Questions tagged [floating-point]

for questions about floating point arithmetic. May be about the format of the word, or an instruction set, or a particular implementation.

9
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0answers
324 views

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 ...
11
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3answers
4k views

When did game consoles begin including FPUs?

Floating-point coprocessors (FPUs) were an expensive, niche, add-on product for early desktop and home computers. but became commonplace by the mid-1990s, as they began to be included within the most ...
6
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3answers
202 views

Why is modulo operation an operator for integer types but only a function for floating-point ones?

In C, we have the % operator which finds remainder of division. But it's only applicable to integral types. For floating-point types we have to use fmod function from math.h. This makes an impression ...
35
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5answers
5k views

Did any compiler fully use Intel x87 80-bit floating point?

There is a paradox about floating point that I'm trying to understand. Floating point is an eternal struggle with the problem that real numbers are both essential and incomputable. It's the best ...
22
votes
2answers
5k views

What was the last x86 CPU that did not have the x87 floating-point unit built in?

This Wikipedia page says the following: Most x86 processors since the Intel 80486 have had these x87 instructions implemented in the main CPU So the above quote implies that some CPUs that were ...
35
votes
1answer
3k views

How did the 8086 interface with the 8087 FPU coprocessor?

The 8087 has many instructions - too many, it seems, to be encoded as part of the 8086 instruction set. How did the Intel 8086 interface with an Intel 8087 FPU that a user added? Consider the ...
4
votes
2answers
398 views

Did any early computers use a different radix to improve accuracy of rational arithmetic?

Fractions like a third, a fifth, a tenth and so on cannot be precisely represented in binary, because those would be recurring fractions and so would never fit in a (reasonable) data structure. And ...
5
votes
3answers
181 views

How does the floating point conversion in Zuse's machines work?

Can someone please help me understand the floating point to readable decimal conversion algorithms of the Z1 and Z3? There is a patent in German containing all the information but I can't speak German....
4
votes
1answer
201 views

ENIAC stands for Electrical Numerical Integrator And Calculator; what made it particularly suitable for numerical integration?

The acronym ENIAC stands for Electrical Numerical Integrator And Calculator. The fact that it was simpy a numerical computer means it probably could be used to perform numerical integration in some ...
15
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3answers
1k views

Commodore BASIC and binary floating point precision

I am mildly curious that though the 6502 provides BCD arithmetic which would be useful for implementing decimal floating point, Commodore BASIC uses, like all (?) Micro-Soft BASIC, binary floating ...
5
votes
2answers
422 views

Why does Sinclair BASIC have two formats for storing numbers in the same structure?

The ZX Spectrum has two formats for storing numbers, both 40 bits, or five bytes. The first is a floating point format, which consists of one exponent byte, and four mantissa bytes. The first bit of ...
8
votes
1answer
401 views

How can floating point addition be so slow on a BESM-6?

In the BESM-6 technical manuals — for example, in the ALU description, page 4 — there is a table specifying min/max/average instruction latencies in clock cycles (the last 3 columns; the ...
7
votes
1answer
277 views

Which pre-IEEE computers had a single precision FPU and implemented double precision floats in software?

Before the formats of floating point numbers have been standardized in IEEE 754 in 1985, different vendors had used many different floating point formats, some of them listed on the Data Format and ...
4
votes
2answers
381 views

Floating Point on Konrad Zuse's computers

From what I understand, with floating point arithmetic, shifting values up and down is important, since a floating point value essentially is an equation like 2e×m. This supposition may be supported ...
2
votes
2answers
332 views

Using C64 floating point kernal routines with 16 bit integer

How to use floating point kernal routines for 16 bit arithmetics such as: $1234*$ABCD or $1234/$ABCD ?
45
votes
11answers
17k views

Why not use fractions instead of floating point?

Considering all those early home computers, the ZX Spectrum, the Galaksija, the VIC-20, the Apple I/II/III, and all of those, they all have some 8-bit CPU which does integer arithmetic and no floating ...
1
vote
1answer
329 views

How adequate would 48-bit floating point be? [closed]

Though power of 2 word sizes look in hindsight like a natural consensus, historical computers used quite a wide variety, including but not limited to 9, 18, 36, 12, 24 and 60 bits. Power-of-2 ...
8
votes
3answers
2k views

Floating point performance of classic minicomputers

Are there any numbers available for the floating point performance of classic minicomputers of the seventies and eighties? For example, the VAX 11/780 for integer calculations was generally rated in ...
8
votes
1answer
712 views

128-bit floating point

IEEE 754 defines 128-bit floating point, though perhaps in a three-way chicken and egg problem, it's rarely supported by hardware, rarely supported by compilers, and rarely used. Have there been, ...
19
votes
3answers
945 views

What other computers used this floating-point format?

I have discovered that the DEC PDP-10 used a floating-point format that differed from IEEE-754 in an interesting way. IEEE-754 is like sign-magnitude representation. The only difference between a ...
5
votes
1answer
347 views

When were floating point rounding modes first implemented?

It appears that at least some pre-IEEE 754 computers had only one hardwired floating point rounding mode, e.g. away from zero as in PDP-11 (page 154 of PDF). Which historical architectures were the ...