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uxarray.utils.computing._err_fmac

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uxarray.utils.computing._err_fmac#

uxarray.utils.computing._err_fmac(a, b, c)#

Error-free transformation for the FMA operation. such that x = FMA(a,b,c) and a * b + c = x + y + z exactly. Thhis function is only available in round to the nearest mode and takes approximately 17 flops

Parameters:

  • a (float) – The operands for the FMA operation.

  • b (float) – The operands for the FMA operation.

  • c (float) – The operands for the FMA operation.

Returns:

The result of the FMA operation and two error terms.

Return type:

tuple of float

References

Graillat, Stef & Langlois, Philippe & Louvet, Nicolas. (2006). Improving the compensated Horner scheme with a Fused Multiply and Add. 2. 1323-1327. 10.1145/1141277.1141585.

Ogita, Takeshi & Rump, Siegfried & Oishi, Shin’ichi. (2005). Accurate Sum and Dot Product. SIAM J. Scientific Computing. 26. 1955-1988. 10.1137/030601818.

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