
Formulas can work with integer numbers as well as with real numbers.
You can type many real numbers by using a decimal notation, for instance 3.14159, 299792.5, or 0.000123456789. For very large or small numbers, you can use the enotation: 6.022·10^{23} is typed as 6.022e23 or 6.022e+23, and 1.6021917·10^{19} is typed as 1.6021917e19. You can use also use the percent notation: 0.157 can be typed as 15.7%.
There are some limitations as to the values that real numbers can have in Praat. The numbers must lie between 10^{308} and +10^{308}. If you type
1e200 * 1e100
the outcome will be
1e+300
but if you type
1e300 * 1e100
the outcome will be
undefined
Another limitation is that the smallest nonzero numbers lie near 10^{308} and +10^{308}. If you type
1e200 / 1e100
the outcome will be
1e300
but if you type
1e300 / 1e100
the outcome will be
0
Finally, the precision of real numbers is limited by the number of bits that every real number is stored with in the computer, namely 64. For instance, if you type
pi
the outcome will be
3.141592653589793
because only 16 digits of precision are stored. This can lead to unexpected results caused by rounding. For instance, the formula
0.34999999999999999  0.35
will result in
0
rather than the correct value of 1e17. This is because the numbers 0.34999999999999999 and 0.35 cannot be distinguished in the computer's memory. If you simply type
0.34999999999999999
the outcome will be
0.35
(as in this example, the calculator will always come up with the minimum number of digits needed to represent the number unambiguously).
Another example of inaccuracy is the formula
1 / 7 / 59 * 413
Because of rounding errors, the result will be
0.9999999999999999
Formulas can work with integer (whole) numbers between 1,000,000,000,000,000 and +1,000,000,000,000,000. You type them without commas and without the plus sign: 337, 848947328345289.
You can work with larger numbers than that (up to 10^{308}), but there will again be rounding errors. For instance, the formula
1000000000000000 + 1
correctly yields
1000000000000001
but the formula
10000000000000000 + 1
yields an incorrect outcome:
1e16
© ppgb, April 14, 2004