In 1980 I started working with a straightforward algorithm that was computerized then by agreeing on its implementation in a few pages of 32-bit double-precision floating-point Fortran code.
Up until then, aggregate data had been manually compiled and published in kilos of handbooks over the decades.
This was the first acceptable computer approach since it was the exact same pre-1980 algorithm, and expected to play a part in correct 20-digit decimal billable amounts based on computer data which had been meticulously rounded to 4 decimal places, which is what took up most of the Fortran code.
Well, I needed to do the same calculations on an 8-bit Radio Shack Pocket Computer. And there was only 512 bytes of user space for my TRS-80 Basic code.
The exact algorithm would fit, but not any of the standard multi-step rounding procedure. The floating point output was not often good to 4 decimal places.
Massaged it iteratively until the algorithm was no longer fully recognizable. Still no good.
Changed from floats to integers. This also saved more memory for workspace.
I was no mathematician, and in order to get integers to do the whole thing, leaving only the need for a final move of decimal point, it was not easy.
Ended up with a very dissimilar representation of the algorithm, using numbers specifically geared to the problem at hand, nothing universal like Gustafson.
When I read his material I was intrigued that one of the objectives was to obtain more numerical accuracy from lesser-bit computers himself.
Up until then, aggregate data had been manually compiled and published in kilos of handbooks over the decades.
This was the first acceptable computer approach since it was the exact same pre-1980 algorithm, and expected to play a part in correct 20-digit decimal billable amounts based on computer data which had been meticulously rounded to 4 decimal places, which is what took up most of the Fortran code.
Well, I needed to do the same calculations on an 8-bit Radio Shack Pocket Computer. And there was only 512 bytes of user space for my TRS-80 Basic code.
The exact algorithm would fit, but not any of the standard multi-step rounding procedure. The floating point output was not often good to 4 decimal places.
Massaged it iteratively until the algorithm was no longer fully recognizable. Still no good.
Changed from floats to integers. This also saved more memory for workspace.
I was no mathematician, and in order to get integers to do the whole thing, leaving only the need for a final move of decimal point, it was not easy.
Ended up with a very dissimilar representation of the algorithm, using numbers specifically geared to the problem at hand, nothing universal like Gustafson.
When I read his material I was intrigued that one of the objectives was to obtain more numerical accuracy from lesser-bit computers himself.