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// Copyright 2015 The Rust Project Developers. See the COPYRIGHT // file at the top-level directory of this distribution and at // http://rust-lang.org/COPYRIGHT. // // Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or // http://www.apache.org/licenses/LICENSE-2.0> or the MIT license // <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your // option. This file may not be copied, modified, or distributed // except according to those terms. //! Decodes a floating-point value into individual parts and error ranges. use {f32, f64}; use num::FpCategory; use 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) }