[PATCH v3] math: Refactor how to use libm-test-ulps

[Paul Zimmermann]

       Dear Adhemerval,

> The manual error table is also removed, Paul Zimmermann has been

it would be more accurate to write "Paul Zimmermann and others have been"
since I initiated this comparison, but now we are 4 co-authors

> Changes from v2:
> * Expanded the manual entry for accuracy papers and added the complex
>   analysis one.
> * More type fixes in commit message.

type -> typo :-)

> +A more comprehensive analysis of @theglibc{} math functions precision could
> +be found in 'Accuracy of Mathematical Functions in Single, Double, Double
> +Extended, and Quadruple Precision'; Brian Gladman, Vincenzo Innocente,
> +John Mather, and Paul Zimmermann at 
> +@url{<https://inria.hal.science/hal-03141101>}.  It does cover complex

you mean "It does not cover" ?

> +functions, or @code{jn}/@code{yn}, and it is only for x86_64, and for

or -> nor ?

> +rounding to nearest, and does not cover any architecture variations (in
> +particular IBM long double is out of scope).

also some results might differ on other x86_64's, due to the use of fma or not
for example (but we might ignore this level of detail)

> +For complex functions, some analysis of @theglibc{} math functions can be
> +found in 'Accuracy of Complex Mathematical Operations and Functions in Single
> +and Double Precision'; Paul Caprioli, Vincenzo Innocente, Paul Zimmermann
> +at @url{https://inria.hal.science/hal-04714173}.  It is only for x86_64,
> +and for rounding to nearest, and does not cover any architecture
> +variations.

ok

> +A "libm-test-ulps" is required only to test for extra constraints in
> +the math tests.  The file contains lines for maximal errors of single
> +functions, like:
> +
> +Function "yn":
> +float: 2
> +double: 6
> +
> +It means that if the "yn" shows error larger than 2 ULP for float
> +or 6 ULP for double, the related test for "symbol" will fail.  It can
> +be useful to check for correctly rounded implementation, where the
> +expected ULP is 0.
> +
> +The function is tested with default FE_TONEAREST rounding mode.  To
> +check with a differnt ione, the function definition name should be

differnt ione -> different one

> +prepended with an underline plus the rounding mode 'downward' (FE_DOWNWARD),
> +'towardzero' (FE_TOWARDZERO), or 'upward' (FE_UPWARD).  For instance,
> +
> +Function "yn_downward":
> +float: 3
> +double: 7
> +
> +It means that 'yn' will be check with FE_TOWARDZERO rounding mode

check -> checked
FE_TOWARDZERO -> FE_DOWNWARD

>  Note that the test drivers have an option "-u" to output an unsorted
>  list of all epsilons that the functions have.  The output can be read

it might be useful to output all inputs that yield the largest ulp error
(if not already available, this might be in a later patch)

Paul