Unsigned 64-bit integer operations
Module std::math::u64 contains a set of procedures which can be used to perform unsigned 64-bit integer operations. These operations fall into the following categories:
- Arithmetic operations - addition, multiplication, division etc.
- Comparison operations - equality, less than, greater than etc.
- Bitwise operations - binary AND, OR, XOR, bit shifts etc.
All procedures assume that an unsigned 64-bit integer (u64) is encoded using two elements, each containing an unsigned 32-bit integer (u32). When placed on the stack, the least-significant limb is assumed to be deeper in the stack. For example, a u64 value a consisting of limbs a_hi and a_lo would be position on the stack like so:
[a_hi, a_lo, ... ]
Many of the procedures listed below (e.g., overflowing_add, wrapping_add, lt) do not check whether the inputs are encoded using valid u32 values. These procedures do not fail when the inputs are encoded incorrectly, but rather produce undefined results. Thus, it is important to be certain that limbs of input values are valid u32 values prior to calling such procedures.
Arithmetic operations
| Procedure | Description |
|---|---|
| overflowing_add | Performs addition of two unsigned 64-bit integers preserving the overflow. The input values are assumed to be represented using 32-bit limbs, but this is not checked. The stack transition looks as follows: [b_hi, b_lo, a_hi, a_lo, ...] -> [overflow_flag, c_hi, c_lo, ...], where c = (a + b) % 2^64 This takes 6 cycles. |
| wrapping_add | Performs addition of two unsigned 64-bit integers discarding the overflow. The input values are assumed to be represented using 32-bit limbs, but this is not checked. The stack transition looks as follows: [b_hi, b_lo, a_hi, a_lo, ...] -> [c_hi, c_lo, ...], where c = (a + b) % 2^64 This takes 7 cycles. |
| overflowing_sub | Performs subtraction of two unsigned 64-bit integers preserving the overflow. The input values are assumed to be represented using 32-bit limbs, but this is not checked. The stack transition looks as follows: [b_hi, b_lo, a_hi, a_lo, ...] -> [underflow_flag, c_hi, c_lo, ...], where c = (a - b) % 2^64 This takes 11 cycles. |
| wrapping_sub | Performs subtraction of two unsigned 64-bit integers discarding the overflow. The input values are assumed to be represented using 32-bit limbs, but this is not checked. The stack transition looks as follows: [b_hi, b_lo, a_hi, a_lo, ...] -> [c_hi, c_lo, ...], where c = (a - b) % 2^64 This takes 10 cycles. |
| overflowing_mul | Performs multiplication of two unsigned 64-bit integers preserving the overflow. The input values are assumed to be represented using 32-bit limbs, but this is not checked. The stack transition looks as follows: [b_hi, b_lo, a_hi, a_lo, ...] -> [c_hi_hi, c_hi_lo, c_lo_hi, c_lo_lo, ...], where c = (a * b) % 2^64 This takes 18 cycles. |
| wrapping_mul | Performs multiplication of two unsigned 64-bit integers discarding the overflow. The input values are assumed to be represented using 32-bit limbs, but this is not checked. The stack transition looks as follows: [b_hi, b_lo, a_hi, a_lo, ...] -> [c_hi, c_lo, ...], where c = (a * b) % 2^64 This takes 11 cycles. |
| div | Performs division of two unsigned 64-bit integers discarding the remainder. The input values are assumed to be represented using 32-bit limbs, but this is not checked. The stack transition looks as follows: [b_hi, b_lo, a_hi, a_lo, ...] -> [c_hi, c_lo, ...], where c = a // b This takes 54 cycles. |
| mod | Performs modulo operation of two unsigned 64-bit integers. The input values are assumed to be represented using 32-bit limbs, but this is not checked. The stack transition looks as follows: [b_hi, b_lo, a_hi, a_lo, ...] -> [c_hi, c_lo, ...], where c = a % b This takes 54 cycles. |
| divmod | Performs divmod operation of two unsigned 64-bit integers. The input values are assumed to be represented using 32-bit limbs, but this is not checked. The stack transition looks as follows: [b_hi, b_lo, a_hi, a_lo, ...] -> [r_hi, r_lo, q_hi, q_lo ...], where r = a % b, q = a // b This takes 54 cycles. |
Comparison operations
| Procedure | Description |
|---|---|
| lt | Performs less-than comparison of two unsigned 64-bit integers. The input values are assumed to be represented using 32-bit limbs, but this is not checked. The stack transition looks as follows: [b_hi, b_lo, a_hi, a_lo, ...] -> [c, ...], where c = 1 when a < b, and 0 otherwise. This takes 11 cycles. |
| gt | Performs greater-than comparison of two unsigned 64-bit integers. The input values are assumed to be represented using 32-bit limbs, but this is not checked. The stack transition looks as follows: [b_hi, b_lo, a_hi, a_lo, ...] -> [c, ...], where c = 1 when a > b, and 0 otherwise. This takes 11 cycles. |
| lte | Performs less-than-or-equal comparison of two unsigned 64-bit integers. The input values are assumed to be represented using 32-bit limbs, but this is not checked. The stack transition looks as follows: [b_hi, b_lo, a_hi, a_lo, ...] -> [c, ...], where c = 1 when a <= b, and 0 otherwise. This takes 12 cycles. |
| gte | Performs greater-than-or-equal comparison of two unsigned 64-bit integers. The input values are assumed to be represented using 32-bit limbs, but this is not checked. The stack transition looks as follows: [b_hi, b_lo, a_hi, a_lo, ...] -> [c, ...], where c = 1 when a >= b, and 0 otherwise. This takes 12 cycles. |
| eq | Performs equality comparison of two unsigned 64-bit integers. The input values are assumed to be represented using 32-bit limbs, but this is not checked. The stack transition looks as follows: [b_hi, b_lo, a_hi, a_lo, ...] -> [c, ...], where c = 1 when a == b, and 0 otherwise. This takes 6 cycles. |
| neq | Performs inequality comparison of two unsigned 64-bit integers. The input values are assumed to be represented using 32-bit limbs, but this is not checked. The stack transition looks as follows: [b_hi, b_lo, a_hi, a_lo, ...] -> [c, ...], where c = 1 when a != b, and 0 otherwise. This takes 6 cycles. |
| eqz | Performs comparison to zero of an unsigned 64-bit integer. The input value is assumed to be represented using 32-bit limbs, but this is not checked. The stack transition looks as follows: [a_hi, a_lo, ...] -> [c, ...], where c = 1 when a == 0, and 0 otherwise. This takes 4 cycles. |
| min | Compares two unsigned 64-bit integers and drop the larger one from the stack. The input values are assumed to be represented using 32-bit limbs, but this is not checked. The stack transition looks as follows: [b_hi, b_lo, a_hi, a_lo, ...] -> [c_hi, c_lo, ...], where c = a when a < b, and b otherwise. This takes 23 cycles. |
| max | Compares two unsigned 64-bit integers and drop the smaller one from the stack. The input values are assumed to be represented using 32-bit limbs, but this is not checked. The stack transition looks as follows: [b_hi, b_lo, a_hi, a_lo, ...] -> [c_hi, c_lo, ...], where c = a when a > b, and b otherwise. This takes 23 cycles. |
Bitwise operations
| Procedure | Description |
|---|---|
| and | Performs bitwise AND of two unsigned 64-bit integers. The input values are assumed to be represented using 32-bit limbs, but this is not checked. The stack transition looks as follows: [b_hi, b_lo, a_hi, a_lo, ...] -> [c_hi, c_lo, ...], where c = a AND b. This takes 6 cycles. |
| or | Performs bitwise OR of two unsigned 64-bit integers. The input values are expected to be represented using 32-bit limbs, and the procedure will fail if they are not. The stack transition looks as follows: [b_hi, b_lo, a_hi, a_lo, ...] -> [c_hi, c_lo, ...], where c = a OR b. This takes 16 cycles. |
| xor | Performs bitwise XOR of two unsigned 64-bit integers. The input values are expected to be represented using 32-bit limbs, and the procedure will fail if they are not. The stack transition looks as follows: [b_hi, b_lo, a_hi, a_lo, ...] -> [c_hi, c_lo, ...], where c = a XOR b. This takes 6 cycles. |
| shl | Performs left shift of one unsigned 64-bit integer using the pow2 operation. The input value to be shifted is assumed to be represented using 32-bit limbs. The shift value should be in the range [0, 64), otherwise it will result in an error. The stack transition looks as follows: [b, a_hi, a_lo, ...] -> [c_hi, c_lo, ...], where c = a << b mod 2^64. This takes 28 cycles. |
| shr | Performs right shift of one unsigned 64-bit integer using the pow2 operation. The input value to be shifted is assumed to be represented using 32-bit limbs. The shift value should be in the range [0, 64), otherwise it will result in an error. The stack transition looks as follows: [b, a_hi, a_lo, ...] -> [c_hi, c_lo, ...], where c = a >> b. This takes 44 cycles. |
| rotl | Performs left rotation of one unsigned 64-bit integer using the pow2 operation. The input value to be shifted is assumed to be represented using 32-bit limbs. The shift value should be in the range [0, 64), otherwise it will result in an error. The stack transition looks as follows: [b, a_hi, a_lo, ...] -> [c_hi, c_lo, ...], where c = a << b mod 2^64. This takes 35 cycles. |
| rotr | Performs right rotation of one unsigned 64-bit integer using the pow2 operation. The input value to be shifted is assumed to be represented using 32-bit limbs. The shift value should be in the range [0, 64), otherwise it will result in an error. The stack transition looks as follows: [b, a_hi, a_lo, ...] -> [c_hi, c_lo, ...], where c = a << b mod 2^64. This takes 40 cycles. |
| clz | Counts the number of leading zeros of one unsigned 64-bit integer. The input value is assumed to be represented using 32 bit limbs, but this is not checked. The stack transition looks as follows: [n_hi, n_lo, ...] -> [clz, ...], where clz is a number of leading zeros of value n.This takes 43 cycles. |
| ctz | Counts the number of trailing zeros of one unsigned 64-bit integer. The input value is assumed to be represented using 32 bit limbs, but this is not checked. The stack transition looks as follows: [n_hi, n_lo, ...] -> [ctz, ...], where ctz is a number of trailing zeros of value n.This takes 41 cycles. |
| clo | Counts the number of leading ones of one unsigned 64-bit integer. The input value is assumed to be represented using 32 bit limbs, but this is not checked. The stack transition looks as follows: [n_hi, n_lo, ...] -> [clo, ...], where clo is a number of leading ones of value n.This takes 42 cycles. |
| cto | Counts the number of trailing ones of one unsigned 64-bit integer. The input value is assumed to be represented using 32 bit limbs, but this is not checked. The stack transition looks as follows: [n_hi, n_lo, ...] -> [cto, ...], where cto is a number of trailing ones of value n.This takes 40 cycles. |