Improve accuracy testing method#4
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The range1 should be [0.140625,pi/2], which is from 0x3E10 (0.140625) to 0x3FC9 (1.5703125, rounded pi/2) and the representable number is 441 not 450. Since the inf and -inf in BF16 are 0x7F80 and 0xFF80, the test range2 should be fixed as [pi/2,+largest], where +largest is the largest positive normal BF16, that is +largest=0x7F7F. Similarly, range3 should fixed as [-smallest, -largest], where -largest is the largest negative normal BF16, that is +largest=0xFF7F.
The current accuracy testing method is based on the sinf implementation
in glibc. This implementation, introduced by Wilco Dijkstra in
release 2.29 [1], reports:
Worst-case ULP is 0.5607, maximum relative error is 0.5303 * 2^-23
Use GNU MPFR (GNU Multiple Precision Floating-Point Reliable) [3], a
verified high-precision floating-point library, as the comparison
baseline—similar to the approach used in glibc benchtests.
This avoids relying on any particular standard library.
Reference:
[1] glibc - release 2.29 - s_sinf.c
[2] Gladman, B., Innocente, V., Mather, J., & Zimmermann, P. (2025).
Accuracy of mathematical functions in single, double, double
extended, and quadruple precision.
[3] https://www.mpfr.org/
Signed-off-by: jouae <oipc9801@gmail.com>
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Improve testing method, including
For example, range1.log
The difference of output is as following:
Close issue #3
Reference:
[1] https://www.mpfr.org/