CALC - Evaluates a mathematical expression

Description:

This task evaluates an arithmetic expression and reports the result. It main rôle is to perform floating-point arithmetic in scripts. A value "Bad" is reported if there was an error during the calculation, such as a divide by zero.

Usage:

calc exp [prec] fa-fz=? pa-pz=?

Parameters:

EXP = LITERAL (Read)

The mathematical expression to be evaluated, e.g. "-2.5$*$LOG10(PA)". In this expression constants may either be given literally or represented by the variables PA, PB, ... PZ. The expression may contain sub-expressions represented by the variables FA, FB, ...FZ. Values for those sub-expressions and constants which appear in the expression will be requested via the application's parameter of the same name.

FORTRAN 77 syntax is used for specifying the expression, which may contain the usual intrinsic functions, plus a few extra ones. An appendix in SUN/61 gives a full description of the syntax used and an up-to-date list of the functions available. The arithmetic operators ($+$,-,/,$*$,$*$$*$) follow the normal order of precedence. Using matching (nested) parentheses will explicitly define the order of expression evaluation. The expression may be up to 132 characters long.

FA-FZ = LITERAL (Read)

These parameters supply the values of `sub-expressions' used in the expression EXP. Any of the 26 may appear; there is no restriction on order. These parameters should be used when repeated expressions are present in complex expressions, or to shorten the value of EXP to fit within the 132-character limit. Sub-expressions may contain references to other sub-expressions and constants (PA-PZ). An example of using sub-expressions is:

EXP $>$ PA$*$ASIND(FA/PA)$*$X/FA

FA $>$ SQRT(X $*\textit{x}+\textit{y}*$Y)

PA $>$ 10.1

where the parameter name is to the left of $>$ and its value is to the right of the $>$.

PA-PZ = _DOUBLE (Read)

These parameters supply the values of constants used in the expression EXP and sub-expressions FA-FZ. Any of the 26 may appear; there is no restriction on order. Using parameters allows the substitution of repeated constants using one reference. This is especially convenient for constants with many significant digits. It also allows easy modification of parameterised expressions provided the application has not been used with a different EXP in the interim. The parameter PI has a default value of 3.14159265359D0. An example of using parameters is:

EXP $>$ SQRT(PX$*$PX$+$PY$*$PY)$*$EXP(PX-PY)

PX $>$ 2.345

PY $>$ -0.987

where the parameter name is to the left of $>$ and its value is to the right of the $>$.

PREC = LITERAL (Read)

The arithmetic precision with which the transformation functions will be evaluated when used. This may be either "_REAL" for single precision, "_DOUBLE" for double precision, or "_INTEGER" for integer precision. Elastic precisions are used, such that a higher precision will be used if the input data warrant it. So for example if PREC="_REAL", but double-precision data were to be transformed, double-precision arithmetic would actually be used. The result is reported using the chosen precision. ["_REAL"]

Results Parameters:

RESULT = LITERAL (Write)

The result of the evaluation.

Examples:

Shell usage:

The syntax in the following examples apply to the shell.

calc "27.3$*$1.26"

The reports the value of the expression 27.3$*$1.26, i.e. 34.398.

calc exp="(pa$+$pb$+$pc$+$pd)/4.0" pa=$med1 pb=$med2 pc=$med3 pd=$med4

This reports the average of four values defined by script variables med1, med2, med3, and med4.

calc "42.6$*$pi/180"

This reports the value in radians of 42.6 degrees.

calc "(mod(PO,3)$+$1)/2" prec=_integer po=$count

This reports the value of the expression "(mod($count,3)$+$1)/2)" where $count is the value of the shell variable count. The calculation is performed in integer arithmetic, thus if count equals 2, the result is 1 not 1.5.

calc "sind(pa/fa)$*$fa" fa="log(abs(pb$+$pc))" pa=2.0e-4 pb=-1 pc=$x

This evaluates sind(0.0002/log(abs($x$-$1)))$*$log(abs($x$-$1)) where $x is the value of the shell variable x.

ICL usage:

For ICL usage only those expressions containing parentheses need to be in quotes, though ICL itself provides the arithmetic. So the above examples would be

calc 27.3$*$1.26

The reports the value of the expression 27.3$*$1.26, i.e. 34.398.

calc exp="(pa$+$pb$+$pc$+$pd)/4.0" pa=(med1) pb=(med2) pc=(med3) pd=(med4)

This reports the average of four values defined by ICL variables med1, med2, med3, and med4.

calc 42.6$*$pi/180

This reports the value in radians of 42.6 degrees.

calc "(mod(PO,3)$+$1)/2" prec=_integer po=(count)

This reports the value of the expression "(mod((count),3)$+$1)/2)" where (count) is the value of the ICL variable count. The calculation is performed in integer arithmetic, thus if count equals 2, the result is 1 not 1.5.

calc "sind(pa/fa)$*$fa" fa="log(abs(pb$+$pc))" pa=2.0e-4 pb=-1 pc=(x)

This evaluates sind(0.0002/log(abs((x)$-$1)))$*$log(abs((x)$-$1)) where (x) is the value of the ICL variable x.

Implementation Status:

On OSF/1 systems an error during the calculation results in a core dump. On Solaris, undefined values are set to one. These are due to problems with the TRANSFORM infrastructure.

Related Applications

KAPPA: MATHS.