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v/vlib/math/big/division_array_ops.v
2021-09-16 19:31:07 +03:00

141 lines
3.7 KiB
V

module big
import math.bits
// suppose operand_a bigger than operand_b and both not null.
// Both quotient and remaider are allocated but of length 0
fn binary_divide_array_by_array(operand_a []u32, operand_b []u32, mut quotient []u32, mut remainder []u32) {
for index in 0 .. operand_a.len {
remainder << operand_a[index]
}
len_diff := operand_a.len - operand_b.len
assert len_diff >= 0
// we must do in place shift and operations.
mut divisor := []u32{cap: operand_b.len}
for _ in 0 .. len_diff {
divisor << u32(0)
}
for index in 0 .. operand_b.len {
divisor << operand_b[index]
}
for _ in 0 .. len_diff + 1 {
quotient << u32(0)
}
lead_zer_remainder := u32(bits.leading_zeros_32(remainder.last()))
lead_zer_divisor := u32(bits.leading_zeros_32(divisor.last()))
bit_offset := (u32(32) * u32(len_diff)) + (lead_zer_divisor - lead_zer_remainder)
// align
if lead_zer_remainder < lead_zer_divisor {
lshift_in_place(mut divisor, lead_zer_divisor - lead_zer_remainder)
} else if lead_zer_remainder > lead_zer_divisor {
lshift_in_place(mut remainder, lead_zer_remainder - lead_zer_divisor)
}
assert left_align_p(divisor[divisor.len - 1], remainder[remainder.len - 1])
for bit_idx := int(bit_offset); bit_idx >= 0; bit_idx-- {
if greater_equal_from_end(remainder, divisor) {
bit_set(mut quotient, bit_idx)
subtract_align_last_byte_in_place(mut remainder, divisor)
}
rshift_in_place(mut divisor, 1)
}
// adjust
if lead_zer_remainder > lead_zer_divisor {
// rshift_in_place(mut quotient, lead_zer_remainder - lead_zer_divisor)
rshift_in_place(mut remainder, lead_zer_remainder - lead_zer_divisor)
}
for remainder.len > 0 && remainder.last() == 0 {
remainder.delete_last()
}
for quotient.len > 0 && quotient.last() == 0 {
quotient.delete_last()
}
}
// help routines for cleaner code but inline for performance
// quicker than BitField.set_bit
[inline]
fn bit_set(mut a []u32, n int) {
byte_offset := n >> 5
mask := u32(1) << u32(n % 32)
assert a.len >= byte_offset
a[byte_offset] |= mask
}
// a.len is greater or equal to b.len
// returns true if a >= b (completed with zeroes)
[inline]
fn greater_equal_from_end(a []u32, b []u32) bool {
assert a.len >= b.len
offset := a.len - b.len
for index := a.len - 1; index >= offset; index-- {
if a[index] > b[index - offset] {
return true
} else if a[index] < b[index - offset] {
return false
}
}
return true
}
// a := a - b supposed a >= b
// attention the b operand is align with the a operand before the subtraction
[inline]
fn subtract_align_last_byte_in_place(mut a []u32, b []u32) {
mut carry := u32(0)
mut new_carry := u32(0)
offset := a.len - b.len
for index := a.len - b.len; index < a.len; index++ {
if a[index] < (b[index - offset] + carry) {
new_carry = 1
} else {
new_carry = 0
}
a[index] -= (b[index - offset] + carry)
carry = new_carry
}
assert carry == 0
}
// logical left shift
// there is no overflow. We know that the last bits are zero
// and that n <= 32
[inline]
fn lshift_in_place(mut a []u32, n u32) {
mut carry := u32(0)
mut prec_carry := u32(0)
mask := ((u32(1) << n) - 1) << (32 - n)
for index in 0 .. a.len {
prec_carry = carry >> (32 - n)
carry = a[index] & mask
a[index] <<= n
a[index] |= prec_carry
}
}
// logical right shift without control because these digits have already been
// shift left before
[inline]
fn rshift_in_place(mut a []u32, n u32) {
mut carry := u32(0)
mut prec_carry := u32(0)
mask := u32((1 << n) - 1)
for index := a.len - 1; index >= 0; index-- {
carry = a[index] & mask
a[index] >>= n
a[index] |= prec_carry << (32 - n)
prec_carry = carry
}
}
// for assert
[inline]
fn left_align_p(a u32, b u32) bool {
return bits.leading_zeros_32(a) == bits.leading_zeros_32(b)
}