (7).	sinh(a)	1	SINH	SINH DSINH QSINH @	REAL DOUBLE REAL*16	REAL DOUBLE REAL*16
Hyperbolic Cosine  See Note (7).	cosh(a)	1	COSH	COSH DCOSH QCOSH @	REAL DOUBLE REAL*16	REAL DOUBLE REAL*16
Hyperbolic Tangent  See Note (7).	tanh(a)	1	TANH	TANH DTANH QTANH @	REAL DOUBLE REAL*16	REAL DOUBLE REAL*16

Other Mathematical Functions

Table 6-4 Other Mathematical Functions

Intrinsic Function	Definition	No. of Args.	Generic Name	Specific Names	Argument Type	Function Type
Imaginary part of a complex number  See Note (6).	ai	1	IMAG	AIMAG DIMAG @ QIMAG @	COMPLEX DOUBLE COMPLEX COMPLEX*32	REAL DOUBLE REAL*16
Conjugate of a complex number  See Note (6).	(ar, -ai)	1	CONJG	CONJG DCONJG @ QCONJG @	COMPLEX DOUBLE COMPLEX COMPLEX*32	COMPLEX DOUBLE COMPLEX COMPLEX*32
Square root	a**(1/2)	1	SQRT	SQRT DSQRT QSQRT @ CSQRT ZSQRT @ CDSQRT @ CQSQRT @	REAL DOUBLE REAL*16 COMPLEX DOUBLE COMPLEX DOUBLE COMPLEX COMPLEX*32	REAL DOUBLE REAL*16 COMPLEX DOUBLE COMPLEX DOUBLE COMPLEX COMPLEX*32
Cube root  See Note(8').	a**(1/3)	1	CBRT	CBRT @ DCBRT @ QCBRT @ CCBRT @ ZCBRT @ CDCBRT @ CQCBRT @	REAL DOUBLE REAL*16 COMPLEX DOUBLE COMPLEX DOUBLE COMPLEX COMPLEX*32	REAL DOUBLE REAL*16 COMPLEX DOUBLE COMPLEX DOUBLE COMPLEX COMPLEX*32
Exponential	e**a	1	EXP	EXP DEXP QEXP @ CEXP ZEXP @ CDEXP @ CQEXP @	REAL DOUBLE REAL*16 COMPLEX DOUBLE COMPLEX DOUBLE COMPLEX COMPLEX*32	REAL DOUBLE REAL*16 COMPLEX DOUBLE COMPLEX DOUBLE COMPLEX COMPLEX*32
Natural logarithm	log(a)	1	LOG	ALOG DLOG QLOG @ CLOG ZLOG @ CDLOG @ CQLOG @	REAL DOUBLE REAL*16 COMPLEX DOUBLE COMPLEX DOUBLE COMPLEX COMPLEX*32	REAL DOUBLE REAL*16 COMPLEX DOUBLE COMPLEX DOUBLE COMPLEX COMPLEX*32
Common logarithm	log10(a)	1	LOG10	ALOG10 DLOG10 QLOG10 @	REAL DOUBLE REAL*16	REAL DOUBLE REAL*16
Error function (See note below)	erf(a)	1	ERF	ERF @ DERF @	REAL DOUBLE	REAL DOUBLE
Error function	1.0 - erf(a)	1	ERFC	ERFC @ DERFC @	REAL DOUBLE	REAL DOUBLE

• The error function: 2/sqrt(pi)* integral from 0 to a of exp(-t*t) dt

Character Functions

Table 6-5 Character Functions

Intrinsic Function	Definition	No. of Args.	Specific  Names	Argument Type	Function Type
Conversion See Note (5).	Conversion to character  Conversion to integer  See also: Table 6-2.	1    1	CHAR ACHAR @ ICHAR IACHAR @	INTEGER CHARACTER	CHARACTER INTEGER
Index of a substring	Location of substring a2 in string a1   See Note (10).	2	INDEX	CHARACTER	INTEGER
Length	Length of character entity   See Note (11).	1	LEN	CHARACTER	INTEGER
Lexically greater than or equal	a1 a2  See Note (12).	2	LGE	CHARACTER	LOGICAL
Lexically greater than	a1 > a2  See Note (12).	2	LGT	CHARACTER	LOGICAL
Lexically less than or equal	a1 £ a2 See Note (12).	2	LLE	CHARACTER	LOGICAL
Lexically less than	a1 < a2  See Note (12).	2	LLT	CHARACTER	LOGICAL

On an ASCII machine (including Sun systems):

• ACHAR is a nonstandard synonym for CHAR

• IACHAR is a nonstandard synonym for ICHAR

On a non-ASCII machine, ACHAR and IACHAR were intended to provide a way to deal directly with ASCII.

Miscellaneous Functions

Other miscellaneous functions include bitwise functions, environmental inquiry functions, and memory allocation and deallocation functions.

Bit Manipulation @

None of these functions are part of the FORTRAN 77 Standard.

Table 6-6 Bitwise Functions

Bitwise Operations	No. of Args.	Specific Name	Argument Type	Function Type
Complement	1	NOT	INTEGER	INTEGER
And	2 2	AND IAND	INTEGER INTEGER	INTEGER INTEGER
Inclusive or	2 2	OR IOR	INTEGER INTEGER	INTEGER INTEGER
Exclusive or	2 2	XOR IEOR	INTEGER INTEGER	INTEGER INTEGER
Shift See Note (14).	2	ISHFT	INTEGER	INTEGER
Left shift See Note (14).	2	LSHIFT	INTEGER	INTEGER
Right shift See Note (14).	2	RSHIFT	INTEGER	INTEGER
Logical right shift See Note (14).	2	LRSHFT	INTEGER	INTEGER
Circular shift	3	ISHFTC	INTEGER	INTEGER
Bit extraction	3	IBITS	INTEGER	INTEGER
Bit set	2	IBSET	INTEGER	INTEGER
Bit test	2	BTEST	INTEGER	LOGICAL
Bit clear	2	IBCLR	INTEGER	INTEGER

The above functions are available as intrinsic or extrinsic functions. See also the discussion of the library bit manipulation routines in the Fortran Library Reference manual.

Environmental Inquiry Functions @

None of these functions are part of the FORTRAN 77 Standard.

Table 6-7 Environmental Inquiry Functions

Definition	No. of Args.	Generic Name	Argument Type	Function Type
Base of Number System	1	EPBASE	INTEGER REAL DOUBLE REAL*16	INTEGER INTEGER INTEGER INTEGER
Number of Significant Bits	1	EPPREC	INTEGER REAL DOUBLE REAL*16	INTEGER INTEGER INTEGER INTEGER
Minimum Exponent	1	EPEMIN	REAL DOUBLE REAL*16	INTEGER INTEGER INTEGER
Maximum Exponent	1	EPEMAX	REAL DOUBLE REAL*16	INTEGER INTEGER INTEGER
Least Nonzero Number	1	EPTINY	REAL DOUBLE REAL*16	REAL DOUBLE REAL*16
Largest Number Representable	1	EPHUGE	INTEGER REAL DOUBLE REAL*16	INTEGER REAL DOUBLE REAL*16
Epsilon See Note (16).	1	EPMRSP	REAL DOUBLE REAL*16	REAL DOUBLE REAL*16

Memory @

None of these functions are part of the FORTRAN 77 Standard.

Table 6-8 Memory Functions

Intrinsic Function	Definition	No. of Args	Specific Name	Argument Type	Function Type
Location	Address of  See Note (17).	1	LOC	Any	INTEGER*4 INTEGER*8
Allocate	Allocate memory and return address.  See Note (17).	1	MALLOC MALLOC64	INTEGER*4 INTEGER*8	INTEGER INTEGER*8
Deallocate	Deallocate memory allocated by MALLOC. See Note (17).	1	FREE	Any	-
Size	Return the size of the argument in bytes.  See Note (18).	1	SIZEOF	Any expression	INTEGER

Although malloc and free are not, strictly speaking, intrinsics, they are listed here and in the Fortran Library Reference.

Remarks

The following remarks apply to all of the intrinsic function tables in this chapter.

• The abbreviation DOUBLE stands for DOUBLE PRECISION.

• An intrinsic that takes INTEGER arguments accepts INTEGER*2, INTEGER*4, or INTEGER*8.

• INTEGER intrinsics that take INTEGER arguments return values of INTEGER type determined as follows - note that options -i2, -dbl, and -xtypemap may alter the default sizes of actual arguments:

  • mod sign dim max min and iand or ior xor ieor -- size of the value returned is the largest of the sizes of the arguments.

  • abs ishft lshift rshift lrshft ibset btest ivclr ishftc ibits -- size of the value returned is the size of the first argument.

  • int epbase epprec -- size of the value returned is the size of default INTEGER.

  • ephuge -- size of the value returned is the size of the default INTEGER, or the size of the argument, whichever is largest.

• Options that change the default data sizes (see "Size and Alignment of Data Types " ) also change the way some intrinsics are used. For example, with -dbl in effect, a call to ZCOS with a DOUBLE COMPLEX argument will automatically become a call to CQCOS because the argument has been promoted to COMPLEX*32. The following functions have this capability:

  aimag alog amod cabs ccbrt ccos cdabs cdcbrt cdcos cdexp cdlog cdsin cdsqrt cexp clog csin csqrt dabs dacos dacosd dasin dasind datan datand dcbrt dconjg dcos dcosd dcosh ddim derf derfc dexp dimag dint dlog dmod dnint dprod dsign dsin dsind dsinh dsqrt dtan dtand dtanh idnint iidnnt jidnnt zabs zcbrt zcos zexp zlog zsin zsqrt

  The following functions permit arguments of an integer or logical type of any size:

  and iand ieor iiand iieor iior inot ior jiand jieor jior jnot lrshft lshift not or rshift xor

• (SPARC only) An intrinsic that is shown to return a default REAL, DOUBLE PRECISION, COMPLEX, or DOUBLE COMPLEX value will return the prevailing type depending on certain compilation options. (See "Size and Alignment of Data Types ".) For example, if compiled with -xtypemap=real:64,double:64:

  • A call to a REAL function returns REAL*8

  • A call to a DOUBLE PRECISION function returns REAL*8

  • A call to a COMPLEX function returns COMPLEX*16

  • A call to a DOUBLE COMPLEX function returns COMPLEX*16

    Other options that alter the data sizes of default data types are -r8 and -dbl, which also promote DOUBLE to QUAD. The -xtypemap= option provides more flexibility than these older compiler options and is preferred.

• A function with a generic name returns a value with the same type as the argument--except for type conversion functions, the nearest integer function, the absolute value of a complex argument, and others. If there is more than one argument, they must all be of the same type.

• If a function name is used as an actual argument, then it must be a specific name.

• If a function name is used as a dummy argument, then it does not identify an intrinsic function in the subprogram, and it has a data type according to the same rules as for variables and arrays.

Notes on Functions

Tables and notes 1 through 12 are based on the "Table of Intrinsic Functions," from ANSI X3.9-1978 Programming Language FORTRAN, with the FORTRAN extensions added.

(1) INT

If A is type integer, then INT(A) is A.

If A is type real or double precision, then:

if |A| < 1, then INT(A) is 0 if |A| 1, then INT(A) is the greatest integer that does not exceed the magnitude of A, and whose sign is the same as the sign of A. (Such a mathematical integer value may be too large to fit in the computer integer type.)

If A is type complex or double complex, then apply the above rule to the real part of A.

If A is type real, then IFIX(A) is the same as INT(A).

(2) REAL

If A is type real, then REAL(A) is A.

If A is type integer or double precision, then REAL(A) is as much precision of the significant part of A as a real datum can contain.

If A is type complex, then REAL(A) is the real part of A.

If A is type double complex, then REAL(A) is as much precision of the significant part of the real part of A as a real datum can contain.

(3) DBLE

If A is type double precision, then DBLE(A) is A.

If A is type integer or real, then DBLE(A) is as much precision of the significant part of A as a double precision datum can contain.

If A is type complex, then DBLE(A) is as much precision of the significant part of the real part of A as a double precision datum can contain.

If A is type COMPLEX*16, then DBLE(A) is the real part of A.

(3') QREAL

If A is type REAL*16, then QREAL(A) is A.

If A is type integer, real, or double precision, then QREAL(A) is as much precision of the significant part of A as a REAL*16 datum can contain.

If A is type complex or double complex, then QREAL(A) is as much precision of the significant part of the real part of A as a REAL*16 datum can contain.

If A is type COMPLEX*16 or COMPLEX*32, then QREAL(A) is the real part of A.

(4) CMPLX

If A is type complex, then CMPLX(A) is A.

If A is type integer, real, or double precision, then CMPLX(A) is REAL(A) + 0i.

If A1 and A2 are type integer, real, or double precision, then CMPLX(A1,A2) is REAL(A1) + REAL(A2)*i.

If A is type double complex, then CMPLX(A) is REAL( DBLE(A) ) + i*REAL( DIMAG(A) ).

If CMPLX has two arguments, then they must be of the same type, and they may be one of integer, real, or double precision.

If CMPLX has one argument, then it may be one of integer, real, double precision, complex, COMPLEX*16, or COMPLEX*32.

(4') DCMPLX

If A is type COMPLEX*16, then DCMPLX(A) is A.

If A is type integer, real, or double precision, then DCMPLX(A) is DBLE(A) + 0i.

If A1 and A2 are type integer, real, or double precision, then DCMPLX(A1,A2) is DBLE(A1) + DBLE(A2)*i.

If DCMPLX has two arguments, then they must be of the same type, and they may be one of integer, real, or double precision.

If DCMPLX has one argument, then it may be one of integer, real, double precision, complex, COMPLEX*16, or COMPLEX*32.

(5) ICHAR

ICHAR(A) is the position of A in the collating sequence.

The first position is 0, the last is N-1, 0£ICHAR(A)£N-1, where N is the number of characters in the collating sequence, and A is of type character of length one.

CHAR and ICHAR are inverses in the following sense:

• ICHAR(CHAR(I)) = I, for 0£I£N-1

• CHAR(ICHAR(C)) = C, for any character C capable of representation in the processor

(6) COMPLEX

A COMPLEX value is expressed as an ordered pair of reals, (ar, ai), where ar is the real part, and ai is the imaginary part.

(7) Radians

All angles are expressed in radians, unless the "Intrinsic Function" column includes the "(degrees)" remark.

(8) COMPLEX Function

The result of a function of type COMPLEX is the principal value.

(8') CBRT

If a is of COMPLEX type, CBRT results in COMPLEX RT1=(A, B), where: A>= 0.0, and -60 degrees <= arctan (B/A) < + 60 degrees.

Other two possible results can be evaluated as follows:

• RT2 = RT1 * (-0.5, square_root (0.75))

• RT3 = RT1 * (-0.5, square_root (0.75))

(9) Argument types

All arguments in an intrinsic function reference must be of the same type.

(10) INDEX

INDEX(X,Y) is the place in X where Y starts. That is, it is the starting position within character string X of the first occurrence of character string Y.

If Y does not occur in X, then INDEX(X,Y) is 0.

If LEN(X) < LEN(Y), then INDEX(X,Y) is 0.

INDEX returns default INTEGER*4 data. If compiling for a 64-bit environment, the compiler will issue a warning if the result overflows the INTEGER*4 data range. To use INDEX in a 64-bit environment with character strings larger than the INTEGER*4 limit (2 Gbytes), the INDEX function and the variables receiving the result must be declared INTEGER*8.

(11) LEN

LEN returns the declared length of the CHARACTER argument variable. The actual value of the argument is of no importance.

LEN returns default INTEGER*4 data. If compiling for a 64-bit environment, the compiler will issue a warning if the result overflows the INTEGER*4 data range. To use LEN in a 64-bit environment with character variables larger than the INTEGER*4 limit (2 Gbytes), the LEN function and the variables receiving the result must be declared INTEGER*8.

(12) Lexical Compare

LGE( X, Y ) is true if X=Y, or if X follows Y in the collating sequence; otherwise, it is false.

LGT( X, Y ) is true if X follows Y in the collating sequence; otherwise, it is false.

LLE( X, Y ) is true if X=Y, or if X precedes Y in the collating sequence; otherwise, it is false.

LLT( X, Y ) is true if X precedes Y in the collating sequence; otherwise, it is false.

If the operands for LGE, LGT, LLE, and LLT are of unequal length, the shorter operand is considered as if it were extended on the right with blanks.

(13) Bit Functions

See Appendix D, VMS Language Extensions for details on other bitwise operations.

(14) Shift

LSHIFT shifts a1 logically left by a2 bits (inline code).

LRSHFT shifts a1 logically right by a2 bits (inline code).

RSHIFT shifts a1 arithmetically right by a2 bits.

ISHFT shifts a1 logically left if a2 > 0 and right if a2 < 0.

The LSHIFT and RSHIFT functions are the FORTRAN analogs of the C << and >> operators. As in C, the semantics depend on the hardware.

The behavior of the shift functions with an out of range shift count is hardware dependent and generally unpredictable. In this release, shift counts larger than 31 result in hardware dependent behavior.

(15) Environmental inquiries

Only the type of the argument is significant.

(16) Epsilon

Epsilon is the least e, such that 1.0 + e 1.0.

(17) LOC, MALLOC, and FREE

The LOC function returns the address of a variable or of an external procedure. The function call MALLOC( n ) allocates a block of at least n bytes, and returns the address of that block.

LOC returns default INTEGER*4 in 32-bit environments, INTEGER*8 in 64-bit environments.

MALLOC is a library function and not an intrinsic. It too returns default INTEGER*4 in 32-bit environments, INTEGER*8 in 64-bit environments. However, MALLOC must be explicitly declared INTEGER*8 when compiling for 64-bit environments.

The value returned by LOC or MALLOC should be stored in variables typed POINTER, INTEGER*4, or INTEGER*8 in 64-bit environments. The argument to FREE must be the value returned by a previous call to MALLOC and hence should have data type POINTER, INTEGER*4, or INTEGER*8.

MALLOC64 always takes an INTEGER*8 argument (size of memory request in bytes) and always returns an INTEGER*8 value. Use this routine rather than MALLOC when compiling programs that must run in both 32-bit and 64-bit environments. The receiving variable must be declared either POINTER or INTEGER*8.

(18) SIZEOF

The SIZEOF intrinsic cannot be applied to arrays of an assumed size, characters of a length that is passed, or subroutine calls or names. SIZEOF returns default INTEGER*4 data. If compiling for a 64-bit environment, the compiler will issue a warning if the result overflows the INTEGER*4 data range. To use SIZEOF in a 64-bit environment with arrays larger than the INTEGER*4 limit (2 Gbytes), the SIZEOF function and the variables receiving the result must be declared INTEGER*8.

VMS Intrinsic Functions

This section lists VMS FORTRAN intrinsic routines recognized by f77. They are, of course, nonstandard. @

VMS Double-Precision Complex

Table 6-9 VMS Double-Precision Complex Functions

Generic Name	Specific Names	Function	Argument Type	Result Type
	CDABS CDEXP CDLOG CDSQRT	Absolute value  Exponential, e**a Natural log  Square root	COMPLEX*16 COMPLEX*16 COMPLEX*16 COMPLEX*16	REAL*8 COMPLEX*16 COMPLEX*16 COMPLEX*16
	CDSIN CDCOS	Sine  Cosine	COMPLEX*16 COMPLEX*16	COMPLEX*16 COMPLEX*16
DCMPLX	DCONJG DIMAG DREAL	Convert to DOUBLE COMPLEX Complex conjugate  Imaginary part of complex  Real part of complex	Any numeric COMPLEX*16 COMPLEX*16 COMPLEX*16	COMPLEX*16 COMPLEX*16 REAL*8 REAL*8

VMS Degree-Based Trigonometric

Table 6-10 VMS Degree-Based Trigonometric Functions

Generic Name	Specific Names	Function	Argument Type	Result Type
SIND	SIND DSIND QSIND	Sine	- REAL*4 REAL*8 REAL*16	- REAL*4 REAL*8 REAL*16
COSD	COSD DCOSD QCOSD	Cosine	- REAL*4 REAL*8 REAL*16	- REAL*4 REAL*8 REAL*16
TAND	TAND DTAND QTAND	Tangent	- REAL*4 REAL*8 REAL*16	- REAL*4 REAL*8 REAL*16
ASIND	ASIND DASIND QASIND	Arc sine	- REAL*4 REAL*8 REAL*16	- REAL*4 REAL*8 REAL*16
ACOSD	ACOSD DACOSD QACOSD	Arc cosine	- REAL*4 REAL*8 REAL*16	- REAL*4 REAL*8 REAL*16
ATAND	ATAND DATAND QATAND	Arc tangent	- REAL*4 REAL*8 REAL*16	- REAL*4 REAL*8 REAL*16
ATAN2D	ATAN2D DATAN2D QATAN2D	Arc tangent of a1/a2	- REAL*4 REAL*8 REAL*16	- REAL*4 REAL*8 REAL*16

VMS Bit-Manipulation

Table 6-11 VMS Bit-Manipulation Functions

Generic Name	Specific Names	Function	Argument Type	Result Type
IBITS	IIBITS JIBITS	From a1, initial bit a2, extract a3 bits	- INTEGER*2 INTEGER*4	- INTEGER*2 INTEGER*4
ISHFT	IISHFT JISHFT	Shift a1 logically by a2 bits; if a2 positive shift left, if a2 negative shift right Shift a1 logically left by a2 bits Shift a1 logically left by a2 bits	- INTEGER*2 INTEGER*4	- INTEGER*2 INTEGER*4
ISHFTC	IISHFTC JISHFTC	In a1, circular shift by a2 places, of right a3 bits	- INTEGER*2 INTEGER*4	- INTEGER*2 INTEGER*4
IAND	IIAND JIAND	Bitwise AND of a1, a2	- INTEGER*2 INTEGER*4	- INTEGER*2 INTEGER*4
IOR	IIOR JIOR	Bitwise OR of a1, a2	- INTEGER*2 INTEGER*4	- INTEGER*2 INTEGER*4
IEOR	IIEOR JIEOR	Bitwise exclusive OR of a1, a2	- INTEGER*2 INTEGER*4	- INTEGER*2 INTEGER*4
NOT	INOT JNOT	Bitwise complement	- INTEGER*2 INTEGER*4	- INTEGER*2 INTEGER*4
IBSET	IIBSET JIBSET	In a1, set bit a2 to 1 In a1, set bit a2 to 1; return new a1 In a1, set bit a2 to 1; return new a1	- INTEGER*2 INTEGER*4	- INTEGER*2 INTEGER*4
BTEST	BITEST BJTEST	If bit a2 of a1 is 1, return .TRUE.	- INTEGER*2 INTEGER*4	- INTEGER*2 INTEGER*4
IBCLR	IIBCLR JIBCLR	In a1, set bit a2 to 0; return new a1	- INTEGER*2 INTEGER*4	- INTEGER*2 INTEGER*4

VMS Multiple Integer Types

The possibility of multiple integer types is not addressed by the FORTRAN Standard. f77 copes with their existence by treating a specific INTEGER-to-INTEGER function name (IABS, and so forth) as a special sort of generic. The argument type is used to select the appropriate runtime routine name, which is not accessible to the programmer.

VMS FORTRAN takes a similar approach, but makes the specific names available.

Table 6-12 VMS Integer Functions

Specific Names	Function	Argument Type	Result Type
IIABS JIABS	Absolute value  Absolute value	INTEGER*2 INTEGER*4	INTEGER*2 INTEGER*4
IMAX0 JMAX0	Maximum [There must be at least two arguments.] Maximum 1	INTEGER*2 INTEGER*4	INTEGER*2 INTEGER*4
IMIN0 JMIN0	Minimum 1 Minimum 1	INTEGER*2 INTEGER*4	INTEGER*2 INTEGER*4
IIDIM JIDIM	Positive difference [The positive difference is: a1-min(a1,a2))] Positive difference 2	INTEGER*2 INTEGER*4	INTEGER*2 INTEGER*4
IMOD JMOD	Remainder of a1/a2  Remainder of a1/a2	INTEGER*2 INTEGER*4	INTEGER*2 INTEGER*4
IISIGN JISIGN	Transfer of sign, |a1|* sign(a2)  Transfer of sign, |a1|* sign(a2)	INTEGER*2 INTEGER*4	INTEGER*2 INTEGER*4

Functions Coerced to a Particular Type

Some VMS FORTRAN functions coerce to a particular INTEGER type.

Table 6-13 Translated Functions that VMS Coerces to a Particular Type

Specific Names	Function	Argument Type	Result Type
IINT JINT	Truncation toward zero  Truncation toward zero	REAL*4 REAL*4	INTEGER*2 INTEGER*4
IIDINT JIDINT	Truncation toward zero  Truncation toward zero	REAL*8 REAL*8	INTEGER*2 INTEGER*4
IIQINT JIQINT	Truncation toward zero  Truncation toward zero	REAL*16 REAL*16	INTEGER*2 INTEGER*4
ININT JNINT	Nearest integer, INT(a+.5*sign(a)) Nearest integer, INT(a+.5*sign(a))	REAL*4 REAL*4	INTEGER*2 INTEGER*4
IIDNNT JIDNNT	Nearest integer, INT(a+.5*sign(a)) Nearest integer, INT(a+.5*sign(a))	REAL*8 REAL*8	INTEGER*2 INTEGER*4
IIQNNT JIQNNT	Nearest integer, INT(a+.5*sign(a)) Nearest integer, INT(a+.5*sign(a))	REAL*16 REAL*16	INTEGER*2 INTEGER*4
IIFIX JIFIX	Fix  Fix	REAL*4 REAL*4	INTEGER*2 INTEGER*4
IMAX1(a,a2,...) JMAX1(a,a2,...)	Maximum of two or more arguments  Maximum of two or more arguments	REAL*4 REAL*4	INTEGER*2 INTEGER*4
IMIN1(a,a2,... JMIN1(a,a2,...	Minimum of two or more arguments  Minimum of two or more arguments	READ*4 READ*4	INTEGER*2 INTEGER*4

Functions Translated to a Generic Name

In some cases, each VMS-specific name is translated into an f77 generic name.

Table 6-14 VMS Functions That Are Translated into f77 Generic Names

Specific Names	Function	Argument Type	Result Type
FLOATI FLOATJ	Convert to REAL*4 Convert to REAL*4	INTEGER*2 INTEGER*4	REAL*4 REAL*4
DFLOTI DFLOTJ	Convert to REAL*8 Convert to REAL*8	INTEGER*2 INTEGER*4	REAL*8 REAL*8
AIMAX0 AJMAX0	Maximum  Maximum	INTEGER*2 INTEGER*4	REAL*4 REAL*4
AIMIN0 AJMIN0	Minimum  Minimum	INTEGER*2 INTEGER*4	REAL*4 REAL*4

Zero Extend

The following zero-extend functions are recognized by f77. The first unused high-order bit is set to zero and extended toward the higher-order end to the width indicated in the table

Table 6-15 Zero-Extend Functions

Generic Name	Specific Names	Function	Argument Type	Result Type
ZEXT		Zero-extend	-	-
	IZEXT	Zero-extend	BYTE LOGICAL*1 LOGICAL*2 INTEGER*2	INTEGER*2
	JZEXT	Zero-extend	BYTE LOGICAL*1 LOGICAL*2 LOGICAL*4 INTEGER INTEGER*2 INTEGER*4	INTEGER*4