diff --git a/library/compiler-builtins/libm/crates/libm-test/src/lib.rs b/library/compiler-builtins/libm/crates/libm-test/src/lib.rs index ed7131713d52..48b382d20c1c 100644 --- a/library/compiler-builtins/libm/crates/libm-test/src/lib.rs +++ b/library/compiler-builtins/libm/crates/libm-test/src/lib.rs @@ -4,12 +4,14 @@ mod f8_impl; pub mod gen; #[cfg(feature = "test-multiprecision")] pub mod mpfloat; +mod num; pub mod op; mod precision; mod test_traits; pub use f8_impl::f8; -pub use libm::support::{Float, Int, IntTy}; +pub use libm::support::{Float, Int, IntTy, MinInt}; +pub use num::{FloatExt, logspace}; pub use op::{BaseName, Identifier, MathOp, OpCFn, OpFTy, OpRustFn, OpRustRet}; pub use precision::{MaybeOverride, SpecialCase, default_ulp}; pub use test_traits::{CheckBasis, CheckCtx, CheckOutput, GenerateInput, Hex, TupleCall}; diff --git a/library/compiler-builtins/libm/crates/libm-test/src/num.rs b/library/compiler-builtins/libm/crates/libm-test/src/num.rs new file mode 100644 index 000000000000..4aa7f61b05a2 --- /dev/null +++ b/library/compiler-builtins/libm/crates/libm-test/src/num.rs @@ -0,0 +1,458 @@ +//! Helpful numeric operations. + +use std::cmp::min; + +use libm::support::{CastInto, Float}; + +use crate::{Int, MinInt}; + +/// Extension to `libm`'s `Float` trait with methods that are useful for tests but not +/// needed in `libm` itself. +pub trait FloatExt: Float { + /// The minimum subnormal number. + const TINY_BITS: Self::Int = Self::Int::ONE; + + /// Retrieve additional constants for this float type. + fn consts() -> Consts { + Consts::new() + } + + /// Increment by one ULP, saturating at infinity. + fn next_up(self) -> Self { + let bits = self.to_bits(); + if self.is_nan() || bits == Self::INFINITY.to_bits() { + return self; + } + + let abs = self.abs().to_bits(); + let next_bits = if abs == Self::Int::ZERO { + // Next up from 0 is the smallest subnormal + Self::TINY_BITS + } else if bits == abs { + // Positive: counting up is more positive + bits + Self::Int::ONE + } else { + // Negative: counting down is more positive + bits - Self::Int::ONE + }; + Self::from_bits(next_bits) + } + + /// A faster way to effectively call `next_up` `n` times. + fn n_up(self, n: Self::Int) -> Self { + let bits = self.to_bits(); + if self.is_nan() || bits == Self::INFINITY.to_bits() || n == Self::Int::ZERO { + return self; + } + + let abs = self.abs().to_bits(); + let is_positive = bits == abs; + let crosses_zero = !is_positive && n > abs; + let inf_bits = Self::INFINITY.to_bits(); + + let next_bits = if abs == Self::Int::ZERO { + min(n, inf_bits) + } else if crosses_zero { + min(n - abs, inf_bits) + } else if is_positive { + // Positive, counting up is more positive but this may overflow + match bits.checked_add(n) { + Some(v) if v >= inf_bits => inf_bits, + Some(v) => v, + None => inf_bits, + } + } else { + // Negative, counting down is more positive + bits - n + }; + Self::from_bits(next_bits) + } + + /// Decrement by one ULP, saturating at negative infinity. + fn next_down(self) -> Self { + let bits = self.to_bits(); + if self.is_nan() || bits == Self::NEG_INFINITY.to_bits() { + return self; + } + + let abs = self.abs().to_bits(); + let next_bits = if abs == Self::Int::ZERO { + // Next up from 0 is the smallest negative subnormal + Self::TINY_BITS | Self::SIGN_MASK + } else if bits == abs { + // Positive: counting down is more negative + bits - Self::Int::ONE + } else { + // Negative: counting up is more negative + bits + Self::Int::ONE + }; + Self::from_bits(next_bits) + } + + /// A faster way to effectively call `next_down` `n` times. + fn n_down(self, n: Self::Int) -> Self { + let bits = self.to_bits(); + if self.is_nan() || bits == Self::NEG_INFINITY.to_bits() || n == Self::Int::ZERO { + return self; + } + + let abs = self.abs().to_bits(); + let is_positive = bits == abs; + let crosses_zero = is_positive && n > abs; + let inf_bits = Self::INFINITY.to_bits(); + let ninf_bits = Self::NEG_INFINITY.to_bits(); + + let next_bits = if abs == Self::Int::ZERO { + min(n, inf_bits) | Self::SIGN_MASK + } else if crosses_zero { + min(n - abs, inf_bits) | Self::SIGN_MASK + } else if is_positive { + // Positive, counting down is more negative + bits - n + } else { + // Negative, counting up is more negative but this may overflow + match bits.checked_add(n) { + Some(v) if v > ninf_bits => ninf_bits, + Some(v) => v, + None => ninf_bits, + } + }; + Self::from_bits(next_bits) + } +} + +impl FloatExt for F where F: Float {} + +/// Extra constants that are useful for tests. +#[derive(Debug, Clone, Copy)] +pub struct Consts { + /// The default quiet NaN, which is also the minimum quiet NaN. + pub pos_nan: F, + /// The default quiet NaN with negative sign. + pub neg_nan: F, + /// NaN with maximum (unsigned) significand to be a quiet NaN. The significand is saturated. + pub max_qnan: F, + /// NaN with minimum (unsigned) significand to be a signaling NaN. + pub min_snan: F, + /// NaN with maximum (unsigned) significand to be a signaling NaN. + pub max_snan: F, + pub neg_max_qnan: F, + pub neg_min_snan: F, + pub neg_max_snan: F, +} + +impl Consts { + fn new() -> Self { + let top_sigbit_mask = F::Int::ONE << (F::SIG_BITS - 1); + let pos_nan = F::EXP_MASK | top_sigbit_mask; + let max_qnan = F::EXP_MASK | F::SIG_MASK; + let min_snan = F::EXP_MASK | F::Int::ONE; + let max_snan = (F::EXP_MASK | F::SIG_MASK) ^ top_sigbit_mask; + + let neg_nan = pos_nan | F::SIGN_MASK; + let neg_max_qnan = max_qnan | F::SIGN_MASK; + let neg_min_snan = min_snan | F::SIGN_MASK; + let neg_max_snan = max_snan | F::SIGN_MASK; + + Self { + pos_nan: F::from_bits(pos_nan), + neg_nan: F::from_bits(neg_nan), + max_qnan: F::from_bits(max_qnan), + min_snan: F::from_bits(min_snan), + max_snan: F::from_bits(max_snan), + neg_max_qnan: F::from_bits(neg_max_qnan), + neg_min_snan: F::from_bits(neg_min_snan), + neg_max_snan: F::from_bits(neg_max_snan), + } + } + + pub fn iter(self) -> impl Iterator { + // Destructure so we get unused warnings if we forget a list entry. + let Self { + pos_nan, + neg_nan, + max_qnan, + min_snan, + max_snan, + neg_max_qnan, + neg_min_snan, + neg_max_snan, + } = self; + + [pos_nan, neg_nan, max_qnan, min_snan, max_snan, neg_max_qnan, neg_min_snan, neg_max_snan] + .into_iter() + } +} + +/// Return the number of steps between two floats, returning `None` if either input is NaN. +/// +/// This is the number of steps needed for `n_up` or `n_down` to go between values. Infinities +/// are treated the same as those functions (will return the nearest finite value), and only one +/// of `-0` or `+0` is counted. It does not matter which value is greater. +pub fn ulp_between(x: F, y: F) -> Option { + let a = as_ulp_steps(x)?; + let b = as_ulp_steps(y)?; + Some(a.abs_diff(b)) +} + +/// Return the (signed) number of steps from zero to `x`. +fn as_ulp_steps(x: F) -> Option { + let s = x.to_bits_signed(); + let val = if s >= F::SignedInt::ZERO { + // each increment from `s = 0` is one step up from `x = 0.0` + s + } else { + // each increment from `s = F::SignedInt::MIN` is one step down from `x = -0.0` + F::SignedInt::MIN - s + }; + + // If `x` is NaN, return `None` + (!x.is_nan()).then_some(val) +} + +/// An iterator that returns floats with linearly spaced integer representations, which translates +/// to logarithmic spacing of their values. +/// +/// Note that this tends to skip negative zero, so that needs to be checked explicitly. +pub fn logspace(start: F, end: F, steps: F::Int) -> impl Iterator { + assert!(!start.is_nan()); + assert!(!end.is_nan()); + assert!(end >= start); + + let mut steps = steps.checked_sub(F::Int::ONE).expect("`steps` must be at least 2"); + let between = ulp_between(start, end).expect("`start` or `end` is NaN"); + let spacing = (between / steps).max(F::Int::ONE); + steps = steps.min(between); // At maximum, one step per ULP + + let mut x = start; + (0..=steps.cast()).map(move |_| { + let ret = x; + x = x.n_up(spacing); + ret + }) +} + +#[cfg(test)] +mod tests { + use std::cmp::max; + + use super::*; + use crate::f8; + + #[test] + fn test_next_up_down() { + for (i, v) in f8::ALL.into_iter().enumerate() { + let down = v.next_down().to_bits(); + let up = v.next_up().to_bits(); + + if i == 0 { + assert_eq!(down, f8::NEG_INFINITY.to_bits(), "{i} next_down({v:#010b})"); + } else { + let expected = + if v == f8::ZERO { 1 | f8::SIGN_MASK } else { f8::ALL[i - 1].to_bits() }; + assert_eq!(down, expected, "{i} next_down({v:#010b})"); + } + + if i == f8::ALL_LEN - 1 { + assert_eq!(up, f8::INFINITY.to_bits(), "{i} next_up({v:#010b})"); + } else { + let expected = if v == f8::NEG_ZERO { 1 } else { f8::ALL[i + 1].to_bits() }; + assert_eq!(up, expected, "{i} next_up({v:#010b})"); + } + } + } + + #[test] + fn test_next_up_down_inf_nan() { + assert_eq!(f8::NEG_INFINITY.next_up().to_bits(), f8::ALL[0].to_bits(),); + assert_eq!(f8::NEG_INFINITY.next_down().to_bits(), f8::NEG_INFINITY.to_bits(),); + assert_eq!(f8::INFINITY.next_down().to_bits(), f8::ALL[f8::ALL_LEN - 1].to_bits(),); + assert_eq!(f8::INFINITY.next_up().to_bits(), f8::INFINITY.to_bits(),); + assert_eq!(f8::NAN.next_up().to_bits(), f8::NAN.to_bits(),); + assert_eq!(f8::NAN.next_down().to_bits(), f8::NAN.to_bits(),); + } + + #[test] + fn test_n_up_down_quick() { + assert_eq!(f8::ALL[0].n_up(4).to_bits(), f8::ALL[4].to_bits(),); + assert_eq!( + f8::ALL[f8::ALL_LEN - 1].n_down(4).to_bits(), + f8::ALL[f8::ALL_LEN - 5].to_bits(), + ); + + // Check around zero + assert_eq!(f8::from_bits(0b0).n_up(7).to_bits(), 0b0_0000_111); + assert_eq!(f8::from_bits(0b0).n_down(7).to_bits(), 0b1_0000_111); + + // Check across zero + assert_eq!(f8::from_bits(0b1_0000_111).n_up(8).to_bits(), 0b0_0000_001); + assert_eq!(f8::from_bits(0b0_0000_111).n_down(8).to_bits(), 0b1_0000_001); + } + + #[test] + fn test_n_up_down_one() { + // Verify that `n_up(1)` and `n_down(1)` are the same as `next_up()` and next_down()`.` + for i in 0..u8::MAX { + let v = f8::from_bits(i); + assert_eq!(v.next_up().to_bits(), v.n_up(1).to_bits()); + assert_eq!(v.next_down().to_bits(), v.n_down(1).to_bits()); + } + } + + #[test] + fn test_n_up_down_inf_nan_zero() { + assert_eq!(f8::NEG_INFINITY.n_up(1).to_bits(), f8::ALL[0].to_bits()); + assert_eq!(f8::NEG_INFINITY.n_up(239).to_bits(), f8::ALL[f8::ALL_LEN - 1].to_bits()); + assert_eq!(f8::NEG_INFINITY.n_up(240).to_bits(), f8::INFINITY.to_bits()); + assert_eq!(f8::NEG_INFINITY.n_down(u8::MAX).to_bits(), f8::NEG_INFINITY.to_bits()); + + assert_eq!(f8::INFINITY.n_down(1).to_bits(), f8::ALL[f8::ALL_LEN - 1].to_bits()); + assert_eq!(f8::INFINITY.n_down(239).to_bits(), f8::ALL[0].to_bits()); + assert_eq!(f8::INFINITY.n_down(240).to_bits(), f8::NEG_INFINITY.to_bits()); + assert_eq!(f8::INFINITY.n_up(u8::MAX).to_bits(), f8::INFINITY.to_bits()); + + assert_eq!(f8::NAN.n_up(u8::MAX).to_bits(), f8::NAN.to_bits()); + assert_eq!(f8::NAN.n_down(u8::MAX).to_bits(), f8::NAN.to_bits()); + + assert_eq!(f8::ZERO.n_down(1).to_bits(), f8::TINY_BITS | f8::SIGN_MASK); + assert_eq!(f8::NEG_ZERO.n_up(1).to_bits(), f8::TINY_BITS); + } + + /// True if the specified range of `f8::ALL` includes both +0 and -0 + fn crossed_zero(start: usize, end: usize) -> bool { + let crossed = &f8::ALL[start..=end]; + crossed.iter().any(|f| f8::eq_repr(*f, f8::ZERO)) + && crossed.iter().any(|f| f8::eq_repr(*f, f8::NEG_ZERO)) + } + + #[test] + fn test_n_up_down() { + for (i, v) in f8::ALL.into_iter().enumerate() { + for n in 0..f8::ALL_LEN { + let down = v.n_down(n as u8).to_bits(); + let up = v.n_up(n as u8).to_bits(); + + if let Some(down_exp_idx) = i.checked_sub(n) { + // No overflow + let mut expected = f8::ALL[down_exp_idx].to_bits(); + if n >= 1 && crossed_zero(down_exp_idx, i) { + // If both -0 and +0 are included, we need to adjust our expected value + match down_exp_idx.checked_sub(1) { + Some(v) => expected = f8::ALL[v].to_bits(), + // Saturate to -inf if we are out of values + None => expected = f8::NEG_INFINITY.to_bits(), + } + } + assert_eq!(down, expected, "{i} {n} n_down({v:#010b})"); + } else { + // Overflow to -inf + assert_eq!(down, f8::NEG_INFINITY.to_bits(), "{i} {n} n_down({v:#010b})"); + } + + let mut up_exp_idx = i + n; + if up_exp_idx < f8::ALL_LEN { + // No overflow + if n >= 1 && up_exp_idx < f8::ALL_LEN && crossed_zero(i, up_exp_idx) { + // If both -0 and +0 are included, we need to adjust our expected value + up_exp_idx += 1; + } + + let expected = if up_exp_idx >= f8::ALL_LEN { + f8::INFINITY.to_bits() + } else { + f8::ALL[up_exp_idx].to_bits() + }; + + assert_eq!(up, expected, "{i} {n} n_up({v:#010b})"); + } else { + // Overflow to +inf + assert_eq!(up, f8::INFINITY.to_bits(), "{i} {n} n_up({v:#010b})"); + } + } + } + } + + #[test] + fn test_ulp_between() { + for (i, x) in f8::ALL.into_iter().enumerate() { + for (j, y) in f8::ALL.into_iter().enumerate() { + let ulp = ulp_between(x, y).unwrap(); + let make_msg = || format!("i: {i} j: {j} x: {x:b} y: {y:b} ulp {ulp}"); + + let i_low = min(i, j); + let i_hi = max(i, j); + let mut expected = u8::try_from(i_hi - i_low).unwrap(); + if crossed_zero(i_low, i_hi) { + expected -= 1; + } + + assert_eq!(ulp, expected, "{}", make_msg()); + + // Skip if either are zero since `next_{up,down}` will count over it + let either_zero = x == f8::ZERO || y == f8::ZERO; + if x < y && !either_zero { + assert_eq!(x.n_up(ulp).to_bits(), y.to_bits(), "{}", make_msg()); + assert_eq!(y.n_down(ulp).to_bits(), x.to_bits(), "{}", make_msg()); + } else if !either_zero { + assert_eq!(y.n_up(ulp).to_bits(), x.to_bits(), "{}", make_msg()); + assert_eq!(x.n_down(ulp).to_bits(), y.to_bits(), "{}", make_msg()); + } + } + } + } + + #[test] + fn test_ulp_between_inf_nan_zero() { + assert_eq!(ulp_between(f8::NEG_INFINITY, f8::INFINITY).unwrap(), f8::ALL_LEN as u8); + assert_eq!(ulp_between(f8::INFINITY, f8::NEG_INFINITY).unwrap(), f8::ALL_LEN as u8); + assert_eq!( + ulp_between(f8::NEG_INFINITY, f8::ALL[f8::ALL_LEN - 1]).unwrap(), + f8::ALL_LEN as u8 - 1 + ); + assert_eq!(ulp_between(f8::INFINITY, f8::ALL[0]).unwrap(), f8::ALL_LEN as u8 - 1); + + assert_eq!(ulp_between(f8::ZERO, f8::NEG_ZERO).unwrap(), 0); + assert_eq!(ulp_between(f8::NAN, f8::ZERO), None); + assert_eq!(ulp_between(f8::ZERO, f8::NAN), None); + } + + #[test] + fn test_logspace() { + let ls: Vec<_> = logspace(f8::from_bits(0x0), f8::from_bits(0x4), 2).collect(); + let exp = [f8::from_bits(0x0), f8::from_bits(0x4)]; + assert_eq!(ls, exp); + + let ls: Vec<_> = logspace(f8::from_bits(0x0), f8::from_bits(0x4), 3).collect(); + let exp = [f8::from_bits(0x0), f8::from_bits(0x2), f8::from_bits(0x4)]; + assert_eq!(ls, exp); + + // Check that we include all values with no repeats if `steps` exceeds the maximum number + // of steps. + let ls: Vec<_> = logspace(f8::from_bits(0x0), f8::from_bits(0x3), 10).collect(); + let exp = [f8::from_bits(0x0), f8::from_bits(0x1), f8::from_bits(0x2), f8::from_bits(0x3)]; + assert_eq!(ls, exp); + } + + #[test] + fn test_consts() { + let Consts { + pos_nan, + neg_nan, + max_qnan, + min_snan, + max_snan, + neg_max_qnan, + neg_min_snan, + neg_max_snan, + } = f8::consts(); + + assert_eq!(pos_nan.to_bits(), 0b0_1111_100); + assert_eq!(neg_nan.to_bits(), 0b1_1111_100); + assert_eq!(max_qnan.to_bits(), 0b0_1111_111); + assert_eq!(min_snan.to_bits(), 0b0_1111_001); + assert_eq!(max_snan.to_bits(), 0b0_1111_011); + assert_eq!(neg_max_qnan.to_bits(), 0b1_1111_111); + assert_eq!(neg_min_snan.to_bits(), 0b1_1111_001); + assert_eq!(neg_max_snan.to_bits(), 0b1_1111_011); + } +}