| //! Decodes a floating-point value into individual parts and error ranges. |
| |
| use crate::{f32, f64}; |
| use crate::num::FpCategory; |
| use crate::num::dec2flt::rawfp::RawFloat; |
| |
| /// 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) |
| } |
| |