Math
Arithmetic computations.
Logo understands quite a lot of math commands, from simple addition and subtraction up to functions like the cosecant, or the square root. Random numbers are part of the math functions as well.
POWER
Also: ^
Raises a number to the power of another number.
Syntax
number ^ number
POWER number number
(POWER number number number ...)
Description
POWER raises the first number to the power of the second number. Its abbreviation is ^. When given multiple inputs, POWER and all its inputs must be enclosed in parentheses. The ^ symbol for POWER may be used as either a prefix or infix operator. See also EXPN.
Example
2 ^ 3 Result: 8 POWER 3 2 Result: 9 (POWER 2 3 4) Result: 4096
DIFFERENCE
Also: -
Outputs the difference of two or more numbers.
Syntax
number1 - number2
DIFFERENCE number1 number2
(DIFFERENCE number1 number2 number3 ...)
Description
DIFFERENCE reports the result of subtracting its inputs. DIFFERENCE expects two inputs, but will accept more if it and its inputs are enclosed in parentheses. DIFFERENCE is equivalent to the prefix or infix operator -.
Example
6 - 3 Result: 3 DIFFERENCE 6 3 Result: 3 (DIFFERENCE 6 3 2) Result: 1
SUM
Also: +
Reports the sum of its inputs.
Syntax
number1 + number2
SUM number1 number2
(SUM number1 number2 number3 ...)
Description
SUM reports the result of adding its inputs. SUM expects two inputs, but will accept more if it and its inputs are enclosed in parentheses. SUM is equivalent to the infix operator +.
Example
SUM 3 6 Result: 9 SUM 3.2 6.4 Result:9.6 (SUM 3.2 6.4 1) Result: 10.6
PRODUCT
Also: *
Calculates the product of its inputs.
Syntax
number * number
PRODUCT number number
(PRODUCT number number number)
Description
PRODUCT multiplies its inputs and reports the result. PRODUCT expects two inputs, but will accept more if it and all its inputs are enclosed in parentheses. PRODUCT is equivalent to *. When used as the * symbol, PRODUCT may be a prefix or an infix operator.
Example
PRODUCT 2 3 Result: 6 PRODUCT 4 -1.2 Result: -4.8 PRODUCT -.5 -1.5 Result: 0.75 (PRODUCT 2 3 4 5) Result: 120
QUOTIENT
Also: /
Reports the quotient of its inputs.
Syntax
number / number
QUOTIENT number number
(QUOTIENT number number number ...)
Description
QUOTIENT reports the result of dividing the first input by the second input. QUOTIENT expects two inputs, but will accept more if it and all its inputs are enclosed in parentheses. The symbol “/” can be used as a prefix or an infix operator. See also % and MODULO.
Example
10 / 5 Result: 2 QUOTIENT 10 2 Result: 5 QUOTIENT 10 3 Result: 3.33
REMAINDER
Also: %
Outputs the remainder of two numbers.
Syntax
dividend % divisor
REMAINDER dividend divisor
Description
REMAINDER reports the number that is the remainder of dividing the first input by the second. The symbol “%” can be used as a prefix or an infix operator. See also /.
REMAINDER reports the result of (dividend - (divisor * int(dividend
/divisor))). The result is the same as for MODULO if the
signs of both operand are the same, but are different from
MODULO when the signs are different.
Until Logo version 4.0.4, REMAINDER was an alias for MODULO.
Example
REMAINDER 6 3 Result: 0 REMAINDER 159 2 Result: 1 689 % 468 Result: 221 REMAINDER -123 4 Result: -3
.EQ
Also: =, EQUAL?, EQUALP
Tests its inputs for equality.
Syntax
object = object
= object object
Description
The equality operator compares two objects. If they are equal, the output is TRUE; otherwise it is FALSE. This operator is the same as the = command. The operator “=” may be used either as a prefix or as an infix operator.
The value of the :EPSILON variable determines how the equality operator compares two numbers. See :EPSILON for details.
Example
4 = 5 Result: FALSE = 4 5 Result: FALSE .EQ 5 5 Result: TRUE EQUAL? [6] [6] Result: TRUE EQUAL? 6 [6] Result: FALSE
.NE
Also: <>, !=, NOT.EQUAL?, NOT.EQUALP, NOTEQUAL?, NOTEQUALP
Tests its inputs for inequality.
Syntax
object != object
object <> object
NOTEQUAL? object object
Description
NOTEQUAL? reports TRUE if its two inputs are not equal; otherwise it reports FALSE. Its inputs may be numbers, words, or lists. The symbols != and <> are abbreviations for NOTEQUAL?. The symbols “<>” and “!=” may be used as infix or prefix operators.
The value of the :EPSILON variable determines how the inequality operator compares two numbers. See :EPSILON for details.
Example
NOTEQUAL? 6 6 Result: FALSE NOTEQUAL? 6 66 Result: TRUE NOTEQUAL? “AZURE “AZURE Result: FALSE NOTEQUAL? [SPRING GREEN] [SPRING GREEN] Result: FALSE NOTEQUAL? “AZURE [AZURE] Result: TRUE
.LT
Also: <, LESS?, LESSP
Tests if its first input is less than its second input.
Syntax
number < number
.LT number number
Description
The Less Than operator compares two numbers. If the first number is less than the second number, the output is TRUE; otherwise it is FALSE. The symbol “<” may be used either as a prefix or an infix operator.
Example
4 < 5 Result: TRUE < 4 5 Result: TRUE .LT 5 5 Result: FALSE
GREATER?
Also: >, GREATERP, .GT
Tests if its first input is greater than its second input.
Syntax
number > number
.GT number number
Description
The Greater Than operator compares two numbers. If the first number is greater than the second number, the output is TRUE; otherwise it is FALSE. The symbol “>” may be used either as a prefix or an infix operator.
Example
4 > 5 Result: FALSE .GT 5 5 Result: FALSE
.GE
Also: >=, GREATEREQUAL?, GREATEREQUALP
Tests if its first input is greater than or equal to its second input.
Syntax
number >= number
.GE number number
Description
The Greater Than or Equal operator compares two numbers. If the first number is greater than or equal to the second number, the output is TRUE; otherwise, it is FALSE. The symbol “>=” may be used either as a prefix or as an infix operator.
Example
4 >= 5 Result: FALSE .GE 5 5 Result: TRUE
.LE
Also: <=, LESSEQUAL?, LESSEQUALP
Tests if its first input is less than or equal to its second input.
Syntax
number <= number
.LE number number
Description
The Less Than or Equal operator compares two numbers. If the first number is less than or equal to the second number, the output is TRUE; otherwise it is FALSE. The symbol “<=” may be used either as a prefix or as an infix operator.
Example
4 <= 5 Result: TRUE .LE 5 5 Result: TRUE
ABS
Reports the absolute value of a number.
Syntax
ABS number
Description
ABS reports the absolute value of its input, its non-negative value regardless of its sign.
Example
ABS -30 Result: 30 ABS 30 Result: 30
AND
Logical AND.
Syntax
AND input1 input2
(AND input1 input2 input3 ...)
Description
AND accepts two or more inputs, which must be either TRUE or FALSE. AND reports TRUE if all of its inputs are true; otherwise it reports FALSE. By default, AND expects two inputs. If more inputs are supplied, both AND and its inputs must be enclosed in parentheses. See also OR.
Example
AND TRUE TRUE Result: TRUE AND TRUE FALSE Result: FALSE (AND TRUE FALSE TRUE) Result: FALSE AND 3=3 3=4 Result: FALSE AND 10=10 6=6 Result: TRUE
ARCCOS
Also: ACOS
Reports the arccosine.
Syntax
ARCCOS number
Description
ARCCOS takes as input a number between -1 and 1 and reports its arccosine, a value between 0 and 180.
Example
ARCCOS 0.5 Result: 60
ARCCOT
Also: ACOT
Reports the arccotangent.
Syntax
ARCCOT number
Description
ARCCOT reports the arccotangent of its input.
Example
ARCCOT 1 Result: 45
ARCCSC
Also: ACSC
Reports the arccosecant.
Syntax
ARCCSC number
Description
ARCCSC reports the arccosecant of its input.
Example
ARCCSC 60 Result: 0.95
ARCSEC
Also: ASEC
Reports the arcsecant.
Syntax
ARCSEC number
Description
ARCSEC reports the arcsecant of its input.
Example
ARCSEC 45 Result: 88.73
ARCSIN
Also: ASIN
Reports the arcsine.
Syntax
ARCSIN number
Description
ARCSIN takes as input a number between -1 and 1 and reports its arcsine, a value between -90 and 90.
Example
ARCSIN 0.5 Result: 30
ARCTAN
Also: ATAN
Reports the arctangent.
Syntax
ARCTAN number
Description
ARCTAN reports the arc tangent of its input as degrees.
Example
ARCTAN 0.5 Result: 26.57
ARCTAN2 (ATAN2)
Reports the polar angle heading of the motion vector (position change) deltaX deltaY.
Syntax
ARCTAN2 deltaX deltaY
Description
ARCTAN2 reports the full-circle polar angle (in degrees) of its input motion vector deltaX deltaY. Output 0 represents the positive x-axis direction (3 o’clock). Polar angles increase going counter-clockwise.
See also PANGLE, PSETHEADING and PHEADING.
Example
ARCTAN2 -5 -5 Result: 225
COS
Reports the cosine.
Syntax
COS number
Description
COS reports the cosine of its input, a number of degrees. Remember that COS x = adjacent / hypotenuse. See also ARCTAN and SIN.
Example
COS 0 Result:1 COS 90 Result: 0
COT
Reports the cotangent.
Syntax
COT number
Description
COT reports the cotangent of its input.
Example
COT 1 Result: 57.29
CSC
Reports the cosecant.
Syntax
CSC number
Description
CSC reports the cosecant of its input.
Example
CSC 60 Result: 1.15
EXPN
Also: EXP
Calculates the natural base e raised to a power.
Syntax
EXPN number
Description
EXPN calculates the natural base e (2.7183. . .) raised to the power specified by its input. See also [^](#).
Example
EXPN 3 Result: 20.09 EXPN 0 Result: 1
INT
Reports the integer part of a number.
Syntax
INT number
Description
INT reports the integer portion of its input by removing the decimal portion, if any. No rounding occurs. See also ROUND.
Example
INT 2.345 Result: 2 INT 2.789 Result: 2 INT 57.999 Result: 57
LOG
Also: LN
Outputs the natural logarithm of its input.
Syntax
LOG number
Description
LOG reports the natural logarithm of its input. See also LOG10.
Example
LOG 10 Result: 2.3 LOG 1 Result: 0 LOG EXPN 1 Result: 1
LOG10
Outputs the logarithm of its input.
Syntax
LOG10 number
Description
LOG10 reports the base 10 logarithm of its input. See also LOG.
Example
LOG10 1 Result: 0 LOG10 100 Result: 2 LOG10 0.001 Result: -3
LOGAND
Combines its inputs with a boolean AND operation.
Syntax
LOGAND integer1 integer2
Description
LOGAND reports the bitwise logical AND of its two inputs. Each input is expressed internally as a 32-digit binary number. A logical AND operation is performed on the pair of binary digits (bits) in each position, resulting in a 32-bit integer. The logical AND operation is defined on the binary digits 0 and 1 as follows:
LOGAND 0 0 equals 0
LOGAND 1 0 equals 0
LOGAND 0 1 equals 0
LOGAND 1 1 equals 1
See also LOGNOT, LOGOR, LOGXOR.
Example
LOGAND 2 1 Result: 0 LOGAND 2 3 Result: 2
LOGNOT
Reports the bitwise logical complement of its input.
Syntax
LOGNOT integer
Description
LOGNOT reports the bitwise logical complement of its input, replacing all 1’s with 0’s and all 0’s with 1’s. Since integers are stored in the computer as base 2 numbers 32 digits long, all the leading 0’s turn into 1’s. See also LOGAND, LOGOR, and LOGXOR.
Example
The number 21 in binary notation would be
21 = 00000000000000000000000000010101
With all bits inverted, it is
-22 = 11111111111111111111111111101010
Note that negative numbers always start with a “1” bit.
TO PRINT.BITS :N MAKE “N ROUND :N REPEAT 32 [ IF (LOGAND :N #H80000000) <> 0 [TYPE 1][TYPE 0] MAKE “N LSHIFT :N 1 ] (PR) END PRINT.BITS 21 00000000000000000000000000010101 PRINT.BITS LOGNOT 21 11111111111111111111111111101010 LOGNOT 21 Result: -22
LOGOR
Combines its inputs with a boolean OR operation.
Syntax
LOGOR integer1 integer2
Description
LOGOR reports the bitwise logical OR of its two inputs. Each input is expressed internally as a 32-digit binary number. A logical OR operation is performed on the pair of binary digits (bits) in each position, resulting in a 32-bit integer. The logical OR operation is defined on the binary digits 0 and 1 as follows:
LOGOR 0 0 equals 0
LOGOR 1 0 equals 1
LOGOR 0 1 equals 1
LOGOR 1 1 equals 1
See also LOGNOT, LOGOR, LOGXOR.
Example
LOGOR 2 0 Result: 2 LOGOR 2 3 Result: 3
LOGXOR
Combines its inputs with a boolean XOR operation.
Syntax
LOGXOR integer1 integer2
Description
LOGXOR reports the bitwise logical XOR of its two inputs. Each input is expressed internally as a 32-digit binary number. A logical XOR operation is performed on the pair of binary digits (bits) in each position, resulting in a 32-bit integer. The logical XOR operation is defined on the binary digits 0 and 1 as follows:
LOGXOR 0 0 equals 0
LOGXOR 1 0 equals 1
LOGXOR 0 1 equals 1
LOGXOR 1 1 equals 0
See also LOGNOT, LOGOR, LOGOR.
Example
LOGXOR 2 1 Result: 3 LOGXOR 2 3 Result: 1
LSH
Also: ASHIFT
Shifts its input with sign extension.
Syntax
LSH integer integer
Description
LSH reports the first input logically shifted the number of bit positions specified by the second input. If the second input is positive, the logical shift is to the left. If the second input is negative, the logical shift is to the right, with the extension of the sign bit. This is the difference to LSHIFT.
Example
LSH 2 1 Result: 4 LSH -2 -1 Result: -1 LSHIFT -2 -1 Result: 2147483647
LSHIFT
Shifts its input without sign extension.
Syntax
LSHIFT integer integer
Description
LSHIFT reports the first input logically shifted the number of bit positions specified by the second input. If the second input is positive, the logical shift is to the left. If the second input is negative, the logical shift is to the right, filling up the field with zero bits. This is the difference to LSH.
See also LSH.
Example
LSHIFT 2 1 Result: 4 LSHIFT -2 -1 Result: 2147483647 LSH -2 -1 Result: -1
MINUS
Outputs the negative value of its input.
Syntax
MINUS number
Description
MINUS reports the result of subtracting its input from 0. Note that MINUS binds less than other operators. Thus, MINUS 3 + 4 is -7 (-(3+4)) and not 1 (-3+4).
Example
MINUS 5 Result: -5 MINUS 3 + 4 Result: -7
MODULO
Outputs the remainder of two numbers.
Syntax
MODULO dividend divisor
Description
MODULO reports the number that is the remainder of dividing the first input by the second. See also % and /.
MODULO reports the result of (dividend - (divisor * floor(dividend /
divisor))). The result is the same as for % if the signs of both
operand are the same, but are different from % when the signs are
different.
Example
MODULO 6 3 Result: 0 MODULO 159 2 Result: 1 MODULO -123 4 Result: 3
NOT
Negates its input.
Syntax
NOT expression
Description
NOT reports TRUE if its input is false; otherwise it reports FALSE.
Example
NOT “FALSE Result: TRUE NOT “TRUE Result: FALSE NOT NUMBER? “A Result: TRUE IF NOT (2 > 3) THEN PRINT “YES YES
OR
Performs a logical OR on its input.
Syntax
OR object1 object2
(OR object1 object2 object3 ...)
Description
OR reports FALSE if all of its inputs are false; otherwise, it reports TRUE. OR accepts two or more inputs, which must be either TRUE or FALSE. With more than two inputs, OR and all inputs must be enclosed in parentheses.
Example
OR “TRUE “TRUE Result: TRUE OR “TRUE “FALSE Result: TRUE (OR “FALSE “TRUE “FALSE) Result: TRUE IF OR (2 = 3) (3 = 3) [PRINT “YES] YES
PI
Reports the number Pi.
Syntax
PI
Description
PI reports the value of pi. The number of digits displayed for PI is determined by the current value of :PRECISION. The full value of PI is always used in calculations, regardless of the value of :PRECISION.
Example
MAKE “PRECISION 10 PI Result: 3.14159265356 MAKE “PRECISION 2 PI Result: 3.14
RADARCTAN
Also: RADATAN
Reports the arc tangent of an angle expressed in radians.
Syntax
RADARCTAN number
Description
RADARCTAN reports the arc tangent of its input as radians. If RADARCTAN has two inputs x and y, it uses y/x if x is nonzero; if x is zero, it outputs PI/2 if y is positive, or -PI/2 if y is negative. To compute the value of pi, use 2*(RADARCTAN 0 1), or use PI.
Example
RADARCTAN 0.5
RADCOS
Reports the cosine of an angle expressed in radians.
Syntax
RADCOS number
Description
RADCOS reports the cosine of its input as radians. Remember that RADCOS x = adjacent / hypotenuse. See also RADARCTAN and RADSIN.
Example
RADCOS 0
RADCOS PI / 4
RADCOS PI / 2
RADSIN
Reports the sine of an angle expressed in radians.
Syntax
RADSIN number
Description
RADSIN reports the sine of its input, which is the number of radians in an angle. Remember that SIN x = opposite/hypotenuse. See also RADARCTAN and RADCOS.
Example
RADSIN PI / 4
RADSIN PI / 2
RANDOM
Outputs a random number.
Syntax
RANDOM number
(RANDOM bottom top)
Description
RANDOM reports a randomly selected number from 1 through its input. The output can only be a positive integer. For example: RANDOM 5 could report 1, 2, 3, 4, or 5. If RANDOM has two inputs, RANDOM outputs a random number between, and including, these two numbers. RANDOM delivers cryptographically secure numbers.
Example
RANDOM 4 Result: 3 (RANDOM 100 200) Result: 115
RERANDOM
Seed the random number generator.
Syntax
RERANDOM number
(RERANDOM)
Description
RERANDOM seeds the random number generator with its input. If RERANDOM is used without inputs, it uses a random number to seed the gemerator. See also RANDOM.
ROUND
Rounds a number.
Syntax
ROUND number
Description
ROUND reports the input number rounded to the nearest integer. See also INT.
Example
ROUND 1.45 Result: 1 ROUND 1.50 Result: 2 ROUND -57.99 Result: -58
SEC
Reports the secant.
Syntax
SEC number
Description
SEC reports the secant of its input.
Example
SEC 30 Result: 1.15
SIN
Reports the sine.
Syntax
SIN number
Description
SIN reports the sine of its input, which is the number of degrees in an angle. Remember that SIN x = opposite/hypotenuse. See also ARCTAN and COS.
Example
SIN 30 Result: 0.5 SIN 90 Result: 1
SQRT
Reports the square root.
Syntax
SQRT number
Description
SQRT reports the square root of its input. The input number must be a positive number or 0.
Example
SQRT 25 Result: 5 SQRT -1 Error: SQRT cannot work with negative numbers
TAN
Reports the tangent.
Syntax
TAN number
Description
TAN reports the tangent of its input, specified in degrees.
Example
TAN 45 Result: 1