Appendix C: List of Builtin -calc- Functions
| Trigonometry Functions | |
|---|---|
| sin(x) | sine |
| cos(x) | cosine |
| arctan(x) | arctangent |
Angles are measured in radians. For example, sin(45) means sine of 45 radians, but sin (45Β°) means sine of 45 degrees (0.707). The degree sign (MICRO-o) converts to radians. Similarly, arctan(1) is .785 radians, which can be converted to degrees by dividing by 1Β°, the number of radians in one degree; arctan(1)/1Β° is 45. Using the degree sign after a number is equivalent to multiplying the number by (2Ο/360). Ο (MICRO-p) is 3.14159. . . .
| Arithmetic Functions | |
|---|---|
| sqrt(x) | square root; can also be written x1/2 or x.5 |
| log(x) | logarithm, base 10 |
| ln(x) | natural logarithm, base e |
| exp(x) | ex |
| abs(x) | absolute value; abs(-7) is 7 |
| round(x) | round to nearest integer; round(8.6) is 9 |
| int(x) | integer part; int(8.6) is 8 |
| frac(x) | fractional part; frac(8.6) is 0.6 |
| sign(x) | +1 if x>0, 0 if x=0, -1 if x<0 |
| Logical Tests | |
| =, β , <, >, β€, β₯ | produce logical values (true=-1,false=0) |
| not(x) | true if both x and y are true |
| x $or$ y | true if either x or y is true (or both) |
| Bit Manipulation | |
| x $cls$ y | circular left shift x by y bit positions |
| x $ars$ Y | arithmetic right shift x by y bit positions |
| x $mask$ y | sets bits where both x and y have bits set |
| x $union$ y | sets bits where either x or y has bits set (or both) |
| x $diff$ y | sets bits where x and y differ (exclusive union) |
| bitcnt(x) | counts bits |
The logical operators (=, β , <, >, β€, and β₯) consider two quantities to be equal if they differ by less than one part in 1011 (relative tolerance) or by an absolute difference of 10-9. One consequence is that all numbers within 10-9 of zero are considered equal. Similarly, βintβ and βfracβ round their arguments by 10-9 so that int(3.999999999) is 4, not 3, and frac(3.999999999) is 0, not 1. This is done because a value of 3.999999999 is usually due to roundoff errors made by the computer in attempting to calculate a result of 4.
System Variables
| Discussed in This Book | Not Discussed in This Book | |
|---|---|---|
| anscnt | baseu | aarea |
| args | capital | aarrows |
| clock | dataon | ahelp |
| formok | entire | ahelpn |
| jcount | error | aok |
| key | errtype | aokist |
| opcnt | extra | asno |
| spell | judged | aterm |
| station | ldone | atermn |
| varcnt | lscore | atime |
| vocab | lstatus | auno |
| where | mainu | |
| wherex | mode | |
| wherey | nhelpop | |
| ntries | ||
| order | ||
| phrase | ||
| size | ||
| user | ||
| wcount | ||
| zreturn | ||
The third column consists of counters associated with the -area- command.
There are some additional system variables available for special purposes. See the on-line PLATO aids for information.