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Added README, added examples, and updated documentation.

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Alex Huszagh
2020-02-06 23:57:55 -06:00
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.gitignore
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/target
**/*.rs.bk
Cargo.lock
/build
Cargo.toml
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[package]
authors = ["Alex Huszagh <ahuszagh@gmail.com>"]
categories = ["parsing", "no-std"]
description = "Float parsing conversion routines."
edition = "2018"
name = "minimal_lexical"
version = "0.0.1"
readme = "README.md"
repository = "https://github.com/Alexhuszagh/minimal-lexical"
[features]
default = ["std"]
std = []
LICENSE-APACHE
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README.md
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minimal_lexical
===============
This is a minimal version of [rust-lexical](https://github.com/Alexhuszagh/rust-lexical), meant to allow efficient round-trip float parsing. This does not implement a correct float parser, however, it will be accurate for round-trip values.
# Getting Started
```rust
extern crate minimal_lexical;
// Let's say we want to parse "1.2345".
// First, we have an external parser parse all the significant digits
// into a u64 (`12345`), and then we have the exponent adjusted to
// the mantissa (`-4`, since the value is `12345e-4`). Finally,
// we store whether digits were truncated from the mantissa during
// parsing (false).
let float = minimal_lexical::parse_float::<f64>(12345, -4, false);
println!("float={:?}", float); // 1.235
```
# License
Lexical is dual licensed under the Apache 2.0 license as well as the MIT license. See the LICENCE-MIT and the LICENCE-APACHE files for the licenses.
# Contributing
Unless you explicitly state otherwise, any contribution intentionally submitted for inclusion in lexical by you, as defined in the Apache-2.0 license, shall be dual licensed as above, without any additional terms or conditions.
src/cached.rs
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//! Cached powers trait for extended-precision floats.
use super::cached_float80;
use super::float::ExtendedFloat;
@@ -65,7 +67,7 @@ impl ModeratePathPowers {
// CACHED EXTENDED POWERS
/// Cached powers as a trait for a floating-point type.
pub(super) trait ModeratePathCache {
pub(crate) trait ModeratePathCache {
/// Get cached powers.
fn get_powers() -> &'static ModeratePathPowers;
}
src/cached_float80.rs
+1 -150
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@@ -7,155 +7,6 @@
//! These values were calculated using Python, using the arbitrary-precision
//! integer to calculate exact extended-representation of each value.
//! These values are all normalized.
//!
//! This files takes ~ 26KB of storage.
//!
//! This file is mostly automatically generated, do not change values
//! manually, unless you know what you are doing. The script to generate
//! the values is as follows:
//!
//! ```text
//! import math
//! from collections import deque
//!
//! STEP_STR = "const BASE{0}_STEP: i32 = {1};"
//! SMALL_MANTISSA_STR = "const BASE{0}_SMALL_MANTISSA: [u64; {1}] = ["
//! SMALL_EXPONENT_STR = "const BASE{0}_SMALL_EXPONENT: [i32; {1}] = ["
//! LARGE_MANTISSA_STR = "const BASE{0}_LARGE_MANTISSA: [u64; {1}] = ["
//! LARGE_EXPONENT_STR = "const BASE{0}_LARGE_EXPONENT: [i32; {1}] = ["
//! SMALL_INT_STR = "const BASE{0}_SMALL_INT_POWERS: [u64; {1}] = {2};"
//! BIAS_STR = "const BASE{0}_BIAS: i32 = {1};"
//! EXP_STR = "// {}^{}"
//! POWER_STR = """pub(crate) const BASE{0}_POWERS: ModeratePathPowers<u64> = ModeratePathPowers {{
//! small: ExtendedFloatArray {{ mant: &BASE{0}_SMALL_MANTISSA, exp: &BASE{0}_SMALL_EXPONENT }},
//! large: ExtendedFloatArray {{ mant: &BASE{0}_LARGE_MANTISSA, exp: &BASE{0}_LARGE_EXPONENT }},
//! small_int: &BASE{0}_SMALL_INT_POWERS,
//! step: BASE{0}_STEP,
//! bias: BASE{0}_BIAS,
//! }};\n"""
//!
//! def calculate_bitshift(base, exponent):
//! '''
//! Calculate the bitshift required for a given base. The exponent
//! is the absolute value of the max exponent (log distance from 1.)
//! '''
//!
//! return 63 + math.ceil(math.log2(base**exponent))
//!
//!
//! def next_fp(fp, base, step = 1):
//! '''Generate the next extended-floating point value.'''
//!
//! return (fp[0] * (base**step), fp[1])
//!
//!
//! def prev_fp(fp, base, step = 1):
//! '''Generate the previous extended-floating point value.'''
//!
//! return (fp[0] // (base**step), fp[1])
//!
//!
//! def normalize_fp(fp):
//! '''Normalize a extended-float so the MSB is the 64th bit'''
//!
//! while fp[0] >> 64 != 0:
//! fp = (fp[0] >> 1, fp[1] + 1)
//! return fp
//!
//!
//! def generate_small(base, count):
//! '''Generate the small powers for a given base'''
//!
//! bitshift = calculate_bitshift(base, count)
//! fps = []
//! fp = (1 << bitshift, -bitshift)
//! for exp in range(count):
//! fps.append((normalize_fp(fp), exp))
//! fp = next_fp(fp, base)
//!
//! # Print the small powers as integers.
//! ints = [base**i for _, i in fps]
//!
//! return fps, ints
//!
//!
//! def generate_large(base, step):
//! '''Generate the large powers for a given base.'''
//!
//! # Get our starting parameters
//! min_exp = math.floor(math.log(5e-324, base) - math.log(0xFFFFFFFFFFFFFFFF, base))
//! max_exp = math.ceil(math.log(1.7976931348623157e+308, base))
//! bitshift = calculate_bitshift(base, abs(min_exp - step))
//! fps = deque()
//!
//! # Add negative exponents
//! # We need to go below the minimum exponent, since we need
//! # all resulting exponents to be positive.
//! fp = (1 << bitshift, -bitshift)
//! for exp in range(-step, min_exp-step, -step):
//! fp = prev_fp(fp, base, step)
//! fps.appendleft((normalize_fp(fp), exp))
//!
//! # Add positive exponents
//! fp = (1 << bitshift, -bitshift)
//! fps.append((normalize_fp(fp), 0))
//! for exp in range(step, max_exp, step):
//! fp = next_fp(fp, base, step)
//! fps.append((normalize_fp(fp), exp))
//!
//! # Return the smallest exp, AKA, the bias
//! return fps, -fps[0][1]
//!
//!
//! def print_array(base, string, fps, index):
//! '''Print an entire array'''
//!
//! print(string.format(base, len(fps)))
//! for fp, exp in fps:
//! value = " {},".format(fp[index])
//! exp = EXP_STR.format(base, exp)
//! print(value.ljust(30, " ") + exp)
//! print("];")
//!
//!
//! def generate_base(base):
//! '''Generate all powers and variables.'''
//!
//! step = math.floor(math.log(1e10, base))
//! small, ints = generate_small(base, step)
//! large, bias = generate_large(base, step)
//!
//! print_array(base, SMALL_MANTISSA_STR, small, 0)
//! print_array(base, SMALL_EXPONENT_STR, small, 1)
//! print_array(base, LARGE_MANTISSA_STR, large, 0)
//! print_array(base, LARGE_EXPONENT_STR, large, 1)
//! print(SMALL_INT_STR.format(base, len(ints), ints))
//! print(STEP_STR.format(base, step))
//! print(BIAS_STR.format(base, bias))
//!
//!
//! def generate():
//! '''Generate all bases.'''
//!
//! bases = [
//! 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21,
//! 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35, 36
//! ]
//!
//! for base in bases:
//! print("// BASE{}\n".format(base))
//! generate_base(base)
//! print("")
//!
//! print("// HIGH LEVEL\n// ----------\n")
//!
//! for base in bases:
//! print(POWER_STR.format(base))
//!
//!
//! if __name__ == '__main__':
//! generate()
//! ```
use super::cached::{ExtendedFloatArray, ModeratePathPowers};
@@ -331,7 +182,7 @@ const BASE10_BIAS: i32 = 350;
// HIGH LEVEL
// ----------
pub(crate) const BASE10_POWERS: ModeratePathPowers = ModeratePathPowers {
const BASE10_POWERS: ModeratePathPowers = ModeratePathPowers {
small: ExtendedFloatArray { mant: &BASE10_SMALL_MANTISSA, exp: &BASE10_SMALL_EXPONENT },
large: ExtendedFloatArray { mant: &BASE10_LARGE_MANTISSA, exp: &BASE10_LARGE_EXPONENT },
small_int: &BASE10_SMALL_INT_POWERS,
src/convert.rs
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@@ -1,32 +0,0 @@
use super::float::ExtendedFloat;
use super::num::*;
// INTO FLOAT
// Export extended-precision float to native float.
//
// The extended-precision float must be in native float representation,
// with overflow/underflow appropriately handled.
pub(crate) fn into_float<F>(fp: ExtendedFloat) -> F
where F: Float
{
// Export floating-point number.
if fp.mant == 0 || fp.exp < F::DENORMAL_EXPONENT {
// sub-denormal, underflow
F::ZERO
} else if fp.exp >= F::MAX_EXPONENT {
// overflow
F::from_bits(F::INFINITY_BITS)
} else {
// calculate the exp and fraction bits, and return a float from bits.
let exp: u64;
if (fp.exp == F::DENORMAL_EXPONENT) && (fp.mant & F::HIDDEN_BIT_MASK.as_u64()) == 0 {
exp = 0;
} else {
exp = (fp.exp + F::EXPONENT_BIAS).as_u64();
}
let exp = exp << F::MANTISSA_SIZE;
let mant = fp.mant & F::MANTISSA_MASK.as_u64();
F::from_bits(F::Unsigned::as_cast(mant | exp))
}
}
src/float.rs
+36 -6
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@@ -1,6 +1,5 @@
// FLOAT TYPE
use super::convert::*;
use super::num::*;
use super::rounding::*;
use super::shift::*;
@@ -10,7 +9,7 @@ use super::shift::*;
/// Private implementation, exposed only for testing purposes.
#[doc(hidden)]
#[derive(Clone, Copy, Debug, PartialEq, Eq)]
pub struct ExtendedFloat {
pub(crate) struct ExtendedFloat {
/// Mantissa for the extended-precision float.
pub mant: u64,
/// Binary exponent for the extended-precision float.
@@ -32,7 +31,7 @@ impl ExtendedFloat {
/// 1. Non-signed multiplication of mantissas (requires 2x as many bits as input).
/// 2. Normalization of the result (not done here).
/// 3. Addition of exponents.
pub fn mul(&self, b: &ExtendedFloat) -> ExtendedFloat {
pub(crate) fn mul(&self, b: &ExtendedFloat) -> ExtendedFloat {
// Logic check, values must be decently normalized prior to multiplication.
debug_assert!((self.mant & u64::HIMASK != 0) && (b.mant & u64::HIMASK != 0));
@@ -61,7 +60,7 @@ impl ExtendedFloat {
/// Multiply in-place, as if by `a*b`.
///
/// The result is not normalized.
pub fn imul(&mut self, b: &ExtendedFloat) {
pub(crate) fn imul(&mut self, b: &ExtendedFloat) {
*self = self.mul(b);
}
@@ -73,7 +72,7 @@ impl ExtendedFloat {
/// itself is 0.
///
/// Get the number of bytes shifted.
pub fn normalize(&mut self) -> u32 {
pub(crate) fn normalize(&mut self) -> u32 {
// Note:
// Using the cltz intrinsic via leading_zeros is way faster (~10x)
// than shifting 1-bit at a time, via while loop, and also way
@@ -104,8 +103,39 @@ impl ExtendedFloat {
// INTO
/// Convert into lower-precision native float.
pub fn into_float<F: Float>(mut self) -> F {
pub(crate) fn into_float<F: Float>(mut self) -> F {
self.round_to_native::<F>();
into_float(self)
}
}
// INTO FLOAT
// Export extended-precision float to native float.
//
// The extended-precision float must be in native float representation,
// with overflow/underflow appropriately handled.
pub(crate) fn into_float<F>(fp: ExtendedFloat) -> F
where F: Float
{
// Export floating-point number.
if fp.mant == 0 || fp.exp < F::DENORMAL_EXPONENT {
// sub-denormal, underflow
F::ZERO
} else if fp.exp >= F::MAX_EXPONENT {
// overflow
F::from_bits(F::INFINITY_BITS)
} else {
// calculate the exp and fraction bits, and return a float from bits.
let exp: u64;
if (fp.exp == F::DENORMAL_EXPONENT) && (fp.mant & F::HIDDEN_BIT_MASK.as_u64()) == 0 {
exp = 0;
} else {
exp = (fp.exp + F::EXPONENT_BIAS).as_u64();
}
let exp = exp << F::MANTISSA_SIZE;
let mant = fp.mant & F::MANTISSA_MASK.as_u64();
F::from_bits(F::Unsigned::as_cast(mant | exp))
}
}
src/lib.rs
+11 -1
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@@ -1,6 +1,14 @@
/// Facade around the core features for name mangling.
pub(crate) mod lib {
#[cfg(feature = "std")]
pub(crate) use std::*;
#[cfg(not(feature = "std"))]
pub(crate) use core::*;
}
mod cached;
mod cached_float80;
mod convert;
mod float;
mod num;
mod parse;
@@ -8,4 +16,6 @@ mod rounding;
mod shift;
// API.
pub use self::num::Float;
pub use self::parse::parse_float;
src/num.rs
+130 -13
View File
@@ -1,5 +1,8 @@
use std::ops;
//! Utilities for Rust numbers.
use crate::lib::ops;
/// Type that can be converted to primitive with `as`.
pub trait AsPrimitive:
Sized +
Copy +
@@ -135,6 +138,7 @@ as_cast_impl!(isize, as_isize);
as_cast_impl!(f32, as_f32);
as_cast_impl!(f64, as_f64);
/// Numerical type trait.
pub trait Number:
AsCast +
ops::Add<Output=Self> +
@@ -158,6 +162,7 @@ macro_rules! number_impl {
number_impl! { u8 u16 u32 u64 u128 usize i8 i16 i32 i64 i128 isize f32 f64 }
/// Defines a trait that supports integral operations.
pub trait Integer:
Number +
ops::BitAnd<Output=Self> +
@@ -176,18 +181,8 @@ macro_rules! integer_impl {
integer_impl! { u8 u16 u32 u64 u128 usize i8 i16 i32 i64 i128 isize }
pub trait UnsignedInteger: Integer {}
macro_rules! unsigned_integer_impl {
($($t:ty)*) => ($(
impl UnsignedInteger for $t {}
)*)
}
unsigned_integer_impl! { u8 u16 u32 u64 u128 usize }
/// Type trait for the mantissa type.
pub trait Mantissa: UnsignedInteger {
pub trait Mantissa: Integer {
/// Mask for the left-most bit, to check if the value is normalized.
const NORMALIZED_MASK: Self;
/// Mask to extract the high bits from the integer.
@@ -210,7 +205,7 @@ impl Mantissa for u64 {
/// Get exact exponent limit for radix.
pub trait Float: Number {
/// Unsigned type of the same size.
type Unsigned: UnsignedInteger;
type Unsigned: Integer;
const ZERO: Self;
@@ -377,3 +372,125 @@ impl Float for f64 {
f64::to_bits(self)
}
}
// TEST
// ----
#[cfg(test)]
mod tests {
use super::*;
fn check_as_primitive<T: AsPrimitive>(t: T) {
let _: u8 = t.as_u8();
let _: u16 = t.as_u16();
let _: u32 = t.as_u32();
let _: u64 = t.as_u64();
let _: u128 = t.as_u128();
let _: usize = t.as_usize();
let _: i8 = t.as_i8();
let _: i16 = t.as_i16();
let _: i32 = t.as_i32();
let _: i64 = t.as_i64();
let _: i128 = t.as_i128();
let _: isize = t.as_isize();
let _: f32 = t.as_f32();
let _: f64 = t.as_f64();
}
#[test]
fn as_primitive_test() {
check_as_primitive(1u8);
check_as_primitive(1u16);
check_as_primitive(1u32);
check_as_primitive(1u64);
check_as_primitive(1u128);
check_as_primitive(1usize);
check_as_primitive(1i8);
check_as_primitive(1i16);
check_as_primitive(1i32);
check_as_primitive(1i64);
check_as_primitive(1i128);
check_as_primitive(1isize);
check_as_primitive(1f32);
check_as_primitive(1f64);
}
fn check_number<T: Number>(x: T, mut y: T) {
// Copy, partialeq, partialord
let _ = x;
assert!(x < y);
assert!(x != y);
// Operations
let _ = y + x;
let _ = y - x;
let _ = y * x;
let _ = y / x;
let _ = y % x;
y += x;
y -= x;
y *= x;
y /= x;
y %= x;
// Conversions already tested.
}
#[test]
fn number_test() {
check_number(1u8, 5);
check_number(1u16, 5);
check_number(1u32, 5);
check_number(1u64, 5);
check_number(1u128, 5);
check_number(1usize, 5);
check_number(1i8, 5);
check_number(1i16, 5);
check_number(1i32, 5);
check_number(1i64, 5);
check_number(1i128, 5);
check_number(1isize, 5);
check_number(1f32, 5.0);
check_number(1f64, 5.0);
}
fn check_integer<T: Integer>(x: T) {
// Bitwise operations
let _ = x & T::ZERO;
}
#[test]
fn integer_test() {
check_integer(65u8);
check_integer(65u16);
check_integer(65u32);
check_integer(65u64);
check_integer(65u128);
check_integer(65usize);
check_integer(65i8);
check_integer(65i16);
check_integer(65i32);
check_integer(65i64);
check_integer(65i128);
check_integer(65isize);
}
fn check_float<T: Float>(x: T) {
// Check functions
let _ = x.powi(5);
let _ = x.to_bits();
assert!(T::from_bits(x.to_bits()) == x);
// Check properties
let _ = x.to_bits() & T::SIGN_MASK;
let _ = x.to_bits() & T::EXPONENT_MASK;
let _ = x.to_bits() & T::HIDDEN_BIT_MASK;
let _ = x.to_bits() & T::MANTISSA_MASK;
}
#[test]
fn float_test() {
check_float(123f32);
check_float(123f64);
}
}
src/parse.rs
+87 -1
View File
@@ -116,7 +116,7 @@ fn multiply_exponent_extended<F>(fp: &mut ExtendedFloat, exponent: i32)
///
/// Return the float approximation and if the value can be accurately
/// represented with mantissa bits of precision.
pub(super) fn moderate_path<F>(mantissa: u64, exponent: i32) -> F
fn moderate_path<F>(mantissa: u64, exponent: i32) -> F
where F: Float
{
let mut fp = ExtendedFloat { mant: mantissa, exp: 0 };
@@ -156,3 +156,89 @@ pub fn parse_float<F>(mantissa: u64, exponent: i32, truncated: bool) -> F
moderate_path(mantissa, exponent)
}
}
// TESTS
// -----
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn float_fast_path_test() {
// valid
let mantissa = (1 << f32::MANTISSA_SIZE) - 1;
let (min_exp, max_exp) = f32::exponent_limit();
for exp in min_exp..max_exp+1 {
let f = fast_path::<f32>(mantissa, exp);
assert!(f.is_some(), "should be valid {:?}.", (mantissa, exp));
}
// Check slightly above valid exponents
let f = fast_path::<f32>(123, 15);
assert_eq!(f, Some(1.23e+17));
// Exponent is 1 too high, pushes over the mantissa.
let f = fast_path::<f32>(123, 16);
assert!(f.is_none());
// Mantissa is too large, checked_mul should overflow.
let f = fast_path::<f32>(mantissa, 11);
assert!(f.is_none());
// invalid mantissa
#[cfg(feature = "radix")] {
let (_, max_exp) = f64::exponent_limit(3);
let f = fast_path::<f32>(1<<f32::MANTISSA_SIZE, 3, max_exp+1);
assert!(f.is_none(), "invalid mantissa");
}
// invalid exponents
let (min_exp, max_exp) = f32::exponent_limit();
let f = fast_path::<f32>(mantissa, min_exp-1);
assert!(f.is_none(), "exponent under min_exp");
let f = fast_path::<f32>(mantissa, max_exp+1);
assert!(f.is_none(), "exponent above max_exp");
}
#[test]
fn double_fast_path_test() {
// valid
let mantissa = (1 << f64::MANTISSA_SIZE) - 1;
let (min_exp, max_exp) = f64::exponent_limit();
for exp in min_exp..max_exp+1 {
let f = fast_path::<f64>(mantissa, exp);
assert!(f.is_some(), "should be valid {:?}.", (mantissa, exp));
}
// invalid mantissa
#[cfg(feature = "radix")] {
let (_, max_exp) = f64::exponent_limit(3);
let f = fast_path::<f64>(1<<f64::MANTISSA_SIZE, 3, max_exp+1);
assert!(f.is_none(), "invalid mantissa");
}
// invalid exponents
let (min_exp, max_exp) = f64::exponent_limit();
let f = fast_path::<f64>(mantissa, min_exp-1);
assert!(f.is_none(), "exponent under min_exp");
let f = fast_path::<f64>(mantissa, max_exp+1);
assert!(f.is_none(), "exponent above max_exp");
}
#[test]
fn parse_double_test() {
assert_eq!(123456789.0, moderate_path::<f64>(1234567890, -1));
assert_eq!(123456789.1, moderate_path::<f64>(1234567891, -1));
assert_eq!(123456789.12, moderate_path::<f64>(12345678912, -2));
assert_eq!(123456789.123, moderate_path::<f64>(123456789123, -3));
assert_eq!(123456789.1234, moderate_path::<f64>(1234567891234, -4));
assert_eq!(123456789.12345, moderate_path::<f64>(12345678912345, -5));
assert_eq!(123456789.123456, moderate_path::<f64>(123456789123456, -6));
assert_eq!(123456789.1234567, moderate_path::<f64>(1234567891234567, -7));
assert_eq!(123456789.12345679, moderate_path::<f64>(12345678912345679, -8));
assert_eq!(123456789.12345, moderate_path::<f64>(12345678912345, -5));
}
}
src/rounding.rs
+259 -3
View File
@@ -1,4 +1,6 @@
use std::mem;
//! Defines rounding schemes for floating-point numbers.
use crate::lib::mem;
use super::float::ExtendedFloat;
use super::num::*;
use super::shift::*;
@@ -75,6 +77,31 @@ pub(crate) fn round_nearest(fp: &mut ExtendedFloat, shift: i32)
(is_above, is_halfway)
}
// Tie rounded floating point to event.
pub(crate) fn tie_even(fp: &mut ExtendedFloat, is_above: bool, is_halfway: bool)
{
// Extract the last bit after shifting (and determine if it is odd).
let is_odd = fp.mant & 1 == 1;
// Calculate if we need to roundup.
// We need to roundup if we are above halfway, or if we are odd
// and at half-way (need to tie-to-even).
if is_above || (is_odd && is_halfway) {
fp.mant += 1;
}
}
// Shift right N-bytes and round nearest, tie-to-even.
//
// Floating-point arithmetic uses round to nearest, ties to even,
// which rounds to the nearest value, if the value is halfway in between,
// round to an even value.
pub(crate) fn round_nearest_tie_even(fp: &mut ExtendedFloat, shift: i32)
{
let (is_above, is_halfway) = round_nearest(fp, shift);
tie_even(fp, is_above, is_halfway);
}
// ROUND TO FLOAT
// Shift the ExtendedFloat fraction to the fraction bits in a native float.
@@ -98,14 +125,14 @@ pub(crate) fn round_to_float<F>(fp: &mut ExtendedFloat)
let diff = F::DENORMAL_EXPONENT - fp.exp;
if diff <= u64::FULL {
// We can avoid underflow, can get a valid representation.
round_nearest(fp, diff);
round_nearest_tie_even(fp, diff);
} else {
// Certain underflow, assign literal 0s.
fp.mant = 0;
fp.exp = 0;
}
} else {
round_nearest(fp, F::DEFAULT_SHIFT);
round_nearest_tie_even(fp, F::DEFAULT_SHIFT);
}
if fp.mant & F::CARRY_MASK == F::CARRY_MASK {
@@ -158,3 +185,232 @@ pub(crate) fn round_to_native<F>(fp: &mut ExtendedFloat)
round_to_float::<F>(fp);
avoid_overflow::<F>(fp);
}
// TESTS
// -----
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn lower_n_mask_test() {
assert_eq!(lower_n_mask(0u64), 0b0);
assert_eq!(lower_n_mask(1u64), 0b1);
assert_eq!(lower_n_mask(2u64), 0b11);
assert_eq!(lower_n_mask(10u64), 0b1111111111);
assert_eq!(lower_n_mask(32u64), 0b11111111111111111111111111111111);
}
#[test]
fn lower_n_halfway_test() {
assert_eq!(lower_n_halfway(0u64), 0b0);
assert_eq!(lower_n_halfway(1u64), 0b1);
assert_eq!(lower_n_halfway(2u64), 0b10);
assert_eq!(lower_n_halfway(10u64), 0b1000000000);
assert_eq!(lower_n_halfway(32u64), 0b10000000000000000000000000000000);
}
#[test]
fn nth_bit_test() {
assert_eq!(nth_bit(0u64), 0b1);
assert_eq!(nth_bit(1u64), 0b10);
assert_eq!(nth_bit(2u64), 0b100);
assert_eq!(nth_bit(10u64), 0b10000000000);
assert_eq!(nth_bit(31u64), 0b10000000000000000000000000000000);
}
#[test]
fn internal_n_mask_test() {
assert_eq!(internal_n_mask(1u64, 0u64), 0b0);
assert_eq!(internal_n_mask(1u64, 1u64), 0b1);
assert_eq!(internal_n_mask(2u64, 1u64), 0b10);
assert_eq!(internal_n_mask(4u64, 2u64), 0b1100);
assert_eq!(internal_n_mask(10u64, 2u64), 0b1100000000);
assert_eq!(internal_n_mask(10u64, 4u64), 0b1111000000);
assert_eq!(internal_n_mask(32u64, 4u64), 0b11110000000000000000000000000000);
}
// NEAREST ROUNDING
#[test]
fn round_nearest_test() {
// Check exactly halfway (b'1100000')
let mut fp = ExtendedFloat { mant: 0x60, exp: 0 };
let (above, halfway) = round_nearest(&mut fp, 6);
assert!(!above);
assert!(halfway);
assert_eq!(fp.mant, 1);
// Check above halfway (b'1100001')
let mut fp = ExtendedFloat { mant: 0x61, exp: 0 };
let (above, halfway) = round_nearest(&mut fp, 6);
assert!(above);
assert!(!halfway);
assert_eq!(fp.mant, 1);
// Check below halfway (b'1011111')
let mut fp = ExtendedFloat { mant: 0x5F, exp: 0 };
let (above, halfway) = round_nearest(&mut fp, 6);
assert!(!above);
assert!(!halfway);
assert_eq!(fp.mant, 1);
}
#[test]
fn round_nearest_tie_even_test() {
// Check round-up, halfway
let mut fp = ExtendedFloat { mant: 0x60, exp: 0 };
round_nearest_tie_even(&mut fp, 6);
assert_eq!(fp.mant, 2);
// Check round-down, halfway
let mut fp = ExtendedFloat { mant: 0x20, exp: 0 };
round_nearest_tie_even(&mut fp, 6);
assert_eq!(fp.mant, 0);
// Check round-up, above halfway
let mut fp = ExtendedFloat { mant: 0x61, exp: 0 };
round_nearest_tie_even(&mut fp, 6);
assert_eq!(fp.mant, 2);
let mut fp = ExtendedFloat { mant: 0x21, exp: 0 };
round_nearest_tie_even(&mut fp, 6);
assert_eq!(fp.mant, 1);
// Check round-down, below halfway
let mut fp = ExtendedFloat { mant: 0x5F, exp: 0 };
round_nearest_tie_even(&mut fp, 6);
assert_eq!(fp.mant, 1);
let mut fp = ExtendedFloat { mant: 0x1F, exp: 0 };
round_nearest_tie_even(&mut fp, 6);
assert_eq!(fp.mant, 0);
}
// HIGH-LEVEL
#[test]
fn round_to_float_test() {
// Denormal
let mut fp = ExtendedFloat { mant: 1<<63, exp: f64::DENORMAL_EXPONENT - 15 };
round_to_float::<f64>(&mut fp);
assert_eq!(fp.mant, 1<<48);
assert_eq!(fp.exp, f64::DENORMAL_EXPONENT);
// Halfway, round-down (b'1000000000000000000000000000000000000000000000000000010000000000')
let mut fp = ExtendedFloat { mant: 0x8000000000000400, exp: -63 };
round_to_float::<f64>(&mut fp);
assert_eq!(fp.mant, 1<<52);
assert_eq!(fp.exp, -52);
// Halfway, round-up (b'1000000000000000000000000000000000000000000000000000110000000000')
let mut fp = ExtendedFloat { mant: 0x8000000000000C00, exp: -63 };
round_to_float::<f64>(&mut fp);
assert_eq!(fp.mant, (1<<52) + 2);
assert_eq!(fp.exp, -52);
// Above halfway
let mut fp = ExtendedFloat { mant: 0x8000000000000401, exp: -63 };
round_to_float::<f64>(&mut fp);
assert_eq!(fp.mant, (1<<52)+1);
assert_eq!(fp.exp, -52);
let mut fp = ExtendedFloat { mant: 0x8000000000000C01, exp: -63 };
round_to_float::<f64>(&mut fp);
assert_eq!(fp.mant, (1<<52) + 2);
assert_eq!(fp.exp, -52);
// Below halfway
let mut fp = ExtendedFloat { mant: 0x80000000000003FF, exp: -63 };
round_to_float::<f64>(&mut fp);
assert_eq!(fp.mant, 1<<52);
assert_eq!(fp.exp, -52);
let mut fp = ExtendedFloat { mant: 0x8000000000000BFF, exp: -63 };
round_to_float::<f64>(&mut fp);
assert_eq!(fp.mant, (1<<52) + 1);
assert_eq!(fp.exp, -52);
}
#[test]
fn avoid_overflow_test() {
// Avoid overflow, fails by 1
let mut fp = ExtendedFloat { mant: 0xFFFFFFFFFFFF, exp: f64::MAX_EXPONENT + 5 };
avoid_overflow::<f64>(&mut fp);
assert_eq!(fp.mant, 0xFFFFFFFFFFFF);
assert_eq!(fp.exp, f64::MAX_EXPONENT+5);
// Avoid overflow, succeeds
let mut fp = ExtendedFloat { mant: 0xFFFFFFFFFFFF, exp: f64::MAX_EXPONENT + 4 };
avoid_overflow::<f64>(&mut fp);
assert_eq!(fp.mant, 0x1FFFFFFFFFFFE0);
assert_eq!(fp.exp, f64::MAX_EXPONENT-1);
}
#[test]
fn round_to_native_test() {
// Overflow
let mut fp = ExtendedFloat { mant: 0xFFFFFFFFFFFF, exp: f64::MAX_EXPONENT + 4 };
round_to_native::<f64>(&mut fp);
assert_eq!(fp.mant, 0x1FFFFFFFFFFFE0);
assert_eq!(fp.exp, f64::MAX_EXPONENT-1);
// Need denormal
let mut fp = ExtendedFloat { mant: 1, exp: f64::DENORMAL_EXPONENT +48 };
round_to_native::<f64>(&mut fp);
assert_eq!(fp.mant, 1<<48);
assert_eq!(fp.exp, f64::DENORMAL_EXPONENT);
// Halfway, round-down (b'10000000000000000000000000000000000000000000000000000100000')
let mut fp = ExtendedFloat { mant: 0x400000000000020, exp: -58 };
round_to_native::<f64>(&mut fp);
assert_eq!(fp.mant, 1<<52);
assert_eq!(fp.exp, -52);
// Halfway, round-up (b'10000000000000000000000000000000000000000000000000001100000')
let mut fp = ExtendedFloat { mant: 0x400000000000060, exp: -58 };
round_to_native::<f64>(&mut fp);
assert_eq!(fp.mant, (1<<52) + 2);
assert_eq!(fp.exp, -52);
// Above halfway
let mut fp = ExtendedFloat { mant: 0x400000000000021, exp: -58 };
round_to_native::<f64>(&mut fp);
assert_eq!(fp.mant, (1<<52)+1);
assert_eq!(fp.exp, -52);
let mut fp = ExtendedFloat { mant: 0x400000000000061, exp: -58 };
round_to_native::<f64>(&mut fp);
assert_eq!(fp.mant, (1<<52) + 2);
assert_eq!(fp.exp, -52);
// Below halfway
let mut fp = ExtendedFloat { mant: 0x40000000000001F, exp: -58 };
round_to_native::<f64>(&mut fp);
assert_eq!(fp.mant, 1<<52);
assert_eq!(fp.exp, -52);
let mut fp = ExtendedFloat { mant: 0x40000000000005F, exp: -58 };
round_to_native::<f64>(&mut fp);
assert_eq!(fp.mant, (1<<52) + 1);
assert_eq!(fp.exp, -52);
// Underflow
// Adapted from failures in strtod.
let mut fp = ExtendedFloat { exp: -1139, mant: 18446744073709550712 };
round_to_native::<f64>(&mut fp);
assert_eq!(fp.mant, 0);
assert_eq!(fp.exp, 0);
let mut fp = ExtendedFloat { exp: -1139, mant: 18446744073709551460 };
round_to_native::<f64>(&mut fp);
assert_eq!(fp.mant, 0);
assert_eq!(fp.exp, 0);
let mut fp = ExtendedFloat { exp: -1138, mant: 9223372036854776103 };
round_to_native::<f64>(&mut fp);
assert_eq!(fp.mant, 1);
assert_eq!(fp.exp, -1074);
}
}
src/shift.rs
+3 -1
View File
@@ -1,4 +1,6 @@
use std::mem;
//! Bit-shift helpers.
use crate::lib::mem;
use super::float::ExtendedFloat;
// Shift extended-precision float right `shift` bytes.