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<wob_jonas> learn Aristotle said that every illness can be cured by balancing the four vitreous humors, and everyone believed him for two thousand years, even though people still died of illnesses. It wasn\'t until the 20th century that Szent-Gy\xc3\xb6rgyi Albert realized that Aristotle didn\'t find fifth kind of vitreous humor, vitamin C, because the Greek alphabet
| author | HackBot |
|---|---|
| date | Mon, 01 Jan 2018 17:57:43 +0000 |
| parents | 859f9b4339e6 |
| children |
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; ; NAME ; idiotism.oil -- optimizer idioms for C-INTERCAL ; ; LICENSE TERMS ; Copyright (C) 2007 Alex Smith ; ; This program is free software; you can redistribute it and/or modify ; it under the terms of the GNU General Public License as published by ; the Free Software Foundation; either version 2 of the License, or ; (at your option) any later version. ; ; This program is distributed in the hope that it will be useful, ; but WITHOUT ANY WARRANTY; without even the implied warranty of ; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ; GNU General Public License for more details. ; ; You should have received a copy of the GNU General Public License ; along with this program; if not, write to the Free Software ; Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. ; ; Optimizer Idiom Language input file for C-INTERCAL ; See the appendix "Optimizer Idiom Language" in the Revamped manual ; for information about the format of this file. ; Some useful constants: ; 0x55555555 1431655765 ; 0xAAAAAAAA 2863311530 ; 0x0000FFFF 65535 ; 0xFFFF0000 4294901760 ; 0xFFFFFFFF 4294967295 ; Constant folding [minglefold] (#{1}1$#{1}2)->(#{mingle(x1,x2)}0) [selectfold] (#{1}1~#{1}2)->(#{iselect(x1,x2)}0) [and32fold] (&32 #{1}1)->(#{and32(x1)}0) [or32fold] (V32 #{1}1)->(#{or32(x1)}0) [xor32fold] (?32 #{1}1)->(#{xor32(x1)}0) [and16fold] (&16 #{1}1)->(#{and16(x1)}0) [or16fold] (V16 #{1}1)->(#{or16(x1)}0) [xor16fold] (?16 #{1}1)->(#{xor16(x1)}0) ; C operations can, and should, be folded too [cfold] (#{1}1 & #{1}2)->(#{x1 & x2}0) (#{1}1 | #{1}2)->(#{x1 | x2}0) (#{1}1 ^ #{1}2)->(#{x1 ^ x2}0) (#{1}1 + #{1}2)->(#{x1 + x2}0) (#{1}1 - #{1}2)->(#{x1 - x2}0) (#{1}1 * #{1}2)->(#{x1 * x2}0) (#{1}1 / #{1}2)->(#{x1 / x2}0) (#{1}1 % #{1}2)->(#{x1 % x2}0) (#{1}1 > #{1}2)->(#{x1 > x2}0) (#{1}1 < #{1}2)->(#{x1 < x2}0) (#{1}1 >> #{1}2)->(#{x1 >> x2}0) (#{1}1 << #{1}2)->(#{x1 << x2}0) (#{1}1 == #{1}2)->(#{x1 == x2}0) (#{1}1 != #{1}2)->(#{x1 != x2}0) ; Reducing constants inside a C or operation can help to recognize idioms [cfoldintoorinand] (((_1) | #{1}2) & #{1}3)->(((_1) | #{x2 & x3}0) & _3) ; Binary bitwise optimizations [cbinand] ((&32(_{!(c&4294901760LU)}1$_{!(c&4294901760LU)}2))~ #{!(x&2863311530LU)&&iselect(x,1431655765LU)==xselx(iselect(x,1431655765LU))}3 )->((_1 & _2) & #{iselect(x3,1431655765LU)}0) [cbinor] ((V32(_{!(c&4294901760LU)}1$_{!(c&4294901760LU)}2))~ #{!(x&2863311530LU)&&iselect(x,1431655765LU)==xselx(iselect(x,1431655765LU))}3 )->((_1 | _2) & #{iselect(x3,1431655765LU)}0) [cbinxor] ((?32(_{!(c&4294901760LU)}1$_{!(c&4294901760LU)}2))~ #{!(x&2863311530LU)&&iselect(x,1431655765LU)==xselx(iselect(x,1431655765LU))}3 )->((_1 ^ _2) & #{iselect(x3,1431655765LU)}0) ; Sometimes, an expanded output is wanted, optimizations happen in the wrong ; order, and we end up with & rather than ~ on the previous idiom. Correct ; such situations now. [cbinandnoselect] ((&32(_{!(c&4294901760LU)}1$_{!(c&4294901760LU)}2))& #{!(x&2863311530LU)&&iselect(x,1431655765LU)==xselx(iselect(x,1431655765LU))}3 )->(#0 $ ((_1 & _2) & #{iselect(x3,1431655765LU)}0)) [cbinornoselect] ((V32(_{!(c&4294901760LU)}1$_{!(c&4294901760LU)}2))& #{!(x&2863311530LU)&&iselect(x,1431655765LU)==xselx(iselect(x,1431655765LU))}3 )->(#0 $ ((_1 | _2) & #{iselect(x3,1431655765LU)}0)) [cbinxornoselect] ((?32(_{!(c&4294901760LU)}1$_{!(c&4294901760LU)}2))& #{!(x&2863311530LU)&&iselect(x,1431655765LU)==xselx(iselect(x,1431655765LU))}3 )->(#0 $ ((_1 ^ _2) & #{iselect(x3,1431655765LU)}0)) ; Sometimes, there isn't even a mingle... [cbinandnomingle] ((&32(_{!(c&2863311530LU)}1|_{!(c&1431655765LU)}2))~ #{!(x&2863311530LU)&&iselect(x,1431655765LU)==xselx(iselect(x,1431655765LU))}3 )->(((_2 >> #1) & _1) ~ _3) ((&32(_{!(c&1431655765LU)}2|_{!(c&2863311530LU)}1))~ #{!(x&2863311530LU)&&iselect(x,1431655765LU)==xselx(iselect(x,1431655765LU))}3 )->(((_2 >> #1) & _1) ~ _3) ((&32(_{!(c&2863311530LU)}1|_{!(c&1431655765LU)}2))& #{!(x&2863311530LU)&&iselect(x,1431655765LU)==xselx(iselect(x,1431655765LU))}3 )->(((_2 >> #1) & _1) & _3) ((&32(_{!(c&1431655765LU)}2|_{!(c&2863311530LU)}1))& #{!(x&2863311530LU)&&iselect(x,1431655765LU)==xselx(iselect(x,1431655765LU))}3 )->(((_2 >> #1) & _1) & _3) [cbinornomingle] ((V32(_{!(c&2863311530LU)}1|_{!(c&1431655765LU)}2))~ #{!(x&2863311530LU)&&iselect(x,1431655765LU)==xselx(iselect(x,1431655765LU))}3 )->(((_2 >> #1) | _1) ~ _3) ((V32(_{!(c&1431655765LU)}2|_{!(c&2863311530LU)}1))~ #{!(x&2863311530LU)&&iselect(x,1431655765LU)==xselx(iselect(x,1431655765LU))}3 )->(((_2 >> #1) | _1) ~ _3) ((V32(_{!(c&2863311530LU)}1|_{!(c&1431655765LU)}2))& #{!(x&2863311530LU)&&iselect(x,1431655765LU)==xselx(iselect(x,1431655765LU))}3 )->(((_2 >> #1) | _1) & _3) ((V32(_{!(c&1431655765LU)}2|_{!(c&2863311530LU)}1))& #{!(x&2863311530LU)&&iselect(x,1431655765LU)==xselx(iselect(x,1431655765LU))}3 )->(((_2 >> #1) | _1) & _3) [cbinxornomingle] ((?32(_{!(c&2863311530LU)}1|_{!(c&1431655765LU)}2))~ #{!(x&2863311530LU)&&iselect(x,1431655765LU)==xselx(iselect(x,1431655765LU))}3 )->(((_2 >> #1) ^ _1) ~ _3) ((?32(_{!(c&1431655765LU)}2|_{!(c&2863311530LU)}1))~ #{!(x&2863311530LU)&&iselect(x,1431655765LU)==xselx(iselect(x,1431655765LU))}3 )->(((_2 >> #1) ^ _1) ~ _3) ((?32(_{!(c&2863311530LU)}1|_{!(c&1431655765LU)}2))& #{!(x&2863311530LU)&&iselect(x,1431655765LU)==xselx(iselect(x,1431655765LU))}3 )->(((_2 >> #1) ^ _1) & _3) ((?32(_{!(c&1431655765LU)}2|_{!(c&2863311530LU)}1))& #{!(x&2863311530LU)&&iselect(x,1431655765LU)==xselx(iselect(x,1431655765LU))}3 )->(((_2 >> #1) ^ _1) & _3) ; Bitwise complements. (The INTERCAL which ultimately leads to cases 3 and 4 ; is not the most efficient way to do this, by the way.) [cnot1] (#65535 ^ .{!(c&4294901760LU)}1)->(~16 .1) [cnot2] (.{!(c&4294901760LU)}1 ^ #65535)->(~16 .1) [cnot3] (#4294967295 ^ :1)->(~32 :1) [cnot4] (:1 ^ #4294967295)->(~32 :1) ; bitwise logical equivalence [cxorand16] ((.1 ^ _2) & _2)->((~16 .1) & _2) ((_2 ^ .1) & _2)->((~16 .1) & _2) ((.1 & _2) ^ _2)->((~16 .1) & _2) ((_2 & .1) ^ _2)->((~16 .1) & _2) (_2 ^ (.1 & _2))->((~16 .1) & _2) (_2 ^ (_2 & .1))->((~16 .1) & _2) (_2 & (.1 ^ _2))->((~16 .1) & _2) (_2 & (_2 ^ .1))->((~16 .1) & _2) [cxorand32] ((:1 ^ _2) & _2)->((~32 _1) & _2) ((_2 ^ :1) & _2)->((~32 _1) & _2) ((:1 & _2) ^ _2)->((~32 _1) & _2) ((_2 & :1) ^ _2)->((~32 _1) & _2) (_2 ^ (:1 & _2))->((~32 _1) & _2) (_2 ^ (_2 & :1))->((~32 _1) & _2) (_2 & (:1 ^ _2))->((~32 _1) & _2) (_2 & (_2 ^ :1))->((~32 _1) & _2) ; Special cases of select ; Selecting the rightmost bits of a number [xselpow2m1] (_1 ~ #{x==xselx(x)}2)->(_1 & _2) ; Selecting one bit from a number [xselpow2] (_1 ~ #{xselx(x)==1}2)->(!(!(_1 & _2))) ; Selecting a number against itself and then selecting 1 from that [xselxsel1] ((_1~_1)~#1)->(!(!_1)) ((_1~_1))->(!(!_1)) (#1&(_1~_1))->(!(!_1)) ((_1~_1)&_{c==1}2)->(_1 && _2) (_{c==1}2&(_1~_1))->(_1 && _2) ; Selecting a number from a constant that's just below a power of 2 [pow2m1selx] ((#{x==xselx(x)}1 ~ _2) ~ #1)->(!(!(_1 & _2))) ; Boolean-negating a select [notselect] (!(_1~_2))->(!(_1&_2)) ; Sometimes select and mingle cancel each other out [selectmingle1] ((_1~#2863311530)$_2)->((_1�)|(#0$_2)) [selectmingle2] (_1$(_2~#1431655765))->((_1$#0)|(_2�)) [selectmingle3] ((_1~#1431655765)$_2)->(((_1�)<<#1)|(#0$_2)) [selectmingle4] (_1$(_2~#2863311530))->(((_2�)>>#1)|(_1$#0)) [selectmingle5] ((_{!(c&4294901760UL)}1$_{!(c&4294901760UL)}2)~#3579139412) ->((_1耀)|(_2>>#1)) ; special cases of V16/?16; the top bit was 0, so becomes equal to the ; bottom bit [or16and] ((V16 _{!(c&4294934528UL)}1)耀)->((_1)<<#15) [xor16and] ((?16 _{!(c&4294934528UL)}1)耀)->((_1)<<#15) ; Shifts ; A helper in calculating 32-bit shifts; this is a shift on half the bits of ; a 32-bit number. [lshift32half] (#0$((_1~#715827882)<<#1))->((_1�)<<#1) ; Rightshift some of the bits [rshift] <#1-#31 (_1~#{xselx(x)<<r==x&&x}2)->((_1&_2)>>#{r}0) > ; General 16-bit leftshifts ; ; Large left-shifts can be written in an optimized way using knowledge of the ; rightmost bits to shift more than one bit at a time. ; If the rightmost few bits of a number are known to be 0, it can be mingled ; with 0, and then selected with a number which has many 0s to do a leftshift. ; Here, if none of the bits marked l are set this is a right-shift by 3, and ; for each bit set, the shift goes 1 leftwards. ; (xxxxxxxxxxxxxttt $ 000000000000uuuu) ~ (h0h0h0h0h0h0h0h0h0h0h0h01lllllll) ; x0x0x0x0x0x0x0x0x0x0x0x0xutututu ; h0h0h0h0h0h0h0h0h0h0h0h01lllllll ; There's three cases here for each possible width for the ts, including one ; which has them as zeros and two which have them higher. [lshift16] <#0-#14 ((_{c<=65535&&!(c&((1LU<<r)-1LU))}1$ #{!(x&(4294967294LU<<r))}2)~#{!(x&(1431655765LU<<(r*2+2)))}3) ->((((_1>>#{r}0)~#{iselect(x3>>(r*2+1),1431655765LU)}0) <<#{setbitcount(x3&((2LU<<(r*2))-1))}0)|#{iselect(mingle(0,x2),x3)}0) (((_{c<=65535&&!(c&((1LU<<r)-1LU))}1|#{x<=65535&&!(c&~((1LU<<r)-1LU))}4)$ #{!(x&(4294967294LU<<r))}2)~#{!(x&(1431655765LU<<(r*2+2)))}3) ->((((_1>>#{r}0)~#{iselect(x3>>(r*2+1),1431655765LU)}0) <<#{setbitcount(x3&((2LU<<(r*2))-1))}0)|#{iselect(mingle(x4,x2),x3)}0) (((#{x<=65535&&!(c&~((1LU<<r)-1LU))}4|_{c<=65535&&!(c&((1LU<<r)-1LU))}1)$ #{!(x&(4294967294LU<<r))}2)~#{!(x&(1431655765LU<<(r*2+2)))}3) ->((((_1>>#{r}0)~#{iselect(x3>>(r*2+1),1431655765LU)}0) <<#{setbitcount(x3&((2LU<<(r*2))-1))}0)|#{iselect(mingle(x4,x2),x3)}0) > ; 32-bit leftshift by 1; there are 8 ways to write this. [lshift32by1] (((_1�)<<#1)|((_1�)<<#1))->((_1�)<<#1) (((#1431655765&_1)<<#1)|((_1�)<<#1))->((_1�)<<#1) (((_1�)<<#1)|((#715827882&_1)<<#1))->((_1�)<<#1) (((#1431655765&_1)<<#1)|((#715827882&_1)<<#1))->((_1�)<<#1) (((_1�)<<#1)|((_1�)<<#1))->((_1�)<<#1) (((_1�)<<#1)|((#1431655765&_1)<<#1))->((_1�)<<#1) (((#715827882&_1)<<#1)|((_1�)<<#1))->((_1�)<<#1) (((#715827882&_1)<<#1)|((#1431655765&_1)<<#1))->((_1�)<<#1) ; a weird part of a leftshift [lshift32half] (#0$((:1�)~#715827883))->((:1�)<<#1) ; Move rshift, AND out of neg [rshiftoutofneg] (~16 (.1 >> #{1}2))->(((~16 .1) >> _2) | #32768) (~32 (:1 >> #{1}2))->(((~32 :1) >> _2) | #2147483648) [andoutofneg] (~16 (.1 & #{1}2))->(((~16 .1) & _2) | #{(~x2)&65535}0) (~32 (:1 & #{1}2))->(((~32 :1) & _2) | #{~x2}0) ; Move AND inside shifts, and OR and XOR outside shifts [andintoshift] ((_1 << #{1}2) & #{1}3)->((_1 & #{x3>>x2}0) << _2) ((_1 >> #{1}2) & #{1}3)->((_1 & #{x3<<x2}0) >> _2) [oroutofshift] ((_1 | #{1}2) << #{1}3)->((_1 << _3) | #{x2<<x3}0) ((_1 | #{1}2) >> #{1}3)->((_1 >> _3) | #{x2>>x3}0) [xoroutofshift] ((_1 ^ #{1}2) << #{1}3)->((_1 << _3) ^ #{x2<<x3}0) ((_1 ^ #{1}2) >> #{1}3)->((_1 >> _3) ^ #{x2>>x3}0) ; Larger leftshifts can be created by combining smaller ones, although there ; are shortcuts that can be used and this idiom only works if they haven't ; been. Also, idioms later on can create shifts that cancel each other out, so ; the code for cancelling them is here. [combinellshift] ((_1 << #{1}2) << #{1}3)->(_1 << #{x2+x3}0) [combinelrshift] ((_1 << #{1}2) >> #{x>x2}3)->(_1 >> #{x3-x2}0) ((_1 << #{1}2) >> #{x==x2}3)->(_1) ((_1 << #{1}2) >> #{x<x2}3)->(_1 << #{x2-x3}0) [combinerlshift] ((_1 >> #{1}2) << #{x>x2}3)->(_1 << #{x3-x2}0) ((_1 >> #{1}2) << #{x==x2}3)->(_1) ((_1 >> #{1}2) << #{x<x2}3)->(_1 >> #{x2-x3}0) [combinerrshift] ((_1 >> #{1}2) >> #{1}3)->(_1 >> #{x2+x3}0) [nullshift] (_1 >> #0)->(_1) (_1 << #0)->(_1) ; INTERCAL logical values are 1 and 2. [xorto1or2] ((?32(_{!(c&4294901760LU)}1$#1)))->((_1)+#1) ((?32(_{!(c&4294901760LU)}1$#2)))->(#2-(_1)) ; Removing, combining and weakening unneeded C_ANDs [unneededand] (_1&#{!(c1&~x)}0)->(_1) (#{!(c1&~x)}0&_1)->(_1) [combineand] ((_1&#{1}2)&#{1}3)->(_1&#{x2&x3}0) ((#{1}2&_1)&#{1}3)->(_1&#{x2&x3}0) (#{1}3&(_1&#{1}2))->(_1&#{x2&x3}0) (#{1}3&(#{1}2&_1))->(_1&#{x2&x3}0) [weakenand] (_1&#{(~c1)&x}2)->(_1&#{c1&x2}0) (#{(~c1)&x}2&_1)->(_1&#{c1&x2}0) ; 32-bit complements ; Complement odd bits, zero even bits [com1z0] (((?32(_1|#1431655765))�)<<#1)->((_1�)^#2863311530) (((?32(#1431655765|_1))�)<<#1)->((_1�)^#2863311530) ((#1431655765&(?32(_1|#1431655765)))<<#1)->((_1�)^#2863311530) ((#1431655765&(?32(#1431655765|_1)))<<#1)->((_1�)^#2863311530) ; Complement even bits, zero odd bits [com0z1] ((?32(((_1�)<<#1)|#1431655765))�) ->((_1�)^#1431655765) ((?32(((#1431655765&_1)<<#1)|#1431655765))�) ->((_1�)^#1431655765) ((?32(#1431655765|((_1�)<<#1)))�) ->((_1�)^#1431655765) ((?32(#1431655765|((#1431655765&_1)<<#1)))�) ->((_1�)^#1431655765) (#1431655765&(?32(((_1�)<<#1)|#1431655765))) ->((_1�)^#1431655765) (#1431655765&(?32(((#1431655765&_1)<<#1)|#1431655765))) ->((_1�)^#1431655765) (#1431655765&(?32(#1431655765|((_1�)<<#1)))) ->((_1�)^#1431655765) (#1431655765&(?32(#1431655765|((#1431655765&_1)<<#1)))) ->((_1�)^#1431655765) ; 32-bit complements, in full [cnot5] (((:1&#{1}2)^#{x==x2}0)|((:1&#{(x^x2)==4294967295LU}3)^#{x==x3}0))->(~32 :1) ; Distributive laws ; Several of these laws go towards helping finish off 32-bit C binary logical ; operations, but are useful in other places as well (especially distributions ; involving shifts). [distribll] ((_1&_3)&(_2&_3))->((_1&_2)&_3) ((_1|_3)&(_2|_3))->((_1&_2)|_3) ((_1&_3)|(_2&_3))->((_1|_2)&_3) ((_1|_3)|(_2|_3))->((_1|_2)|_3) ((_1&_3)^(_2&_3))->((_1^_2)&_3) ((_1<<_3)&(_2<<_3))->((_1&_2)<<_3) ((_1<<_3)|(_2<<_3))->((_1|_2)<<_3) ((_1<<_3)^(_2<<_3))->((_1^_2)<<_3) ((_1>>_3)&(_2>>_3))->((_1&_2)>>_3) ((_1>>_3)|(_2>>_3))->((_1|_2)>>_3) ((_1>>_3)^(_2>>_3))->((_1^_2)>>_3) [distribrl] ((_3&_1)&(_2&_3))->((_1&_2)&_3) ((_3|_1)&(_2|_3))->((_1&_2)|_3) ((_3&_1)|(_2&_3))->((_1|_2)&_3) ((_3|_1)|(_2|_3))->((_1|_2)|_3) ((_3&_1)^(_2&_3))->((_1^_2)&_3) [distriblr] ((_1&_3)&(_3&_2))->((_1&_2)&_3) ((_1|_3)&(_3|_2))->((_1&_2)|_3) ((_1&_3)|(_3&_2))->((_1|_2)&_3) ((_1|_3)|(_3|_2))->((_1|_2)|_3) ((_1&_3)^(_3&_2))->((_1^_2)&_3) [distribrr] ((_3&_1)&(_3&_2))->((_1&_2)&_3) ((_3|_1)&(_3|_2))->((_1&_2)|_3) ((_3&_1)|(_3&_2))->((_1|_2)&_3) ((_3|_1)|(_3|_2))->((_1|_2)|_3) ((_3&_1)^(_3&_2))->((_1^_2)&_3) [distribunary] ((!_1)&(!_2))->(!(_1|_2)) ; 32-bit C binary logical operations ; Strangely enough, these can be done for the most part with the combined ; effect of many small optimizations (of course, that's the best way to do it). ; The only potential problem is that the distributive law isn't quite general ; enough for some cases involving constants, and for some cases where one side ; or the other is known to have no set evenbits or no set oddbits. ; Some generalised versions of the distributive law are needed here. ; Unfortunately, there are lots of binary operators here that need to be ; written both ways round. The 96 cases that follow, combined with weakenand, ; should be enough for all but the most pathological cases. [distribhalfxoroveror1] (((_1 ^ _2) & _3) | (_1 & _{(c&c3)==0}4))->((_1 ^ _2) & (_3 | _4)) ((_1 & _{(c&c3)==0}4) | ((_1 ^ _2) & _3))->((_1 ^ _2) & (_3 | _4)) (((_1 ^ _2) & _3) | (_{(c&c3)==0}4 & _1))->((_1 ^ _2) & (_3 | _4)) ((_{(c&c3)==0}4 & _1) | ((_1 ^ _2) & _3))->((_1 ^ _2) & (_3 | _4)) ((_3 & (_1 ^ _2)) | (_1 & _{(c&c3)==0}4))->((_1 ^ _2) & (_3 | _4)) ((_1 & _{(c&c3)==0}4) | (_3 & (_1 ^ _2)))->((_1 ^ _2) & (_3 | _4)) ((_3 & (_1 ^ _2)) | (_{(c&c3)==0}4 & _1))->((_1 ^ _2) & (_3 | _4)) ((_{(c&c3)==0}4 & _1) | (_3 & (_1 ^ _2)))->((_1 ^ _2) & (_3 | _4)) (((_2 ^ _1) & _3) | (_1 & _{(c&c3)==0}4))->((_1 ^ _2) & (_3 | _4)) ((_1 & _{(c&c3)==0}4) | ((_2 ^ _1) & _3))->((_1 ^ _2) & (_3 | _4)) (((_2 ^ _1) & _3) | (_{(c&c3)==0}4 & _1))->((_1 ^ _2) & (_3 | _4)) ((_{(c&c3)==0}4 & _1) | ((_2 ^ _1) & _3))->((_1 ^ _2) & (_3 | _4)) ((_3 & (_2 ^ _1)) | (_1 & _{(c&c3)==0}4))->((_1 ^ _2) & (_3 | _4)) ((_1 & _{(c&c3)==0}4) | (_3 & (_2 ^ _1)))->((_1 ^ _2) & (_3 | _4)) ((_3 & (_2 ^ _1)) | (_{(c&c3)==0}4 & _1))->((_1 ^ _2) & (_3 | _4)) ((_{(c&c3)==0}4 & _1) | (_3 & (_2 ^ _1)))->((_1 ^ _2) & (_3 | _4)) [distribhalfxoroveror2] (((_1 & _3) ^ _{(c&c3)==c}2) | (_1 & _{(c&c3)==0}4))->((_1 ^ _2) & (_3 | _4)) ((_1 & _{(c&c3)==0}4) | ((_1 & _3) ^ _{(c&c3)==c}2))->((_1 ^ _2) & (_3 | _4)) (((_1 & _3) ^ _{(c&c3)==c}2) | (_{(c&c3)==0}4 & _1))->((_1 ^ _2) & (_3 | _4)) ((_{(c&c3)==0}4 & _1) | ((_1 & _3) ^ _{(c&c3)==c}2))->((_1 ^ _2) & (_3 | _4)) ((_{(c&c3)==c}2 ^ (_1 & _3)) | (_1 & _{(c&c3)==0}4))->((_1 ^ _2) & (_3 | _4)) ((_1 & _{(c&c3)==0}4) | (_{(c&c3)==c}2 ^ (_1 & _3)))->((_1 ^ _2) & (_3 | _4)) ((_{(c&c3)==c}2 ^ (_1 & _3)) | (_{(c&c3)==0}4 & _1))->((_1 ^ _2) & (_3 | _4)) ((_{(c&c3)==0}4 & _1) | (_{(c&c3)==c}2 ^ (_1 & _3)))->((_1 ^ _2) & (_3 | _4)) (((_3 & _1) ^ _{(c&c3)==c}2) | (_1 & _{(c&c3)==0}4))->((_1 ^ _2) & (_3 | _4)) ((_1 & _{(c&c3)==0}4) | ((_3 & _1) ^ _{(c&c3)==c}2))->((_1 ^ _2) & (_3 | _4)) (((_3 & _1) ^ _{(c&c3)==c}2) | (_{(c&c3)==0}4 & _1))->((_1 ^ _2) & (_3 | _4)) ((_{(c&c3)==0}4 & _1) | ((_3 & _1) ^ _{(c&c3)==c}2))->((_1 ^ _2) & (_3 | _4)) ((_{(c&c3)==c}2 ^ (_3 & _1)) | (_1 & _{(c&c3)==0}4))->((_1 ^ _2) & (_3 | _4)) ((_1 & _{(c&c3)==0}4) | (_{(c&c3)==c}2 ^ (_3 & _1)))->((_1 ^ _2) & (_3 | _4)) ((_{(c&c3)==c}2 ^ (_3 & _1)) | (_{(c&c3)==0}4 & _1))->((_1 ^ _2) & (_3 | _4)) ((_{(c&c3)==0}4 & _1) | (_{(c&c3)==c}2 ^ (_3 & _1)))->((_1 ^ _2) & (_3 | _4)) [distribhalforoveror1] (((_1 | _2) & _3) | (_1 & _{(c&c3)==0}4))->((_1 | _2) & (_3 | _4)) ((_1 & _{(c&c3)==0}4) | ((_1 | _2) & _3))->((_1 | _2) & (_3 | _4)) (((_1 | _2) & _3) | (_{(c&c3)==0}4 & _1))->((_1 | _2) & (_3 | _4)) ((_{(c&c3)==0}4 & _1) | ((_1 | _2) & _3))->((_1 | _2) & (_3 | _4)) ((_3 & (_1 | _2)) | (_1 & _{(c&c3)==0}4))->((_1 | _2) & (_3 | _4)) ((_1 & _{(c&c3)==0}4) | (_3 & (_1 | _2)))->((_1 | _2) & (_3 | _4)) ((_3 & (_1 | _2)) | (_{(c&c3)==0}4 & _1))->((_1 | _2) & (_3 | _4)) ((_{(c&c3)==0}4 & _1) | (_3 & (_1 | _2)))->((_1 | _2) & (_3 | _4)) (((_2 | _1) & _3) | (_1 & _{(c&c3)==0}4))->((_1 | _2) & (_3 | _4)) ((_1 & _{(c&c3)==0}4) | ((_2 | _1) & _3))->((_1 | _2) & (_3 | _4)) (((_2 | _1) & _3) | (_{(c&c3)==0}4 & _1))->((_1 | _2) & (_3 | _4)) ((_{(c&c3)==0}4 & _1) | ((_2 | _1) & _3))->((_1 | _2) & (_3 | _4)) ((_3 & (_2 | _1)) | (_1 & _{(c&c3)==0}4))->((_1 | _2) & (_3 | _4)) ((_1 & _{(c&c3)==0}4) | (_3 & (_2 | _1)))->((_1 | _2) & (_3 | _4)) ((_3 & (_2 | _1)) | (_{(c&c3)==0}4 & _1))->((_1 | _2) & (_3 | _4)) ((_{(c&c3)==0}4 & _1) | (_3 & (_2 | _1)))->((_1 | _2) & (_3 | _4)) [distribhalforoveror2] (((_1 & _3) | _{(c&c3)==c}2) | (_1 & _{(c&c3)==0}4))->((_1 | _2) & (_3 | _4)) ((_1 & _{(c&c3)==0}4) | ((_1 & _3) | _{(c&c3)==c}2))->((_1 | _2) & (_3 | _4)) (((_1 & _3) | _{(c&c3)==c}2) | (_{(c&c3)==0}4 & _1))->((_1 | _2) & (_3 | _4)) ((_{(c&c3)==0}4 & _1) | ((_1 & _3) | _{(c&c3)==c}2))->((_1 | _2) & (_3 | _4)) ((_{(c&c3)==c}2 | (_1 & _3)) | (_1 & _{(c&c3)==0}4))->((_1 | _2) & (_3 | _4)) ((_1 & _{(c&c3)==0}4) | (_{(c&c3)==c}2 | (_1 & _3)))->((_1 | _2) & (_3 | _4)) ((_{(c&c3)==c}2 | (_1 & _3)) | (_{(c&c3)==0}4 & _1))->((_1 | _2) & (_3 | _4)) ((_{(c&c3)==0}4 & _1) | (_{(c&c3)==c}2 | (_1 & _3)))->((_1 | _2) & (_3 | _4)) (((_3 & _1) | _{(c&c3)==c}2) | (_1 & _{(c&c3)==0}4))->((_1 | _2) & (_3 | _4)) ((_1 & _{(c&c3)==0}4) | ((_3 & _1) | _{(c&c3)==c}2))->((_1 | _2) & (_3 | _4)) (((_3 & _1) | _{(c&c3)==c}2) | (_{(c&c3)==0}4 & _1))->((_1 | _2) & (_3 | _4)) ((_{(c&c3)==0}4 & _1) | ((_3 & _1) | _{(c&c3)==c}2))->((_1 | _2) & (_3 | _4)) ((_{(c&c3)==c}2 | (_3 & _1)) | (_1 & _{(c&c3)==0}4))->((_1 | _2) & (_3 | _4)) ((_1 & _{(c&c3)==0}4) | (_{(c&c3)==c}2 | (_3 & _1)))->((_1 | _2) & (_3 | _4)) ((_{(c&c3)==c}2 | (_3 & _1)) | (_{(c&c3)==0}4 & _1))->((_1 | _2) & (_3 | _4)) ((_{(c&c3)==0}4 & _1) | (_{(c&c3)==c}2 | (_3 & _1)))->((_1 | _2) & (_3 | _4)) [distribhalfandoveror1] (((_1 & _2) & _3) | (_1 & _{(c&c3)==0}4))->((_1 & _2) & (_3 | _4)) ((_1 & _{(c&c3)==0}4) | ((_1 & _2) & _3))->((_1 & _2) & (_3 | _4)) (((_1 & _2) & _3) | (_{(c&c3)==0}4 & _1))->((_1 & _2) & (_3 | _4)) ((_{(c&c3)==0}4 & _1) | ((_1 & _2) & _3))->((_1 & _2) & (_3 | _4)) ((_3 & (_1 & _2)) | (_1 & _{(c&c3)==0}4))->((_1 & _2) & (_3 | _4)) ((_1 & _{(c&c3)==0}4) | (_3 & (_1 & _2)))->((_1 & _2) & (_3 | _4)) ((_3 & (_1 & _2)) | (_{(c&c3)==0}4 & _1))->((_1 & _2) & (_3 | _4)) ((_{(c&c3)==0}4 & _1) | (_3 & (_1 & _2)))->((_1 & _2) & (_3 | _4)) (((_2 & _1) & _3) | (_1 & _{(c&c3)==0}4))->((_1 & _2) & (_3 | _4)) ((_1 & _{(c&c3)==0}4) | ((_2 & _1) & _3))->((_1 & _2) & (_3 | _4)) (((_2 & _1) & _3) | (_{(c&c3)==0}4 & _1))->((_1 & _2) & (_3 | _4)) ((_{(c&c3)==0}4 & _1) | ((_2 & _1) & _3))->((_1 & _2) & (_3 | _4)) ((_3 & (_2 & _1)) | (_1 & _{(c&c3)==0}4))->((_1 & _2) & (_3 | _4)) ((_1 & _{(c&c3)==0}4) | (_3 & (_2 & _1)))->((_1 & _2) & (_3 | _4)) ((_3 & (_2 & _1)) | (_{(c&c3)==0}4 & _1))->((_1 & _2) & (_3 | _4)) ((_{(c&c3)==0}4 & _1) | (_3 & (_2 & _1)))->((_1 & _2) & (_3 | _4)) [distribhalfandoveror2] (((_1 & _3) & _2) | (_1 & _{(c&c3)==0}4))->((_1 & _2) & (_3 | _4)) ((_1 & _{(c&c3)==0}4) | ((_1 & _3) & _2))->((_1 & _2) & (_3 | _4)) (((_1 & _3) & _2) | (_{(c&c3)==0}4 & _1))->((_1 & _2) & (_3 | _4)) ((_{(c&c3)==0}4 & _1) | ((_1 & _3) & _2))->((_1 & _2) & (_3 | _4)) ((_2 & (_1 & _3)) | (_1 & _{(c&c3)==0}4))->((_1 & _2) & (_3 | _4)) ((_1 & _{(c&c3)==0}4) | (_2 & (_1 & _3)))->((_1 & _2) & (_3 | _4)) ((_2 & (_1 & _3)) | (_{(c&c3)==0}4 & _1))->((_1 & _2) & (_3 | _4)) ((_{(c&c3)==0}4 & _1) | (_2 & (_1 & _3)))->((_1 & _2) & (_3 | _4)) (((_3 & _1) & _2) | (_1 & _{(c&c3)==0}4))->((_1 & _2) & (_3 | _4)) ((_1 & _{(c&c3)==0}4) | ((_3 & _1) & _2))->((_1 & _2) & (_3 | _4)) (((_3 & _1) & _2) | (_{(c&c3)==0}4 & _1))->((_1 & _2) & (_3 | _4)) ((_{(c&c3)==0}4 & _1) | ((_3 & _1) & _2))->((_1 & _2) & (_3 | _4)) ((_2 & (_3 & _1)) | (_1 & _{(c&c3)==0}4))->((_1 & _2) & (_3 | _4)) ((_1 & _{(c&c3)==0}4) | (_2 & (_3 & _1)))->((_1 & _2) & (_3 | _4)) ((_2 & (_3 & _1)) | (_{(c&c3)==0}4 & _1))->((_1 & _2) & (_3 | _4)) ((_{(c&c3)==0}4 & _1) | (_2 & (_3 & _1)))->((_1 & _2) & (_3 | _4)) ; A right-shift idiom in syslib that was written in an unneccessarily complex ; way, by doing the bits separately the same way as left-shifts have to be done ; (of course, select can right-shift by any difference without much trouble); ; the next idiom is a helper for that. Previous code produced a warning when ; this idiom was used, but the optimizer has now been enhanced to the extent ; that it can deal with it without much special-casing, and therefore there's ; no way now to tell that that case is being used, so the warning has been ; removed. ; lshift32half done in the other direction; note that the large constant here ; is 0x55555554, not the all-5s number [rshift32half] ((_1~#1431655764)$#0)->((_1�)>>#1) ; and piecing together this with selectmingle4 gives the syslib idiom, which ; optimizes through distributions over C_OR and then constant folding ; When a 0 is on one side of a C binary logic operation, or the two sides are ; the same, simplification is often possible. The and-0 case has been dealt ; with already. [noopor] (_1|#0)->(_1) (#0|_1)->(_1) [noopxor] (_1^#0)->(_1) (#0^_1)->(_1) [anditself] (_1&_1)->(_1) [oritself] (_1|_1)->(_1) [xoritself] (_1^_1)->(#0) ; The following four idioms by JH ((_1^_2)^_1) -> (_2) ((_2^_1)^_1) -> (_2) (_1^(_1^_2)) -> (_2) (_1^(_2^_1)) -> (_2) ; Equality and inequality [xortoequal] (!(_1^_2))->(_1==_2) [negatingequal] (!(_1==_2))->(_1!=_2) (!(_1!=_2))->(_1==_2) ; Greater than and less than [greaterthan32] ((_1~:2)~((?32(:2~:2))^#2147483648))->(_1>(:2^_1)) ((_1~:2)~(#2147483648^(?32(:2~:2))))->(_1>(:2^_1)) [greaterthan16] ((_1~.2)~((?16(.2~.2))^#32768))->(_1>(.2^_1)) ((_1~.2)~(#32768^(?16(.2~.2))))->(_1>(.2^_1)) ; Consistency in C logical operation nesting, when it doesn't matter [xoroutsideand] ((_1^_2)&_2)->((_1&_2)^_2) (_2&(_1^_2))->((_1&_2)^_2) ((_2^_1)&_2)->((_1&_2)^_2) (_2&(_2^_1))->((_1&_2)^_2) ; Boolean algebra, on 0s and 1s or on 1s and 2s. Unary bitwidth is irrelevant. [booleannot] (_{c==1}1^#1)->(!_1) [not21] (#2-(!(_{c==1}1)))->(_1+#1) (#1+(!(_{c==1}1)))->(#2-_1) ((!(_{c==1}1))+#1)->(#2-_1) [nullmingle] (#0$_{c==1}1)->(_1) ; Thanks to Joris Huizer for suggesting the idea behind the next one; ; this is a more general idiom than the suggested [triplenot]. [redundantdoublenot] (!(!(_{c==1}1)))->(_1)