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use crate::constants::{MAX_PRECISION_I32, POWERS_10};
use crate::decimal::{CalculationResult, Decimal};
use crate::ops::common::{Buf12, Buf16, Dec64};
use core::cmp::Ordering;
use core::ops::BitXor;
impl Buf12 {
// Returns true if successful, else false for an overflow
fn add32(&mut self, value: u32) -> Result<(), DivError> {
let value = value as u64;
let new = self.low64().wrapping_add(value);
self.set_low64(new);
if new < value {
self.data[2] = self.data[2].wrapping_add(1);
if self.data[2] == 0 {
return Err(DivError::Overflow);
}
}
Ok(())
}
// Divide a Decimal union by a 32 bit divisor.
// Self is overwritten with the quotient.
// Return value is a 32 bit remainder.
fn div32(&mut self, divisor: u32) -> u32 {
let divisor64 = divisor as u64;
// See if we can get by using a simple u64 division
if self.data[2] != 0 {
let mut temp = self.high64();
let q64 = temp / divisor64;
self.set_high64(q64);
// Calculate the "remainder"
temp = ((temp - q64 * divisor64) << 32) | (self.data[0] as u64);
if temp == 0 {
return 0;
}
let q32 = (temp / divisor64) as u32;
self.data[0] = q32;
((temp as u32).wrapping_sub(q32.wrapping_mul(divisor))) as u32
} else {
// Super easy divisor
let low64 = self.low64();
if low64 == 0 {
// Nothing to do
return 0;
}
// Do the calc
let quotient = low64 / divisor64;
self.set_low64(quotient);
// Remainder is the leftover that wasn't used
(low64.wrapping_sub(quotient.wrapping_mul(divisor64))) as u32
}
}
// Divide the number by a power constant
// Returns true if division was successful
fn div32_const(&mut self, pow: u32) -> bool {
let pow64 = pow as u64;
let high64 = self.high64();
let lo = self.data[0] as u64;
let div64: u64 = high64 / pow64;
let div = ((((high64 - div64 * pow64) << 32) + lo) / pow64) as u32;
if self.data[0] == div.wrapping_mul(pow) {
self.set_high64(div64);
self.data[0] = div;
true
} else {
false
}
}
}
impl Buf16 {
// Does a partial divide with a 64 bit divisor. The divisor in this case must be 64 bits
// otherwise various assumptions fail (e.g. 32 bit quotient).
// To assist, the upper 64 bits must be greater than the divisor for this to succeed.
// Consequently, it will return the quotient as a 32 bit number and overwrite self with the
// 64 bit remainder.
pub(super) fn partial_divide_64(&mut self, divisor: u64) -> u32 {
// We make this assertion here, however below we pivot based on the data
debug_assert!(divisor > self.mid64());
// If we have an empty high bit, then divisor must be greater than the dividend due to
// the assumption that the divisor REQUIRES 64 bits.
if self.data[2] == 0 {
let low64 = self.low64();
if low64 < divisor {
// We can't divide at at all so result is 0. The dividend remains untouched since
// the full amount is the remainder.
return 0;
}
let quotient = low64 / divisor;
self.set_low64(low64 - (quotient * divisor));
return quotient as u32;
}
// Do a simple check to see if the hi portion of the dividend is greater than the hi
// portion of the divisor.
let divisor_hi32 = (divisor >> 32) as u32;
if self.data[2] >= divisor_hi32 {
// We know that the divisor goes into this at MOST u32::max times.
// So we kick things off, with that assumption
let mut low64 = self.low64();
low64 = low64.wrapping_sub(divisor << 32).wrapping_add(divisor);
let mut quotient = u32::MAX;
// If we went negative then keep adding it back in
loop {
if low64 < divisor {
break;
}
quotient = quotient.wrapping_sub(1);
low64 = low64.wrapping_add(divisor);
}
self.set_low64(low64);
return quotient;
}
let mid64 = self.mid64();
let divisor_hi32_64 = divisor_hi32 as u64;
if mid64 < divisor_hi32_64 as u64 {
// similar situation as above where we've got nothing left to divide
return 0;
}
let mut quotient = mid64 / divisor_hi32_64;
let mut remainder = self.data[0] as u64 | ((mid64 - quotient * divisor_hi32_64) << 32);
// Do quotient * lo divisor
let product = quotient * (divisor & 0xFFFF_FFFF);
remainder = remainder.wrapping_sub(product);
// Check if we've gone negative. If so, add it back
if remainder > product.bitxor(u64::MAX) {
loop {
quotient = quotient.wrapping_sub(1);
remainder = remainder.wrapping_add(divisor);
if remainder < divisor {
break;
}
}
}
self.set_low64(remainder);
quotient as u32
}
// Does a partial divide with a 96 bit divisor. The divisor in this case must require 96 bits
// otherwise various assumptions fail (e.g. 32 bit quotient).
pub(super) fn partial_divide_96(&mut self, divisor: &Buf12) -> u32 {
let dividend = self.high64();
let divisor_hi = divisor.data[2];
if dividend < divisor_hi as u64 {
// Dividend is too small - entire number is remainder
return 0;
}
let mut quo = (dividend / divisor_hi as u64) as u32;
let mut remainder = (dividend as u32).wrapping_sub(quo.wrapping_mul(divisor_hi));
// Compute full remainder
let mut prod1 = quo as u64 * divisor.data[0] as u64;
let mut prod2 = quo as u64 * divisor.data[1] as u64;
prod2 += prod1 >> 32;
prod1 = (prod1 & 0xFFFF_FFFF) | (prod2 << 32);
prod2 >>= 32;
let mut num = self.low64();
num = num.wrapping_sub(prod1);
remainder = remainder.wrapping_sub(prod2 as u32);
// If there are carries make sure they are propagated
if num > prod1.bitxor(u64::MAX) {
remainder = remainder.wrapping_sub(1);
if remainder < (prod2 as u32).bitxor(u32::MAX) {
self.set_low64(num);
self.data[2] = remainder;
return quo;
}
} else if remainder <= (prod2 as u32).bitxor(u32::MAX) {
self.set_low64(num);
self.data[2] = remainder;
return quo;
}
// Remainder went negative, add divisor back until it's positive
prod1 = divisor.low64();
loop {
quo = quo.wrapping_sub(1);
num = num.wrapping_add(prod1);
remainder = remainder.wrapping_add(divisor_hi);
if num < prod1 {
// Detected carry.
let tmp = remainder;
remainder = remainder.wrapping_add(1);
if tmp < divisor_hi {
break;
}
}
if remainder < divisor_hi {
break; // detected carry
}
}
self.set_low64(num);
self.data[2] = remainder;
quo
}
}
enum DivError {
Overflow,
}
pub(crate) fn div_impl(dividend: &Decimal, divisor: &Decimal) -> CalculationResult {
if divisor.is_zero() {
return CalculationResult::DivByZero;
}
if dividend.is_zero() {
return CalculationResult::Ok(Decimal::ZERO);
}
let dividend = Dec64::new(dividend);
let divisor = Dec64::new(divisor);
// Pre calculate the scale and the sign
let mut scale = (dividend.scale as i32) - (divisor.scale as i32);
let sign_negative = dividend.negative ^ divisor.negative;
// Set up some variables for modification throughout
let mut require_unscale = false;
let mut quotient = Buf12::from_dec64(÷nd);
let divisor = Buf12::from_dec64(&divisor);
// Branch depending on the complexity of the divisor
if divisor.data[2] | divisor.data[1] == 0 {
// We have a simple(r) divisor (32 bit)
let divisor32 = divisor.data[0];
// Remainder can only be 32 bits since the divisor is 32 bits.
let mut remainder = quotient.div32(divisor32);
let mut power_scale = 0;
// Figure out how to apply the remainder (i.e. we may have performed something like 10/3 or 8/5)
loop {
// Remainder is 0 so we have a simple situation
if remainder == 0 {
// If the scale is positive then we're actually done
if scale >= 0 {
break;
}
power_scale = 9usize.min((-scale) as usize);
} else {
// We may need to normalize later, so set the flag appropriately
require_unscale = true;
// We have a remainder so we effectively want to try to adjust the quotient and add
// the remainder into the quotient. We do this below, however first of all we want
// to try to avoid overflowing so we do that check first.
let will_overflow = if scale == MAX_PRECISION_I32 {
true
} else {
// Figure out how much we can scale by
if let Some(s) = quotient.find_scale(scale) {
power_scale = s;
} else {
return CalculationResult::Overflow;
}
// If it comes back as 0 (i.e. 10^0 = 1) then we're going to overflow since
// we're doing nothing.
power_scale == 0
};
if will_overflow {
// No more scaling can be done, but remainder is non-zero so we round if necessary.
let tmp = remainder << 1;
let round = if tmp < remainder {
// We round if we wrapped around
true
} else if tmp >= divisor32 {
// If we're greater than the divisor (i.e. underflow)
// or if there is a lo bit set, we round
tmp > divisor32 || (quotient.data[0] & 0x1) > 0
} else {
false
};
// If we need to round, try to do so.
if round {
if let Ok(new_scale) = round_up(&mut quotient, scale) {
scale = new_scale;
} else {
// Overflowed
return CalculationResult::Overflow;
}
}
break;
}
}
// Do some scaling
let power = POWERS_10[power_scale];
scale += power_scale as i32;
// Increase the quotient by the power that was looked up
let overflow = increase_scale(&mut quotient, power as u64);
if overflow > 0 {
return CalculationResult::Overflow;
}
let remainder_scaled = (remainder as u64) * (power as u64);
let remainder_quotient = (remainder_scaled / (divisor32 as u64)) as u32;
remainder = (remainder_scaled - remainder_quotient as u64 * divisor32 as u64) as u32;
if let Err(DivError::Overflow) = quotient.add32(remainder_quotient) {
if let Ok(adj) = unscale_from_overflow(&mut quotient, scale, remainder != 0) {
scale = adj;
} else {
// Still overflowing
return CalculationResult::Overflow;
}
break;
}
}
} else {
// We have a divisor greater than 32 bits. Both of these share some quick calculation wins
// so we'll do those before branching into separate logic.
// The win we can do is shifting the bits to the left as much as possible. We do this to both
// the dividend and the divisor to ensure the quotient is not changed.
// As a simple contrived example: if we have 4 / 2 then we could bit shift all the way to the
// left meaning that the lo portion would have nothing inside of it. Of course, shifting these
// left one has the same result (8/4) etc.
// The advantage is that we may be able to write off lower portions of the number making things
// easier.
let mut power_scale = if divisor.data[2] == 0 {
divisor.data[1].leading_zeros()
} else {
divisor.data[2].leading_zeros()
} as usize;
let mut remainder = Buf16::zero();
remainder.set_low64(quotient.low64() << power_scale);
let tmp_high = ((quotient.data[1] as u64) + ((quotient.data[2] as u64) << 32)) >> (32 - power_scale);
remainder.set_high64(tmp_high);
// Work out the divisor after it's shifted
let divisor64 = divisor.low64() << power_scale;
// Check if the divisor is 64 bit or the full 96 bits
if divisor.data[2] == 0 {
// It's 64 bits
quotient.data[2] = 0;
// Calc mid/lo by shifting accordingly
let rem_lo = remainder.data[0];
remainder.data[0] = remainder.data[1];
remainder.data[1] = remainder.data[2];
remainder.data[2] = remainder.data[3];
quotient.data[1] = remainder.partial_divide_64(divisor64);
remainder.data[2] = remainder.data[1];
remainder.data[1] = remainder.data[0];
remainder.data[0] = rem_lo;
quotient.data[0] = remainder.partial_divide_64(divisor64);
loop {
let rem_low64 = remainder.low64();
if rem_low64 == 0 {
// If the scale is positive then we're actually done
if scale >= 0 {
break;
}
power_scale = 9usize.min((-scale) as usize);
} else {
// We may need to normalize later, so set the flag appropriately
require_unscale = true;
// We have a remainder so we effectively want to try to adjust the quotient and add
// the remainder into the quotient. We do this below, however first of all we want
// to try to avoid overflowing so we do that check first.
let will_overflow = if scale == MAX_PRECISION_I32 {
true
} else {
// Figure out how much we can scale by
if let Some(s) = quotient.find_scale(scale) {
power_scale = s;
} else {
return CalculationResult::Overflow;
}
// If it comes back as 0 (i.e. 10^0 = 1) then we're going to overflow since
// we're doing nothing.
power_scale == 0
};
if will_overflow {
// No more scaling can be done, but remainder is non-zero so we round if necessary.
let mut tmp = remainder.low64();
let round = if (tmp as i64) < 0 {
// We round if we wrapped around
true
} else {
tmp <<= 1;
if tmp > divisor64 {
true
} else {
tmp == divisor64 && quotient.data[0] & 0x1 != 0
}
};
// If we need to round, try to do so.
if round {
if let Ok(new_scale) = round_up(&mut quotient, scale) {
scale = new_scale;
} else {
// Overflowed
return CalculationResult::Overflow;
}
}
break;
}
}
// Do some scaling
let power = POWERS_10[power_scale];
scale += power_scale as i32;
// Increase the quotient by the power that was looked up
let overflow = increase_scale(&mut quotient, power as u64);
if overflow > 0 {
return CalculationResult::Overflow;
}
increase_scale64(&mut remainder, power as u64);
let tmp = remainder.partial_divide_64(divisor64);
if let Err(DivError::Overflow) = quotient.add32(tmp) {
if let Ok(adj) = unscale_from_overflow(&mut quotient, scale, remainder.low64() != 0) {
scale = adj;
} else {
// Still overflowing
return CalculationResult::Overflow;
}
break;
}
}
} else {
// It's 96 bits
// Start by finishing the shift left
let divisor_mid = divisor.data[1];
let divisor_hi = divisor.data[2];
let mut divisor = divisor;
divisor.set_low64(divisor64);
divisor.data[2] = ((divisor_mid as u64 + ((divisor_hi as u64) << 32)) >> (32 - power_scale)) as u32;
let quo = remainder.partial_divide_96(&divisor);
quotient.set_low64(quo as u64);
quotient.data[2] = 0;
loop {
let mut rem_low64 = remainder.low64();
if rem_low64 == 0 && remainder.data[2] == 0 {
// If the scale is positive then we're actually done
if scale >= 0 {
break;
}
power_scale = 9usize.min((-scale) as usize);
} else {
// We may need to normalize later, so set the flag appropriately
require_unscale = true;
// We have a remainder so we effectively want to try to adjust the quotient and add
// the remainder into the quotient. We do this below, however first of all we want
// to try to avoid overflowing so we do that check first.
let will_overflow = if scale == MAX_PRECISION_I32 {
true
} else {
// Figure out how much we can scale by
if let Some(s) = quotient.find_scale(scale) {
power_scale = s;
} else {
return CalculationResult::Overflow;
}
// If it comes back as 0 (i.e. 10^0 = 1) then we're going to overflow since
// we're doing nothing.
power_scale == 0
};
if will_overflow {
// No more scaling can be done, but remainder is non-zero so we round if necessary.
let round = if (remainder.data[2] as i32) < 0 {
// We round if we wrapped around
true
} else {
let tmp = remainder.data[1] >> 31;
rem_low64 <<= 1;
remainder.set_low64(rem_low64);
remainder.data[2] = (&remainder.data[2] << 1) + tmp;
match remainder.data[2].cmp(&divisor.data[2]) {
Ordering::Less => false,
Ordering::Equal => {
let divisor_low64 = divisor.low64();
if rem_low64 > divisor_low64 {
true
} else {
rem_low64 == divisor_low64 && (quotient.data[0] & 1) != 0
}
}
Ordering::Greater => true,
}
};
// If we need to round, try to do so.
if round {
if let Ok(new_scale) = round_up(&mut quotient, scale) {
scale = new_scale;
} else {
// Overflowed
return CalculationResult::Overflow;
}
}
break;
}
}
// Do some scaling
let power = POWERS_10[power_scale];
scale += power_scale as i32;
// Increase the quotient by the power that was looked up
let overflow = increase_scale(&mut quotient, power as u64);
if overflow > 0 {
return CalculationResult::Overflow;
}
let mut tmp_remainder = Buf12 {
data: [remainder.data[0], remainder.data[1], remainder.data[2]],
};
let overflow = increase_scale(&mut tmp_remainder, power as u64);
remainder.data[0] = tmp_remainder.data[0];
remainder.data[1] = tmp_remainder.data[1];
remainder.data[2] = tmp_remainder.data[2];
remainder.data[3] = overflow;
let tmp = remainder.partial_divide_96(&divisor);
if let Err(DivError::Overflow) = quotient.add32(tmp) {
if let Ok(adj) =
unscale_from_overflow(&mut quotient, scale, (remainder.low64() | remainder.high64()) != 0)
{
scale = adj;
} else {
// Still overflowing
return CalculationResult::Overflow;
}
break;
}
}
}
}
if require_unscale {
scale = unscale(&mut quotient, scale);
}
CalculationResult::Ok(Decimal::from_parts(
quotient.data[0],
quotient.data[1],
quotient.data[2],
sign_negative,
scale as u32,
))
}
// Multiply num by power (multiple of 10). Power must be 32 bits.
// Returns the overflow, if any
fn increase_scale(num: &mut Buf12, power: u64) -> u32 {
let mut tmp = (num.data[0] as u64) * power;
num.data[0] = tmp as u32;
tmp >>= 32;
tmp += (num.data[1] as u64) * power;
num.data[1] = tmp as u32;
tmp >>= 32;
tmp += (num.data[2] as u64) * power;
num.data[2] = tmp as u32;
(tmp >> 32) as u32
}
// Multiply num by power (multiple of 10). Power must be 32 bits.
fn increase_scale64(num: &mut Buf16, power: u64) {
let mut tmp = (num.data[0] as u64) * power;
num.data[0] = tmp as u32;
tmp >>= 32;
tmp += (num.data[1] as u64) * power;
num.set_mid64(tmp)
}
// Adjust the number to deal with an overflow. This function follows being scaled up (i.e. multiplied
// by 10, so this effectively tries to reverse that by dividing by 10 then feeding in the high bit
// to undo the overflow and rounding instead.
// Returns the updated scale.
fn unscale_from_overflow(num: &mut Buf12, scale: i32, sticky: bool) -> Result<i32, DivError> {
let scale = scale - 1;
if scale < 0 {
return Err(DivError::Overflow);
}
// This function is called when the hi portion has "overflowed" upon adding one and has wrapped
// back around to 0. Consequently, we need to "feed" that back in, but also rescaling down
// to reverse out the overflow.
const HIGH_BIT: u64 = 0x1_0000_0000;
num.data[2] = (HIGH_BIT / 10) as u32;
// Calc the mid
let mut tmp = ((HIGH_BIT % 10) << 32) + (num.data[1] as u64);
let mut val = (tmp / 10) as u32;
num.data[1] = val;
// Calc the lo using a similar method
tmp = ((tmp - (val as u64) * 10) << 32) + (num.data[0] as u64);
val = (tmp / 10) as u32;
num.data[0] = val;
// Work out the remainder, and round if we have one (since it doesn't fit)
let remainder = (tmp - (val as u64) * 10) as u32;
if remainder > 5 || (remainder == 5 && (sticky || num.data[0] & 0x1 > 0)) {
let _ = num.add32(1);
}
Ok(scale)
}
#[inline]
fn round_up(num: &mut Buf12, scale: i32) -> Result<i32, DivError> {
let low64 = num.low64().wrapping_add(1);
num.set_low64(low64);
if low64 != 0 {
return Ok(scale);
}
let hi = num.data[2].wrapping_add(1);
num.data[2] = hi;
if hi != 0 {
return Ok(scale);
}
unscale_from_overflow(num, scale, true)
}
fn unscale(num: &mut Buf12, scale: i32) -> i32 {
// Since 10 = 2 * 5, there must be a factor of 2 for every power of 10 we can extract.
// We use this as a quick test on whether to try a given power.
let mut scale = scale;
while num.data[0] == 0 && scale >= 8 && num.div32_const(100000000) {
scale -= 8;
}
if (num.data[0] & 0xF) == 0 && scale >= 4 && num.div32_const(10000) {
scale -= 4;
}
if (num.data[0] & 0x3) == 0 && scale >= 2 && num.div32_const(100) {
scale -= 2;
}
if (num.data[0] & 0x1) == 0 && scale >= 1 && num.div32_const(10) {
scale -= 1;
}
scale
}