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    //! Integer and floating-point number formatting

    use crate::fmt;
    use crate::ops::{Div, Rem, Sub};
    use crate::str;
    use crate::slice;
    use crate::ptr;
    use crate::mem::MaybeUninit;

    #[doc(hidden)]
    trait Int: 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;
        fn to_u16(&self) -> u16;
        fn to_u32(&self) -> u32;
        fn to_u64(&self) -> u64;
        fn to_u128(&self) -> u128;
    }

    macro_rules! doit {
        ($($t:ident)*) => ($(impl Int for $t {
            fn zero() -> $t { 0 }
            fn from_u8(u: u8) -> $t { u as $t }
            fn to_u8(&self) -> u8 { *self as u8 }
            fn to_u16(&self) -> u16 { *self as u16 }
            fn to_u32(&self) -> u32 { *self as u32 }
            fn to_u64(&self) -> u64 { *self as u64 }
            fn to_u128(&self) -> u128 { *self as u128 }
        })*)
    }
    doit! { i8 i16 i32 i64 i128 isize u8 u16 u32 u64 u128 usize }

    /// A type that represents a specific radix
    #[doc(hidden)]
    trait GenericRadix {
        /// 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: Int>(&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..];
            let buf = unsafe { str::from_utf8_unchecked(slice::from_raw_parts(
                MaybeUninit::first_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),+) => {
            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 {
        ($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! 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)
                    }
                }
            }
        }
    }

    macro_rules! integer {
        ($Int:ident, $Uint:ident) => {
            int_base! { Binary   for $Int as $Uint  -> Binary }
            int_base! { Octal    for $Int as $Uint  -> Octal }
            int_base! { LowerHex for $Int as $Uint  -> LowerHex }
            int_base! { UpperHex for $Int as $Uint  -> UpperHex }
            debug! { $Int }

            int_base! { Binary   for $Uint as $Uint -> Binary }
            int_base! { Octal    for $Uint as $Uint -> Octal }
            int_base! { LowerHex for $Uint as $Uint -> LowerHex }
            int_base! { UpperHex for $Uint as $Uint -> UpperHex }
            debug! { $Uint }
        }
    }
    integer! { isize, usize }
    integer! { i8, u8 }
    integer! { i16, u16 }
    integer! { i32, u32 }
    integer! { i64, u64 }
    integer! { i128, u128 }

    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 {
                let mut buf = [MaybeUninit::<u8>::uninit(); 39];
                let mut curr = buf.len() as isize;
                let buf_ptr = MaybeUninit::first_ptr_mut(&mut buf);
                let lut_ptr = DEC_DIGITS_LUT.as_ptr();

                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 isize;
                        n /= 10000;

                        let d1 = (rem / 100) << 1;
                        let d2 = (rem % 100) << 1;
                        curr -= 4;
                        ptr::copy_nonoverlapping(lut_ptr.offset(d1), buf_ptr.offset(curr), 2);
                        ptr::copy_nonoverlapping(lut_ptr.offset(d2), buf_ptr.offset(curr + 2), 2);
                    }

                    // if we reach here numbers are <= 9999, so at most 4 chars long
                    let mut n = n as isize; // 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.offset(d1), buf_ptr.offset(curr), 2);
                    }

                    // decode last 1 or 2 chars
                    if n < 10 {
                        curr -= 1;
                        *buf_ptr.offset(curr) = (n as u8) + b'0';
                    } else {
                        let d1 = n << 1;
                        curr -= 2;
                        ptr::copy_nonoverlapping(lut_ptr.offset(d1), buf_ptr.offset(curr), 2);
                    }
                }

                let buf_slice = unsafe {
                    str::from_utf8_unchecked(
                        slice::from_raw_parts(buf_ptr.offset(curr), buf.len() - curr as usize))
                };
                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)
                    }
                })*
        };
    }

    // 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
        );
    }

    #[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_Display!(i128, u128 as u128 via to_u128 named fmt_u128);

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