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v/vlib/math/big/array_ops.v

342 lines
9.8 KiB
V

module big
// Compares the magnitude of the two unsigned integers represented the given
// digit arrays. Returns -1 if a < b, 0 if a == b and +1 if a > b. Here
// a is operand_a and b is operand_b (for brevity).
[direct_array_access]
fn compare_digit_array(operand_a []u32, operand_b []u32) int {
a_len := operand_a.len
b_len := operand_b.len
if a_len != b_len {
return if a_len < b_len { -1 } else { 1 }
}
// They have the same number of digits now
// Go from the most significant digit to the least significant one
for index := a_len - 1; index >= 0; index-- {
a_digit := operand_a[index]
b_digit := operand_b[index]
if a_digit != b_digit {
return if a_digit < b_digit { -1 } else { 1 }
}
}
return 0
}
// Add the digits in operand_a and operand_b and stores the result in sum.
// This function does not perform any allocation and assumes that the storage is
// large enough. It may affect the last element, based on the presence of a carry
[direct_array_access]
fn add_digit_array(operand_a []u32, operand_b []u32, mut sum []u32) {
// Zero length cases
if operand_a.len == 0 {
for index in 0 .. operand_b.len {
sum[index] = operand_b[index]
}
}
if operand_b.len == 0 {
for index in 0 .. operand_a.len {
sum[index] = operand_a[index]
}
}
// First pass intersects with both operands
smaller_limit := imin(operand_a.len, operand_b.len)
larger_limit := imax(operand_a.len, operand_b.len)
mut a, mut b := if operand_a.len >= operand_b.len {
operand_a, operand_b
} else {
operand_b, operand_a
}
mut carry := u64(0)
for index in 0 .. smaller_limit {
partial := carry + a[index] + b[index]
sum[index] = u32(partial)
carry = u32(partial >> 32)
}
for index in smaller_limit .. larger_limit {
partial := carry + a[index]
sum[index] = u32(partial)
carry = u32(partial >> 32)
}
if carry == 0 {
sum.delete_last()
} else {
sum[larger_limit] = u32(carry)
}
}
// Subtracts operand_b from operand_a and stores the difference in storage.
// It assumes operand_a contains the larger "integer" and that storage is
// the same size as operand_a and is 0
[direct_array_access]
fn subtract_digit_array(operand_a []u32, operand_b []u32, mut storage []u32) {
// Zero length cases
if operand_a.len == 0 {
// nothing to subtract from
return
}
if operand_b.len == 0 {
// nothing to subtract
for index in 0 .. operand_a.len {
storage[index] = operand_a[index]
}
}
mut carry := false
for index in 0 .. operand_b.len {
mut a_digit := u64(operand_a[index])
b_digit := operand_b[index] + if carry { u64(1) } else { u64(0) }
carry = a_digit < b_digit
if carry {
a_digit += 0x100000000
}
storage[index] = u32(a_digit - b_digit)
}
for index in operand_b.len .. operand_a.len {
mut a_digit := u64(operand_a[index])
b_digit := if carry { u64(1) } else { u64(0) }
carry = a_digit < b_digit
if carry {
a_digit += 0x100000000
}
storage[index] = u32(a_digit - b_digit)
}
shrink_tail_zeros(mut storage)
}
const karatsuba_multiplication_limit = 240
const toom3_multiplication_limit = 10_000
[inline]
fn multiply_digit_array(operand_a []u32, operand_b []u32, mut storage []u32) {
max_len := if operand_a.len >= operand_b.len {
operand_a.len
} else {
operand_b.len
}
if max_len >= big.toom3_multiplication_limit {
toom3_multiply_digit_array(operand_a, operand_b, mut storage)
} else if max_len >= big.karatsuba_multiplication_limit {
karatsuba_multiply_digit_array(operand_a, operand_b, mut storage)
} else {
simple_multiply_digit_array(operand_a, operand_b, mut storage)
}
}
// Multiplies the unsigned (non-negative) integers represented in a and b and the product is
// stored in storage. It assumes that storage has length equal to the sum of lengths
// of a and b. Length refers to length of array, that is, digit count.
[direct_array_access]
fn simple_multiply_digit_array(operand_a []u32, operand_b []u32, mut storage []u32) {
for b_index in 0 .. operand_b.len {
mut carry := u64(0)
for a_index in 0 .. operand_a.len {
partial_product := u64(storage[a_index + b_index]) + carry +
u64(operand_a[a_index]) * u64(operand_b[b_index])
storage[a_index + b_index] = u32(partial_product)
carry = partial_product >> 32
}
if carry != 0 {
storage[b_index + operand_a.len] = u32(carry)
}
}
shrink_tail_zeros(mut storage)
}
// Stores the product of the unsigned (non-negative) integer represented in a and the digit in value
// in the storage array. It assumes storage is pre-initialised and populated with 0's
[direct_array_access]
fn multiply_array_by_digit(operand_a []u32, value u32, mut storage []u32) {
if value == 0 {
storage.clear()
return
}
if value == 1 {
for index in 0 .. operand_a.len {
storage[index] = operand_a[index]
}
shrink_tail_zeros(mut storage)
return
}
mut carry := u32(0)
for index in 0 .. operand_a.len {
product := u64(operand_a[index]) * value + carry
storage[index] = u32(product)
carry = u32(product >> 32)
}
if carry > 0 {
if storage.last() == 0 {
storage[operand_a.len] = carry
} else {
storage << carry
}
}
shrink_tail_zeros(mut storage)
}
// Divides the non-negative integer in a by non-negative integer b and store the two results
// in quotient and remainder respectively. It is different from the rest of the functions
// because it assumes that quotient and remainder are empty zero length arrays. They can be
// made to have appropriate capacity though
[direct_array_access]
fn divide_digit_array(operand_a []u32, operand_b []u32, mut quotient []u32, mut remainder []u32) {
cmp_result := compare_digit_array(operand_a, operand_b)
// a == b => q, r = 1, 0
if cmp_result == 0 {
quotient << 1
for quotient.len > 1 {
quotient.delete_last()
}
remainder.clear()
return
}
// a < b => q, r = 0, a
if cmp_result < 0 {
quotient.clear()
for index in 0 .. operand_a.len {
remainder << operand_a[index]
}
return
}
if operand_b.len == 1 {
divide_array_by_digit(operand_a, operand_b[0], mut quotient, mut remainder)
} else {
divide_array_by_array(operand_a, operand_b, mut quotient, mut remainder)
}
}
// Performs division on the non-negative dividend in a by the single digit divisor b. It assumes
// quotient and remainder are empty zero length arrays without previous allocation
[direct_array_access]
fn divide_array_by_digit(operand_a []u32, divisor u32, mut quotient []u32, mut remainder []u32) {
if operand_a.len == 1 {
// 1 digit for both dividend and divisor
dividend := operand_a[0]
q := dividend / divisor
if q != 0 {
quotient << q
}
rem := dividend % divisor
if rem != 0 {
remainder << rem
}
return
}
// Dividend has more digits
mut rem := u64(0)
divisor64 := u64(divisor)
// Pad quotient to contain sufficient space
for _ in 0 .. operand_a.len {
quotient << 0
}
// Perform division step by step
for index := operand_a.len - 1; index >= 0; index-- {
dividend := (rem << 32) + operand_a[index]
quotient[index] = u32(dividend / divisor64)
rem = dividend % divisor64
}
// Remove leading zeros from quotient
shrink_tail_zeros(mut quotient)
remainder << u32(rem)
shrink_tail_zeros(mut remainder)
}
const newton_division_limit = 10_000
[inline]
fn divide_array_by_array(operand_a []u32, operand_b []u32, mut quotient []u32, mut remainder []u32) {
if operand_a.len >= big.newton_division_limit {
newton_divide_array_by_array(operand_a, operand_b, mut quotient, mut remainder)
} else {
binary_divide_array_by_array(operand_a, operand_b, mut quotient, mut remainder)
}
}
// Shifts the contents of the original array by the given amount of bits to the left.
// This function assumes that the amount is less than 32. The storage is expected to
// allocated with zeroes.
[direct_array_access]
fn shift_digits_left(original []u32, amount u32, mut storage []u32) {
mut leftover := u32(0)
offset := 32 - amount
for index in 0 .. original.len {
value := leftover | (original[index] << amount)
leftover = (original[index] & (u32(-1) << offset)) >> offset
storage[index] = value
}
if leftover != 0 {
storage << leftover
}
}
// Shifts the contents of the original array by the given amount of bits to the right.
// This function assumes that the amount is less than 32. The storage is expected to
// be allocated with zeroes.
[direct_array_access]
fn shift_digits_right(original []u32, amount u32, mut storage []u32) {
mut moveover := u32(0)
mask := (u32(1) << amount) - 1
offset := 32 - amount
for index := original.len - 1; index >= 0; index-- {
value := (moveover << offset) | (original[index] >> amount)
moveover = original[index] & mask
storage[index] = value
}
shrink_tail_zeros(mut storage)
}
[direct_array_access]
fn bitwise_or_digit_array(operand_a []u32, operand_b []u32, mut storage []u32) {
lower, upper, bigger := if operand_a.len < operand_b.len {
operand_a.len, operand_b.len, operand_b
} else {
operand_b.len, operand_a.len, operand_a
}
for index in 0 .. lower {
storage[index] = operand_a[index] | operand_b[index]
}
for index in lower .. upper {
storage[index] = bigger[index]
}
shrink_tail_zeros(mut storage)
}
[direct_array_access]
fn bitwise_and_digit_array(operand_a []u32, operand_b []u32, mut storage []u32) {
lower := imin(operand_a.len, operand_b.len)
for index in 0 .. lower {
storage[index] = operand_a[index] & operand_b[index]
}
shrink_tail_zeros(mut storage)
}
[direct_array_access]
fn bitwise_xor_digit_array(operand_a []u32, operand_b []u32, mut storage []u32) {
lower, upper, bigger := if operand_a.len < operand_b.len {
operand_a.len, operand_b.len, operand_b
} else {
operand_b.len, operand_a.len, operand_a
}
for index in 0 .. lower {
storage[index] = operand_a[index] ^ operand_b[index]
}
for index in lower .. upper {
storage[index] = bigger[index]
}
shrink_tail_zeros(mut storage)
}
[direct_array_access]
fn bitwise_not_digit_array(original []u32, mut storage []u32) {
for index in 0 .. original.len {
storage[index] = ~original[index]
}
shrink_tail_zeros(mut storage)
}