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//! Integer and floating-point number formatting
use crate::fmt;
use crate::mem::MaybeUninit;
use crate::num::fmt as numfmt;
use crate::ops::{Div, Rem, Sub};
use crate::ptr;
use crate::slice;
use crate::str;
#[doc(hidden)]
trait DisplayInt:
PartialEq + PartialOrd + Div<Output = Self> + Rem<Output = Self> + Sub<Output = Self> + Copy
{
fn zero() -> Self;
fn from_u8(u: u8) -> Self;
fn to_u8(&self) -> u8;
#[cfg(not(any(target_pointer_width = "64", target_arch = "wasm32")))]
fn to_u32(&self) -> u32;
fn to_u64(&self) -> u64;
fn to_u128(&self) -> u128;
}
macro_rules! impl_int {
($($t:ident)*) => (
$(impl DisplayInt for $t {
fn zero() -> Self { 0 }
fn from_u8(u: u8) -> Self { u as Self }
fn to_u8(&self) -> u8 { *self as u8 }
#[cfg(not(any(target_pointer_width = "64", target_arch = "wasm32")))]
fn to_u32(&self) -> u32 { *self as u32 }
fn to_u64(&self) -> u64 { *self as u64 }
fn to_u128(&self) -> u128 { *self as u128 }
})*
)
}
macro_rules! impl_uint {
($($t:ident)*) => (
$(impl DisplayInt for $t {
fn zero() -> Self { 0 }
fn from_u8(u: u8) -> Self { u as Self }
fn to_u8(&self) -> u8 { *self as u8 }
#[cfg(not(any(target_pointer_width = "64", target_arch = "wasm32")))]
fn to_u32(&self) -> u32 { *self as u32 }
fn to_u64(&self) -> u64 { *self as u64 }
fn to_u128(&self) -> u128 { *self as u128 }
})*
)
}
impl_int! { i8 i16 i32 i64 i128 isize }
impl_uint! { u8 u16 u32 u64 u128 usize }
/// A type that represents a specific radix
///
/// # Safety
///
/// `digit` must return an ASCII character.
#[doc(hidden)]
unsafe trait GenericRadix: Sized {
/// The number of digits.
const BASE: u8;
/// A radix-specific prefix string.
const PREFIX: &'static str;
/// Converts an integer to corresponding radix digit.
fn digit(x: u8) -> u8;
/// Format an integer using the radix using a formatter.
fn fmt_int<T: DisplayInt>(&self, mut x: T, f: &mut fmt::Formatter<'_>) -> fmt::Result {
// The radix can be as low as 2, so we need a buffer of at least 128
// characters for a base 2 number.
let zero = T::zero();
let is_nonnegative = x >= zero;
let mut buf = [MaybeUninit::<u8>::uninit(); 128];
let mut curr = buf.len();
let base = T::from_u8(Self::BASE);
if is_nonnegative {
// Accumulate each digit of the number from the least significant
// to the most significant figure.
for byte in buf.iter_mut().rev() {
let n = x % base; // Get the current place value.
x = x / base; // Deaccumulate the number.
byte.write(Self::digit(n.to_u8())); // Store the digit in the buffer.
curr -= 1;
if x == zero {
// No more digits left to accumulate.
break;
};
}
} else {
// Do the same as above, but accounting for two's complement.
for byte in buf.iter_mut().rev() {
let n = zero - (x % base); // Get the current place value.
x = x / base; // Deaccumulate the number.
byte.write(Self::digit(n.to_u8())); // Store the digit in the buffer.
curr -= 1;
if x == zero {
// No more digits left to accumulate.
break;
};
}
}
let buf = &buf[curr..];
// SAFETY: The only chars in `buf` are created by `Self::digit` which are assumed to be
// valid UTF-8
let buf = unsafe {
str::from_utf8_unchecked(slice::from_raw_parts(
MaybeUninit::slice_as_ptr(buf),
buf.len(),
))
};
f.pad_integral(is_nonnegative, Self::PREFIX, buf)
}
}
/// A binary (base 2) radix
#[derive(Clone, PartialEq)]
struct Binary;
/// An octal (base 8) radix
#[derive(Clone, PartialEq)]
struct Octal;
/// A hexadecimal (base 16) radix, formatted with lower-case characters
#[derive(Clone, PartialEq)]
struct LowerHex;
/// A hexadecimal (base 16) radix, formatted with upper-case characters
#[derive(Clone, PartialEq)]
struct UpperHex;
macro_rules! radix {
($T:ident, $base:expr, $prefix:expr, $($x:pat => $conv:expr),+) => {
unsafe impl GenericRadix for $T {
const BASE: u8 = $base;
const PREFIX: &'static str = $prefix;
fn digit(x: u8) -> u8 {
match x {
$($x => $conv,)+
x => panic!("number not in the range 0..={}: {}", Self::BASE - 1, x),
}
}
}
}
}
radix! { Binary, 2, "0b", x @ 0 ..= 1 => b'0' + x }
radix! { Octal, 8, "0o", x @ 0 ..= 7 => b'0' + x }
radix! { LowerHex, 16, "0x", x @ 0 ..= 9 => b'0' + x, x @ 10 ..= 15 => b'a' + (x - 10) }
radix! { UpperHex, 16, "0x", x @ 0 ..= 9 => b'0' + x, x @ 10 ..= 15 => b'A' + (x - 10) }
macro_rules! int_base {
(fmt::$Trait:ident for $T:ident as $U:ident -> $Radix:ident) => {
#[stable(feature = "rust1", since = "1.0.0")]
impl fmt::$Trait for $T {
fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
$Radix.fmt_int(*self as $U, f)
}
}
};
}
macro_rules! integer {
($Int:ident, $Uint:ident) => {
int_base! { fmt::Binary for $Int as $Uint -> Binary }
int_base! { fmt::Octal for $Int as $Uint -> Octal }
int_base! { fmt::LowerHex for $Int as $Uint -> LowerHex }
int_base! { fmt::UpperHex for $Int as $Uint -> UpperHex }
int_base! { fmt::Binary for $Uint as $Uint -> Binary }
int_base! { fmt::Octal for $Uint as $Uint -> Octal }
int_base! { fmt::LowerHex for $Uint as $Uint -> LowerHex }
int_base! { fmt::UpperHex for $Uint as $Uint -> UpperHex }
};
}
integer! { isize, usize }
integer! { i8, u8 }
integer! { i16, u16 }
integer! { i32, u32 }
integer! { i64, u64 }
integer! { i128, u128 }
macro_rules! debug {
($($T:ident)*) => {$(
#[stable(feature = "rust1", since = "1.0.0")]
impl fmt::Debug for $T {
#[inline]
fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
if f.debug_lower_hex() {
fmt::LowerHex::fmt(self, f)
} else if f.debug_upper_hex() {
fmt::UpperHex::fmt(self, f)
} else {
fmt::Display::fmt(self, f)
}
}
}
)*};
}
debug! {
i8 i16 i32 i64 i128 isize
u8 u16 u32 u64 u128 usize
}
// 2 digit decimal look up table
static DEC_DIGITS_LUT: &[u8; 200] = b"0001020304050607080910111213141516171819\
2021222324252627282930313233343536373839\
4041424344454647484950515253545556575859\
6061626364656667686970717273747576777879\
8081828384858687888990919293949596979899";
macro_rules! impl_Display {
($($t:ident),* as $u:ident via $conv_fn:ident named $name:ident) => {
fn $name(mut n: $u, is_nonnegative: bool, f: &mut fmt::Formatter<'_>) -> fmt::Result {
// 2^128 is about 3*10^38, so 39 gives an extra byte of space
let mut buf = [MaybeUninit::<u8>::uninit(); 39];
let mut curr = buf.len();
let buf_ptr = MaybeUninit::slice_as_mut_ptr(&mut buf);
let lut_ptr = DEC_DIGITS_LUT.as_ptr();
// SAFETY: Since `d1` and `d2` are always less than or equal to `198`, we
// can copy from `lut_ptr[d1..d1 + 1]` and `lut_ptr[d2..d2 + 1]`. To show
// that it's OK to copy into `buf_ptr`, notice that at the beginning
// `curr == buf.len() == 39 > log(n)` since `n < 2^128 < 10^39`, and at
// each step this is kept the same as `n` is divided. Since `n` is always
// non-negative, this means that `curr > 0` so `buf_ptr[curr..curr + 1]`
// is safe to access.
unsafe {
// need at least 16 bits for the 4-characters-at-a-time to work.
assert!(crate::mem::size_of::<$u>() >= 2);
// eagerly decode 4 characters at a time
while n >= 10000 {
let rem = (n % 10000) as usize;
n /= 10000;
let d1 = (rem / 100) << 1;
let d2 = (rem % 100) << 1;
curr -= 4;
// We are allowed to copy to `buf_ptr[curr..curr + 3]` here since
// otherwise `curr < 0`. But then `n` was originally at least `10000^10`
// which is `10^40 > 2^128 > n`.
ptr::copy_nonoverlapping(lut_ptr.add(d1), buf_ptr.add(curr), 2);
ptr::copy_nonoverlapping(lut_ptr.add(d2), buf_ptr.add(curr + 2), 2);
}
// if we reach here numbers are <= 9999, so at most 4 chars long
let mut n = n as usize; // possibly reduce 64bit math
// decode 2 more chars, if > 2 chars
if n >= 100 {
let d1 = (n % 100) << 1;
n /= 100;
curr -= 2;
ptr::copy_nonoverlapping(lut_ptr.add(d1), buf_ptr.add(curr), 2);
}
// decode last 1 or 2 chars
if n < 10 {
curr -= 1;
*buf_ptr.add(curr) = (n as u8) + b'0';
} else {
let d1 = n << 1;
curr -= 2;
ptr::copy_nonoverlapping(lut_ptr.add(d1), buf_ptr.add(curr), 2);
}
}
// SAFETY: `curr` > 0 (since we made `buf` large enough), and all the chars are valid
// UTF-8 since `DEC_DIGITS_LUT` is
let buf_slice = unsafe {
str::from_utf8_unchecked(
slice::from_raw_parts(buf_ptr.add(curr), buf.len() - curr))
};
f.pad_integral(is_nonnegative, "", buf_slice)
}
$(#[stable(feature = "rust1", since = "1.0.0")]
impl fmt::Display for $t {
#[allow(unused_comparisons)]
fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
let is_nonnegative = *self >= 0;
let n = if is_nonnegative {
self.$conv_fn()
} else {
// convert the negative num to positive by summing 1 to it's 2 complement
(!self.$conv_fn()).wrapping_add(1)
};
$name(n, is_nonnegative, f)
}
})*
};
}
macro_rules! impl_Exp {
($($t:ident),* as $u:ident via $conv_fn:ident named $name:ident) => {
fn $name(
mut n: $u,
is_nonnegative: bool,
upper: bool,
f: &mut fmt::Formatter<'_>
) -> fmt::Result {
let (mut n, mut exponent, trailing_zeros, added_precision) = {
let mut exponent = 0;
// count and remove trailing decimal zeroes
while n % 10 == 0 && n >= 10 {
n /= 10;
exponent += 1;
}
let (added_precision, subtracted_precision) = match f.precision() {
Some(fmt_prec) => {
// number of decimal digits minus 1
let mut tmp = n;
let mut prec = 0;
while tmp >= 10 {
tmp /= 10;
prec += 1;
}
(fmt_prec.saturating_sub(prec), prec.saturating_sub(fmt_prec))
}
None => (0, 0)
};
for _ in 1..subtracted_precision {
n /= 10;
exponent += 1;
}
if subtracted_precision != 0 {
let rem = n % 10;
n /= 10;
exponent += 1;
// round up last digit, round to even on a tie
if rem > 5 || (rem == 5 && (n % 2 != 0 || subtracted_precision > 1 )) {
n += 1;
// if the digit is rounded to the next power
// instead adjust the exponent
if n.ilog10() > (n - 1).ilog10() {
n /= 10;
exponent += 1;
}
}
}
(n, exponent, exponent, added_precision)
};
// 39 digits (worst case u128) + . = 40
// Since `curr` always decreases by the number of digits copied, this means
// that `curr >= 0`.
let mut buf = [MaybeUninit::<u8>::uninit(); 40];
let mut curr = buf.len(); //index for buf
let buf_ptr = MaybeUninit::slice_as_mut_ptr(&mut buf);
let lut_ptr = DEC_DIGITS_LUT.as_ptr();
// decode 2 chars at a time
while n >= 100 {
let d1 = ((n % 100) as usize) << 1;
curr -= 2;
// SAFETY: `d1 <= 198`, so we can copy from `lut_ptr[d1..d1 + 2]` since
// `DEC_DIGITS_LUT` has a length of 200.
unsafe {
ptr::copy_nonoverlapping(lut_ptr.add(d1), buf_ptr.add(curr), 2);
}
n /= 100;
exponent += 2;
}
// n is <= 99, so at most 2 chars long
let mut n = n as isize; // possibly reduce 64bit math
// decode second-to-last character
if n >= 10 {
curr -= 1;
// SAFETY: Safe since `40 > curr >= 0` (see comment)
unsafe {
*buf_ptr.add(curr) = (n as u8 % 10_u8) + b'0';
}
n /= 10;
exponent += 1;
}
// add decimal point iff >1 mantissa digit will be printed
if exponent != trailing_zeros || added_precision != 0 {
curr -= 1;
// SAFETY: Safe since `40 > curr >= 0`
unsafe {
*buf_ptr.add(curr) = b'.';
}
}
// SAFETY: Safe since `40 > curr >= 0`
let buf_slice = unsafe {
// decode last character
curr -= 1;
*buf_ptr.add(curr) = (n as u8) + b'0';
let len = buf.len() - curr as usize;
slice::from_raw_parts(buf_ptr.add(curr), len)
};
// stores 'e' (or 'E') and the up to 2-digit exponent
let mut exp_buf = [MaybeUninit::<u8>::uninit(); 3];
let exp_ptr = MaybeUninit::slice_as_mut_ptr(&mut exp_buf);
// SAFETY: In either case, `exp_buf` is written within bounds and `exp_ptr[..len]`
// is contained within `exp_buf` since `len <= 3`.
let exp_slice = unsafe {
*exp_ptr.add(0) = if upper { b'E' } else { b'e' };
let len = if exponent < 10 {
*exp_ptr.add(1) = (exponent as u8) + b'0';
2
} else {
let off = exponent << 1;
ptr::copy_nonoverlapping(lut_ptr.add(off), exp_ptr.add(1), 2);
3
};
slice::from_raw_parts(exp_ptr, len)
};
let parts = &[
numfmt::Part::Copy(buf_slice),
numfmt::Part::Zero(added_precision),
numfmt::Part::Copy(exp_slice),
];
let sign = if !is_nonnegative {
"-"
} else if f.sign_plus() {
"+"
} else {
""
};
let formatted = numfmt::Formatted { sign, parts };
// SAFETY: `buf_slice` and `exp_slice` contain only ASCII characters.
unsafe { f.pad_formatted_parts(&formatted) }
}
$(
#[stable(feature = "integer_exp_format", since = "1.42.0")]
impl fmt::LowerExp for $t {
#[allow(unused_comparisons)]
fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
let is_nonnegative = *self >= 0;
let n = if is_nonnegative {
self.$conv_fn()
} else {
// convert the negative num to positive by summing 1 to it's 2 complement
(!self.$conv_fn()).wrapping_add(1)
};
$name(n, is_nonnegative, false, f)
}
})*
$(
#[stable(feature = "integer_exp_format", since = "1.42.0")]
impl fmt::UpperExp for $t {
#[allow(unused_comparisons)]
fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
let is_nonnegative = *self >= 0;
let n = if is_nonnegative {
self.$conv_fn()
} else {
// convert the negative num to positive by summing 1 to it's 2 complement
(!self.$conv_fn()).wrapping_add(1)
};
$name(n, is_nonnegative, true, f)
}
})*
};
}
// Include wasm32 in here since it doesn't reflect the native pointer size, and
// often cares strongly about getting a smaller code size.
#[cfg(any(target_pointer_width = "64", target_arch = "wasm32"))]
mod imp {
use super::*;
impl_Display!(
i8, u8, i16, u16, i32, u32, i64, u64, usize, isize
as u64 via to_u64 named fmt_u64
);
impl_Exp!(
i8, u8, i16, u16, i32, u32, i64, u64, usize, isize
as u64 via to_u64 named exp_u64
);
}
#[cfg(not(any(target_pointer_width = "64", target_arch = "wasm32")))]
mod imp {
use super::*;
impl_Display!(i8, u8, i16, u16, i32, u32, isize, usize as u32 via to_u32 named fmt_u32);
impl_Display!(i64, u64 as u64 via to_u64 named fmt_u64);
impl_Exp!(i8, u8, i16, u16, i32, u32, isize, usize as u32 via to_u32 named exp_u32);
impl_Exp!(i64, u64 as u64 via to_u64 named exp_u64);
}
impl_Exp!(i128, u128 as u128 via to_u128 named exp_u128);
/// Helper function for writing a u64 into `buf` going from last to first, with `curr`.
fn parse_u64_into<const N: usize>(mut n: u64, buf: &mut [MaybeUninit<u8>; N], curr: &mut usize) {
let buf_ptr = MaybeUninit::slice_as_mut_ptr(buf);
let lut_ptr = DEC_DIGITS_LUT.as_ptr();
assert!(*curr > 19);
// SAFETY:
// Writes at most 19 characters into the buffer. Guaranteed that any ptr into LUT is at most
// 198, so will never OOB. There is a check above that there are at least 19 characters
// remaining.
unsafe {
if n >= 1e16 as u64 {
let to_parse = n % 1e16 as u64;
n /= 1e16 as u64;
// Some of these are nops but it looks more elegant this way.
let d1 = ((to_parse / 1e14 as u64) % 100) << 1;
let d2 = ((to_parse / 1e12 as u64) % 100) << 1;
let d3 = ((to_parse / 1e10 as u64) % 100) << 1;
let d4 = ((to_parse / 1e8 as u64) % 100) << 1;
let d5 = ((to_parse / 1e6 as u64) % 100) << 1;
let d6 = ((to_parse / 1e4 as u64) % 100) << 1;
let d7 = ((to_parse / 1e2 as u64) % 100) << 1;
let d8 = ((to_parse / 1e0 as u64) % 100) << 1;
*curr -= 16;
ptr::copy_nonoverlapping(lut_ptr.add(d1 as usize), buf_ptr.add(*curr + 0), 2);
ptr::copy_nonoverlapping(lut_ptr.add(d2 as usize), buf_ptr.add(*curr + 2), 2);
ptr::copy_nonoverlapping(lut_ptr.add(d3 as usize), buf_ptr.add(*curr + 4), 2);
ptr::copy_nonoverlapping(lut_ptr.add(d4 as usize), buf_ptr.add(*curr + 6), 2);
ptr::copy_nonoverlapping(lut_ptr.add(d5 as usize), buf_ptr.add(*curr + 8), 2);
ptr::copy_nonoverlapping(lut_ptr.add(d6 as usize), buf_ptr.add(*curr + 10), 2);
ptr::copy_nonoverlapping(lut_ptr.add(d7 as usize), buf_ptr.add(*curr + 12), 2);
ptr::copy_nonoverlapping(lut_ptr.add(d8 as usize), buf_ptr.add(*curr + 14), 2);
}
if n >= 1e8 as u64 {
let to_parse = n % 1e8 as u64;
n /= 1e8 as u64;
// Some of these are nops but it looks more elegant this way.
let d1 = ((to_parse / 1e6 as u64) % 100) << 1;
let d2 = ((to_parse / 1e4 as u64) % 100) << 1;
let d3 = ((to_parse / 1e2 as u64) % 100) << 1;
let d4 = ((to_parse / 1e0 as u64) % 100) << 1;
*curr -= 8;
ptr::copy_nonoverlapping(lut_ptr.add(d1 as usize), buf_ptr.add(*curr + 0), 2);
ptr::copy_nonoverlapping(lut_ptr.add(d2 as usize), buf_ptr.add(*curr + 2), 2);
ptr::copy_nonoverlapping(lut_ptr.add(d3 as usize), buf_ptr.add(*curr + 4), 2);
ptr::copy_nonoverlapping(lut_ptr.add(d4 as usize), buf_ptr.add(*curr + 6), 2);
}
// `n` < 1e8 < (1 << 32)
let mut n = n as u32;
if n >= 1e4 as u32 {
let to_parse = n % 1e4 as u32;
n /= 1e4 as u32;
let d1 = (to_parse / 100) << 1;
let d2 = (to_parse % 100) << 1;
*curr -= 4;
ptr::copy_nonoverlapping(lut_ptr.add(d1 as usize), buf_ptr.add(*curr + 0), 2);
ptr::copy_nonoverlapping(lut_ptr.add(d2 as usize), buf_ptr.add(*curr + 2), 2);
}
// `n` < 1e4 < (1 << 16)
let mut n = n as u16;
if n >= 100 {
let d1 = (n % 100) << 1;
n /= 100;
*curr -= 2;
ptr::copy_nonoverlapping(lut_ptr.add(d1 as usize), buf_ptr.add(*curr), 2);
}
// decode last 1 or 2 chars
if n < 10 {
*curr -= 1;
*buf_ptr.add(*curr) = (n as u8) + b'0';
} else {
let d1 = n << 1;
*curr -= 2;
ptr::copy_nonoverlapping(lut_ptr.add(d1 as usize), buf_ptr.add(*curr), 2);
}
}
}
#[stable(feature = "rust1", since = "1.0.0")]
impl fmt::Display for u128 {
fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
fmt_u128(*self, true, f)
}
}
#[stable(feature = "rust1", since = "1.0.0")]
impl fmt::Display for i128 {
fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
let is_nonnegative = *self >= 0;
let n = if is_nonnegative {
self.to_u128()
} else {
// convert the negative num to positive by summing 1 to it's 2 complement
(!self.to_u128()).wrapping_add(1)
};
fmt_u128(n, is_nonnegative, f)
}
}
/// Specialized optimization for u128. Instead of taking two items at a time, it splits
/// into at most 2 u64s, and then chunks by 10e16, 10e8, 10e4, 10e2, and then 10e1.
/// It also has to handle 1 last item, as 10^40 > 2^128 > 10^39, whereas
/// 10^20 > 2^64 > 10^19.
fn fmt_u128(n: u128, is_nonnegative: bool, f: &mut fmt::Formatter<'_>) -> fmt::Result {
// 2^128 is about 3*10^38, so 39 gives an extra byte of space
let mut buf = [MaybeUninit::<u8>::uninit(); 39];
let mut curr = buf.len();
let (n, rem) = udiv_1e19(n);
parse_u64_into(rem, &mut buf, &mut curr);
if n != 0 {
// 0 pad up to point
let target = buf.len() - 19;
// SAFETY: Guaranteed that we wrote at most 19 bytes, and there must be space
// remaining since it has length 39
unsafe {
ptr::write_bytes(
MaybeUninit::slice_as_mut_ptr(&mut buf).add(target),
b'0',
curr - target,
);
}
curr = target;
let (n, rem) = udiv_1e19(n);
parse_u64_into(rem, &mut buf, &mut curr);
// Should this following branch be annotated with unlikely?
if n != 0 {
let target = buf.len() - 38;
// The raw `buf_ptr` pointer is only valid until `buf` is used the next time,
// buf `buf` is not used in this scope so we are good.
let buf_ptr = MaybeUninit::slice_as_mut_ptr(&mut buf);
// SAFETY: At this point we wrote at most 38 bytes, pad up to that point,
// There can only be at most 1 digit remaining.
unsafe {
ptr::write_bytes(buf_ptr.add(target), b'0', curr - target);
curr = target - 1;
*buf_ptr.add(curr) = (n as u8) + b'0';
}
}
}
// SAFETY: `curr` > 0 (since we made `buf` large enough), and all the chars are valid
// UTF-8 since `DEC_DIGITS_LUT` is
let buf_slice = unsafe {
str::from_utf8_unchecked(slice::from_raw_parts(
MaybeUninit::slice_as_mut_ptr(&mut buf).add(curr),
buf.len() - curr,
))
};
f.pad_integral(is_nonnegative, "", buf_slice)
}
/// Partition of `n` into n > 1e19 and rem <= 1e19
///
/// Integer division algorithm is based on the following paper:
///
/// T. Granlund and P. Montgomery, “Division by Invariant Integers Using Multiplication”
/// in Proc. of the SIGPLAN94 Conference on Programming Language Design and
/// Implementation, 1994, pp. 61–72
///
fn udiv_1e19(n: u128) -> (u128, u64) {
const DIV: u64 = 1e19 as u64;
const FACTOR: u128 = 156927543384667019095894735580191660403;
let quot = if n < 1 << 83 {
((n >> 19) as u64 / (DIV >> 19)) as u128
} else {
u128_mulhi(n, FACTOR) >> 62
};
let rem = (n - quot * DIV as u128) as u64;
(quot, rem)
}
/// Multiply unsigned 128 bit integers, return upper 128 bits of the result
#[inline]
fn u128_mulhi(x: u128, y: u128) -> u128 {
let x_lo = x as u64;
let x_hi = (x >> 64) as u64;
let y_lo = y as u64;
let y_hi = (y >> 64) as u64;
// handle possibility of overflow
let carry = (x_lo as u128 * y_lo as u128) >> 64;
let m = x_lo as u128 * y_hi as u128 + carry;
let high1 = m >> 64;
let m_lo = m as u64;
let high2 = (x_hi as u128 * y_lo as u128 + m_lo as u128) >> 64;
x_hi as u128 * y_hi as u128 + high1 + high2
}