C library for multiple-precision floating-point arithmetic with correct rounding

Re:C library for multiple-precision floating-point arithmeti... by thxg on Friday June 03, 2022 @11:22AM (#31609543)

That's a legitimate question. It's just floating-point jargon. Here's what it means:

> I’m well aware of banker’s rounding, and rounding up, and round down, and rounding towards zero, and rounding towards signed infinity, etc.

MPFR supports most of those rounding modes you mentioned:

https://www.mpfr.org/mpfr-current/mpfr.html#Rounding

> But “correct” as a formal modifier is new to me

It just means that once you select a rounding mode, it is guaranteed (modulo bugs) to give you the correct answer rounded according to your selected rounding mode.

At first one can think: "obviously, who wants incorrect rounding?". And indeed all recent floating-point hardware implements correct rounding... But only for 32- or 64-bit floats, and only for addition, subtraction, multiplication and division.

By contrast, most libc/libm implementations do not have correct rounding for transcendental functions (cos, sin, tan, exp, log, etc.). There are some exceptions (Rlibm, CRlibm).

MPFR implements correct rounding

- at any bit width and

- for all transcendental functions.

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Re:C library for multiple-precision floating-point arithmeti... by gnulinux on Friday June 03, 2022 @04:52PM (#31613462)

In a big application, wouldn't rounding to a random direction (a feature GNU MP supports) be the most accurate probabilistically? If you round up or down all your numbers and you perform a lot of arithmetic operations, you create a lot of bias.

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Re:C library for multiple-precision floating-point arithmeti... by klyrs on Friday June 03, 2022 @07:47PM (#31615251)

Consider the logarithm. In almost any interval, rounding down will be more accurate than rounding up the majority of the time -- so random rounding will bias you away from an accurate result. Random rounding can be a good idea, but it's not always a good idea. Random rounding is an okay default, but having fine-grain control over rounding direction is vastly superior to always sticking to the default.

For another example, interval arithmetic is a really cool approach to keeping an eye on your accuracy. There, you want to round your upper bounds up, and round your lower bounds down.

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Re:C library for multiple-precision floating-point arithmeti... by pertymcpert on Friday June 03, 2022 @05:08PM (#31613630)

Maybe, but having random "accurate" behavior in a program is generally worse than being incorrect all of the time.

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