| #![feature(stmt_expr_attributes)] |
| #![feature(float_erf)] |
| #![feature(float_gamma)] |
| #![feature(core_intrinsics)] |
| #![feature(f128)] |
| #![feature(f16)] |
| #![allow(arithmetic_overflow)] |
| #![allow(internal_features)] |
| #![allow(unnecessary_transmutes)] |
| |
| #[path = "../utils/mod.rs"] |
| mod utils; |
| use std::any::type_name; |
| use std::cmp::min; |
| use std::fmt::{Debug, Display, LowerHex}; |
| use std::hint::black_box; |
| use std::{f32, f64}; |
| |
| use utils::check_nondet; |
| |
| /// Compare the two floats, allowing for $ulp many ULPs of error. |
| /// |
| /// ULP means "Units in the Last Place" or "Units of Least Precision". |
| /// The ULP of a float `a`` is the smallest possible change at `a`, so the ULP difference represents how |
| /// many discrete floating-point steps are needed to reach the actual value from the expected value. |
| /// |
| /// Essentially ULP can be seen as a distance metric of floating-point numbers, but with |
| /// the same amount of "spacing" between all consecutive representable values. So even though 2 very large floating point numbers |
| /// have a large value difference, their ULP can still be 1, so they are still "approximatly equal", |
| /// but the EPSILON check would have failed. |
| macro_rules! assert_approx_eq { |
| ($a:expr, $b:expr, $ulp:expr) => {{ |
| let (actual, expected) = ($a, $b); |
| let allowed_ulp_diff = $ulp; |
| let _force_same_type = actual == expected; |
| // Approximate the ULP by taking half the distance between the number one place "up" |
| // and the number one place "down". |
| let ulp = (expected.next_up() - expected.next_down()) / 2.0; |
| let ulp_diff = ((actual - expected) / ulp).abs().round() as i32; |
| if ulp_diff > allowed_ulp_diff { |
| panic!("{actual:?} is not approximately equal to {expected:?}\ndifference in ULP: {ulp_diff} > {allowed_ulp_diff}"); |
| }; |
| }}; |
| |
| ($a:expr, $b: expr) => { |
| // accept up to 8ULP (4ULP for host floats and 4ULP for miri artificial error). |
| assert_approx_eq!($a, $b, 8); |
| }; |
| } |
| |
| /// From IEEE 754 a Signaling NaN for single precision has the following representation: |
| /// ``` |
| /// s | 1111 1111 | 0x..x |
| /// ```` |
| /// Were at least one `x` is a 1. |
| /// |
| /// This sNaN has the following representation and is used for testing purposes.: |
| /// ``` |
| /// 0 | 1111111 | 01..0 |
| /// ``` |
| const SNAN_F32: f32 = f32::from_bits(0x7fa00000); |
| |
| /// From IEEE 754 a Signaling NaN for double precision has the following representation: |
| /// ``` |
| /// s | 1111 1111 111 | 0x..x |
| /// ```` |
| /// Were at least one `x` is a 1. |
| /// |
| /// This sNaN has the following representation and is used for testing purposes.: |
| /// ``` |
| /// 0 | 1111 1111 111 | 01..0 |
| /// ``` |
| const SNAN_F64: f64 = f64::from_bits(0x7ff4000000000000); |
| |
| fn main() { |
| basic(); |
| casts(); |
| more_casts(); |
| ops(); |
| nan_casts(); |
| rounding(); |
| mul_add(); |
| libm(); |
| test_fast(); |
| test_algebraic(); |
| test_fmuladd(); |
| test_min_max_nondet(); |
| test_non_determinism(); |
| } |
| |
| trait Float: Copy + PartialEq + Debug { |
| /// The unsigned integer with the same bit width as this float |
| type Int: Copy + PartialEq + LowerHex + Debug; |
| const BITS: u32 = size_of::<Self>() as u32 * 8; |
| const EXPONENT_BITS: u32 = Self::BITS - Self::SIGNIFICAND_BITS - 1; |
| const SIGNIFICAND_BITS: u32; |
| |
| /// The saturated (all ones) value of the exponent (infinity representation) |
| const EXPONENT_SAT: u32 = (1 << Self::EXPONENT_BITS) - 1; |
| |
| /// The exponent bias value (max representable positive exponent) |
| const EXPONENT_BIAS: u32 = Self::EXPONENT_SAT >> 1; |
| |
| fn to_bits(self) -> Self::Int; |
| } |
| |
| macro_rules! impl_float { |
| ($ty:ty, $ity:ty) => { |
| impl Float for $ty { |
| type Int = $ity; |
| // Just get this from std's value, which includes the implicit digit |
| const SIGNIFICAND_BITS: u32 = <$ty>::MANTISSA_DIGITS - 1; |
| |
| fn to_bits(self) -> Self::Int { |
| self.to_bits() |
| } |
| } |
| }; |
| } |
| |
| impl_float!(f16, u16); |
| impl_float!(f32, u32); |
| impl_float!(f64, u64); |
| impl_float!(f128, u128); |
| |
| trait FloatToInt<Int>: Copy { |
| fn cast(self) -> Int; |
| unsafe fn cast_unchecked(self) -> Int; |
| } |
| |
| macro_rules! float_to_int { |
| ($fty:ty => $($ity:ty),+ $(,)?) => { |
| $( |
| impl FloatToInt<$ity> for $fty { |
| fn cast(self) -> $ity { |
| self as _ |
| } |
| unsafe fn cast_unchecked(self) -> $ity { |
| self.to_int_unchecked() |
| } |
| } |
| )* |
| }; |
| } |
| |
| float_to_int!(f16 => i8, u8, i16, u16, i32, u32, i64, u64, i128, u128); |
| float_to_int!(f32 => i8, u8, i16, u16, i32, u32, i64, u64, i128, u128); |
| float_to_int!(f64 => i8, u8, i16, u16, i32, u32, i64, u64, i128, u128); |
| float_to_int!(f128 => i8, u8, i16, u16, i32, u32, i64, u64, i128, u128); |
| |
| /// Test this cast both via `as` and via `approx_unchecked` (i.e., it must not saturate). |
| #[track_caller] |
| #[inline(never)] |
| fn test_both_cast<F, I>(x: F, y: I, msg: impl Display) |
| where |
| F: FloatToInt<I>, |
| I: PartialEq + Debug, |
| { |
| let f_tname = type_name::<F>(); |
| let i_tname = type_name::<I>(); |
| assert_eq!(x.cast(), y, "{f_tname} -> {i_tname}: {msg}"); |
| assert_eq!(unsafe { x.cast_unchecked() }, y, "{f_tname} -> {i_tname}: {msg}",); |
| } |
| |
| /// Helper function to avoid promotion so that this tests "run-time" casts, not CTFE. |
| /// Doesn't make a big difference when running this in Miri, but it means we can compare this |
| /// with the LLVM backend by running `rustc -Zmir-opt-level=0 -Zsaturating-float-casts`. |
| #[track_caller] |
| #[inline(never)] |
| fn assert_eq<T: PartialEq + Debug>(x: T, y: T) { |
| assert_eq!(x, y); |
| } |
| |
| /// The same as `assert_eq` except prints a specific message on failure |
| #[track_caller] |
| #[inline(never)] |
| fn assert_eq_msg<T: PartialEq + Debug>(x: T, y: T, msg: impl Display) { |
| assert_eq!(x, y, "{msg}"); |
| } |
| |
| /// Check that floats have bitwise equality |
| #[track_caller] |
| fn assert_biteq<F: Float>(a: F, b: F, msg: impl Display) { |
| let ab = a.to_bits(); |
| let bb = b.to_bits(); |
| let tname = type_name::<F>(); |
| let width = (2 + F::BITS / 4) as usize; |
| assert_eq_msg::<F::Int>( |
| ab, |
| bb, |
| format_args!("({ab:#0width$x} != {bb:#0width$x}) {tname}: {msg}"), |
| ); |
| } |
| |
| /// Check that two floats have equality |
| #[track_caller] |
| fn assert_feq<F: Float>(a: F, b: F, msg: impl Display) { |
| let ab = a.to_bits(); |
| let bb = b.to_bits(); |
| let tname = type_name::<F>(); |
| let width = (2 + F::BITS / 4) as usize; |
| assert_eq_msg::<F>(a, b, format_args!("({ab:#0width$x} != {bb:#0width$x}) {tname}: {msg}")); |
| } |
| |
| fn basic() { |
| // basic arithmetic |
| assert_eq(6.0_f16 * 6.0_f16, 36.0_f16); |
| assert_eq(6.0_f32 * 6.0_f32, 36.0_f32); |
| assert_eq(6.0_f64 * 6.0_f64, 36.0_f64); |
| assert_eq(6.0_f128 * 6.0_f128, 36.0_f128); |
| assert_eq(-{ 5.0_f16 }, -5.0_f16); |
| assert_eq(-{ 5.0_f32 }, -5.0_f32); |
| assert_eq(-{ 5.0_f64 }, -5.0_f64); |
| assert_eq(-{ 5.0_f128 }, -5.0_f128); |
| |
| // infinities, NaN |
| assert!((5.0_f16 / 0.0).is_infinite()); |
| assert_ne!({ 5.0_f16 / 0.0 }, { -5.0_f16 / 0.0 }); |
| assert!((5.0_f32 / 0.0).is_infinite()); |
| assert_ne!({ 5.0_f32 / 0.0 }, { -5.0_f32 / 0.0 }); |
| assert!((5.0_f64 / 0.0).is_infinite()); |
| assert_ne!({ 5.0_f64 / 0.0 }, { 5.0_f64 / -0.0 }); |
| assert!((5.0_f128 / 0.0).is_infinite()); |
| assert_ne!({ 5.0_f128 / 0.0 }, { 5.0_f128 / -0.0 }); |
| assert_ne!(f16::NAN, f16::NAN); |
| assert_ne!(f32::NAN, f32::NAN); |
| assert_ne!(f64::NAN, f64::NAN); |
| assert_ne!(f128::NAN, f128::NAN); |
| |
| // negative zero |
| let posz = 0.0f16; |
| let negz = -0.0f16; |
| assert_eq(posz, negz); |
| assert_ne!(posz.to_bits(), negz.to_bits()); |
| let posz = 0.0f32; |
| let negz = -0.0f32; |
| assert_eq(posz, negz); |
| assert_ne!(posz.to_bits(), negz.to_bits()); |
| let posz = 0.0f64; |
| let negz = -0.0f64; |
| assert_eq(posz, negz); |
| assert_ne!(posz.to_bits(), negz.to_bits()); |
| let posz = 0.0f128; |
| let negz = -0.0f128; |
| assert_eq(posz, negz); |
| assert_ne!(posz.to_bits(), negz.to_bits()); |
| |
| // byte-level transmute |
| let x: u16 = unsafe { std::mem::transmute(42.0_f16) }; |
| let y: f16 = unsafe { std::mem::transmute(x) }; |
| assert_eq(y, 42.0_f16); |
| let x: u32 = unsafe { std::mem::transmute(42.0_f32) }; |
| let y: f32 = unsafe { std::mem::transmute(x) }; |
| assert_eq(y, 42.0_f32); |
| let x: u64 = unsafe { std::mem::transmute(42.0_f64) }; |
| let y: f64 = unsafe { std::mem::transmute(x) }; |
| assert_eq(y, 42.0_f64); |
| let x: u128 = unsafe { std::mem::transmute(42.0_f128) }; |
| let y: f128 = unsafe { std::mem::transmute(x) }; |
| assert_eq(y, 42.0_f128); |
| |
| // `%` sign behavior, some of this used to be buggy |
| assert!((black_box(1.0f16) % 1.0).is_sign_positive()); |
| assert!((black_box(1.0f16) % -1.0).is_sign_positive()); |
| assert!((black_box(-1.0f16) % 1.0).is_sign_negative()); |
| assert!((black_box(-1.0f16) % -1.0).is_sign_negative()); |
| assert!((black_box(1.0f32) % 1.0).is_sign_positive()); |
| assert!((black_box(1.0f32) % -1.0).is_sign_positive()); |
| assert!((black_box(-1.0f32) % 1.0).is_sign_negative()); |
| assert!((black_box(-1.0f32) % -1.0).is_sign_negative()); |
| assert!((black_box(1.0f64) % 1.0).is_sign_positive()); |
| assert!((black_box(1.0f64) % -1.0).is_sign_positive()); |
| assert!((black_box(-1.0f64) % 1.0).is_sign_negative()); |
| assert!((black_box(-1.0f64) % -1.0).is_sign_negative()); |
| assert!((black_box(1.0f128) % 1.0).is_sign_positive()); |
| assert!((black_box(1.0f128) % -1.0).is_sign_positive()); |
| assert!((black_box(-1.0f128) % 1.0).is_sign_negative()); |
| assert!((black_box(-1.0f128) % -1.0).is_sign_negative()); |
| |
| assert_eq!((-1.0f16).abs(), 1.0f16); |
| assert_eq!(34.2f16.abs(), 34.2f16); |
| assert_eq!((-1.0f32).abs(), 1.0f32); |
| assert_eq!(34.2f32.abs(), 34.2f32); |
| assert_eq!((-1.0f64).abs(), 1.0f64); |
| assert_eq!(34.2f64.abs(), 34.2f64); |
| assert_eq!((-1.0f128).abs(), 1.0f128); |
| assert_eq!(34.2f128.abs(), 34.2f128); |
| |
| assert_eq!(64_f16.sqrt(), 8_f16); |
| assert_eq!(64_f32.sqrt(), 8_f32); |
| assert_eq!(64_f64.sqrt(), 8_f64); |
| assert_eq!(64_f128.sqrt(), 8_f128); |
| assert_eq!(f16::INFINITY.sqrt(), f16::INFINITY); |
| assert_eq!(f32::INFINITY.sqrt(), f32::INFINITY); |
| assert_eq!(f64::INFINITY.sqrt(), f64::INFINITY); |
| assert_eq!(f128::INFINITY.sqrt(), f128::INFINITY); |
| assert_eq!(0.0_f16.sqrt().total_cmp(&0.0), std::cmp::Ordering::Equal); |
| assert_eq!(0.0_f32.sqrt().total_cmp(&0.0), std::cmp::Ordering::Equal); |
| assert_eq!(0.0_f64.sqrt().total_cmp(&0.0), std::cmp::Ordering::Equal); |
| assert_eq!(0.0_f128.sqrt().total_cmp(&0.0), std::cmp::Ordering::Equal); |
| assert_eq!((-0.0_f16).sqrt().total_cmp(&-0.0), std::cmp::Ordering::Equal); |
| assert_eq!((-0.0_f32).sqrt().total_cmp(&-0.0), std::cmp::Ordering::Equal); |
| assert_eq!((-0.0_f64).sqrt().total_cmp(&-0.0), std::cmp::Ordering::Equal); |
| assert_eq!((-0.0_f128).sqrt().total_cmp(&-0.0), std::cmp::Ordering::Equal); |
| assert!((-5.0_f16).sqrt().is_nan()); |
| assert!((-5.0_f32).sqrt().is_nan()); |
| assert!((-5.0_f64).sqrt().is_nan()); |
| assert!((-5.0_f128).sqrt().is_nan()); |
| assert!(f16::NEG_INFINITY.sqrt().is_nan()); |
| assert!(f32::NEG_INFINITY.sqrt().is_nan()); |
| assert!(f64::NEG_INFINITY.sqrt().is_nan()); |
| assert!(f128::NEG_INFINITY.sqrt().is_nan()); |
| assert!(f16::NAN.sqrt().is_nan()); |
| assert!(f32::NAN.sqrt().is_nan()); |
| assert!(f64::NAN.sqrt().is_nan()); |
| assert!(f128::NAN.sqrt().is_nan()); |
| } |
| |
| /// Test casts from floats to ints and back |
| macro_rules! test_ftoi_itof { |
| ( |
| f: $fty:ty, |
| i: $ity:ty, |
| // Int min and max as float literals |
| imin_f: $imin_f:literal, |
| imax_f: $imax_f:literal $(,)? |
| ) => {{ |
| /// By default we test float to int `as` casting as well as to_int_unchecked |
| fn assert_ftoi(f: $fty, i: $ity, msg: &str) { |
| #[allow(unused_comparisons)] |
| if <$ity>::MIN >= 0 && f < 0.0 { |
| // If `ity` is signed and `f` is negative, it is unrepresentable so skip |
| // unchecked casts. |
| assert_ftoi_unrep(f, i, msg); |
| } else { |
| test_both_cast::<$fty, $ity>(f, i, msg); |
| } |
| } |
| |
| /// Unrepresentable values only get tested with `as` casting, not unchecked |
| fn assert_ftoi_unrep(f: $fty, i: $ity, msg: &str) { |
| assert_eq_msg::<$ity>( |
| f as $ity, |
| i, |
| format_args!("{} -> {}: {msg}", stringify!($fty), stringify!($ity)), |
| ); |
| } |
| |
| /// Int to float checks |
| fn assert_itof(i: $ity, f: $fty, msg: &str) { |
| assert_eq_msg::<$fty>( |
| i as $fty, |
| f, |
| format_args!("{} -> {}: {msg}", stringify!($ity), stringify!($fty)), |
| ); |
| } |
| |
| /// Check both float to int and int to float |
| fn assert_bidir(f: $fty, i: $ity, msg: &str) { |
| assert_ftoi(f, i, msg); |
| assert_itof(i, f, msg); |
| } |
| |
| /// Check both float to int and int to float for unrepresentable numbers |
| fn assert_bidir_unrep(f: $fty, i: $ity, msg: &str) { |
| assert_ftoi_unrep(f, i, msg); |
| assert_itof(i, f, msg); |
| } |
| |
| let fbits = <$fty>::BITS; |
| let fsig_bits = <$fty>::SIGNIFICAND_BITS; |
| let ibits = <$ity>::BITS; |
| let imax: $ity = <$ity>::MAX; |
| let imin: $ity = <$ity>::MIN; |
| let izero: $ity = 0; |
| #[allow(unused_comparisons)] |
| let isigned = <$ity>::MIN < 0; |
| |
| #[allow(overflowing_literals)] |
| let imin_f: $fty = $imin_f; |
| #[allow(overflowing_literals)] |
| let imax_f: $fty = $imax_f; |
| |
| // If an integer can fit entirely in the mantissa (counting the hidden bit), every value |
| // can be represented exactly. |
| let all_ints_exact_rep = ibits <= fsig_bits + 1; |
| |
| // We can represent the full range of the integer (but possibly not every value) without |
| // saturating to infinity if `1 << (I::BITS - 1)` (single one in the MSB position) is |
| // within the float's dynamic range. |
| let int_range_rep = ibits - 1 < <$fty>::EXPONENT_BIAS; |
| |
| // Skip unchecked cast when int min/max would be unrepresentable |
| let assert_ftoi_big = if all_ints_exact_rep { assert_ftoi } else { assert_ftoi_unrep }; |
| let assert_bidir_big = if all_ints_exact_rep { assert_bidir } else { assert_bidir_unrep }; |
| |
| // Near zero representations |
| assert_bidir(0.0, 0, "zero"); |
| assert_ftoi(-0.0, 0, "negative zero"); |
| assert_ftoi(1.0, 1, "one"); |
| assert_ftoi(-1.0, izero.saturating_sub(1), "negative one"); |
| assert_ftoi(1.0 - <$fty>::EPSILON, 0, "1.0 - ε"); |
| assert_ftoi(1.0 + <$fty>::EPSILON, 1, "1.0 + ε"); |
| assert_ftoi(-1.0 + <$fty>::EPSILON, 0, "-1.0 + ε"); |
| assert_ftoi(-1.0 - <$fty>::EPSILON, izero.saturating_sub(1), "-1.0 - ε"); |
| assert_ftoi(<$fty>::from_bits(0x1), 0, "min subnormal"); |
| assert_ftoi(<$fty>::from_bits(0x1 | 1 << (fbits - 1)), 0, "min neg subnormal"); |
| |
| // Spot checks. Use `saturating_sub` to create negative integers so that unsigned |
| // integers stay at zero. |
| assert_ftoi(0.9, 0, "0.9"); |
| assert_ftoi(-0.9, 0, "-0.9"); |
| assert_ftoi(1.1, 1, "1.1"); |
| assert_ftoi(-1.1, izero.saturating_sub(1), "-1.1"); |
| assert_ftoi(1.9, 1, "1.9"); |
| assert_ftoi(-1.9, izero.saturating_sub(1), "-1.9"); |
| assert_ftoi(5.0, 5, "5.0"); |
| assert_ftoi(-5.0, izero.saturating_sub(5), "-5.0"); |
| assert_ftoi(5.9, 5, "5.0"); |
| assert_ftoi(-5.9, izero.saturating_sub(5), "-5.0"); |
| |
| // Exercise the middle of the integer's bit range. A power of two fits as long as the |
| // exponent can fit its log2, so cap at the maximum representable power of two (which |
| // is the exponent's bias). |
| let half_i_max: $ity = 1 << min(ibits / 2, <$fty>::EXPONENT_BIAS); |
| let half_i_min = izero.saturating_sub(half_i_max); |
| assert_bidir(half_i_max as $fty, half_i_max, "half int max"); |
| assert_bidir(half_i_min as $fty, half_i_min, "half int min"); |
| |
| // Integer limits |
| assert_bidir_big(imax_f, imax, "i max"); |
| assert_bidir_big(imin_f, imin, "i min"); |
| |
| // We need a small perturbation to test against that does not round up to the next |
| // integer. `f16` needs a smaller perturbation since it only has resolution for ~1 decimal |
| // place near 10^3. |
| let perturb = if fbits < 32 { 0.9 } else { 0.99 }; |
| assert_ftoi_big(imax_f + perturb, <$ity>::MAX, "slightly above i max"); |
| assert_ftoi_big(imin_f - perturb, <$ity>::MIN, "slightly below i min"); |
| |
| // Tests for when we can represent the integer's magnitude |
| if int_range_rep { |
| // If the float can represent values larger than the integer, float extremes |
| // will saturate. |
| assert_ftoi_unrep(<$fty>::MAX, imax, "f max"); |
| assert_ftoi_unrep(<$fty>::MIN, imin, "f min"); |
| |
| // Max representable power of 10 |
| let pow10_max = (10 as $ity).pow(imax.ilog10()); |
| |
| // If the power of 10 should be representable (fits in a mantissa), check it |
| if ibits - pow10_max.leading_zeros() - pow10_max.trailing_zeros() <= fsig_bits + 1 { |
| assert_bidir(pow10_max as $fty, pow10_max, "pow10 max"); |
| } |
| } |
| |
| // Test rounding the largest and smallest integers, but skip this when |
| // all integers have an exact representation (it's less interesting then and the arithmetic gets more complicated). |
| if int_range_rep && !all_ints_exact_rep { |
| // The maximum representable integer is a saturated mantissa (including the implicit |
| // bit), shifted into the int's leftmost position. |
| // |
| // Positive signed integers never use their top bit, so shift by one bit fewer. |
| let sat_mantissa: $ity = (1 << (fsig_bits + 1)) - 1; |
| let adj = if isigned { 1 } else { 0 }; |
| let max_rep = sat_mantissa << (sat_mantissa.leading_zeros() - adj); |
| |
| // This value should roundtrip exactly |
| assert_bidir(max_rep as $fty, max_rep, "max representable int"); |
| |
| // The cutoff for where to round to `imax` is halfway between the maximum exactly |
| // representable integer and `imax`. This should round down (to `max_rep`), |
| // i.e., `max_rep as $fty == max_non_sat as $fty`. |
| let max_non_sat = max_rep + ((imax - max_rep) / 2); |
| assert_bidir(max_non_sat as $fty, max_rep, "max non saturating int"); |
| |
| // So the next value up should round up to the maximum value of the integer |
| assert_bidir_unrep((max_non_sat + 1) as $fty, imax, "min infinite int"); |
| |
| if isigned { |
| // Floats can always represent the minimum signed number if they can fit the |
| // exponent, because it is just a `1` in the MSB. So, no negative int -> float |
| // conversion will round to negative infinity (if the exponent fits). |
| // |
| // Since `imin` is thus the minimum representable value, we test rounding near |
| // the next value. This happens to be the opposite of the maximum representable |
| // value, and it should roundtrip exactly. |
| let next_min_rep = max_rep.wrapping_neg(); |
| assert_bidir(next_min_rep as $fty, next_min_rep, "min representable above imin"); |
| |
| // Following a similar pattern as for positive numbers, halfway between this value |
| // and `imin` should round back to `next_min_rep`. |
| let min_non_sat = imin - ((imin - next_min_rep) / 2) + 1; |
| assert_bidir( |
| min_non_sat as $fty, |
| next_min_rep, |
| "min int that does not round to imin", |
| ); |
| |
| // And then anything else saturates to the minimum value. |
| assert_bidir_unrep( |
| (min_non_sat - 1) as $fty, |
| imin, |
| "max negative int that rounds to imin", |
| ); |
| } |
| } |
| |
| // Check potentially saturating int ranges. (`imax_f` here will be `$fty::INFINITY` if |
| // it cannot be represented as a finite value.) |
| assert_itof(imax, imax_f, "imax"); |
| assert_itof(imin, imin_f, "imin"); |
| |
| // Float limits |
| assert_ftoi_unrep(<$fty>::INFINITY, imax, "f inf"); |
| assert_ftoi_unrep(<$fty>::NEG_INFINITY, imin, "f neg inf"); |
| assert_ftoi_unrep(<$fty>::NAN, 0, "f nan"); |
| assert_ftoi_unrep(-<$fty>::NAN, 0, "f neg nan"); |
| }}; |
| } |
| |
| /// Test casts from one float to another |
| macro_rules! test_ftof { |
| ( |
| f1: $f1:ty, |
| f2: $f2:ty $(,)? |
| ) => {{ |
| type F2Int = <$f2 as Float>::Int; |
| |
| let f1zero: $f1 = 0.0; |
| let f2zero: $f2 = 0.0; |
| let f1five: $f1 = 5.0; |
| let f2five: $f2 = 5.0; |
| |
| assert_biteq((f1zero as $f2), f2zero, "0.0"); |
| assert_biteq(((-f1zero) as $f2), (-f2zero), "-0.0"); |
| assert_biteq((f1five as $f2), f2five, "5.0"); |
| assert_biteq(((-f1five) as $f2), (-f2five), "-5.0"); |
| |
| assert_feq(<$f1>::INFINITY as $f2, <$f2>::INFINITY, "max -> inf"); |
| assert_feq(<$f1>::NEG_INFINITY as $f2, <$f2>::NEG_INFINITY, "max -> inf"); |
| assert!((<$f1>::NAN as $f2).is_nan(), "{} -> {} nan", stringify!($f1), stringify!($f2)); |
| |
| let min_sub_casted = <$f1>::from_bits(0x1) as $f2; |
| let min_neg_sub_casted = <$f1>::from_bits(0x1 | 1 << (<$f1>::BITS - 1)) as $f2; |
| |
| if <$f1>::BITS > <$f2>::BITS { |
| assert_feq(<$f1>::MAX as $f2, <$f2>::INFINITY, "max -> inf"); |
| assert_feq(<$f1>::MIN as $f2, <$f2>::NEG_INFINITY, "max -> inf"); |
| assert_biteq(min_sub_casted, f2zero, "min subnormal -> 0.0"); |
| assert_biteq(min_neg_sub_casted, -f2zero, "min neg subnormal -> -0.0"); |
| } else { |
| // When increasing precision, the minimum subnormal will just roll to the next |
| // exponent. This exponent will be the current exponent (with bias), plus |
| // `sig_bits - 1` to account for the implicit change in exponent (since the |
| // mantissa starts with 0). |
| let sub_casted = <$f2>::from_bits( |
| ((<$f2>::EXPONENT_BIAS - (<$f1>::EXPONENT_BIAS + <$f1>::SIGNIFICAND_BITS - 1)) |
| as F2Int) |
| << <$f2>::SIGNIFICAND_BITS, |
| ); |
| assert_biteq(min_sub_casted, sub_casted, "min subnormal"); |
| assert_biteq(min_neg_sub_casted, -sub_casted, "min neg subnormal"); |
| } |
| }}; |
| } |
| |
| /// Many of these test patterns were adapted from the values in |
| /// https://github.com/WebAssembly/testsuite/blob/master/conversions.wast. |
| fn casts() { |
| /* int <-> float generic tests */ |
| |
| test_ftoi_itof! { f: f16, i: i8, imin_f: -128.0, imax_f: 127.0 }; |
| test_ftoi_itof! { f: f16, i: u8, imin_f: 0.0, imax_f: 255.0 }; |
| test_ftoi_itof! { f: f16, i: i16, imin_f: -32_768.0, imax_f: 32_767.0 }; |
| test_ftoi_itof! { f: f16, i: u16, imin_f: 0.0, imax_f: 65_535.0 }; |
| test_ftoi_itof! { f: f16, i: i32, imin_f: -2_147_483_648.0, imax_f: 2_147_483_647.0 }; |
| test_ftoi_itof! { f: f16, i: u32, imin_f: 0.0, imax_f: 4_294_967_295.0 }; |
| test_ftoi_itof! { |
| f: f16, |
| i: i64, |
| imin_f: -9_223_372_036_854_775_808.0, |
| imax_f: 9_223_372_036_854_775_807.0 |
| }; |
| test_ftoi_itof! { f: f16, i: u64, imin_f: 0.0, imax_f: 18_446_744_073_709_551_615.0 }; |
| test_ftoi_itof! { |
| f: f16, |
| i: i128, |
| imin_f: -170_141_183_460_469_231_731_687_303_715_884_105_728.0, |
| imax_f: 170_141_183_460_469_231_731_687_303_715_884_105_727.0, |
| }; |
| test_ftoi_itof! { |
| f: f16, |
| i: u128, |
| imin_f: 0.0, |
| imax_f: 340_282_366_920_938_463_463_374_607_431_768_211_455.0 |
| }; |
| |
| test_ftoi_itof! { f: f32, i: i8, imin_f: -128.0, imax_f: 127.0 }; |
| test_ftoi_itof! { f: f32, i: u8, imin_f: 0.0, imax_f: 255.0 }; |
| test_ftoi_itof! { f: f32, i: i16, imin_f: -32_768.0, imax_f: 32_767.0 }; |
| test_ftoi_itof! { f: f32, i: u16, imin_f: 0.0, imax_f: 65_535.0 }; |
| test_ftoi_itof! { f: f32, i: i32, imin_f: -2_147_483_648.0, imax_f: 2_147_483_647.0 }; |
| test_ftoi_itof! { f: f32, i: u32, imin_f: 0.0, imax_f: 4_294_967_295.0 }; |
| test_ftoi_itof! { |
| f: f32, |
| i: i64, |
| imin_f: -9_223_372_036_854_775_808.0, |
| imax_f: 9_223_372_036_854_775_807.0 |
| }; |
| test_ftoi_itof! { f: f32, i: u64, imin_f: 0.0, imax_f: 18_446_744_073_709_551_615.0 }; |
| test_ftoi_itof! { |
| f: f32, |
| i: i128, |
| imin_f: -170_141_183_460_469_231_731_687_303_715_884_105_728.0, |
| imax_f: 170_141_183_460_469_231_731_687_303_715_884_105_727.0, |
| }; |
| test_ftoi_itof! { |
| f: f32, |
| i: u128, |
| imin_f: 0.0, |
| imax_f: 340_282_366_920_938_463_463_374_607_431_768_211_455.0 |
| }; |
| |
| test_ftoi_itof! { f: f64, i: i8, imin_f: -128.0, imax_f: 127.0 }; |
| test_ftoi_itof! { f: f64, i: u8, imin_f: 0.0, imax_f: 255.0 }; |
| test_ftoi_itof! { f: f64, i: i16, imin_f: -32_768.0, imax_f: 32_767.0 }; |
| test_ftoi_itof! { f: f64, i: u16, imin_f: 0.0, imax_f: 65_535.0 }; |
| test_ftoi_itof! { f: f64, i: i32, imin_f: -2_147_483_648.0, imax_f: 2_147_483_647.0 }; |
| test_ftoi_itof! { f: f64, i: u32, imin_f: 0.0, imax_f: 4_294_967_295.0 }; |
| test_ftoi_itof! { |
| f: f64, |
| i: i64, |
| imin_f: -9_223_372_036_854_775_808.0, |
| imax_f: 9_223_372_036_854_775_807.0 |
| }; |
| test_ftoi_itof! { f: f64, i: u64, imin_f: 0.0, imax_f: 18_446_744_073_709_551_615.0 }; |
| test_ftoi_itof! { |
| f: f64, |
| i: i128, |
| imin_f: -170_141_183_460_469_231_731_687_303_715_884_105_728.0, |
| imax_f: 170_141_183_460_469_231_731_687_303_715_884_105_727.0, |
| }; |
| test_ftoi_itof! { |
| f: f64, |
| i: u128, |
| imin_f: 0.0, |
| imax_f: 340_282_366_920_938_463_463_374_607_431_768_211_455.0 |
| }; |
| |
| test_ftoi_itof! { f: f128, i: i8, imin_f: -128.0, imax_f: 127.0 }; |
| test_ftoi_itof! { f: f128, i: u8, imin_f: 0.0, imax_f: 255.0 }; |
| test_ftoi_itof! { f: f128, i: i16, imin_f: -32_768.0, imax_f: 32_767.0 }; |
| test_ftoi_itof! { f: f128, i: u16, imin_f: 0.0, imax_f: 65_535.0 }; |
| test_ftoi_itof! { f: f128, i: i32, imin_f: -2_147_483_648.0, imax_f: 2_147_483_647.0 }; |
| test_ftoi_itof! { f: f128, i: u32, imin_f: 0.0, imax_f: 4_294_967_295.0 }; |
| test_ftoi_itof! { |
| f: f128, |
| i: i64, |
| imin_f: -9_223_372_036_854_775_808.0, |
| imax_f: 9_223_372_036_854_775_807.0 |
| }; |
| test_ftoi_itof! { f: f128, i: u64, imin_f: 0.0, imax_f: 18_446_744_073_709_551_615.0 }; |
| test_ftoi_itof! { |
| f: f128, |
| i: i128, |
| imin_f: -170_141_183_460_469_231_731_687_303_715_884_105_728.0, |
| imax_f: 170_141_183_460_469_231_731_687_303_715_884_105_727.0, |
| }; |
| test_ftoi_itof! { |
| f: f128, |
| i: u128, |
| imin_f: 0.0, |
| imax_f: 340_282_366_920_938_463_463_374_607_431_768_211_455.0 |
| }; |
| |
| /* int <-> float spot checks */ |
| |
| // int -> f32 |
| assert_eq::<f32>(1234567890i32 as f32, /*0x1.26580cp+30*/ f32::from_bits(0x4e932c06)); |
| assert_eq::<f32>( |
| 0x7fffff4000000001i64 as f32, |
| /*0x1.fffffep+62*/ f32::from_bits(0x5effffff), |
| ); |
| assert_eq::<f32>( |
| 0x8000004000000001u64 as i64 as f32, |
| /*-0x1.fffffep+62*/ f32::from_bits(0xdeffffff), |
| ); |
| assert_eq::<f32>( |
| 0x0020000020000001i64 as f32, |
| /*0x1.000002p+53*/ f32::from_bits(0x5a000001), |
| ); |
| assert_eq::<f32>( |
| 0xffdfffffdfffffffu64 as i64 as f32, |
| /*-0x1.000002p+53*/ f32::from_bits(0xda000001), |
| ); |
| |
| // int -> f64 |
| assert_eq::<f64>(987654321i32 as f64, 987654321.0); |
| assert_eq::<f64>(4669201609102990i64 as f64, 4669201609102990.0); // Feigenbaum (?) |
| assert_eq::<f64>(9007199254740993i64 as f64, 9007199254740992.0); |
| assert_eq::<f64>(-9007199254740993i64 as f64, -9007199254740992.0); |
| assert_eq::<f64>(9007199254740995i64 as f64, 9007199254740996.0); |
| assert_eq::<f64>(-9007199254740995i64 as f64, -9007199254740996.0); |
| |
| /* float -> float generic tests */ |
| |
| test_ftof! { f1: f16, f2: f32 }; |
| test_ftof! { f1: f16, f2: f64 }; |
| test_ftof! { f1: f16, f2: f128 }; |
| test_ftof! { f1: f32, f2: f16 }; |
| test_ftof! { f1: f32, f2: f64 }; |
| test_ftof! { f1: f32, f2: f128 }; |
| test_ftof! { f1: f64, f2: f16 }; |
| test_ftof! { f1: f64, f2: f32 }; |
| test_ftof! { f1: f64, f2: f128 }; |
| test_ftof! { f1: f128, f2: f16 }; |
| test_ftof! { f1: f128, f2: f32 }; |
| test_ftof! { f1: f128, f2: f64 }; |
| |
| /* float -> float spot checks */ |
| |
| // f32 -> f64 |
| assert_eq::<f64>( |
| /*0x1.fffffep+127*/ f32::from_bits(0x7f7fffff) as f64, |
| /*0x1.fffffep+127*/ f64::from_bits(0x47efffffe0000000), |
| ); |
| assert_eq::<f64>( |
| /*-0x1.fffffep+127*/ (-f32::from_bits(0x7f7fffff)) as f64, |
| /*-0x1.fffffep+127*/ -f64::from_bits(0x47efffffe0000000), |
| ); |
| assert_eq::<f64>( |
| /*0x1p-119*/ f32::from_bits(0x4000000) as f64, |
| /*0x1p-119*/ f64::from_bits(0x3880000000000000), |
| ); |
| assert_eq::<f64>( |
| /*0x1.8f867ep+125*/ f32::from_bits(0x7e47c33f) as f64, |
| 6.6382536710104395e+37, |
| ); |
| |
| // f64 -> f32 |
| assert_eq::<f32>( |
| /*0x1.fffffe0000000p-127*/ f64::from_bits(0x380fffffe0000000) as f32, |
| /*0x1p-149*/ f32::from_bits(0x800000), |
| ); |
| assert_eq::<f32>( |
| /*0x1.4eae4f7024c7p+108*/ f64::from_bits(0x46b4eae4f7024c70) as f32, |
| /*0x1.4eae5p+108*/ f32::from_bits(0x75a75728), |
| ); |
| } |
| |
| fn ops() { |
| // f16 min/max |
| assert_eq((1.0_f16).max(-1.0), 1.0); |
| assert_eq((1.0_f16).min(-1.0), -1.0); |
| assert_eq(f16::NAN.min(9.0), 9.0); |
| assert_eq(f16::NAN.max(-9.0), -9.0); |
| assert_eq((9.0_f16).min(f16::NAN), 9.0); |
| assert_eq((-9.0_f16).max(f16::NAN), -9.0); |
| |
| // f32 min/max |
| assert_eq((1.0 as f32).max(-1.0), 1.0); |
| assert_eq((1.0 as f32).min(-1.0), -1.0); |
| assert_eq(f32::NAN.min(9.0), 9.0); |
| assert_eq(f32::NAN.max(-9.0), -9.0); |
| assert_eq((9.0 as f32).min(f32::NAN), 9.0); |
| assert_eq((-9.0 as f32).max(f32::NAN), -9.0); |
| |
| // f64 min/max |
| assert_eq((1.0 as f64).max(-1.0), 1.0); |
| assert_eq((1.0 as f64).min(-1.0), -1.0); |
| assert_eq(f64::NAN.min(9.0), 9.0); |
| assert_eq(f64::NAN.max(-9.0), -9.0); |
| assert_eq((9.0 as f64).min(f64::NAN), 9.0); |
| assert_eq((-9.0 as f64).max(f64::NAN), -9.0); |
| |
| // f128 min/max |
| assert_eq((1.0_f128).max(-1.0), 1.0); |
| assert_eq((1.0_f128).min(-1.0), -1.0); |
| assert_eq(f128::NAN.min(9.0), 9.0); |
| assert_eq(f128::NAN.max(-9.0), -9.0); |
| assert_eq((9.0_f128).min(f128::NAN), 9.0); |
| assert_eq((-9.0_f128).max(f128::NAN), -9.0); |
| |
| // f16 copysign |
| assert_eq(3.5_f16.copysign(0.42), 3.5_f16); |
| assert_eq(3.5_f16.copysign(-0.42), -3.5_f16); |
| assert_eq((-3.5_f16).copysign(0.42), 3.5_f16); |
| assert_eq((-3.5_f16).copysign(-0.42), -3.5_f16); |
| assert!(f16::NAN.copysign(1.0).is_nan()); |
| |
| // f32 copysign |
| assert_eq(3.5_f32.copysign(0.42), 3.5_f32); |
| assert_eq(3.5_f32.copysign(-0.42), -3.5_f32); |
| assert_eq((-3.5_f32).copysign(0.42), 3.5_f32); |
| assert_eq((-3.5_f32).copysign(-0.42), -3.5_f32); |
| assert!(f32::NAN.copysign(1.0).is_nan()); |
| |
| // f64 copysign |
| assert_eq(3.5_f64.copysign(0.42), 3.5_f64); |
| assert_eq(3.5_f64.copysign(-0.42), -3.5_f64); |
| assert_eq((-3.5_f64).copysign(0.42), 3.5_f64); |
| assert_eq((-3.5_f64).copysign(-0.42), -3.5_f64); |
| assert!(f64::NAN.copysign(1.0).is_nan()); |
| |
| // f128 copysign |
| assert_eq(3.5_f128.copysign(0.42), 3.5_f128); |
| assert_eq(3.5_f128.copysign(-0.42), -3.5_f128); |
| assert_eq((-3.5_f128).copysign(0.42), 3.5_f128); |
| assert_eq((-3.5_f128).copysign(-0.42), -3.5_f128); |
| assert!(f128::NAN.copysign(1.0).is_nan()); |
| } |
| |
| /// Tests taken from rustc test suite. |
| /// |
| |
| macro_rules! test { |
| ($val:expr, $src_ty:ident -> $dest_ty:ident, $expected:expr) => ( |
| // black_box disables constant evaluation to test run-time conversions: |
| assert_eq!(black_box::<$src_ty>($val) as $dest_ty, $expected, |
| "run-time {} -> {}", stringify!($src_ty), stringify!($dest_ty)); |
| |
| { |
| const X: $src_ty = $val; |
| const Y: $dest_ty = X as $dest_ty; |
| assert_eq!(Y, $expected, |
| "const eval {} -> {}", stringify!($src_ty), stringify!($dest_ty)); |
| } |
| ); |
| |
| ($fval:expr, f* -> $ity:ident, $ival:expr) => ( |
| test!($fval, f32 -> $ity, $ival); |
| test!($fval, f64 -> $ity, $ival); |
| ) |
| } |
| |
| macro_rules! common_fptoi_tests { |
| ($fty:ident -> $($ity:ident)+) => ({ $( |
| test!($fty::NAN, $fty -> $ity, 0); |
| test!($fty::INFINITY, $fty -> $ity, $ity::MAX); |
| test!($fty::NEG_INFINITY, $fty -> $ity, $ity::MIN); |
| // These two tests are not solely float->int tests, in particular the latter relies on |
| // `u128::MAX as f32` not being UB. But that's okay, since this file tests int->float |
| // as well, the test is just slightly misplaced. |
| test!($ity::MIN as $fty, $fty -> $ity, $ity::MIN); |
| test!($ity::MAX as $fty, $fty -> $ity, $ity::MAX); |
| test!(0., $fty -> $ity, 0); |
| test!($fty::MIN_POSITIVE, $fty -> $ity, 0); |
| test!(-0.9, $fty -> $ity, 0); |
| test!(1., $fty -> $ity, 1); |
| test!(42., $fty -> $ity, 42); |
| )+ }); |
| |
| (f* -> $($ity:ident)+) => ({ |
| common_fptoi_tests!(f32 -> $($ity)+); |
| common_fptoi_tests!(f64 -> $($ity)+); |
| }) |
| } |
| |
| macro_rules! fptoui_tests { |
| ($fty: ident -> $($ity: ident)+) => ({ $( |
| test!(-0., $fty -> $ity, 0); |
| test!(-$fty::MIN_POSITIVE, $fty -> $ity, 0); |
| test!(-0.99999994, $fty -> $ity, 0); |
| test!(-1., $fty -> $ity, 0); |
| test!(-100., $fty -> $ity, 0); |
| test!(#[allow(overflowing_literals)] -1e50, $fty -> $ity, 0); |
| test!(#[allow(overflowing_literals)] -1e130, $fty -> $ity, 0); |
| )+ }); |
| |
| (f* -> $($ity:ident)+) => ({ |
| fptoui_tests!(f32 -> $($ity)+); |
| fptoui_tests!(f64 -> $($ity)+); |
| }) |
| } |
| |
| fn more_casts() { |
| common_fptoi_tests!(f* -> i8 i16 i32 i64 u8 u16 u32 u64); |
| fptoui_tests!(f* -> u8 u16 u32 u64); |
| common_fptoi_tests!(f* -> i128 u128); |
| fptoui_tests!(f* -> u128); |
| |
| // The following tests cover edge cases for some integer types. |
| |
| // # u8 |
| test!(254., f* -> u8, 254); |
| test!(256., f* -> u8, 255); |
| |
| // # i8 |
| test!(-127., f* -> i8, -127); |
| test!(-129., f* -> i8, -128); |
| test!(126., f* -> i8, 126); |
| test!(128., f* -> i8, 127); |
| |
| // # i32 |
| // -2147483648. is i32::MIN (exactly) |
| test!(-2147483648., f* -> i32, i32::MIN); |
| // 2147483648. is i32::MAX rounded up |
| test!(2147483648., f32 -> i32, 2147483647); |
| // With 24 significand bits, floats with magnitude in [2^30 + 1, 2^31] are rounded to |
| // multiples of 2^7. Therefore, nextDown(round(i32::MAX)) is 2^31 - 128: |
| test!(2147483520., f32 -> i32, 2147483520); |
| // Similarly, nextUp(i32::MIN) is i32::MIN + 2^8 and nextDown(i32::MIN) is i32::MIN - 2^7 |
| test!(-2147483904., f* -> i32, i32::MIN); |
| test!(-2147483520., f* -> i32, -2147483520); |
| |
| // # u32 |
| // round(MAX) and nextUp(round(MAX)) |
| test!(4294967040., f* -> u32, 4294967040); |
| test!(4294967296., f* -> u32, 4294967295); |
| |
| // # u128 |
| // float->int: |
| test!(f32::MAX, f32 -> u128, 0xffffff00000000000000000000000000); |
| // nextDown(f32::MAX) = 2^128 - 2 * 2^104 |
| const SECOND_LARGEST_F32: f32 = 340282326356119256160033759537265639424.; |
| test!(SECOND_LARGEST_F32, f32 -> u128, 0xfffffe00000000000000000000000000); |
| } |
| |
| fn nan_casts() { |
| let nan1 = f64::from_bits(0x7FF0_0001_0000_0001u64); |
| let nan2 = f64::from_bits(0x7FF0_0000_0000_0001u64); |
| |
| assert!(nan1.is_nan()); |
| assert!(nan2.is_nan()); |
| |
| let nan1_32 = nan1 as f32; |
| let nan2_32 = nan2 as f32; |
| |
| assert!(nan1_32.is_nan()); |
| assert!(nan2_32.is_nan()); |
| } |
| |
| fn rounding() { |
| // Test cases taken from the library's tests for this feature |
| // f16 |
| assert_eq(2.5f16.round_ties_even(), 2.0f16); |
| assert_eq(1.0f16.round_ties_even(), 1.0f16); |
| assert_eq(1.3f16.round_ties_even(), 1.0f16); |
| assert_eq(1.5f16.round_ties_even(), 2.0f16); |
| assert_eq(1.7f16.round_ties_even(), 2.0f16); |
| assert_eq(0.0f16.round_ties_even(), 0.0f16); |
| assert_eq((-0.0f16).round_ties_even(), -0.0f16); |
| assert_eq((-1.0f16).round_ties_even(), -1.0f16); |
| assert_eq((-1.3f16).round_ties_even(), -1.0f16); |
| assert_eq((-1.5f16).round_ties_even(), -2.0f16); |
| assert_eq((-1.7f16).round_ties_even(), -2.0f16); |
| // f32 |
| assert_eq(2.5f32.round_ties_even(), 2.0f32); |
| assert_eq(1.0f32.round_ties_even(), 1.0f32); |
| assert_eq(1.3f32.round_ties_even(), 1.0f32); |
| assert_eq(1.5f32.round_ties_even(), 2.0f32); |
| assert_eq(1.7f32.round_ties_even(), 2.0f32); |
| assert_eq(0.0f32.round_ties_even(), 0.0f32); |
| assert_eq((-0.0f32).round_ties_even(), -0.0f32); |
| assert_eq((-1.0f32).round_ties_even(), -1.0f32); |
| assert_eq((-1.3f32).round_ties_even(), -1.0f32); |
| assert_eq((-1.5f32).round_ties_even(), -2.0f32); |
| assert_eq((-1.7f32).round_ties_even(), -2.0f32); |
| // f64 |
| assert_eq(2.5f64.round_ties_even(), 2.0f64); |
| assert_eq(1.0f64.round_ties_even(), 1.0f64); |
| assert_eq(1.3f64.round_ties_even(), 1.0f64); |
| assert_eq(1.5f64.round_ties_even(), 2.0f64); |
| assert_eq(1.7f64.round_ties_even(), 2.0f64); |
| assert_eq(0.0f64.round_ties_even(), 0.0f64); |
| assert_eq((-0.0f64).round_ties_even(), -0.0f64); |
| assert_eq((-1.0f64).round_ties_even(), -1.0f64); |
| assert_eq((-1.3f64).round_ties_even(), -1.0f64); |
| assert_eq((-1.5f64).round_ties_even(), -2.0f64); |
| assert_eq((-1.7f64).round_ties_even(), -2.0f64); |
| // f128 |
| assert_eq(2.5f128.round_ties_even(), 2.0f128); |
| assert_eq(1.0f128.round_ties_even(), 1.0f128); |
| assert_eq(1.3f128.round_ties_even(), 1.0f128); |
| assert_eq(1.5f128.round_ties_even(), 2.0f128); |
| assert_eq(1.7f128.round_ties_even(), 2.0f128); |
| assert_eq(0.0f128.round_ties_even(), 0.0f128); |
| assert_eq((-0.0f128).round_ties_even(), -0.0f128); |
| assert_eq((-1.0f128).round_ties_even(), -1.0f128); |
| assert_eq((-1.3f128).round_ties_even(), -1.0f128); |
| assert_eq((-1.5f128).round_ties_even(), -2.0f128); |
| assert_eq((-1.7f128).round_ties_even(), -2.0f128); |
| |
| assert_eq!(3.8f16.floor(), 3.0f16); |
| assert_eq!((-1.1f16).floor(), -2.0f16); |
| assert_eq!(3.8f32.floor(), 3.0f32); |
| assert_eq!((-1.1f32).floor(), -2.0f32); |
| assert_eq!(3.8f64.floor(), 3.0f64); |
| assert_eq!((-1.1f64).floor(), -2.0f64); |
| assert_eq!(3.8f128.floor(), 3.0f128); |
| assert_eq!((-1.1f128).floor(), -2.0f128); |
| |
| assert_eq!(3.8f16.ceil(), 4.0f16); |
| assert_eq!((-2.3f16).ceil(), -2.0f16); |
| assert_eq!(3.8f32.ceil(), 4.0f32); |
| assert_eq!((-2.3f32).ceil(), -2.0f32); |
| assert_eq!(3.8f64.ceil(), 4.0f64); |
| assert_eq!((-2.3f64).ceil(), -2.0f64); |
| assert_eq!(3.8f128.ceil(), 4.0f128); |
| assert_eq!((-2.3f128).ceil(), -2.0f128); |
| |
| assert_eq!(0.1f16.trunc(), 0.0f16); |
| assert_eq!((-0.1f16).trunc(), 0.0f16); |
| assert_eq!(0.1f32.trunc(), 0.0f32); |
| assert_eq!((-0.1f32).trunc(), 0.0f32); |
| assert_eq!(0.1f64.trunc(), 0.0f64); |
| assert_eq!((-0.1f64).trunc(), 0.0f64); |
| assert_eq!(0.1f128.trunc(), 0.0f128); |
| assert_eq!((-0.1f128).trunc(), 0.0f128); |
| |
| assert_eq!(3.3_f16.round(), 3.0); |
| assert_eq!(2.5_f16.round(), 3.0); |
| assert_eq!(3.3_f32.round(), 3.0); |
| assert_eq!(2.5_f32.round(), 3.0); |
| assert_eq!(3.9_f64.round(), 4.0); |
| assert_eq!(2.5_f64.round(), 3.0); |
| assert_eq!(3.9_f128.round(), 4.0); |
| assert_eq!(2.5_f128.round(), 3.0); |
| } |
| |
| fn mul_add() { |
| // FIXME(f16_f128): add when supported |
| |
| assert_eq!(3.0f32.mul_add(2.0f32, 5.0f32), 11.0); |
| assert_eq!(0.0f32.mul_add(-2.0, f32::consts::E), f32::consts::E); |
| assert_eq!(3.0f64.mul_add(2.0, 5.0), 11.0); |
| assert_eq!(0.0f64.mul_add(-2.0f64, f64::consts::E), f64::consts::E); |
| assert_eq!((-3.2f32).mul_add(2.4, f32::NEG_INFINITY), f32::NEG_INFINITY); |
| assert_eq!((-3.2f64).mul_add(2.4, f64::NEG_INFINITY), f64::NEG_INFINITY); |
| |
| let f = f32::mul_add( |
| -0.000000000000000000000000000000000000014728589, |
| 0.0000037105144, |
| 0.000000000000000000000000000000000000000000055, |
| ); |
| assert_eq!(f.to_bits(), f32::to_bits(-0.0)); |
| } |
| |
| pub fn libm() { |
| fn ldexp(a: f64, b: i32) -> f64 { |
| extern "C" { |
| fn ldexp(x: f64, n: i32) -> f64; |
| } |
| unsafe { ldexp(a, b) } |
| } |
| |
| assert_approx_eq!(25f32.powi(-2), 0.0016f32); |
| assert_approx_eq!(23.2f64.powi(2), 538.24f64); |
| |
| assert_approx_eq!(25f32.powf(-2f32), 0.0016f32); |
| assert_approx_eq!(400f64.powf(0.5f64), 20f64); |
| |
| // Some inputs to powf and powi result in fixed outputs |
| // and thus must be exactly equal to that value. |
| // C standard says: |
| // 1^y = 1 for any y, even a NaN. |
| assert_eq!(1f32.powf(10.0), 1.0); |
| assert_eq!(1f64.powf(100.0), 1.0); |
| assert_eq!(1f32.powf(f32::INFINITY), 1.0); |
| assert_eq!(1f64.powf(f64::INFINITY), 1.0); |
| assert_eq!(1f32.powf(f32::NAN), 1.0); |
| assert_eq!(1f64.powf(f64::NAN), 1.0); |
| |
| // f*::NAN is a quiet NAN and should return 1 as well. |
| assert_eq!(f32::NAN.powf(0.0), 1.0); |
| assert_eq!(f64::NAN.powf(0.0), 1.0); |
| |
| assert_eq!(42f32.powf(0.0), 1.0); |
| assert_eq!(42f64.powf(0.0), 1.0); |
| assert_eq!(f32::INFINITY.powf(0.0), 1.0); |
| assert_eq!(f64::INFINITY.powf(0.0), 1.0); |
| assert_eq!(f32::NEG_INFINITY.powi(3), f32::NEG_INFINITY); |
| assert_eq!(f32::NEG_INFINITY.powi(2), f32::INFINITY); |
| assert_eq!(f64::INFINITY.powi(3), f64::INFINITY); |
| assert_eq!(f64::INFINITY.powi(2), f64::INFINITY); |
| |
| // f*::NAN is a quiet NAN and should return 1 as well. |
| assert_eq!(f32::NAN.powi(0), 1.0); |
| assert_eq!(f64::NAN.powi(0), 1.0); |
| |
| assert_eq!(10.0f32.powi(0), 1.0); |
| assert_eq!(10.0f64.powi(0), 1.0); |
| assert_eq!(f32::INFINITY.powi(0), 1.0); |
| assert_eq!(f64::INFINITY.powi(0), 1.0); |
| |
| assert_eq!((-1f32).powf(f32::INFINITY), 1.0); |
| assert_eq!((-1f64).powf(f64::INFINITY), 1.0); |
| assert_eq!((-1f32).powf(f32::NEG_INFINITY), 1.0); |
| assert_eq!((-1f64).powf(f64::NEG_INFINITY), 1.0); |
| |
| assert_eq!(0f32.powi(10), 0.0); |
| assert_eq!(0f64.powi(100), 0.0); |
| assert_eq!(0f32.powi(9), 0.0); |
| assert_eq!(0f64.powi(99), 0.0); |
| |
| assert_biteq((-0f32).powf(10.0), 0.0, "-0^x = +0 where x is positive"); |
| assert_biteq((-0f64).powf(100.0), 0.0, "-0^x = +0 where x is positive"); |
| assert_biteq((-0f32).powf(9.0), -0.0, "-0^x = -0 where x is negative"); |
| assert_biteq((-0f64).powf(99.0), -0.0, "-0^x = -0 where x is negative"); |
| |
| assert_biteq((-0f32).powi(10), 0.0, "-0^x = +0 where x is positive"); |
| assert_biteq((-0f64).powi(100), 0.0, "-0^x = +0 where x is positive"); |
| assert_biteq((-0f32).powi(9), -0.0, "-0^x = -0 where x is negative"); |
| assert_biteq((-0f64).powi(99), -0.0, "-0^x = -0 where x is negative"); |
| |
| assert_approx_eq!(1f32.exp(), f32::consts::E); |
| assert_approx_eq!(1f64.exp(), f64::consts::E); |
| assert_eq!(0f32.exp(), 1.0); |
| assert_eq!(0f64.exp(), 1.0); |
| |
| assert_approx_eq!(1f32.exp_m1(), f32::consts::E - 1.0); |
| assert_approx_eq!(1f64.exp_m1(), f64::consts::E - 1.0); |
| assert_approx_eq!(f32::NEG_INFINITY.exp_m1(), -1.0); |
| assert_approx_eq!(f64::NEG_INFINITY.exp_m1(), -1.0); |
| |
| assert_approx_eq!(10f32.exp2(), 1024f32); |
| assert_approx_eq!(50f64.exp2(), 1125899906842624f64); |
| assert_eq!(0f32.exp2(), 1.0); |
| assert_eq!(0f64.exp2(), 1.0); |
| |
| assert_approx_eq!(f32::consts::E.ln(), 1f32); |
| assert_approx_eq!(f64::consts::E.ln(), 1f64); |
| assert_eq!(1f32.ln(), 0.0); |
| assert_eq!(1f64.ln(), 0.0); |
| |
| assert_approx_eq!(0f32.ln_1p(), 0f32); |
| assert_approx_eq!(0f64.ln_1p(), 0f64); |
| |
| assert_approx_eq!(10f32.log10(), 1f32); |
| assert_approx_eq!(f64::consts::E.log10(), f64::consts::LOG10_E); |
| |
| assert_approx_eq!(8f32.log2(), 3f32); |
| assert_approx_eq!(f64::consts::E.log2(), f64::consts::LOG2_E); |
| |
| #[allow(deprecated)] |
| { |
| assert_approx_eq!(5.0f32.abs_sub(3.0), 2.0); |
| assert_approx_eq!(3.0f64.abs_sub(5.0), 0.0); |
| } |
| |
| assert_approx_eq!(27.0f32.cbrt(), 3.0f32); |
| assert_approx_eq!(27.0f64.cbrt(), 3.0f64); |
| |
| assert_approx_eq!(3.0f32.hypot(4.0f32), 5.0f32); |
| assert_approx_eq!(3.0f64.hypot(4.0f64), 5.0f64); |
| |
| assert_eq!(ldexp(0.65f64, 3i32), 5.2f64); |
| assert_eq!(ldexp(1.42, 0xFFFF), f64::INFINITY); |
| assert_eq!(ldexp(1.42, -0xFFFF), 0f64); |
| assert_eq!(ldexp(42.0, 0), 42.0); |
| |
| // Trigonometric functions. |
| |
| assert_eq!(0f32.sin(), 0f32); |
| assert_eq!(0f64.sin(), 0f64); |
| assert_approx_eq!((f64::consts::PI / 2f64).sin(), 1f64); |
| assert_approx_eq!(f32::consts::FRAC_PI_6.sin(), 0.5); |
| assert_approx_eq!(f64::consts::FRAC_PI_6.sin(), 0.5); |
| // Increase error tolerance to 16ULP because of the extra operation. |
| assert_approx_eq!(f32::consts::FRAC_PI_4.sin().asin(), f32::consts::FRAC_PI_4, 16); |
| assert_approx_eq!(f64::consts::FRAC_PI_4.sin().asin(), f64::consts::FRAC_PI_4, 16); |
| assert_biteq(0.0f32.asin(), 0.0f32, "asin(+0) = +0"); |
| assert_biteq((-0.0f32).asin(), -0.0, "asin(-0) = -0"); |
| assert_biteq(0.0f64.asin(), 0.0, "asin(+0) = +0"); |
| assert_biteq((-0.0f64).asin(), -0.0, "asin(-0) = -0"); |
| |
| assert_approx_eq!(1.0f32.sinh(), 1.1752012f32); |
| assert_approx_eq!(1.0f64.sinh(), 1.1752011936438014f64); |
| assert_approx_eq!(2.0f32.asinh(), 1.443635475178810342493276740273105f32); |
| assert_approx_eq!((-2.0f64).asinh(), -1.443635475178810342493276740273105f64); |
| |
| // Ensure `sin` always returns something that is a valid input for `asin`, and same for |
| // `cos` and `acos`. |
| let halve_pi_f32 = std::f32::consts::FRAC_PI_2; |
| let halve_pi_f64 = std::f64::consts::FRAC_PI_2; |
| let pi_f32 = std::f32::consts::PI; |
| let pi_f64 = std::f64::consts::PI; |
| for _ in 0..64 { |
| // sin() should be clamped to [-1, 1] so asin() can never return NaN |
| assert!(!halve_pi_f32.sin().asin().is_nan()); |
| assert!(!halve_pi_f64.sin().asin().is_nan()); |
| // cos() should be clamped to [-1, 1] so acos() can never return NaN |
| assert!(!pi_f32.cos().acos().is_nan()); |
| assert!(!pi_f64.cos().acos().is_nan()); |
| } |
| |
| assert_eq!(0f32.cos(), 1f32); |
| assert_eq!(0f64.cos(), 1f64); |
| assert_approx_eq!((f64::consts::PI * 2f64).cos(), 1f64); |
| assert_approx_eq!(f32::consts::FRAC_PI_3.cos(), 0.5); |
| assert_approx_eq!(f64::consts::FRAC_PI_3.cos(), 0.5); |
| // Increase error tolerance to 16ULP because of the extra operation. |
| assert_approx_eq!(f32::consts::FRAC_PI_4.cos().acos(), f32::consts::FRAC_PI_4, 16); |
| assert_approx_eq!(f64::consts::FRAC_PI_4.cos().acos(), f64::consts::FRAC_PI_4, 16); |
| assert_biteq(1.0f32.acos(), 0.0, "acos(1) = 0"); |
| assert_biteq(1.0f64.acos(), 0.0, "acos(1) = 0"); |
| |
| assert_approx_eq!(1.0f32.cosh(), 1.5430806f32); |
| assert_approx_eq!(1.0f64.cosh(), 1.5430806348152437f64); |
| assert_eq!(0.0f32.cosh(), 1.0); |
| assert_eq!(0.0f64.cosh(), 1.0); |
| assert_eq!((-0.0f32).cosh(), 1.0); |
| assert_eq!((-0.0f64).cosh(), 1.0); |
| assert_approx_eq!(2.0f32.acosh(), 1.31695789692481670862504634730796844f32); |
| assert_approx_eq!(3.0f64.acosh(), 1.76274717403908605046521864995958461f64); |
| |
| assert_approx_eq!(1.0f32.tan(), 1.557408f32); |
| assert_approx_eq!(1.0f64.tan(), 1.5574077246549023f64); |
| assert_approx_eq!(1.0_f32, 1.0_f32.tan().atan()); |
| assert_approx_eq!(1.0_f64, 1.0_f64.tan().atan()); |
| assert_approx_eq!(1.0f32.atan2(2.0f32), 0.46364761f32); |
| assert_approx_eq!(1.0f32.atan2(2.0f32), 0.46364761f32); |
| // C standard defines a bunch of fixed outputs for atan2 |
| macro_rules! fixed_atan2_cases{ |
| ($float_type:ident) => {{ |
| use std::$float_type::consts::{PI, FRAC_PI_2, FRAC_PI_4}; |
| use $float_type::{INFINITY, NEG_INFINITY}; |
| |
| // atan2(±0,−0) = ±π. |
| assert_eq!($float_type::atan2(0.0, -0.0), PI, "atan2(0,−0) = π"); |
| assert_eq!($float_type::atan2(-0.0, -0.0), -PI, "atan2(-0,−0) = -π"); |
| |
| // atan2(±0, y) = ±π for y < 0. |
| assert_eq!($float_type::atan2(0.0, -1.0), PI, "atan2(0, y) = π for y < 0."); |
| assert_eq!($float_type::atan2(-0.0, -1.0), -PI, "atan2(-0, y) = -Ï€ for y < 0."); |
| |
| // atan2(x, ±0) = −π/2 for x < 0. |
| assert_eq!($float_type::atan2(-1.0, 0.0), -FRAC_PI_2, "atan2(x, 0) = −π/2 for x < 0"); |
| assert_eq!($float_type::atan2(-1.0, -0.0), -FRAC_PI_2, "atan2(x, -0) = −π/2 for x < 0"); |
| |
| // atan2(x, ±0) = π/2 for x > 0. |
| assert_eq!($float_type::atan2(1.0, 0.0), FRAC_PI_2, "atan2(x, 0) = π/2 for x > 0."); |
| assert_eq!($float_type::atan2(1.0, -0.0), FRAC_PI_2, "atan2(x, -0) = π/2 for x > 0."); |
| |
| // atan2(±x,−∞) = ±π for finite x > 0. |
| assert_eq!($float_type::atan2(1.0, NEG_INFINITY), PI, "atan2(x, −∞) = π for finite x > 0"); |
| assert_eq!($float_type::atan2(-1.0, NEG_INFINITY), -PI, "atan2(-x, −∞) = -π for finite x > 0"); |
| |
| // atan2(±∞, y) returns ±π/2 for finite y. |
| assert_eq!($float_type::atan2(INFINITY, 1.0), FRAC_PI_2, "atan2(+∞, y) returns π/2 for finite y"); |
| assert_eq!($float_type::atan2(NEG_INFINITY, 1.0), -FRAC_PI_2, "atan2(-∞, y) returns -π/2 for finite y"); |
| |
| // atan2(±∞, −∞) = ±3π/4 |
| assert_eq!($float_type::atan2(INFINITY, NEG_INFINITY), 3.0 * FRAC_PI_4, "atan2(+∞, −∞) = 3π/4"); |
| assert_eq!($float_type::atan2(NEG_INFINITY, NEG_INFINITY), -3.0 * FRAC_PI_4, "atan2(-∞, −∞) = -3π/4"); |
| |
| // atan2(±∞, +∞) = ±π/4 |
| assert_eq!($float_type::atan2(INFINITY, INFINITY), FRAC_PI_4, "atan2(+∞, +∞) = π/4"); |
| assert_eq!($float_type::atan2(NEG_INFINITY, INFINITY), -FRAC_PI_4, "atan2(-∞, +∞) = -π/4"); |
| }} |
| } |
| fixed_atan2_cases!(f32); |
| fixed_atan2_cases!(f64); |
| |
| assert_approx_eq!( |
| 1.0f32.tanh(), |
| (1.0 - f32::consts::E.powi(-2)) / (1.0 + f32::consts::E.powi(-2)) |
| ); |
| assert_approx_eq!( |
| 1.0f64.tanh(), |
| (1.0 - f64::consts::E.powi(-2)) / (1.0 + f64::consts::E.powi(-2)) |
| ); |
| assert_eq!(f32::INFINITY.tanh(), 1.0); |
| assert_eq!(f32::NEG_INFINITY.tanh(), -1.0); |
| assert_eq!(f64::INFINITY.tanh(), 1.0); |
| assert_eq!(f64::NEG_INFINITY.tanh(), -1.0); |
| |
| assert_approx_eq!(0.5f32.atanh(), 0.54930614433405484569762261846126285f32); |
| assert_approx_eq!(0.5f64.atanh(), 0.54930614433405484569762261846126285f64); |
| |
| assert_approx_eq!(5.0f32.gamma(), 24.0); |
| assert_approx_eq!(5.0f64.gamma(), 24.0); |
| assert_approx_eq!((-0.5f32).gamma(), (-2.0) * f32::consts::PI.sqrt()); |
| assert_approx_eq!((-0.5f64).gamma(), (-2.0) * f64::consts::PI.sqrt()); |
| |
| assert_eq!(2.0f32.ln_gamma(), (0.0, 1)); |
| assert_eq!(2.0f64.ln_gamma(), (0.0, 1)); |
| // Gamma(-0.5) = -2*sqrt(Ï€) |
| let (val, sign) = (-0.5f32).ln_gamma(); |
| assert_approx_eq!(val, (2.0 * f32::consts::PI.sqrt()).ln()); |
| assert_eq!(sign, -1); |
| let (val, sign) = (-0.5f64).ln_gamma(); |
| assert_approx_eq!(val, (2.0 * f64::consts::PI.sqrt()).ln()); |
| assert_eq!(sign, -1); |
| |
| assert_approx_eq!(1.0f32.erf(), 0.84270079294971486934122063508260926f32); |
| assert_approx_eq!(1.0f64.erf(), 0.84270079294971486934122063508260926f64); |
| assert_eq!(f32::INFINITY.erf(), 1.0); |
| assert_eq!(f64::INFINITY.erf(), 1.0); |
| assert_approx_eq!(1.0f32.erfc(), 0.15729920705028513065877936491739074f32); |
| assert_approx_eq!(1.0f64.erfc(), 0.15729920705028513065877936491739074f64); |
| assert_eq!(f32::NEG_INFINITY.erfc(), 2.0); |
| assert_eq!(f64::NEG_INFINITY.erfc(), 2.0); |
| assert_eq!(f32::INFINITY.erfc(), 0.0); |
| assert_eq!(f64::INFINITY.erfc(), 0.0); |
| } |
| |
| fn test_fast() { |
| use std::intrinsics::{fadd_fast, fdiv_fast, fmul_fast, frem_fast, fsub_fast}; |
| |
| #[inline(never)] |
| pub fn test_operations_f16(a: f16, b: f16) { |
| // make sure they all map to the correct operation |
| unsafe { |
| assert_approx_eq!(fadd_fast(a, b), a + b); |
| assert_approx_eq!(fsub_fast(a, b), a - b); |
| assert_approx_eq!(fmul_fast(a, b), a * b); |
| assert_approx_eq!(fdiv_fast(a, b), a / b); |
| assert_approx_eq!(frem_fast(a, b), a % b); |
| } |
| } |
| |
| #[inline(never)] |
| pub fn test_operations_f32(a: f32, b: f32) { |
| // make sure they all map to the correct operation |
| unsafe { |
| assert_approx_eq!(fadd_fast(a, b), a + b); |
| assert_approx_eq!(fsub_fast(a, b), a - b); |
| assert_approx_eq!(fmul_fast(a, b), a * b); |
| assert_approx_eq!(fdiv_fast(a, b), a / b); |
| assert_approx_eq!(frem_fast(a, b), a % b); |
| } |
| } |
| |
| #[inline(never)] |
| pub fn test_operations_f64(a: f64, b: f64) { |
| // make sure they all map to the correct operation |
| unsafe { |
| assert_approx_eq!(fadd_fast(a, b), a + b); |
| assert_approx_eq!(fsub_fast(a, b), a - b); |
| assert_approx_eq!(fmul_fast(a, b), a * b); |
| assert_approx_eq!(fdiv_fast(a, b), a / b); |
| assert_approx_eq!(frem_fast(a, b), a % b); |
| } |
| } |
| |
| #[inline(never)] |
| pub fn test_operations_f128(a: f128, b: f128) { |
| // make sure they all map to the correct operation |
| unsafe { |
| assert_approx_eq!(fadd_fast(a, b), a + b); |
| assert_approx_eq!(fsub_fast(a, b), a - b); |
| assert_approx_eq!(fmul_fast(a, b), a * b); |
| assert_approx_eq!(fdiv_fast(a, b), a / b); |
| assert_approx_eq!(frem_fast(a, b), a % b); |
| } |
| } |
| |
| test_operations_f16(11., 2.); |
| test_operations_f16(10., 15.); |
| test_operations_f32(11., 2.); |
| test_operations_f32(10., 15.); |
| test_operations_f64(1., 2.); |
| test_operations_f64(10., 5.); |
| test_operations_f128(1., 2.); |
| test_operations_f128(10., 5.); |
| } |
| |
| fn test_algebraic() { |
| use std::intrinsics::{ |
| fadd_algebraic, fdiv_algebraic, fmul_algebraic, frem_algebraic, fsub_algebraic, |
| }; |
| |
| #[inline(never)] |
| pub fn test_operations_f16(a: f16, b: f16) { |
| // make sure they all map to the correct operation |
| assert_approx_eq!(fadd_algebraic(a, b), a + b); |
| assert_approx_eq!(fsub_algebraic(a, b), a - b); |
| assert_approx_eq!(fmul_algebraic(a, b), a * b); |
| assert_approx_eq!(fdiv_algebraic(a, b), a / b); |
| assert_approx_eq!(frem_algebraic(a, b), a % b); |
| } |
| |
| #[inline(never)] |
| pub fn test_operations_f32(a: f32, b: f32) { |
| // make sure they all map to the correct operation |
| assert_approx_eq!(fadd_algebraic(a, b), a + b); |
| assert_approx_eq!(fsub_algebraic(a, b), a - b); |
| assert_approx_eq!(fmul_algebraic(a, b), a * b); |
| assert_approx_eq!(fdiv_algebraic(a, b), a / b); |
| assert_approx_eq!(frem_algebraic(a, b), a % b); |
| } |
| |
| #[inline(never)] |
| pub fn test_operations_f64(a: f64, b: f64) { |
| // make sure they all map to the correct operation |
| assert_approx_eq!(fadd_algebraic(a, b), a + b); |
| assert_approx_eq!(fsub_algebraic(a, b), a - b); |
| assert_approx_eq!(fmul_algebraic(a, b), a * b); |
| assert_approx_eq!(fdiv_algebraic(a, b), a / b); |
| assert_approx_eq!(frem_algebraic(a, b), a % b); |
| } |
| |
| #[inline(never)] |
| pub fn test_operations_f128(a: f128, b: f128) { |
| // make sure they all map to the correct operation |
| assert_approx_eq!(fadd_algebraic(a, b), a + b); |
| assert_approx_eq!(fsub_algebraic(a, b), a - b); |
| assert_approx_eq!(fmul_algebraic(a, b), a * b); |
| assert_approx_eq!(fdiv_algebraic(a, b), a / b); |
| assert_approx_eq!(frem_algebraic(a, b), a % b); |
| } |
| |
| test_operations_f16(11., 2.); |
| test_operations_f16(10., 15.); |
| test_operations_f32(11., 2.); |
| test_operations_f32(10., 15.); |
| test_operations_f64(1., 2.); |
| test_operations_f64(10., 5.); |
| test_operations_f128(1., 2.); |
| test_operations_f128(10., 5.); |
| } |
| |
| fn test_fmuladd() { |
| use std::intrinsics::{fmuladdf32, fmuladdf64}; |
| |
| // FIXME(f16_f128): add when supported |
| |
| #[inline(never)] |
| pub fn test_operations_f32(a: f32, b: f32, c: f32) { |
| assert_approx_eq!(fmuladdf32(a, b, c), a * b + c); |
| } |
| |
| #[inline(never)] |
| pub fn test_operations_f64(a: f64, b: f64, c: f64) { |
| assert_approx_eq!(fmuladdf64(a, b, c), a * b + c); |
| } |
| |
| test_operations_f32(0.1, 0.2, 0.3); |
| test_operations_f64(1.1, 1.2, 1.3); |
| } |
| |
| /// `min` and `max` on equal arguments are non-deterministic. |
| fn test_min_max_nondet() { |
| check_nondet(|| f16::min(0.0, -0.0).is_sign_positive()); |
| check_nondet(|| f16::max(0.0, -0.0).is_sign_positive()); |
| check_nondet(|| f32::min(0.0, -0.0).is_sign_positive()); |
| check_nondet(|| f32::max(0.0, -0.0).is_sign_positive()); |
| check_nondet(|| f64::min(0.0, -0.0).is_sign_positive()); |
| check_nondet(|| f64::max(0.0, -0.0).is_sign_positive()); |
| check_nondet(|| f128::min(0.0, -0.0).is_sign_positive()); |
| check_nondet(|| f128::max(0.0, -0.0).is_sign_positive()); |
| } |
| |
| fn test_non_determinism() { |
| use std::intrinsics::{ |
| fadd_algebraic, fadd_fast, fdiv_algebraic, fdiv_fast, fmul_algebraic, fmul_fast, |
| frem_algebraic, frem_fast, fsub_algebraic, fsub_fast, |
| }; |
| use std::{f32, f64}; |
| |
| macro_rules! test_operations_f { |
| ($a:expr, $b:expr) => { |
| check_nondet(|| fadd_algebraic($a, $b)); |
| check_nondet(|| fsub_algebraic($a, $b)); |
| check_nondet(|| fmul_algebraic($a, $b)); |
| check_nondet(|| fdiv_algebraic($a, $b)); |
| check_nondet(|| frem_algebraic($a, $b)); |
| |
| unsafe { |
| check_nondet(|| fadd_fast($a, $b)); |
| check_nondet(|| fsub_fast($a, $b)); |
| check_nondet(|| fmul_fast($a, $b)); |
| check_nondet(|| fdiv_fast($a, $b)); |
| check_nondet(|| frem_fast($a, $b)); |
| } |
| }; |
| } |
| |
| pub fn test_operations_f16(a: f16, b: f16) { |
| test_operations_f!(a, b); |
| } |
| pub fn test_operations_f32(a: f32, b: f32) { |
| test_operations_f!(a, b); |
| check_nondet(|| a.powf(b)); |
| check_nondet(|| a.powi(2)); |
| check_nondet(|| a.log(b)); |
| check_nondet(|| a.exp()); |
| check_nondet(|| 10f32.exp2()); |
| check_nondet(|| f32::consts::E.ln()); |
| check_nondet(|| 10f32.log10()); |
| check_nondet(|| 8f32.log2()); |
| check_nondet(|| 1f32.ln_1p()); |
| check_nondet(|| 27.0f32.cbrt()); |
| check_nondet(|| 3.0f32.hypot(4.0f32)); |
| check_nondet(|| 1f32.sin()); |
| check_nondet(|| 1f32.cos()); |
| // On i686-pc-windows-msvc , these functions are implemented by calling the `f64` version, |
| // which means the little rounding errors Miri introduces are discarded by the cast down to |
| // `f32`. Just skip the test for them. |
| if !cfg!(all(target_os = "windows", target_env = "msvc", target_arch = "x86")) { |
| check_nondet(|| 1.0f32.tan()); |
| check_nondet(|| 1.0f32.asin()); |
| check_nondet(|| 5.0f32.acos()); |
| check_nondet(|| 1.0f32.atan()); |
| check_nondet(|| 1.0f32.atan2(2.0f32)); |
| check_nondet(|| 1.0f32.sinh()); |
| check_nondet(|| 1.0f32.cosh()); |
| check_nondet(|| 1.0f32.tanh()); |
| } |
| check_nondet(|| 1.0f32.asinh()); |
| check_nondet(|| 2.0f32.acosh()); |
| check_nondet(|| 0.5f32.atanh()); |
| check_nondet(|| 5.0f32.gamma()); |
| check_nondet(|| 5.0f32.ln_gamma()); |
| check_nondet(|| 5.0f32.erf()); |
| check_nondet(|| 5.0f32.erfc()); |
| } |
| pub fn test_operations_f64(a: f64, b: f64) { |
| test_operations_f!(a, b); |
| check_nondet(|| a.powf(b)); |
| check_nondet(|| a.powi(2)); |
| check_nondet(|| a.log(b)); |
| check_nondet(|| a.exp()); |
| check_nondet(|| 50f64.exp2()); |
| check_nondet(|| 3f64.ln()); |
| check_nondet(|| f64::consts::E.log10()); |
| check_nondet(|| f64::consts::E.log2()); |
| check_nondet(|| 1f64.ln_1p()); |
| check_nondet(|| 27.0f64.cbrt()); |
| check_nondet(|| 3.0f64.hypot(4.0f64)); |
| check_nondet(|| 1f64.sin()); |
| check_nondet(|| 1f64.cos()); |
| check_nondet(|| 1.0f64.tan()); |
| check_nondet(|| 1.0f64.asin()); |
| check_nondet(|| 5.0f64.acos()); |
| check_nondet(|| 1.0f64.atan()); |
| check_nondet(|| 1.0f64.atan2(2.0f64)); |
| check_nondet(|| 1.0f64.sinh()); |
| check_nondet(|| 1.0f64.cosh()); |
| check_nondet(|| 1.0f64.tanh()); |
| check_nondet(|| 1.0f64.asinh()); |
| check_nondet(|| 3.0f64.acosh()); |
| check_nondet(|| 0.5f64.atanh()); |
| check_nondet(|| 5.0f64.gamma()); |
| check_nondet(|| 5.0f64.ln_gamma()); |
| check_nondet(|| 5.0f64.erf()); |
| check_nondet(|| 5.0f64.erfc()); |
| } |
| pub fn test_operations_f128(a: f128, b: f128) { |
| test_operations_f!(a, b); |
| } |
| |
| test_operations_f16(5., 7.); |
| test_operations_f32(12., 5.); |
| test_operations_f64(19., 11.); |
| test_operations_f128(25., 18.); |
| |
| // SNaN^0 = (1 | NaN) |
| check_nondet(|| f32::powf(SNAN_F32, 0.0).is_nan()); |
| check_nondet(|| f64::powf(SNAN_F64, 0.0).is_nan()); |
| |
| // 1^SNaN = (1 | NaN) |
| check_nondet(|| f32::powf(1.0, SNAN_F32).is_nan()); |
| check_nondet(|| f64::powf(1.0, SNAN_F64).is_nan()); |
| |
| // same as powf (keep it consistent): |
| // x^SNaN = (1 | NaN) |
| check_nondet(|| f32::powi(SNAN_F32, 0).is_nan()); |
| check_nondet(|| f64::powi(SNAN_F64, 0).is_nan()); |
| } |
