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|
;; Cuong Chau <cuong.chau@arm.com>
;; January 2022
(in-package "RTL")
(include-book "round")
(local (arith-5-for-rtl))
;; ======================================================================
(local
(defundd rz ()
(if (and (equal (fzp) 1)
(not (equal (f) (hp)))
(or (denormp (opaw) (f))
(denormp (opbw) (f))))
(set-flag (idc) (rin))
(rin))))
(local
(encapsulate
()
(local
(defthm decode-opz-rewrite
(implies (not (specialp))
(and (equal (decode (opaz) (f)) (a))
(equal (decode (opbz) (f)) (b))))
:hints (("Goal" :in-theory (enable specialp
opaz
opbz
a
b
a-class
b-class)))))
(local
(defthm arm-binary-spec-to-arm-binary-comp
(implies (not (specialp))
(equal (arm-binary-spec 'div (opaw) (opbw) (rin) (f))
(arm-binary-comp 'div (opaz) (opbz) (rz) (f))))
:hints (("Goal" :in-theory (enable specialp
opaz
opbz
rz
fzp
a-class
b-class
binary-undefined-p)))))
(defthmd arm-binary-spec-to-arm-post-comp
(implies (not (specialp))
(equal (arm-binary-spec 'div (opaw) (opbw) (rin) (f))
(arm-post-comp (/ (a) (b)) (rz) (f))))
:hints (("Goal"
:in-theory (e/d (specialp
a-class
b-class
binary-eval)
(arm-binary-spec
arm-post-comp)))))
))
(local
(defthmd data-non-special
(implies (not (specialp))
(equal (data)
(mv-nth 0 (final (qrnd)
(inx)
(sign)
(expq)
(rmode)
(fzp)
(fnum)
(flags-b)))))
:hints (("Goal" :in-theory (enable specialp data result)))))
(local
(defthmd flags-non-special
(implies (not (specialp))
(equal (flags)
(mv-nth 1 (final (qrnd)
(inx)
(sign)
(expq)
(rmode)
(fzp)
(fnum)
(flags-b)))))
:hints (("Goal" :in-theory (enable specialp flags result)))))
(defthmd signa-a-rel
(implies (not (specialp))
(equal (signa)
(if (< (a) 0) 1 0)))
:hints (("Goal"
:use nonzero-a
:in-theory (enable spec-fields a decode ndecode ddecode))))
(defthmd signb-b-rel
(implies (not (specialp))
(equal (signb)
(if (< (b) 0) 1 0)))
:hints (("Goal"
:use nonzero-b
:in-theory (enable spec-fields b decode ndecode ddecode))))
(defthmd sign-a/b-rel
(implies (not (specialp))
(equal (sign)
(if (< (/ (a) (b)) 0)
1
0)))
:hints (("Goal" :in-theory (enable sign signa-a-rel signb-b-rel))))
;; Overflow
(local
(defthm fpscr-rc-to-rmode
(equal (fpscr-rc (rin))
(mode (rmode)))
:hints (("Goal" :in-theory (enable fpscr-rc mode rmode)))))
(local
(defthmd si13-expq-not-ovf
(implies (and (<= 1 (si (expq) 13))
(not (specialp)))
(equal (<= (rnd (abs (/ (a) (b)))
(rmode-prime (mode (rmode)) (sign))
(prec (f)))
(lpn (f)))
(<= (si (expq) 13)
(- (expt 2 (expw (f))) 2))))
:hints (("Goal"
:use (expo-rnd-abs-a/b
(:instance expo-monotone
(x (rnd (abs (/ (a) (b)))
(rmode-prime (mode (rmode)) (sign))
(prec (f))))
(y (lpn (f))))
(:instance expo-monotone
(x (lpn (f)))
(y (rnd (abs (/ (a) (b)))
(rmode-prime (mode (rmode)) (sign))
(prec (f)))))
(:instance exactp2
(x (rnd (abs (/ (a) (b)))
(rmode-prime (mode (rmode)) (sign))
(prec (f))))
(n (prec (f))))
(:instance expo-upper-bound
(x (rnd (abs (/ (a) (b)))
(rmode-prime (mode (rmode)) (sign))
(prec (f)))))
(:instance int+1<=
(x (* (rnd (abs (/ (a) (b)))
(rmode-prime (mode (rmode)) (sign))
(prec (f)))
(expt 2 (- (1- (prec (f)))
(expo
(rnd (abs (/ (a) (b)))
(rmode-prime
(mode (rmode)) (sign))
(prec (f))))))))
(y (expt 2 (prec (f))))))
:in-theory (enable f lpn)))))
(local
(defthmd data-when-ovf
(implies (and (not (specialp))
(< (lpn (f))
(rnd (abs (/ (a) (b)))
(rmode-prime (mode (rmode)) (sign))
(prec (f)))))
(equal (data)
(mv-nth 0 (arm-post-comp (/ (a) (b)) (rz) (f)))))
:hints (("Goal"
:use (si13-expq-not-ovf
rnd-abs-a/b-denormal-upper-bound)
:in-theory (e/d (data-non-special
rz
f
final
rnd-minus
mode
sgn
lpn
nencode
sign-a/b-rel)
(acl2::default-expt-2))))))
(local
(defthm logior-to-set-flag
(and (equal (logior 8 (rin))
(set-flag 3 (rin)))
(equal (logior 16 (rin))
(set-flag 4 (rin)))
(equal (logior 20 (rin))
(set-flag 2 (set-flag 4 (rin))))
(equal (logior 24 (rin))
(set-flag 4 (set-flag 3 (rin))))
(equal (logior 128 (rin))
(set-flag 7 (rin)))
(equal (logior 136 (rin))
(set-flag 3 (set-flag 7 (rin))))
(equal (logior 144 (rin))
(set-flag 4 (set-flag 7 (rin))))
(equal (logior 148 (rin))
(set-flag 2 (set-flag 4 (set-flag 7 (rin))))))
:hints (("Goal" :in-theory (enable set-flag)))))
(local
(defthmd flags-when-ovf
(implies (and (not (specialp))
(< (lpn (f))
(rnd (abs (/ (a) (b)))
(rmode-prime (mode (rmode)) (sign))
(prec (f)))))
(equal (logior (rin) (flags))
(mv-nth 1 (arm-post-comp (/ (a) (b)) (rz) (f)))))
:hints (("Goal"
:use (si13-expq-not-ovf
rnd-abs-a/b-denormal-upper-bound)
:in-theory (e/d (flags-non-special
rz
fzp
f
final
rnd-minus
mode
lpn
flags-b-rewrite
sign-a/b-rel)
(acl2::default-expt-2
acl2::default-logior-2))))))
;; Flush-to-zero
(local
(defthmd fdivlane-correct-when-fz
(implies (and (not (specialp))
(<= (rnd (abs (/ (a) (b)))
(rmode-prime (mode (rmode)) (sign))
(prec (f)))
(lpn (f)))
(< (abs (/ (a) (b))) (spn (f)))
(equal (fzp) 1))
(mv-let (data-spec r-spec) (arm-post-comp (/ (a) (b)) (rz) (f))
(and (equal (data) data-spec)
(equal (logior (rin) (flags)) r-spec))))
:hints (("Goal"
:use si13-expq-denormal
:in-theory (enable data-non-special
flags-non-special
rz
fzp
f
final
rnd-minus
rmode-prime
flip-mode
flags-b-rewrite
bitn-logior
sign-a/b-rel)))))
;; Denormal round to zero
(local
(defthmd data-when-drnd-=-0
(implies (and (not (specialp))
(<= (rnd (abs (/ (a) (b)))
(rmode-prime (mode (rmode)) (sign))
(prec (f)))
(lpn (f)))
(< (abs (/ (a) (b))) (spn (f)))
(equal (fzp) 0)
(equal (drnd (/ (a) (b))
(mode (rmode))
(f))
0))
(equal (data)
(mv-nth 0 (arm-post-comp (/ (a) (b)) (rz) (f)))))
:hints (("Goal"
:use (si13-expq-denormal
drnd-abs-a/b-to-qrnd)
:in-theory (enable data-non-special
rz
f
final
rnd-minus
drnd-minus
rmode-prime
flip-mode
sign-a/b-rel)))))
(local
(defthmd flags-when-drnd-=-0
(implies (and (not (specialp))
(<= (rnd (abs (/ (a) (b)))
(rmode-prime (mode (rmode)) (sign))
(prec (f)))
(lpn (f)))
(< (abs (/ (a) (b))) (spn (f)))
(equal (fzp) 0)
(equal (drnd (/ (a) (b))
(mode (rmode))
(f))
0))
(equal (logior (rin) (flags))
(mv-nth 1 (arm-post-comp (/ (a) (b)) (rz) (f)))))
:hints (("Goal"
:use (si13-expq-denormal
inx-exact-a/b-denormal-rel)
:in-theory (enable flags-non-special
rz
fzp
final
rnd-minus
drnd-minus
rmode-prime
flip-mode
flags-b-rewrite
sign-a/b-rel)))))
;; Denormal round to SPN
(local
(defthmd data-when-abs-drnd-=-spn
(implies (and (not (specialp))
(<= (rnd (abs (/ (a) (b)))
(rmode-prime (mode (rmode)) (sign))
(prec (f)))
(lpn (f)))
(< (abs (/ (a) (b))) (spn (f)))
(equal (fzp) 0)
(equal (abs (drnd (/ (a) (b))
(mode (rmode))
(f)))
(spn (f))))
(equal (data)
(mv-nth 0 (arm-post-comp (/ (a) (b)) (rz) (f)))))
:hints (("Goal"
:use (si13-expq-denormal
drnd-abs-a/b-to-qrnd)
:in-theory (e/d (data-non-special
rz
fzp
f
final
rnd-minus
drnd-minus
rmode-prime
flip-mode
spn
nencode
sign-a/b-rel)
(acl2::|(<= x (/ y)) with (< y 0)|
acl2::|(< (/ x) y) with (< x 0)|
acl2::not-integerp-1b
acl2::not-integerp-2b
acl2::not-integerp-3b
acl2::not-integerp-4b))))))
(local
(defthmd flags-when-abs-drnd-=-spn
(implies (and (not (specialp))
(<= (rnd (abs (/ (a) (b)))
(rmode-prime (mode (rmode)) (sign))
(prec (f)))
(lpn (f)))
(< (abs (/ (a) (b))) (spn (f)))
(equal (fzp) 0)
(equal (abs (drnd (/ (a) (b))
(mode (rmode))
(f)))
(spn (f))))
(equal (logior (rin) (flags))
(mv-nth 1 (arm-post-comp (/ (a) (b)) (rz) (f)))))
:hints (("Goal"
:use (si13-expq-denormal
inx-exact-a/b-denormal-rel)
:in-theory (enable flags-non-special
rz
fzp
final
rnd-minus
drnd-minus
rmode-prime
flip-mode
flags-b-rewrite
sign-a/b-rel)))))
;; Denormal case
(local
(defthm common-mode-p-rmode
(common-mode-p (mode (rmode)))
:hints (("Goal" :in-theory (enable mode)))))
(local
(defthm sgnf-data
(implies (not (specialp))
(equal (sgnf (data) (f))
(sign)))
:hints (("Goal" :in-theory (enable sgnf data-non-special f final bvecp)))))
(local
(defthmd drnd-<=-spn
(implies (<= (abs (/ (a) (b))) (spn (f)))
(<= (abs (drnd (/ (a) (b))
(mode (rmode))
(f)))
(spn (f))))
:hints (("Goal"
:use ((:instance rnd-monotone
(x (+ (/ (a) (b))
(* (sgn (/ (a) (b)))
(spn (f)))))
(y (+ (spn (f))
(* (sgn (/ (a) (b)))
(spn (f)))))
(mode (mode (rmode)))
(n (prec (f))))
(:instance rnd-monotone
(x (+ (- (spn (f)))
(* (sgn (/ (a) (b)))
(spn (f)))))
(y (+ (/ (a) (b))
(* (sgn (/ (a) (b)))
(spn (f)))))
(mode (mode (rmode)))
(n (prec (f)))))
:in-theory (enable drnd-rewrite spn f mode sgn)))
:rule-classes :linear))
(local
(defthm expf-data-denormal
(implies (and (not (specialp))
(< (abs (/ (a) (b))) (spn (f)))
(not (equal (abs (drnd (/ (a) (b))
(mode (rmode))
(f)))
(spn (f)))))
(and (equal (expf (data) (f))
0)
(equal (bits (qrnd) (+ -1 (prec (f))) 0)
(bits (qrnd) (+ -2 (prec (f))) 0))))
:hints (("Goal"
:use (si13-expq-denormal
drnd-<=-spn
drnd-abs-a/b-to-qrnd
(:instance bitn-plus-bits
(x (qrnd))
(m 0)
(n (1- (prec (f))))))
:in-theory (e/d (expf
data-non-special
f
final
drnd-minus
rmode-prime
flip-mode
spn
sign-a/b-rel)
(acl2::default-expt-2
acl2::|(<= x (/ y)) with (< y 0)|
acl2::|(< (/ x) y) with (< x 0)|
acl2::not-integerp-1b
acl2::not-integerp-2b
acl2::not-integerp-3b
acl2::not-integerp-4b))))))
(local
(defthm manf-data-denormal
(implies (and (not (specialp))
(< (abs (/ (a) (b))) (spn (f)))
(equal (fzp) 0))
(equal (manf (data) (f))
(bits (qrnd) (- (prec (f)) 2) 0)))
:hints (("Goal"
:use si13-expq-denormal
:in-theory (enable manf
data-non-special
f
final
sign-a/b-rel)))))
(defthm not-explicitp-f
(not (explicitp (f)))
:hints (("Goal" :in-theory (enable f))))
(local
(defthmd drnd-to-ddecode-data
(implies (and (not (specialp))
(< (abs (/ (a) (b))) (spn (f)))
(equal (fzp) 0)
(not (equal (abs (drnd (/ (a) (b))
(mode (rmode))
(f)))
(spn (f)))))
(equal (drnd (/ (a) (b))
(mode (rmode))
(f))
(ddecode (data) (f))))
:hints (("Goal"
:use drnd-abs-a/b-to-qrnd
:in-theory (enable ddecode
drnd-minus
rmode-prime
flip-mode
sign-a/b-rel)))))
(defthmd si-expq-non-neg
(implies (<= 0 (si (expq) 13))
(equal (si (expq) 13) (expq)))
:hints (("Goal" :in-theory (enable si))))
(local
(defthm encodingp-data
(implies (not (specialp))
(encodingp (data) (f)))
:hints (("Goal"
:cases ((equal (sign) 0))
:use ((:instance bits-shift-up-1
(x (+ (expt 2 (expw (f)))
(expq)))
(i 63)
(j (1- (prec (f))))
(k (1- (prec (f)))))
(:instance bits-shift-up-1
(x (+ (expt 2 (expw (f)))
(bitn (qrnd) (1- (prec (f))))))
(i 63)
(j (1- (prec (f))))
(k (1- (prec (f)))))
(:instance bits-shift-up-1
(x (expq))
(i 63)
(j (1- (prec (f))))
(k (1- (prec (f)))))
(:instance bits-shift-up-1
(x (bitn (qrnd) (1- (prec (f)))))
(i 63)
(j (1- (prec (f))))
(k (1- (prec (f))))))
:in-theory (enable encodingp
data-non-special
f
final
si-expq-non-neg
cat
bvecp)))))
(local
(defthm denormp-data
(implies (and (not (specialp))
(< (abs (/ (a) (b))) (spn (f)))
(equal (fzp) 0)
(not (equal (drnd (/ (a) (b))
(mode (rmode))
(f))
0))
(not (equal (abs (drnd (/ (a) (b))
(mode (rmode))
(f)))
(spn (f)))))
(denormp (data) (f)))
:hints (("Goal"
:use drnd-abs-a/b-to-qrnd
:in-theory (enable denormp
drnd-minus
rmode-prime
flip-mode
sign-a/b-rel)))))
(local
(defthmd data-to-dencode-drnd
(implies (and (not (specialp))
(< (abs (/ (a) (b))) (spn (f)))
(equal (fzp) 0)
(not (equal (drnd (/ (a) (b))
(mode (rmode))
(f))
0))
(not (equal (abs (drnd (/ (a) (b))
(mode (rmode))
(f)))
(spn (f)))))
(equal (data)
(dencode (drnd (/ (a) (b))
(mode (rmode))
(f))
(f))))
:hints (("Goal" :use drnd-to-ddecode-data))))
(local
(defthmd data-when-denormal
(implies (and (not (specialp))
(< (abs (/ (a) (b))) (spn (f)))
(equal (fzp) 0)
(not (equal (drnd (/ (a) (b))
(mode (rmode))
(f))
0))
(not (equal (abs (drnd (/ (a) (b))
(mode (rmode))
(f)))
(spn (f)))))
(equal (data)
(mv-nth 0 (arm-post-comp (/ (a) (b)) (rz) (f)))))
:hints (("Goal"
:use (si13-expq-denormal
rnd-abs-a/b-denormal-upper-bound)
:in-theory (enable data-to-dencode-drnd
rz
fzp
f
rnd-minus
rmode-prime
flip-mode
lpn
sign-a/b-rel)))))
(local
(defthmd flags-when-denormal
(implies (and (not (specialp))
(< (abs (/ (a) (b))) (spn (f)))
(equal (fzp) 0)
(not (equal (drnd (/ (a) (b))
(mode (rmode))
(f))
0))
(not (equal (abs (drnd (/ (a) (b))
(mode (rmode))
(f)))
(spn (f)))))
(equal (logior (rin) (flags))
(mv-nth 1 (arm-post-comp (/ (a) (b)) (rz) (f)))))
:hints (("Goal"
:use (si13-expq-denormal
rnd-abs-a/b-denormal-upper-bound
inx-exact-a/b-denormal-rel)
:in-theory (enable flags-non-special
rz
fzp
f
final
rnd-minus
drnd-minus
rmode-prime
flip-mode
flags-b-rewrite
lpn
sign-a/b-rel)))))
;; Normal case
(local
(defthm expf-data-normal
(implies (and (not (specialp))
(<= (rnd (abs (/ (a) (b)))
(rmode-prime (mode (rmode)) (sign))
(prec (f)))
(lpn (f)))
(<= (spn (f)) (abs (/ (a) (b)))))
(equal (expf (data) (f))
(si (expq) 13)))
:hints (("Goal"
:use (si13-expq-denormal
si13-expq-not-ovf)
:in-theory (enable expf
data-non-special
f
final
si-expq-non-neg
bvecp)))))
(local
(defthm manf-data-normal
(implies (and (not (specialp))
(<= (rnd (abs (/ (a) (b)))
(rmode-prime (mode (rmode)) (sign))
(prec (f)))
(lpn (f)))
(<= (spn (f)) (abs (/ (a) (b)))))
(equal (manf (data) (f))
(bits (qrnd) (- (prec (f)) 2) 0)))
:hints (("Goal"
:use (si13-expq-denormal
si13-expq-not-ovf)
:in-theory (enable manf
data-non-special
f
final
expo-lpn)))))
(local
(defthmd rnd-to-ndecode-data
(implies (and (not (specialp))
(<= (rnd (abs (/ (a) (b)))
(rmode-prime (mode (rmode)) (sign))
(prec (f)))
(lpn (f)))
(<= (spn (f)) (abs (/ (a) (b)))))
(equal (rnd (/ (a) (b))
(mode (rmode))
(prec (f)))
(ndecode (data) (f))))
:hints (("Goal"
:use (rnd-abs-a/b-to-qrnd
si13-expq-denormal)
:in-theory (enable ndecode
rnd-minus
rmode-prime
flip-mode
sign-a/b-rel)))))
(local
(defthm normp-data
(implies (and (not (specialp))
(<= (rnd (abs (/ (a) (b)))
(rmode-prime (mode (rmode)) (sign))
(prec (f)))
(lpn (f)))
(<= (spn (f)) (abs (/ (a) (b)))))
(normp (data) (f)))
:hints (("Goal"
:use (si13-expq-denormal
si13-expq-not-ovf)
:in-theory (enable normp)))))
(local
(defthmd data-to-nencode-rnd
(implies (and (not (specialp))
(<= (rnd (abs (/ (a) (b)))
(rmode-prime (mode (rmode)) (sign))
(prec (f)))
(lpn (f)))
(<= (spn (f)) (abs (/ (a) (b)))))
(equal (data)
(nencode (rnd (/ (a) (b))
(mode (rmode))
(prec (f)))
(f))))
:hints (("Goal" :use rnd-to-ndecode-data))))
(local
(defthmd data-when-normal
(implies (and (not (specialp))
(<= (rnd (abs (/ (a) (b)))
(rmode-prime (mode (rmode)) (sign))
(prec (f)))
(lpn (f)))
(<= (spn (f)) (abs (/ (a) (b)))))
(equal (data)
(mv-nth 0 (arm-post-comp (/ (a) (b)) (rz) (f)))))
:hints (("Goal"
:in-theory (enable data-to-nencode-rnd
rz
f
rnd-minus
rmode-prime
flip-mode
sign-a/b-rel)))))
(local
(defthmd flags-when-normal
(implies (and (not (specialp))
(<= (rnd (abs (/ (a) (b)))
(rmode-prime (mode (rmode)) (sign))
(prec (f)))
(lpn (f)))
(<= (spn (f)) (abs (/ (a) (b)))))
(equal (logior (rin) (flags))
(mv-nth 1 (arm-post-comp (/ (a) (b)) (rz) (f)))))
:hints (("Goal"
:use (si13-expq-denormal
si13-expq-not-ovf
inx-exact-a/b-rel)
:in-theory (e/d (flags-non-special
rz
f
final
rnd-minus
rmode-prime
flip-mode
flags-b-rewrite
sign-a/b-rel)
(acl2::default-logior-2
acl2::not-integerp-1b
acl2::not-integerp-2b
acl2::not-integerp-3b
acl2::not-integerp-4b))))))
;; Combine all cases
(local
(defthmd data-non-special-correct
(implies (not (specialp))
(equal (data)
(mv-nth 0 (arm-binary-spec 'div (opaw) (opbw) (rin) (f)))))
:hints (("Goal"
:use (data-when-ovf
fdivlane-correct-when-fz
data-when-drnd-=-0
data-when-abs-drnd-=-spn
data-when-denormal
data-when-normal)
:in-theory (e/d (arm-binary-spec-to-arm-post-comp)
(arm-binary-spec arm-post-comp abs))))))
(local
(defthmd flags-non-special-correct
(implies (not (specialp))
(equal (logior (rin) (flags))
(mv-nth 1 (arm-binary-spec 'div (opaw) (opbw) (rin) (f)))))
:hints (("Goal"
:use (flags-when-ovf
fdivlane-correct-when-fz
flags-when-drnd-=-0
flags-when-abs-drnd-=-spn
flags-when-denormal
flags-when-normal)
:in-theory (e/d (arm-binary-spec-to-arm-post-comp)
(arm-binary-spec arm-post-comp abs))))))
(defthmd fdivlane-main
(mv-let
(data-spec r-spec)
(arm-binary-spec 'div (opaw) (opbw) (rin) (f))
(and (equal (data) data-spec)
(equal (logior (rin) (flags)) r-spec)))
:hints (("Goal"
:use (fdivlane-special-correct
data-non-special-correct
flags-non-special-correct)
:in-theory (disable arm-binary-spec))))
(local
(defthmd fdivlane-main-inst
(let* ((f (case (fnum) (1 (hp)) (2 (sp)) (3 (dp))))
(fmtw (+ 1 (expw f) (sigw f)))
(fzp (bitn (rin) 24))
(dnp (bitn (rin) 25))
(rmode (bits (rin) 23 22)))
(mv-let (data flags) (fdivlane (opa) (opb) (fnum) (vec) fzp dnp rmode)
(mv-let
(data-spec r-spec)
(arm-binary-spec 'div
(bits (opa) (1- fmtw) 0)
(bits (opb) (1- fmtw) 0)
(rin)
f)
(and (equal data data-spec)
(equal (logior (rin) flags) r-spec)))))
:hints (("Goal"
:use fdivlane-main
:in-theory (e/d (fdivlane-lemma
data flags
opaw opbw fmtw
f
fzp dnp rmode)
(arm-binary-spec))))))
(local
(defmacro ic ()
'(input-constraints opa opb fnum vec rin)))
(defthmd fdivlane-correct
(implies (input-constraints opa opb fnum vec rin)
(let* ((f (case fnum (1 (hp)) (2 (sp)) (3 (dp))))
(fmtw (+ 1 (expw f) (sigw f)))
(fzp (bitn rin 24))
(dnp (bitn rin 25))
(rmode (bits rin 23 22)))
(mv-let (data flags) (fdivlane opa opb fnum vec fzp dnp rmode)
(mv-let
(data-spec r-spec)
(arm-binary-spec 'div
(bits opa (1- fmtw) 0)
(bits opb (1- fmtw) 0)
rin
f)
(and (equal data data-spec)
(equal (logior rin flags) r-spec))))))
:hints (("Goal"
:use (:functional-instance
fdivlane-main-inst
(opa (lambda () (if (ic) opa (opa))))
(opb (lambda () (if (ic) opb (opb))))
(fnum (lambda () (if (ic) fnum (fnum))))
(vec (lambda () (if (ic) vec (vec))))
(rin (lambda () (if (ic) rin (rin)))))
:in-theory (disable arm-binary-spec))))
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