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3.5 Numeric Conversions

To convert an integer to floating point, use the function float.

— Function: float number

This returns number converted to floating point. If number is already floating point, float returns it unchanged.

There are four functions to convert floating-point numbers to integers; they differ in how they round. All accept an argument number and an optional argument divisor. Both arguments may be integers or floating-point numbers. divisor may also be nil. If divisor is nil or omitted, these functions convert number to an integer, or return it unchanged if it already is an integer. If divisor is non-nil, they divide number by divisor and convert the result to an integer. If divisor is zero (whether integer or floating point), Emacs signals an arith-error error.

— Function: truncate number &optional divisor

This returns number, converted to an integer by rounding towards zero. 

          (truncate 1.2)
               ⇒ 1
          (truncate 1.7)
               ⇒ 1
          (truncate -1.2)
               ⇒ -1
          (truncate -1.7)
               ⇒ -1
— Function: floor number &optional divisor

This returns number, converted to an integer by rounding downward (towards negative infinity).

If divisor is specified, this uses the kind of division operation that corresponds to mod, rounding downward. 

          (floor 1.2)
               ⇒ 1
          (floor 1.7)
               ⇒ 1
          (floor -1.2)
               ⇒ -2
          (floor -1.7)
               ⇒ -2
          (floor 5.99 3)
               ⇒ 1
— Function: ceiling number &optional divisor

This returns number, converted to an integer by rounding upward (towards positive infinity). 

          (ceiling 1.2)
               ⇒ 2
          (ceiling 1.7)
               ⇒ 2
          (ceiling -1.2)
               ⇒ -1
          (ceiling -1.7)
               ⇒ -1
— Function: round number &optional divisor

This returns number, converted to an integer by rounding towards the nearest integer. Rounding a value equidistant between two integers returns the even integer. 

          (round 1.2)
               ⇒ 1
          (round 1.7)
               ⇒ 2
          (round -1.2)
               ⇒ -1
          (round -1.7)
               ⇒ -2