fractiondemo.gno

 1// Package fractiondemo is a small gnoweb demo of the exact rational arithmetic
 2// provided by the [p/moul/x/daily/fraction](/p/moul/x/daily/fraction/v0)
 3// library: it shows thirds summing to exactly one, and a comparison that a
 4// decimal detour would get wrong.
 5//
 6// It contains no arithmetic of its own. Stateless, so Render is deterministic.
 7package fractiondemo
 8
 9import (
10	"strings"
11
12	"gno.land/p/moul/x/daily/fraction/v0"
13)
14
15// Render renders the demo for gnoweb.
16func Render(path string) string {
17	var b strings.Builder
18	b.WriteString("# Fractions\n\n")
19	b.WriteString("Exact rational arithmetic, demoing the ")
20	b.WriteString("[`p/moul/x/daily/fraction`](/p/moul/x/daily/fraction/v0) library.\n\n")
21
22	third, _ := fraction.New(1, 3)
23	sum, _ := third.Add(third)
24	sum, _ = sum.Add(third)
25
26	b.WriteString("## A third, three times\n\n")
27	b.WriteString("`1/3 + 1/3 + 1/3` = **")
28	b.WriteString(sum.String())
29	b.WriteString("**, exactly — not 0.9999…\n\n")
30	b.WriteString("As a decimal it is only ever an approximation: `")
31	b.WriteString(fraction.Decimal(third, 10))
32	b.WriteString("`\n")
33
34	half, _ := fraction.New(1, 2)
35	b.WriteString("\n## Arithmetic\n\n| expression | result |\n|---|---|\n")
36	add, _ := half.Add(third)
37	sub, _ := half.Sub(third)
38	mul, _ := half.Mul(third)
39	div, _ := half.Div(third)
40	row(&b, "1/2 + 1/3", add.String())
41	row(&b, "1/2 - 1/3", sub.String())
42	row(&b, "1/2 × 1/3", mul.String())
43	row(&b, "1/2 ÷ 1/3", div.String())
44
45	approx, _ := fraction.New(33333, 100000)
46	b.WriteString("\n## Exact comparison\n\n")
47	b.WriteString("`1/3` vs `33333/100000` — identical to five decimal places, ")
48	b.WriteString("yet the library still knows which is larger: **")
49	if third.Cmp(approx) > 0 {
50		b.WriteString("1/3 is greater")
51	} else {
52		b.WriteString("33333/100000 is greater or equal")
53	}
54	b.WriteString("**\n\n")
55	b.WriteString("> Comparison cross-multiplies, so it never takes a decimal detour. ")
56	b.WriteString("There are no floats here: on a chain, an answer that depends on ")
57	b.WriteString("rounding is a consensus bug.\n")
58	return b.String()
59}
60
61func row(b *strings.Builder, expr, res string) {
62	b.WriteString("| `")
63	b.WriteString(expr)
64	b.WriteString("` | `")
65	b.WriteString(res)
66	b.WriteString("` |\n")
67}