What

parse() does not lowercase the scheme, although it already lowercases the host:

const fastUri = require('fast-uri')

fastUri.parse('HTTP://EXAMPLE.com/p').scheme   // 'HTTP'  (host is 'example.com')
fastUri.normalize('HTTP://EXAMPLE.com/p')      // 'HTTP://example.com/p'

Why it's a bug

• RFC 3986 §6.2.2.1 (Case Normalization): "the scheme and host are case-insensitive and therefore should be normalized to lowercase." The host is normalized; the scheme is not.
• equal() already lowercases the scheme when comparing (fastUri.equal('HTTP://a', 'http://a') === true), so the library already treats the scheme as case-insensitive — normalize()/parse() were just inconsistent with that.
• uri-js (which this library aims to be iso-compatible with) returns the lowercased scheme:

require('uri-js').parse('HTTP://EXAMPLE.com/p').scheme   // 'http'
require('uri-js').normalize('HTTP://EXAMPLE.com/p')      // 'http://example.com/p'

Change

Lowercase the scheme at parse time, next to where the host is already lowercased — one line, no new branches.

Tests

Added test/scheme-normalization.test.js (red before the change, green after). Full npm run test:unit passes (878).