Lesson 03 · Sign and canonical zero - Build an Arbitrary-Precision Integer Library

Sign and canonical zero

A magnitude only carries size, not direction. Today you wrap it in the public BigInt type - a magnitude plus a sign - and make zero canonical so a negative zero can never exist.

The goal

Define BigInt as a signed magnitude and report its sign, with zero always sign 0.

Start here - the target

TO DO

Scenario: BigInt pairs a magnitude with a sign and forbids negative zero

Giventhe BigInt built from the machine integer -5

Whenits sign is queried

ThenSign() is -1 and IsZero() is false

Andthe BigInt built from 0 has Sign() 0, IsZero() true, and an empty magnitude (no negative zero), while the BigInt from 7 has Sign() 1

Background

A magnitude tells you how big a number is but not whether it is positive or negative. The public type, BigInt, adds that: a sign alongside the magnitude. We use -1, 0, and +1 for the sign, and we hold one firm rule - the sign is 0 if and only if the magnitude is empty. That is what makes zero canonical: there is exactly one zero, and it is never negative.

NewFromInt64 is where this rule first bites. Take the absolute value into a magnitude, set the sign from the input, but if the magnitude comes out empty force the sign back to 0. Getting this invariant right once, here, means every later operation can simply preserve it: whenever an operation produces an empty magnitude, it sets the sign to 0, and negative zero never appears.

Make it work

type BigInt struct {
  sign int // -1, 0, or +1; 0 only for zero
  mag  mag // normalized magnitude, empty when zero
}
func NewFromInt64(n int64) BigInt {
  // set sign from n, build mag from the absolute value,
  // and force sign 0 when the magnitude is empty
}
func (x BigInt) Sign() int { return x.sign }

CheckpointDONE

BigInt is a signed magnitude with a canonical zero. Commit and stop here.