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SamiraKhanUniversityofVirginia
Jan31,2017
BinaryOperationsCS3330
AGENDA
• Logistics
• ReviewfromlastLecture
• BinaryOperations– LogicalOperations– BitwiseOperations– Examples
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Feedbacks
• Quizzesarehard– Usethebook,lectures,internet,whateveryoucan– Pastquizzesareavailableonline
• Forthequizquestionwith:typedef struct bar{intx;}foo;Itriedcompilingstruct foo*c;inC,anditcompiledfine.Sowhyisitwrong?– Droppedit– Goodcatch– AskinPiazza,sothatotherscanlearn,too
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Feedbacks
• Isastringstillastringifitisexpressedinbits?thatseemslikemoreofaphilosophicalquestiontomeI'mreferringtothequizquestion– Yes– Thereisno“abcde…”– Everythingisjust0sand1s– Itisjusthowyouinterpretit
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AGENDA
• Logistics
• ReviewfromlastLecture
• BinaryOperations– LogicalOperations– BitwiseOperations– Examples
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UndefinedBehavior
• CFAQdefinition:• Anythingatallcanhappen– Standardimposesnorequirements;– Programmayfailtocompile,– oritmayexecuteincorrectly,– oritmaydoexactlywhattheprogrammerintended
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AddingonetoINT_MAXifweaddonetothelargestrepresentableinteger,istheresultnegative?
#include<limits.h>#include<stdio.h>
int main(void){printf ("%d\n",(INT_MAX+1)<0);return0;}
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Undefined,outputcouldbezeroorone
MoreUndefinedBehavior• Attemptingtomodifyastringliteral– char*p="wikipedia";//validC– p[0]='W';//undefinedbehavior
• Integerdivisionbyzero– int x=1;– return x/0;//undefinedbehavior
• Certainpointeroperations– int arr[4]={0,1,2,3};– int *p=arr +5; //undefinedbehavior
• Incrementandassignment– i =i+++1;//undefinedbehavior
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UndefinedBehavior
• Pros:– Simplifies thecompiler’sjob– Generatesveryefficientcode– Example:incrementINT_MAX• Doesnotneedtoworryaboutoverflowsandresultbecomenegative
• Cons:–Misbehavedprograms– Securityissues– Example:Arrayoutofbound
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AGENDA
• Logistics
• ReviewfromlastLecture
• BinaryOperations– LogicalOperations– BitwiseOperations– Examples
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Howdodigitalcomputersrepresentnumbers?
• Madeoftransistors(thinkasaswitch)• Haveonlytwostates:ON,OFF
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• Canonlyuse0and1torepresentnumbers• 3à 0011,10à 1010
BinaryOperations• Weneedtooperateonthesebinarynumbers• ArithmeticOperations– ADD,SUB,MUL,DIV
• LogicalOperations• AND,OR,NOT
• BitwiseOperations– AND,OR,NOT,XOR,SHIFT
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LogicalOperations
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Operator Description ExampleA=2,B=0
LogicalAND(&&)
Boththeoperandsarenon-zeroà conditionbecomes
true
A&&B=False/0
LogicalOR(||)
Anyofthetwooperandsisnon-zeroà thecondition
becomestrue
A||B=1/true
LogicalNOT(!/~)
Reversethelogicalstate !(A&&B)= 1/true
LogicalOperations
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Operator Description ExampleA=2,B=0
LogicalAND(&&)
Boththeoperandsarenon-zeroà conditionbecomes
true
A&&B=False/0
LogicalOR(||)
Anyofthetwooperandsisnon-zeroà thecondition
becomestrue
A||B=1/true
LogicalNOT(!/~)
Reversethelogicalstate !(A&&B)= 1/true
LogicalOperations
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Operator Description ExampleA=2,B=0
LogicalAND(&&)
Boththeoperandsarenon-zeroà conditionbecomes
true
A&&B=False/0
LogicalOR(||)
Anyofthetwooperandsisnon-zeroà thecondition
becomestrue
A||B=1/true
LogicalNOT(!/~)
Reversethelogicalstate !(A&&B)= 1/true
LogicalOperations
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Operator Description ExampleA=2,B=0
LogicalAND(&&)
Boththeoperandsarenon-zeroà conditionbecomes
true
A&&B=False/0
LogicalOR(||)
Anyofthetwooperandsisnon-zeroà thecondition
becomestrue
A||B=1/true
LogicalNOT(!/~)
Reversethelogicalstate !(A&&B)= 1/true
Example:Short-Circuit#include<stdio.h>int zero(){printf("zero()\n");return0;}int one(){printf("one()\n");return1;}
int main(){printf(">␣%d\n",zero()&&one());printf(">␣%d\n",one()&&zero());return0;}
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OUTPUTzero()>0one()zero()>0
AGENDA
• Logistics
• ReviewfromlastLecture
• BinaryOperations– LogicalOperations– BitwiseOperations– Examples
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X Y X ANDY XOR Y XXORY NOT X0 0 0 0 0 10 1 0 1 1 11 0 0 1 1 01 1 1 1 0 0
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BitwiseOperations
X Y X ANDY XOR Y XXORY NOT X0 0 0 0 0 10 1 0 1 1 11 0 0 1 1 01 1 1 1 0 0
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BitwiseOperations
Operatesoneachbit
X Y X ANDY XOR Y XXORY NOT X0 0 0 0 0 10 1 0 1 1 11 0 0 1 1 01 1 1 1 0 0
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BitwiseOperations
Operatesoneachbit
X Y X ANDY XOR Y XXORY NOT X0 0 0 0 0 10 1 0 1 1 11 0 0 1 1 01 1 1 1 0 0
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BitwiseOperations
Operatesoneachbit
X Y X ANDY XOR Y XXORY NOT X0 0 0 0 0 10 1 0 1 1 11 0 0 1 1 01 1 1 1 0 0
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BitwiseOperations
Operatesoneachbit
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BitwiseOperations
0010&0100------------0000
0010|0100------------0110
0010^ 0100------------
0110
~0100------------
1011
0010>>0001------------
0001
Whataboutnegativenumbers?
AND OR XOR NOT SHIFT
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SHIFTBitwiseOperations
• WhatvalueshouldbeplacedintheMSB?• −10>>1==???
• -10=1111…11110110• -10>>1==?111…11111011
• Option1:copysignbità Arithmeticshift• Option2:alwayskeepzeroà Logicalshift
SignedandUnsignedShift• /*signed*/int x=−10;• /*arithmetic:*/• x>>1==−5• x>>4==−1
• unsignedint y=0xFFFFFFF6;• /*logical*/• y>>1==0x7FFFFFFB• y>>4==0x0FFFFFFF
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UndefinedBehaviorwithSHIFTS
• 0>>32à undefinedbehavior
• 0<<32à undefinedbehavior
• (long)0>>32à okay
• (long)0>>64à undefinedbehavior
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AGENDA
• Logistics
• ReviewfromlastLecture
• BinaryOperations
– LogicalOperations– BitwiseOperations– Examples
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RECAP:BinaryOperations
• BitwiseOperations– AND,OR,NOT,XOR,SHIFT
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WhydoBitManipulation?
WhydoBitManipulation?• Fasterthanmanycomplexoperations– DIV25-123cycles– ADD/AND/CMP/OR/SUB/XOR1cycle
• Examples:– Supposeyouaredesigningareliablesystem,wanttodetectifanybitflipped
– Parity:countthenumberofones,store1ifeven– Howmanyonesarethereinanumber?
– SupposeyouwanttomakeDIVfasterifitisapoweroftwo
– Isanumberapoweroftwo?
30Intel®64andIA-32ArchitecturesOptimizationReferenceManual
BuildingBlocksofBitManipulation• Setabit,keepotherbitsunchanged– 0à 1;1à 1
• Reset/Clearabit,keepotherbitsunchanged– 1à 0;0à 0
• Toggleabit,keepotherbitsunchanged– 1à 0;0à 1
• Extractandshift– 10101111 10101010à 0000000000001111
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BuildingBlocksofBitManipulation• Setabit– 0à 1;1à 1– X|1– Example:– Setthethirdbitof1010– 1010|0100=1110– X3X2X1X0 |0100=X31X1X0
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BuildingBlocksofBitManipulation• Reset/Clearabit– 1à 0;0à 0– X&0– Example:– Clearthethirdbitof1110– 1110&1011=1010– X3X2X1X0 & 1011=X30X1X0
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BuildingBlocksofBitManipulation• Toggleabit,keepotherbitsunchanged– 1à 0;0à 1– X^1– Example:– Togglethethirdbitofthebitvector– 1110^0100=1010– 1010^0100=1110– X3X2X1X0 |0100=X3𝑿𝟐X1X0
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BuildingBlocksofBitManipulation• Extractandshift– 10101111 10101010à 0000000000001111
–Mask:X&0x0F00=0000X3X2X1X0 00000000– Shift:X>>8=000000000000X3X2X1X
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ExampleProblems• Isanybitsetinthebitvector?
• Howmanybitsareset?
• HowtomanipulatecolorsinRGB?
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Isanybitsetinthebitvector?
• NaïveSolution
• Shiftabitandcheckifitis1• (X&1)|((X>>1)&1)|((X>>2)&1)…• 00110010&1=0• 00011001&1=1• 00001100&1=0• ....
• Anyothersolution? 37
Isanybitsetinthebitvector?• Operateonlyonhalf• Assume16bitsinteger• A =(X>>8)|X• TaketheupperhalfandorwithX• IfanybitinXisset,lowerhalfofawillhaveasetbit
• X=0000010000000000
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0000000000000100X>>8|0000010000000000X--------------------------------------- ------ 00000100A
• A=(X>>8)|X• A=(A>>4)|A• A=(A>>2)|A• A=(A>>1)|A• returnA&1
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----- ------ 00000000A>>4| ----- ------ 00000100A--------------------------------------- ----- ---- 0100A
Isanybitsetinthebitvector?
• A=(X>>8)|X• A=(A>>4)|A• A=(A>>2)|A• A=(A>>1)|A• returnA&1
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----- ------ ----- 0001A>>2| ----- ------ ----- 0100A--------------------------------------- ----- ---- -- 01A
Isanybitsetinthebitvector?
• A=(X>>8)|X• A=(A>>4)|A• A=(A>>2)|A• A=(A>>1)|A• returnA&1
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----- ------ ----- -- 00A>>1| ----- ------ ----- -- 01A--------------------------------------- ----- ---- -- - 1A
Isanybitsetinthebitvector?
ExampleProblems• Isanybitsetinthebitvector?
• Howmanybitsareset?
• HowtomanipulatecolorsinRGB?
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CountSetbits
• Count=X&1• Count+=(X>>1)&1• Count+=(X>>2)&1• …
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ExampleProblems• Isanybitsetinthebitvector?
• Howmanybitsareset?
• HowtomanipulatecolorsinRGB?
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HowtomanipulatecolorsinRGB?• RGB8bits– Eachcolorisrepresentedusing8bit– 0to255
• 32bits:0x00BBGG RR• int blueMask =0xFF0000int greenMask =0xFF00int redMask =0xFF;int r=12,g=13,b=14;int bgrValue =(b<<16)+(g<<8)+r;printf("blue:%d\n”,((bgrValue &blueMask)>>16));printf("red:%d\n”,((bgrValue &redMask)));printf("green:%d\n”,((bgrValue &greenMask)>>8));
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SamiraKhanUniversityofVirginia
Jan31,2017
BinaryOperationsCS3330
