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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):
; Cuong Chau <ckcuong@cs.utexas.edu>
;; Specifications of FP Converts
(in-package "X86ISA")
(include-book "base")
(local (include-book "centaur/bitops/ihs-extensions" :dir :system))
(local (include-book "arithmetic/top-with-meta" :dir :system))
(local (in-theory (e/d (bitops::ash-1-removal) ())))
;; ======================================================================
(defsection floating-point-converts
:parents (floating-point-specifications)
:short "Specification of floating-point conversion operations" )
(local (xdoc::set-default-parents floating-point-converts))
;; ======================================================================
;; FP to Integer:
(define rat-round-to-int-rn ((rat rationalp))
:returns (r integerp :rule-classes :type-prescription)
(round rat 1))
(define rat-round-to-int-rd ((rat rationalp))
:returns (r integerp :rule-classes :type-prescription)
(let ((rn (round rat 1)))
(if (> rn rat) (1- rn) rn)))
(define rat-round-to-int-ru ((rat rationalp))
:returns (r integerp :rule-classes :type-prescription)
(let ((rn (round rat 1)))
(if (< rn rat) (1+ rn) rn)))
(define rat-round-to-int-rz ((rat rationalp))
:returns (r integerp :rule-classes :type-prescription)
(truncate rat 1))
(define rat-round-to-int ((rat rationalp)
(rc natp))
:inline t
:no-function t
:returns (r integerp :rule-classes :type-prescription)
(rc-cases
:rn (rat-round-to-int-rn rat)
:rd (rat-round-to-int-rd rat)
:ru (rat-round-to-int-ru rat)
:rz (rat-round-to-int-rz rat)
;; Should never get here.
:other 0))
(define sse-cvt-fp-to-int-special (kind (nbytes natp))
:short "Check whether the operand is NaN or infinity. If so, return
the integer indefinite."
;; Return (mv flag integer-result invalid).
:returns (mv flg
(r integerp :hyp :guard :rule-classes :type-prescription)
invalid)
(let ((invalid (or (eq kind 'snan) (eq kind 'qnan)
(eq kind 'indef) (eq kind 'inf))))
(if invalid
(mv t (ash 1 (1- (ash nbytes 3))) invalid)
(mv nil 0 invalid))))
(define sse-cvt-fp-to-int ((nbytes natp)
(op natp)
(mxcsr :type (unsigned-byte 32))
(trunc booleanp)
(exp-width posp)
(frac-width posp))
:prepwork ((local (in-theory (e/d* () (bitops::logand-with-negated-bitmask)))))
(b* ((mxcsr (mbe :logic (loghead 32 mxcsr)
:exec mxcsr))
((mv kind sign exp ?implicit frac)
(fp-decode op exp-width frac-width))
(daz (logbitp #.*mxcsr-daz* mxcsr))
((mv kind exp frac)
(sse-daz kind exp frac daz))
((mv special-ok result invalid)
(sse-cvt-fp-to-int-special kind nbytes))
;; Check invalid operation
(mxcsr (if invalid (!mxcsrBits->ie 1 mxcsr) mxcsr))
(im (equal (mxcsrBits->im mxcsr) 1))
((when (and invalid (not im)))
(mv 'invalid-operand-exception-is-not-masked 0 mxcsr)))
(if special-ok
(mv nil result mxcsr)
(b* ((bias (nfix (ec-call (RTL::bias (list nil (1+ frac-width) exp-width)))))
(rat (fp-to-rat sign exp frac bias exp-width frac-width))
(rc (mbe :logic
(part-select mxcsr :low #.*mxcsr-rc* :high (1+ #.*mxcsr-rc*))
;; (get-bits #.*mxcsr-rc* (1+ #.*mxcsr-rc*) mxcsr)
:exec (logand #b11 (ash mxcsr (- #.*mxcsr-rc*)))))
(rc (if trunc #b11 rc))
(rat-to-int (rat-round-to-int rat rc))
(nbits (ash nbytes 3))
(min-signed-int (- (expt 2 (1- nbits))))
(max-signed-int (1- (expt 2 (1- nbits))))
(out-of-range (or (< rat-to-int min-signed-int)
(> rat-to-int max-signed-int)))
;; If the converted integer is out-of-range, set IE flag.
(mxcsr (if out-of-range (!mxcsrBits->ie 1 mxcsr) mxcsr))
((when (and out-of-range (not im)))
(mv 'invalid-operand-exception-is-not-masked 0 mxcsr))
;; If out-of-range and IM is masked, return integer indefinite.
((when out-of-range)
(mv nil (ash 1 (1- nbits)) mxcsr))
;; Check precision
(pe (not (= rat-to-int rat)))
(mxcsr (if pe (!mxcsrBits->pe 1 mxcsr) mxcsr))
(pm (equal (mxcsrBits->pm mxcsr) 1))
((when (and pe (not pm)))
(mv 'precision-exception-is-not-masked 0 mxcsr)))
(mv nil rat-to-int mxcsr))))
///
(defthm integerp-result-sse-cvt-fp-to-int
(implies (natp nbytes)
(integerp (mv-nth 1 (sse-cvt-fp-to-int
nbytes op mxcsr trunc exp-width frac-width))))
:rule-classes :type-prescription)
(defthm-unsigned-byte-p n32p-mxcsr-sse-cvt-fp-to-int
:bound 32
:concl (mv-nth 2 (sse-cvt-fp-to-int
nbytes op mxcsr trunc exp-width frac-width))
:hints (("Goal" :in-theory (e/d* (unsigned-byte-p-when-mxcsrbits-p) (unsigned-byte-p))))
:gen-type t
:gen-linear t))
;; ======================================================================
;; Integerp to FP:
(define sse-cvt-int-to-fp ((op integerp)
(mxcsr :type (unsigned-byte 32))
(exp-width posp)
(frac-width posp))
:prepwork
((local (in-theory (e/d* () (unsigned-byte-p)))))
(b* ((mxcsr (mbe :logic (loghead 32 mxcsr)
:exec mxcsr))
(rc (mbe :logic
(part-select mxcsr :low #.*mxcsr-rc* :high (1+ #.*mxcsr-rc*))
:exec (logand #b11 (ash mxcsr (- #.*mxcsr-rc*)))))
(bias (nfix (ec-call (RTL::bias (list nil (1+ frac-width) exp-width)))))
(int-to-rat (rat-round op rc bias exp-width frac-width))
(sign (cond ((> int-to-rat 0) 0)
((< int-to-rat 0) 1)
(t (if (int= rc #.*rc-rd*) 1 0))))
;; Check precision
(pe (not (= op int-to-rat)))
(mxcsr (if pe (!mxcsrBits->pe 1 mxcsr) mxcsr))
(pm (equal (mxcsrBits->pm mxcsr) 1))
((when (and pe (not pm)))
(mv 'precision-exception-is-not-masked 0 mxcsr))
(fp-result
(rat-to-fp int-to-rat sign
nil nil nil rc
exp-width frac-width)))
(mv nil fp-result mxcsr))
///
(defthm integerp-result-sse-cvt-int-to-fp
(integerp (mv-nth 1 (sse-cvt-int-to-fp op mxcsr exp-width frac-width)))
:rule-classes :type-prescription)
(defthm-unsigned-byte-p n32p-mxcsr-sse-cvt-int-to-fp
:bound 32
:concl (mv-nth 2 (sse-cvt-int-to-fp op mxcsr exp-width frac-width))
:hints (("Goal" :in-theory (e/d* (unsigned-byte-p-when-mxcsrbits-p) (unsigned-byte-p))))
:gen-type t
:gen-linear t))
;; ======================================================================
;; Convert FP1 to FP2:
(define denormalp ((rat rationalp)
(rounded-expo integerp)
(bias natp))
(let ((expo (RTL::expo rat))
(minus-bias (- bias)))
(or (<= rounded-expo minus-bias)
(and (= rounded-expo 0)
(<= expo minus-bias))))
///
(defthm booleanp-denormalp
(booleanp (denormalp rat rounded-expo bias))))
(define sse-cvt-fp1-to-fp2-special (kind
(sign :type (unsigned-byte 1))
(implicit :type (unsigned-byte 1))
(frac natp)
(frac-width1 posp)
(exp-width2 posp)
(frac-width2 posp))
:short "Check whether the operand is SNaN or QNaN and then return
corresponding result. Also handle the infinities."
;; Return (mv flag sign exp implicit frac invalid).
(let ((invalid (eq kind 'snan)))
(cond
((eq kind 'snan)
(let ((exp-width exp-width2)
(frac-width frac-width2)
(nan-frac-bits (ash
(part-select frac :low 0 :high (nfix (- frac-width1 2)))
(- frac-width2 frac-width1))))
(flag-make-special-bp 'qnan nan-frac-bits
sign invalid)))
((or (eq kind 'qnan) (eq kind 'indef))
(let ((exp-width exp-width2)
(frac (ash frac (- frac-width2 frac-width1))))
(mv t sign (fp-max-exp exp-width) implicit frac invalid)))
((eq kind 'inf)
(let ((exp-width exp-width2)
(frac-width frac-width2))
(flag-make-special-bp 'inf 0 sign invalid)))
(t (mv nil 0 0 0 0 invalid))))
///
(defthm integerp-sse-cvt-fp1-to-fp2-special-1
(implies (integerp sign)
(integerp
(mv-nth
1
(sse-cvt-fp1-to-fp2-special
kind sign implicit frac frac-width1 exp-width2 frac-width2))))
:rule-classes :type-prescription)
(defthm integerp-sse-cvt-fp1-to-fp2-special-2
(integerp (mv-nth
2
(sse-cvt-fp1-to-fp2-special
kind sign implicit frac frac-width1 exp-width2 frac-width2)))
:rule-classes :type-prescription)
(defthm integerp-sse-cvt-fp1-to-fp2-special-3
(implies (integerp implicit)
(integerp (mv-nth
3 (sse-cvt-fp1-to-fp2-special
kind sign implicit frac frac-width1 exp-width2 frac-width2))))
:rule-classes :type-prescription)
(defthm integerp-sse-cvt-fp1-to-fp2-special-4
(integerp (mv-nth
4
(sse-cvt-fp1-to-fp2-special
kind sign implicit frac frac-width1 exp-width2 frac-width2)))
:rule-classes :type-prescription))
(ACL2::with-supporters
(local (include-book "rtl/rel11/lib/excps" :dir :system))
(defun sse-cvt-fp1-to-fp2 (op mxcsr
exp-width1 frac-width1
exp-width2 frac-width2)
(declare (xargs :guard (and (natp op) (n32p mxcsr)
(posp exp-width1) (posp frac-width1)
(posp exp-width2) (posp frac-width2))
:guard-hints (("Goal" :in-theory (e/d* ()
(rtl::sse-post-comp
bitops::logand-with-negated-bitmask
bitops::loghead-of-loghead-1
unsigned-byte-p
bitops::logtail-of-loghead
bitops::logbitp-of-loghead-in-bounds
bitops::loghead-of-logior))))))
(b* ((mxcsr (mbe :logic (loghead 32 mxcsr)
:exec mxcsr))
((mv kind sign exp ?implicit frac)
(fp-decode op exp-width1 frac-width1))
(daz (logbitp #.*mxcsr-daz* mxcsr))
((mv kind ?exp frac)
(sse-daz kind exp frac daz))
((mv special-ok sign-special exp-special & frac-special invalid)
(sse-cvt-fp1-to-fp2-special kind sign implicit frac frac-width1
exp-width2 frac-width2))
;; Check invalid operation
(mxcsr (if invalid (!mxcsrBits->ie 1 mxcsr) mxcsr))
(im (equal (mxcsrBits->im mxcsr) 1))
((when (and invalid (not im)))
(mv 'invalid-operand-exception-is-not-masked 0 mxcsr))
;; Check denormal operand
(de (eq kind 'denormal))
(mxcsr (if de (!mxcsrBits->de 1 mxcsr) mxcsr))
(dm (equal (mxcsrBits->dm mxcsr) 1))
((when (and de (not dm)))
(mv 'denormal-operand-exception-is-not-masked 0 mxcsr)))
(if special-ok
(mv nil
(fp-encode-integer sign-special exp-special frac-special
exp-width2 frac-width2)
mxcsr)
(b* ((bias1 (nfix (ec-call (RTL::bias (list nil (1+ frac-width1) exp-width1)))))
(bias2 (nfix (ec-call (RTL::bias (list nil (1+ frac-width2) exp-width2)))))
(rat (fp-to-rat sign exp frac bias1 exp-width1 frac-width1))
((mv result flags)
(ec-call (rtl::sse-post-comp rat mxcsr (list nil (1+ frac-width2) exp-width2))))
(result (loghead (+ 1 frac-width2 exp-width2) (ifix result)))
(mxcsr (loghead 32 (logior (ifix flags) mxcsr)))
;; Post-computation Exceptions
;; Check overflow
(overflowp (equal (mxcsrBits->oe mxcsr) 1))
((when (and overflowp
(equal (mxcsrBits->om mxcsr) 0)))
(mv 'overflow-exception-is-not-masked result mxcsr))
;; Check underflow
((when (and (equal (mxcsrBits->ue mxcsr) 1)
(equal (mxcsrBits->um mxcsr) 0)))
(mv 'underflow-exception-is-not-masked result mxcsr))
;; Check precision
((when (and (equal (mxcsrBits->pe mxcsr) 1)
(equal (mxcsrBits->pm mxcsr) 0)))
(mv 'precision-exception-is-not-masked result mxcsr))
(rc
(mbe :logic (part-select mxcsr :low #.*mxcsr-rc* :high (1+ #.*mxcsr-rc*))
:exec (logand #b11 (ash mxcsr (- #.*mxcsr-rc*)))))
(rounded-rat (rat-round rat rc bias2 exp-width2 frac-width2))
(rounded-expo (RTL::expo rounded-rat))
(denormalp (denormalp rat rounded-expo bias2))
(flush (and denormalp
(equal (mxcsrBits->um mxcsr) 1)
(equal (mxcsrBits->ftz mxcsr) 1)))
(fp-result
(rat-to-fp rounded-rat sign overflowp
denormalp flush rc exp-width2 frac-width2)))
(mv nil fp-result mxcsr))))))
(defthm integerp-result-sse-cvt-fp1-to-fp2
(integerp (mv-nth
1
(sse-cvt-fp1-to-fp2 op mxcsr exp-width1 frac-width1 exp-width2 frac-width2)))
:hints (("Goal" :in-theory (e/d* ()
(rtl::sse-post-comp
bitops::loghead-of-loghead-1
unsigned-byte-p
bitops::logtail-of-loghead
bitops::logbitp-of-loghead-in-bounds
bitops::loghead-of-logior))))
:rule-classes :type-prescription)
(defthm-unsigned-byte-p n32p-mxcsr-sse-cvt-fp1-to-fp2
:bound 32
:concl (mv-nth
2
(sse-cvt-fp1-to-fp2 op mxcsr exp-width1 frac-width1 exp-width2 frac-width2))
:hints (("Goal" :in-theory (e/d* (unsigned-byte-p-when-mxcsrbits-p)
(rtl::sse-post-comp
bitops::loghead-of-loghead-1
unsigned-byte-p
bitops::logtail-of-loghead
bitops::logbitp-of-loghead-in-bounds
bitops::loghead-of-logior))))
:gen-type t
:gen-linear t)
(in-theory (e/d () (sse-cvt-fp1-to-fp2)))
;; ======================================================================
;; Single-Precision Operations:
(define sp-sse-cvt-fp-to-int ((nbytes :type (integer 0 *))
(op :type (unsigned-byte 32))
(mxcsr :type (unsigned-byte 32))
(trunc booleanp))
(b* (((mv flg result mxcsr)
(sse-cvt-fp-to-int nbytes op mxcsr trunc
#.*IEEE-SP-EXP-WIDTH* #.*IEEE-SP-FRAC-WIDTH*))
(result (trunc nbytes result)))
(mv flg result mxcsr))
///
(defthm bytesp-sp-sse-cvt-fp-to-int-1
(implies (and (natp nbytes)
(member nbytes '(1 2 4 8 16)))
(unsigned-byte-p
(ash nbytes 3)
(mv-nth 1 (sp-sse-cvt-fp-to-int nbytes op mxcsr trunc)))))
(defthm-unsigned-byte-p n32p-mxcsr-sp-sse-cvt-fp-to-int
:bound 32
:concl (mv-nth 2 (sp-sse-cvt-fp-to-int nbytes op mxcsr trunc))
:hints (("Goal" :in-theory (e/d () (unsigned-byte-p))))
:gen-type t
:gen-linear t))
(define sp-sse-cvt-int-to-fp ((op integerp)
(mxcsr :type (unsigned-byte 32)))
(b* (((mv flg result mxcsr)
(sse-cvt-int-to-fp op mxcsr
#.*IEEE-SP-EXP-WIDTH* #.*IEEE-SP-FRAC-WIDTH*))
(result (n32 result)))
(mv flg result mxcsr))
///
(defthm-unsigned-byte-p n32p-result-sp-sse-cvt-int-to-fp
:bound 32
:concl (mv-nth 1 (sp-sse-cvt-int-to-fp op mxcsr))
:gen-type t
:gen-linear t)
(defthm-unsigned-byte-p n32p-mxcsr-sp-sse-cvt-int-to-fp
:bound 32
:concl (mv-nth 2 (sp-sse-cvt-int-to-fp op mxcsr))
:hints (("Goal" :in-theory (e/d () (unsigned-byte-p))))
:gen-type t
:gen-linear t))
(define sse-cvt-sp-to-dp ((op :type (unsigned-byte 32))
(mxcsr :type (unsigned-byte 32)))
(b* (((mv flg result mxcsr)
(sse-cvt-fp1-to-fp2 op mxcsr
#.*IEEE-SP-EXP-WIDTH* #.*IEEE-SP-FRAC-WIDTH*
#.*IEEE-DP-EXP-WIDTH* #.*IEEE-DP-FRAC-WIDTH*))
(result (n64 result)))
(mv flg result mxcsr))
///
(defthm-unsigned-byte-p n64p-result-sse-cvt-sp-to-dp
:bound 64
:concl (mv-nth 1 (sse-cvt-sp-to-dp op mxcsr))
:gen-type t
:gen-linear t)
(defthm-unsigned-byte-p n32p-mxcsr-sse-cvt-sp-to-dp
:bound 32
:concl (mv-nth 2 (sse-cvt-sp-to-dp op mxcsr))
:hints (("Goal" :in-theory (e/d () (unsigned-byte-p))))
:gen-type t
:gen-linear t))
;; Double-Precision Operations:
(define dp-sse-cvt-fp-to-int ((nbytes :type (integer 0 *))
(op :type (unsigned-byte 64))
(mxcsr :type (unsigned-byte 32))
(trunc booleanp))
(b* (((mv flg result mxcsr)
(sse-cvt-fp-to-int nbytes op mxcsr trunc
#.*IEEE-DP-EXP-WIDTH* #.*IEEE-DP-FRAC-WIDTH*))
(result (trunc nbytes result)))
(mv flg result mxcsr))
///
(defthm bytesp-dp-sse-cvt-fp-to-int-1
(implies (and (natp nbytes)
(member nbytes '(1 2 4 8 16)))
(unsigned-byte-p
(ash nbytes 3)
(mv-nth 1 (dp-sse-cvt-fp-to-int nbytes op mxcsr trunc)))))
(defthm-unsigned-byte-p n32p-mxcsr-dp-sse-cvt-fp-to-int
:bound 32
:concl (mv-nth 2 (dp-sse-cvt-fp-to-int nbytes op mxcsr trunc))
:hints (("Goal" :in-theory (e/d () (unsigned-byte-p))))
:gen-type t
:gen-linear t))
(define dp-sse-cvt-int-to-fp ((op integerp)
(mxcsr :type (unsigned-byte 32)))
(b* (((mv flg result mxcsr)
(sse-cvt-int-to-fp op mxcsr
#.*IEEE-DP-EXP-WIDTH* #.*IEEE-DP-FRAC-WIDTH*))
(result (n64 result)))
(mv flg result mxcsr))
///
(defthm-unsigned-byte-p n64p-result-dp-sse-cvt-int-to-fp
:bound 64
:concl (mv-nth 1 (dp-sse-cvt-int-to-fp op mxcsr))
:gen-type t
:gen-linear t)
(defthm-unsigned-byte-p n32p-mxcsr-dp-sse-cvt-int-to-fp
:bound 32
:concl (mv-nth 2 (dp-sse-cvt-int-to-fp op mxcsr))
:hints (("Goal" :in-theory (e/d () (unsigned-byte-p))))
:gen-type t
:gen-linear t))
(define sse-cvt-dp-to-sp ((op :type (unsigned-byte 64))
(mxcsr :type (unsigned-byte 32)))
(b* (((mv flg result mxcsr)
(sse-cvt-fp1-to-fp2 op mxcsr
#.*IEEE-DP-EXP-WIDTH* #.*IEEE-DP-FRAC-WIDTH*
#.*IEEE-SP-EXP-WIDTH* #.*IEEE-SP-FRAC-WIDTH*))
(result (n32 result)))
(mv flg result mxcsr))
///
(defthm-unsigned-byte-p n32p-result-sse-cvt-dp-to-sp
:bound 32
:concl (mv-nth 1 (sse-cvt-dp-to-sp op mxcsr))
:gen-type t
:gen-linear t)
(defthm-unsigned-byte-p n32p-mxcsr-sse-cvt-dp-to-sp
:bound 32
:concl (mv-nth 2 (sse-cvt-dp-to-sp op mxcsr))
:hints (("Goal" :in-theory (e/d () (unsigned-byte-p))))
:gen-type t
:gen-linear t))
;; ======================================================================
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