math/bits: add examples for Add, Sub, Mul and Div

Change-Id: I2f3619aa827e18f356871511c20cf2c712f496b3
Reviewed-on: https://go-review.googlesource.com/c/go/+/353189
Run-TryBot: Ian Lance Taylor <iant@golang.org>
TryBot-Result: Go Bot <gobot@golang.org>
Reviewed-by: Ian Lance Taylor <iant@golang.org>
Trust: Keith Randall <khr@golang.org>

src/math/bits/example_math_test.go

@@ -0,0 +1,202 @@
+// Copyright 2021 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package bits_test
+
+import (
+	"fmt"
+	"math/bits"
+)
+
+func ExampleAdd32() {
+	// First number is 33<<32 + 12
+	n1 := []uint32{33, 12}
+	// Second number is 21<<32 + 23
+	n2 := []uint32{21, 23}
+	// Add them together without producing carry.
+	d1, carry := bits.Add32(n1[1], n2[1], 0)
+	d0, _ := bits.Add32(n1[0], n2[0], carry)
+	nsum := []uint32{d0, d1}
+	fmt.Printf("%v + %v = %v (carry bit was %v)\n", n1, n2, nsum, carry)
+
+	// First number is 1<<32 + 2147483648
+	n1 = []uint32{1, 0x80000000}
+	// Second number is 1<<32 + 2147483648
+	n2 = []uint32{1, 0x80000000}
+	// Add them together producing carry.
+	d1, carry = bits.Add32(n1[1], n2[1], 0)
+	d0, _ = bits.Add32(n1[0], n2[0], carry)
+	nsum = []uint32{d0, d1}
+	fmt.Printf("%v + %v = %v (carry bit was %v)\n", n1, n2, nsum, carry)
+	// Output:
+	// [33 12] + [21 23] = [54 35] (carry bit was 0)
+	// [1 2147483648] + [1 2147483648] = [3 0] (carry bit was 1)
+}
+
+func ExampleAdd64() {
+	// First number is 33<<64 + 12
+	n1 := []uint64{33, 12}
+	// Second number is 21<<64 + 23
+	n2 := []uint64{21, 23}
+	// Add them together without producing carry.
+	d1, carry := bits.Add64(n1[1], n2[1], 0)
+	d0, _ := bits.Add64(n1[0], n2[0], carry)
+	nsum := []uint64{d0, d1}
+	fmt.Printf("%v + %v = %v (carry bit was %v)\n", n1, n2, nsum, carry)
+
+	// First number is 1<<64 + 9223372036854775808
+	n1 = []uint64{1, 0x8000000000000000}
+	// Second number is 1<<64 + 9223372036854775808
+	n2 = []uint64{1, 0x8000000000000000}
+	// Add them together producing carry.
+	d1, carry = bits.Add64(n1[1], n2[1], 0)
+	d0, _ = bits.Add64(n1[0], n2[0], carry)
+	nsum = []uint64{d0, d1}
+	fmt.Printf("%v + %v = %v (carry bit was %v)\n", n1, n2, nsum, carry)
+	// Output:
+	// [33 12] + [21 23] = [54 35] (carry bit was 0)
+	// [1 9223372036854775808] + [1 9223372036854775808] = [3 0] (carry bit was 1)
+}
+
+func ExampleSub32() {
+	// First number is 33<<32 + 23
+	n1 := []uint32{33, 23}
+	// Second number is 21<<32 + 12
+	n2 := []uint32{21, 12}
+	// Sub them together without producing carry.
+	d1, carry := bits.Sub32(n1[1], n2[1], 0)
+	d0, _ := bits.Sub32(n1[0], n2[0], carry)
+	nsum := []uint32{d0, d1}
+	fmt.Printf("%v - %v = %v (carry bit was %v)\n", n1, n2, nsum, carry)
+
+	// First number is 3<<32 + 2147483647
+	n1 = []uint32{3, 0x7fffffff}
+	// Second number is 1<<32 + 2147483648
+	n2 = []uint32{1, 0x80000000}
+	// Sub them together producing carry.
+	d1, carry = bits.Sub32(n1[1], n2[1], 0)
+	d0, _ = bits.Sub32(n1[0], n2[0], carry)
+	nsum = []uint32{d0, d1}
+	fmt.Printf("%v - %v = %v (carry bit was %v)\n", n1, n2, nsum, carry)
+	// Output:
+	// [33 23] - [21 12] = [12 11] (carry bit was 0)
+	// [3 2147483647] - [1 2147483648] = [1 4294967295] (carry bit was 1)
+}
+
+func ExampleSub64() {
+	// First number is 33<<64 + 23
+	n1 := []uint64{33, 23}
+	// Second number is 21<<64 + 12
+	n2 := []uint64{21, 12}
+	// Sub them together without producing carry.
+	d1, carry := bits.Sub64(n1[1], n2[1], 0)
+	d0, _ := bits.Sub64(n1[0], n2[0], carry)
+	nsum := []uint64{d0, d1}
+	fmt.Printf("%v - %v = %v (carry bit was %v)\n", n1, n2, nsum, carry)
+
+	// First number is 3<<64 + 9223372036854775807
+	n1 = []uint64{3, 0x7fffffffffffffff}
+	// Second number is 1<<64 + 9223372036854775808
+	n2 = []uint64{1, 0x8000000000000000}
+	// Sub them together producing carry.
+	d1, carry = bits.Sub64(n1[1], n2[1], 0)
+	d0, _ = bits.Sub64(n1[0], n2[0], carry)
+	nsum = []uint64{d0, d1}
+	fmt.Printf("%v - %v = %v (carry bit was %v)\n", n1, n2, nsum, carry)
+	// Output:
+	// [33 23] - [21 12] = [12 11] (carry bit was 0)
+	// [3 9223372036854775807] - [1 9223372036854775808] = [1 18446744073709551615] (carry bit was 1)
+}
+
+func ExampleMul32() {
+	// First number is 0<<32 + 12
+	n1 := []uint32{0, 12}
+	// Second number is 0<<32 + 12
+	n2 := []uint32{0, 12}
+	// Multiply them together without producing overflow.
+	hi, lo := bits.Mul32(n1[1], n2[1])
+	nsum := []uint32{hi, lo}
+	fmt.Printf("%v * %v = %v\n", n1[1], n2[1], nsum)
+
+	// First number is 0<<32 + 2147483648
+	n1 = []uint32{0, 0x80000000}
+	// Second number is 0<<32 + 2
+	n2 = []uint32{0, 2}
+	// Multiply them together producing overflow.
+	hi, lo = bits.Mul32(n1[1], n2[1])
+	nsum = []uint32{hi, lo}
+	fmt.Printf("%v * %v = %v\n", n1[1], n2[1], nsum)
+	// Output:
+	// 12 * 12 = [0 144]
+	// 2147483648 * 2 = [1 0]
+}
+
+func ExampleMul64() {
+	// First number is 0<<64 + 12
+	n1 := []uint64{0, 12}
+	// Second number is 0<<64 + 12
+	n2 := []uint64{0, 12}
+	// Multiply them together without producing overflow.
+	hi, lo := bits.Mul64(n1[1], n2[1])
+	nsum := []uint64{hi, lo}
+	fmt.Printf("%v * %v = %v\n", n1[1], n2[1], nsum)
+
+	// First number is 0<<64 + 9223372036854775808
+	n1 = []uint64{0, 0x8000000000000000}
+	// Second number is 0<<64 + 2
+	n2 = []uint64{0, 2}
+	// Multiply them together producing overflow.
+	hi, lo = bits.Mul64(n1[1], n2[1])
+	nsum = []uint64{hi, lo}
+	fmt.Printf("%v * %v = %v\n", n1[1], n2[1], nsum)
+	// Output:
+	// 12 * 12 = [0 144]
+	// 9223372036854775808 * 2 = [1 0]
+}
+
+func ExampleDiv32() {
+	// First number is 0<<32 + 6
+	n1 := []uint32{0, 6}
+	// Second number is 0<<32 + 3
+	n2 := []uint32{0, 3}
+	// Divide them together.
+	quo, rem := bits.Div32(n1[0], n1[1], n2[1])
+	nsum := []uint32{quo, rem}
+	fmt.Printf("[%v %v] / %v = %v\n", n1[0], n1[1], n2[1], nsum)
+
+	// First number is 2<<32 + 2147483648
+	n1 = []uint32{2, 0x80000000}
+	// Second number is 0<<32 + 2147483648
+	n2 = []uint32{0, 0x80000000}
+	// Divide them together.
+	quo, rem = bits.Div32(n1[0], n1[1], n2[1])
+	nsum = []uint32{quo, rem}
+	fmt.Printf("[%v %v] / %v = %v\n", n1[0], n1[1], n2[1], nsum)
+	// Output:
+	// [0 6] / 3 = [2 0]
+	// [2 2147483648] / 2147483648 = [5 0]
+}
+
+func ExampleDiv64() {
+	// First number is 0<<64 + 6
+	n1 := []uint64{0, 6}
+	// Second number is 0<<64 + 3
+	n2 := []uint64{0, 3}
+	// Divide them together.
+	quo, rem := bits.Div64(n1[0], n1[1], n2[1])
+	nsum := []uint64{quo, rem}
+	fmt.Printf("[%v %v] / %v = %v\n", n1[0], n1[1], n2[1], nsum)
+
+	// First number is 2<<64 + 9223372036854775808
+	n1 = []uint64{2, 0x8000000000000000}
+	// Second number is 0<<64 + 9223372036854775808
+	n2 = []uint64{0, 0x8000000000000000}
+	// Divide them together.
+	quo, rem = bits.Div64(n1[0], n1[1], n2[1])
+	nsum = []uint64{quo, rem}
+	fmt.Printf("[%v %v] / %v = %v\n", n1[0], n1[1], n2[1], nsum)
+	// Output:
+	// [0 6] / 3 = [2 0]
+	// [2 9223372036854775808] / 9223372036854775808 = [5 0]
+}