Numbers
The everyday numeric functions are built in and need no import: absolute value, square root, trigonometry, logarithms, rounding toward a whole number. Two of them round in a direction their names do not announce, and that is what to watch for.
'' The built-in numeric functions need no import.
print "abs( -3.5 ) ="; abs( -3.5 ); ", sgn( -2 ) ="; sgn( -2 )
print "sqr( 2 ) ="; sqr( 2 )
print "exp( 1 ) ="; exp( 1 )
print "log( 100 ) ="; log( 100 ); " (natural log)"
'' Trigonometry works in radians.
dim as float64 pi = atn( 1 ) * 4
print "pi ="; pi
print "sin( pi / 6 ) ="; sin( pi / 6 )
print "atan2( 1, 1 ) ="; atan2( 1, 1 )
'' int rounds down, fix rounds toward zero, frac is what fix drops.
print "int( -2.5 ) ="; int( -2.5 ); ", fix( -2.5 ) ="; fix( -2.5 ); _
", frac( -2.5 ) ="; frac( -2.5 )
'' / divides as floating point; \ divides whole numbers.
print "7 / 2 ="; 7 / 2; ", 7 \ 2 ="; 7 \ 2; ", 7 mod 2 ="; 7 mod 2
'' mod and \ truncate: the remainder takes the sign of the left side.
print "-7 mod 3 ="; -7 mod 3; ", -7 \ 3 ="; -7 \ 3
'' ^ raises to a power, in floating point.
print "2 ^ 10 ="; 2 ^ 10; ", 2 ^ 0.5 ="; 2 ^ 0.5
Output
abs( -3.5 ) = 3.5, sgn( -2 ) =-1
sqr( 2 ) = 1.414213562373095
exp( 1 ) = 2.718281828459045
log( 100 ) = 4.605170185988092 (natural log)
pi = 3.141592653589793
sin( pi / 6 ) = 0.4999999999999999
atan2( 1, 1 ) = 0.7853981633974483
int( -2.5 ) =-3, fix( -2.5 ) =-2, frac( -2.5 ) =-0.5
7 / 2 = 3.5, 7 \ 2 = 3, 7 mod 2 = 1
-7 mod 3 =-1, -7 \ 3 =-2
2 ^ 10 = 1024, 2 ^ 0.5 = 1.414213562373095
| Function | Gives |
|---|---|
abs( x ), sgn( x ) | the magnitude; -1, 0 or 1 |
sqr( x ) | the square root |
exp( x ), log( x ) | e to the power x, and the natural logarithm |
sin, cos, tan, asin, acos, atn, atan2 | trigonometry, in radians |
int( x ) | the largest whole number not above x: it rounds down |
fix( x ), frac( x ) | the whole part toward zero, and what is left |
int( -2.5 ) is -3, because int is a floor; code that uses it believing it
truncates is wrong for every negative number. fix is the one that truncates.
/ always divides as floating point. \ divides whole numbers and mod gives
the remainder; both truncate toward zero, so the remainder takes the sign of
the left-hand side and -7 mod 3 is -1. ^ raises to a power, working in
float64.
sin( pi / 6 ) prints 0.4999999999999999 rather than 0.5: pi holds the
nearest float64 to pi, not pi itself. Results from the square root,
logarithms and trigonometry come from each platform's maths library.
The std/numeric module fills the gaps: rounding that names its direction,
exact integer arithmetic, overflow control, and more. The pages that follow use
it.
Activities
- Print
int( 2.7 ),int( -2.7 ),fix( 2.7 )andfix( -2.7 ), and predict each before you run it. - Convert 90 degrees to radians and print its sine.