TweetFollow Us on Twitter

Nov 95 Challenge
Volume Number:11
Issue Number:11
Column Tag:Programmer’s Challenge

Programmer’s Challenge

By Bob Boonstra, Westford, Massachusetts

Note: Source code files accompanying article are located on MacTech CD-ROM or source code disks.

Enclosing Bounds

The Challenge this month is based on a suggestion by Mike Scanlin, who remains a fan of the column. (We’re still waiting for Mike’s first Challenge entry, however.) The problem is to write a routine that will return a rectangle enclosing all non-white pixels in a selected area of an image. This code might be useful in a drawing or painting program, where the user would be allowed to select a subset of the image by clicking and dragging, and the software would select all of the elements of the image contained within that selection. The prototype of the code you will write is:

void EnclosingBounds(
 PixMapHandle pm,  /* handle to PixMap containing image */
 Rect selection, /* subset of image to enclose */
 Rect *enclosingRect /* enclosing rect return value */
);

Your code should examine all of the pixels within the selection rectangle of the PixMap and return the smallest rectangle containing all of the non-white pixels. Pixels outside the selection rectangle should be ignored. The bounds rectangle of the PixMap will be no larger than 2048 pixels in each dimension, the baseAddr pointer will be longword aligned, and rowBytes will be a multiple of 4. You should deal with pixelSize values of 1, 8, or 32, with values of 8 and 32 being weighted most heavily in measuring performance. For PixMaps with indexed pixels (cmpCount==1), the color table will contain white as the first table entry (as all good color tables are supposed to). For PixMaps with direct pixels, the unused (alpha) bits of each pixel will be zero.

You may use either the Metrowerks or the Symantec compilers for this native PowerPC Challenge. If you have any questions, or would like some test data for your code, please send me e-mail at one of the Programmer’s Challenge addresses, or directly to boonstra@ultranet.com.

Two Months Ago Winner

Congratulations to Eric Lengyel (Blacksburg, VA) for submitting the fastest and smallest entry to the Reversible Scrambling Algorithm Challenge. Despite an unfortunate delay in publication of the magazine that left participants with less time than usual to complete the Challenge, three of the four entries I received by the extended deadline worked correctly, at least in part.

You might recall that the Challenge was to write code that would raise a large integer message to a power and compute the remainder modulo another large integer. The name of the Challenge comes from the fact that this technique is reversible, given properly chosen integers. Eric is a graduate student in Mathematics at Virginia Tech, and he took advantage of a highly optimized multiple precision integer arithmetic library that he had written as part of a number theory project involving the factorization of very large numbers.

Each of the working entries converted the BigNum representation provided in the problem into one that right-justified numbers into a fixed-length data structure. While this imposes a restriction on the maximum size integer that the code can handle, this assumption was permitted by the problem statement. In Eric’s code, the restriction is controlled by a single #define statement.

Eric uses a binary exponentiation algorithm to raise the message to the specified power, and takes advantage of facts from number theory that allow the remainder to be computed at each step of the exponentiation. The time to perform the exponentiation is therefore proportional to the logarithm of the exponent. Eric’s multiplication and division routines use the 68020’s capability to compute the 64-bit product of two longwords and to divide a 64-bit dividend by a longword. The multiplication, division, exponentiation, and compare routines in Eric’s code are general purpose and could be used in any 68K application that needs large integers.

Honorable mention goes to Ernst Munter, who submitted an entry in pure C that was actually the fastest code for the short modulus test cases. Unfortunately, his entry did not produce correct results for the longer moduli.

Here are the times and code sizes for the entries that worked correctly (or partially correctly). Execution time is presented for two specific test cases, with modulus lengths of 22 and 88 bytes, respectively, as well as the total time for all of the test cases I ran. Cases that produced incorrect results are indicated with an asterisk. Numbers in parens after a person’s name indicate that person’s cumulative point total for all previous Challenges, not including this one.

Name time1 time2 Total time code data

(22) (88)
bytes bytes

Eric Lengyel 47 463 2083 1190 0

Xan Gregg (51) 35 967 3175 1558 0

Ernst Munter (C entry) (90) 17 * * 4266 11788

Top 20 Contestants of All Time

Here are the Top 20 Contestants for the Programmer’s Challenges to date. The numbers below include points awarded for this month’s entrants. (Note: ties are listed alphabetically by last name - there are more than 20 people listed this month because of ties.)

Rank Name Points

1. [Name deleted] 176

2. Munter, Ernst 90

3. Karsh, Bill 78

4. Stenger, Allen 65

5. Gregg, Xan 61

6. Larsson, Gustav 60

7. Riha, Stepan 51

8. Goebel, James 49

9. Nepsund, Ronald 47

10. Cutts, Kevin 46

11. Mallett, Jeff 44

12. Kasparian, Raffi 42

13. Vineyard, Jeremy 42

14. Darrah, Dave 31

15. Landry, Larry 29

16. Elwertowski, Tom 24

17. Lee, Johnny 22

18. Noll, Robert 22

19. Anderson, Troy 20

20. Beith, Gary 20

21. Burgoyne, Nick 20

22. Galway, Will 20

23. Israelson, Steve 20

24. Landweber, Greg 20

25. Lengyel, Eric 20

26. Pinkerton, Tom 20

There are three ways to earn points: (1) scoring in the top 5 of any Challenge, (2) being the first person to find a bug in a published winning solution or, (3) being the first person to suggest a Challenge that I use. The points you can win are:

1st place 20 points

2nd place 10 points

3rd place 7 points

4th place 4 points

5th place 2 points

finding bug 2 points

suggesting Challenge 2 points

Here is Eric’s winning solution:

PowerAndRemainder.c

Copyright © 1995 Eric Lengyel
/*
I call my fixed length numbers “BigFixed” and translate from BigNum’s to BigFixed’s in the PowerAndRemainder 
routine.  These are the assembly language routines which are the guts of my program:

(1) PowerMod - raises a number to a power and reduces it by a modulus.  It uses a fast binary exponentiation 
algorithm, reducing by the modulus at each step.
(2) Multiply - multiplies 2 BigNum’s together.
(3) MultQ - mutliplies a BigNum by a long int.
(4) Divide - divides one BigNum by another and supplies the quotient and remainder.
(5) Compare - determines the ordering of 2 BigNum’s.

Some of the loops have been expanded to make more efficient use of the instruction cache.
*/

#define NumSize 72

typedef struct BigNum
{
   short           numDig;
   unsigned char   *dig;
} BigNum;

typedef struct BigFixed
{
   unsigned char   dig[NumSize*4];
} BigFixed;

/* We need 72 longs because the division routine needs the most significant longword to be zero and the 
speed optimization requires that NumSize be a multiple of four. */

void PowerAndRemainder(BigNum *msg, BigNum *exp, BigNum *n,
   BigNum *res);
void PowerMod(BigFixed *msg, BigFixed *exp, BigFixed *n,
   BigFixed *res);
void Multiply(BigFixed *src1, BigFixed *src2, BigFixed *dst);
void MultQ(BigFixed *src1, long src2, BigFixed *dst);
void Divide(BigFixed *end, BigFixed *sor, BigFixed *dst);
short Compare(BigFixed *src1, BigFixed *src2);

PowerAndRemainder

void PowerAndRemainder(BigNum *msg, BigNum *exp, BigNum *n,
   BigNum *res)
{
   short      a, b, numDigits;
   BigFixed   msg0, exp0, n0, res0;
   
   for (a = 0; a < NumSize*4; a++)
   {
      b = NumSize*4 - msg->numDig;
      if (a < b) msg0.dig[a] = 0;
      else msg0.dig[a] = msg->dig[a - b];
      b = NumSize*4 - exp->numDig;
      if (a < b) exp0.dig[a] = 0;
      else exp0.dig[a] = exp->dig[a - b];
      b = NumSize*4 - n->numDig;
      if (a < b) n0.dig[a] = 0;
      else n0.dig[a] = n->dig[a - b];
   }
   PowerMod(&msg0, &exp0, &n0, &res0);
   a = 0;
   while (res0.dig[a] == 0) a++;
   numDigits = res->numDig = NumSize*4 - a;
   for (b = 0; b < numDigits; b++)
      res->dig[b] = res0.dig[a++];
}

PowerMod

void PowerMod(BigFixed *msg, BigFixed *exp, BigFixed *n,
   BigFixed *res)
{
   BigFixed   acc, scrap;

   asm
   {
   LEA      acc, A0            ;   Start with one in
   MOVEQ    #NumSize/4-2, D0   ;   accumulator
1} ; Test a bit in current
                               ;   longword of exponent
   BEQ      @1                 ;   If zero, skip multiply
   PEA      acc                ;   Multiply accumulator
   PEA      acc                ;   by base
   MOVE.L   msg, -(A7)
   JSR      Multiply
   ADDA.W   #12, A7
   MOVE.L   n, -(A7)           ;   Compare accumulator
   PEA      acc                ;   to modulus
   JSR      Compare
   ADDQ.W   #8, A7
   TST.B    D0
   BMI      @1                 ;   If it’s less, skip
                               ;   reduction
   PEA      scrap              ;   Reduce modulo “n”
   MOVE.L   n, -(A7)
   PEA      acc
   JSR      Divide
   ADDA.W   #12, A7
Multiply

/* Multiply src1 by src2 and put product in dst */

void Multiply(BigFixed *src1, BigFixed *src2, BigFixed *dst)
{
   short      topStop, botStop;
   BigFixed   acc, line;
   
   asm
   {
   MOVEM.L  D0-D7/A0-A4, -(A7)
   LEA      acc, A0            ;   Clear accumulator
   MOVEQ    #NumSize/4-1, D0
D5       ;   Do 64-bit multiply
   ADD.L    D2, D5             ;   Add carry to low
                               ;   longword of product
   CLR.L    D2                 ;   Use D2 as dummy to
                               ;   extend carry
   ADDX.L   D2, D6             ;   Add zero to high
                               ;   longword with carry
   MOVE.L   D6, D2             ;   Anything in high
                               ;   longword gets carried
   MOVE.L   D5, 00(A2, D3.W*4) ;   Store low longword in
                               ;   partial product
   SUBQ.W   #1, D3             ;   Loop through all
   CMP.W    topStop, D3        ;   longwords in top number
   BGE      @1
   MOVEA.L  A2, A0             ;   Now add partial product
                               ;   to accumulator
   MOVE.L   D4, D0             ;   Calculate correct
                               ;   position in product
   LEA      acc, A1            ;   Get accumulator’s addr
   ADDQ.W   #1, D0
   ADDA.W   #NumSize * 4, A0
   LSL.W    #2, D0
   ADDA.W   D0, A1
   MOVE.W   D4, D1
   MOVE.L   -(A1), D0          ;   Get longword of product
   SUBQ     #1, D1
   ADD.L    -(A0), D0          ;   Add longword of
   MOVE.L   D0, (A1)           ;   partial product
   TST.W    D1                 ;   If no more longwords,
   BMI      @2                 ;   then branch
MultQ
/* Multiply src1 by src2 and put product in dst */

void MultQ(BigFixed *src1, long src2, BigFixed *dst)
{
   BigFixed   pro;
   
   asm
   {
   MOVEM.L  D0-D7/A0/A1, -(A7)
   LEA      pro, A0            ;   Clear product
   MOVEQ    #NumSize/4-1, D0
D4          ;   Do 64-bit multiply
                               ;   by bottom number
   ADD.L    D2, D4             ;   Add carry
   CLR.L    D2                 ;   Use D2 as dummy to
                               ;   extend carry
   ADDX.L   D2, D5             ;   Add zero with carry
   MOVE.L   D5, D2             ;   High longword
                               ;   becomes carry
   MOVE.L   D4, 00(A1, D0.W*4) ;   Put partial product
                               ;   into result
   SUBQ.W   #1, D0             ;   Loop through all
   CMP.W    D1, D0             ;   longwords in top #
   BGE      @1
Divide

/* Divide end (dividend) by sor (divisor) and put quotient in dst.  Remainder will end
    up in end */

void Divide(BigFixed *end, BigFixed *sor, BigFixed *dst)
{
   long      pq;
   BigFixed  quo, line;
   
   asm
   {
   MOVEM.L  D0-D7/A0-A4, -(A7)
   LEA      quo, A0            ;   Clear quotient
   MOVEQ    #NumSize/4-1, D0
D4          ;   Do 64-bit division
Compare

/* Compare src1 and src2.  Returns 1 if src1 > src2, 0 if they’re equal, and -1 if src1 < 
    rc2. */

short Compare(BigFixed *src1, BigFixed *src2)
{
   asm
   {
   MOVEM.L  D1/D2/A0/A1, -(A7)
   MOVEA.L  src1, A0           ;   Get src1’s address
   MOVEA.L  src2, A1           ;   Get src2’s address
   MOVEQ    #1, D0             ;   Start with +1
   MOVE.L   (A0)+, D2
   CMP.L    (A1)+, D2          ;   Compare 1st longwords
   BLT      @1                 ;   If src1 less, branch
   BNE      @2                 ;   If !=, src1 must
   MOVE.L   (A0)+, D2          ;   be greater
   CMP.L    (A1)+, D2          ;   Cmp 3 more longwords
   BCS      @1                 ;   (Unsigned)
   BNE      @2
   MOVE.L   (A0)+, D2
   CMP.L    (A1)+, D2
   BCS      @1
   BNE      @2
   MOVE.L   (A0)+, D2
   CMP.L    (A1)+, D2
   BCS      @1
   BNE      @2
   MOVEQ    #NumSize/4-2, D1   ;   Number of longwords
                               ;   remaining / 4

 

Community Search:
MacTech Search:

Software Updates via MacUpdate

Apple Configurator 2.6 - Configure and d...
Apple Configurator makes it easy to deploy iPad, iPhone, iPod touch, and Apple TV devices in your school or business. Use Apple Configurator to quickly configure large numbers of devices connected to... Read more
Amadeus Pro 2.4.4 - Multitrack sound rec...
Amadeus Pro lets you use your Mac for any audio-related task, such as live audio recording, digitizing tapes and records, converting between a variety of sound formats, etc. Thanks to its outstanding... Read more
Mellel 4.0.3 - The word processor for sc...
Mellel is the leading word processor for OS X and has been widely considered the industry standard for long form documents since its inception. Mellel focuses on writers and scholars for technical... Read more
Suitcase Fusion 8 19.0.3 - Font manageme...
Suitcase Fusion 8 is the creative professional's font manager. Every professional font manager should deliver the basics: spectacular previews, powerful search tools, and efficient font organization... Read more
Final Cut Pro X 10.4 - Professional vide...
Final Cut Pro X is a professional video editing solution. Completely redesigned from the ground up, Final Cut Pro adds extraordinary speed, quality, and flexibility to every part of the post-... Read more
Compressor 4.4 - Adds power and flexibil...
Compressor adds power and flexibility to Final Cut Pro X export. Customize output settings, work faster with distributed encoding, and tap into a comprehensive set of delivery features. Features... Read more
Cocktail 11.2 - General maintenance and...
Cocktail is a general purpose utility for macOS that lets you clean, repair and optimize your Mac. It is a powerful digital toolset that helps hundreds of thousands of Mac users around the world get... Read more
Microsoft Office 2016 15.41 - Popular pr...
Microsoft Office 2016 - Unmistakably Office, designed for Mac. The new versions of Word, Excel, PowerPoint, Outlook and OneNote provide the best of both worlds for Mac users - the familiar Office... Read more
Motion 5.4 - Create and customize Final...
Motion is designed for video editors, Motion 5 lets you customize Final Cut Pro titles, transitions, and effects. Or create your own dazzling animations in 2D or 3D space, with real-time feedback as... Read more
Apple Pro Video Formats 2.0.6 - Updates...
Apple Pro Video Formats brings updates to Apple's professional-level codes for Final Cut Pro X, Motion 5, and Compressor 4. Pro Video Formats includes support for the following professional video... Read more

Latest Forum Discussions

See All

Lineage 2: Revolution’s end of year upda...
Now available in 54 countries worldwide, Lineage 2: Revolution is continuing its global quest to be the most popular mobile MMORPG by launching a jam-packed end of year update. Complete with many subtle tweaks to help improve users’ online... | Read more »
The 5 best Star Wars games on iOS
The time has almost come.Star Wars: The Last Jedifinally hits theaters in the cinematic event that might be bigger than Christmas. To celebrate, we're taking a look at the best--and only the best--Star Warsmobile games to date. [Read more] | Read more »
Life Is Strange (Games)
Life Is Strange 1.1 Device: iOS Universal Category: Games Price: $2.99, Version: 1.1 (iTunes) Description: Life Is Strange is a five part episodic game that sets out to revolutionize story-based choice and consequence games by... | Read more »
Oddworld: New 'n' Tasty (Game...
Oddworld: New 'n' Tasty 1.0 Device: iOS Universal Category: Games Price: $7.99, Version: 1.0 (iTunes) Description: ** PLEASE NOTE: Requires 3.6GB free space to install. Runs at variable resolutions based on device capabilities.... | Read more »
Gorogoa (Games)
Gorogoa 1.0 Device: iOS Universal Category: Games Price: $4.99, Version: 1.0 (iTunes) Description: Gorogoa is an elegant evolution of the puzzle genre, told through a beautifully hand-drawn story designed and illustrated by Jason... | Read more »
Why Guns of Boom will be big for mobile...
Earlier this week, Game Insight, the minds that brought you Guns of Boom, revealed plans for an esports mode in the popular FPS title, with big implications for the game's future. Guns of Boom has been quite popular for some time now, so it's... | Read more »
The best mobile games to play on lazy ho...
With the holidays in full swing, there's hopefully going to be a lot of time off work lazing around the house. With all of that free time, it's a perfect opportunity to catch up on some mobile games that you might have missed out on earlier this... | Read more »
Rules of Survival guide - how to boost y...
It's not easy surviving in the "every-man-for-himself" world of Rules of Survival. You'll be facing off against many other players who might be more skilled than you, or are luckier than you. There are a lot of factors weighing against you. With... | Read more »
FEZ Pocket Edition (Games)
FEZ Pocket Edition 1.0 Device: iOS Universal Category: Games Price: $4.99, Version: 1.0 (iTunes) Description: | Read more »
Amazing Katamari Damacy guide - beginner...
Amazing Katamari Damacy brings the bizarro world of the original games to mobile and shifts them into an endless format that's just as addictive as the PlayStation entries. Your goal is still to roll as much random stuff as you possibly can, though... | Read more »

Price Scanner via MacPrices.net

How to preorder a new iMac Pro and pay zero s...
B&H Photo and Adorama are accepting preorders on multiple configurations of the new Apple iMac Pro. Both resellers charge sales tax for residents of NY & NJ only, and shipping is free.... Read more
Apple Macs back in stock at Amazon with model...
Amazon has MacBook Pros, MacBook Airs, MacBooks, and iMacs on sale for up to $200 off MSRP as part of their Holiday/Christmas sale. Shipping is free. Note that stock of some Macs may come and go (and... Read more
Apple offering free overnight delivery on all...
Apple is now offering free overnight delivery on all in stock products until 3pm local time on December 22nd. This includes new as well as refurbished computers. Click here for more information. Read more
Beats Holiday sale at B&H, headphones and...
B&H Photo has Beats by Dr. Dre headphones, earphones, and speakers on sale for up to $80 off MSRP as part of their Holiday sale. Expedited shipping is free, and B&H charges sales tax to NY... Read more
Holiday sale: Apple resellers offer 2017 15″...
MacMall has 15″ MacBook Pros on sale for $220-$300 off MSRP, each including free shipping: – 15″ 2.8GHz MacBook Pro Space Gray (MPTR2LL/A): $2179, $220 off MSRP – 15″ 2.8GHz MacBook Pro Silver (... Read more
Holiday sale: Apple resellers offer 13″ MacBo...
B&H Photo has 13″ MacBook Pros on sale for up to $150 off MSRP. Shipping is free, and B&H charges sales tax for NY & NJ residents only: – 13-inch 2.3GHz/128GB Space Gray MacBook Pro (... Read more
Apple Watch Series 2, Certified Refurbished,...
Apple has Certified Refurbished Apple Watch Nike+ Series 2s, 42mm Space Gray Aluminum Case with Anthracite/Black Nike Sport Bands, available for $249 (38mm) or $279 (42mm). The 38mm model was out of... Read more
Apple offers Certified Refurbished 2016 12″ R...
Apple has Certified Refurbished 2016 12″ Retina MacBooks available starting at $949. Apple will include a standard one-year warranty with each MacBook, and shipping is free. The following... Read more
B&H drops price on 13″ 256GB MacBook Air...
B&H has the 13″ 1.8GHz/256GB Apple MacBook Air (MQD42LL/A) now on sale for $1079 including free shipping plus NY & NJ sales tax only. Their price is $120 off MSRP, and it’s the lowest price... Read more
Holiday sale: 9″ iPads starting at $299, take...
MacMall has 9″ WiFi iPads on sale for $30 off including free shipping: – 9″ 32GB WiFi iPad: $299 – 9″ 128GB WiFi iPad: $399 Read more

Jobs Board

*Apple* Retail - Multiple Positions - Apple,...
Job Description: Sales Specialist - Retail Customer Service and Sales Transform Apple Store visitors into loyal Apple customers. When customers enter the store, Read more
Payments Counsel, *Apple* Pay (payments, cr...
# Payments Counsel, Apple Pay (payments, credit/debit) Job Number: 112941729 Santa Clara Valley, California, United States Posted: 13-Dec-2017 Weekly Hours: 40.00 Read more
*Apple* Solutions Consultant - Apple (United...
# Apple Solutions Consultant Job Number: 113124408 Waterford, CT, Connecticut, United States Posted: 17-Oct-2017 Weekly Hours: 40.00 **Job Summary** Are you Read more
QA Automation Engineer, *Apple* Pay - Apple...
# QA Automation Engineer, Apple Pay Job Number: 113202642 Santa Clara Valley, California, United States Posted: 11-Dec-2017 Weekly Hours: 40.00 **Job Summary** At Read more
*Apple* Retail - Multiple Positions - Apple,...
Job Description:SalesSpecialist - Retail Customer Service and SalesTransform Apple Store visitors into loyal Apple customers. When customers enter the store, Read more
All contents are Copyright 1984-2011 by Xplain Corporation. All rights reserved. Theme designed by Icreon.