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Posts Tagged ‘error’

Spreadsheet errors: open source or survival of the fittest

April 17th, 2013 No comments

There is a bit of a kerfuffle going on in the economics world at the moment over spreadsheet errors and data cherry picking in an influential paper about the current economic crisis. I don’t know anything about economics and will leave commentary on the data cherry picking to others, but I can claim to know something about coding errors.

Stories of companies loosing lots of money because of small mistakes in a spreadsheet are fairly common, this problem is not rare or unimportant. Academic research on spreadsheets seems to be slowly gathering steam, with PhDs appearing every now and again. Industry appears to be more active, with a variety of companies offering tools aimed at finding faults in spreadsheets.

Based on my somewhat limited experience of helping people fix spreadsheet problems I suspect that no amount of research or tool availability from industry will solve the real problem that faces spreadsheet users, which is that they don’t appreciate their own fallibility.

Back when software development first started people were very surprised to discover the existence of software faults. As every new programmer discovers, computers are merciless and will punish the slightest coding mistake. A large part of becoming a professional developer involves learning how to structure development to deal with personal fallibility, plus developing a mental attitude capable of handling the constant reminder of personal fallibility that computers provide to anybody writing code to tell them what to do (something that deters some people from becoming developers).

It rarely enters the head’s of people who are sporadic authors of code or spreadsheets that they may be making subtle mistakes that can have a significant impact on the results produced. Getting somebody with this frame of mind to perform testing on what they have written is well nigh on impossible.

In a research context one very practical solution to the code reliability issue is to insist that code or/and spreadsheets be made freely available. Only when the spreadsheet used to create the results in the paper linked to above was made available to others were the mistakes it contained uncovered.

In a commercial context it is down to survival of the fittest, those companies who do not keep their spreadsheet errors below a recoverable level die.

Using identifier prefixes results in more developer errors

April 25th, 2012 1 comment

Human speech communication has to be processed in real time using a cpu with a very low clock rate (i.e., the human brain whose neurons fire at rates between 10-100 Hz). Biological evolution has mitigated the clock rate problem by producing a brain with parallel processing capabilities and cultural evolution has chipped in by organizing the information content of languages to take account of the brains strengths and weaknesses. Words provide a good example of the way information content can be structured to be handled by a very slow processor/memory system, e.g., 85% of English words start with a strong syllable (for more details search for initial in this detailed analysis of human word processing).

Given that the start of a word plays an important role as an information retrieval key we would expect the code reading performance of software developers to be affected by whether the identifiers they see all start with the same letter sequence or all started with different letter sequences. For instance, developers would be expected to make fewer errors or work quicker when reading the visually contiguous sequence consoleStr, startStr, memoryStr and lineStr, compared to say strConsole, strStart, strMemory and strLine.

An experiment I ran at the 2011 ACCU conference provided the first empirical evidence of the letter prefix effect that I am aware of. Subjects were asked to remember a list of four assignment statements, each having the form id=constant;, perform an unrelated task for a short period of time and then recall information about the previously seen constants (e.g., their value and which variable they were assigned to).

During recall subjects saw a list of five identifiers and one of the questions asked was which identifier was not in the previously seen list? When the list of identifiers started with different letters (e.g., cat, mat, hat, pat and bat) the error rate was 2.6% and when the identifiers all started with the same letter (e.g., pin, pat, pod, peg, and pen) the error rate was 5.9% (the standard deviation was 4.5% and 6.8% respectively, but ANOVA p-value was 0.038). Having identifiers share the same initial letter appears to double the error rate.

This looks like great news; empirical evidence of software developer behavior following the predictions of a model of human human speech/reading processing. A similar experiment was run in 2006, this asked subjects to remember a list of three assignment statements and they had to select the ‘not seen’ identifier from a list of four possibilities. An analysis of the results did not find any statistically significant difference in performance for the same/different first letter manipulation.

The 2011/2006 experiments throw up lots of questions, including: does the sharing a prefix only make a difference to performance when there are four or more identifiers, how does the error rate change as the number of identifiers increases, how does the error rate change as the number of letters in the identifier change, would the effect be seen for a list of three identifiers if there was a longer period between seeing the information and having to recall it, would the effect be greater if the shared prefix contained more than one letter?

Don’t expect answers to appear quickly. Experimenting using people as subjects is a slow, labour intensive process and software developers don’t always answer the question that you think they are answering. If anybody is interested in replicating the 2011 experiment the tools needed to generate the question sheets are available for download.

For many years I have strongly recommended that developers don’t prefix a set of identifiers sharing some attribute with a common letter sequence (its great to finally have some experimental backup, however small). If it is considered important that an attribute be visible in an identifiers spelling put it at the end of the identifier.

See you all at the ACCU conference tomorrow and don’t forget to bring a pen/pencil. I have only printed 40 experiment booklets, first come first served.

Quality comparison of floating-point maths libraries

April 11th, 2011 No comments

What is the best way to compare the quality of floating-point math libraries (e.g., sin, cos and log)? The traditional approach for evaluating the quality of an algorithm implementing a mathematical function is based on mathematics; methods have been developed to calculate the maximum error between the calculated and the actual value. The answer produced by this approach does not say anything about how frequently this maximum error will occur, only that it occurs at least once.

The log (natural logarithm) is probably the most frequently used mathematical function and I decided to compare a few implementations; R statistical package version 2.11.1 and glibc (libm version 2.11.2) both running under Suse 11.3 on an AMD Athlon 64 X2, and Cygwin version 1.7.1 under Windows XP SP 2 on another AMD Athlon 64 X2.

The algorithm often used to implement mathematical functions involves evaluating a polynomial expression (e.g., Chebyshev polynomials) within a small range of values (various methods are used to map the argument into this range and then scale the calculated result). I decided to initially treat the implementations under test as black boxes and did not know the ranges they used; a range of 0.1 to 1.0 seemed like a good idea and I generated all single precision floating-point values between these two bounds (all 28,521,267 of them, with each adjacent pair still having 2^29 double precision values between them).

#include <math.h>
#include <stdio.h>
 
int main(int argc, char *argv[])
{
float val = 0.1,
       max_val = 1.0;
 
while (val < max_val)
   {
   printf("%12.10f\n", val);
   val=nextafterf(val, 1.1);
   }
}

This list of 28 million values was fed as input to three programs:

  • bc, which was used to generate the list of assumed to be correct logarithm of these 28 million values. R supports 64-bit IEEE compliant floating-point values, as do the C compilers/libraries used, and the number of decimal digits supported in this representation is 15. To provide greater accuracy to compare against the values generated by bc contained 17 digits, an extra two decimal digits over the IEEE values.
    scale=17
    while ((val=read() > 0))
       l(val)
  • A C program.
    #include <math.h>
    #include <stdio.h>
     
    int main(int argc, char *argv[])
    {
    double val;
     
    while (!feof(stdin))
       {
       scanf("%lf", &val);
       printf("%17.15f\n", log(val));
       }
    }
  • A R program.
    base_range=file("stdin", open="r")
     
    base_val=as.numeric(readLines(base_range, n=1))
    while (length(base_val) != 0)
       {
       cat(format(log(base_val), nsmall=15), file=stdout())
       cat("\n", file=stdout())
     
       base_val=as.numeric(readLines(base_range, n=1))
       }

The output of the C and R programs was then compared against the output from bc; which unfortunately creates a dependency on the accuracy of the C & R binary to decimal output routines (the subsequent comparison process gets around the decimal-to-binary input problem by reading the log values as strings and comparing the last few digits of each respective value). Accurate floating-point I/O needs something like hexadecimal floating constants.

Plotting the number of computed values of log that differ by a given amount from the value computed by bc we get (values whose error is below -50 will be rounded down and those above 50 rounded up, ignoring the issue of round to even):

Error in evaluation of log

The results (raw data for R, Linux C and Cygwin C) show that around 5.6% of values are off by one in the last (15th) digit (Cygwin was slightly worse at 5.7%). The results for R/Linux C were almost identical and a quick check of the R source tree showed that R calls the C library function to evaluate log (it is a bit worrying that R is dependent on the host maths library, they should think about replacing this dependency by something like MPFR tout suite; even though the 64-bit glibc library is of very high quality it still has an environmental dependency).

Being off by one in the last decimal place is unlikely to keep many people awake at night. But if we want a measure of quality, is percentage of inaccurate values a useful measure of math library quality? Provided it is coupled with the amount of inaccuracy I think this is a useful measure.

CPUs also exhibit hardware faults

October 31st, 2009 No comments

The cpu is the one element of a computing platform that people rarely treat as a source of error caused by physically malfunction, i.e., randomly flipping a bit in a register or instruction pipeline. I once worked on a compiler for the Mototola 88000 using a test platform that contained alpha silicon (i.e., not yet saleable components where some of the instructions were known not to work; the generated assembler code was piped through a sed script that mapped these instructions into an alternative instruction sequence that did work) and the cpus in a few of the hardware updates turned out to be temperature sensitive; some of the instructions changed their behavior when they got too hot. People who write compilers using alpha silicon learn to expect this sort of thing.

Quite a bit has been published on faults in other hardware components. Some of the best recent empirical hardware fault data and analysis I have seen is that published by Google engineers on hard disc and dram memory fault occurrences in their server farms. They might have a problem publishing such results for the cpus they use because these commodity items generally don’t have the ability to report any detailed fault data, they just die or one of the programs being executed crashes.

As device fabrication continues to shrink erroneous behavior caused by cosmic ray impact will become more and more common. Housing a computer farm at a high altitude might not be a good idea (at 7500 ft cosmic ray-induced neutrons that can lead to soft errors are 6.4 times more common than at sea level).

IBM’s Power4 chip (“Power4 System Design for High Reliability” by Bossen, Tendler and Reick) is one of the few that provides error checking of cache contents, while IBM’s System z9 is one of the very few that provide parity checking on the cpu registers (“Enhanced I/O subsystem recovery and availability on the IBM System z9″ by Oakes et al).

One solution to the problem of unreliable cpu behavior is for the compiler to insert consistency checks into the generated code. Two such checking methods are:

  • ‘Signature Analysis’ which performs consistency checks between signatures calculated at compile time and runtime. A signature is associated with every basic block with the current signature being derived from the execution history. This technique can detect spurious changes to the flow of control caused by a hardware glitch.
  • ‘Error Detection by Duplicated Instructions’ generates code which duplicates the behavior of some instruction sequence and compares the result calculated by both sequences, i.e., a source language construct is executed twice and an error raised if the results are different. The parallel instruction sequences use different sets of registers on the same cpu and ideally the instructions are scheduled to exploit instruction level parallelism

At the moment cosmic-ray induced hardware faults are probably very small change compared to faults in the code. Will code quality increase to the point where cosmic-ray faults become an issue or will devices get so small that they have to be lead lined to prevent background radiation corrupting them? Let the race begin.

Monte Carlo arithmetic operations

December 5th, 2008 No comments

Working out whether software based calculations involving floating-point values delivers a sensible answer requires lots of mathematical sophistication and in practice is often impractical or intractable. The vast majority of developers make no effort, indeed most don’t even know why the effort is needed. Various ‘end-user’ solutions have been proposed, e.g., interval arithmetic.

One interesting solution is to perturb the result of floating-point operations and measure the effect on the final answer. Any calculation that is sensitive to small random changes in the result of an operation (there is randomness present in any operation that operates on values that can only be represented to a finite precision) will produce answers that depend on the direction and magnitude of the perturbation. Comparing the answers from several program executions provides a measure of one kind of error present in the calculation.

Monte Carlo arithmetic is a proposed extension of floating-point arithmetic that operates by randomly selecting how round-off errors occur (the proposer provides sample code).

With computing power continuing to increase, running a program several times is often a viable option (we don’t all number crunch for cpu days). Most of the transistors on a modern CPU chip are devoted to memory cache, using a few of these to support Monte Carlo arithmetic instructions is entirely practical. Perhaps when vendors get over supporting the base-10 radix required by the latest IEEE 754R standard and are looking for something new to attract customers they will provide a mechanism that makes it practical to obtain estimates of some of the error in floating-point calculations.