B.1 Details of expressions

B.2 Mathematical functions provided

B.3 Rules for expressions

B.4 Operator precedence

B.2 Mathematical functions provided

B.3 Rules for expressions

B.4 Operator precedence

This appendix discusses the syntax permitted for expressions passed to the expression parser.
Expressions are input to CAT as argument `EXPR`

of subroutine `CAT_EIDNT`

(see Section 7).

Expressions have an algebraic format, and comprise: columns, vector column elements, parameters
and constants linked by arithmetic operators and mathematical functions. For example, suppose that a
catalogue contained scalar columns called `x`

, `y`

and `z`

and parameters called `p`

and `q`

. Some valid
expressions are:

$$\begin{array}{c}\hfill \end{array}$$
| (2) |

Remember that in CAT column and parameter names are not case-sensitive. Thus the following column or parameter names would all be considered equivalent:

`HD_NUMBER`

`HD_Number`

`hd_number`

`FLUX`

would be
‘`FLUX[4] + 2.0`

’.
The arithmetic operators are:

`+` | addition, |

`-` | subtraction, |

`*` | multiplication, |

`/` | division. |

brackets (‘`(`

’ and ‘`)`

’) may be used as required.

Table 16 lists the mathematical functions which are provided. The letters denote data types permitted, coded as follows: B = BYTE, H = half INTEGER, I = INTEGER, R = REAL, D = DOUBLE PRECISION, C = CHARACTER, L = LOGICAL. The appearance of N as an argument means that any numeric type (BHIRD) is permitted, as a result it means that the type is the widest type of any of the arguments. R/D means that the result is REAL unless one or more arguments is of DOUBLE PRECISION type in which case D is the result.

Function | Notes |

B = BYTE(N) | convert to BYTE data type |

H = HALF(N) | convert to INTEGER*2 data type |

I = INT(N) | convert to INTEGER data type |

R = REAL(N) | convert to REAL data type |

D = DBLE(N) | convert to DOUBLE PRECISION data type |

I = NINT(N) | convert to nearest INTEGER |

N = MIN(N,N) | the function must have precisely two arguments |

N = MAX(N,N) | the function must have precisely two arguments |

N = MOD(N,N) | remainder |

N = ABS(N) | absolute value |

R/D = SQRT(N) | square root |

R/D = LOG(N) | natural logarithm |

R/D = LOG10(N) | logarithm to the base 10 |

R/D = EXP(N) | exponential |

R/D = SIN(N) | sine; argument in radians |

R/D = COS(N) | cosine; argument in radians |

R/D = TAN(N) | tangent; argument in radians |

R/D = ASIN(N) | arc-sine; result in radians |

R/D = ACOS(N) | arc-cosine; result in radians |

R/D = ATAN(N) | arc-tangent; result in radians |

R/D = ATAN2(N,N) | arc-tangent (two arguments) result in radians |

I = IAND(I,I) | bitwise logical AND |

I = IOR(I,I) | bitwise logical OR |

I = XOR(I,I) | bitwise logical exclusive OR |

R/D = DTOR(N) | degrees to radians conversion |

R/D = RTOD(N) | radians to degrees conversion |

C = UPCASE(C) | convert character string to upper case |

C = STRIP(C) | leading and trailing spaces are removed |

C = SUBSTR(C,N,N) | returns characters from positions argument 2 |

to argument 3 inclusive, with the positions | |

starting at 1 | |

L = NULL(*) | .TRUE. if argument is NULL |

D = HMSRAD(N,N,N) | converts 3 arguments hours, minutes and |

seconds to radians | |

D = DMSRAD(C,N,N,N) | first argument is the sign (‘$+$’ or ‘-’ ), |

converts degrees, minutes and seconds to radians | |

D = GREAT(N,N,N,N) | great circle distance between two spherical |

coordinates. All the input arguments and the | |

return argument are in radians. The input arguments | |

are in the order: $({\alpha}_{1},{\delta}_{1}$,${\alpha}_{2},{\delta}_{2})$ | |

D = PANGLE(N,N,N,N) | Position angle of point $\left({\alpha}_{2},{\delta}_{2}\right)$ from point |

$\left({\alpha}_{1},{\delta}_{1}\right)$. All the input arguments and the return | |

argument are in radians. The input arguments are in | |

the order: $({\alpha}_{1},{\delta}_{1}$,${\alpha}_{2},{\delta}_{2})$ | |

The expression string can contain constants, column and parameter names, operators, functions, and parentheses. In general the usual rules of algebra and Fortran should be followed, with some minor exceptions, as noted below.

- (1)
- Spaces are permitted between items, except that a function-name must be followed immediately by a left parenthesis. Spaces are not permitted within items such as names and numerical constants, but can be used within character strings and date/time values in curly braces.
- (2)
- Lower-case letters are treated everywhere as identical to the corresponding upper-case letter.
- (3)
- Column and parameter names can be up to
`CAT__SZCMP`

characters long, and may consist of letters, digits, and underscores, except that the first character must not be a digit. - (4)
- Vector elements are supported but with a restricted syntax: they may consist of a name
followed by an unsigned integer constant subscript enclosed in square brackets, for
example
`FLUX[4]`

or`MAGNITUDE[13]`

. The first element of the vector is numbered one. - (5)
- CHARACTER constants may be enclosed in a pair of single or double quotes; embedded quotes of the same type may be denoted by doubling up on the quote character within the string, for example ’DON’’T’ or "DON""T".
- (6)
- LOGICAL constants may be
`.TRUE.`

or`.FALSE.`

but abbreviations of these words are allowed down to`.T.`

and`.F.`

- (7)
- Numerical constants may appear in any valid form for Fortran 77 (except that embedded spaces are not allowed). Some additional forms are also permitted, as shown below.
- (8)
- %Xstring %Ostring %Bstring for hexadecimal, octal and binary INTEGER constants respectively.
- (9)
- Angles in sexagesimal notation: colons must be used to separate items, for example hours:minutes:seconds (or degrees:minutes:seconds). If there is a leading sign then the value will be taken as degrees:minutes:seconds, otherwise hours:minutes:seconds. In either case the value is converted to RADIANS.
- (10)
- A date/time value may be given as a string enclosed in curly braces; a range of common formats
are permitted, with order year-month-day or day-month-year, and the month as a
number or three-character abbreviation. The time may follow with colons separating
hours:minutes:seconds. Examples of some valid dates:
`1992-JUL-26 12:34:56`

`92.7.26`

`26/7/92T3:45`

- (11)
- Relational operators are supported in both Fortran 77 form (for
example
`.GE. .NE.`

) as well as in the Fortran 90 forms (for example, $$

$$>=

)./= - (12)
- Single-symbol forms for
`.AND. .OR. and .NOT.`

are provided as an alternative:`&`

$$| `#`

respectively. - (13)
- The dots may be left off the Fortran 77 forms of the relational operators and the logical operators
`.AND.`

and`.OR.`

where spaces or parentheses separate them from names or constants, but the logical constants and the`.NOT.`

operator need the enclosing dots to distinguish them from other lexical items in all cases. - (14)
- INTEGER division does not result in truncation (as in Fortran) but produces a floating-point
result. The
`NINT`

or`INT`

function should be used (as appropriate) if an INTEGER result is required. - (15)
- The functions
`MAX`

and`MIN`

must have exactly two arguments. - (16)
- All arithmetic is carried out internally in DOUBLE PRECISION (but the compiler works out the effective data type of the result using the normal expression rules).
- (17)
- Exponentiation is performed by log/exp functions, with use of ABS to avoid taking logs of
negative arguments, thus
`-2**3`

will come out as ‘+8’ not ‘-8’.

The operator precedence rules are show in Table 17. The rules of Fortran 90 are used as far as possible; in this table the larger numbers denote higher precedence (tighter binding).

Precedence | Function/operator |

2 | start/end of expression |

4 | `( )` |

6 | `,` |

8 | `.EQV. .NEQV.` |

10 | `.OR.` $$ |

12 | `.AND. &` |

14 | `.NOT. #` |

16 | `.EQ. .GE. .GT. .LE. .LT. .NE.` $$ |

18 | `FROM TO` |

20 | `//` |

22 | `+ -` (binary operators) |

24 | `+ -` (unary operators) |

26 | `* /` |

28 | `**` |

30 | all functions |

Note that all operators except `**`

associate from left to right, but `**`

and functions associate from right
to left.