proptest/

num.rs

//-
// Copyright 2017, 2018 Jason Lingle
//
// 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.

//! Strategies to generate numeric values (as opposed to integers used as bit
//! fields).
//!
//! All strategies in this module shrink by binary searching towards 0.

mod float_samplers;

use crate::test_runner::TestRunner;
use rand::distr::uniform::{SampleUniform, Uniform};
use rand::distr::{Distribution, StandardUniform};

/// Generate a random value of `X`, sampled uniformly from the half
/// open range `[low, high)` (excluding `high`). Panics if `low >= high`.
pub(crate) fn sample_uniform<X: SampleUniform>(
    run: &mut TestRunner,
    start: X,
    end: X,
) -> X {
    Uniform::new(start, end).expect("not uniform").sample(run.rng())
}

/// Generate a random value of `X`, sampled uniformly from the closed
/// range `[low, high]` (inclusive). Panics if `low > high`.
pub fn sample_uniform_incl<X: SampleUniform>(
    run: &mut TestRunner,
    start: X,
    end: X,
) -> X {
    Uniform::new_inclusive(start, end).expect("not uniform").sample(run.rng())
}

macro_rules! sample_uniform {
    ($name: ident, $incl:ident, $from:ty, $to:ty) => {
        fn $name<X>(
            run: &mut TestRunner,
            start: $to,
            end: $to,
        ) -> $to {
            Uniform::<$from>::new(start as $from, end as $from).expect("not uniform").sample(run.rng()) as $to
        }

        fn $incl<X>(
            run: &mut TestRunner,
            start: $to,
            end: $to,
        ) -> $to {
            Uniform::<$from>::new_inclusive(start as $from, end as $from).expect("not uniform").sample(run.rng()) as $to
        }        
    }
}

#[cfg(target_pointer_width = "64")]
sample_uniform!(usize_sample_uniform, usize_sample_uniform_incl, u64, usize);
#[cfg(target_pointer_width = "32")]
sample_uniform!(usize_sample_uniform, usize_sample_uniform_incl, u32, usize);
#[cfg(target_pointer_width = "16")]
sample_uniform!(usize_sample_uniform, usize_sample_uniform_incl, u16, usize);

#[cfg(target_pointer_width = "64")]
sample_uniform!(isize_sample_uniform, isize_sample_uniform_incl, i64, isize);
#[cfg(target_pointer_width = "32")]
sample_uniform!(isize_sample_uniform, isize_sample_uniform_incl, i32, isize);
#[cfg(target_pointer_width = "16")]
sample_uniform!(isize_sample_uniform, isize_sample_uniform_incl, i16, isize);

macro_rules! supported_int_any {
    ($runner:ident, $typ:ty) => {
        $runner.rng().random()
    };
}

#[cfg(target_pointer_width = "64")]
macro_rules! unsupported_int_any {
    ($runner:ident, $typ:ty) => {
        $runner.rng().next_u64() as $typ
    };
}

#[cfg(not(target_pointer_width = "64"))]
macro_rules! unsupported_int_any {
    ($runner:ident, $typ:ty) => {
        $runner.rng().next_u32() as $typ
    };
}

macro_rules! int_any {
    ($typ: ident, $int_any: ident) => {
        /// Type of the `ANY` constant.
        #[derive(Clone, Copy, Debug)]
        #[must_use = "strategies do nothing unless used"]
        pub struct Any(());
        /// Generates integers with completely arbitrary values, uniformly
        /// distributed over the whole range.
        pub const ANY: Any = Any(());

        impl Strategy for Any {
            type Tree = BinarySearch;
            type Value = $typ;

            fn new_tree(&self, runner: &mut TestRunner) -> NewTree<Self> {
                Ok(BinarySearch::new($int_any!(runner, $typ)))
            }
        }
    };
}

macro_rules! numeric_api {
    ($typ:ident, $epsilon:expr) => {
        numeric_api!($typ, $typ, $epsilon);
    };
    ($typ:ident, $sample_typ:ty, $epsilon:expr) => {
        numeric_api!($typ, $sample_typ, $epsilon, sample_uniform, sample_uniform_incl);
    };
    ($typ:ident, $epsilon:expr, $uniform:ident, $incl:ident) => {
        numeric_api!($typ, $typ, $epsilon, $uniform, $incl);
    };
    ($typ:ident, $sample_typ:ty, $epsilon:expr, $uniform:ident, $incl:ident) => {
        impl Strategy for ::core::ops::Range<$typ> {
            type Tree = BinarySearch;
            type Value = $typ;

            fn new_tree(&self, runner: &mut TestRunner) -> NewTree<Self> {
                if self.is_empty() {
                    panic!(
                        "Invalid use of empty range {}..{}.",
                        self.start, self.end
                    );
                }

                Ok(BinarySearch::new_clamped(
                    self.start,
                    $crate::num::$uniform::<$sample_typ>(
                        runner,
                        self.start.into(),
                        self.end.into(),
                    )
                    .into(),
                    self.end - $epsilon,
                ))
            }
        }

        impl Strategy for ::core::ops::RangeInclusive<$typ> {
            type Tree = BinarySearch;
            type Value = $typ;

            fn new_tree(&self, runner: &mut TestRunner) -> NewTree<Self> {
                if self.is_empty() {
                    panic!(
                        "Invalid use of empty range {}..={}.",
                        self.start(),
                        self.end()
                    );
                }

                Ok(BinarySearch::new_clamped(
                    *self.start(),
                    $crate::num::$incl::<$sample_typ>(
                        runner,
                        (*self.start()).into(),
                        (*self.end()).into(),
                    )
                    .into(),
                    *self.end(),
                ))
            }
        }

        impl Strategy for ::core::ops::RangeFrom<$typ> {
            type Tree = BinarySearch;
            type Value = $typ;

            fn new_tree(&self, runner: &mut TestRunner) -> NewTree<Self> {
                Ok(BinarySearch::new_clamped(
                    self.start,
                    $crate::num::$incl::<$sample_typ>(
                        runner,
                        self.start.into(),
                        <$typ>::MAX.into(),
                    )
                    .into(),
                    <$typ>::MAX,
                ))
            }
        }

        impl Strategy for ::core::ops::RangeTo<$typ> {
            type Tree = BinarySearch;
            type Value = $typ;

            fn new_tree(&self, runner: &mut TestRunner) -> NewTree<Self> {
                Ok(BinarySearch::new_clamped(
                    <$typ>::MIN,
                    $crate::num::$uniform::<$sample_typ>(
                        runner,
                        <$typ>::MIN.into(),
                        self.end.into(),
                    )
                    .into(),
                    self.end,
                ))
            }
        }

        impl Strategy for ::core::ops::RangeToInclusive<$typ> {
            type Tree = BinarySearch;
            type Value = $typ;

            fn new_tree(&self, runner: &mut TestRunner) -> NewTree<Self> {
                Ok(BinarySearch::new_clamped(
                    <$typ>::MIN,
                    $crate::num::$incl::<$sample_typ>(
                        runner,
                        <$typ>::MIN.into(),
                        self.end.into(),
                    )
                    .into(),
                    self.end,
                ))
            }
        }
    };
}

macro_rules! signed_integer_bin_search {
    ($typ:ident) => {
        signed_integer_bin_search!($typ, supported_int_any, sample_uniform, sample_uniform_incl);
    };
    ($typ:ident, $int_any: ident, $uniform: ident, $incl: ident) => {
        #[allow(missing_docs)]
        pub mod $typ {
            #[allow(unused_imports)]
            use rand::{Rng, RngCore};

            use crate::strategy::*;
            use crate::test_runner::TestRunner;

            int_any!($typ, $int_any);

            /// Shrinks an integer towards 0, using binary search to find
            /// boundary points.
            #[derive(Clone, Copy, Debug)]
            pub struct BinarySearch {
                lo: $typ,
                curr: $typ,
                hi: $typ,
            }
            impl BinarySearch {
                /// Creates a new binary searcher starting at the given value.
                pub fn new(start: $typ) -> Self {
                    BinarySearch {
                        lo: 0,
                        curr: start,
                        hi: start,
                    }
                }

                /// Creates a new binary searcher which will not produce values
                /// on the other side of `lo` or `hi` from `start`. `lo` is
                /// inclusive, `hi` is exclusive.
                fn new_clamped(lo: $typ, start: $typ, hi: $typ) -> Self {
                    use core::cmp::{max, min};

                    BinarySearch {
                        lo: if start < 0 {
                            min(0, hi - 1)
                        } else {
                            max(0, lo)
                        },
                        hi: start,
                        curr: start,
                    }
                }

                fn reposition(&mut self) -> bool {
                    // Won't ever overflow since lo starts at 0 and advances
                    // towards hi.
                    let interval = self.hi - self.lo;
                    let new_mid = self.lo + interval / 2;

                    if new_mid == self.curr {
                        false
                    } else {
                        self.curr = new_mid;
                        true
                    }
                }

                fn magnitude_greater(lhs: $typ, rhs: $typ) -> bool {
                    if 0 == lhs {
                        false
                    } else if lhs < 0 {
                        lhs < rhs
                    } else {
                        lhs > rhs
                    }
                }
            }
            impl ValueTree for BinarySearch {
                type Value = $typ;

                fn current(&self) -> $typ {
                    self.curr
                }

                fn simplify(&mut self) -> bool {
                    if !BinarySearch::magnitude_greater(self.hi, self.lo) {
                        return false;
                    }

                    self.hi = self.curr;
                    self.reposition()
                }

                fn complicate(&mut self) -> bool {
                    if !BinarySearch::magnitude_greater(self.hi, self.lo) {
                        return false;
                    }

                    self.lo = self.curr + if self.hi < 0 { -1 } else { 1 };

                    self.reposition()
                }
            }

            numeric_api!($typ, 1, $uniform, $incl);
        }
    };
}

macro_rules! unsigned_integer_bin_search {
    ($typ:ident) => {
        unsigned_integer_bin_search!($typ, supported_int_any, sample_uniform, sample_uniform_incl);
    };
    ($typ:ident, $int_any: ident, $uniform: ident, $incl: ident) => {
        #[allow(missing_docs)]
        pub mod $typ {
            #[allow(unused_imports)]
            use rand::{Rng, RngCore};

            use crate::strategy::*;
            use crate::test_runner::TestRunner;

            int_any!($typ, $int_any);

            /// Shrinks an integer towards 0, using binary search to find
            /// boundary points.
            #[derive(Clone, Copy, Debug)]
            pub struct BinarySearch {
                lo: $typ,
                curr: $typ,
                hi: $typ,
            }
            impl BinarySearch {
                /// Creates a new binary searcher starting at the given value.
                pub fn new(start: $typ) -> Self {
                    BinarySearch {
                        lo: 0,
                        curr: start,
                        hi: start,
                    }
                }

                /// Creates a new binary searcher which will not search below
                /// the given `lo` value.
                fn new_clamped(lo: $typ, start: $typ, _hi: $typ) -> Self {
                    BinarySearch {
                        lo: lo,
                        curr: start,
                        hi: start,
                    }
                }

                /// Creates a new binary searcher which will not search below
                /// the given `lo` value.
                pub fn new_above(lo: $typ, start: $typ) -> Self {
                    BinarySearch::new_clamped(lo, start, start)
                }

                fn reposition(&mut self) -> bool {
                    let interval = self.hi - self.lo;
                    let new_mid = self.lo + interval / 2;

                    if new_mid == self.curr {
                        false
                    } else {
                        self.curr = new_mid;
                        true
                    }
                }
            }
            impl ValueTree for BinarySearch {
                type Value = $typ;

                fn current(&self) -> $typ {
                    self.curr
                }

                fn simplify(&mut self) -> bool {
                    if self.hi <= self.lo {
                        return false;
                    }

                    self.hi = self.curr;
                    self.reposition()
                }

                fn complicate(&mut self) -> bool {
                    if self.hi <= self.lo {
                        return false;
                    }

                    self.lo = self.curr + 1;
                    self.reposition()
                }
            }

            numeric_api!($typ, 1, $uniform, $incl);
        }
    };
}

signed_integer_bin_search!(i8);
signed_integer_bin_search!(i16);
signed_integer_bin_search!(i32);
signed_integer_bin_search!(i64);
signed_integer_bin_search!(i128);
signed_integer_bin_search!(isize, unsupported_int_any, isize_sample_uniform, isize_sample_uniform_incl);
unsigned_integer_bin_search!(u8);
unsigned_integer_bin_search!(u16);
unsigned_integer_bin_search!(u32);
unsigned_integer_bin_search!(u64);
unsigned_integer_bin_search!(u128);
unsigned_integer_bin_search!(usize, unsupported_int_any, usize_sample_uniform, usize_sample_uniform_incl);

bitflags! {
    #[derive(Debug, Clone, Copy, PartialEq, Eq, PartialOrd, Ord, Hash)]
    pub(crate) struct FloatTypes: u32 {
        const POSITIVE          = 0b0000_0001;
        const NEGATIVE          = 0b0000_0010;
        const NORMAL            = 0b0000_0100;
        const SUBNORMAL         = 0b0000_1000;
        const ZERO              = 0b0001_0000;
        const INFINITE          = 0b0010_0000;
        const QUIET_NAN         = 0b0100_0000;
        const SIGNALING_NAN     = 0b1000_0000;
        const ANY =
            Self::POSITIVE.bits() |
            Self::NEGATIVE.bits() |
            Self::NORMAL.bits() |
            Self::SUBNORMAL.bits() |
            Self::ZERO.bits() |
            Self::INFINITE.bits() |
            Self::QUIET_NAN.bits();
    }
}

impl FloatTypes {
    fn normalise(mut self) -> Self {
        if !self.intersects(FloatTypes::POSITIVE | FloatTypes::NEGATIVE) {
            self |= FloatTypes::POSITIVE;
        }

        if !self.intersects(
            FloatTypes::NORMAL
                | FloatTypes::SUBNORMAL
                | FloatTypes::ZERO
                | FloatTypes::INFINITE
                | FloatTypes::QUIET_NAN
                | FloatTypes::SIGNALING_NAN,
        ) {
            self |= FloatTypes::NORMAL;
        }
        self
    }
}

trait FloatLayout
where
    StandardUniform: Distribution<Self::Bits>,
{
    type Bits: Copy;

    const SIGN_MASK: Self::Bits;
    const EXP_MASK: Self::Bits;
    const EXP_ZERO: Self::Bits;
    const MANTISSA_MASK: Self::Bits;
}

#[cfg(feature = "f16")]
impl FloatLayout for f16 {
    type Bits = u16;

    const SIGN_MASK: u16 = 0x8000;
    const EXP_MASK: u16 = 0x7c00;
    const EXP_ZERO: u16 = f16::to_bits(1.0);
    const MANTISSA_MASK: u16 = !(Self::SIGN_MASK | Self::EXP_MASK);
}

impl FloatLayout for f32 {
    type Bits = u32;

    const SIGN_MASK: u32 = 0x8000_0000;
    const EXP_MASK: u32 = 0x7F80_0000;
    const EXP_ZERO: u32 = 0x3F80_0000;
    const MANTISSA_MASK: u32 = 0x007F_FFFF;
}

impl FloatLayout for f64 {
    type Bits = u64;

    const SIGN_MASK: u64 = 0x8000_0000_0000_0000;
    const EXP_MASK: u64 = 0x7FF0_0000_0000_0000;
    const EXP_ZERO: u64 = 0x3FF0_0000_0000_0000;
    const MANTISSA_MASK: u64 = 0x000F_FFFF_FFFF_FFFF;
}

macro_rules! float_any {
    ($typ:ident) => {
        /// Strategies which produce floating-point values from particular
        /// classes. See the various `Any`-typed constants in this module.
        ///
        /// Note that this usage is fairly advanced and primarily useful to
        /// implementors of algorithms that need to handle wild values in a
        /// particular way. For testing things like graphics processing or game
        /// physics, simply using ranges (e.g., `-1.0..2.0`) will often be more
        /// practical.
        ///
        /// `Any` can be OR'ed to combine multiple classes. For example,
        /// `POSITIVE | INFINITE` will generate arbitrary positive, non-NaN
        /// floats, including positive infinity (but not negative infinity, of
        /// course).
        ///
        /// If neither `POSITIVE` nor `NEGATIVE` has been OR'ed into an `Any`
        /// but a type to be generated requires a sign, `POSITIVE` is assumed.
        /// If no classes are OR'ed into an `Any` (i.e., only `POSITIVE` and/or
        /// `NEGATIVE` are given), `NORMAL` is assumed.
        ///
        /// The various float classes are assigned fixed weights for generation
        /// which are believed to be reasonable for most applications. Roughly:
        ///
        /// - If `POSITIVE | NEGATIVE`, the sign is evenly distributed between
        ///   both options.
        ///
        /// - Classes are weighted as follows, in descending order:
        ///   `NORMAL` > `ZERO` > `SUBNORMAL` > `INFINITE` > `QUIET_NAN` =
        ///   `SIGNALING_NAN`.
        #[derive(Clone, Copy, Debug)]
        #[must_use = "strategies do nothing unless used"]
        pub struct Any(FloatTypes);

        #[cfg(test)]
        impl Any {
            pub(crate) fn from_bits(bits: u32) -> Self {
                Any(FloatTypes::from_bits_truncate(bits))
            }

            pub(crate) fn normal_bits(&self) -> FloatTypes {
                self.0.normalise()
            }
        }

        impl ops::BitOr for Any {
            type Output = Self;

            fn bitor(self, rhs: Self) -> Self {
                Any(self.0 | rhs.0)
            }
        }

        impl ops::BitOrAssign for Any {
            fn bitor_assign(&mut self, rhs: Self) {
                self.0 |= rhs.0
            }
        }

        /// Generates positive floats
        ///
        /// By itself, implies the `NORMAL` class, unless another class is
        /// OR'ed in. That is, using `POSITIVE` as a strategy by itself will
        /// generate arbitrary values between the type's `MIN_POSITIVE` and
        /// `MAX`, while `POSITIVE | INFINITE` would only allow generating
        /// positive infinity.
        pub const POSITIVE: Any = Any(FloatTypes::POSITIVE);
        /// Generates negative floats.
        ///
        /// By itself, implies the `NORMAL` class, unless another class is
        /// OR'ed in. That is, using `POSITIVE` as a strategy by itself will
        /// generate arbitrary values between the type's `MIN` and
        /// `-MIN_POSITIVE`, while `NEGATIVE | INFINITE` would only allow
        /// generating positive infinity.
        pub const NEGATIVE: Any = Any(FloatTypes::NEGATIVE);
        /// Generates "normal" floats.
        ///
        /// These are finite values where the first bit of the mantissa is an
        /// implied `1`. When positive, this represents the range
        /// `MIN_POSITIVE` through `MAX`, both inclusive.
        ///
        /// Generated values are uniform over the discrete floating-point
        /// space, which means the numeric distribution is an inverse
        /// exponential step function. For example, values between 1.0 and 2.0
        /// are generated with the same frequency as values between 2.0 and
        /// 4.0, even though the latter covers twice the numeric range.
        ///
        /// If neither `POSITIVE` nor `NEGATIVE` is OR'ed with this constant,
        /// `POSITIVE` is implied.
        pub const NORMAL: Any = Any(FloatTypes::NORMAL);
        /// Generates subnormal floats.
        ///
        /// These are finite non-zero values where the first bit of the
        /// mantissa is not an implied zero. When positive, this represents the
        /// range `MIN`, inclusive, through `MIN_POSITIVE`, exclusive.
        ///
        /// Subnormals are generated with a uniform distribution both in terms
        /// of discrete floating-point space and numerically.
        ///
        /// If neither `POSITIVE` nor `NEGATIVE` is OR'ed with this constant,
        /// `POSITIVE` is implied.
        pub const SUBNORMAL: Any = Any(FloatTypes::SUBNORMAL);
        /// Generates zero-valued floats.
        ///
        /// Note that IEEE floats support both positive and negative zero, so
        /// this class does interact with the sign flags.
        ///
        /// If neither `POSITIVE` nor `NEGATIVE` is OR'ed with this constant,
        /// `POSITIVE` is implied.
        pub const ZERO: Any = Any(FloatTypes::ZERO);
        /// Generates infinity floats.
        ///
        /// If neither `POSITIVE` nor `NEGATIVE` is OR'ed with this constant,
        /// `POSITIVE` is implied.
        pub const INFINITE: Any = Any(FloatTypes::INFINITE);
        /// Generates "Quiet NaN" floats.
        ///
        /// Operations on quiet NaNs generally simply propagate the NaN rather
        /// than invoke any exception mechanism.
        ///
        /// The payload of the NaN is uniformly distributed over the possible
        /// values which safe Rust allows, including the sign bit (as
        /// controlled by `POSITIVE` and `NEGATIVE`).
        ///
        /// Note however that in Rust 1.23.0 and earlier, this constitutes only
        /// one particular payload due to apparent issues with particular MIPS
        /// and PA-RISC processors which fail to implement IEEE 754-2008
        /// correctly.
        ///
        /// On Rust 1.24.0 and later, this does produce arbitrary payloads as
        /// documented.
        ///
        /// On platforms where the CPU and the IEEE standard disagree on the
        /// format of a quiet NaN, values generated conform to the hardware's
        /// expectations.
        pub const QUIET_NAN: Any = Any(FloatTypes::QUIET_NAN);
        /// Generates "Signaling NaN" floats if allowed by the platform.
        ///
        /// On most platforms, signalling NaNs by default behave the same as
        /// quiet NaNs, but it is possible to configure the OS or CPU to raise
        /// an asynchronous exception if an operation is performed on a
        /// signalling NaN.
        ///
        /// In Rust 1.23.0 and earlier, this silently behaves the same as
        /// [`QUIET_NAN`](const.QUIET_NAN.html).
        ///
        /// On platforms where the CPU and the IEEE standard disagree on the
        /// format of a quiet NaN, values generated conform to the hardware's
        /// expectations.
        ///
        /// Note that certain platforms — most notably, x86/AMD64 — allow the
        /// architecture to turn a signalling NaN into a quiet NaN with the
        /// same payload. Whether this happens can depend on what registers the
        /// compiler decides to use to pass the value around, what CPU flags
        /// are set, and what compiler settings are in use.
        pub const SIGNALING_NAN: Any = Any(FloatTypes::SIGNALING_NAN);

        /// Generates literally arbitrary floating-point values, including
        /// infinities and quiet NaNs (but not signaling NaNs).
        ///
        /// Equivalent to `POSITIVE | NEGATIVE | NORMAL | SUBNORMAL | ZERO |
        /// INFINITE | QUIET_NAN`.
        ///
        /// See [`SIGNALING_NAN`](const.SIGNALING_NAN.html) if you also want to
        /// generate signalling NaNs. This signalling NaNs are not included by
        /// default since in most contexts they either make no difference, or
        /// if the process enabled the relevant CPU mode, result in
        /// hardware-triggered exceptions that usually just abort the process.
        ///
        /// Before proptest 0.4.1, this erroneously generated values in the
        /// range 0.0..1.0.
        pub const ANY: Any = Any(FloatTypes::ANY);

        impl Strategy for Any {
            type Tree = BinarySearch;
            type Value = $typ;

            fn new_tree(&self, runner: &mut TestRunner) -> NewTree<Self> {
                let flags = self.0.normalise();
                let sign_mask = if flags.contains(FloatTypes::NEGATIVE) {
                    $typ::SIGN_MASK
                } else {
                    0
                };
                let sign_or = if flags.contains(FloatTypes::POSITIVE) {
                    0
                } else {
                    $typ::SIGN_MASK
                };

                macro_rules! weight {
                    ($case:ident, $weight:expr) => {
                        if flags.contains(FloatTypes::$case) {
                            $weight
                        } else {
                            0
                        }
                    }
                }

                // A few CPUs disagree with IEEE about the meaning of the
                // signalling bit. Assume the `NAN` constant is a quiet NaN as
                // interpreted by the hardware and generate values based on
                // that.
                let quiet_or = $typ::NAN.to_bits() &
                    ($typ::EXP_MASK | ($typ::EXP_MASK >> 1));
                let signaling_or = (quiet_or ^ ($typ::EXP_MASK >> 1)) |
                    $typ::EXP_MASK;

                let (class_mask, class_or, allow_edge_exp, allow_zero_mant) =
                    prop_oneof![
                        weight!(NORMAL, 20) => Just(
                            ($typ::EXP_MASK | $typ::MANTISSA_MASK, 0,
                             false, true)),
                        weight!(SUBNORMAL, 3) => Just(
                            ($typ::MANTISSA_MASK, 0, true, false)),
                        weight!(ZERO, 4) => Just(
                            (0, 0, true, true)),
                        weight!(INFINITE, 2) => Just(
                            (0, $typ::EXP_MASK, true, true)),
                        weight!(QUIET_NAN, 1) => Just(
                            ($typ::MANTISSA_MASK >> 1, quiet_or,
                             true, false)),
                        weight!(SIGNALING_NAN, 1) => Just(
                            ($typ::MANTISSA_MASK >> 1, signaling_or,
                             true, false)),
                    ].new_tree(runner)?.current();

                let mut generated_value: <$typ as FloatLayout>::Bits =
                    runner.rng().random();
                generated_value &= sign_mask | class_mask;
                generated_value |= sign_or | class_or;
                let exp = generated_value & $typ::EXP_MASK;
                if !allow_edge_exp && (0 == exp || $typ::EXP_MASK == exp) {
                    generated_value &= !$typ::EXP_MASK;
                    generated_value |= $typ::EXP_ZERO;
                }
                if !allow_zero_mant &&
                    0 == generated_value & $typ::MANTISSA_MASK
                {
                    generated_value |= 1;
                }

                Ok(BinarySearch::new_with_types(
                    $typ::from_bits(generated_value), flags))
            }
        }
    }
}

macro_rules! float_bin_search {
    ($typ:ident, $sample_typ:ident) => {
        #[allow(missing_docs)]
        pub mod $typ {
            use super::float_samplers::$sample_typ;

            use core::ops;
            #[cfg(not(feature = "std"))]
            use num_traits::float::FloatCore;

            use rand::Rng;

            use super::{FloatLayout, FloatTypes};
            use crate::strategy::*;
            use crate::test_runner::TestRunner;

            float_any!($typ);

            /// Shrinks a float towards 0, using binary search to find boundary
            /// points.
            ///
            /// Non-finite values immediately shrink to 0.
            #[derive(Clone, Copy, Debug)]
            pub struct BinarySearch {
                lo: $typ,
                curr: $typ,
                hi: $typ,
                allowed: FloatTypes,
            }

            impl BinarySearch {
                /// Creates a new binary searcher starting at the given value.
                pub fn new(start: $typ) -> Self {
                    BinarySearch {
                        lo: 0.0,
                        curr: start,
                        hi: start,
                        allowed: FloatTypes::all(),
                    }
                }

                fn new_with_types(start: $typ, allowed: FloatTypes) -> Self {
                    BinarySearch {
                        lo: 0.0,
                        curr: start,
                        hi: start,
                        allowed,
                    }
                }

                /// Creates a new binary searcher which will not produce values
                /// on the other side of `lo` or `hi` from `start`. `lo` is
                /// inclusive, `hi` is exclusive.
                fn new_clamped(lo: $typ, start: $typ, hi: $typ) -> Self {
                    BinarySearch {
                        lo: if start.is_sign_negative() {
                            hi.min(0.0)
                        } else {
                            lo.max(0.0)
                        },
                        hi: start,
                        curr: start,
                        allowed: FloatTypes::all(),
                    }
                }

                fn current_allowed(&self) -> bool {
                    use core::num::FpCategory::*;

                    // Don't reposition if the new value is not allowed
                    let class_allowed = match self.curr.classify() {
                        Nan =>
                        // We don't need to inspect whether the
                        // signallingness of the NaN matches the allowed
                        // set, as we never try to switch between them,
                        // instead shrinking to 0.
                        {
                            self.allowed.contains(FloatTypes::QUIET_NAN)
                                || self
                                    .allowed
                                    .contains(FloatTypes::SIGNALING_NAN)
                        }
                        Infinite => self.allowed.contains(FloatTypes::INFINITE),
                        Zero => self.allowed.contains(FloatTypes::ZERO),
                        Subnormal => {
                            self.allowed.contains(FloatTypes::SUBNORMAL)
                        }
                        Normal => self.allowed.contains(FloatTypes::NORMAL),
                    };
                    let signum = self.curr.signum();
                    let sign_allowed = if signum > 0.0 {
                        self.allowed.contains(FloatTypes::POSITIVE)
                    } else if signum < 0.0 {
                        self.allowed.contains(FloatTypes::NEGATIVE)
                    } else {
                        true
                    };

                    class_allowed && sign_allowed
                }

                fn ensure_acceptable(&mut self) {
                    while !self.current_allowed() {
                        if !self.complicate_once() {
                            panic!(
                                "Unable to complicate floating-point back \
                                 to acceptable value"
                            );
                        }
                    }
                }

                fn reposition(&mut self) -> bool {
                    let interval = self.hi - self.lo;
                    let interval =
                        if interval.is_finite() { interval } else { 0.0 };
                    let new_mid = self.lo + interval / 2.0;

                    let new_mid = if new_mid == self.curr || 0.0 == interval {
                        new_mid
                    } else {
                        self.lo
                    };

                    if new_mid == self.curr {
                        false
                    } else {
                        self.curr = new_mid;
                        true
                    }
                }

                fn done(lo: $typ, hi: $typ) -> bool {
                    (lo.abs() > hi.abs() && !hi.is_nan()) || lo.is_nan()
                }

                fn complicate_once(&mut self) -> bool {
                    if BinarySearch::done(self.lo, self.hi) {
                        return false;
                    }

                    self.lo = if self.curr == self.lo {
                        self.hi
                    } else {
                        self.curr
                    };

                    self.reposition()
                }
            }
            impl ValueTree for BinarySearch {
                type Value = $typ;

                fn current(&self) -> $typ {
                    self.curr
                }

                fn simplify(&mut self) -> bool {
                    if BinarySearch::done(self.lo, self.hi) {
                        return false;
                    }

                    self.hi = self.curr;
                    if self.reposition() {
                        self.ensure_acceptable();
                        true
                    } else {
                        false
                    }
                }

                fn complicate(&mut self) -> bool {
                    if self.complicate_once() {
                        self.ensure_acceptable();
                        true
                    } else {
                        false
                    }
                }
            }

            numeric_api!($typ, $sample_typ, 0.0);
        }
    };
}

#[cfg(feature = "f16")]
float_bin_search!(f16, F16U);
float_bin_search!(f32, F32U);
float_bin_search!(f64, F64U);

#[cfg(test)]
mod test {
    use crate::strategy::*;
    use crate::test_runner::*;

    use super::*;

    #[test]
    fn u8_inclusive_end_included() {
        let mut runner = TestRunner::deterministic();
        let mut ok = 0;
        for _ in 0..20 {
            let tree = (0..=1).new_tree(&mut runner).unwrap();
            let test = runner.run_one(tree, |v| {
                prop_assert_eq!(v, 1);
                Ok(())
            });
            if test.is_ok() {
                ok += 1;
            }
        }
        assert!(ok > 1, "inclusive end not included.");
    }

    #[test]
    fn u8_inclusive_to_end_included() {
        let mut runner = TestRunner::deterministic();
        let mut ok = 0;
        for _ in 0..20 {
            let tree = (..=1u8).new_tree(&mut runner).unwrap();
            let test = runner.run_one(tree, |v| {
                prop_assert_eq!(v, 1);
                Ok(())
            });
            if test.is_ok() {
                ok += 1;
            }
        }
        assert!(ok > 1, "inclusive end not included.");
    }

    #[test]
    fn i8_binary_search_always_converges() {
        fn assert_converges<P: Fn(i32) -> bool>(start: i8, pass: P) {
            let mut state = i8::BinarySearch::new(start);
            loop {
                if !pass(state.current() as i32) {
                    if !state.simplify() {
                        break;
                    }
                } else {
                    if !state.complicate() {
                        break;
                    }
                }
            }

            assert!(!pass(state.current() as i32));
            assert!(
                pass(state.current() as i32 - 1)
                    || pass(state.current() as i32 + 1)
            );
        }

        for start in -128..0 {
            for target in start + 1..1 {
                assert_converges(start as i8, |v| v > target);
            }
        }

        for start in 0..128 {
            for target in 0..start {
                assert_converges(start as i8, |v| v < target);
            }
        }
    }

    #[test]
    fn u8_binary_search_always_converges() {
        fn assert_converges<P: Fn(u32) -> bool>(start: u8, pass: P) {
            let mut state = u8::BinarySearch::new(start);
            loop {
                if !pass(state.current() as u32) {
                    if !state.simplify() {
                        break;
                    }
                } else {
                    if !state.complicate() {
                        break;
                    }
                }
            }

            assert!(!pass(state.current() as u32));
            assert!(pass(state.current() as u32 - 1));
        }

        for start in 0..255 {
            for target in 0..start {
                assert_converges(start as u8, |v| v <= target);
            }
        }
    }

    #[test]
    fn signed_integer_range_including_zero_converges_to_zero() {
        let mut runner = TestRunner::default();
        for _ in 0..100 {
            let mut state = (-42i32..64i32).new_tree(&mut runner).unwrap();
            let init_value = state.current();
            assert!(init_value >= -42 && init_value < 64);

            while state.simplify() {
                let v = state.current();
                assert!(v >= -42 && v < 64);
            }

            assert_eq!(0, state.current());
        }
    }

    #[test]
    fn negative_integer_range_stays_in_bounds() {
        let mut runner = TestRunner::default();
        for _ in 0..100 {
            let mut state = (..-42i32).new_tree(&mut runner).unwrap();
            let init_value = state.current();
            assert!(init_value < -42);

            while state.simplify() {
                assert!(
                    state.current() < -42,
                    "Violated bounds: {}",
                    state.current()
                );
            }

            assert_eq!(-43, state.current());
        }
    }

    #[test]
    fn positive_signed_integer_range_stays_in_bounds() {
        let mut runner = TestRunner::default();
        for _ in 0..100 {
            let mut state = (42i32..).new_tree(&mut runner).unwrap();
            let init_value = state.current();
            assert!(init_value >= 42);

            while state.simplify() {
                assert!(
                    state.current() >= 42,
                    "Violated bounds: {}",
                    state.current()
                );
            }

            assert_eq!(42, state.current());
        }
    }

    #[test]
    fn unsigned_integer_range_stays_in_bounds() {
        let mut runner = TestRunner::default();
        for _ in 0..100 {
            let mut state = (42u32..56u32).new_tree(&mut runner).unwrap();
            let init_value = state.current();
            assert!(init_value >= 42 && init_value < 56);

            while state.simplify() {
                assert!(
                    state.current() >= 42,
                    "Violated bounds: {}",
                    state.current()
                );
            }

            assert_eq!(42, state.current());
        }
    }

    mod contract_sanity {
        macro_rules! contract_sanity {
            ($t:tt) => {
                mod $t {
                    use crate::strategy::check_strategy_sanity;

                    const FORTY_TWO: $t = 42 as $t;
                    const FIFTY_SIX: $t = 56 as $t;

                    #[test]
                    fn range() {
                        check_strategy_sanity(FORTY_TWO..FIFTY_SIX, None);
                    }

                    #[test]
                    fn range_inclusive() {
                        check_strategy_sanity(FORTY_TWO..=FIFTY_SIX, None);
                    }

                    #[test]
                    fn range_to() {
                        check_strategy_sanity(..FIFTY_SIX, None);
                    }

                    #[test]
                    fn range_to_inclusive() {
                        check_strategy_sanity(..=FIFTY_SIX, None);
                    }

                    #[test]
                    fn range_from() {
                        check_strategy_sanity(FORTY_TWO.., None);
                    }
                }
            };
        }
        contract_sanity!(u8);
        contract_sanity!(i8);
        contract_sanity!(u16);
        contract_sanity!(i16);
        contract_sanity!(u32);
        contract_sanity!(i32);
        contract_sanity!(u64);
        contract_sanity!(i64);
        contract_sanity!(usize);
        contract_sanity!(isize);
        #[cfg(feature = "f16")]
        contract_sanity!(f16);
        contract_sanity!(f32);
        contract_sanity!(f64);
    }

    #[test]
    fn unsigned_integer_binsearch_simplify_complicate_contract_upheld() {
        check_strategy_sanity(0u32..1000u32, None);
        check_strategy_sanity(0u32..1u32, None);
    }

    #[test]
    fn signed_integer_binsearch_simplify_complicate_contract_upheld() {
        check_strategy_sanity(0i32..1000i32, None);
        check_strategy_sanity(0i32..1i32, None);
    }

    #[test]
    fn positive_float_simplifies_to_zero() {
        let mut runner = TestRunner::default();
        let mut value = (0.0f64..2.0).new_tree(&mut runner).unwrap();

        while value.simplify() {}

        assert_eq!(0.0, value.current());
    }

    #[test]
    fn positive_float_simplifies_to_base() {
        let mut runner = TestRunner::default();
        let mut value = (1.0f64..2.0).new_tree(&mut runner).unwrap();

        while value.simplify() {}

        assert_eq!(1.0, value.current());
    }

    #[test]
    fn negative_float_simplifies_to_zero() {
        let mut runner = TestRunner::default();
        let mut value = (-2.0f64..0.0).new_tree(&mut runner).unwrap();

        while value.simplify() {}

        assert_eq!(0.0, value.current());
    }

    #[test]
    fn positive_float_complicates_to_original() {
        let mut runner = TestRunner::default();
        let mut value = (1.0f64..2.0).new_tree(&mut runner).unwrap();
        let orig = value.current();

        assert!(value.simplify());
        while value.complicate() {}

        assert_eq!(orig, value.current());
    }

    #[test]
    fn positive_infinity_simplifies_directly_to_zero() {
        let mut value = f64::BinarySearch::new(::std::f64::INFINITY);

        assert!(value.simplify());
        assert_eq!(0.0, value.current());
        assert!(value.complicate());
        assert_eq!(::std::f64::INFINITY, value.current());
        assert!(!value.clone().complicate());
        assert!(!value.clone().simplify());
    }

    #[test]
    fn negative_infinity_simplifies_directly_to_zero() {
        let mut value = f64::BinarySearch::new(::std::f64::NEG_INFINITY);

        assert!(value.simplify());
        assert_eq!(0.0, value.current());
        assert!(value.complicate());
        assert_eq!(::std::f64::NEG_INFINITY, value.current());
        assert!(!value.clone().complicate());
        assert!(!value.clone().simplify());
    }

    #[test]
    fn nan_simplifies_directly_to_zero() {
        let mut value = f64::BinarySearch::new(::std::f64::NAN);

        assert!(value.simplify());
        assert_eq!(0.0, value.current());
        assert!(value.complicate());
        assert!(value.current().is_nan());
        assert!(!value.clone().complicate());
        assert!(!value.clone().simplify());
    }

    #[test]
    fn float_simplifies_to_smallest_normal() {
        let mut runner = TestRunner::default();
        let mut value = (f64::MIN_POSITIVE..2.0)
            .new_tree(&mut runner)
            .unwrap();

        while value.simplify() {}

        assert_eq!(f64::MIN_POSITIVE, value.current());
    }

    macro_rules! float_generation_test_body {
        ($strategy:ident, $typ:ident) => {
            use std::num::FpCategory;

            let strategy = $strategy;
            let bits = strategy.normal_bits();

            let mut seen_positive = 0;
            let mut seen_negative = 0;
            let mut seen_normal = 0;
            let mut seen_subnormal = 0;
            let mut seen_zero = 0;
            let mut seen_infinite = 0;
            let mut seen_quiet_nan = 0;
            let mut seen_signaling_nan = 0;
            let mut runner = TestRunner::deterministic();

            // Check whether this version of Rust honours the NaN payload in
            // from_bits
            let fidelity_1 = f32::from_bits(0x7F80_0001).to_bits();
            let fidelity_2 = f32::from_bits(0xFF80_0001).to_bits();
            let nan_fidelity = fidelity_1 != fidelity_2;

            for _ in 0..1024 {
                let mut tree = strategy.new_tree(&mut runner).unwrap();
                let mut increment = 1;

                loop {
                    let value = tree.current();

                    let sign = value.signum(); // So we correctly handle -0
                    if sign < 0.0 {
                        prop_assert!(bits.contains(FloatTypes::NEGATIVE));
                        seen_negative += increment;
                    } else if sign > 0.0 {
                        // i.e., not NaN
                        prop_assert!(bits.contains(FloatTypes::POSITIVE));
                        seen_positive += increment;
                    }

                    match value.classify() {
                        FpCategory::Nan if nan_fidelity => {
                            let raw = value.to_bits();
                            let is_negative = raw << 1 >> 1 != raw;
                            if is_negative {
                                prop_assert!(
                                    bits.contains(FloatTypes::NEGATIVE)
                                );
                                seen_negative += increment;
                            } else {
                                prop_assert!(
                                    bits.contains(FloatTypes::POSITIVE)
                                );
                                seen_positive += increment;
                            }

                            let is_quiet = raw & ($typ::EXP_MASK >> 1)
                                == $typ::NAN.to_bits() & ($typ::EXP_MASK >> 1);
                            if is_quiet {
                                // x86/AMD64 turn signalling NaNs into quiet
                                // NaNs quite aggressively depending on what
                                // registers LLVM decides to use to pass the
                                // value around, so accept either case here.
                                prop_assert!(
                                    bits.contains(FloatTypes::QUIET_NAN)
                                        || bits.contains(
                                            FloatTypes::SIGNALING_NAN
                                        )
                                );
                                seen_quiet_nan += increment;
                                seen_signaling_nan += increment;
                            } else {
                                prop_assert!(
                                    bits.contains(FloatTypes::SIGNALING_NAN)
                                );
                                seen_signaling_nan += increment;
                            }
                        }

                        FpCategory::Nan => {
                            // Since safe Rust doesn't currently allow
                            // generating any NaN other than one particular
                            // payload, don't check the sign or signallingness
                            // and consider this to be both signs and
                            // signallingness for counting purposes.
                            seen_positive += increment;
                            seen_negative += increment;
                            seen_quiet_nan += increment;
                            seen_signaling_nan += increment;
                            prop_assert!(
                                bits.contains(FloatTypes::QUIET_NAN)
                                    || bits.contains(FloatTypes::SIGNALING_NAN)
                            );
                        }
                        FpCategory::Infinite => {
                            prop_assert!(bits.contains(FloatTypes::INFINITE));
                            seen_infinite += increment;
                        }
                        FpCategory::Zero => {
                            prop_assert!(bits.contains(FloatTypes::ZERO));
                            seen_zero += increment;
                        }
                        FpCategory::Subnormal => {
                            prop_assert!(bits.contains(FloatTypes::SUBNORMAL));
                            seen_subnormal += increment;
                        }
                        FpCategory::Normal => {
                            prop_assert!(bits.contains(FloatTypes::NORMAL));
                            seen_normal += increment;
                        }
                    }

                    // Don't count simplified values towards the counts
                    increment = 0;
                    if !tree.simplify() {
                        break;
                    }
                }
            }

            if bits.contains(FloatTypes::POSITIVE) {
                prop_assert!(seen_positive > 200);
            }
            if bits.contains(FloatTypes::NEGATIVE) {
                prop_assert!(seen_negative > 200);
            }
            if bits.contains(FloatTypes::NORMAL) {
                prop_assert!(seen_normal > 100);
            }
            if bits.contains(FloatTypes::SUBNORMAL) {
                prop_assert!(seen_subnormal > 5);
            }
            if bits.contains(FloatTypes::ZERO) {
                prop_assert!(seen_zero > 5);
            }
            if bits.contains(FloatTypes::INFINITE) {
                prop_assert!(seen_infinite > 0);
            }
            if bits.contains(FloatTypes::QUIET_NAN) {
                prop_assert!(seen_quiet_nan > 0);
            }
            if bits.contains(FloatTypes::SIGNALING_NAN) {
                prop_assert!(seen_signaling_nan > 0);
            }
        };
    }

    proptest! {
        #![proptest_config(crate::test_runner::Config::with_cases(1024))]

        #[cfg(feature = "f16")]
        #[test]
        fn f16_any_generates_desired_values(
            strategy in crate::bits::u32::ANY.prop_map(f16::Any::from_bits)
        ) {
            float_generation_test_body!(strategy, f16);
        }

        #[cfg(feature = "f16")]
        #[test]
        fn f16_any_sanity(
            strategy in crate::bits::u32::ANY.prop_map(f16::Any::from_bits)
        ) {
            check_strategy_sanity(strategy, Some(CheckStrategySanityOptions {
                strict_complicate_after_simplify: false,
                .. CheckStrategySanityOptions::default()
            }));
        }

        #[test]
        fn f32_any_generates_desired_values(
            strategy in crate::bits::u32::ANY.prop_map(f32::Any::from_bits)
        ) {
            float_generation_test_body!(strategy, f32);
        }

        #[test]
        fn f32_any_sanity(
            strategy in crate::bits::u32::ANY.prop_map(f32::Any::from_bits)
        ) {
            check_strategy_sanity(strategy, Some(CheckStrategySanityOptions {
                strict_complicate_after_simplify: false,
                .. CheckStrategySanityOptions::default()
            }));
        }

        #[test]
        fn f64_any_generates_desired_values(
            strategy in crate::bits::u32::ANY.prop_map(f64::Any::from_bits)
        ) {
            float_generation_test_body!(strategy, f64);
        }

        #[test]
        fn f64_any_sanity(
            strategy in crate::bits::u32::ANY.prop_map(f64::Any::from_bits)
        ) {
            check_strategy_sanity(strategy, Some(CheckStrategySanityOptions {
                strict_complicate_after_simplify: false,
                .. CheckStrategySanityOptions::default()
            }));
        }
    }

    mod panic_on_empty {
        macro_rules! panic_on_empty {
            ($t:tt) => {
                mod $t {
                    use crate::strategy::Strategy;
                    use crate::test_runner::TestRunner;
                    use std::panic;
                    use std::string::String;

                    const ZERO: $t = 0 as $t;
                    const ONE: $t = 1 as $t;

                    #[test]
                    fn range() {
                        assert_eq!(
                            panic::catch_unwind(|| {
                                let mut runner = TestRunner::deterministic();
                                let _ = (ZERO..ZERO).new_tree(&mut runner);
                            })
                            .err()
                            .and_then(|a| a
                                .downcast_ref::<String>()
                                .map(|s| {
                                    s == "Invalid use of empty range 0..0."
                                })),
                            Some(true)
                        );
                    }

                    #[test]
                    fn range_inclusive() {
                        assert_eq!(
                            panic::catch_unwind(|| {
                                let mut runner = TestRunner::deterministic();
                                let _ = (ONE..=ZERO).new_tree(&mut runner);
                            })
                            .err()
                            .and_then(|a| a
                                .downcast_ref::<String>()
                                .map(|s| {
                                    s == "Invalid use of empty range 1..=0."
                                })),
                            Some(true)
                        );
                    }
                }
            };
        }
        panic_on_empty!(u8);
        panic_on_empty!(i8);
        panic_on_empty!(u16);
        panic_on_empty!(i16);
        panic_on_empty!(u32);
        panic_on_empty!(i32);
        panic_on_empty!(u64);
        panic_on_empty!(i64);
        panic_on_empty!(usize);
        panic_on_empty!(isize);
        #[cfg(feature = "f16")]
        panic_on_empty!(f16);
        panic_on_empty!(f32);
        panic_on_empty!(f64);
    }
}