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Mathematical proofs contain faults, just like software

February 19th, 2018 (1 hour ago) No comments

The idea of proving programs correct, like mathematical proofs, is appealing, but is based on an incorrect assumption often made by non-mathematicians, e.g., mathematical proofs are fault free. In practice, mathematicians make mistakes and create proofs that contain serious errors; those of us who are taught mathematical techniques, but are not mathematicians, only get to see the good stuff that has been checked over many years.

An appreciation that published proofs contain mistakes is starting to grow, but Magnificent mistakes in mathematics is an odd choice for a book title on the topic. Quotes from De Millo’s article on “Social Processes and Proofs of Theorems and Programs” now appear regularly; On proof and progress in mathematics is worth a read.

Are there patterns to the faults that appear in claimed mathematical proofs?

A surprisingly common approach, used by mathematicians to avoid faults in their proofs, is to state theorems without giving a formal proof (giving an informal one is given instead). There are plenty of mathematicians who don’t think proofs are a big part of mathematics (various papers from the linked-to book are available as pdfs).

Next time you encounter an advocate of proving programs correct using mathematics, ask them what they think about the uncertainty about claimed mathematical proofs and all the mistakes that have been found in published proofs.

Compiler validation is now part of history

February 11th, 2018 No comments

Compiler validation makes sense in a world where there are many different hardware platforms, each with their own independent compilers (third parties often implemented compilers for popular platforms, competing against the hardware vendor). A large organization that spends hundreds of millions on a multitude of computer systems (e.g., the U.S. government) wants to keep prices down, which means the cost of porting its software to different platforms needs to be kept down (or at least suppliers need to think it will not cost too much to switch hardware).

A crucial requirement for source code portability is that different compilers be able to compile the same source, generating code that produces the same behavior. The same behavior requirement is an issue when the underlying word-size varies or has different alignment requirements (lots of code relies on data structures following particular patterns of behavior), but management on all sides always seems to think that being able to compile the source is enough. Compilers vendors often supported extensions to the language standard, and developers got to learn they were extensions when porting to a different compiler.

The U.S. government funded a conformance testing service, and paid for compiler validation suites to be written (source code for what were once the Cobol 85, Fortran 78 and
SQL validation suites). While it was in business, this conformance testing service was involved C compiler validation, but it did not have to fund any development because commercial test suites were available.

The 1990s was the mass-extinction decade for companies selling non-Intel hardware. The widespread use of Open source compilers, coupled with the disappearance of lots of different cpus (porting compilers to new vendor cpus was always a good money spinner, for the compiler writing cottage industry), meant that many compilers disappeared from the market.

These days, language portability issues have been essentially solved by a near mono-culture of compilers and cpus. It’s the libraries that are the primary cause of application portability problems. There is a test suite for POSIX and Linux has its own tests.

There are companies selling compiler C/C++ test suites (e.g., Perennial and PlumHall); when maintaining a compiler it’s cost effective to have a set of third-party tests designed to exercise all the language.

The OpenGroup offer to test your C compiler and issue a brand certificate if it passes the tests.

Source code portability requires compilers to have the same behavior and traditionally the generally accepted behavior has been defined by an ISO Standard or how one particular implementation behaved. In an Open source world behavior is defined by what needs to be done to run the majority of existing code. Does it matter if Open source compilers evolve in a direction that is different from the behavior specified in an ISO Standard? I think not, it makes no difference to the majority of developers; but be careful, saying this can quickly generate a major storm in a tiny teacup.

What instructions should a computer support?

February 5th, 2018 No comments

The modern answer to what instructions should a computer support is: lots (e.g., many kinds of: add, subtract, compare, branch, load, store, etc). John von Neumann’s famous First Draft of a Report on the EDVAC, written in 1945, specifies 97 instructions (later, actual implementations contained fewer instructions) and modern Intel processors contain several thousand instructions.

The Turing machine has a very simple instruction set; the machine is driven by a lookup table that specifies one or more of the operations: erase/write a symbol (to the cell currently under the read/write head), move the read/write head left or right (on a tape containing cells), and load a new state (which may be the same as the current one).

When computers were new, the lure of creating a minimalist instruction set had theoretical and practical appeal (valve computers were large and unreliable, reducing the number of components improved reliability and reduced costs).

The design of the IAS machine, built in the late 1940s, was based on von Neumann’s design. Haskell Curry came up with a minimalist set of four instructions that could be used to implement its supported instructions (the idea was that programs would be stored in minimalist form to reduce storage overheads).

Minimalist instruction sets still have theoretical appeal.

Simplicity (rather than minimalism) became fashionable in the 1980s with RISC. This was a reaction to the implementation/runtime costs of very complicated of instructions found in DEC’s VAX and later Motorola’s 68000 processors. Supporting these complicated instructions generated additional overhead for the simpler instructions (which is what most programs spent most of their time executing). The idea behind RISC was that simplifying the instruction set would reduce cpu design costs, improve performance (by making simple instructions fast); leaving the complicated stuff to be supported via software.

Starting out with ‘simple’ MIPS, RISC cpus got successively more complicated with SPARC, Motorola’s MC88000 and then IBM’s RS/6000. I worked on code generators for the SPARC and MC88000 and found them somewhat dull after working on CISC processors. There were huge arguments around RISC vs. CISC (I suspect that many of those involved had never used a RISC processor), but then this was back in the days when many programmers knew a lot of the technical details about the processors they used. (How many of today’s programmers can name the Intel x86 registers?)

More background on 1950s minimalism in the paper: Less is more in the Fifties. Encounters between Logical Minimalism and Computer Design during the 1950s.

These days people are inventing very different architectures within which existing instructions have to operate, rather than radically new instructions.

Learning a cpu’s instruction set

January 25th, 2018 No comments

A few years ago I wrote about the possibility of secret instruction sets making a comeback and the minimum information needed to write a code generator. A paper from the sporadic (i.e., they don’t release umpteen slices of the same overall paper), but always interesting, group at Stanford describes a tool that goes a long way to solving the secret instruction set problem; stratified synthesis learns an instruction set, starting from a small set of known instructions.

After feeding in 51 base instructions and 11 templates, 1,795.42 instruction ‘formulas’ were learned (119.42 were 8-bit constant instructions, every variant counted as 1/256 of an instruction); out of a maximum of 3,683 possible instructions (depending on how you count instructions).

As well as discovering ‘new’ instructions, they also discovered bugs in the Intel 64 and IA-32 Architectures Software Developer Manuals. In my compiler writing days, bugs in cpu documentation were a pet hate (they cause huge amounts of time to be wasted).

The initial starting information used is rather large, from the perspective of understanding the instruction set of an unknown cpu. I’m sure others will be working to reduce the necessary startup information needed to obtain useful results. The Intel Management Engine is an obvious candidate for investigation.

Vendors sometimes add support for instructions without publicizing them and sometimes certain bit patterns happen to do something sensible in a particular version of a design because some random pattern of bits happens to do whatever it does without being treated as an illegal opcode. You journey down the rabbit hole starts here.

On a related note, I continue to be amazed that widely used disassemblers fail to correctly handle surprisingly many, documented, x86 opcodes; benchmarks from 2010 and 2016

First use of: software, software engineering and source code

January 16th, 2018 No comments

While reading some software related books/reports/articles written during the 1950s, I suddenly realized that the word ‘software’ was not being used. This set me off looking for the earliest use of various computer terms.

My search process consisted of using pfgrep on my collection of pdfs of documents from the 1950s and 60s, and looking in the index of the few old computer books I still have.

Software: The Oxford English Dictionary (OED) cites an article by John Tukey published in the American Mathematical Monthly during 1958 as the first published use of software: “The ‘software’ comprising … interpretive routines, compilers, and other aspects of automotive programming are at least as important to the modern electronic calculator as its ‘hardware’.”

I have a copy of the second edition of “An Introduction to Automatic Computers” by Ned Chapin, published in 1963, which does a great job of defining the various kinds of software. Earlier editions were published in 1955 and 1957. Did these earlier edition also contain various definitions of software? I cannot find any reasonably prices copies on the second-hand book market. Do any readers have a copy?

Software engineering: The OED cites a 1966 “letter to the ACM membership” by Anthony A. Oettinger, then ACM President: “We must recognize ourselves … as members of an engineering profession, be it hardware engineering or software engineering.”

The June 1965 issue of COMPUTERS and AUTOMATION, in its Roster of organizations in the computer field, has the list of services offered by Abacus Information Management Co.: “systems software engineering”, and by Halbrecht Associates, Inc.: “software engineering”. This pushes the first use of software engineering back by a year.

Source code: The OED cites a 1965 issue of Communications ACM: “The PUFFT source language listing provides a cross reference between the source code and the object code.”

The December 1959 Proceedings of the EASTERN JOINT COMPUTER CONFERENCE contains the article: “SIMCOM – The Simulator Compiler” by Thomas G. Sanborn. On page 140 we have: “The compiler uses this convention to aid in distinguishing between SIMCOM statements and SCAT instructions which may be included in the source code.”

Running pdfgrep over the archive of documents on bitsavers would probably throw up all manners of early users of software related terms.

Computer books your great grandfather might have read

January 12th, 2018 No comments

I have been reading two very different computer books written for a general readership: Giant Brains or Machines that Think, published in 1949 (with a retrospective chapter added in 1961) and LET ERMA DO IT, published in 1956.

‘Giant Brains’ by Edmund Berkeley, was very popular in its day.

Berkeley marvels at a computer performing 5,000 additions per second; performing all the calculations in a week that previously required 500 human computers (i.e., people using mechanical adding machines) working 40 hours per week. His mind staggers at the “calculating circuits being developed” that can perform 100,00 additions a second; “A mechanical brain that can do 10,000 additions a second can very easily finish almost all its work at once.”

The chapter discussing the future, “Machines that think, and what they might do for men”, sees Berkeley struggling for non-mathematical applications; a common problem with all new inventions. Automatic translator and automatic stenographer (typist who transcribe dictation) are listed. There is also a chapter on social control, which is just as applicable today.

This was the first widely read book to promote Shannon‘s idea of using the algebra invented by George Boole to analyze switching circuits symbolically (THE 1940 Masters thesis).

The ‘ERMA’ book paints a very rosy picture of the future with computer automation removing the drudgery that so many jobs require; it is so upbeat. A year later the USSR launched Sputnik and things suddenly looked a lot less rosy.

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Was a C90, C99, or C11 compiler used?

January 2nd, 2018 2 comments

How can a program figure out whether it has been compiled with a C90, C99 or C11 compiler?

Support for the // style of commenting was added in C99.

Support for Unicode string literals (e.g., U"Hello World") was added in C11.

Putting these together we get the following:

#include <stdio.h>
 
#define M(U) sizeof(U"s"[0])
 
int main(void)
{
    switch(M("")*2 //**/ 2
                          )
       {
       case 1: printf("C90\n"); break;
       case 2: printf("C99\n"); break;
       case 8: printf("C11\n"); break;
       }
 
}
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Almost all published analysis of fault data is worthless

December 27th, 2017 No comments

Faults are the subject of more published papers that any other subject in empirical software engineering. Unfortunately, over 98.5% of these fault related papers are at best worthless and at worst harmful, i.e., make recommendations whose impact may increase the number of faults.

The reason most fault papers are worthless is the data they use and the data they don’t to use.

The data used

Data on faults in programs used to be hard to obtain, a friend in a company that maintained a fault database was needed. Open source changed this. Now public fault tracking systems are available containing tens, or even hundreds, of thousands of reported faults. Anybody can report a fault, and unfortunately anybody does; there is a lot of noise mixed in with the signal. One study found 43% of reported faults were enhancement requests, the same underlying fault is reported multiple times (most eventually get marked as duplicate, at the cost of much wasted time) and …

Fault tracking systems don’t always contain all known faults. One study found that the really important faults are handled via email discussion lists, i.e., they are important enough to require involving people directly.

Other problems with fault data include: biased reported of problems, reported problem caused by a fault in a third-party library, and reported problem being intermittent or not reproducible.

Data cleaning is the essential first step that many of those who analyze fault data fail to perform.

The data not used

Users cause faults, i.e., if nobody ever used the software, no faults would be reported. This statement is as accurate as saying: “Source code causes faults”.

Reported faults are the result of software being used with a set of inputs that causes the execution of some sequence of tokens in the source code to have an effect that was not intended.

The number and kind of reported faults in a program depends on the variety of the input and the number of faults in the code.

Most fault related studies do not include any user related usage data in their analysis (the few that do really stand out from the crowd), which can lead to very wrong conclusions being drawn.

User usage data is very hard to obtain, but without it many kinds of evidence-based fault analysis are doomed to fail (giving completely misleading answers).

The first compiler was implemented in itself

December 20th, 2017 No comments

I have been reading about the world’s first actual compiler (i.e., not a paper exercise), described in Corrado Böhm’s PhD thesis (French version from 1954, an English translation by Peter Sestoft). The thesis, submitted in 1951 to the Federal Technical University in Zurich, takes some untangling; when you are inventing a new field, ideas tend to be expressed using existing concepts and terminology, e.g., computer peripherals are called organs and registers are denoted by the symbol pi.

Böhm had work with Konrad Zuse and must have known about his language, Plankalkül. The language also has a APL feel to it (but without the vector operations).

Böhm’s language does not have a name, his thesis is really about translating mathematical expressions to machine code; the expressions are organised by what we today call basic blocks (Böhm calls them groups). The compiler for the unnamed language (along with a loader) is written in itself; a Java implementation is being worked on.

Böhm’s work is discussed in Donald Knuth’s early development of programming languages, but there is nothing like reading the actual work (if only in translation) to get a feel for it.

Update (3 days later): Correspondence with Donald Knuth.

Update (3 days later): A January 1949 memo from Haskell Curry (he of Curry fame and more recently of Haskell association) also uses the term organ. Might we claim, based on two observations on different continents, that it was in general use?

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The shadow of the input distribution

December 12th, 2017 2 comments

Two things need to occur for a user to experience a fault in a program:

  • a fault has to exist in the code,
  • the user has to provide input that causes program execution to include the faulty code in a way that exhibits the incorrect behavior.

Data on the distribution of user input values is extremely rare, and we are left having to look for the shadows that the input distribution creates.

Csmith is a well-known tool for generating random C source code. I spotted an interesting plot in a compiler fuzzing paper and Yang Chen kindly sent me a copy of the data. In compiler fuzzing, source code is automatically generated and fed to the compiler, various techniques are used to figure out when the compiler gets things wrong.

The plot below is a count of the number of times each fault in gcc has been triggered (code+data). Multiple occurrences of the same fault are experienced because the necessary input values occur multiple times in the generated source code (usually in different files).

Duplicate fault counts, plus fitted regression

The green line is a fitted regression model, it’s a bi-exponential, i.e., the sum of two exponentials (the straight lines in red and blue).

The obvious explanation for this bi-exponential behavior (explanations invented after seeing the data can have the flavor of just-so stories, which is patently not true here :-) is that one exponential is driven by the presence of faults in the code and the other exponential is driven by the way in which Csmith meanders over the possible C source.

So, which exponential is generated by the faults and which by Csmith? I’m still trying to figure this out; suggestions welcome, along with alternative explanations.

Is the same pattern seen in duplicates of user reported faults? It does in the small amount of data I have; more data welcome.