wasmi/src/value.rs

use byteorder::{ByteOrder, LittleEndian};
use core::{f32, i32, i64, u32, u64};
use nan_preserving_float::{F32, F64};
use types::ValueType;
use TrapKind;

/// Error for `LittleEndianConvert`
#[derive(Debug)]
pub enum Error {
    /// The buffer is too short for the type being deserialized
    InvalidLittleEndianBuffer,
}

/// Runtime representation of a value.
///
/// Wasm code manipulate values of the four basic value types:
/// integers and floating-point (IEEE 754-2008) data of 32 or 64 bit width each, respectively.
///
/// There is no distinction between signed and unsigned integer types. Instead, integers are
/// interpreted by respective operations as either unsigned or signed in two’s complement representation.
#[derive(Copy, Clone, Debug, PartialEq)]
pub enum RuntimeValue {
    /// Value of 32-bit signed or unsigned integer.
    I32(i32),
    /// Value of 64-bit signed or unsigned integer.
    I64(i64),
    /// Value of 32-bit IEEE 754-2008 floating point number.
    F32(F32),
    /// Value of 64-bit IEEE 754-2008 floating point number.
    F64(F64),
}

/// Trait for creating value from a [`RuntimeValue`].
///
/// Typically each implementation can create a value from the specific type.
/// For example, values of type `bool` or `u32` are both represented by [`I32`] and `f64` values are represented by
/// [`F64`].
///
/// [`I32`]: enum.RuntimeValue.html#variant.I32
/// [`F64`]: enum.RuntimeValue.html#variant.F64
/// [`RuntimeValue`]: enum.RuntimeValue.html
pub trait FromRuntimeValue
where
    Self: Sized,
{
    /// Create a value of type `Self` from a given [`RuntimeValue`].
    ///
    /// Returns `None` if the [`RuntimeValue`] is of type different than
    /// expected by the conversion in question.
    ///
    /// [`RuntimeValue`]: enum.RuntimeValue.html
    fn from_runtime_value(val: RuntimeValue) -> Option<Self>;
}

/// Convert one type to another by wrapping.
pub trait WrapInto<T> {
    /// Convert one type to another by wrapping.
    fn wrap_into(self) -> T;
}

/// Convert one type to another by rounding to the nearest integer towards zero.
pub trait TryTruncateInto<T, E> {
    /// Convert one type to another by rounding to the nearest integer towards zero.
    fn try_truncate_into(self) -> Result<T, E>;
}

/// Convert one type to another by extending with leading zeroes.
pub trait ExtendInto<T> {
    /// Convert one type to another by extending with leading zeroes.
    fn extend_into(self) -> T;
}

/// Reinterprets the bits of a value of one type as another type.
pub trait TransmuteInto<T> {
    /// Reinterprets the bits of a value of one type as another type.
    fn transmute_into(self) -> T;
}

/// Convert from and to little endian.
pub trait LittleEndianConvert
where
    Self: Sized,
{
    /// Convert to little endian buffer.
    fn into_little_endian(self, buffer: &mut [u8]);
    /// Convert from little endian buffer.
    fn from_little_endian(buffer: &[u8]) -> Result<Self, Error>;
}

/// Arithmetic operations.
pub trait ArithmeticOps<T> {
    /// Add two values.
    fn add(self, other: T) -> T;
    /// Subtract two values.
    fn sub(self, other: T) -> T;
    /// Multiply two values.
    fn mul(self, other: T) -> T;
    /// Divide two values.
    fn div(self, other: T) -> Result<T, TrapKind>;
}

/// Integer value.
pub trait Integer<T>: ArithmeticOps<T> {
    /// Counts leading zeros in the bitwise representation of the value.
    fn leading_zeros(self) -> T;
    /// Counts trailing zeros in the bitwise representation of the value.
    fn trailing_zeros(self) -> T;
    /// Counts 1-bits in the bitwise representation of the value.
    fn count_ones(self) -> T;
    /// Get left bit rotation result.
    fn rotl(self, other: T) -> T;
    /// Get right bit rotation result.
    fn rotr(self, other: T) -> T;
    /// Get division remainder.
    fn rem(self, other: T) -> Result<T, TrapKind>;
}

/// Float-point value.
pub trait Float<T>: ArithmeticOps<T> {
    /// Get absolute value.
    fn abs(self) -> T;
    /// Returns the largest integer less than or equal to a number.
    fn floor(self) -> T;
    /// Returns the smallest integer greater than or equal to a number.
    fn ceil(self) -> T;
    /// Returns the integer part of a number.
    fn trunc(self) -> T;
    /// Returns the nearest integer to a number. Round half-way cases away from 0.0.
    fn round(self) -> T;
    /// Returns the nearest integer to a number. Ties are round to even number.
    fn nearest(self) -> T;
    /// Takes the square root of a number.
    fn sqrt(self) -> T;
    /// Returns the minimum of the two numbers.
    fn min(self, other: T) -> T;
    /// Returns the maximum of the two numbers.
    fn max(self, other: T) -> T;
    /// Sets sign of this value to the sign of other value.
    fn copysign(self, other: T) -> T;
}

impl RuntimeValue {
    /// Creates new default value of given type.
    pub fn default(value_type: ValueType) -> Self {
        match value_type {
            ValueType::I32 => RuntimeValue::I32(0),
            ValueType::I64 => RuntimeValue::I64(0),
            ValueType::F32 => RuntimeValue::F32(0f32.into()),
            ValueType::F64 => RuntimeValue::F64(0f64.into()),
        }
    }

    /// Creates new value by interpreting passed u32 as f32.
    pub fn decode_f32(val: u32) -> Self {
        RuntimeValue::F32(F32::from_bits(val))
    }

    /// Creates new value by interpreting passed u64 as f64.
    pub fn decode_f64(val: u64) -> Self {
        RuntimeValue::F64(F64::from_bits(val))
    }

    /// Get variable type for this value.
    pub fn value_type(&self) -> ValueType {
        match *self {
            RuntimeValue::I32(_) => ValueType::I32,
            RuntimeValue::I64(_) => ValueType::I64,
            RuntimeValue::F32(_) => ValueType::F32,
            RuntimeValue::F64(_) => ValueType::F64,
        }
    }

    /// Returns `T` if this particular [`RuntimeValue`] contains
    /// appropriate type.
    ///
    /// See [`FromRuntimeValue`] for details.
    ///
    /// [`FromRuntimeValue`]: trait.FromRuntimeValue.html
    /// [`RuntimeValue`]: enum.RuntimeValue.html
    pub fn try_into<T: FromRuntimeValue>(self) -> Option<T> {
        FromRuntimeValue::from_runtime_value(self)
    }
}

impl From<i8> for RuntimeValue {
    fn from(val: i8) -> Self {
        RuntimeValue::I32(val as i32)
    }
}

impl From<i16> for RuntimeValue {
    fn from(val: i16) -> Self {
        RuntimeValue::I32(val as i32)
    }
}

impl From<i32> for RuntimeValue {
    fn from(val: i32) -> Self {
        RuntimeValue::I32(val)
    }
}

impl From<i64> for RuntimeValue {
    fn from(val: i64) -> Self {
        RuntimeValue::I64(val)
    }
}

impl From<u8> for RuntimeValue {
    fn from(val: u8) -> Self {
        RuntimeValue::I32(val as i32)
    }
}

impl From<u16> for RuntimeValue {
    fn from(val: u16) -> Self {
        RuntimeValue::I32(val as i32)
    }
}

impl From<u32> for RuntimeValue {
    fn from(val: u32) -> Self {
        RuntimeValue::I32(val.transmute_into())
    }
}

impl From<u64> for RuntimeValue {
    fn from(val: u64) -> Self {
        RuntimeValue::I64(val.transmute_into())
    }
}

impl From<F32> for RuntimeValue {
    fn from(val: F32) -> Self {
        RuntimeValue::F32(val)
    }
}

impl From<F64> for RuntimeValue {
    fn from(val: F64) -> Self {
        RuntimeValue::F64(val)
    }
}

macro_rules! impl_from_runtime_value {
    ($expected_rt_ty: ident, $into: ty) => {
        impl FromRuntimeValue for $into {
            fn from_runtime_value(val: RuntimeValue) -> Option<Self> {
                match val {
                    RuntimeValue::$expected_rt_ty(val) => Some(val.transmute_into()),
                    _ => None,
                }
            }
        }
    };
}

/// This conversion assumes that boolean values are represented by
/// [`I32`] type.
///
/// [`I32`]: enum.RuntimeValue.html#variant.I32
impl FromRuntimeValue for bool {
    fn from_runtime_value(val: RuntimeValue) -> Option<Self> {
        match val {
            RuntimeValue::I32(val) => Some(val != 0),
            _ => None,
        }
    }
}

///  This conversion assumes that `i8` is represented as an [`I32`].
///
/// [`I32`]: enum.RuntimeValue.html#variant.I32
impl FromRuntimeValue for i8 {
    fn from_runtime_value(val: RuntimeValue) -> Option<Self> {
        let min = i8::min_value() as i32;
        let max = i8::max_value() as i32;
        match val {
            RuntimeValue::I32(val) if min <= val && val <= max => Some(val as i8),
            _ => None,
        }
    }
}

///  This conversion assumes that `i16` is represented as an [`I32`].
///
/// [`I32`]: enum.RuntimeValue.html#variant.I32
impl FromRuntimeValue for i16 {
    fn from_runtime_value(val: RuntimeValue) -> Option<Self> {
        let min = i16::min_value() as i32;
        let max = i16::max_value() as i32;
        match val {
            RuntimeValue::I32(val) if min <= val && val <= max => Some(val as i16),
            _ => None,
        }
    }
}

///  This conversion assumes that `u8` is represented as an [`I32`].
///
/// [`I32`]: enum.RuntimeValue.html#variant.I32
impl FromRuntimeValue for u8 {
    fn from_runtime_value(val: RuntimeValue) -> Option<Self> {
        let min = u8::min_value() as i32;
        let max = u8::max_value() as i32;
        match val {
            RuntimeValue::I32(val) if min <= val && val <= max => Some(val as u8),
            _ => None,
        }
    }
}

///  This conversion assumes that `u16` is represented as an [`I32`].
///
/// [`I32`]: enum.RuntimeValue.html#variant.I32
impl FromRuntimeValue for u16 {
    fn from_runtime_value(val: RuntimeValue) -> Option<Self> {
        let min = u16::min_value() as i32;
        let max = u16::max_value() as i32;
        match val {
            RuntimeValue::I32(val) if min <= val && val <= max => Some(val as u16),
            _ => None,
        }
    }
}

impl_from_runtime_value!(I32, i32);
impl_from_runtime_value!(I64, i64);
impl_from_runtime_value!(F32, F32);
impl_from_runtime_value!(F64, F64);
impl_from_runtime_value!(I32, u32);
impl_from_runtime_value!(I64, u64);

macro_rules! impl_wrap_into {
    ($from:ident, $into:ident) => {
        impl WrapInto<$into> for $from {
            fn wrap_into(self) -> $into {
                self as $into
            }
        }
    };
    ($from:ident, $intermediate:ident, $into:ident) => {
        impl WrapInto<$into> for $from {
            fn wrap_into(self) -> $into {
                $into::from(self as $intermediate)
            }
        }
    };
}

impl_wrap_into!(i32, i8);
impl_wrap_into!(i32, i16);
impl_wrap_into!(i64, i8);
impl_wrap_into!(i64, i16);
impl_wrap_into!(i64, i32);
impl_wrap_into!(i64, f32, F32);
impl_wrap_into!(u64, f32, F32);
// Casting from an f64 to an f32 will produce the closest possible value (rounding strategy unspecified)
// NOTE: currently this will cause Undefined Behavior if the value is finite but larger or smaller than the
// largest or smallest finite value representable by f32. This is a bug and will be fixed.
impl_wrap_into!(f64, f32);

impl WrapInto<F32> for F64 {
    fn wrap_into(self) -> F32 {
        (f64::from(self) as f32).into()
    }
}

macro_rules! impl_try_truncate_into {
    ($from: ident, $into: ident) => {
        impl TryTruncateInto<$into, TrapKind> for $from {
            fn try_truncate_into(self) -> Result<$into, TrapKind> {
                // Casting from a float to an integer will round the float towards zero
                // NOTE: currently this will cause Undefined Behavior if the rounded value cannot be represented by the
                // target integer type. This includes Inf and NaN. This is a bug and will be fixed.
                if self.is_nan() || self.is_infinite() {
                    return Err(TrapKind::InvalidConversionToInt);
                }

                // range check
                let result = self as $into;
                if result as $from != self.trunc() {
                    return Err(TrapKind::InvalidConversionToInt);
                }

                Ok(self as $into)
            }
        }
    };
    ($from:ident, $intermediate:ident, $into:ident) => {
        impl TryTruncateInto<$into, TrapKind> for $from {
            fn try_truncate_into(self) -> Result<$into, TrapKind> {
                $intermediate::from(self).try_truncate_into()
            }
        }
    };
}

impl_try_truncate_into!(f32, i32);
impl_try_truncate_into!(f32, i64);
impl_try_truncate_into!(f64, i32);
impl_try_truncate_into!(f64, i64);
impl_try_truncate_into!(f32, u32);
impl_try_truncate_into!(f32, u64);
impl_try_truncate_into!(f64, u32);
impl_try_truncate_into!(f64, u64);
impl_try_truncate_into!(F32, f32, i32);
impl_try_truncate_into!(F32, f32, i64);
impl_try_truncate_into!(F64, f64, i32);
impl_try_truncate_into!(F64, f64, i64);
impl_try_truncate_into!(F32, f32, u32);
impl_try_truncate_into!(F32, f32, u64);
impl_try_truncate_into!(F64, f64, u32);
impl_try_truncate_into!(F64, f64, u64);

macro_rules! impl_extend_into {
    ($from:ident, $into:ident) => {
        impl ExtendInto<$into> for $from {
            fn extend_into(self) -> $into {
                self as $into
            }
        }
    };
    ($from:ident, $intermediate:ident, $into:ident) => {
        impl ExtendInto<$into> for $from {
            fn extend_into(self) -> $into {
                $into::from(self as $intermediate)
            }
        }
    };
}

impl_extend_into!(i8, i32);
impl_extend_into!(u8, i32);
impl_extend_into!(i16, i32);
impl_extend_into!(u16, i32);
impl_extend_into!(i8, i64);
impl_extend_into!(u8, i64);
impl_extend_into!(i16, i64);
impl_extend_into!(u16, i64);
impl_extend_into!(i32, i64);
impl_extend_into!(u32, i64);
impl_extend_into!(u32, u64);
impl_extend_into!(i32, f32);
impl_extend_into!(i32, f64);
impl_extend_into!(u32, f32);
impl_extend_into!(u32, f64);
impl_extend_into!(i64, f64);
impl_extend_into!(u64, f64);
impl_extend_into!(f32, f64);

impl_extend_into!(i32, f32, F32);
impl_extend_into!(i32, f64, F64);
impl_extend_into!(u32, f32, F32);
impl_extend_into!(u32, f64, F64);
impl_extend_into!(i64, f64, F64);
impl_extend_into!(u64, f64, F64);
impl_extend_into!(f32, f64, F64);

impl ExtendInto<F64> for F32 {
    fn extend_into(self) -> F64 {
        (f32::from(self) as f64).into()
    }
}

macro_rules! impl_transmute_into_self {
    ($type: ident) => {
        impl TransmuteInto<$type> for $type {
            fn transmute_into(self) -> $type {
                self
            }
        }
    };
}

impl_transmute_into_self!(i32);
impl_transmute_into_self!(i64);
impl_transmute_into_self!(f32);
impl_transmute_into_self!(f64);
impl_transmute_into_self!(F32);
impl_transmute_into_self!(F64);

macro_rules! impl_transmute_into_as {
    ($from: ident, $into: ident) => {
        impl TransmuteInto<$into> for $from {
            fn transmute_into(self) -> $into {
                self as $into
            }
        }
    };
}

impl_transmute_into_as!(i8, u8);
impl_transmute_into_as!(i32, u32);
impl_transmute_into_as!(i64, u64);

macro_rules! impl_transmute_into_npf {
    ($npf:ident, $float:ident, $signed:ident, $unsigned:ident) => {
        impl TransmuteInto<$float> for $npf {
            fn transmute_into(self) -> $float {
                self.into()
            }
        }

        impl TransmuteInto<$npf> for $float {
            fn transmute_into(self) -> $npf {
                self.into()
            }
        }

        impl TransmuteInto<$signed> for $npf {
            fn transmute_into(self) -> $signed {
                self.to_bits() as _
            }
        }

        impl TransmuteInto<$unsigned> for $npf {
            fn transmute_into(self) -> $unsigned {
                self.to_bits()
            }
        }

        impl TransmuteInto<$npf> for $signed {
            fn transmute_into(self) -> $npf {
                $npf::from_bits(self as _)
            }
        }

        impl TransmuteInto<$npf> for $unsigned {
            fn transmute_into(self) -> $npf {
                $npf::from_bits(self)
            }
        }
    };
}

impl_transmute_into_npf!(F32, f32, i32, u32);
impl_transmute_into_npf!(F64, f64, i64, u64);

impl TransmuteInto<i32> for f32 {
    fn transmute_into(self) -> i32 {
        self.to_bits() as i32
    }
}

impl TransmuteInto<i64> for f64 {
    fn transmute_into(self) -> i64 {
        self.to_bits() as i64
    }
}

impl TransmuteInto<f32> for i32 {
    fn transmute_into(self) -> f32 {
        f32::from_bits(self as u32)
    }
}

impl TransmuteInto<f64> for i64 {
    fn transmute_into(self) -> f64 {
        f64::from_bits(self as u64)
    }
}

impl TransmuteInto<i32> for u32 {
    fn transmute_into(self) -> i32 {
        self as _
    }
}

impl TransmuteInto<i64> for u64 {
    fn transmute_into(self) -> i64 {
        self as _
    }
}

impl LittleEndianConvert for i8 {
    fn into_little_endian(self, buffer: &mut [u8]) {
        buffer[0] = self as u8;
    }

    fn from_little_endian(buffer: &[u8]) -> Result<Self, Error> {
        buffer
            .get(0)
            .map(|v| *v as i8)
            .ok_or_else(|| Error::InvalidLittleEndianBuffer)
    }
}

impl LittleEndianConvert for u8 {
    fn into_little_endian(self, buffer: &mut [u8]) {
        buffer[0] = self;
    }

    fn from_little_endian(buffer: &[u8]) -> Result<Self, Error> {
        buffer
            .get(0)
            .cloned()
            .ok_or_else(|| Error::InvalidLittleEndianBuffer)
    }
}

impl LittleEndianConvert for i16 {
    fn into_little_endian(self, buffer: &mut [u8]) {
        LittleEndian::write_i16(buffer, self);
    }

    fn from_little_endian(buffer: &[u8]) -> Result<Self, Error> {
        buffer
            .get(0..2)
            .map(LittleEndian::read_i16)
            .ok_or_else(|| Error::InvalidLittleEndianBuffer)
    }
}

impl LittleEndianConvert for u16 {
    fn into_little_endian(self, buffer: &mut [u8]) {
        LittleEndian::write_u16(buffer, self);
    }

    fn from_little_endian(buffer: &[u8]) -> Result<Self, Error> {
        buffer
            .get(0..2)
            .map(LittleEndian::read_u16)
            .ok_or_else(|| Error::InvalidLittleEndianBuffer)
    }
}

impl LittleEndianConvert for i32 {
    fn into_little_endian(self, buffer: &mut [u8]) {
        LittleEndian::write_i32(buffer, self);
    }

    fn from_little_endian(buffer: &[u8]) -> Result<Self, Error> {
        buffer
            .get(0..4)
            .map(LittleEndian::read_i32)
            .ok_or_else(|| Error::InvalidLittleEndianBuffer)
    }
}

impl LittleEndianConvert for u32 {
    fn into_little_endian(self, buffer: &mut [u8]) {
        LittleEndian::write_u32(buffer, self);
    }

    fn from_little_endian(buffer: &[u8]) -> Result<Self, Error> {
        buffer
            .get(0..4)
            .map(LittleEndian::read_u32)
            .ok_or_else(|| Error::InvalidLittleEndianBuffer)
    }
}

impl LittleEndianConvert for i64 {
    fn into_little_endian(self, buffer: &mut [u8]) {
        LittleEndian::write_i64(buffer, self);
    }

    fn from_little_endian(buffer: &[u8]) -> Result<Self, Error> {
        buffer
            .get(0..8)
            .map(LittleEndian::read_i64)
            .ok_or_else(|| Error::InvalidLittleEndianBuffer)
    }
}

impl LittleEndianConvert for f32 {
    fn into_little_endian(self, buffer: &mut [u8]) {
        LittleEndian::write_f32(buffer, self);
    }

    fn from_little_endian(buffer: &[u8]) -> Result<Self, Error> {
        buffer
            .get(0..4)
            .map(LittleEndian::read_f32)
            .ok_or_else(|| Error::InvalidLittleEndianBuffer)
    }
}

impl LittleEndianConvert for f64 {
    fn into_little_endian(self, buffer: &mut [u8]) {
        LittleEndian::write_f64(buffer, self);
    }

    fn from_little_endian(buffer: &[u8]) -> Result<Self, Error> {
        buffer
            .get(0..8)
            .map(LittleEndian::read_f64)
            .ok_or_else(|| Error::InvalidLittleEndianBuffer)
    }
}

impl LittleEndianConvert for F32 {
    fn into_little_endian(self, buffer: &mut [u8]) {
        (self.to_bits() as i32).into_little_endian(buffer)
    }

    fn from_little_endian(buffer: &[u8]) -> Result<Self, Error> {
        i32::from_little_endian(buffer).map(|val| Self::from_bits(val as _))
    }
}

impl LittleEndianConvert for F64 {
    fn into_little_endian(self, buffer: &mut [u8]) {
        (self.to_bits() as i64).into_little_endian(buffer)
    }

    fn from_little_endian(buffer: &[u8]) -> Result<Self, Error> {
        i64::from_little_endian(buffer).map(|val| Self::from_bits(val as _))
    }
}

macro_rules! impl_integer_arithmetic_ops {
    ($type: ident) => {
        impl ArithmeticOps<$type> for $type {
            fn add(self, other: $type) -> $type {
                self.wrapping_add(other)
            }
            fn sub(self, other: $type) -> $type {
                self.wrapping_sub(other)
            }
            fn mul(self, other: $type) -> $type {
                self.wrapping_mul(other)
            }
            fn div(self, other: $type) -> Result<$type, TrapKind> {
                if other == 0 {
                    Err(TrapKind::DivisionByZero)
                } else {
                    let (result, overflow) = self.overflowing_div(other);
                    if overflow {
                        Err(TrapKind::InvalidConversionToInt)
                    } else {
                        Ok(result)
                    }
                }
            }
        }
    };
}

impl_integer_arithmetic_ops!(i32);
impl_integer_arithmetic_ops!(u32);
impl_integer_arithmetic_ops!(i64);
impl_integer_arithmetic_ops!(u64);

macro_rules! impl_float_arithmetic_ops {
    ($type: ident) => {
        impl ArithmeticOps<$type> for $type {
            fn add(self, other: $type) -> $type {
                self + other
            }
            fn sub(self, other: $type) -> $type {
                self - other
            }
            fn mul(self, other: $type) -> $type {
                self * other
            }
            fn div(self, other: $type) -> Result<$type, TrapKind> {
                Ok(self / other)
            }
        }
    };
}

impl_float_arithmetic_ops!(f32);
impl_float_arithmetic_ops!(f64);
impl_float_arithmetic_ops!(F32);
impl_float_arithmetic_ops!(F64);

macro_rules! impl_integer {
    ($type: ident) => {
        impl Integer<$type> for $type {
            fn leading_zeros(self) -> $type {
                self.leading_zeros() as $type
            }
            fn trailing_zeros(self) -> $type {
                self.trailing_zeros() as $type
            }
            fn count_ones(self) -> $type {
                self.count_ones() as $type
            }
            fn rotl(self, other: $type) -> $type {
                self.rotate_left(other as u32)
            }
            fn rotr(self, other: $type) -> $type {
                self.rotate_right(other as u32)
            }
            fn rem(self, other: $type) -> Result<$type, TrapKind> {
                if other == 0 {
                    Err(TrapKind::DivisionByZero)
                } else {
                    Ok(self.wrapping_rem(other))
                }
            }
        }
    };
}

impl_integer!(i32);
impl_integer!(u32);
impl_integer!(i64);
impl_integer!(u64);

// Use std float functions in std environment.
// And libm's implementation in no_std
#[cfg(feature = "std")]
macro_rules! call_math {
    ($op:ident, $e:expr, $fXX:ident, $FXXExt:ident) => {
        $fXX::$op($e)
    };
}
#[cfg(not(feature = "std"))]
macro_rules! call_math {
    ($op:ident, $e:expr, $fXX:ident, $FXXExt:ident) => {
        ::libm::$FXXExt::$op($e)
    };
}

// We cannot call the math functions directly, because there are multiple available implementaitons in no_std.
// In std, there are only `Value::$op` and `std::$fXX:$op`.
// The `std` ones are preferred, because they are not from a trait.
// For `no_std`, the implementations are `Value::$op` and `libm::FXXExt::$op`,
// both of which are trait implementations and hence ambiguous.
// So we have to use a full path, which is what `call_math!` does.
macro_rules! impl_float {
    ($type:ident, $fXX:ident, $FXXExt:ident, $iXX:ident) => {
        impl Float<$type> for $type {
            fn abs(self) -> $type {
                call_math!(abs, $fXX::from(self), $fXX, $FXXExt).into()
            }
            fn floor(self) -> $type {
                call_math!(floor, $fXX::from(self), $fXX, $FXXExt).into()
            }
            fn ceil(self) -> $type {
                call_math!(ceil, $fXX::from(self), $fXX, $FXXExt).into()
            }
            fn trunc(self) -> $type {
                call_math!(trunc, $fXX::from(self), $fXX, $FXXExt).into()
            }
            fn round(self) -> $type {
                call_math!(round, $fXX::from(self), $fXX, $FXXExt).into()
            }
            fn nearest(self) -> $type {
                let round = self.round();
                if call_math!(fract, $fXX::from(self), $fXX, $FXXExt).abs() != 0.5 {
                    return round;
                }

                use core::ops::Rem;
                if round.rem(2.0) == 1.0 {
                    self.floor()
                } else if round.rem(2.0) == -1.0 {
                    self.ceil()
                } else {
                    round
                }
            }
            fn sqrt(self) -> $type {
                call_math!(sqrt, $fXX::from(self), $fXX, $FXXExt).into()
            }
            // This instruction corresponds to what is sometimes called "minNaN" in other languages.
            fn min(self, other: $type) -> $type {
                if self.is_nan() {
                    return self;
                }
                if other.is_nan() {
                    return other;
                }

                self.min(other)
            }
            // This instruction corresponds to what is sometimes called "maxNaN" in other languages.
            fn max(self, other: $type) -> $type {
                if self.is_nan() {
                    return self;
                }
                if other.is_nan() {
                    return other;
                }

                self.max(other)
            }
            fn copysign(self, other: $type) -> $type {
                use core::mem::size_of;

                if self.is_nan() {
                    return self;
                }

                let sign_mask: $iXX = 1 << ((size_of::<$iXX>() << 3) - 1);
                let self_int: $iXX = self.transmute_into();
                let other_int: $iXX = other.transmute_into();
                let is_self_sign_set = (self_int & sign_mask) != 0;
                let is_other_sign_set = (other_int & sign_mask) != 0;
                if is_self_sign_set == is_other_sign_set {
                    self
                } else if is_other_sign_set {
                    (self_int | sign_mask).transmute_into()
                } else {
                    (self_int & !sign_mask).transmute_into()
                }
            }
        }
    };
}

impl_float!(f32, f32, F32Ext, i32);
impl_float!(f64, f64, F64Ext, i64);
impl_float!(F32, f32, F32Ext, i32);
impl_float!(F64, f64, F64Ext, i64);