Chapter 11  Math
REBOL/Core Users Guide Main Table of Contents Send Us Feedback
Contents:
1. Overview
2. Scalar Data Types
3. Evaluation Order
4. Standard Functions and Operators
4.1 absolute
4.2 add
4.3 complement
4.4 divide
4.5 multiply
4.6 negate
4.7 random
4.8 remainder
4.9 subtract
5. Type Conversion
6. Comparison Functions
6.1 equal
6.2 greater
6.3 greaterorequal
6.4 lesser
6.5 lesserorequal
6.6 not equal to
6.7 same
6.8 strictequal
6.9 strictnotequal
7. Logarithmic Functions
7.1 exp
7.2 log10
7.3 log2
7.4 loge
7.5 power
7.6 squareroot
8. Trigonometric Functions
8.1 arccosine
8.2 arcsine
8.3 arctangent
8.4 cosine
8.5 sine
8.6 tangent
9. Logic Functions
9.1 and
9.2 or
9.3 xor
9.4 complement
9.5 not
10. Errors
10.1 Attempt to divide by zero
10.2 Math or number overflow
10.3 Positive number required
10.4 Cannot use operator on datatype! value
1. Overview
REBOL provides a comprehensive set of mathematical and trigonometric
operations. Many of these operators can handle multiple datatypes, including
integer, decimal, money, tuple, time, and date. Some of these datatypes may even
be mixed, or coerced.
2. Scalar Data Types
The mathematical functions of REBOL operate in a consistent manner over a
wide range of scalar (numerical) data types. These data types include:
Datatype

Description


Integer!

32 bit numbers without decimal point

Decimal!

64 bit floating point numbers

Money!

currency with 64 bit floating point number

Time!

hours, minutes, seconds, and subseconds

Date!

day, month, year, time, time zone

Pair!

graphical position or size

Tuple!

versions, colors, network addresses

The following are a few examples that show a range of math operations over
the scalar data types. Notice that operators produce useful results for each
data type.
The integer and decimal data types:
print 2 + 1
3
print 2  1
1
print 2 * 10
20
print 20 / 10
2
print 21 // 10
1
print 2.2 + 1
3.2
print 2.2  1
1.2
print 2.2 * 10
22
print 2.2 / 10
0.22
print random 10
5
The time data type:
print 2:20 + 1:40
4:00
print 2:20 + 5
2:20:05
print 2:20 + 60
2:21
print 2:20 + 2.2
2:20:02.2
print 2:20  1:20
1:00
print 2:20  5
2:19:55
print 2:20  120
2:18
print 2:20 * 2
4:40
print 2:20 / 2
1:10
print 2:20:01 / 2
1:10:00.5
print 2:21 // 2
0:00
print  2:20
2:20
print random 10:00
5:30:52
The date data type:
print 1Jan2000 + 1
2Jan2000
print 1Jan2000  1
31Dec1999
print 1Jan2000 + 31
1Feb2000
print 1Jan2000 + 366
1Jan2001
birthday: 7Dec1944
print ["I've lived" (now/date  birthday) "days."]
I've lived 20305 days.
print random 112000
29Apr1695
The money data type:
print $2.20 + $1
$3.20
print $2.20 + 1
$3.20
print $2.20 + 1.1
$3.30
print $2.20  $1
$1.20
print $2.20 * 3
$6.60
print $2.20 / 2
$1.10
print $2.20 / $1.10
2
print $2.21 // 2
$0.21
print random $10.00
$6.00
The pair data type:
print 100x200 + 10x20
110x220
print 10x10 + 3
13x13
print 10x20 * 2x4
20x80
print 100x100 * 3
300x300
print 100x30 / 10x3
10x10
print 100x30 / 10
10x3
print 101x32 // 10x3
1x2
print 101x32 // 10
1x2
print random 100x20
67x12
The tuple data type:
print 1.2.3 + 3.2.1
4.4.4
print 1.2.3  1.0.1
0.2.2
print 1.2.3 * 3
3.6.9
print 10.20.30 / 10
1.2.3
print 11.22.33 // 10
1.2.3
print 1.2.3 * 1.2.3
1.4.9
print 10.20.30 / 10.20.30
1.1.1
print 1.2.3 + 7
8.9.10
print 1.2.3  1
0.1.2
print random 10.20.30
8.18.12
3. Evaluation Order
There are two rules to remember when evaluating mathematical expressions:
 Expressions are evaluated from left to right.
 Operators take precedence over functions.
The evaluation of expressions from left to right is independent of the type
of operator that is used. For example:
print 1 + 2 * 3
9
In the example above, notice that the result is not seven, as would be the
case if multiplication took precedence over addition.
Important Note
The way mathematical expressions are evaluated from left to
right regardless of the operator is different than many other
computer languages. Many languages have rules of precedence that
you must remember that determine the order of evaluation of
operators. For example, a multiply is done before an add. Some
languages have 10 or more such rules.
In REBOL, rather than requiring users to remember the precedence
of operators, you only need to remember the lefttoright rule.
More importantly, for advanced code such as expressions that
handle expressions (in reflection, for example) you do not need
to reorder terms based on precedence. The evaluation order is
kept simple.
For most math expressions, the lefttoright evaluation rule
works quite well and is easy to remember. However, because
this rule is different from other languages, it can be a source
of programming errors, so watch out.
The best solution is to check your work. You can also use
parentheses if necessary to clarify your expression (see below),
and you can always type your expression at the console to verify
your result.
If you need to evaluate in some other order, reorder the expression or use
parentheses:
print 2 * 3 + 1
7
print 1 + (2 * 3)
7
When functions are mixed with operators, the operators are evaluated first,
then the functions:
print absolute 10 + 5
5
In the above example, the addition is performed first, and its result is
provided to the absolute function.
In the next example:
print 10 + sine 30 + 60
11
the expression is evaluated in this order:
30 + 60 => 90
sine 90 => 1
10 + 1 => 11
print
To change the order such that the sine of 30 is done first,
use parentheses:
print 10 + (sine 30) + 60
70.5
or reorder the expression:
print 10 + 60 + sine 30
70.5
4. Standard Functions and Operators
This section describes the standard math functions and operators used in
REBOL.
4.1 absolute
The expressions:
absolute value
abs value
return the absolute value of value.
Works with integer, decimal, money, time, pair
data types.
print absolute 10
10
print absolute 1.2
1.2
print absolute $1.2
$1.20
print absolute 10:20
10:20
print absolute 10x20
10x20
4.2 add
The expressions:
value1 + value2
add value1 value2
return the result of adding value1 to value2.
Works with integer, decimal,
money, time, tuple,
pair, date, char data
types.
print 1 + 2
3
print 1.2 + 3.4
4.6
print 1.2.3 + 3.4.5
4.6.8
print $1 + $2
$3.00
print 1:20 + 3:40
5:00
print 10x20 + 30x40
40x60
print #"A" + 10
K
print add 1 2
3
4.3 complement
The expression:
complement value
returns the numeric complement (bitwise complement) of a value.
Works with integer, decimal,
tuple data types.
print complement 10
11
print complement 10.5
11
print complement 100.100.100
155.155.155
4.4 divide
The expressions:
value1 / value2
divide value1 value2
return the result of dividing value1 by value2.
Works with integer, decimal, money, time, tuple,
pair, char data types.
print 10 / 2
5
print 1.2 / 3
0.4
print 11.22.33 / 10
1.2.3
print $12.34 / 2
$6.17
print 1:20 / 2
0:40
print 10x20 / 2
5x10
print divide 10 2
5
4.5 multiply
The expressions:
value1 * value2
multiply value1 value2
return the result of multiplying value1 by value2.
Works with integer, decimal,
money, time, tuple,
pair, char data types.
print 10 * 2
20
print 1.2 * 3.4
4.08
print 1.2.3 * 3.4.5
3.8.15
print $10 * 2
$20.00
print 1:20 * 3
4:00
print 10x20 * 3
30x60
print multiply 10 2
20
4.6 negate
The expressions:
 value
negate value
change the sign of the value.
Works with integer, decimal,
money, time, pair,
char data types.
<A name=_Toc487519923>print  10
10
print  1.2
1.2
print  $10
$10.00
print  1:20
1:20
print  10x20
10x20
print negate 10
10
4.7 random
The expression:
random value
returns a random value that is less than or equal to value given.
Note that for integers random begins at 1, not 0, and is
inclusive of the value given. This allows random to be used
directly with functions like pick.
When a decimal is used the result is a decimal data type rounded to an
integer.
The /seed refinement restarts the random generator. Use the
/seed refinement with random first it if you want unique
random number generation. You can use the current date and time
to make the seed more random:
random/seed now
Works with integer, decimal, money, time, tuple,
pair, date, char, string, block data types.
print random 10
5
print random 10.5
2
print random 100.100.100
79.95.66
print random $100
$32.00
print random 10:30
6:37:33
print random 10x20
2x4
print random 30Jun2000
27Dec1171
4.8 remainder
The expressions:
value1 // value2
remainder value1 value2
return the remainder of dividing value1 by value2.
Works with integer, decimal,
money, time, tuple,
pair data types.
print 11 // 2
1
print 11.22.33 // 10
1.2.3
print 11x22 // 2
1x0
print remainder 11 2
1
4.9 subtract
The expressions:
value1  value2
subtract value1 value2
return the result of subtracting value2 from value1.
Works with integer, decimal,
money, time, tuple,
pair, date, char data
types.
print 2  1
1
print 3.4  1.2
2.2
print 3.4.5  1.2.3
2.2.2
print $2  $1
$1.00
print 3:40  1:20
2:20
print 30x40  10x20
20x20
print #"Z"  1
Y
print subtract 2 1
1
5. Type Conversion
When math operations are performed between data types, normally the
noninteger or nondecimal data type is returned. When integers are combined
with decimals, a decimal data type is returned.
6. Comparison Functions
All comparison functions return either true or false.
6.1 equal
The expressions:
value1 = value2
equal? value1 value2
return true if the first and second values are equal.
Works with integer, decimal, money, time, date,
tuple, char and series data types.
print 111199 = 111199
true
print equal? 111.112.111.111 111.112.111.111
true
print #"B" = #"B"
true
print equal? "a b c d" "A B C D"
true
6.2 greater
The expressions:
value1 > value2
greater? value1 value2
return true if the first value is greater than the second value.
Works with integer, decimal,
money, time, date,
tuple, char and series data
types.
print 131199 > 121199
true
print greater? 113.111.111.111 111.112.111.111
true
print #"C" > #"B"
true
print greater? [12 23 34] [12 23 33]
true
6.3 greaterorequal
The expressions:
value1 >= value2
greaterorequal? value1 value2
return true if the first value is greater than or equal to the
second value.
Works with integer, decimal,
money, time, date,
tuple, char and series data
types.
print 111299 >= 111199
true
print greaterorequal? 111.112.111.111 111.111.111.111
true
print #"B" >= #"A"
true
print greaterorequal? [b c d e] [a b c d]
true
6.4 lesser
The expressions:
value1 < value2
lesser? value1 value2
return true if the first value is less than second value.
Works with integer, decimal,
money, time, date,
tuple, char and series data
types:
print 25 < 50
true
print lesser? 25.3 25.5
true
print $2.00 < $2.30
true
print lesser? 00:10:11 00:11:11
true
6.5 lesserorequal
The expressions:
value1 <= value2
lesserorequal? value1 value2
return true if the first value is less than or equal to the second
value.
Works with integer, decimal,
money, time, date,
tuple, char and series data
types.
print 25 <= 25
true
print lesserorequal? 25.3 25.5
true
print $2.29 <= $2.30
true
print lesserorequal? 11:11:10 11:11:11
true
6.6 not equal to
The expressions:
value1 <> value2
notequal? value1 value2
return true if the first and second values are not equal.
Works with integer, decimal,
money, time, date,
tuple, char and series data
types.
print 26 <> 25
true
print notequal? 25.3 25.5
true
print $2.29 <> $2.30
true
print notequal? 11:11:10 11:11:11
true
6.7 same
The expressions:
value1 =? value2
same? value1 value2
return true if two words refer to the same value. For instance,
when you want to see if two words are referencing the same index in a series.
Work with all data types.
referenceone: "abcdef"
referencetwo: referenceone
print same? referenceone referencetwo
true
referenceone: next referenceone
print same? referenceone referencetwo
false
referencetwo: next referencetwo
print same? referenceone referencetwo
true
referencetwo: copy referenceone
print same? referenceone referencetwo
false
6.8 strictequal
The expressions:
value1 == value2
strictequal? value1 value2
return true if the first and second values are strictly the same.
Can be used as a casesensitive version of the equal? (
= ) operator for strings and to differentiate between integers and
decimals when their values are the same.
Works with all data types.
print strictequal? "abc" "ABC"
false
print equal? "abc" "ABC"
true
print strictequal? "abc" "abc"
true
print strictequal? 1 1.0
false
print equal? 1 1.0
true
print strictequal? 1.0 1.0
true
6.9 strictnotequal
The expression:
strictnotequal? value1 value2
returns true if the first and second values are strictly not the
same. Can be used as a casesensitive version of the notequal?
( <> ) operator for strings and to differentiate between
integers and decimals when their values are the same.
Works with all data types.
print strictnotequal? "abc" "ABC"
true
print notequal? "abc" "ABC"
false
print strictnotequal? "abc" "abc"
false
print strictnotequal? 1 1.0
true
print notequal? 1 1.0
false
print strictnotequal? 1.0 1.0
false
7. Logarithmic Functions
7.1 exp
The expression:
exp value
raises E (natural number) to the power of value.
7.2 log10
The expression:
log10 value
returns the base10 logarithm of value.
7.3 log2
The expression:
log2 value
returns the base2 logarithm of value.
7.4 loge
The expression:
loge value
returns the baseE (natural number) log. of value.
7.5 power
The expressions:
value1 ** value2
power value1 value2
return the result of raising value1 to value2 power.
7.6 squareroot
The expression:
squareroot value
returns the square root of value.
8. Trigonometric Functions
The trigonometric functions deal in degrees. Use the /radians
refinement with any of the trigonometric functions to operate in
and return radians.
8.1 arccosine
The expression:
arccosine value
returns the trigonometric arccosine of value.
8.2 arcsine
The expression:
arcsine value
returns the trigonometric arcsine of value.
8.3 arctangent
The expression:
arctangent value
returns the trigonometric arctangent of value.
8.4 cosine
The expression:
cosine value
returns the trigonometric cosine of value.
8.5 sine
The expression:
sine value
returns the trigonometric sine of value.
8.6 tangent
The expression:
tangent value
returns the trigonometric tangent of value.
9. Logic Functions
Logic functions can be performed on logic values and on some
scalar values including integer, char, tuple, and
bitset. When working with logic values, the logic functions
return boolean values. When working with other types of values,
the logic functions on the bits.
9.1 and
The and function compares two logic values and returns
true if they are both true :
print (1 < 2) and (2 < 3)
true
print (1 < 2) and (4 < 3)
false
When used with integers, the and function compares bit for
bit and returns 1 if both bits are 1, or 0 if
neither bit is 1 :
print 3 and 5
1
9.2 or
The or function compares two logic values and returns
true if either of them are true or false or if both are
false :
print (1 < 2) or (2 < 3)
true
print (1 < 2) or (4 < 3)
true
print (3 < 2) or (4 < 3)
false
When used with integers, or compares bit for bit and returns
1 if either bit is 1 or 0 if both bits are
0:
print 3 or 5
7
9.3 xor
The xor function compares two logic values and returns
true if and only if one of the values is true and the other is
false.
print (1 < 2) xor (2 < 3)
false
print (1 < 2) xor (4 < 3)
true
print (3 < 2) xor (4 < 3)
false
When used with integers, xor compares bit for bit and
returns 1 if and only if one bit is 1 and the other 0
. Otherwise, it returns 0 :
print 3 xor 5
6
9.4 complement
The complement function returns the logic or bitwise
complement of a value. It is used for bitmask integer numbers and inverting
bitsets.
print complement true
false
print complement 3
4
9.5 not
For a logic value not returns true if the value is
false and false if the value is true. It does not perform numerical
bitwise operations.
print not true
false
print not false
true
10. Errors
Math errors are reported when an illegal operation is performed or when an
overflow or underflow occurs. The following errors may be encountered in math
operations.
10.1 Attempt to divide by zero
An attempt was made to divide a number by 0.
1 / 0
** Math Error: Attempt to divide by zero
** Where: connecttolink
** Near: 1 / 0
10.2 Math or number overflow
An attempt was made to process a number too large for REBOL to handle.
1E+300 + 1E+400
** Math Error: Math or number overflow
** Where: connecttolink
** Near: 1 / 0
10.3 Positive number required
An attempt was made to process a negative number with a math operator that
accepts only positive numbers.
log10 1
** Math Error: Positive number required
** Where: connecttolink
** Near: log10 1
10.4 Cannot use operator on datatype! value
An attempt was made to process incompatible data types. The data type of the
second argument in the operation is returned as listed.
10:30 + 1.2.3
** Script Error: Cannot use add on time! value
** Where: connecttolink
** Near: 10:30 + 1.2.3
