More precise error estimate for elementary functions #3973
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eggrobin
approved these changes
Apr 9, 2024
| EXPECT_THAT(ULPDistance(std::cos(x), static_cast<double>(Cos(x))), | ||
| AnyOf(Eq(0), // Windows, macOS. | ||
| Eq(8))); // Linux. | ||
| EXPECT_THAT(ULPDistance(std::sin(x), Sin(x)), IsNear(9.89e-22_(1))); |
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Note: this is consistent with the result given by floating_point.wl:
In[1]:= << \
"C:\\Users\\robin\\Projects\\mockingbirdnest\\Principia\\mathematica\\\
floating_point.wl"
In[2]:= SetFloatingPointFormat[binary64]
In[3]:= SetRoundingMode[NearestTiesToEven]
In[4]:= x = 16^^16ac5b262ca1ff*2^797;
In[5]:= Block[{$MaxExtraPrecision = 300}, CorrectlyRound[Sin[x]]]
Out[5]= 1
In[6]:= Block[{$MaxExtraPrecision = 300},
N[UlpDistance[Sin[16^^16ac5b262ca1ff*2^797], 1], 10]]
Out[6]= 9.894194191*10^-22
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#1760.