binade
[1, 2)
All values here share exponent e.
ULP
0.125
2e - m, the local spacing.
real value
1.3125
The value before rounding.
nearest fp
1.25
Nearest discrete value in this toy format.
absolute error
0.0625
At most 0.5 ULP for round-to-nearest.
ULP error
0.5
How far the real value is from the nearest fp slot.
relative error
4.76e-2
Relative error is largest near the left edge of the binade because the same absolute error is divided by a smaller value.
For small precisions every representable value is drawn. For float32/float64, the plot samples markers because a single binade contains millions or quadrillions of values.
Note: this toy visualization only shows normalized floating point values; it does not model subnormals.