12.1.1 Numeric Operations

Common Lisp provides a large variety of operations related to numbers. This section provides an overview of those operations by grouping them into categories that emphasize some of the relationships among them.

The next figure shows operators relating to arithmetic operations.

*  1+         gcd   
+  1-         incf  
-  conjugate  lcm   
/  decf             

Figure 12-1. Operators relating to Arithmetic.

The next figure shows defined names relating to exponential, logarithmic, and trigonometric operations.

abs    cos    signum  
acos   cosh   sin     
acosh  exp    sinh    
asin   expt   sqrt    
asinh  isqrt  tan     
atan   log    tanh    
atanh  phase          
cis    pi             

Figure 12-2. Defined names relating to Exponentials, Logarithms, and Trigonometry.

The next figure shows operators relating to numeric comparison and predication.

/=  >=      oddp   
<   evenp   plusp  
<=  max     zerop  
=   min            
>   minusp         

Figure 12-3. Operators for numeric comparison and predication.

The next figure shows defined names relating to numeric type manipulation and coercion.

ceiling          float-radix           rational     
complex          float-sign            rationalize  
decode-float     floor                 realpart     
denominator      fround                rem          
fceiling         ftruncate             round        
ffloor           imagpart              scale-float  
float            integer-decode-float  truncate     
float-digits     mod                                
float-precision  numerator                          

Figure 12-4. Defined names relating to numeric type manipulation and coercion.

12.1.1.1 Associativity and Commutativity in Numeric Operations

12.1.1.2 Contagion in Numeric Operations

12.1.1.3 Viewing Integers as Bits and Bytes