TweetFollow Us on Twitter

Aug 94 Challenge
Volume Number:10
Issue Number:8
Column Tag:Programmer’s Challenge

Programmer’s Challenge

By Mike Scanlin, Mountain View, CA

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


When writing programmer utilities like disassemblers, disk editors and memory viewers it’s useful to have around a very fast “dump” routine that takes a bunch of bytes and displays them in hex and ascii. The MPW tool DumpFile encompasses most of the desired functionality. This month’s challenge is to write a fast version of some of the DumpFile functionality.

The prototype of the function you write is:

/* 1 */
unsigned short
DumpBytes(inputBytes, outputText,
 numInputBytes, maxOutputBytes,
 width, grouping)
unsigned short numInputBytes;
unsigned short maxOutputBytes;
unsigned short width;
unsigned short grouping;

inputBytes and outputText are the pointers to the input bytes (which you’re trying to display) and the output text (which is all printable ascii, ready to display). numInputBytes is the number of input bytes you have to work with (more than zero) and maxOutputBytes is the size of the buffer that outputText points to. The return value of the function is the actual number of output bytes created by DumpBytes and will always be less than or equal to maxOutputBytes (or zero if there’s output buffer overflow). Like the DumpFile tool, the width parameter is the number of input bytes to display on each output line (it will be from 1 to 64 with 16 being given more weight than the other values) and grouping is the number of output bytes to group together without intervening spaces (also from 1 to 64 with 1, 2 and 4 being given more wight than the other values). The width parameter will always be a multiple of the grouping parameter.

Here are a few examples (the comments describe the parameters but are not part of the actual output):

/* 2 */
/* width = 8, grouping = 1 */
 0: 23 09 53 74 61 72 74 75 #.Startu
 8: 70 20 2D 20 4D 50 57 20 p.-.MPW.
 10: 53 68 65 6C 6C 20 53 74 Shell.St

/* width = 8, grouping = 8 */
 0: 2309537461727475 #.Startu
 8: 70202D204D505720 p.-.MPW.
 10: 5368656C6C205374 Shell.St

/* width = 9, grouping = 3 */
 0: 230953 746172 747570 #.Startup
 9: 202D20 4D5057 205368 .-.MPW.Sh
 12: 656C6C 205374 617274 ell.Start

Non-printable characters should be represented by a dot ‘.’ in the ascii section of the output. You can print a space character as a space or a dot (your choice). When in doubt on how to handle a certain situation, check the MPW DumpFile tool and do what it does (or something very similar). As always, I’m available for questions in case something is not clear (see the e-mail addresses section).

You should be careful about parameters that will cause you to output more bytes than the maxOutputBytes will allow. If you run out of output buffer space then just fill it up as much as you can and return 0. I won’t be testing the output overflow cases much because the goal of this exercise it to have a very fast hex and ascii displayer. If someone were to actually use the code it is assumed that they would know the context and provide an output buffer that was always large enough (and assert that the return value was not zero).

Two Months Ago Winner

Congratulations to Bob Boonstra (Westford, MA) for reclaiming the title of the Programmer Challenge Champion this month. This month’s win brings his 1st place totals to four, which is more than anyone else. Like Bob, second place winner Allen Stenger (Gardena, CA) also based his solution on Fermat’s algorithm but ended up with an implementation that was not quite as fast as Bob’s. Third place winner Ernst Munter (Kanata, ON, Canada) chose a different route and first implemented his solution in 386 assembly (!) and then wrote some graphics routines to illustrate the behavior of his code in order to help him optimize further. But in the end he says he didn’t have enough time to do as much as he would have liked to his C version.

Here are the code sizes and times. The time1 numbers are the times to factor some 64 bit numbers while the time2 numbers are the times to factor some 32 bit numbers (where highHalf is zero), which was not given much weight when ranking (but it’s interesting to see how some people optimized for this case). Numbers in parens after a person’s name indicate how many times that person has finished in the top 5 places of all previous Programmer Challenges, not including this one:

Name time1 time2 code

Bob Boonstra (9) 5 7 820

Allen Stenger (6) 11 24 896

Ernst Munter 15 2 1190

John Raley 25 186 520

Liber, Anspach, Phillips 436 14 620

Clement Goebel (3) 1094 1 1026

Jim Lloyd (1) 3920 20 4279

Alex Novickis 18800 53 9542

Bob’s code is well commented so I won’t go over it here. Also, for a discussion of Fermat’s factoring algorithm you can check out The Art of Computer Programming, v.2, by Donald Knuth.

One thing that made this problem slightly harder than normal was that you had to work with 64 bit integers. Allen Stenger ended up creating his own set of double-long macros which I’ll give here because they might come in handy some day if you ever have to work with 64 bit integers:

/* 3 */
#define OVERFLOW(x) (0 != (0x80000000 & (x)))

#define DOCARRY(x) { x ## high++; x ## low &= 0x7FFFFFFF;}
#define DOBORROW(x) { x ## high--; x ## low &= 0x7FFFFFFF;}
#define GT_ZERO(x) ((x ## high >= 0) && (x ## low != 0)) 
#define EQ_ZERO(x) ((x ## high == 0) && (x ## low == 0)) 
#define LT_ZERO(x) ((x ## high < 0)) 

#define INCR(x,a) {if (OVERFLOW(x ## low += a)) DOCARRY(x);}
#define DECR(x,a) {if (OVERFLOW(x ## low -= a)) DOBORROW(x);}
#define PLUS_EQUALS(x, y) { \
 x ## high += y ## high;  \
 if (OVERFLOW(x ## low += y ## low))\

#define MINUS_EQUALS(x, y) { \
 x ## high -= y ## high;  \
 if (OVERFLOW(x ## low -= y ## low))\

Here’s Bob’s winning solution:

Solution strategy

Factoring is a field which has been the subject of a great deal of research because of the implications for cryptography, especially techniques that depend on the difficulty of factoring very large numbers. Therefore, it is possible that some of these algorithms could be applied to the challenge.

However, in the event that no mathematician specializing in the field chooses to enter the Challenge, this relatively simple solution takes advantage of some of the simplifying conditions in the problem statement:

1) the numbers are relatively small (64 bits, or ~<20 digits)

2) the prime factors are even smaller (32 bits, or ~<10 digits)

This solution depends on no precomputed information. It is based on Fermat's algorithm, described in Knuth Vol II, which is especially well suited to the problem because it is most efficient when the two p, [sorry, the rest of the sentence was missing - Ed stb]

Fermat's algorithm requires ~(p-1)sqrt(n) iterations, where n=u*v and u~=p*sqrt(n), v~=sqrt(n)/p. Other algorithms require half as many iterations, but require more calculation per iteration.

Fermat's algorithm works as follows:

1) Let n - u*v, u and v odd primes.

2) Set a = (u+v)/2 and b = (u-v)/2.

3) Then n = uv = a**2 - b**2

4) Initialize a = trunc(sqrt(n)), b=0, r=a**2-b**2-n

5) Iterate looking for r==0, with an inner loop that keeps a=(u+v)/2 constant and increases b=(u-v)/2 by 1 each iteration until r becomes negative. When this happens, the halfsum a is increased by 1, and the difference loop is repeated.

The algorithm in Knuth uses auxiliary variables x,y for efficiency, where x = 2*a+1 and y = 2*b+1

This works fine in most cases, but causes overflow of a longword when x,y are the full 32-bits in size. So we have augmented the algorithm to deal with this case.

This solution also uses an efficient integer sqrt algorithm due to Ron Hunsinger, and extends that algorithm to 64 bits.

/* 4 */
#pragma options(assign_registers,honor_register)

#define ulong unsigned long
#define ushort unsigned short

#define kLo16Bits 0xFFFF
#define kHiBit 0x80000000UL
#define kLo2Bits 3
#define kLo1Bit 1

Macros RightShift2 and RightShift1 shift a 64-bit value right by 2 and 
1 bits, respectively.
#define RightShift32By2(xL,xH)                            \
{                                                         \
  xL >>= 2;                                               \
  xL |= (xH & kLo2Bits)<<30;                              \
  xH >>= 2;                                               \

#define RightShift32By1(xL,xH)                            \
{                                                         \
  xL >>= 1;                                               \
  xL |= (xH & kLo1Bit)<<31;                               \
  xH >>= 1;                                               \

Macros Add32To64 (Sub32From64) add (subtract) a 32-bit value to (from) 
a 64-bit value.
#define Add32To64(rL,rH, a)                               \
  temp = rL;                                              \
  if ((rL += a) < temp) ++rH;

#define Add2NPlus1To64(lowR,highR,a)                      \
  Add32To64(lowR,highR,a);                                \
  Add32To64(lowR,highR,a);                                \

#define Sub32From64(rL,rH, s)                             \
  temp = rL;                                              \
  if ((rL -= s) > temp) --rH;

#define Sub2NPlus1From64(lowR,highR,s)                    \
  Sub32From64(lowR,highR,s);                              \
  Sub32From64(lowR,highR,s);                              \

//Macros Add64 (Sub64) add (subtract) two 64-bit values.
#define Add64(qL,qH, eL,eH)                               \
  Add32To64(qL,qH,eL);                                    \
  qH += eH;

#define Sub64(qL,qH, eL,eH)                               \
  Sub32From64(qL,qH, eL);                                 \
  qH -= eH;

Macro Square64 multiplies a 32-bit value by itself to produce the square 
as a 64-bit value.  For this solution, we only need to execute this macro 
expansion once.
#define Square64(a,rL,rH,temp)                            \
{                                                         \
  ulong lohi,lolo,hihi;                                   \
  ushort aHi,aLo;                                         \
  aHi = a>>16;                                            \
  aLo = a;                                                \
  rL = (lolo = (ulong)aLo*aLo)&kLo16Bits;                 \
  lohi = (ulong)aLo*aHi;                                  \
  temp = ((lohi&kLo16Bits)<<1) + (lolo>>16);              \
  rL |= temp<<16;                                         \
  temp>>=16;                                              \
  temp += ((hihi = (ulong)aHi*aHi)&kLo16Bits) +           \
                             (lohi>>(16-1));              \
  rH = temp&kLo16Bits;                                    \
  temp>>=16;                                              \
  temp += hihi>>16;                                       \
  rH |= temp<<16;                                         \

Macros LessEqualZero64 and EqualZero64 determine if 64-bit (signed) values 
are <= 0 or == 0, respectively.
#define LessEqualZero64(vL,vH)                            \
    ( (0>(long)vH) || ((0==vH) && (0==vL)) )

#define EqualZero64(vL,vH)                                \
     ((0==vL) && (0==vH))

//Macro LessEqual64 determines if one 64-bit quantity is less than or 
equal to another.
#define LessEqual64(uL,uH, vL,vH)                         \
    ( (uH< vH) || ((uH==vH) && (uL<=vL)))

//Function prototypes.
ulong sqrt64 (ulong nLo,ulong nHi);
void Factor64(ulong lowHalf,ulong highHalf,
              ulong *prime1Ptr,ulong *prime2Ptr);
The solution ...
void Factor64(lowHalf,highHalf,prime1Ptr,prime2Ptr)
unsigned long lowHalf,highHalf;
unsigned long *prime1Ptr,*prime2Ptr;
register ulong x,y,lowR,highR;
register ulong temp;
ulong sqrtN;

Fermat's algorithm (Knuth)

Assume n=u*v, u<v, n odd, u,v odd
Let a=(u+v)/2  b=(u-v)/2  n=a**2-b**2  0<=y<x<=n
Search for a,b that satisfy x**2-y**2-n==0

NOTE:  u,v given as being < 2**32 (fit in one word).  Therefore a,b also 
are < 2**32 (and fit in one word).

C1: Set x=2*floor(srt(n))+1,
     x corresponds to 2a+1, y to 2b+1, r to a**2-b**2-n
C2: if r<=0 goto C4
       (algorithm modified to keep r positive)
C3: r=r-y, y=y+2,
     goto C2
C4: if (r==0) terminate with n = p*q,
         p=(x-y)/2, q=(x+y-2)/2
C5: r=r+x, x=x+2,
     goto C3

This solution modifies the algorithm to:
(1) reorder arithmetic on r to keep it positive
(2) extend r to 64 bits when necessary
(3) handle the trivial case where one of the primes is 2.
//Handle the trivial case with an even prime factor.
  if (0 == (lowHalf&1)) {
    *prime1Ptr = 2;
    *prime2Ptr = (lowHalf>>1) | ((highHalf&kLo1Bit)<<31);
//Compute truncated square root of input 64-bit number.
  sqrtN = temp = sqrt64(lowHalf,highHalf);
//Initialize r to s*s - n, but calculate n-s*s to keep r positive, and 
fix later when it is time
//to add x to r by calculating r = x - (n-s*s).
  Sub64(lowHalf,highHalf, lowR,highR);
//Handle perfect square case.
  if ((0==highHalf) && (0==lowHalf)) {
    *prime1Ptr = *prime2Ptr = sqrtN;
  y = 1;
  highR = 0;
//Separate out the overflow case where x=2a+1 does not fit into a long 
  if ((temp=sqrtN) >= kHiBit-1) goto doLargeX;
//If sqrt(n) < 0x80000000, then 2*sqrt(n)+1 fits in one long word.  
//Also, n-trunc(sqrt(n))**2 < 2*trunc(sqrt(n)) also fits in a long word.
  x = 1+2*temp;
  lowR = x - lowHalf;
  x += 2;
  do {
    if (lowR<=y) break;
    lowR -= y;
    y += 2;
  } while (true); /* exit when r<=y */
  if (y==lowR) {
    *prime1Ptr = (x-y-2)>>1;
    *prime2Ptr = (x+y)>>1;
  lowR += (x-y);
  y += 2;
//Fall through to modified algorithm if x overflows a long word.
  if ((x += 2) < (ulong)0xFFFFFFFF-2) goto C2;
Adjust x and y to guarantee they will not overflow.  This requires some 
extra arithmetic to add 2*a+1 and subtract 2*b+1, but that is preferable 
to using two longs to represent each of x and y.
  goto C3L;

//x=2*a+1 no longer fits in 32 bits, so we sacrifice a little loop efficiency 
and let x=a. //Likewise, we let y=b instead of 2*b+1.
  lowR = x = temp;
  Sub64(lowR,highR, lowHalf,highHalf);
  do {
    if ( LessEqualZero64(lowR,highR) ) break;
  } while (true); /* exit when lowR,highR<=0 */
  if ( EqualZero64(lowR,highR)) {
    *prime1Ptr = x-y;
    *prime2Ptr = x+y;
  goto C3L;

//sqrt_max4pow is the largest power of 4 that can be represented in an 
unsigned long.
#define sqrt_max4pow (1UL << 30)
//undef sqrt_truncate if rounded sqrts are desired; for the factoring 
problem we want
//truncated sqrts.
#define sqrt_truncate

//sqrt64 is based on code posted by Ron Hunsinger to comp.sys.mac.programmer. 
//Modified to handle 64-bit values.
ulong sqrt64 (ulong lowN, ulong highN) {
Compute the integer square root of the integer argument n.  Method is 
to divide n by x computing the quotient x and remainder r.  Notice that 
the divisor x is changing as the quotient x changes.
 Instead of shifting the dividend/remainder left, we shift the quotient/divisor 
right.  The binary point starts at the extreme left, and shifts two bits 
at a time to the extreme right.
 The residue contains n-x**2.  Since (x + 1/2)**2 == x**2 + x + 1/4, 

n - (x + 1/2)**2 == (n - x**2) - (x + 1/4)
 Thus, we can increase x by 1/2 if we decrease (n-x**2) by (x+1/4)
  register ulong lowResidue,highResidue; /* n - x**2 */
  register ulong lowRoot,highRoot;       /* x + 1/4 */
  register ulong half;                   /* 1/2     */
  ulong highhalf,lowhalf,temp;

  lowResidue = lowN;
  if (0 != (highResidue = highN)) {
//This code extends the original algorithm from 32 bits to 64 bits. 
// It parallels the 32-bit code; see below for comments.
    highRoot = sqrt_max4pow; lowRoot = 0;
    while (highRoot>highResidue)
    Sub64(lowResidue,highResidue, lowRoot,highRoot);
//The binary point for half is now in the high order of two 32-bit words 

//representing the 64-bit value.
    lowhalf = lowRoot; highhalf = highRoot;
    Add64(lowRoot,highRoot, lowhalf,highhalf);
    if (0==highhalf) goto sqrt2;
    half = highhalf<<1;
    do {
      if (LessEqual64(lowRoot,highRoot,lowResidue,highResidue))
        highResidue -= highRoot;
        highRoot += half;
      if (0 == (half>>=2)) {
        half = sqrt_max4pow<<1;
        goto sqrt2a;
      highRoot -= half;
      highRoot >>= 1;
    } while (true);
//The binary point for half is now in the lower of the two 32-bit words 

//representing the 64-bit value.
    half = lowhalf<<1;
    do {
      if ((0==highResidue) && (0==highRoot)) goto sqrt3;
      if (LessEqual64(lowRoot,highRoot,lowResidue,
                            highResidue)) {
        Sub64(lowResidue,highResidue, lowRoot,highRoot);
      half >>= 2;
    } while (half);
  } else /* if (0 == highResidue) */ {
#ifndef sqrt_truncate
    if (lowResidue <= 12)
      return (0x03FFEA94 >> (lowResidue *= 2)) & 3;
    if (lowResidue <= 15)
      return (0xFFFEAA54 >> (lowResidue *= 2)) & 3;
    lowRoot = sqrt_max4pow;
    while (lowRoot>lowResidue) lowRoot>>=2;

//Decrease (n-x**2) by (0+1/4)
    lowResidue -= lowRoot;
//1/4, with binary point shifted right 2
    half = lowRoot >> 2;
//x=1.  (lowRoot is now (x=1)+1/4.)
    lowRoot += half;
//1/2, properly aligned
    half <<= 1;

//Normal loop (there is at least one iteration remaining)
    do {
      if (lowRoot <= lowResidue) {
// Whenever we can, decrease (n-x**2) by (x+1/4)
        lowResidue -= lowRoot;
        lowRoot += half;
//Shift binary point 2 places right
      half >>= 2;
//x{+1/2}+1/4 - 1/8 == x{+1/2}+1/8
      lowRoot -= half;
//2x{+1}+1/4, shifted right 2 places
      lowRoot >>= 1;
//When 1/2 == 0, bin point is at far right
    } while (half);
#ifndef sqrt_truncate
  if (lowRoot < lowResidue) ++lowRoot;

//Return value guaranteed to be correctly rounded (or truncated)
    return lowRoot;


Community Search:
MacTech Search:

Software Updates via MacUpdate

iFFmpeg 6.4.0 - Convert multimedia files...
iFFmpeg is a comprehensive media tool to convert movie, audio and media files between formats. The FFmpeg command line instructions can be very hard to master/understand, so iFFmpeg does all the hard... Read more
Thunderbird 52.2.0 - Email client from M...
As of July 2012, Thunderbird has transitioned to a new governance model, with new features being developed by the broader free software and open source community, and security fixes and improvements... Read more
Airfoil 5.6.1 - Send audio from any app...
Airfoil allows you to send any audio to AirPort Express units, Apple TVs, and even other Macs and PCs, all in sync! It's your audio - everywhere. With Airfoil you can take audio from any... Read more
Apple Remote Desktop Client 3.9.3 - Clie...
Apple Remote Desktop Client is the best way to manage the Mac computers on your network. Distribute software, provide real-time online help to end users, create detailed software and hardware reports... Read more
jAlbum Pro 14.0 - Organize your digital...
jAlbum Pro has all the features you love in jAlbum, but comes with a commercial license. You can create gorgeous custom photo galleries for the Web without writing a line of code! Beginner-friendly... Read more
jAlbum 14.0 - Create custom photo galler...
With jAlbum, you can create gorgeous custom photo galleries for the Web without writing a line of code! Beginner-friendly, with pro results - Simply drag and drop photos into groups, choose a design... Read more
Vitamin-R 2.48 - Personal productivity t...
Vitamin-R creates the optimal conditions for your brain to work at its best by structuring your work into short bursts of distraction-free, highly focused activity alternating with opportunities for... Read more
Beamer 3.3 - Stream any movie file from...
Beamer streams to your Apple TV.... Plays any movie file - Just like the popular desktop movie players, Beamer accepts all common formats, codecs and resolutions. AVI, MKV, MOV, MP4, WMV, FLV. To... Read more
Shredo 1.2.2 - $9.99
Shredo is a beautiful, functional file-shredding and privacy scan utility. It permanently shreds files, folders, and external volumes' contents to keep information secure and impossible for anyone to... Read more
Final Draft 10.0.3 - Industry-leading sc...
Final Draft allows you to use your creative energy to focus on the content; let Final Draft take care of the style. Final Draft is the number-one selling application specifically designed for writing... Read more

Latest Forum Discussions

See All

The House of da Vinci (Games)
The House of da Vinci 1.0.0 Device: iOS Universal Category: Games Price: $4.99, Version: 1.0.0 (iTunes) Description: Enter The House of Da Vinci, a new must-try 3D puzzle adventure game. Solve mechanical puzzles, discover hidden... | Read more »
Solve the disappearance of history’s gre...
Blue Brain Games invites you to indulge in an immersive hands-on 3D puzzle adventure in similar vein to The Room series, with its debut release The House of Da Vinci. Set during the historic period of the Italian Renaissance (when Leonardo himself... | Read more »
Age of Rivals (Games)
Age of Rivals 3.3 Device: iOS Universal Category: Games Price: $.99, Version: 3.3 (iTunes) Description: Deep civilization-building strategy in a fast-paced card game! | Read more »
Panthera Frontier (Games)
Panthera Frontier 1.0 Device: iOS Universal Category: Games Price: $4.99, Version: 1.0 (iTunes) Description: | Read more »
Angry Birds Evolution beginner's gu...
Angry Birds changes things up a fair bit in its latest iteration, Angry Birds Evolution. The familiar sling-shot physics mechanics are still there, but the game now features team-based gameplay, RPG elements, and a new top-down view. With all of... | Read more »
Sega Forever is for the retro game fans
Sega is launching a new retro games service titled Sega Forever, in a move that's sure to delight games enthusiasts with a bit of nostalgia. Sega's releasing five classic games for free. The titles include Sonic the Hedgehog, Phantasy Star II,... | Read more »
The Little Acre (Games)
The Little Acre 1.0 Device: iOS Universal Category: Games Price: $2.99, Version: 1.0 (iTunes) Description: | Read more »
Lovely adventure game 'The Little A...
The Little Acre makes its way from PC to iOS today and it's a real charmer. It's a lovely little adventure game set in 1950's Ireland, gorgeously animated in a style slightly reminiscent of old Disney films. The game won a lot of praise for its... | Read more »
Futurama: Worlds of Tomorrow officially...
Futurama: Worlds of Tomorrow arrives next Thursday, and it features . . . Stephen Hawking? Turns out a few of your favorite science super stars, including Bill Nye, Neil DeGrasse Tyson, and George Takei will be making an appearance alongside the... | Read more »
MU Origin’s new update offers exciting c...
MU Origin is kicking off the summer with style. Its latest update is a real doozy, offering up plenty of fresh content. New challenges, some extra help for newcomers, and new costumes are just a few of the things you will find in the new patch. | Read more »

Price Scanner via

Clearance 2016 MacBook Pros available for up...
B&H Photo has clearance 2016 13″ and 15″ MacBook Pros in stock today and on sale for up to $400 off original MSRP. Shipping is free, and B&H charges NY & NJ sales tax only: - 15″ 2.7GHz... Read more
Apple Ranks 9th In comScore Top 50 U.S. Digit...
comScore, Inc. has released its monthly ranking of U.S. online activity at the top digital media properties for May 2017 based on data from comScore Media Metrix Multi-Platform. * Entity has... Read more
10.5-inch iPad Pros available for up to $20 o...
B&H Photo has the new 2017 10.5″ iPad Pros available for up to $20 off MSRP including free shipping plus NY & NJ sales tax only: - 64GB iPad Pro WiFi: $649 - 256GB iPad Pro WiFi: $749 - 512GB... Read more
Three Off-The-Beaten-Track iOS Apps That Dese...
One of the great things about using iPads and iPhones is the vast selection of apps available for most anything you want or need to do. The three outlined in this article have been in my core app... Read more
Apple No. 1 Spot In Gartner Top 100 Vendors i...
Gartner, Inc. has unveiled the top global 100 vendors in IT in 2016 based on their revenue across IT (excluding communication services) and component market segments. In the Gartner Global Top 100:... Read more
Clearance iMacs available for up to $300 off...
B&H Photo has clearance 21″ and 27″ Apple iMacs available starting at $949, each including free shipping plus NY & NJ sales tax only: - 27″ 3.3GHz iMac 5K: $1999 $300 off original MSRP - 27″... Read more
1.4GHz Mac mini, refurbished, available for $...
The Apple Store has Apple Certified Refurbished 1.4GHz Mac minis available for $419. Apple’s one-year warranty is included, and shipping is free. Their price is $80 off MSRP, and it’s the lowest... Read more
Free Mixoo iOS Photo Editing App Gets Major U...
Button Software Technology has announced Mixoo 3.0, an important feature update to the company’s photo editor for iOS devices. Mixoo offers amazing ways to edit as well as decorate personal photo... Read more
FNable 2.0 Function Key Enabling Software Get...
Briksoftware has released FNable 2.0 With Touch Bar Support, a major new version of the function key enabling software now compatible with Touch Bar keyboards. FNable’s simplicity that allows users... Read more
Clearance 2016 12-inch Retina MacBooks, Apple...
Apple recently dropped prices on Certified Refurbished 2016 12″ Retina MacBooks, with models now available starting at $1019. Apple will include a standard one-year warranty with each MacBook, and... Read more

Jobs Board

Lead *Apple* Solutions Consultant - Apple I...
…integrity, and trust.Success Metrics/Key Performance Indicators:Quantitative* Year over Year growth in Apple Product and Beyond the Box sales in the assigned Point of Read more
*Apple* Solutions Consultant till v%u00E5r...
…ethics, integrity, and trust.Success Metrics/Key Performance Indicators:QuantitativeYear over Year growth in Apple Product and Beyond the Box sales in the assigned Point Read more
Sr. Software Engineer, *Apple* Retail - App...
Apple Retail is looking for a Software Engineer…You'll work on projects that touch all aspects of Apple Retail Point-of-Sale system, and will leverage your strong Read more
*Apple* Solutions Consultant (Asc) - PT - Cu...
…important role that the ASC serves is that of providing an excellent Apple Customer Experience. Responsibilities include:* Promoting Apple products and solutions Read more
Product Metrics Manager - *Apple* Media Pro...
- Identify blind spots in existing product metrics- Presenting on how Apple Media Products are used and perceived by our customers- Work with data science and Read more
All contents are Copyright 1984-2011 by Xplain Corporation. All rights reserved. Theme designed by Icreon.