Sorry to be late to this discussion. Please be aware that there are a number of variations of the original posit definition that preserve the elegant properties (2's complement negation, perfect reciprocals of the…
IEEE 754 is just the codification of the Intel 8087 coprocessor design that John Palmer and Bruce Ravenel came up with. They brought in William Kahan as a consultant, and Kahan disagreed with almost every aspect of…
Lots of free information on posits at www.posithub.org.
The real hope is that 32-bit posits (with 512-bit quire for exact dot products and exact sums) can replace 64-bit floats where users hope 15-decimal accuracy in every variable means they don't have to learn numerical…
Exactly. Floating-point numbers cannot represent such numbers without error, yet we still see people asserting that floats represent "the entire real number line." The first format to represent such numbers honestly was…
"The End of Error: Unum Computing" is written for a popular audience, not fellow mathematicians. Only high school math is needed, and it's got plenty of humor and full-color illustrations and figures, in an attempt to…
The original Stanford talk on posits suggested that they generate an exception and not the equivalent of a NaN. A few months later, I changed my mind and the (unique) NaR bit pattern serves the same purpose as NaN does…
I hope I'm not too late to the party to correct some things I see here. The big accomplishment of Kahan and IEEE 754 was to get companies to agree on where the sign, exponent, and fraction should go, so that data…
At the risk of a "flame war" where there are no winners, I would like to comment on some the statements here before they get stale. If we avoid ad hominem attacks and stick to the math, the claims, and counterexamples,…
Actually, posits handle NaNs already, by interrupting the calculation and doing whatever you have set up to handle the exception. What they do NOT do is represent Not-a-Number with a number. If a programmer is about to…
Isaac Yonemoto has suggested the use of ±∞ as a NaN, and it seems to work exactly like NaN does other than x/±∞ = 0 whereas you want x/NaN = NaN. I hate hardware exceptions. If you have a code that occasionally hits a…
I have been following this bug in its various form for 30 years, and it is covered in pages 55-62 of The End of Error: Unum Computing. It is the "hidden scratchpad" bug where designers of a computing environment try to…
You say 1/0 = INF, but the 754 standard says negative zero is different, and 1/(-0) = -INF. Yet it says -0 is numerically equal to 0. It also specifies that the square root of -0 is -0. This is neither straightforward…
Plenty of experts refereed the book, believe me. William Kahan, David Bailey, Gordon Bell, Horst Simon, Ulrich Kulisch, John Gunnels, and anonymous reviewers as well. It was vetted for months before it was released. If…
I have a chronic problem with people taking a partial description of some of my math, and then complaining about all the things that are missing. Well, those things are in the part you didn't see! Ordinary differential…
There is a whole chapter on "fixed-size unums" and the issues of making them just as easy to index as arrays as are floats. It really is not an obstacle; it's just more work for the CPU to manage pointers and variable…
First of all, a correction: the 4-bit unums can represent any of -inf, (-inf, -2), -2, (-2, -1), (-1, 0), 0, (0, 1), (1, 2), 2, (2, inf), inf, and both quiet and signaling NaN. They do not represent ±1/2 or use ±1/2 as…
There are actually quite a number of places where Mathematica gives a wrong answer and unum math does not! For example, if you ask Mathematica to find all real values of x for which 1 == 1, it returns the empty set.…
Suppose x and y are exact numbers. Then x+y is represented as the open interval (x, x+ULP) where x+ULP is the smallest representable exact unum greater than x. Since x is disjoint from the open interval (x, x+ULP), it…
Sorry to be late to this discussion. Please be aware that there are a number of variations of the original posit definition that preserve the elegant properties (2's complement negation, perfect reciprocals of the…
IEEE 754 is just the codification of the Intel 8087 coprocessor design that John Palmer and Bruce Ravenel came up with. They brought in William Kahan as a consultant, and Kahan disagreed with almost every aspect of…
Lots of free information on posits at www.posithub.org.
The real hope is that 32-bit posits (with 512-bit quire for exact dot products and exact sums) can replace 64-bit floats where users hope 15-decimal accuracy in every variable means they don't have to learn numerical…
Exactly. Floating-point numbers cannot represent such numbers without error, yet we still see people asserting that floats represent "the entire real number line." The first format to represent such numbers honestly was…
"The End of Error: Unum Computing" is written for a popular audience, not fellow mathematicians. Only high school math is needed, and it's got plenty of humor and full-color illustrations and figures, in an attempt to…
The original Stanford talk on posits suggested that they generate an exception and not the equivalent of a NaN. A few months later, I changed my mind and the (unique) NaR bit pattern serves the same purpose as NaN does…
I hope I'm not too late to the party to correct some things I see here. The big accomplishment of Kahan and IEEE 754 was to get companies to agree on where the sign, exponent, and fraction should go, so that data…
At the risk of a "flame war" where there are no winners, I would like to comment on some the statements here before they get stale. If we avoid ad hominem attacks and stick to the math, the claims, and counterexamples,…
Actually, posits handle NaNs already, by interrupting the calculation and doing whatever you have set up to handle the exception. What they do NOT do is represent Not-a-Number with a number. If a programmer is about to…
Isaac Yonemoto has suggested the use of ±∞ as a NaN, and it seems to work exactly like NaN does other than x/±∞ = 0 whereas you want x/NaN = NaN. I hate hardware exceptions. If you have a code that occasionally hits a…
I have been following this bug in its various form for 30 years, and it is covered in pages 55-62 of The End of Error: Unum Computing. It is the "hidden scratchpad" bug where designers of a computing environment try to…
You say 1/0 = INF, but the 754 standard says negative zero is different, and 1/(-0) = -INF. Yet it says -0 is numerically equal to 0. It also specifies that the square root of -0 is -0. This is neither straightforward…
Plenty of experts refereed the book, believe me. William Kahan, David Bailey, Gordon Bell, Horst Simon, Ulrich Kulisch, John Gunnels, and anonymous reviewers as well. It was vetted for months before it was released. If…
I have a chronic problem with people taking a partial description of some of my math, and then complaining about all the things that are missing. Well, those things are in the part you didn't see! Ordinary differential…
There is a whole chapter on "fixed-size unums" and the issues of making them just as easy to index as arrays as are floats. It really is not an obstacle; it's just more work for the CPU to manage pointers and variable…
There is a whole chapter on "fixed-size unums" and the issues of making them just as easy to index as arrays as are floats. It really is not an obstacle; it's just more work for the CPU to manage pointers and variable…
First of all, a correction: the 4-bit unums can represent any of -inf, (-inf, -2), -2, (-2, -1), (-1, 0), 0, (0, 1), (1, 2), 2, (2, inf), inf, and both quiet and signaling NaN. They do not represent ±1/2 or use ±1/2 as…
There are actually quite a number of places where Mathematica gives a wrong answer and unum math does not! For example, if you ask Mathematica to find all real values of x for which 1 == 1, it returns the empty set.…
Suppose x and y are exact numbers. Then x+y is represented as the open interval (x, x+ULP) where x+ULP is the smallest representable exact unum greater than x. Since x is disjoint from the open interval (x, x+ULP), it…