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|
; X86ISA Library
; Note: The license below is based on the template at:
; http://opensource.org/licenses/BSD-3-Clause
; Copyright (C) 2015, Regents of the University of Texas
; All rights reserved.
; Redistribution and use in source and binary forms, with or without
; modification, are permitted provided that the following conditions are
; met:
; o Redistributions of source code must retain the above copyright
; notice, this list of conditions and the following disclaimer.
; o Redistributions in binary form must reproduce the above copyright
; notice, this list of conditions and the following disclaimer in the
; documentation and/or other materials provided with the distribution.
; o Neither the name of the copyright holders nor the names of its
; contributors may be used to endorse or promote products derived
; from this software without specific prior written permission.
; THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
; "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
; LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
; A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
; HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
; SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
; LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
; DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
; THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
; (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
; OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
; Original Author(s):
; Shilpi Goel <shigoel@cs.utexas.edu>
(in-package "X86ISA")
(include-book "app-view/user-level-memory-utils" :dir :proof-utils :ttags :all)
(include-book "centaur/bitops/ihs-extensions" :dir :system)
(local (include-book "centaur/bitops/signed-byte-p" :dir :system))
(local (include-book "arithmetic/top-with-meta" :dir :system))
(local (in-theory (e/d* (x86-operation-mode
rime-size
rme-size
wime-size
wme-size)
(las-to-pas
xr-fault-wb-in-system-level-marking-view
xr-fault-wb-in-sys-view))))
;; ======================================================================
;; Here is the sub-routine:
;; void copyData (int* src, int* dst, unsigned int n) {
;; int* dstEnd = dst + n;
;; while (dst != dstEnd)
;; *dst++ = *src++;
;; }
;; O1 optimization:
;; 0000000000000000 <_copyData>:
;; 0: 55 push %rbp
;; 1: 48 89 e5 mov %rsp,%rbp
;; 4: 85 d2 test %edx,%edx
;; 6: 74 1a je 22 <_copyData+0x22>
;; 8: 89 d0 mov %edx,%eax
;; a: 48 c1 e0 02 shl $0x2,%rax
;; e: 66 90 xchg %ax,%ax
;; 10: 8b 0f mov (%rdi),%ecx
;; 12: 48 83 c7 04 add $0x4,%rdi
;; 16: 89 0e mov %ecx,(%rsi)
;; 18: 48 83 c6 04 add $0x4,%rsi
;; 1c: 48 83 c0 fc add $0xfffffffffffffffc,%rax
;; 20: 75 ee jne 10 <_copyData+0x10>
;; 22: 5d pop %rbp
;; 23: c3 retq
(defconst *copyData* ;; 15 instructions
'(
#x55 ;; push %rbp 1
#x48 #x89 #xe5 ;; mov %rsp,%rbp 2
#x85 #xd2 ;; test %edx,%edx 3
#x74 #x1a ;; je 22 <_copyData+0x22> 4 (jump if ZF = 1)
#x89 #xd0 ;; mov %edx,%eax 5
#x48 #xc1 #xe0 #x02 ;; shl $0x2,%rax 6
#x66 #x90 ;; xchg %ax,%ax 7
#x8b #x0f ;; mov (%rdi),%ecx 8
#x48 #x83 #xc7 #x04 ;; add $0x4,%rdi 9
#x89 #x0e ;; mov %ecx,(%rsi) 10
#x48 #x83 #xc6 #x04 ;; add $0x4,%rsi 11
#x48 #x83 #xc0 #xfc ;; add $0xfffffffffffffffc,%rax 12
#x75 #xee ;; jne 10 <_copyData+0x10> 13 (jump if ZF = 0)
#x5d ;; pop %rbp 14
#xc3 ;; retq 15
))
(defconst *prog-len* (len *copyData*))
;; Some important registers:
;; EDX: n
;; RSI: Destination address
;; RDI: Source address
;; ======================================================================
;; Some GL Theorems:
(encapsulate
()
(local (include-book "centaur/gl/gl" :dir :system))
(defthm-using-gl loop-clk-measure-helper
:hyp (and (signed-byte-p 64 m)
(<= 4 m))
:concl (< (loghead 64 (+ #xfffffffffffffffc m)) m)
:g-bindings (gl::auto-bindings (:int m 64))
:rule-classes :linear)
(defthm-using-gl effects-copyData-loop-helper-1
:hyp (and (<= 4 m)
(unsigned-byte-p 34 m))
:concl (equal (logext 64 (+ #xfffffffffffffffc m))
(loghead 64 (+ #xfffffffffffffffc m)))
:g-bindings (gl::auto-bindings (:nat m 34)))
(defthm-using-gl effects-copyData-loop-helper-6
:hyp (canonical-address-p src/dst)
:concl (equal (logext 64 (+ 4 (loghead 64 src/dst)))
(+ 4 src/dst))
:g-bindings (gl::auto-bindings (:int src/dst 64)))
(defthm-using-gl effects-copyData-loop-helper-7
:hyp (and (canonical-address-p src/dst)
(canonical-address-p (+ m src/dst))
(< 4 m)
(equal (mod m 4) 0)
(unsigned-byte-p 34 m))
:concl (canonical-address-p (+ 4 src/dst (loghead 64 (+ #xfffffffffffffffc m))))
:g-bindings (gl::auto-bindings (:mix (:int m 64)
(:int src/dst 64))))
(defthm-using-gl effects-copyData-loop-helper-9
:hyp (and (< 4 m)
(unsigned-byte-p 34 m))
:concl (not (equal (loghead 64 (+ #xfffffffffffffffc m)) 0))
:g-bindings (gl::auto-bindings (:nat m 34))
:rule-classes (:forward-chaining :rewrite))
(defthm-using-gl effects-copyData-loop-helper-11
:hyp (and (< 4 m)
(equal (mod m 4) 0)
(unsigned-byte-p 34 m))
:concl (equal (loghead 64 (+ #xfffffffffffffffc m))
(+ -4 m))
:g-bindings (gl::auto-bindings (:nat m 34)))
(defthm-using-gl effects-copyData-loop-helper-13
:hyp (and (equal (mod k 4) 0)
(unsigned-byte-p 34 k))
:concl (equal (mod (+ 4 k) 4) 0)
:g-bindings (gl::auto-bindings (:nat k 34)))
(defthm-using-gl effects-copyData-loop-helper-14
:hyp (and (< 4 m)
(equal (mod m 4) 0)
(unsigned-byte-p 34 m))
:concl (equal (mod (+ -4 m) 4) 0)
:g-bindings (gl::auto-bindings (:nat m 34)))
(defthm-using-gl effects-copyData-loop-helper-15
:hyp (and (equal (loghead 2 m) 0)
(canonical-address-p m))
:concl (equal (loghead 2 (+ 4 m)) 0)
:g-bindings (gl::auto-bindings (:int m 48)))
(defthm-using-gl effects-copyData-loop-helper-16
:hyp (and (equal (loghead 3 m) 0)
(canonical-address-p m))
:concl (equal (loghead 3 (+ 8 m)) 0)
:g-bindings (gl::auto-bindings (:int m 48)))
(in-theory (e/d ()
(effects-copyData-loop-helper-11
effects-copyData-loop-helper-14))))
;; ======================================================================
(defun-nx source-bytes (k src-addr x86)
(mv-nth 1 (rb k (+ (- k) src-addr) :r x86)))
(defun-nx destination-bytes (k dst-addr x86)
(mv-nth 1 (rb k (+ (- k) dst-addr) :r x86)))
(defun-nx loop-invariant (k m addr x86)
;; The initial value of m is (ash n 2), where n is the same n as defined in
;; preconditions later in this book.
;; k: number of bytes already copied (in previous loop iterations)
;; this will increase by 4 in every iteration
;; m: number of bytes to be copied
;; this will decrease by 4 in every iteration
(and (x86p x86)
(64-bit-modep x86)
(xr :app-view nil x86)
(equal (xr :ms nil x86) nil)
(equal (xr :fault nil x86) nil)
(unsigned-byte-p 34 m)
(equal (mod m 4) 0)
(unsigned-byte-p 34 k)
(equal (mod k 4) 0)
(unsigned-byte-p 34 (+ m k))
(equal (xr :rgf *rax* x86) m)
;; Stack addresses are canonical.
(canonical-address-p (xr :rgf *rsp* x86))
(canonical-address-p (+ 8 (xr :rgf *rsp* x86)))
;; Return address of the copyData sub-routine is canonical.
(canonical-address-p
(logext 64 (mv-nth 1 (rb 8 (+ 8 (xr :rgf *rsp* x86)) :r x86))))
;; All the destination addresses are canonical.
(canonical-address-p (+ (- k) (xr :rgf *rsi* x86)))
(canonical-address-p (+ m (xr :rgf *rsi* x86)))
;; All the source addresses are canonical.
(canonical-address-p (+ (- k) (xr :rgf *rdi* x86)))
(canonical-address-p (+ m (xr :rgf *rdi* x86)))
;; Alignment Checking
(if (alignment-checking-enabled-p x86)
;; rsi and rdi point to doublewords (four bytes), so their
;; natural boundary will be addresses divisible by 4.
(and (equal (loghead 2 (xr :rgf *rsi* x86)) 0)
(equal (loghead 2 (xr :rgf *rdi* x86)) 0))
t)
;; Memory locations of interest are disjoint.
(separate
;; Program addresses
:x *prog-len* addr
;; Destination addresses
:w (+ m k) (+ (- k) (xr :rgf *rsi* x86)))
(separate
;; Return Address
:r 8 (+ 8 (xr :rgf *rsp* x86))
;; Destination Addresses
:w (+ m k) (+ (- k) (xr :rgf *rsi* x86)))
;; We could modify the following pre-condition to say the following:
;; either the source and destination addresses are completely disjoint
;; or they are equal. However, the equality of the source and
;; destination isn't what we are interested in for this program and so I
;; choose to leave that out.
(separate
;; Source Addresses
:r (+ m k) (+ (- k) (xr :rgf *rdi* x86))
;; Destination Addresses
:w (+ m k) (+ (- k) (xr :rgf *rsi* x86)))
;; Program is located at addr.
;; All program addresses are canonical.
(canonical-address-p addr)
(canonical-address-p (+ *prog-len* addr))
(program-at addr *copyData* x86)
;; Values copied in the previous iterations of the loop are unaltered.
;; dst[(+ -k dst-addr) to dst-addr] = src[(+ -k src-addr) to src-addr]
(equal (destination-bytes k (xr :rgf *rsi* x86) x86)
(source-bytes k (xr :rgf *rdi* x86) x86))))
(defun-nx loop-preconditions (k m addr src-addr dst-addr x86)
(and (loop-invariant k m addr x86)
;; At the beginning of every iteration, we have some bytes left to be
;; copied.
(posp m)
(equal (xr :rgf *rdi* x86) src-addr)
(equal (xr :rgf *rsi* x86) dst-addr)
(equal addr (+ -16 (xr :rip nil x86)))))
(defthm loop-preconditions-fwd-chain-to-its-body
(implies (loop-preconditions k m addr src-addr dst-addr x86)
(and (x86p x86)
(64-bit-modep x86)
(xr :app-view nil x86)
(equal (xr :ms nil x86) nil)
(equal (xr :fault nil x86) nil)
(unsigned-byte-p 34 m)
(equal (mod m 4) 0)
(unsigned-byte-p 34 k)
(equal (mod k 4) 0)
(unsigned-byte-p 34 (+ m k))
(equal (xr :rgf *rax* x86) m)
;; Stack addresses are canonical.
(canonical-address-p (xr :rgf *rsp* x86))
(canonical-address-p (+ 8 (xr :rgf *rsp* x86)))
;; Return address of the copyData sub-routine is canonical.
(canonical-address-p
(logext 64 (mv-nth 1 (rb 8 (+ 8 (xr :rgf *rsp* x86)) :r x86))))
;; All the destination addresses are canonical.
(canonical-address-p (+ (- k) (xr :rgf *rsi* x86)))
(canonical-address-p (+ m (xr :rgf *rsi* x86)))
;; All the source addresses are canonical.
(canonical-address-p (+ (- k) (xr :rgf *rdi* x86)))
(canonical-address-p (+ m (xr :rgf *rdi* x86)))
;; Alignment Checking
(if (alignment-checking-enabled-p x86)
;; rsi and rdi point to doublewords (four bytes), so their
;; natural boundary will be addresses divisible by 4.
(and (equal (loghead 2 (xr :rgf *rsi* x86)) 0)
(equal (loghead 2 (xr :rgf *rdi* x86)) 0))
t)
;; Memory locations of interest are disjoint.
(separate
;; Program addresses
:x *prog-len* addr
;; Destination addresses
:w (+ m k) (+ (- k) (xr :rgf *rsi* x86)))
(separate
;; Return Address
:r 8 (+ 8 (xr :rgf *rsp* x86))
;; Destination Addresses
:w (+ m k) (+ (- k) (xr :rgf *rsi* x86)))
;; We could modify the following pre-condition to say the following:
;; either the source and destination addresses are completely disjoint
;; or they are equal. However, the equality of the source and
;; destination isn't what we are interested in for this program and so I
;; choose to leave that out.
(separate
;; Source Addresses
:r (+ m k) (+ (- k) (xr :rgf *rdi* x86))
;; Destination Addresses
:w (+ m k) (+ (- k) (xr :rgf *rsi* x86)))
;; Program is located at addr.
;; All program addresses are canonical.
(canonical-address-p addr)
(canonical-address-p (+ *prog-len* addr))
(program-at addr *copyData* x86)
;; Values copied in the previous iterations of the loop are unaltered.
;; dst[(+ -k dst-addr) to dst-addr] = src[(+ -k src-addr) to src-addr]
(equal (destination-bytes k (xr :rgf *rsi* x86) x86)
(source-bytes k (xr :rgf *rdi* x86) x86))
;; Values copied in the previous iterations of the loop are unaltered.
;; dst[(+ -k dst-addr) to dst-addr] = src[(+ -k src-addr) to src-addr]
(equal (destination-bytes k (xr :rgf *rsi* x86) x86)
(source-bytes k (xr :rgf *rdi* x86) x86))
(posp m)
(equal (xr :rgf *rdi* x86) src-addr)
(equal (xr :rgf *rsi* x86) dst-addr)
(equal addr (+ -16 (xr :rip nil x86)))))
:rule-classes :forward-chaining)
;; ======================================================================
;; Clock functions:
(defun pre-clk (n)
(if (zp n) 4 7))
(defun loop-clk-base () 6)
(defun loop-clk-recur () 6)
(defun loop-clk (m)
;; I use m to refer to (ash n 2).
(if (signed-byte-p 64 m)
(let ((new-m (loghead 64 (+ #xfffffffffffffffc m))))
(if (<= m 4)
(loop-clk-base)
(clk+ (loop-clk-recur) (loop-clk new-m))))
0))
(defun post-clk () 2)
(defun clk (n)
(if (zp n)
(pre-clk n)
(clk+ (pre-clk n)
(loop-clk (ash n 2)))))
(defun program-clk (n)
(clk+ (clk n) (post-clk)))
;; ======================================================================
;; Some lemmas for effects theorems:
(encapsulate
()
(local (include-book "arithmetic-3/top" :dir :system))
(defthm ash-n-2-bound
(implies (and (< 0 n)
(integerp n))
(<= 4 (ash n 2)))
:hints (("Goal" :in-theory (e/d* (ash) ())))
:rule-classes (:rewrite :linear)))
(encapsulate
()
(local (include-book "ihs/quotient-remainder-lemmas" :dir :system))
(defthm mod-thm-1
(implies (and (equal (mod m 4) 0)
(posp m))
(<= 4 m))
:rule-classes (:forward-chaining))
(defthm mod-thm-2
(implies (natp n)
(equal (mod (ash n 2) 4) 0))
:hints (("Goal" :in-theory (e/d* (ash) ())))))
;; ======================================================================
|
