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    100

    //! Decodes a floating-point value into individual parts and error ranges.

    use crate::num::dec2flt::rawfp::RawFloat;
    use crate::num::FpCategory;

    /// Decoded unsigned finite value, such that:
    ///
    /// - The original value equals to `mant * 2^exp`.
    ///
    /// - Any number from `(mant - minus) * 2^exp` to `(mant + plus) * 2^exp` will
    ///   round to the original value. The range is inclusive only when
    ///   `inclusive` is `true`.
    #[derive(Copy, Clone, Debug, PartialEq, Eq)]
    pub struct Decoded {
        /// The scaled mantissa.
        pub mant: u64,
        /// The lower error range.
        pub minus: u64,
        /// The upper error range.
        pub plus: u64,
        /// The shared exponent in base 2.
        pub exp: i16,
        /// True when the error range is inclusive.
        ///
        /// In IEEE 754, this is true when the original mantissa was even.
        pub inclusive: bool,
    }

    /// Decoded unsigned value.
    #[derive(Copy, Clone, Debug, PartialEq, Eq)]
    pub enum FullDecoded {
        /// Not-a-number.
        Nan,
        /// Infinities, either positive or negative.
        Infinite,
        /// Zero, either positive or negative.
        Zero,
        /// Finite numbers with further decoded fields.
        Finite(Decoded),
    }

    /// A floating point type which can be `decode`d.
    pub trait DecodableFloat: RawFloat + Copy {
        /// The minimum positive normalized value.
        fn min_pos_norm_value() -> Self;
    }

    impl DecodableFloat for f32 {
        fn min_pos_norm_value() -> Self {
            f32::MIN_POSITIVE
        }
    }

    impl DecodableFloat for f64 {
        fn min_pos_norm_value() -> Self {
            f64::MIN_POSITIVE
        }
    }

    /// Returns a sign (true when negative) and `FullDecoded` value
    /// from given floating point number.
    pub fn decode<T: DecodableFloat>(v: T) -> (/*negative?*/ bool, FullDecoded) {
        let (mant, exp, sign) = v.integer_decode();
        let even = (mant & 1) == 0;
        let decoded = match v.classify() {
            FpCategory::Nan => FullDecoded::Nan,
            FpCategory::Infinite => FullDecoded::Infinite,
            FpCategory::Zero => FullDecoded::Zero,
            FpCategory::Subnormal => {
                // neighbors: (mant - 2, exp) -- (mant, exp) -- (mant + 2, exp)
                // Float::integer_decode always preserves the exponent,
                // so the mantissa is scaled for subnormals.
                FullDecoded::Finite(Decoded { mant, minus: 1, plus: 1, exp, inclusive: even })
            }
            FpCategory::Normal => {
                let minnorm = <T as DecodableFloat>::min_pos_norm_value().integer_decode();
                if mant == minnorm.0 {
                    // neighbors: (maxmant, exp - 1) -- (minnormmant, exp) -- (minnormmant + 1, exp)
                    // where maxmant = minnormmant * 2 - 1
                    FullDecoded::Finite(Decoded {
                        mant: mant << 2,
                        minus: 1,
                        plus: 2,
                        exp: exp - 2,
                        inclusive: even,
                    })
                } else {
                    // neighbors: (mant - 1, exp) -- (mant, exp) -- (mant + 1, exp)
                    FullDecoded::Finite(Decoded {
                        mant: mant << 1,
                        minus: 1,
                        plus: 1,
                        exp: exp - 1,
                        inclusive: even,
                    })
                }
            }
        };
        (sign < 0, decoded)
    }