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Field-arithmetic-operations

Op-field-inv

Leo field inverse (reciprocal) operation.

Signature
(op-field-inv arg curve) → result
Arguments: arg — Guard (valuep arg).; curve — Guard (curvep curve).
Returns: result — Type (value-resultp result).

Definitions and Theorems

Function: op-field-inv

(defun op-field-inv (arg curve)
  (declare (xargs :guard (and (valuep arg) (curvep curve))))
  (declare (xargs :guard (value-case arg :field)))
  (let ((__function__ 'op-field-inv))
    (declare (ignorable __function__))
    (b* ((err (list :op-field-inv (value-fix arg)))
         (p (curve-base-prime curve))
         (x (value-field->get arg))
         ((unless (pfield::fep x p))
          (reserrf err))
         ((when (= x 0)) (reserrf err)))
      (value-field (pfield::div 1 x p)))))

Theorem: value-resultp-of-op-field-inv

(defthm value-resultp-of-op-field-inv
  (b* ((result (op-field-inv arg curve)))
    (value-resultp result))
  :rule-classes :rewrite)

Theorem: op-field-inv-of-value-fix-arg

(defthm op-field-inv-of-value-fix-arg
  (equal (op-field-inv (value-fix arg) curve)
         (op-field-inv arg curve)))

Theorem: op-field-inv-value-equiv-congruence-on-arg

(defthm op-field-inv-value-equiv-congruence-on-arg
  (implies (value-equiv arg arg-equiv)
           (equal (op-field-inv arg curve)
                  (op-field-inv arg-equiv curve)))
  :rule-classes :congruence)

Theorem: op-field-inv-of-curve-fix-curve

(defthm op-field-inv-of-curve-fix-curve
  (equal (op-field-inv arg (curve-fix curve))
         (op-field-inv arg curve)))

Theorem: op-field-inv-curve-equiv-congruence-on-curve

(defthm op-field-inv-curve-equiv-congruence-on-curve
  (implies (curve-equiv curve curve-equiv)
           (equal (op-field-inv arg curve)
                  (op-field-inv arg curve-equiv)))
  :rule-classes :congruence)