12 Numbers   12.1 Number Concepts   12.1.4 Floating-point Computations   12.1.4.1 Rule of Float and Rational Contagion

12.1.4.1.1 Examples of Rule of Float and Rational Contagion

 ;;;; Combining rationals with floats.
 ;;; This example assumes an implementation in which 
 ;;; (float-radix 0.5) is 2 (as in IEEE) or 16 (as in IBM/360),
 ;;; or else some other implementation in which 1/2 has an exact 
 ;;;  representation in floating point.
 (+ 1/2 0.5)  1.0
 (- 1/2 0.5d0)  0.0d0
 (+ 0.5 -0.5 1/2)  0.5

 ;;;; Comparing rationals with floats.
 ;;; This example assumes an implementation in which the default float 
 ;;; format is IEEE single-float, IEEE double-float, or some other format
 ;;; in which 5/7 is rounded upwards by FLOAT.
 (< 5/7 (float 5/7))  true
 (< 5/7 (rational (float 5/7)))  true
 (< (float 5/7) (float 5/7))  false