Scalar

structure Scalar

Members

(Scalar values have no suffixes other than the ones inherited from Structure.)

A Scalar value is the kind the system gives you whenever you are working with a number of some sort which, unlike with a Vector, does not have a pointing orientation in 3D space.

In other words, it’s just a number. A plain no-frills ordinary number.

Experienced programmers will be aware of the concept of there being different kinds of number depending on what you want to do with it. There’s “integer” versus “floating point” versus “fixed point”, and theres single-precision, double-precision and so on.

kOS tries to be friendly to the new person just playing around with simple programming without a lot of expertise, and to that end, the difference between these types is abstracted away as much as possible.

Operators

The following basic arithmetic operators are defined when both a and b are scalars:

• a ^ b exponent: a to the power b
• -a negative of a
• a * b a / b muiltiply or divide two numbers.
• a + b a - b add or subtract two numbers

The order of operations is in the order of the table listing above. (for example multiplication and division happen before subtraction and addition).

Scientific Notation

You can specify a number using scientific notation using the letter ‘e’, as shown:

set x to 1.23e5.
print x.  // prints 123000
set x to 1.23e-5.
print x.  // prints 0.0000123

Limitations of Scalars

The implementation of Scalars can currently only store values that fit the following criteria:

The value is a real number

Or “What the heck does ‘attempted to push NaN onto the stack’ mean?”.

kOS does not have a numeric type designed to deal with imaginary numbers or complex numbers. Therefore, for example, if you attempted to perform sqrt(-4), you would get a “NaN error”, rather than the irrational number 2i. NaN means “Not a Number” and it means the system is incapable of storing the correct answer. Another example of where you will get a “NaN error” would be if you attempted to perform arcsin(1.01), since there is no such thing as the angle that gives a sine of 1.01.

The value must be a rational number

When you ask kOS to tell you constant:pi, you are technically not getting the actual correct value. Instead you are getting a rational number approximation that is accurate to about 15 decimal places. In kOS, Scalar values cannot store irrational numbers.

The larger the magnitude, the less the precision

For example, while it is possible to store exactly the number 99.001, it is not possible to store exactly the number 999999999999999.001, even though both numbers are only precise up to the thousandths place.

If you attempt to set x to 999999999999999.001. and then print x., you’ll find that the value you get back has been rounded off a bit.

In a nutshell, what really matters is how many significant digits there are, not how many places after the decimal point. You can’t have more than roughly 15 significant decimal digits (it’s not exactly 15 because of differences between binary and decimal counting, but that gives you a rough estimate).