stdlib: Implement correctly rounded sqrt (4/4/4) #424
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Robust: 4/4 (Does it work for all input values?) Accurate: 4/4 (How accurate is the result?) Well behaved: 4/4 (Does it preserve math properties?) 算經.平方根 should return exactly the same result as Math.sqrt for all input numbers except -0, for which Math.sqrt(-0) = -0 complying to IEEE 754, but 算經.平方根(-0) = +0. This will also make the current implementation of hypot a tiny bit more accurate than before. I'll rate hypot 4/2/3 after this patch (previously 4/2/2) due to the following property being preserved when sqrt is correctly rounded: hypot(x, y) >= |x| && hypot(x, y) >= |y|
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stdlib: Implement correctly rounded sqrt (4/4/4)
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Robust: 4/4 (Does it work for all input values?)
Accurate: 4/4 (How accurate is the result?)
Well behaved: 4/4 (Does it preserve math properties?)
算經.平方根 should return exactly the same result as Math.sqrt for all input numbers except -0, for which Math.sqrt(-0) = -0 complying to IEEE 754, but 算經.平方根(-0) = +0.
This will also make the current implementation of hypot a tiny bit more accurate than before. I'll rate hypot 4/2/3 after this patch (previously 4/2/2) due to the following property being preserved when sqrt is correctly rounded:
hypot(x, y) >= |x| && hypot(x, y) >= |y|