library/compiler-builtins/builtins-test/src/lib.rs - rust - Git at Google

 //! This crate is for integration testing and fuzz testing of functions in `compiler-builtins`. This
 //! includes publicly documented intrinsics and some internal alternative implementation functions
 //! such as `usize_leading_zeros_riscv` (which are tested because they are configured for
 //! architectures not tested by the CI).
 //!
 //! The general idea is to use a combination of edge case testing and randomized fuzz testing. The
 //! edge case testing is crucial for checking cases like where both inputs are equal or equal to
 //! special values such as `i128::MIN`, which is unlikely for the random fuzzer by itself to
 //! encounter. The randomized fuzz testing is specially designed to cover wide swaths of search
 //! space in as few iterations as possible. See `fuzz_values` in `builtins-test/tests/misc.rs` for
 //! an example.
 //!
 //! Some floating point tests are disabled for specific architectures, because they do not have
 //! correct rounding.
 #![no_std]
 #![cfg_attr(f128_enabled, feature(f128))]
 #![cfg_attr(f16_enabled, feature(f16))]

 pub mod bench;
 extern crate alloc;

 use compiler_builtins::float::Float;
 use compiler_builtins::int::{Int, MinInt};
 use rand_xoshiro::Xoshiro128StarStar;
 use rand_xoshiro::rand_core::{RngCore, SeedableRng};

 /// Sets the number of fuzz iterations run for most tests. In practice, the vast majority of bugs
 /// are caught by the edge case testers. Most of the remaining bugs triggered by more complex
 /// sequences are caught well within 10_000 fuzz iterations. For classes of algorithms like division
 /// that are vulnerable to rare edge cases, we want 1_000_000 iterations to be more confident. In
 /// practical CI, however, we only want to run the more strenuous test once to catch algorithmic
 /// level bugs, and run the 10_000 iteration test on most targets. Target-dependent bugs are likely
 /// to involve miscompilation and misconfiguration that is likely to break algorithms in quickly
 /// caught ways. We choose to configure `N = 1_000_000` iterations for `x86_64` targets (and if
 /// debug assertions are disabled. Tests without `--release` would take too long) which are likely
 /// to have fast hardware, and run `N = 10_000` for all other targets.
 pub const N: u32 = if cfg!(target_arch = "x86_64") && !cfg!(debug_assertions) {
     1_000_000
 } else {
     10_000
 };

 /// Additional constants that determine how the integer gets fuzzed.
 trait FuzzInt: MinInt {
     /// LUT used for maximizing the space covered and minimizing the computational cost of fuzzing
     /// in `builtins-test`. For example, Self = u128 produces [0,1,2,7,8,15,16,31,32,63,64,95,96,
     /// 111,112,119,120,125,126,127].
     const FUZZ_LENGTHS: [u8; 20] = make_fuzz_lengths(Self::BITS);

     /// The number of entries of `FUZZ_LENGTHS` actually used. The maximum is 20 for u128.
     const FUZZ_NUM: usize = {
         let log2 = Self::BITS.ilog2() as usize;
         if log2 == 3 {
             // case for u8
             6
         } else {
             // 3 entries on each extreme, 2 in the middle, and 4 for each scale of intermediate
             // boundaries.
             8 + (4 * (log2 - 4))
         }
     };
 }

 impl<I> FuzzInt for I where I: MinInt {}

 const fn make_fuzz_lengths(bits: u32) -> [u8; 20] {
     let mut v = [0u8; 20];
     v[0] = 0;
     v[1] = 1;
     v[2] = 2; // important for parity and the iX::MIN case when reversed
     let mut i = 3;

     // No need for any more until the byte boundary, because there should be no algorithms
     // that are sensitive to anything not next to byte boundaries after 2. We also scale
     // in powers of two, which is important to prevent u128 corner tests from getting too
     // big.
     let mut l = 8;
     loop {
         if l >= ((bits / 2) as u8) {
             break;
         }
         // get both sides of the byte boundary
         v[i] = l - 1;
         i += 1;
         v[i] = l;
         i += 1;
         l *= 2;
     }

     if bits != 8 {
         // add the lower side of the middle boundary
         v[i] = ((bits / 2) - 1) as u8;
         i += 1;
     }

     // We do not want to jump directly from the Self::BITS/2 boundary to the Self::BITS
     // boundary because of algorithms that split the high part up. We reverse the scaling
     // as we go to Self::BITS.
     let mid = i;
     let mut j = 1;
     loop {
         v[i] = (bits as u8) - (v[mid - j]) - 1;
         if j == mid {
             break;
         }
         i += 1;
         j += 1;
     }
     v
 }

 /// Random fuzzing step. When run several times, it results in excellent fuzzing entropy such as:
 /// 11110101010101011110111110011111
 /// 10110101010100001011101011001010
 /// 1000000000000000
 /// 10000000000000110111110000001010
 /// 1111011111111101010101111110101
 /// 101111111110100000000101000000
 /// 10000000110100000000100010101
 /// 1010101010101000
 fn fuzz_step<I: Int>(rng: &mut Xoshiro128StarStar, x: &mut I) {
     let ones = !I::ZERO;
     let bit_indexing_mask: u32 = I::BITS - 1;
     // It happens that all the RNG we need can come from one call. 7 bits are needed to index a
     // worst case 128 bit integer, and there are 4 indexes that need to be made plus 4 bits for
     // selecting operations
     let rng32 = rng.next_u32();

     // Randomly OR, AND, and XOR randomly sized and shifted continuous strings of
     // ones with `lhs` and `rhs`.
     let r0 = bit_indexing_mask & rng32;
     let r1 = bit_indexing_mask & (rng32 >> 7);
     let mask = ones.wrapping_shl(r0).rotate_left(r1);
     match (rng32 >> 14) % 4 {
         0 => *x |= mask,
         1 => *x &= mask,
         // both 2 and 3 to make XORs as common as ORs and ANDs combined
         _ => *x ^= mask,
     }

     // Alternating ones and zeros (e.x. 0b1010101010101010). This catches second-order
     // problems that might occur for algorithms with two modes of operation (potentially
     // there is some invariant that can be broken and maintained via alternating between modes,
     // breaking the algorithm when it reaches the end).
     let mut alt_ones = I::ONE;
     for _ in 0..(I::BITS / 2) {
         alt_ones <<= 2;
         alt_ones |= I::ONE;
     }
     let r0 = bit_indexing_mask & (rng32 >> 16);
     let r1 = bit_indexing_mask & (rng32 >> 23);
     let mask = alt_ones.wrapping_shl(r0).rotate_left(r1);
     match rng32 >> 30 {
         0 => *x |= mask,
         1 => *x &= mask,
         _ => *x ^= mask,
     }
 }

 // We need macros like this, because `#![no_std]` prevents us from using iterators
 macro_rules! edge_cases {
     ($I:ident, $case:ident, $inner:block) => {
         for i0 in 0..$I::FUZZ_NUM {
             let mask_lo = (!$I::Unsigned::ZERO).wrapping_shr($I::FUZZ_LENGTHS[i0] as u32);
             for i1 in i0..I::FUZZ_NUM {
                 let mask_hi = (!$I::Unsigned::ZERO).wrapping_shl($I::FUZZ_LENGTHS[i1 - i0] as u32);
                 let $case = I::from_unsigned(mask_lo & mask_hi);
                 $inner
             }
         }
     };
 }

 /// Feeds a series of fuzzing inputs to `f`. The fuzzer first uses an algorithm designed to find
 /// edge cases, followed by a more random fuzzer that runs `n` times.
 pub fn fuzz<I: Int, F: FnMut(I)>(n: u32, mut f: F)
 where
     <I as MinInt>::Unsigned: Int,
 {
     // edge case tester. Calls `f` 210 times for u128.
     // zero gets skipped by the loop
     f(I::ZERO);
     edge_cases!(I, case, {
         f(case);
     });

     // random fuzzer
     let mut rng = Xoshiro128StarStar::seed_from_u64(0);
     let mut x: I = MinInt::ZERO;
     for _ in 0..n {
         fuzz_step(&mut rng, &mut x);
         f(x)
     }
 }

 /// The same as `fuzz`, except `f` has two inputs.
 pub fn fuzz_2<I: Int, F: Fn(I, I)>(n: u32, f: F)
 where
     <I as MinInt>::Unsigned: Int,
 {
     // Check cases where the first and second inputs are zero. Both call `f` 210 times for `u128`.
     edge_cases!(I, case, {
         f(I::ZERO, case);
     });
     edge_cases!(I, case, {
         f(case, I::ZERO);
     });
     // Nested edge tester. Calls `f` 44100 times for `u128`.
     edge_cases!(I, case0, {
         edge_cases!(I, case1, {
             f(case0, case1);
         })
     });

     // random fuzzer
     let mut rng = Xoshiro128StarStar::seed_from_u64(0);
     let mut x: I = I::ZERO;
     let mut y: I = I::ZERO;
     for _ in 0..n {
         fuzz_step(&mut rng, &mut x);
         fuzz_step(&mut rng, &mut y);
         f(x, y)
     }
 }

 /// Tester for shift functions
 pub fn fuzz_shift<I: Int, F: Fn(I, u32)>(f: F) {
     // Shift functions are very simple and do not need anything other than shifting a small
     // set of random patterns for every fuzz length.
     let mut rng = Xoshiro128StarStar::seed_from_u64(0);
     let mut x: I = MinInt::ZERO;
     for i in 0..I::FUZZ_NUM {
         fuzz_step(&mut rng, &mut x);
         f(x, MinInt::ZERO);
         f(x, I::FUZZ_LENGTHS[i] as u32);
     }
 }

 fn fuzz_float_step<F: Float>(rng: &mut Xoshiro128StarStar, f: &mut F) {
     let rng32 = rng.next_u32();
     // we need to fuzz the different parts of the float separately, because the masking on larger
     // significands will tend to set the exponent to all ones or all zeros frequently

     // sign bit fuzzing
     let sign = (rng32 & 1) != 0;

     // exponent fuzzing. Only 4 bits for the selector needed.
     let ones = (F::Int::ONE << F::EXP_BITS) - F::Int::ONE;
     let r0 = (rng32 >> 1) % F::EXP_BITS;
     let r1 = (rng32 >> 5) % F::EXP_BITS;
     // custom rotate shift. Note that `F::Int` is unsigned, so we can shift right without smearing
     // the sign bit.
     let mask = if r1 == 0 {
         ones.wrapping_shr(r0)
     } else {
         let tmp = ones.wrapping_shr(r0);
         (tmp.wrapping_shl(r1) | tmp.wrapping_shr(F::EXP_BITS - r1)) & ones
     };
     let mut exp = (f.to_bits() & F::EXP_MASK) >> F::SIG_BITS;
     match (rng32 >> 9) % 4 {
         0 => exp |= mask,
         1 => exp &= mask,
         _ => exp ^= mask,
     }

     // significand fuzzing
     let mut sig = f.to_bits() & F::SIG_MASK;
     fuzz_step(rng, &mut sig);
     sig &= F::SIG_MASK;

     *f = F::from_parts(sign, exp, sig);
 }

 macro_rules! float_edge_cases {
     ($F:ident, $case:ident, $inner:block) => {
         for exponent in [
             F::Int::ZERO,
             F::Int::ONE,
             F::Int::ONE << (F::EXP_BITS / 2),
             (F::Int::ONE << (F::EXP_BITS - 1)) - F::Int::ONE,
             F::Int::ONE << (F::EXP_BITS - 1),
             (F::Int::ONE << (F::EXP_BITS - 1)) + F::Int::ONE,
             (F::Int::ONE << F::EXP_BITS) - F::Int::ONE,
         ]
         .iter()
         {
             for significand in [
                 F::Int::ZERO,
                 F::Int::ONE,
                 F::Int::ONE << (F::SIG_BITS / 2),
                 (F::Int::ONE << (F::SIG_BITS - 1)) - F::Int::ONE,
                 F::Int::ONE << (F::SIG_BITS - 1),
                 (F::Int::ONE << (F::SIG_BITS - 1)) + F::Int::ONE,
                 (F::Int::ONE << F::SIG_BITS) - F::Int::ONE,
             ]
             .iter()
             {
                 for sign in [false, true].iter() {
                     let $case = F::from_parts(*sign, *exponent, *significand);
                     $inner
                 }
             }
         }
     };
 }

 pub fn fuzz_float<F: Float, E: Fn(F)>(n: u32, f: E) {
     float_edge_cases!(F, case, {
         f(case);
     });

     // random fuzzer
     let mut rng = Xoshiro128StarStar::seed_from_u64(0);
     let mut x = F::ZERO;
     for _ in 0..n {
         fuzz_float_step(&mut rng, &mut x);
         f(x);
     }
 }

 pub fn fuzz_float_2<F: Float, E: Fn(F, F)>(n: u32, f: E) {
     float_edge_cases!(F, case0, {
         float_edge_cases!(F, case1, {
             f(case0, case1);
         });
     });

     // random fuzzer
     let mut rng = Xoshiro128StarStar::seed_from_u64(0);
     let mut x = F::ZERO;
     let mut y = F::ZERO;
     for _ in 0..n {
         fuzz_float_step(&mut rng, &mut x);
         fuzz_float_step(&mut rng, &mut y);
         f(x, y)
     }
 }

 /// Perform an operation using builtin types if available, falling back to apfloat if not.
 #[macro_export]
 macro_rules! apfloat_fallback {
     (
         $float_ty:ty,
         // Type name in `rustc_apfloat::ieee`. Not a full path, it automatically gets the prefix.
         $apfloat_ty:ident,
         // Cfg expression for when builtin system operations should be used
         $sys_available:meta,
         // The expression to run. This expression may use `FloatTy` for its signature.
         // Optionally, the final conversion back to a float can be suppressed using
         // `=> no_convert` (for e.g. operations that return a bool).
         //
         // If the apfloat needs a different operation, it can be provided here.
         $op:expr $(=> $convert:ident)? $(; $apfloat_op:expr)?,
         // Arguments that get passed to `$op` after converting to a float
         $($arg:expr),+
         $(,)?
     ) => {{
         #[cfg($sys_available)]
         let ret = {
             type FloatTy = $float_ty;
             $op( $($arg),+ )
         };

         #[cfg(not($sys_available))]
         let ret = {
             use rustc_apfloat::Float;
             type FloatTy = rustc_apfloat::ieee::$apfloat_ty;

             apfloat_fallback!(@inner
                 fty: $float_ty,
                 // Apply a conversion to `FloatTy` to each arg, then pass all args to `$op`
                 op_res: $op( $(FloatTy::from_bits($arg.to_bits().into())),+ ),
                 $(apfloat_op: $apfloat_op, )?
                 $(conv_opts: $convert,)?
                 args: $($arg),+
             )
         };

         ret
     }};

     // Operations that do not need converting back to a float
     (@inner fty: $float_ty:ty, op_res: $val:expr, conv_opts: no_convert, args: $($_arg:expr),+) => {
         $val
     };

     // Some apfloat operations return a `StatusAnd` that we need to extract the value from. This
     // is the default.
     (@inner fty: $float_ty:ty, op_res: $val:expr, args: $($_arg:expr),+) => {{
         // ignore the status, just get the value
         let unwrapped = $val.value;

         <$float_ty>::from_bits(FloatTy::to_bits(unwrapped).try_into().unwrap())
     }};

     // This is the case where we can't use the same expression for the default builtin and
     // nonstandard apfloat fallback (e.g. `as` casts in std are normal functions in apfloat, so
     // two separate expressions must be specified.
     (@inner
         fty: $float_ty:ty, op_res: $_val:expr,
         apfloat_op: $apfloat_op:expr, args: $($arg:expr),+
     ) => {{
         $apfloat_op($($arg),+)
     }};
 }
	//! This crate is for integration testing and fuzz testing of functions in `compiler-builtins`. This
	//! includes publicly documented intrinsics and some internal alternative implementation functions
	//! such as `usize_leading_zeros_riscv` (which are tested because they are configured for
	//! architectures not tested by the CI).
	//!
	//! The general idea is to use a combination of edge case testing and randomized fuzz testing. The
	//! edge case testing is crucial for checking cases like where both inputs are equal or equal to
	//! special values such as `i128::MIN`, which is unlikely for the random fuzzer by itself to
	//! encounter. The randomized fuzz testing is specially designed to cover wide swaths of search
	//! space in as few iterations as possible. See `fuzz_values` in `builtins-test/tests/misc.rs` for
	//! an example.
	//!
	//! Some floating point tests are disabled for specific architectures, because they do not have
	//! correct rounding.
	#![no_std]
	#![cfg_attr(f128_enabled, feature(f128))]
	#![cfg_attr(f16_enabled, feature(f16))]

	pub mod bench;
	extern crate alloc;

	use compiler_builtins::float::Float;
	use compiler_builtins::int::{Int, MinInt};
	use rand_xoshiro::Xoshiro128StarStar;
	use rand_xoshiro::rand_core::{RngCore, SeedableRng};

	/// Sets the number of fuzz iterations run for most tests. In practice, the vast majority of bugs
	/// are caught by the edge case testers. Most of the remaining bugs triggered by more complex
	/// sequences are caught well within 10_000 fuzz iterations. For classes of algorithms like division
	/// that are vulnerable to rare edge cases, we want 1_000_000 iterations to be more confident. In
	/// practical CI, however, we only want to run the more strenuous test once to catch algorithmic
	/// level bugs, and run the 10_000 iteration test on most targets. Target-dependent bugs are likely
	/// to involve miscompilation and misconfiguration that is likely to break algorithms in quickly
	/// caught ways. We choose to configure `N = 1_000_000` iterations for `x86_64` targets (and if
	/// debug assertions are disabled. Tests without `--release` would take too long) which are likely
	/// to have fast hardware, and run `N = 10_000` for all other targets.
	pub const N: u32 = if cfg!(target_arch = "x86_64") && !cfg!(debug_assertions) {
	1_000_000
	} else {
	10_000
	};

	/// Additional constants that determine how the integer gets fuzzed.
	trait FuzzInt: MinInt {
	/// LUT used for maximizing the space covered and minimizing the computational cost of fuzzing
	/// in `builtins-test`. For example, Self = u128 produces [0,1,2,7,8,15,16,31,32,63,64,95,96,
	/// 111,112,119,120,125,126,127].
	const FUZZ_LENGTHS: [u8; 20] = make_fuzz_lengths(Self::BITS);

	/// The number of entries of `FUZZ_LENGTHS` actually used. The maximum is 20 for u128.
	const FUZZ_NUM: usize = {
	let log2 = Self::BITS.ilog2() as usize;
	if log2 == 3 {
	// case for u8
	6
	} else {
	// 3 entries on each extreme, 2 in the middle, and 4 for each scale of intermediate
	// boundaries.
	8 + (4 * (log2 - 4))
	}
	};
	}

	impl<I> FuzzInt for I where I: MinInt {}

	const fn make_fuzz_lengths(bits: u32) -> [u8; 20] {
	let mut v = [0u8; 20];
	v[0] = 0;
	v[1] = 1;
	v[2] = 2; // important for parity and the iX::MIN case when reversed
	let mut i = 3;

	// No need for any more until the byte boundary, because there should be no algorithms
	// that are sensitive to anything not next to byte boundaries after 2. We also scale
	// in powers of two, which is important to prevent u128 corner tests from getting too
	// big.
	let mut l = 8;
	loop {
	if l >= ((bits / 2) as u8) {
	break;
	}
	// get both sides of the byte boundary
	v[i] = l - 1;
	i += 1;
	v[i] = l;
	i += 1;
	l *= 2;
	}

	if bits != 8 {
	// add the lower side of the middle boundary
	v[i] = ((bits / 2) - 1) as u8;
	i += 1;
	}

	// We do not want to jump directly from the Self::BITS/2 boundary to the Self::BITS
	// boundary because of algorithms that split the high part up. We reverse the scaling
	// as we go to Self::BITS.
	let mid = i;
	let mut j = 1;
	loop {
	v[i] = (bits as u8) - (v[mid - j]) - 1;
	if j == mid {
	break;
	}
	i += 1;
	j += 1;
	}
	v
	}

	/// Random fuzzing step. When run several times, it results in excellent fuzzing entropy such as:
	/// 11110101010101011110111110011111
	/// 10110101010100001011101011001010
	/// 1000000000000000
	/// 10000000000000110111110000001010
	/// 1111011111111101010101111110101
	/// 101111111110100000000101000000
	/// 10000000110100000000100010101
	/// 1010101010101000
	fn fuzz_step<I: Int>(rng: &mut Xoshiro128StarStar, x: &mut I) {
	let ones = !I::ZERO;
	let bit_indexing_mask: u32 = I::BITS - 1;
	// It happens that all the RNG we need can come from one call. 7 bits are needed to index a
	// worst case 128 bit integer, and there are 4 indexes that need to be made plus 4 bits for
	// selecting operations
	let rng32 = rng.next_u32();

	// Randomly OR, AND, and XOR randomly sized and shifted continuous strings of
	// ones with `lhs` and `rhs`.
	let r0 = bit_indexing_mask & rng32;
	let r1 = bit_indexing_mask & (rng32 >> 7);
	let mask = ones.wrapping_shl(r0).rotate_left(r1);
	match (rng32 >> 14) % 4 {
	0 => *x \|= mask,
	1 => *x &= mask,
	// both 2 and 3 to make XORs as common as ORs and ANDs combined
	_ => *x ^= mask,
	}

	// Alternating ones and zeros (e.x. 0b1010101010101010). This catches second-order
	// problems that might occur for algorithms with two modes of operation (potentially
	// there is some invariant that can be broken and maintained via alternating between modes,
	// breaking the algorithm when it reaches the end).
	let mut alt_ones = I::ONE;
	for _ in 0..(I::BITS / 2) {
	alt_ones <<= 2;
	alt_ones \|= I::ONE;
	}
	let r0 = bit_indexing_mask & (rng32 >> 16);
	let r1 = bit_indexing_mask & (rng32 >> 23);
	let mask = alt_ones.wrapping_shl(r0).rotate_left(r1);
	match rng32 >> 30 {
	0 => *x \|= mask,
	1 => *x &= mask,
	_ => *x ^= mask,
	}
	}

	// We need macros like this, because `#![no_std]` prevents us from using iterators
	macro_rules! edge_cases {
	($I:ident, $case:ident, $inner:block) => {
	for i0 in 0..$I::FUZZ_NUM {
	let mask_lo = (!$I::Unsigned::ZERO).wrapping_shr($I::FUZZ_LENGTHS[i0] as u32);
	for i1 in i0..I::FUZZ_NUM {
	let mask_hi = (!$I::Unsigned::ZERO).wrapping_shl($I::FUZZ_LENGTHS[i1 - i0] as u32);
	let $case = I::from_unsigned(mask_lo & mask_hi);
	$inner
	}
	}
	};
	}

	/// Feeds a series of fuzzing inputs to `f`. The fuzzer first uses an algorithm designed to find
	/// edge cases, followed by a more random fuzzer that runs `n` times.
	pub fn fuzz<I: Int, F: FnMut(I)>(n: u32, mut f: F)
	where
	<I as MinInt>::Unsigned: Int,
	{
	// edge case tester. Calls `f` 210 times for u128.
	// zero gets skipped by the loop
	f(I::ZERO);
	edge_cases!(I, case, {
	f(case);
	});

	// random fuzzer
	let mut rng = Xoshiro128StarStar::seed_from_u64(0);
	let mut x: I = MinInt::ZERO;
	for _ in 0..n {
	fuzz_step(&mut rng, &mut x);
	f(x)
	}
	}

	/// The same as `fuzz`, except `f` has two inputs.
	pub fn fuzz_2<I: Int, F: Fn(I, I)>(n: u32, f: F)
	where
	<I as MinInt>::Unsigned: Int,
	{
	// Check cases where the first and second inputs are zero. Both call `f` 210 times for `u128`.
	edge_cases!(I, case, {
	f(I::ZERO, case);
	});
	edge_cases!(I, case, {
	f(case, I::ZERO);
	});
	// Nested edge tester. Calls `f` 44100 times for `u128`.
	edge_cases!(I, case0, {
	edge_cases!(I, case1, {
	f(case0, case1);
	})
	});

	// random fuzzer
	let mut rng = Xoshiro128StarStar::seed_from_u64(0);
	let mut x: I = I::ZERO;
	let mut y: I = I::ZERO;
	for _ in 0..n {
	fuzz_step(&mut rng, &mut x);
	fuzz_step(&mut rng, &mut y);
	f(x, y)
	}
	}

	/// Tester for shift functions
	pub fn fuzz_shift<I: Int, F: Fn(I, u32)>(f: F) {
	// Shift functions are very simple and do not need anything other than shifting a small
	// set of random patterns for every fuzz length.
	let mut rng = Xoshiro128StarStar::seed_from_u64(0);
	let mut x: I = MinInt::ZERO;
	for i in 0..I::FUZZ_NUM {
	fuzz_step(&mut rng, &mut x);
	f(x, MinInt::ZERO);
	f(x, I::FUZZ_LENGTHS[i] as u32);
	}
	}

	fn fuzz_float_step<F: Float>(rng: &mut Xoshiro128StarStar, f: &mut F) {
	let rng32 = rng.next_u32();
	// we need to fuzz the different parts of the float separately, because the masking on larger
	// significands will tend to set the exponent to all ones or all zeros frequently

	// sign bit fuzzing
	let sign = (rng32 & 1) != 0;

	// exponent fuzzing. Only 4 bits for the selector needed.
	let ones = (F::Int::ONE << F::EXP_BITS) - F::Int::ONE;
	let r0 = (rng32 >> 1) % F::EXP_BITS;
	let r1 = (rng32 >> 5) % F::EXP_BITS;
	// custom rotate shift. Note that `F::Int` is unsigned, so we can shift right without smearing
	// the sign bit.
	let mask = if r1 == 0 {
	ones.wrapping_shr(r0)
	} else {
	let tmp = ones.wrapping_shr(r0);
	(tmp.wrapping_shl(r1) \| tmp.wrapping_shr(F::EXP_BITS - r1)) & ones
	};
	let mut exp = (f.to_bits() & F::EXP_MASK) >> F::SIG_BITS;
	match (rng32 >> 9) % 4 {
	0 => exp \|= mask,
	1 => exp &= mask,
	_ => exp ^= mask,
	}

	// significand fuzzing
	let mut sig = f.to_bits() & F::SIG_MASK;
	fuzz_step(rng, &mut sig);
	sig &= F::SIG_MASK;

	*f = F::from_parts(sign, exp, sig);
	}

	macro_rules! float_edge_cases {
	($F:ident, $case:ident, $inner:block) => {
	for exponent in [
	F::Int::ZERO,
	F::Int::ONE,
	F::Int::ONE << (F::EXP_BITS / 2),
	(F::Int::ONE << (F::EXP_BITS - 1)) - F::Int::ONE,
	F::Int::ONE << (F::EXP_BITS - 1),
	(F::Int::ONE << (F::EXP_BITS - 1)) + F::Int::ONE,
	(F::Int::ONE << F::EXP_BITS) - F::Int::ONE,
	]
	.iter()
	{
	for significand in [
	F::Int::ZERO,
	F::Int::ONE,
	F::Int::ONE << (F::SIG_BITS / 2),
	(F::Int::ONE << (F::SIG_BITS - 1)) - F::Int::ONE,
	F::Int::ONE << (F::SIG_BITS - 1),
	(F::Int::ONE << (F::SIG_BITS - 1)) + F::Int::ONE,
	(F::Int::ONE << F::SIG_BITS) - F::Int::ONE,
	]
	.iter()
	{
	for sign in [false, true].iter() {
	let $case = F::from_parts(sign, exponent, *significand);
	$inner
	}
	}
	}
	};
	}

	pub fn fuzz_float<F: Float, E: Fn(F)>(n: u32, f: E) {
	float_edge_cases!(F, case, {
	f(case);
	});

	// random fuzzer
	let mut rng = Xoshiro128StarStar::seed_from_u64(0);
	let mut x = F::ZERO;
	for _ in 0..n {
	fuzz_float_step(&mut rng, &mut x);
	f(x);
	}
	}

	pub fn fuzz_float_2<F: Float, E: Fn(F, F)>(n: u32, f: E) {
	float_edge_cases!(F, case0, {
	float_edge_cases!(F, case1, {
	f(case0, case1);
	});
	});

	// random fuzzer
	let mut rng = Xoshiro128StarStar::seed_from_u64(0);
	let mut x = F::ZERO;
	let mut y = F::ZERO;
	for _ in 0..n {
	fuzz_float_step(&mut rng, &mut x);
	fuzz_float_step(&mut rng, &mut y);
	f(x, y)
	}
	}

	/// Perform an operation using builtin types if available, falling back to apfloat if not.
	#[macro_export]
	macro_rules! apfloat_fallback {
	(
	$float_ty:ty,
	// Type name in `rustc_apfloat::ieee`. Not a full path, it automatically gets the prefix.
	$apfloat_ty:ident,
	// Cfg expression for when builtin system operations should be used
	$sys_available:meta,
	// The expression to run. This expression may use `FloatTy` for its signature.
	// Optionally, the final conversion back to a float can be suppressed using
	// `=> no_convert` (for e.g. operations that return a bool).
	//
	// If the apfloat needs a different operation, it can be provided here.
	$op:expr $(=> $convert:ident)? $(; $apfloat_op:expr)?,
	// Arguments that get passed to `$op` after converting to a float
	$($arg:expr),+
	$(,)?
	) => {{
	#[cfg($sys_available)]
	let ret = {
	type FloatTy = $float_ty;
	$op( $($arg),+ )
	};

	#[cfg(not($sys_available))]
	let ret = {
	use rustc_apfloat::Float;
	type FloatTy = rustc_apfloat::ieee::$apfloat_ty;

	apfloat_fallback!(@inner
	fty: $float_ty,
	// Apply a conversion to `FloatTy` to each arg, then pass all args to `$op`
	op_res: $op( $(FloatTy::from_bits($arg.to_bits().into())),+ ),
	$(apfloat_op: $apfloat_op, )?
	$(conv_opts: $convert,)?
	args: $($arg),+
	)
	};

	ret
	}};

	// Operations that do not need converting back to a float
	(@inner fty: $float_ty:ty, op_res: $val:expr, conv_opts: no_convert, args: $($_arg:expr),+) => {
	$val
	};

	// Some apfloat operations return a `StatusAnd` that we need to extract the value from. This
	// is the default.
	(@inner fty: $float_ty:ty, op_res: $val:expr, args: $($_arg:expr),+) => {{
	// ignore the status, just get the value
	let unwrapped = $val.value;

	<$float_ty>::from_bits(FloatTy::to_bits(unwrapped).try_into().unwrap())
	}};

	// This is the case where we can't use the same expression for the default builtin and
	// nonstandard apfloat fallback (e.g. `as` casts in std are normal functions in apfloat, so
	// two separate expressions must be specified.
	(@inner
	fty: $float_ty:ty, op_res: $_val:expr,
	apfloat_op: $apfloat_op:expr, args: $($arg:expr),+
	) => {{
	$apfloat_op($($arg),+)
	}};
	}