How Accurate is float64 to uint64 Conversion in Go, Considering Precision Limits?

Converting float64 to uint64: Precision and Representation

When attempting to convert a float64 number to uint64, it's important to consider the precision and representation differences between the two data types.

Constant Representation

Constants in Go are represented with arbitrary precision, meaning they can represent values of very large magnitude without losing accuracy.

Floating-Point Representation

On the other hand, floating-point numbers like float64 follow the IEEE 754 standard, which uses 52 bits (out of 64) to store the significand (the digits). Consequently, float64 can represent a maximum of 2^52 digits.

Precision Issues

In the example provided, the constant value 6161047830682206209 cannot be precisely represented by a float64 because it contains more than 52 digits. When assigned to a float64 variable n, the value is rounded and truncated, resulting in a slight difference from the original constant.

Conversion Considerations

Upon converting n to uint64, the fractional part is discarded, further reducing the accuracy of the representation. This is because uint64 represents only whole numbers without a fractional component.

Calculating Digit Capacity

To determine the maximum number of digits that can be precisely represented by float64, we calculate 2^52, which yields 9007199254740992. Any constant larger than this value will face precision issues when stored in a float64.

Verifying the Value

Printing the original n float64 value reveals that it has already been rounded to 6161047830682206208, which differs slightly from the original constant. This demonstrates that the problem lies in the imprecise conversion from the constant to float64, rather than in the subsequent conversion to uint64.

Smaller Numbers

For smaller numbers whose digits can be precisely represented by float64 (e.g., 7830682206209), the conversion to uint64 works as expected, preserving the original value.

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