example_math_test.go

     1  // Copyright 2021 The Go Authors. All rights reserved.
     2  // Use of this source code is governed by a BSD-style
     3  // license that can be found in the LICENSE file.
     4  
     5  package bits_test
     6  
     7  import (
     8  	"fmt"
     9  	"math/bits"
    10  )
    11  
    12  func ExampleAdd32() {
    13  	// First number is 33<<32 + 12
    14  	n1 := []uint32{33, 12}
    15  	// Second number is 21<<32 + 23
    16  	n2 := []uint32{21, 23}
    17  	// Add them together without producing carry.
    18  	d1, carry := bits.Add32(n1[1], n2[1], 0)
    19  	d0, _ := bits.Add32(n1[0], n2[0], carry)
    20  	nsum := []uint32{d0, d1}
    21  	fmt.Printf("%v + %v = %v (carry bit was %v)\n", n1, n2, nsum, carry)
    22  
    23  	// First number is 1<<32 + 2147483648
    24  	n1 = []uint32{1, 0x80000000}
    25  	// Second number is 1<<32 + 2147483648
    26  	n2 = []uint32{1, 0x80000000}
    27  	// Add them together producing carry.
    28  	d1, carry = bits.Add32(n1[1], n2[1], 0)
    29  	d0, _ = bits.Add32(n1[0], n2[0], carry)
    30  	nsum = []uint32{d0, d1}
    31  	fmt.Printf("%v + %v = %v (carry bit was %v)\n", n1, n2, nsum, carry)
    32  	// Output:
    33  	// [33 12] + [21 23] = [54 35] (carry bit was 0)
    34  	// [1 2147483648] + [1 2147483648] = [3 0] (carry bit was 1)
    35  }
    36  
    37  func ExampleAdd64() {
    38  	// First number is 33<<64 + 12
    39  	n1 := []uint64{33, 12}
    40  	// Second number is 21<<64 + 23
    41  	n2 := []uint64{21, 23}
    42  	// Add them together without producing carry.
    43  	d1, carry := bits.Add64(n1[1], n2[1], 0)
    44  	d0, _ := bits.Add64(n1[0], n2[0], carry)
    45  	nsum := []uint64{d0, d1}
    46  	fmt.Printf("%v + %v = %v (carry bit was %v)\n", n1, n2, nsum, carry)
    47  
    48  	// First number is 1<<64 + 9223372036854775808
    49  	n1 = []uint64{1, 0x8000000000000000}
    50  	// Second number is 1<<64 + 9223372036854775808
    51  	n2 = []uint64{1, 0x8000000000000000}
    52  	// Add them together producing carry.
    53  	d1, carry = bits.Add64(n1[1], n2[1], 0)
    54  	d0, _ = bits.Add64(n1[0], n2[0], carry)
    55  	nsum = []uint64{d0, d1}
    56  	fmt.Printf("%v + %v = %v (carry bit was %v)\n", n1, n2, nsum, carry)
    57  	// Output:
    58  	// [33 12] + [21 23] = [54 35] (carry bit was 0)
    59  	// [1 9223372036854775808] + [1 9223372036854775808] = [3 0] (carry bit was 1)
    60  }
    61  
    62  func ExampleSub32() {
    63  	// First number is 33<<32 + 23
    64  	n1 := []uint32{33, 23}
    65  	// Second number is 21<<32 + 12
    66  	n2 := []uint32{21, 12}
    67  	// Sub them together without producing carry.
    68  	d1, carry := bits.Sub32(n1[1], n2[1], 0)
    69  	d0, _ := bits.Sub32(n1[0], n2[0], carry)
    70  	nsum := []uint32{d0, d1}
    71  	fmt.Printf("%v - %v = %v (carry bit was %v)\n", n1, n2, nsum, carry)
    72  
    73  	// First number is 3<<32 + 2147483647
    74  	n1 = []uint32{3, 0x7fffffff}
    75  	// Second number is 1<<32 + 2147483648
    76  	n2 = []uint32{1, 0x80000000}
    77  	// Sub them together producing carry.
    78  	d1, carry = bits.Sub32(n1[1], n2[1], 0)
    79  	d0, _ = bits.Sub32(n1[0], n2[0], carry)
    80  	nsum = []uint32{d0, d1}
    81  	fmt.Printf("%v - %v = %v (carry bit was %v)\n", n1, n2, nsum, carry)
    82  	// Output:
    83  	// [33 23] - [21 12] = [12 11] (carry bit was 0)
    84  	// [3 2147483647] - [1 2147483648] = [1 4294967295] (carry bit was 1)
    85  }
    86  
    87  func ExampleSub64() {
    88  	// First number is 33<<64 + 23
    89  	n1 := []uint64{33, 23}
    90  	// Second number is 21<<64 + 12
    91  	n2 := []uint64{21, 12}
    92  	// Sub them together without producing carry.
    93  	d1, carry := bits.Sub64(n1[1], n2[1], 0)
    94  	d0, _ := bits.Sub64(n1[0], n2[0], carry)
    95  	nsum := []uint64{d0, d1}
    96  	fmt.Printf("%v - %v = %v (carry bit was %v)\n", n1, n2, nsum, carry)
    97  
    98  	// First number is 3<<64 + 9223372036854775807
    99  	n1 = []uint64{3, 0x7fffffffffffffff}
   100  	// Second number is 1<<64 + 9223372036854775808
   101  	n2 = []uint64{1, 0x8000000000000000}
   102  	// Sub them together producing carry.
   103  	d1, carry = bits.Sub64(n1[1], n2[1], 0)
   104  	d0, _ = bits.Sub64(n1[0], n2[0], carry)
   105  	nsum = []uint64{d0, d1}
   106  	fmt.Printf("%v - %v = %v (carry bit was %v)\n", n1, n2, nsum, carry)
   107  	// Output:
   108  	// [33 23] - [21 12] = [12 11] (carry bit was 0)
   109  	// [3 9223372036854775807] - [1 9223372036854775808] = [1 18446744073709551615] (carry bit was 1)
   110  }
   111  
   112  func ExampleMul32() {
   113  	// First number is 0<<32 + 12
   114  	n1 := []uint32{0, 12}
   115  	// Second number is 0<<32 + 12
   116  	n2 := []uint32{0, 12}
   117  	// Multiply them together without producing overflow.
   118  	hi, lo := bits.Mul32(n1[1], n2[1])
   119  	nsum := []uint32{hi, lo}
   120  	fmt.Printf("%v * %v = %v\n", n1[1], n2[1], nsum)
   121  
   122  	// First number is 0<<32 + 2147483648
   123  	n1 = []uint32{0, 0x80000000}
   124  	// Second number is 0<<32 + 2
   125  	n2 = []uint32{0, 2}
   126  	// Multiply them together producing overflow.
   127  	hi, lo = bits.Mul32(n1[1], n2[1])
   128  	nsum = []uint32{hi, lo}
   129  	fmt.Printf("%v * %v = %v\n", n1[1], n2[1], nsum)
   130  	// Output:
   131  	// 12 * 12 = [0 144]
   132  	// 2147483648 * 2 = [1 0]
   133  }
   134  
   135  func ExampleMul64() {
   136  	// First number is 0<<64 + 12
   137  	n1 := []uint64{0, 12}
   138  	// Second number is 0<<64 + 12
   139  	n2 := []uint64{0, 12}
   140  	// Multiply them together without producing overflow.
   141  	hi, lo := bits.Mul64(n1[1], n2[1])
   142  	nsum := []uint64{hi, lo}
   143  	fmt.Printf("%v * %v = %v\n", n1[1], n2[1], nsum)
   144  
   145  	// First number is 0<<64 + 9223372036854775808
   146  	n1 = []uint64{0, 0x8000000000000000}
   147  	// Second number is 0<<64 + 2
   148  	n2 = []uint64{0, 2}
   149  	// Multiply them together producing overflow.
   150  	hi, lo = bits.Mul64(n1[1], n2[1])
   151  	nsum = []uint64{hi, lo}
   152  	fmt.Printf("%v * %v = %v\n", n1[1], n2[1], nsum)
   153  	// Output:
   154  	// 12 * 12 = [0 144]
   155  	// 9223372036854775808 * 2 = [1 0]
   156  }
   157  
   158  func ExampleDiv32() {
   159  	// First number is 0<<32 + 6
   160  	n1 := []uint32{0, 6}
   161  	// Second number is 0<<32 + 3
   162  	n2 := []uint32{0, 3}
   163  	// Divide them together.
   164  	quo, rem := bits.Div32(n1[0], n1[1], n2[1])
   165  	nsum := []uint32{quo, rem}
   166  	fmt.Printf("[%v %v] / %v = %v\n", n1[0], n1[1], n2[1], nsum)
   167  
   168  	// First number is 2<<32 + 2147483648
   169  	n1 = []uint32{2, 0x80000000}
   170  	// Second number is 0<<32 + 2147483648
   171  	n2 = []uint32{0, 0x80000000}
   172  	// Divide them together.
   173  	quo, rem = bits.Div32(n1[0], n1[1], n2[1])
   174  	nsum = []uint32{quo, rem}
   175  	fmt.Printf("[%v %v] / %v = %v\n", n1[0], n1[1], n2[1], nsum)
   176  	// Output:
   177  	// [0 6] / 3 = [2 0]
   178  	// [2 2147483648] / 2147483648 = [5 0]
   179  }
   180  
   181  func ExampleDiv64() {
   182  	// First number is 0<<64 + 6
   183  	n1 := []uint64{0, 6}
   184  	// Second number is 0<<64 + 3
   185  	n2 := []uint64{0, 3}
   186  	// Divide them together.
   187  	quo, rem := bits.Div64(n1[0], n1[1], n2[1])
   188  	nsum := []uint64{quo, rem}
   189  	fmt.Printf("[%v %v] / %v = %v\n", n1[0], n1[1], n2[1], nsum)
   190  
   191  	// First number is 2<<64 + 9223372036854775808
   192  	n1 = []uint64{2, 0x8000000000000000}
   193  	// Second number is 0<<64 + 9223372036854775808
   194  	n2 = []uint64{0, 0x8000000000000000}
   195  	// Divide them together.
   196  	quo, rem = bits.Div64(n1[0], n1[1], n2[1])
   197  	nsum = []uint64{quo, rem}
   198  	fmt.Printf("[%v %v] / %v = %v\n", n1[0], n1[1], n2[1], nsum)
   199  	// Output:
   200  	// [0 6] / 3 = [2 0]
   201  	// [2 9223372036854775808] / 9223372036854775808 = [5 0]
   202  }
   203
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