Lesson 06 · Rendering a magnitude to decimal - Build an Arbitrary-Precision Integer Library

Rendering a magnitude to decimal

Reading decimal in, we now write it back out. The catch is padding - every limb except the most significant must print as exactly nine digits, or the digits shift. Today you render a magnitude to its decimal string.

The goal

Render a magnitude to decimal with the top limb unpadded and every lower limb zero-padded to nine digits.

Start here - the target

TO DO

Scenario: Lower limbs pad to nine digits so interior zeros survive

Givena magnitude with limbs (1, 0, 1) from least significant to most

Whenit is rendered to decimal

Thenit is "1000000000000000001" (the middle zero limb prints as nine zeros)

Andthe magnitude with limbs (0, 1) renders as "1000000000", and the empty magnitude renders as "0"

Background

Rendering is grouping in reverse: print the limbs from most significant to least and concatenate. The trap is that a limb like 5 means the digits 000000005 everywhere except at the very top of the number. So the most-significant limb prints plainly (no leading zeros), and every limb below it is zero-padded to exactly nine digits. Miss the padding and (1, 0, 1) would print as "101" instead of "1000000000000000001" - the interior zero limb would vanish and every digit above it would slide nine places.

Empty magnitude is the base case: it renders as "0". With this and the parser you have a complete magnitude round-trip; next lesson adds the sign and confirms the whole loop closes on some genuinely large numbers.

Make it work

// most-significant limb plain; every lower limb padded to 9 digits
func (m mag) String() string {
  if len(m) == 0 { return "0" }
  s := strconv.Itoa(int(m[len(m)-1]))
  for i := len(m) - 2; i >= 0; i-- {
    s += fmt.Sprintf("%09d", m[i]) // zero-pad to nine
  }
  return s
}

CheckpointDONE

A magnitude renders back to its exact decimal string. Commit and stop here.