Quire for posits or posits for quire?

[Alex Litronov]

The latest 4.9 draft of the posit standard requires all bits to have es=2. And this creates problems:

Maximum value:   10^37    10^75   10^152     10^306

Number format:  posit32  posit64  posit128  posit256

               float32                     float64

 

The maximum value of 10^306 may seem overwhelming, but the upper bound is useless in terms of precision, so some applications require float128 with its 10^4932, where the precision is smeared over a larger dynamic range.

 

According to this table, posit256 is a replacement for float64. Who needs such a replacement? 4 times thicker.

 

Posit64 compared to float64 seems like a joke. And this joke is useless without quire, which is applicable only to exotic calculations. And this quire is the basis of the posit standard, and the posits are just an accessory to it. It should be the other way around, shouldn't it?

[John L. Gustafson]

Alex,

Which applications are you referring to that require the variables to have a dynamic range of 600 orders of magnitude? I keep asking people to send me examples of any applications for which a 32-bit standard posit (with 512-bit quire, around 157 decimals of accuracy) is insufficient but 64-bit floats do fine, and I'm not seeing them. I'm sure there are some, but I don't think they're common.

You seem to be dismissing the dynamic range of the quire, saying it is specialized. It's actually quite general. The quire can be used to accomplish high-precision plus, minus, times, divide, square root, etc. using unevaluated sums (similar to double-word precision libraries, but not limited to double). This is well documented by Kulisch.

When I see the reasons programmers use 64-bit floats, it almost always is to preserve accuracy when accumulating large sums, or minimize cumulative rounding in solving large linear systems, or evaluate polynomials to high accuracy even when near a root where Horner's rule is numerically ill-behaved. The quire solves all of those problems easily. How are those calculations "exotic"? Have you actually tried using the quire data type?

Assertions about one approach being inferior or superior or "a joke" need to be supported with examples and experiments, in scientific discussions.

John

On Dec 24, 2020, at 2:55 PM, Alex Litronov <litr...@yandex.ru> wrote:

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