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| 1 | +//! Two's Complement Representation |
| 2 | +//! |
| 3 | +//! Two's complement is a mathematical operation on binary numbers and a binary signed |
| 4 | +//! number representation. It is widely used in computing as the most common method of |
| 5 | +//! representing signed integers on computers. |
| 6 | +//! |
| 7 | +//! For more information: <https://en.wikipedia.org/wiki/Two%27s_complement> |
| 8 | + |
| 9 | +/// Takes a negative integer and returns its two's complement binary representation. |
| 10 | +/// |
| 11 | +/// The two's complement of a negative number is calculated by finding the binary |
| 12 | +/// representation that, when added to the positive value with the same magnitude, |
| 13 | +/// equals 2^n (where n is the number of bits). |
| 14 | +/// |
| 15 | +/// # Arguments |
| 16 | +/// |
| 17 | +/// * `number` - A non-positive integer (0 or negative) |
| 18 | +/// |
| 19 | +/// # Returns |
| 20 | +/// |
| 21 | +/// A `Result` containing: |
| 22 | +/// - `Ok(String)` - The two's complement representation with "0b" prefix |
| 23 | +/// - `Err(String)` - An error message if the input is positive |
| 24 | +/// |
| 25 | +/// # Examples |
| 26 | +/// |
| 27 | +/// ``` |
| 28 | +/// use the_algorithms_rust::bit_manipulation::twos_complement; |
| 29 | +/// |
| 30 | +/// assert_eq!(twos_complement(0).unwrap(), "0b0"); |
| 31 | +/// assert_eq!(twos_complement(-1).unwrap(), "0b11"); |
| 32 | +/// assert_eq!(twos_complement(-5).unwrap(), "0b1011"); |
| 33 | +/// assert_eq!(twos_complement(-17).unwrap(), "0b101111"); |
| 34 | +/// assert_eq!(twos_complement(-207).unwrap(), "0b100110001"); |
| 35 | +/// |
| 36 | +/// // Positive numbers return an error |
| 37 | +/// assert!(twos_complement(1).is_err()); |
| 38 | +/// ``` |
| 39 | +/// |
| 40 | +/// # Errors |
| 41 | +/// |
| 42 | +/// Returns an error if the input number is positive. |
| 43 | +pub fn twos_complement(number: i32) -> Result<String, String> { |
| 44 | + if number > 0 { |
| 45 | + return Err("input must be a negative integer".to_string()); |
| 46 | + } |
| 47 | + |
| 48 | + if number == 0 { |
| 49 | + return Ok("0b0".to_string()); |
| 50 | + } |
| 51 | + |
| 52 | + // Calculate the number of bits needed for the binary representation |
| 53 | + // (excluding the sign bit in the original representation) |
| 54 | + let binary_number_length = format!("{:b}", number.abs()).len(); |
| 55 | + |
| 56 | + // Calculate two's complement value |
| 57 | + // This is equivalent to: abs(number) - 2^binary_number_length |
| 58 | + let twos_complement_value = (number.abs() as i64) - (1_i64 << binary_number_length); |
| 59 | + |
| 60 | + // Format as binary string (removing the negative sign) |
| 61 | + let mut twos_complement_str = format!("{:b}", twos_complement_value.abs()); |
| 62 | + |
| 63 | + // Add leading zeros if necessary |
| 64 | + let padding_zeros = binary_number_length.saturating_sub(twos_complement_str.len()); |
| 65 | + if padding_zeros > 0 { |
| 66 | + twos_complement_str = format!("{}{twos_complement_str}", "0".repeat(padding_zeros)); |
| 67 | + } |
| 68 | + |
| 69 | + // Add leading '1' to indicate negative number in two's complement |
| 70 | + Ok(format!("0b1{twos_complement_str}")) |
| 71 | +} |
| 72 | + |
| 73 | +#[cfg(test)] |
| 74 | +mod tests { |
| 75 | + use super::*; |
| 76 | + |
| 77 | + #[test] |
| 78 | + fn test_zero() { |
| 79 | + assert_eq!(twos_complement(0).unwrap(), "0b0"); |
| 80 | + } |
| 81 | + |
| 82 | + #[test] |
| 83 | + fn test_negative_one() { |
| 84 | + assert_eq!(twos_complement(-1).unwrap(), "0b11"); |
| 85 | + } |
| 86 | + |
| 87 | + #[test] |
| 88 | + fn test_negative_five() { |
| 89 | + assert_eq!(twos_complement(-5).unwrap(), "0b1011"); |
| 90 | + } |
| 91 | + |
| 92 | + #[test] |
| 93 | + fn test_negative_seventeen() { |
| 94 | + assert_eq!(twos_complement(-17).unwrap(), "0b101111"); |
| 95 | + } |
| 96 | + |
| 97 | + #[test] |
| 98 | + fn test_negative_two_hundred_seven() { |
| 99 | + assert_eq!(twos_complement(-207).unwrap(), "0b100110001"); |
| 100 | + } |
| 101 | + |
| 102 | + #[test] |
| 103 | + fn test_negative_small_values() { |
| 104 | + assert_eq!(twos_complement(-2).unwrap(), "0b110"); |
| 105 | + assert_eq!(twos_complement(-3).unwrap(), "0b101"); |
| 106 | + assert_eq!(twos_complement(-4).unwrap(), "0b1100"); |
| 107 | + } |
| 108 | + |
| 109 | + #[test] |
| 110 | + fn test_negative_larger_values() { |
| 111 | + assert_eq!(twos_complement(-128).unwrap(), "0b110000000"); |
| 112 | + assert_eq!(twos_complement(-255).unwrap(), "0b100000001"); |
| 113 | + assert_eq!(twos_complement(-1000).unwrap(), "0b10000011000"); |
| 114 | + } |
| 115 | + |
| 116 | + #[test] |
| 117 | + fn test_positive_number_returns_error() { |
| 118 | + let result = twos_complement(1); |
| 119 | + assert!(result.is_err()); |
| 120 | + assert_eq!(result.unwrap_err(), "input must be a negative integer"); |
| 121 | + } |
| 122 | + |
| 123 | + #[test] |
| 124 | + fn test_large_positive_number_returns_error() { |
| 125 | + let result = twos_complement(100); |
| 126 | + assert!(result.is_err()); |
| 127 | + assert_eq!(result.unwrap_err(), "input must be a negative integer"); |
| 128 | + } |
| 129 | + |
| 130 | + #[test] |
| 131 | + fn test_edge_case_negative_powers_of_two() { |
| 132 | + assert_eq!(twos_complement(-8).unwrap(), "0b11000"); |
| 133 | + assert_eq!(twos_complement(-16).unwrap(), "0b110000"); |
| 134 | + assert_eq!(twos_complement(-32).unwrap(), "0b1100000"); |
| 135 | + assert_eq!(twos_complement(-64).unwrap(), "0b11000000"); |
| 136 | + } |
| 137 | +} |
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