Why doesn't python decimal library return the specified number of signficant figures for some inputs

Question

NB: this question is about significant figures. It is not a question about "digits after the decimal point" or anything like that.

EDIT: This question is not a duplicate of Significant figures in the decimal module. The two questions are asking about entirely different problems. I want to know why the function about does not return the desired value for a specific input. None of the answers to Significant figures in the decimal module address this question.

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The following function is supposed to return a string representation of a float with the specified number of significant figures:

import decimal

def to_sigfigs(value, sigfigs):
    return str(decimal.Context(prec=sigfigs).create_decimal(value))

At first glance, it seems to work:

print to_sigfigs(0.000003141592653589793, 5)
# 0.0000031416

print to_sigfigs(0.000001, 5)
# 0.0000010000

print to_sigfigs(3.141592653589793, 5)
# 3.1416

...but

print to_sigfigs(1.0, 5)
# 1

The desired output for the last expression (IOW, the 5-significant figure representation of 1.0) is the string '1.0000'. The actual output is the string '1'.

Am I misunderstanding something or is this a bug in decimal?

Answer 1

The precision of a context is a maximum precision; if an operation would produce a Decimal with less digits than the context's precision, it is not padded out to the context's precision.

When you call to_sigfigs(0.000001, 5), 0.000001 already has some rounding error due to the conversion from source code to binary floating point. It's actually 9.99999999999999954748111825886258685613938723690807819366455078125E-7. Rounding that to 5 significant figures gives decimal.Decimal("0.0000010000").

On the other hand, 1 is exactly representable in binary floating point, so 1.0 is exactly 1. Since only 1 digit is needed to represent this in decimal, the context's precision doesn't require any rounding, and you get a 1-digit Decimal result.

Answer 2

Is it a bug? I don't know, I don't think the documentation is tight enough to make that determination. It certainly is a surprising result.

It is possible to fix your own function with a little more logic.

def to_sigfigs(value, sigfigs):
    sign, digits, exponent = decimal.Context(prec=sigfigs).create_decimal(value).as_tuple()
    if len(digits) < sigfigs:
        missing = sigfigs - len(digits)
        digits = digits + (0,) * missing
        exponent -= missing
    return str(decimal.Decimal((sign, digits, exponent)))