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From: Clark F Morris on 31 Mar 2008 20:55 On Tue, 18 Mar 2008 19:34:51 -0600, Robert <no(a)e.mail> wrote: >On Tue, 18 Mar 2008 09:09:44 -0600, Howard Brazee <howard(a)brazee.net> wrote: > >>On Mon, 17 Mar 2008 21:53:23 -0600, Robert <no(a)e.mail> wrote: >> >>>The others were confused. They thought binary integer was the same as binary floating >>>point. >> >>It could be. I'm glad people I worked with didn't think those were >>the same thing. >> >>>That's why IBM was able to sell them decimal hardware. >> >>So they didn't buy IBM decimal hardware for the same reasons as >>everybody else? Was their thinking in this matter ever published? > >Lots of muddled thinking on numeric errors has been published. Some talk about 'binary >arithmetic' without making a distinction between integer and floating point. Here's an >example: Try doing a simple divide like calculate the value of 1 / 5 in binary. You get a never ending fraction. > >" Why did computers use binary in the first place? > > Many early computers (such as the ENIAC, or the IBM 650) were in fact decimal >machines. In the 1950s, however, most computers turned to binary representations of >numbers as this made useful reductions in the complexity of arithmetic units (for example, >a binary adder requires about 15% less circuitry than a decimal adder). This reduction in >turn led to greater reliability and lower costs. > > Storing decimal integers in a simple binary coded decimal (BCD) form, rather than a >pure binary form, also uses up to 20% more storage than the binary form, depending on the >coding used. > > Decimal arithmetic, therefore, is inherently less efficient than binary arithmetic, >and at the time this justified the switch to binary floating-point arithmetic (just as a >two-digit representation for the year in a date was justifiable at the time). However, the >programming and conversion overheads and other costs of using binary arithmetic suggest >that hardware decimal arithmetic is now the more economical option for most applications. > > Has any company formally announced hardware decimal floating-point support? > > Yes. IBM announced on 18 April 2007 hardware decimal floating point facilities for IBM >z9 EC and z9 BC: > >Since then, IBM has also announced support for decimal floating-point in the Power6 >processors, and has released details of the decimal floating-point unit in the z6 >microprocessor. >http://www2.hursley.ibm.com/decimal/decifaq3.html#calcs > >Cowlishaw accidentally overlooks the fact that every Intel x86 processor/FPU made since >1980 has supported 17 digit hardware decimal floating point. Now that IEEE 754r is on the >horizon, Intel is dropping it (I think they already did in Itanium). > >"based on Intel�s investigation on the frequency of >use and performance requirements for decimal processing in existing applications, the >potential benefits of hardware-implemented decimal arithmetic do not justify its cost in >terms of dedicating transistors and power consumption to it on a processor core. >Consequently, Intel is proposing the use of software emulation instead. > >Just as the computing landscape changed dramatically from the ratification of the first >floating point standard to its current revision, equally big changes are in store for the >next 15 to 20 years. The multi-core processor revolution has begun and is poised to make >even greater leaps in performance (and performance per watt) for personal computers. >Intel�s research and development plans suggest the possibility of a 256-core processor by >the 2015 time frame." >http://www.intel.com/standards/floatingpoint.pdf
From: Robert on 1 Apr 2008 00:37 On Mon, 31 Mar 2008 21:55:10 -0300, Clark F Morris <cfmpublic(a)ns.sympatico.ca> wrote: >On Tue, 18 Mar 2008 19:34:51 -0600, Robert <no(a)e.mail> wrote: > >>Lots of muddled thinking on numeric errors has been published. Some talk about 'binary >>arithmetic' without making a distinction between integer and floating point. Here's an >>example: > >Try doing a simple divide like calculate the value of 1 / 5 in binary. OK. 01 numerator value 1 binary pic 9(9). 01 denominator value 5 binary pic 9(9). 01 quotient binary pic 9(9)v9(4). compute quotient = numerator / denominator display quotient 0000000002000 >You get a never ending fraction. Looks pretty diadic to me.
From: Michael Mattias on 1 Apr 2008 08:44 "Robert" <no(a)e.mail> wrote in message news:jbd3v3tomdipsgke42j5cklujltahbtjle(a)4ax.com... > On Mon, 31 Mar 2008 21:55:10 -0300, Clark F Morris > <cfmpublic(a)ns.sympatico.ca> wrote: > >>Try doing a simple divide like calculate the value of 1 / 5 in binary. > > OK. > > 01 numerator value 1 binary pic 9(9). > 01 denominator value 5 binary pic 9(9). > 01 quotient binary pic 9(9)v9(4). > > compute quotient = numerator / denominator > display quotient > > 0000000002000 > >>You get a never ending fraction. > > Looks pretty diadic to me. That's because you did not do it in binary, you did it in decimal. One-fifth is rational in decimal, but irrational in binary. MCM
From: Clark F Morris on 1 Apr 2008 14:43 On Mon, 31 Mar 2008 22:37:12 -0600, Robert <no(a)e.mail> wrote: >On Mon, 31 Mar 2008 21:55:10 -0300, Clark F Morris <cfmpublic(a)ns.sympatico.ca> wrote: > >>On Tue, 18 Mar 2008 19:34:51 -0600, Robert <no(a)e.mail> wrote: >> > >>>Lots of muddled thinking on numeric errors has been published. Some talk about 'binary >>>arithmetic' without making a distinction between integer and floating point. Here's an >>>example: >> >>Try doing a simple divide like calculate the value of 1 / 5 in binary. > >OK. > >01 numerator value 1 binary pic 9(9). >01 denominator value 5 binary pic 9(9). >01 quotient binary pic 9(9)v9(4). > >compute quotient = numerator / denominator >display quotient > >0000000002000 > >>You get a never ending fraction. > >Looks pretty diadic to me. You may have to do this in Assembler to get the results that I am talking about. Take a look at the generated instructions. If I had access to an IBM mainframe I would compile a small test program to see what the underlying code is. Clark
From: tlmfru on 1 Apr 2008 16:05
Clark F Morris <cfmpublic(a)ns.sympatico.ca> wrote in message news:if05v3503beg04nonbeci3n8eqo2vill79(a)4ax.com... > On Mon, 31 Mar 2008 22:37:12 -0600, Robert <no(a)e.mail> wrote: > > >On Mon, 31 Mar 2008 21:55:10 -0300, Clark F Morris <cfmpublic(a)ns.sympatico.ca> wrote: > > > >>On Tue, 18 Mar 2008 19:34:51 -0600, Robert <no(a)e.mail> wrote: > >> > > > >>>Lots of muddled thinking on numeric errors has been published. Some talk about 'binary > >>>arithmetic' without making a distinction between integer and floating point. Here's an > >>>example: > >> > >>Try doing a simple divide like calculate the value of 1 / 5 in binary. > > > >OK. > > > >01 numerator value 1 binary pic 9(9). > >01 denominator value 5 binary pic 9(9). > >01 quotient binary pic 9(9)v9(4). > > > >compute quotient = numerator / denominator > >display quotient > > > >0000000002000 > > > >>You get a never ending fraction. > > > >Looks pretty diadic to me. He's right, you know. 0.2 (decimal) in binary = 1/8 + 1/16 + 1/128 + 1/256 ... = .00110011 ... = 0.19921875. etc. Obviously binary division is done by black magic involving shifts & counts. PL |