Re: Why is division by zero permitted? (It's actually very useful! Here's why)
On 2013-10-24 09:35, David Cole wrote: The reason that this useful is that this quirk can be exploited to create, for example, a MAX or MIN function that is evaluated at assembly time. (Maybe this has changed, but the last time I looked, the Assembler did not offer native MAX and MIN functions.) Are you confident that was the motivation for the behavior? I suppose it's possible. ... I'll translate this into something more readable: (A/B)/(A/B)*A Here's a better layout (better when your font is courier): A/B --- * A A/B I recognize from the comments that you had a specialized requirement and were not trying to provide a general purpose MAX function. Regardless, I believe I spot the restrictions (by inspection, not tested): o I believe this gives MAX(-5,+3)=-5, not the +3 I'd expect. o I believe MAX(-2147483648,-1) results in an integer overflow error, ASMA057E. (Should I see the source of your macro somewhere, or is it proprietary?) Here's my attempt at it. It has a more symmetric, although (much) more restricted but still useful argument domain. It does not depend on division by zero -- tested by translating to Rexx which treats division by zero as a error. Test code attached: * MAX function through the marvel of integer arithmetic. Valid for * arguments in the range [-357913940,357913940]. Arguments outside * that range will either give correct results or report overflow * with ASMA075E. Division by zero does not occur. * MACRO L MAX X,Y LSYSNDX DCA(X)-(Y))*3)/(((X)-(Y))*3+1))*(Y)+(-3+((Y)-(X, ))*3)/(-2+((Y)-(X))*3)*(X)) MEND * TINY CSECT MAX +5,+3 MAX -5,+3 MAX +5,-3 MAX -5,-3 MAX 08,11 MAX 09,11 MAX 10,11 MAX 11,11 MAX 12,11 MAX 13,11 MAX 14,11 MAX 357913940,-357913940 MAX -357913940,357913940 MAX 9,9 MAX 357913941,-357913941 MAX 357913942,-357913942 END Coefficients chosen empirically. I believe that with much more Diophantine gymnastics I could make it work for all integer values. I'm not much motivated. -- gil
Re: Why is division by zero permitted?
From: glen herrmannsfeldt g...@ugcs.caltech.edu Sent: Thursday, October 24, 2013 4:22 PM From C28-6514-5 on bitsavers, on page 16: What manual is that; for what system, and what date? Division by zero is permitted and yields a zero result. After that, (and presumably also earlier) it has to stay that way as code (macros) might depend on that. There is no reason given.
Re: Why is division by zero permitted?
Ask someone for a web browser and type google.com ;-) OS assembler language; 360, and december 1967 Many moons ago, a friend (who went to math school) showed me his scars and explained that it were evil that compilers could optimize in such a way that an attempt to divide by zero would go unnoticed. I believe most languages now formally specify which parts of the expression may/will not be computed when it can be avoided. Along the lines where you may write ( i n table[i] 0) without being concerned about stepping beyond your table. Rob On 24 October 2013 12:07, robin robi...@dodo.com.au wrote: From: glen herrmannsfeldt g...@ugcs.caltech.edu Sent: Thursday, October 24, 2013 4:22 PM From C28-6514-5 on bitsavers, on page 16: What manual is that; for what system, and what date? Division by zero is permitted and yields a zero result. After that, (and presumably also earlier) it has to stay that way as code (macros) might depend on that. There is no reason given.
Re: Why is division by zero permitted?
From: Rob van der Heij rvdh...@gmail.com Sent: Thursday, October 24, 2013 9:35 PM Ask someone for a web browser and type google.com ;-) OS assembler language; 360, and december 1967 I have better things to do than do other people's research.
Re: Why is division by zero permitted?
The Assembler language book does not describe how processor instructions work. Processor instructions never have allowed division by zero. The Assembler language book quote is describing how an arithmetic expression is evaluated at assembly time by the Assembler program. This misconception is akin to finding a statement in a book about the XYZ compiler (where XYZ might be FORTRAN, PL/1, ALGOL/60, JOVIAL, APL, etc.) that says division by zero is allowed if ...blah blah... and then concluding that the processor itself has some kind of divide instruction which will not indicate an error if it attempts to use a divisor of zero. The Assembler language book also describes Assembler language instructions such as SPACE, EJECT, PRINT NODATA, DSECT, etc. These are also not processor instructions. Without doing my homework, I would wager a large sum that somewhere in the beginning of the Assembler language book (introduction, prologue, whatever) is a statement that clarifies what the Assembler language book is not. Bill Fairchild Franklin, TN - Original Message - From: Rob van der Heij rvdh...@gmail.com To: ASSEMBLER-LIST@LISTSERV.UGA.EDU Sent: Thursday, October 24, 2013 5:35:32 AM Subject: Re: Why is division by zero permitted? Ask someone for a web browser and type google.com ;-) OS assembler language; 360, and december 1967 Many moons ago, a friend (who went to math school) showed me his scars and explained that it were evil that compilers could optimize in such a way that an attempt to divide by zero would go unnoticed. I believe most languages now formally specify which parts of the expression may/will not be computed when it can be avoided. Along the lines where you may write ( i n table[i] 0) without being concerned about stepping beyond your table. Rob On 24 October 2013 12:07, robin robi...@dodo.com.au wrote: From: glen herrmannsfeldt g...@ugcs.caltech.edu Sent: Thursday, October 24, 2013 4:22 PM From C28-6514-5 on bitsavers, on page 16: What manual is that; for what system, and what date? Division by zero is permitted and yields a zero result. After that, (and presumably also earlier) it has to stay that way as code (macros) might depend on that. There is no reason given.
Re: Why is division by zero permitted?
Robin, What manual is that; for what system, and what date? that was your question. I have better things to do than do other people's research. So you are not interested in any answer to your question I guess. -- Martin Pi_cap_CPU - all you ever need around MWLC/SCRT/CMT in z/VSE more at http://www.picapcpu.de
Re: Why is division by zero permitted?
From: DASDBILL2 dasdbi...@comcast.net Sent: Thursday, October 24, 2013 10:44 PM The Assembler language book does not describe how processor instructions work. Mine does. And most assembler langage books do also. Processor instructions never have allowed division by zero. Some early processors did not detect division by zero, nor detected overflow.
Re: Why is division by zero permitted?
Paul Gilmartin said HLASM (not S360). The standard divide instructions get S0C9 when dividing by 0. Is it floating point that allows divide by 0? Is it the macro assembler SETA that allows it? Jon Perryman. - Original Message - From: Rob van der Heij rvdh...@gmail.com Ask someone for a web browser and type google.com ;-) OS assembler language; 360, and december 1967 Many moons ago, a friend (who went to math school) showed me his scars and explained that it were evil that compilers could optimize in such a way that an attempt to divide by zero would go unnoticed.
Re: Why is division by zero permitted?
Let us stipulate that z/Architecture divide instructions, all of them, throw exceptions when a zero divisor is detected. That said, things then get more complicated. These exceptions cannot be disabled using SPM. There is no program-mask bit available for for doing so. They can, however, be ignored more and less systematically. Prototypically, I can write ON ZERODIVIDE ; in PL/I. This null on unit ensures that zero divides will be ignored within its scope. Moreover, there is now a functionally equivalent, albeit less perspicuous, facility available via the LE in all IBM statement-level languages that use it, i.e., for all of the usual suspects and even for LE-compatible assembly language. Paul Gilmartin and I do not always agree, but he knows all about zero-divide exceptions. What he was asserting was not that these exceptions do not occur but there are environments in which they are ignored. John Gilmore, Ashland, MA 01721 - USA
Re: Why is division by zero permitted? (It's actually very useful! Here's why)
At 10/23/2013 08:30 PM, Paul Gilmartin wrote: OK. Pure HLASM. I've long wondered why division by zero is permitted in arithmetic expressions when otherwise overflows (even in division) are reported as errors. The only rationale I can think of (and a poor one) is that it was initially an implementation oversight that was so rapidly codified by use that when it was discovered no repair was feasible. -- gil For several of you that were confused by this, let me first point out that Gill's question pertained to division allowed in the Assembler at assembly time, not in runtime machine instruction execution. More specifically, here are a couple of Assembler examples showing what is allowed: ANSWER SETA 12/0 ANSWER EQU 12/0 In both cases, the assigned value is 0. The reason that this useful is that this quirk can be exploited to create, for example, a MAX or MIN function that is evaluated at assembly time. (Maybe this has changed, but the last time I looked, the Assembler did not offer native MAX and MIN functions.) Here's how: Below is some commentary from a macro of mine that needs to compute, at assembly time, the size of a buffer that has to be big enough to hold around 50 or so variations of a control block. Following that commentary, I will try to translate this stuff into plainer English. Note, the following will display best with a fixed pitch font. If necessary, copy/paste it all into NOTEPAD for better readability. Anyway, here it is: * * * * Required length of AUTOPARM. * * * * The following EQUs calculate the length that the * * AUTOPARM, TWAPARM and RSTKPARM fields need to be in order * * to hold the largest of the above defined parameter maps. * * It does this by calculating the maximum of all AL * * symbols, and it does that by repeatedly calculating the * * maximum of a given AL symbol against the maximum of * * all prior AL symbols. * * * * The computation is made possible by the following two * * facts:* * (1) The assembler defines x/0 to =0.* * (2) All divisions are integral with no remainder or * * fraction. * * So each MAX computation looks like this: * * * * * *oldmax oldmax [This is non-0 ] * * newmax = -- / -- * oldmax [if and only if] * *newlen newlen [oldmax=newlen] * * * *newlen newlen [This is non-0 ] * * + -- / -- * newlen [if and only if] * *oldmax oldmax [newlen=oldmax] * * * *newlen oldmax [This is non-0 ] * * - 0 - -- / -- * newlen [if and only if] * *oldmax newlen [newlen=oldmax ] * * * * Note, the - 0 - is present simply for spacing * * reasons: Each of the following EQU statements is so long * * that it has to be continued for a total of three lines. * * The extra -0 shifts the statement definition such that * * no variable symbol name is broken by a continuation * * character. This makes future editing somewhat easier. * * * * SPACE 3 ABEGIN EQU 1 STARTING POINT (CAN'T =0) SPACE 1 AAD64Q EQU (ABEGIN/AAD64L)/(ABEGIN/AAD64L)*ABEGIN+(AAD64L/ABEGIN)/(| AAD64L/ABEGIN)*AAD64L-0-(ABEGIN/AAD64L)*(AAD64L/ABEGIN)*| ABEGIN * MAX(1,AAD64L) SPACE 1 AAFINQ EQU (AAD64Q/AAFINL)/(AAD64Q/AAFINL)*AAD64Q+(AAFINL/AAD64Q)/(| AAFINL/AAD64Q)*AAFINL-0-(AAD64Q/AAFINL)*(AAFINL/AAD64Q)*| AAD64Q * MAX(AAD64L,AAFINL) etc. etc. etc Basically, in order to compute a maximum of two values you need to add together three terms: - One that equals the first value but only when it is high or equal. - One that equals the second value but only when it is high or equal. - One
Re: Why is division by zero permitted?
On 2013-10-24, at 04:35, Rob van der Heij wrote: Ask someone for a web browser and type google.com ;-) OS assembler language; 360, and december 1967 ... which seems to take me to a bitsavers page, already discussed here. Many moons ago, a friend (who went to math school) showed me his scars and explained that it were evil that compilers could optimize in such a way that an attempt to divide by zero would go unnoticed. I believe most languages now formally specify which parts of the expression may/will not be computed when it can be avoided. ... Pascal, with which I am most familiar (oh, damn! OT!), makes it clear, if only by omission, that such constructs are syntactically valid but should be reported at execution. From: glen herrmannsfeldt g...@ugcs.caltech.edu Sent: Thursday, October 24, 2013 4:22 PM From C28-6514-5 on bitsavers, on page 16: Division by zero is permitted and yields a zero result. After that, (and presumably also earlier) it has to stay that way as code (macros) might depend on that. There is no reason given. I don't see that it's so necessary to maintain compatibility with all historic design blunders. Consider the relatively recent detection and warnings of questionable address resolutions. Similarly a warning could be issued for division by zero, even as an error is reported for overflow. On 2013-10-24, at 06:18, robin wrote: From: DASDBILL2 Sent: Thursday, October 24, 2013 10:44 PM The Assembler language book does not describe how processor instructions work. Mine does. And most assembler langage books do also. More to the point, it describes how the Assembler (HLASM) works, and has done so since the earliest days, which is what I was wondering about. -- gil
Re: Why is division by zero permitted?
The assembler allows division by zero in arithmetic expressions whereas the instructions of the System/360 architecture do not. Keven -Original Message- From: IBM Mainframe Assembler List [mailto:ASSEMBLER-LIST@LISTSERV.UGA.EDU] On Behalf Of glen herrmannsfeldt Sent: Thursday, October 24, 2013 00:22 To: ASSEMBLER-LIST@LISTSERV.UGA.EDU Subject: Re: Why is division by zero permitted? From C28-6514-5 on bitsavers, on page 16: Division by zero is permitted and yields a zero result. After that, (and presumably also earlier) it has to stay that way as code (macros) might depend on that. There is no reason given. -- glen
Why is division by zero permitted?
On 2013-10-23 17:54, Kurt LeBesco wrote: I've been reading quietly and wondering how the dialog drifted off to rexx and pl1 land. Can we get back on topic? Thanks OK. Pure HLASM. I've long wondered why division by zero is permitted in arithmetic expressions when otherwise overflows (even in division) are reported as errors. The only rationale I can think of (and a poor one) is that it was initially an implementation oversight that was so rapidly codified by use that when it was discovered no repair was feasible. -- gil
Re: Why is division by zero permitted?
From: Paul Gilmartin paulgboul...@aim.com Sent: Thursday, October 24, 2013 11:30 AM OK. Pure HLASM. I've long wondered why division by zero is permitted It is? According to my manual, the operation is suppressed, and an exception occurs. in arithmetic expressions when otherwise overflows (even in division) are reported as errors.
Re: Why is division by zero permitted?
Never has been allowed. From the POPS for all integer divide instructions: When the divisor is zero, or when the magnitudes of the dividend and divisor are such that the quotient cannot be expressed by a 32-bit signed binary integer, a fixed-point-divide exception is recognized. This includes the case of division of zero by zero. For HFP divide it says: When the divisor fraction is zero, an HFP-divide exception is recognized. This includes the case of division of zero by zero. For BFP and DFP divide it says: If the divisor is zero but the dividend is a finite number, an IEEE-division-by-zero exception is recognized. If the dividend and divisor are both zero, or if both are infinity, regardless of sign, an IEEE-invalid operation exception is recognized. Chris Blaicher Principal Software Engineer, Software Development Syncsort Incorporated 50 Tice Boulevard, Woodcliff Lake, NJ 07677 P: 201-930-8260 | M: 512-627-3803 E: cblaic...@syncsort.com -Original Message- From: IBM Mainframe Assembler List [mailto:ASSEMBLER-LIST@LISTSERV.UGA.EDU] On Behalf Of Paul Gilmartin Sent: Wednesday, October 23, 2013 7:31 PM To: MVS List Server 2 Subject: Why is division by zero permitted? On 2013-10-23 17:54, Kurt LeBesco wrote: I've been reading quietly and wondering how the dialog drifted off to rexx and pl1 land. Can we get back on topic? Thanks OK. Pure HLASM. I've long wondered why division by zero is permitted in arithmetic expressions when otherwise overflows (even in division) are reported as errors. The only rationale I can think of (and a poor one) is that it was initially an implementation oversight that was so rapidly codified by use that when it was discovered no repair was feasible. -- gil
Re: Why is division by zero permitted?
What arithmetic expression allows divide by 0? Jon Perryman. From: Paul Gilmartin paulgboul...@aim.com OK. Pure HLASM. I've long wondered why division by zero is permitted in arithmetic expressions when otherwise overflows (even in division) are reported as errors. The only rationale I can think of (and a poor one) is that it was initially an implementation oversight that was so rapidly codified by use that when it was discovered no repair was feasible. -- gil
Re: Why is division by zero permitted?
From C28-6514-5 on bitsavers, on page 16: Division by zero is permitted and yields a zero result. After that, (and presumably also earlier) it has to stay that way as code (macros) might depend on that. There is no reason given. -- glen
