FORTRAN 77 Language Reference

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\| = (ar2+ai2)**.5	1	`ABS`	`IABS` `ABS` `DABS` `CABS` `QABS` `@` `ZABS` `@` `CDABS` `@` `CQABS` `@`	`INTEGER` `REAL` `DOUBLE` `COMPLEX` `REAL16` `DOUBLE COMPLEX` `DOUBLE COMPLEX` `COMPLEX32`	`INTEGER` `REAL` `DOUBLE` `REAL` `REAL16` `DOUBLE` `DOUBLE` `REAL16`
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` `COMPLEX16` `COMPLEX32` `REAL*16`	`INTEGER` `INTEGER` `INTEGER` `INTEGER` `INTEGER` `INTEGER` `INTEGER` `INTEGER`
`REAL` `See Note (2)`.	1	`REAL`	`REAL` `FLOAT` `-` `SNGL` `SNGLQ` `@` `-` `-` `-`	`INTEGER` `INTEGER` `REAL` `DOUBLE` `REAL16` `COMPLEX` `COMPLEX16` `COMPLEX*32`	`REAL` `REAL` `REAL` `REAL` `REAL` `REAL` `REAL` `REAL`
`DOUBLE` `See Note (3).`	1	`DBLE`	`DBLE` `DFLOAT` `DREAL` `@` `DBLEQ` `@` `-` `-` `-` `-`	`INTEGER` `INTEGER` `REAL` `DOUBLE` `REAL16` `COMPLEX` `COMPLEX16` `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` REAL16 `COMPLEX` `COMPLEX16` `COMPLEX*32`	`REAL16` `REAL16` `REAL16` REAL16 `REAL16` REAL16 `REAL16` `REAL16` `REAL*16`
`COMPLEX` `See Notes (4) and (8).`	1 or 2	`CMPLX`	`-` `-` `-` `-` `-` `-` `-`	`INTEGER` `REAL` `DOUBLE` `REAL16` `COMPLEX` `COMPLEX16` `COMPLEX*32`	`COMPLEX` `COMPLEX` `COMPLEX` `COMPLEX` `COMPLEX` `COMPLEX` `COMPLEX`
`DOUBLE COMPLEX` `See Note (8).`	1 or 2	`DCMPLX@`	`-` `-` `-` `-` `-` `-` `-`	`INTEGER` `REAL` `DOUBLE` `REAL16` `COMPLEX` `COMPLEX16` `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` `REAL16` `COMPLEX` `COMPLEX16` `COMPLEX*32`	`COMPLEX32` `COMPLEX32` `COMPLEX32` `COMPLEX32` `COMPLEX32` `COMPLEX32` `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` `REAL16` `COMPLEX` `DOUBLE COMPLEX` `DOUBLE COMPLEX` `COMPLEX32`	`REAL` `DOUBLE` `REAL16` `COMPLEX` `DOUBLE COMPLEX` `DOUBLE COMPLEX` `COMPLEX32`
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` `REAL16` `COMPLEX` `DOUBLE COMPLEX` `DOUBLE COMPLEX` `COMPLEX32`	`REAL` `DOUBLE` `REAL16` `COMPLEX` `DOUBLE COMPLEX` `DOUBLE COMPLEX` `COMPLEX32`
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`
Arctangent `See Note (7).`	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`
Arctangent (degrees) `See Note (7)`.	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` `REAL16` `COMPLEX` `DOUBLE COMPLEX` `DOUBLE COMPLEX` `COMPLEX32`	`REAL` `DOUBLE` `REAL16` `COMPLEX` `DOUBLE COMPLEX` `DOUBLE COMPLEX` `COMPLEX32`
Cube root `See Note(8')`.	a**(1/3)	1	`CBRT`	`CBRT` `@` `DCBRT` `@` `QCBRT` `@` `CCBRT` `@` ZCBRT `@` `CDCBRT` `@` `CQCBRT` `@`	`REAL` `DOUBLE` `REAL16` `COMPLEX` `DOUBLE COMPLEX` `DOUBLE COMPLEX` `COMPLEX32`	`REAL` `DOUBLE` `REAL16` `COMPLEX` `DOUBLE COMPLEX` `DOUBLE COMPLEX` `COMPLEX32`
Exponential	e**a	1	`EXP`	`EXP` `DEXP` `QEXP` `@` `CEXP` `ZEXP` `@` `CDEXP` `@` `CQEXP` `@`	`REAL` `DOUBLE` `REAL16` `COMPLEX` `DOUBLE COMPLEX` `DOUBLE COMPLEX` `COMPLEX32`	`REAL` `DOUBLE` `REAL16` `COMPLEX` `DOUBLE COMPLEX` `DOUBLE COMPLEX` `COMPLEX32`
Natural logarithm	log(a)	1	`LOG`	`ALOG` `DLOG` `QLOG` `@` `CLOG` `ZLOG` `@` `CDLOG` `@` `CQLOG` `@`	`REAL` `DOUBLE` `REAL16` `COMPLEX` `DOUBLE COMPLEX` `DOUBLE COMPLEX` `COMPLEX32`	`REAL` `DOUBLE` `REAL16` `COMPLEX` `DOUBLE COMPLEX` `DOUBLE COMPLEX` `COMPLEX32`
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