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# 4 Arithmetic

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## 4.1 Numeric Operations

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### sum

```SUM num1 num2
(SUM num1 num2 num3 ...)
num1 + num2
```

outputs the sum of its inputs.

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### difference

```DIFFERENCE num1 num2
num1 - num2
```

outputs the difference of its inputs. Minus sign means infix difference in ambiguous contexts (when preceded by a complete expression), unless it is preceded by a space and followed by a nonspace. (See also `MINUS`.)

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### minus

```MINUS num
- num
```

outputs the negative of its input. Minus sign means unary minus if the previous token is an infix operator or open parenthesis, or it is preceded by a space and followed by a nonspace. There is a difference in binding strength between the two forms:

```MINUS 3 + 4     means   -(3+4)
- 3 + 4         means   (-3)+4
```

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### product

```PRODUCT num1 num2
(PRODUCT num1 num2 num3 ...)
num1 * num2
```

outputs the product of its inputs.

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### quotient

```QUOTIENT num1 num2
(QUOTIENT num)
num1 / num2
```

outputs the quotient of its inputs. The quotient of two integers is an integer if and only if the dividend is a multiple of the divisor. (In other words, QUOTIENT 5 2 is 2.5, not 2, but QUOTIENT 4 2 is 2, not 2.0 — it does the right thing.) With a single input, `QUOTIENT` outputs the reciprocal of the input.

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### remainder

```REMAINDER num1 num2
```

outputs the remainder on dividing num1 by num2; both must be integers and the result is an integer with the same sign as num1.

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### modulo

```MODULO num1 num2
```

outputs the remainder on dividing num1 by num2; both must be integers and the result is an integer with the same sign as num2.

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### int

```INT num
```

outputs its input with fractional part removed, i.e., an integer with the same sign as the input, whose absolute value is the largest integer less than or equal to the absolute value of the input.

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### round

```ROUND num
```

outputs the nearest integer to the input.

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### sqrt

```SQRT num
```

outputs the square root of the input, which must be nonnegative.

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### power

```POWER num1 num2
```

outputs num1 to the num2 power. If num1 is negative, then num2 must be an integer.

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### exp

```EXP num
```

outputs e (2.718281828+) to the input power.

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### log10

```LOG10 num
```

outputs the common logarithm of the input.

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### ln

```LN num
```

outputs the natural logarithm of the input.

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### sin

```SIN degrees
```

outputs the sine of its input, which is taken in degrees.

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```RADSIN radians
```

outputs the sine of its input, which is taken in radians.

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### cos

```COS degrees
```

outputs the cosine of its input, which is taken in degrees.

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```RADCOS radians
```

outputs the cosine of its input, which is taken in radians.

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### arctan

```ARCTAN num
(ARCTAN x y)
```

outputs the arctangent, in degrees, of its input. With two inputs, outputs the arctangent of y/x, if x is nonzero, or 90 or –90 depending on the sign of y, if x is zero.

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```RADARCTAN num
```

outputs the arctangent, in radians, of its input. With two inputs, outputs the arctangent of y/x, if x is nonzero, or pi/2 or –pi/2 depending on the sign of y, if x is zero.

The expression 2*(RADARCTAN 0 1) can be used to get the value of pi.

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### iseq

```ISEQ from to					(library procedure)
```

outputs a list of the integers from from to to, inclusive.

```? show iseq 3 7
[3 4 5 6 7]
? show iseq 7 3
[7 6 5 4 3]
```

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### rseq

```RSEQ from to count				(library procedure)
```

outputs a list of count equally spaced rational numbers between from and to, inclusive.

```? show rseq 3 5 9
[3 3.25 3.5 3.75 4 4.25 4.5 4.75 5]
? show rseq 3 5 5
[3 3.5 4 4.5 5]
```

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## 4.2 Numeric Predicates

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### lessp

```LESSP num1 num2
LESS? num1 num2
num1 < num2
```

outputs `TRUE` if its first input is strictly less than its second.

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### greaterp

```GREATERP num1 num2
GREATER? num1 num2
num1 > num2
```

outputs `TRUE` if its first input is strictly greater than its second.

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### lessequalp

```LESSEQUALP num1 num2
LESSEQUAL? num1 num2
num1 <= num2
```

outputs `TRUE` if its first input is less than or equal to its second.

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### greaterequalp

```GREATEREQUALP num1 num2
GREATEREQUAL? num1 num2
num1 >= num2
```

outputs `TRUE` if its first input is greater than or equal to its second.

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## 4.3 Random Numbers

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### random

```RANDOM num
(RANDOM start end)
```

with one input, outputs a random nonnegative integer less than its input, which must be a positive integer.

With two inputs, `RANDOM` outputs a random integer greater than or equal to the first input, and less than or equal to the second input. Both inputs must be integers, and the first must be less than the second. (RANDOM 0 9) is equivalent to RANDOM 10; (RANDOM 3 8) is equivalent to (RANDOM 6)+3.

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### rerandom

```RERANDOM
(RERANDOM seed)
```

command. Makes the results of `RANDOM` reproducible. Ordinarily the sequence of random numbers is different each time Logo is used. If you need the same sequence of pseudo-random numbers repeatedly, e.g. to debug a program, say `RERANDOM` before the first invocation of `RANDOM`. If you need more than one repeatable sequence, you can give `RERANDOM` an integer input; each possible input selects a unique sequence of numbers.

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## 4.4 Print Formatting

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### form

```FORM num width precision
```

outputs a word containing a printable representation of num, possibly preceded by spaces (and therefore not a number for purposes of performing arithmetic operations), with at least width characters, including exactly precision digits after the decimal point. (If precision is 0 then there will be no decimal point in the output.)

As a debugging feature, (FORM num -1 format) will print the floating point num according to the C printf format, to allow

```to hex :num
op form :num -1 "|%08X %08X|
end
```

to allow finding out the exact result of floating point operations. The precise format needed may be machine-dependent.

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## 4.5 Bitwise Operations

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### bitand

```BITAND num1 num2
(BITAND num1 num2 num3 ...)
```

outputs the bitwise and of its inputs, which must be integers.

See section and .

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### bitor

```BITOR num1 num2
(BITOR num1 num2 num3 ...)
```

outputs the bitwise or of its inputs, which must be integers.

See section or .

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### bitxor

```BITXOR num1 num2
(BITXOR num1 num2 num3 ...)
```

outputs the bitwise exclusive or of its inputs, which must be integers.

See section or .

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### bitnot

```BITNOT num
```

outputs the bitwise not of its input, which must be an integer.

See section not .

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### ashift

```ASHIFT num1 num2
```

outputs num1 arithmetic-shifted to the left by num2 bits. If num2 is negative, the shift is to the right with sign extension. The inputs must be integers.

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### lshift

```LSHIFT num1 num2
```

outputs num1 logical-shifted to the left by num2 bits. If num2 is negative, the shift is to the right with zero fill. The inputs must be integers.

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