LISP - Numbers

Common Lisp defines several kinds of numbers. The number data type includes various kinds of numbers supported by LISP.
The number types supported by LISP are −
Integers
Ratios
Floating-point numbers
Complex numbers
The following diagram shows the number hierarchy and various numeric data types available in LISP −
The following table describes various number type data available in LISP −
fixnum
This data type represents integers which are not too large and mostly in the range  -215  to 215-1 (it is machine-dependent)
bignum
These are very large numbers with size limited by the amount of memory allocated for LISP, they are not fixnum numbers.
ratio
Represents the ratio of two numbers in the numerator/denominator form. The / function always produce the result in ratios, when its arguments are integers.
float
It represents non-integer numbers. There are four float data types with increasing precision.
complex
It represents complex numbers, which are denoted by #c. The real and imaginary parts could be both either rational or floating point numbers.
Create a new source code file named main.lisp and type the following code in it.
(write (/ 1 2))
(terpri)
(write ( + (/ 1 2) (/ 3 4)))
(terpri)
(write ( + #c( 1 2) #c( 3 -4)))
When you execute the code, it returns the following result −
1/2
5/4
#C(4 -2)

The following table describes some commonly used numeric functions −
+, -, *, /
Respective arithmetic operations
sin, cos, tan, acos, asin, atan
Respective trigonometric functions.
sinh, cosh, tanh, acosh, asinh, atanh
Respective hyperbolic functions.
exp
Exponentiation function. Calculates ex
expt
Exponentiation function, takes base and power both.
sqrt
It calculates the square root of a number.
log
Logarithmic function. It one parameter is given, then it calculates its natural logarithm, otherwise the second parameter is used as base.
conjugate
It calculates the complex conjugate of a number. In case of a real number, it returns the number itself.
abs
It returns the absolute value (or magnitude) of a number.
gcd
It calculates the greatest common divisor of the given numbers.
lcm
It calculates the least common multiple of the given numbers.
isqrt
It gives the greatest integer less than or equal to the exact square root of a given natural number.
floor, ceiling, truncate, round
All these functions take two arguments as a number and returns the quotient; floor returns the largest integer that is not greater than ratio, ceiling chooses the smaller integer that is larger than ratio, truncate chooses the integer of the same sign as ratio with the largest absolute value that is less than absolute value of ratio, and round chooses an integer that is closest to ratio.
ffloor, fceiling, ftruncate, fround
Does the same as above, but returns the quotient as a floating point number.
mod, rem
Returns the remainder in a division operation.
float
Converts a real number to a floating point number.
rational, rationalize
Converts a real number to rational number.
numerator, denominator
Returns the respective parts of a rational number.
realpart, imagpart
Returns the real and imaginary part of a complex number.
Create a new source code file named main.lisp and type the following code in it.
(write (/ 45 78))
(terpri)
(write (floor 45 78))
(terpri)
(write (/ 3456 75))
(terpri)
(write (floor 3456 75))
(terpri)
(write (ceiling 3456 75))
(terpri)
(write (truncate 3456 75))
(terpri)
(write (round 3456 75))
(terpri)
(write (ffloor 3456 75))
(terpri)
(write (fceiling 3456 75))
(terpri)
(write (ftruncate 3456 75))
(terpri)
(write (fround 3456 75))
(terpri)
(write (mod 3456 75))
(terpri)
(setq c (complex 6 7))
(write c)
(terpri)
(write (complex 5 -9))
(terpri)
(write (realpart c))
(terpri)
(write (imagpart c))
When you execute the code, it returns the following result −
15/26
0
1152/25
46
47
46
46
46.0
47.0
46.0
46.0
6
#C(6 7)
#C(5 -9)
6
7


    79 Lectures 
     7 hours 

 Arnold Higuit
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