Questions tagged [floating-point]
Floating point arithmetic: number formats, instruction sets, software and hardware implementations.
69 questions
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Did CRAY's computers have a guard bit?
The paper What Every Computer Scientist Should Know About Floating-Point Arithmetic uses the Cray's systems as an example of computers without a guard bit:
Although most modern computers have a guard ...
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When and why is fwait necessary when using the 8087 coprocessor?
I am writing 8086/8087 assembly code that performs floating-point operations, specifically converting numbers to scientific notation. While testing on real hardware (an IBM 5150 with a working 8087 ...
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Where can I find a tutorial on using floating point arithmetic via BASIC ROM calls as part of a machine language program
I am trying to reproduce a program I wrote for a Office of Surface Mining scientists back in 1985 that was written on a commodore 128 in BASIC 7.0.
The program performed a Monte Carlo simulation of ...
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When did Lotus 1-2-3 for DOS start supporting the 8087 math coprocessor?
I upgraded a friend's computer who only used Lotus 1-2-3, and I added memory and dropped in an 8087. Later, I found out their version of Lotus 1-2-3 didn't make use of the 8087.
When did Lotus 1-2-3 ...
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Looking for early examples of extended precision by interpretation
The other day I came across a clever way of implementing variable-length extended precision, dated 1967 (on the BESM-6, apparently as part of the system software available at the time of introduction ...
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What floating point libraries were written to meet the IEEE 754 standard before it was accepted in 1985?
The IEEE 754 floating point arithmetic working group began in 1977 and was formally accepted in 1985. One of the original driving factors of the standard itself was Intel who wanted a standard to go ...
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Why was BASIC's INT() a floor, and not a truncate?
Reading over some older bits I've collected over the years, it appears that some early BASICs used a truncate for their INT function, but this was standardized on floor.
Any ideas why? Poking about I ...
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Looking for help understanding a 'Reciproot' routine on the Manchester Mark I (1951)
I'm hoping to understand a routine written for the Manchester Mark I [NOTE: a comment from Raffzahn suggests this may be the Ferranti (wikipedia link) and not the Manchester Mark I] which computes ...
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Was the design of the PDP-11 Floating Point Processor responsible for C's willingness to do arithmetic on floats at double precision?
The Wikipedia page on PDP-11 architecture has a very interesting bullet point in the section on the Floating Point Processor extension to the basic architecture:
full floating point operations on ...
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How robust was floating point format output in pre-IEEE systems?
Most pre-IEEE floating point formats that used biased exponent and a 2's-complement mantissa without a hidden bit, were asymmetric. That is, there was a representable negative value which had no ...
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Did any hardware-supported floating-point format ever fast-track integers?
The floating-point format on the ZX Spectrum has the unusual feature of special-casing small integers: Why does Sinclair BASIC have two formats for storing numbers in the same structure?
There are ...
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Did any PC software floating point use non-IEEE format?
During the 1980s, prior to the 486 (well, strictly speaking, prior to the discontinuing of the 486SX in the nineties), IBM PCs and compatibles had hardware floating point only in the form of an ...
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Did any computer ever signal floating-point overflow purely with a sticky flag?
Every implementer of floating-point arithmetic, needs to think about how to signal overflow.
One possible way to do it is by raising an exception, though this creates the problem that 'exception' can ...
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What was this book about floating-point system design/construction?
A comment on the question Why did 8-bit Basic use 40-bit floating point? says the following (emphasis added):
Re, "Nowadays, floating point is usually either 32 or 64 bits." More ...
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Why did the 8087 need a special socket?
The IBM PC included a coprocessor socket for the 8087 floating-point unit. Logical enough; some customers wanted to use the 8087 to make numeric calculations run faster.
But why was the 8087 designed ...
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Why did decimal arithmetic slow down VisiCalc?
There is an excellent article about VisiCalc that goes into all the details about what happened and why, highly recommended if you are interested in that part of computing history. I was reading this ...
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Why did 8-bit Basic use 40-bit floating point?
Nowadays floating point is usually either 32 or 64 bits, sometimes 16, occasionally 128. But of course, the Basic interpreters on the 8-bit machines, having to implement floating point in software ...
- 65.3k
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How did VisiCalc decide how many decimal places to display?
VisiCalc represented numbers in BCD to be able to handle decimals precisely. But how did it decide how many decimal places to display?
In some screenshots like https://www.researchgate.net/figure/A-...
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What were the most common applications of the 8087?
The original IBM PC had a slot for the 8087 floating-point coprocessor. This was a somewhat esoteric feature at the time – previous microcomputers had done all their floating-point in software – but ...
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Detecting the external x87 FPU
On modern processors the x87 FPU is integrated in the CPU chip, but it used to be a separate chip before the 80486. So is there any way to detect its presence, and maybe even its generation (8087, ...
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How can I understand numerical precision of values in Microsoft BASIC (on the Dragon 32)?
I implemented a differential equation solver on my Dragon 32 (which uses Microsoft Extended Color BASIC) but the results I get quickly diverge from those I expect, which are the same as those I get ...
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What was the performance penalty for denormal inputs on 80s-era FPUs?
Some FPUs exhibit as much as an order of magnitude slowdown when given denormal inputs, due to having to trap to microcode to handle them.
Did early FPUs of the microprocessor era, exhibit substantial ...
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Why did the CDC 6600 expand the word size to 60 bits?
According to http://www.quadibloc.com/comp/cp0201.htm
The CDC 1604 used 48-bit floating point with 11 bits exponent and 36 bits mantissa. There was also a double precision format (which I believe was ...
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Where to share/who may be interested in IEEE 16 bit half float library for Zilog Z80?
I have recently developed a half-float/16-bit float library (link to Github) for Zilog Z80. It was a part of my project to run some neural network and graphics POCs for ZX Spectrum.
The library uses ...
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How good was Woz's FP code?
I just came across this amazing 1976 article by Woz. In it he describes a relatively complete floating-point system for the 6502 with a 32-bit format (similar to earlier MS code).
I understand the ...
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