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|
(in-package "RTL")
(include-book "clz")
(local-defund siga-1 ()
(case (fnum)
(2 (mana))
(1 (setbits (bits 0 52 0) 53 51 29 (mana)))
(0 (setbits (bits 0 52 0) 53 51 42 (mana)))
(t (bits 0 52 0))))
(local-defund bs* ()
(case (fnum)
(2 1023)
(1 127)
(0 15)
(t 0)))
(local-defund siga* ()
(if1 (log= (si (expa) 13) 0)
(bits (ash (siga-1) (bits (clz53 (siga-1)) 5 0)) 52 0)
(setbitn (siga-1) 53 52 1)))
(local-defund expshft* ()
(if1 (log= (si (expa) 13) 0)
(bits (- 1 (bits (clz53 (siga-1)) 5 0)) 12 0)
(expa)))
(local-defund expq* ()
(bits (bits (+ (si (expshft*) 13) (bs*)) 11 0) 11 1))
(local-in-theory (disable (siga-1) (bs*) (siga*) (expshft*) (expq*)))
(local-defthmd normalize-lemma
(and (equal (siga) (siga*))
(equal (expshft) (expshft*))
(equal (expq) (expq*)))
:hints (("Goal" :do-not '(preprocess) :expand :lambdas
:in-theory '(normalize siga expshft expq siga-1 bs* siga* expshft* expq*))))
(defthm integerp-siga
(integerp (siga))
:rule-classes (:type-prescription :rewrite)
:hints (("Goal" :in-theory (enable normalize-lemma siga*))))
(defund a () (decode (opaw) (f)))
(defund p () (prec (f)))
(defund e () (expw (f)))
(defund bs () (bias (f)))
(in-theory (disable (a) (p) (e) (bs)))
(local-defthm bs*-rewrite
(equal (bs*) (bias (f)))
:hints (("Goal" :use (fnum-vals)
:in-theory (enable hp sp dp bias expw f bs*))))
(defthm opz-opw
(implies (not (specialp))
(equal (opaz) (opaw)))
:hints (("Goal" :in-theory (enable specialp))))
(defthmd spec-fields
(implies (not (specialp))
(and (equal (sgnf (opaw) (f)) (signa))
(equal (expf (opaw) (f)) (expa))
(equal (manf (opaw) (f)) (mana))))
:hints (("Goal" :use (a-fields) :in-theory (enable specialp))))
(defthm spec-class
(implies (not (specialp))
(or (normp (opaw) (f))
(denormp (opaw) (f))))
:rule-classes ()
:hints (("Goal" :in-theory (enable specialp)
:use (member-classa a-class))))
(local-defthm a-normp
(implies (and (not (specialp))
(not (= (expa) 0)))
(normp (opaw) (f)))
:hints (("Goal" :use (spec-class spec-fields)
:in-theory (enable denormp))))
(local-defthm a-denormp
(implies (and (not (specialp))
(= (expa) 0))
(denormp (opaw) (f)))
:hints (("Goal" :use (spec-class spec-fields)
:in-theory (enable normp))))
(defthmd bvecp-mana
(implies (not (specialp))
(bvecp (mana) (sigw (f))))
:hints (("Goal" :in-theory (enable manf sigw f hp sp dp)
:use (spec-fields fnum-vals))))
(defthmd bvecp-expa
(implies (not (specialp))
(bvecp (expa) (expw (f))))
:hints (("Goal" :in-theory (enable expf expw f hp sp dp)
:use (spec-fields fnum-vals))))
(local-defthm siga-1-rewrite
(implies (not (specialp))
(equal (siga-1)
(* (expt 2 (- 52 (sigw (f))))
(mana))))
:hints (("Goal" :in-theory (enable bvecp cat siga-1 sigw f hp sp dp)
:use (bvecp-mana fnum-vals))))
(local-defthm siga-normp
(implies (and (not (specialp))
(not (= (expa) 0)))
(equal (siga) (* (expt 2 52) (sig (a)))))
:hints (("Goal" :in-theory (enable si bvecp a cat normalize-lemma siga* f hp sp dp ndecode decode manf prec)
:use (spec-fields a-normp bvecp-mana fnum-vals a-normp (:instance sig-ndecode (x (opaw)) (f (f)))))))
(local-defthm bvecp-siga-1
(implies (and (not (specialp))
(= (expa) 0))
(bvecp (siga-1) 53))
:rule-classes ()
:hints (("Goal" :in-theory (enable denormp bvecp cat siga-1 sigw sigf f hp sp dp)
:use (a-denormp bvecp-mana fnum-vals))))
(local-defthm siga-1-pos
(implies (and (not (specialp))
(= (expa) 0))
(not (= (siga-1) 0)))
:rule-classes ()
:hints (("Goal" :in-theory (enable manf specialp denormp bvecp cat siga-1 sigw sigf f hp sp dp)
:use (a-fields bvecp-mana a-denormp fnum-vals))))
(local-defthmd clz-siga-1
(implies (and (not (specialp))
(= (expa) 0))
(equal (bits (clz53 (siga-1)) 5 0)
(- 52 (expo (siga-1)))))
:hints (("Goal" :use (bvecp-siga-1 siga-1-pos
(:instance expo<= (x (siga-1)) (n 52))
(:instance expo>= (x (siga-1)) (n 1))
(:instance clz-expo (s (siga-1))))
:in-theory (enable bvecp))))
(local-in-theory (disable siga-1-rewrite))
(local-defthmd siga-siga-1
(implies (and (not (specialp))
(= (expa) 0))
(equal (siga)
(* (expt 2 (- 52 (expo (siga-1))))
(siga-1))))
:hints (("Goal" :in-theory (enable ash bvecp clz-siga-1 siga*)
:nonlinearp t
:use (siga-1-pos bvecp-siga-1 normalize-lemma
(:instance expo<= (x (siga-1)) (n 52))
(:instance expo-upper-bound (x (siga-1)))))))
(defthmd siga-mana
(implies (and (not (specialp))
(= (expa) 0))
(equal (siga)
(* (expt 2 (- 52 (expo (mana))))
(mana))))
:hints (("Goal" :in-theory (enable siga-siga-1 siga-1-rewrite f dp sp hp sigw)
:use (bvecp-siga-1 siga-1-pos fnum-vals
(:instance expo-shift (x (mana)) (n (- 52 (sigw (f)))))))))
(local-defthmd siga-sig-mana
(implies (and (not (specialp))
(= (expa) 0))
(equal (siga)
(* (expt 2 52) (sig (mana)))))
:hints (("Goal" :in-theory (enable siga-mana)
:use (bvecp-mana
(:instance fp-abs (x (mana)))))))
(local-defthm siga-denormp
(implies (and (not (specialp))
(= (expa) 0))
(equal (siga) (* (expt 2 52) (sig (a)))))
:hints (("Goal" :in-theory (enable siga-sig-mana manf specialp a decode prec f dp sp hp sigf)
:use (fnum-vals a-denormp a-fields (:instance sig-ddecode (x (opaw)) (f (f)))))))
(defthmd siga-rewrite
(implies (not (specialp))
(equal (siga) (* (expt 2 52) (sig (a)))))
:hints (("Goal" :use (siga-normp siga-denormp))))
(in-theory (disable sgn-ddecode))
(defthmd a-pos
(implies (not (specialp))
(> (a) 0))
:hints (("Goal" :in-theory (enable sgn specialp encodingp normp denormp decode a f dp sp hp prec p)
:use (signa-0-1 a-fields member-classa a-class fnum-vals a-fields
(:instance sgn-ndecode (x (opaw)) (f (f)))
(:instance sgn-ddecode (x (opaw)) (f (f)))))))
(defthmd siga-bounds
(implies (not (specialp))
(and (<= (expt 2 52) (siga))
(< (siga) (expt 2 53))))
:hints (("Goal" :use (a-pos
(:instance sig-upper-bound (x (a)))
(:instance sig-lower-bound (x (a))))
:in-theory (enable siga-rewrite)
:nonlinearp t)))
(local-defthmd clz-mana
(implies (and (not (specialp))
(= (expa) 0))
(equal (bits (clz53 (siga-1)) 5 0)
(- (sigw (f)) (expo (mana)))))
:hints (("Goal" :in-theory (enable clz-siga-1 dp sp hp prec f sigw)
:use (fnum-vals bvecp-mana siga-1-pos siga-1-rewrite
(:instance expo-shift (x (mana)) (n (- 52 (sigw (f)))))))))
(local-defthmd expshft-denorm
(implies (and (not (specialp))
(= (expa) 0))
(equal (expshft)
(bits (1+ (- (expo (mana)) (sigw (f)))) 12 0)))
:hints (("Goal" :in-theory (enable clz-mana expshft* normalize-lemma))))
(local-defthmd si-expshft-denorm
(implies (and (not (specialp))
(= (expa) 0))
(equal (si (expshft) 13)
(+ (expo (a)) (bias (f)))))
:hints (("Goal" :in-theory (enable manf specialp a sigf prec decode expshft-denorm bvecp dp sp hp f)
:use (bvecp-mana fnum-vals a-denormp a-fields
(:instance expo-ddecode (x (opaw)) (f (f)))
(:instance si-bits (x (1+ (- (expo (mana)) (sigw (f))))) (n 13))
(:instance expo<= (x (mana)) (n (1- (sigw (f)))))
(:instance expo>= (x (mana)) (n 0))))))
(local-defthmd si-expshft-norm
(implies (and (not (specialp))
(not (= (expa) 0)))
(equal (si (expshft) 13)
(+ (expo (a)) (bias (f)))))
:hints (("Goal" :in-theory (enable expf expw specialp a si decode expshft* normalize-lemma bvecp dp sp hp f)
:use (bvecp-expa fnum-vals a-normp a-fields
(:instance expo-ndecode (x (opaw)) (f (f)))
(:instance si-bits (x (expa)) (n 13))
(:instance expo<= (x (expa)) (n (1- (expw (f)))))
(:instance expo>= (x (expa)) (n 0))))))
(defthmd si-expshft
(implies (not (specialp))
(equal (si (expshft) 13)
(+ (expo (a)) (bias (f)))))
:hints (("Goal" :use (si-expshft-denorm si-expshft-norm))))
(defthm nrepp-drepp
(implies (not (specialp))
(or (nrepp (a) (f))
(drepp (a) (f))))
:rule-classes ()
:hints (("Goal" :use (a-fields a-normp a-denormp)
:in-theory (enable specialp decode a))))
(defthm rationalp-abs
(implies (rationalp x) (rationalp (abs x)))
:rule-classes (:type-prescription :rewrite))
(defthmd exactp-a
(implies (not (specialp))
(integerp (* (expt 2 (1- (p))) (sig (a)))))
:hints (("Goal" :in-theory (enable exactp f dp sp hp p prec sigw nrepp drepp)
:use (nrepp-drepp
(:instance exactp-<= (x (a)) (m (+ (1- (p)) (bias (f)) (expo (a)))) (n (p)))))))
(defthmd exactp-siga
(implies (not (specialp))
(integerp (* (expt 2 (- (p) 53)) (siga))))
:hints (("Goal" :in-theory (enable siga-rewrite)
:use (exactp-a))))
(defthm p-vals
(member (p) '(53 24 11))
:rule-classes ()
:hints (("Goal" :use (fnum-vals)
:in-theory (enable dp sp hp p prec f))))
(defthmd siga-low
(implies (not (specialp))
(equal (bits (siga) (- 52 (p)) 0)
0))
:hints (("Goal" :in-theory (enable bits)
:use (a-pos exactp-siga p-vals
(:instance mod-prod (k (expt 2 (- 53 (p)))) (m (* (expt 2 (- (p) 53)) (siga))) (n 1))))))
(defthmd a-siga
(implies (not (specialp))
(equal (a)
(* (expt 2 (- (si (expshft) 13) (+ 52 (bias (f)))))
(siga))))
:hints (("Goal" :in-theory (enable siga-rewrite si-expshft)
:use (a-pos (:instance fp-rep (x (a)))))))
(defthmd si-expshft-bounds
(implies (not (specialp))
(and (>= (si (expshft) 13) (- 2 (p)))
(< (si (expshft) 13) (1- (expt 2 (expw (f)))))))
:hints (("Goal" :in-theory (enable p prec expw dp sp hp bias f nrepp drepp si-expshft)
:use (nrepp-drepp))))
(local-defthmd expq-rewrite-1
(implies (not (specialp))
(equal (expq)
(bits (+ (si (expshft) 13) (bias (f))) 11 1)))
:hints (("Goal" :use (fnum-vals)
:in-theory (enable si p prec expw dp sp hp bias f bits-bits expq* expshft* normalize-lemma))))
(defthmd expq-rewrite
(implies (not (specialp))
(equal (expq)
(fl (/ (+ (si (expshft) 13) (bias (f))) 2))))
:hints (("Goal" :use (fnum-vals si-expshft-bounds)
:in-theory (enable bits expq-rewrite-1 si p prec expw dp sp hp bias f))))
(defthm integerp-expshft
(implies (not (specialp))
(integerp (expshft)))
:rule-classes (:type-prescription :rewrite)
:hints (("Goal" :in-theory (enable normalize-lemma expshft* expa analyze))))
(defthm integerp-si-expshft
(implies (not (specialp))
(integerp (si (expshft) 13)))
:rule-classes (:type-prescription :rewrite)
:hints (("Goal" :in-theory (enable si))))
(defthmd expq-bounds
(implies (not (specialp))
(and (< 0 (expq))
(< (expq) (- (expt 2 (expw (f))) 2))))
:hints (("Goal" :use (fnum-vals si-expshft-bounds)
:in-theory (enable bits expq-rewrite p prec expw dp sp hp bias f))))
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