Quadibloc

2021-05-21 20:33:06 UTC

Most floating-point formats found on historical computers fall into two

categories.

The IEEE-754 floating-point format, and the IBM 360 floating point format,

and many others, are organized like this:

(sign)

(exponent sign)

(exponent)

(significand, mantissa, coefficient)

Computers that don't have hardware floating-point, however, instead of

ordering the components of a floating-point number in terms of significance,

order them in a way that makes it easier for them to handle:

(exponent sign)

(exponent)

(sign)

(significand, mantissa, coefficient)

Since they don't have hardware floating-point, they organize a floating-point

number as two separate integers. The exponent doesn't have to come first.

And then there's a third kind of format, which I found on a few computers,

mostly with a 24-bit word length. It was similar to the format listed above,

but with the significand first and the exponent second. But one strange thing

stood out; the first bit of the second word of the floating-point number was

unused.

I put this down to those computers being large enough to come with a

hardware multiply feature. Omitting the first bit on the second word, or

treating it as a duplicate sign bit, avoided an extra step in the use of the

hardware multiply in processing floating quantities.

Well, the Model 709 and the TC-16, two closely related computers fromt he

People's Republic of China, finally came up with a floating-point format that

is not related to this systematic summary of floating-point formats.

(Of course, the double-precision floating-point numbers on the ICL 1900 is

fairly weird too, but that's a Group III format also doubled-up in the classic

way used for 128-bit floats on the 360/85 and subsequent IBM mainframes,

or for double-precision on the IBM 704 to 7090.)

The order of components is:

(exponent)

(exponent sign)

(sign)

(significand, mantissa, coefficient)

One can think of it as a compromise between Group I and Group II. The two

signs are together, as in Group I, and yet the exponent and the number part

are both contiguous as well.

John Savard

categories.

The IEEE-754 floating-point format, and the IBM 360 floating point format,

and many others, are organized like this:

(sign)

(exponent sign)

(exponent)

(significand, mantissa, coefficient)

Computers that don't have hardware floating-point, however, instead of

ordering the components of a floating-point number in terms of significance,

order them in a way that makes it easier for them to handle:

(exponent sign)

(exponent)

(sign)

(significand, mantissa, coefficient)

Since they don't have hardware floating-point, they organize a floating-point

number as two separate integers. The exponent doesn't have to come first.

And then there's a third kind of format, which I found on a few computers,

mostly with a 24-bit word length. It was similar to the format listed above,

but with the significand first and the exponent second. But one strange thing

stood out; the first bit of the second word of the floating-point number was

unused.

I put this down to those computers being large enough to come with a

hardware multiply feature. Omitting the first bit on the second word, or

treating it as a duplicate sign bit, avoided an extra step in the use of the

hardware multiply in processing floating quantities.

Well, the Model 709 and the TC-16, two closely related computers fromt he

People's Republic of China, finally came up with a floating-point format that

is not related to this systematic summary of floating-point formats.

(Of course, the double-precision floating-point numbers on the ICL 1900 is

fairly weird too, but that's a Group III format also doubled-up in the classic

way used for 128-bit floats on the 360/85 and subsequent IBM mainframes,

or for double-precision on the IBM 704 to 7090.)

The order of components is:

(exponent)

(exponent sign)

(sign)

(significand, mantissa, coefficient)

One can think of it as a compromise between Group I and Group II. The two

signs are together, as in Group I, and yet the exponent and the number part

are both contiguous as well.

John Savard