• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
  • Debugging
  • Std
  • Community
  • Proof-automation
  • ACL2
  • Macro-libraries
  • Interfacing-tools
  • Hardware-verification
    • Gl
    • Esim
    • Vl2014
    • Sv
    • Fgl
    • Vwsim
    • Vl
    • X86isa
    • Svl
    • Rtl
      • Floating-Point Exceptions and Specification of Elementary Arithmetic Instructions
      • Implementation of Elementary Operations
      • Register-Transfer Logic
      • Floating-Point Arithmetic
        • Rounding
        • Floating-Point Formats
          • Normal Encodings
          • Denormals and Zeroes
          • Classification of Formats
          • Rebiasing Exponents
          • Infinities and NaNs
        • Floating-Point Numbers
      • Modeling Algorithms in C++ and ACL2
      • Bibliography
  • Software-verification
  • Math
  • Testing-utilities

• Floating-Point Formats

Infinities and NaNs

Infinities and NaNs

Definitions and Theorems

Function: infp

(defun infp (x f)
  (declare (xargs :guard (encodingp x f)))
  (and (mbt (encodingp x f))
       (= (expf x f) (1- (expt 2 (expw f))))
       (not (unsupp x f))
       (= (manf x f) 0)))

Function: iencode

(defun iencode (sgn f)
  (declare (xargs :guard (and (bvecp sgn 1) (formatp f))))
  (if (explicitp f)
      (cat sgn 1 (1- (expt 2 (expw f)))
           (expw f)
           1 1 0 (1- (sigw f)))
    (cat sgn 1 (1- (expt 2 (expw f)))
         (expw f)
         0 (sigw f))))

Function: nanp

(defun nanp (x f)
  (declare (xargs :guard (encodingp x f)))
  (and (mbt (encodingp x f))
       (= (expf x f) (1- (expt 2 (expw f))))
       (not (unsupp x f))
       (not (= (manf x f) 0))))

Function: qnanp

(defun qnanp (x f)
  (declare (xargs :guard (encodingp x f)))
  (and (nanp x f)
       (= (bitn x (- (prec f) 2)) 1)))

Function: snanp

(defun snanp (x f)
  (declare (xargs :guard (encodingp x f)))
  (and (nanp x f)
       (= (bitn x (- (prec f) 2)) 0)))

Function: qnanize

(defun qnanize (x f)
  (declare (xargs :guard (encodingp x f)))
  (logior x (expt 2 (- (prec f) 2))))

Function: indef

(defun indef (f)
  (declare (xargs :guard (formatp f)))
  (if (explicitp f)
      (cat (1- (expt 2 (+ (expw f) 2)))
           (+ (expw f) 2)
           0 (- (sigw f) 2))
    (cat (1- (expt 2 (+ (expw f) 1)))
         (+ (expw f) 1)
         0 (1- (sigw f)))))