W-expressions

Besides expressions, as described above (see Expressions), the MIXAL assembler is able to handle the so called w-expressions as the operands of the directives ORIG, EQU, CON and END (see MIXAL directives). The general form of a w-expression is the following:

          WEXP = EXP[(EXP)][,WEXP]
     

where EXP stands for an expression and square brackets denote optional items. Thus, a w-expression is made by an expression, followed by an optional expression between parenthesis, followed by any number of similar constructs separated by commas. Sample w-expressions are:

     2000
     235(3)
     S1+3(S2),3000
     S1,S2(3:5),23
     

W-expressions are evaluated from left to right as follows:

• Start with an accumulated result w equal to 0.
• Take the first expression of the comma-separated list and evaluate it. For instance, if the w-expression is S1+2(2:4),2000(S2), we evaluate first S1+2; let's suppose that S1 equals 265230: then S1+2 = 265232 = + 00 01 00 48 16.
• Evaluate the expression within parenthesis, reducing it to an f-spec of the form L:R. In our previous example, the expression between parenthesis already has the desired form: 2:4.
• Substitute the bytes of the accumulated result w designated by the f-spec using those of the previous expression value. In our sample, w = + 00 00 00 00 00, and we must substitute bytes 2, 3 and 4 of w using values from 265232. We need 3 bytes, and we take the least significant ones: 00, 48, and 16, and insert them in positions 2, 3 and 4 of w, obtaining w = + 00 00 48 16 00.
• Repeat this operation with the remaining terms, acting on the new value of w. In our example, if, say, S2 = 1:1, we must substitute the first byte of w using one byte (the least significant) from 2000, that is, 16 (since 2000 = + 00 00 00 31 16) and, therefore, we obtain w = + 16 00 48 16 00; summing up, we have obtained 265232(1:4),2000(1:1) = + 16 00 48 16 00 = 268633088.

As a second example, in the w-expression

     1(1:2),66(4:5)
     

we first take two bytes from 1 (00 and 01) and store them as bytes 1 and 2 of the result (obtaining + 00 01 00 00 00) and, afterwards, take two bytes from 66 (01 and 02) and store them as bytes 4 and 5 of the result, obtaining + 00 01 00 01 02 (262210). The process is repeated for each new comma-separated example. For instance:

     1(1:1),2(2:2),3(3:3),4(4:4) = 01 02 03 04 00
     

As stated before, w-expressions can only appear as the operands of MIXAL directives taking a constant value (ORIG, EQU, CON and END). Future references are not allowed within w-expressions (i.e., all symbols appearing in a w-expression must be defined before it is used).