use core::f64; use core::f64::consts; use super::{assert_approx_eq, assert_biteq}; /// Smallest number const TINY_BITS: u64 = 0x1; /// Next smallest number const TINY_UP_BITS: u64 = 0x2; /// Exponent = 0b11...10, Sifnificand 0b1111..10. Min val > 0 const MAX_DOWN_BITS: u64 = 0x7fef_ffff_ffff_fffe; /// Zeroed exponent, full significant const LARGEST_SUBNORMAL_BITS: u64 = 0x000f_ffff_ffff_ffff; /// Exponent = 0b1, zeroed significand const SMALLEST_NORMAL_BITS: u64 = 0x0010_0000_0000_0000; /// First pattern over the mantissa const NAN_MASK1: u64 = 0x000a_aaaa_aaaa_aaaa; /// Second pattern over the mantissa const NAN_MASK2: u64 = 0x0005_5555_5555_5555; #[test] fn test_abs() { assert_biteq!(f64::INFINITY.abs(), f64::INFINITY); assert_biteq!(1f64.abs(), 1f64); assert_biteq!(0f64.abs(), 0f64); assert_biteq!((-0f64).abs(), 0f64); assert_biteq!((-1f64).abs(), 1f64); assert_biteq!(f64::NEG_INFINITY.abs(), f64::INFINITY); assert_biteq!((1f64 / f64::NEG_INFINITY).abs(), 0f64); assert!(f64::NAN.abs().is_nan()); } #[test] fn test_signum() { assert_biteq!(f64::INFINITY.signum(), 1f64); assert_biteq!(1f64.signum(), 1f64); assert_biteq!(0f64.signum(), 1f64); assert_biteq!((-0f64).signum(), -1f64); assert_biteq!((-1f64).signum(), -1f64); assert_biteq!(f64::NEG_INFINITY.signum(), -1f64); assert_biteq!((1f64 / f64::NEG_INFINITY).signum(), -1f64); assert!(f64::NAN.signum().is_nan()); } #[test] fn test_is_sign_positive() { assert!(f64::INFINITY.is_sign_positive()); assert!(1f64.is_sign_positive()); assert!(0f64.is_sign_positive()); assert!(!(-0f64).is_sign_positive()); assert!(!(-1f64).is_sign_positive()); assert!(!f64::NEG_INFINITY.is_sign_positive()); assert!(!(1f64 / f64::NEG_INFINITY).is_sign_positive()); assert!(f64::NAN.is_sign_positive()); assert!(!(-f64::NAN).is_sign_positive()); } #[test] fn test_is_sign_negative() { assert!(!f64::INFINITY.is_sign_negative()); assert!(!1f64.is_sign_negative()); assert!(!0f64.is_sign_negative()); assert!((-0f64).is_sign_negative()); assert!((-1f64).is_sign_negative()); assert!(f64::NEG_INFINITY.is_sign_negative()); assert!((1f64 / f64::NEG_INFINITY).is_sign_negative()); assert!(!f64::NAN.is_sign_negative()); assert!((-f64::NAN).is_sign_negative()); } #[test] fn test_next_up() { let tiny = f64::from_bits(TINY_BITS); let tiny_up = f64::from_bits(TINY_UP_BITS); let max_down = f64::from_bits(MAX_DOWN_BITS); let largest_subnormal = f64::from_bits(LARGEST_SUBNORMAL_BITS); let smallest_normal = f64::from_bits(SMALLEST_NORMAL_BITS); assert_biteq!(f64::NEG_INFINITY.next_up(), f64::MIN); assert_biteq!(f64::MIN.next_up(), -max_down); assert_biteq!((-1.0 - f64::EPSILON).next_up(), -1.0f64); assert_biteq!((-smallest_normal).next_up(), -largest_subnormal); assert_biteq!((-tiny_up).next_up(), -tiny); assert_biteq!((-tiny).next_up(), -0.0f64); assert_biteq!((-0.0f64).next_up(), tiny); assert_biteq!(0.0f64.next_up(), tiny); assert_biteq!(tiny.next_up(), tiny_up); assert_biteq!(largest_subnormal.next_up(), smallest_normal); assert_biteq!(1.0f64.next_up(), 1.0 + f64::EPSILON); assert_biteq!(f64::MAX.next_up(), f64::INFINITY); assert_biteq!(f64::INFINITY.next_up(), f64::INFINITY); let nan0 = f64::NAN; let nan1 = f64::from_bits(f64::NAN.to_bits() ^ NAN_MASK1); let nan2 = f64::from_bits(f64::NAN.to_bits() ^ NAN_MASK2); assert_biteq!(nan0.next_up(), nan0); assert_biteq!(nan1.next_up(), nan1); assert_biteq!(nan2.next_up(), nan2); } #[test] fn test_next_down() { let tiny = f64::from_bits(TINY_BITS); let tiny_up = f64::from_bits(TINY_UP_BITS); let max_down = f64::from_bits(MAX_DOWN_BITS); let largest_subnormal = f64::from_bits(LARGEST_SUBNORMAL_BITS); let smallest_normal = f64::from_bits(SMALLEST_NORMAL_BITS); assert_biteq!(f64::NEG_INFINITY.next_down(), f64::NEG_INFINITY); assert_biteq!(f64::MIN.next_down(), f64::NEG_INFINITY); assert_biteq!((-max_down).next_down(), f64::MIN); assert_biteq!((-1.0f64).next_down(), -1.0 - f64::EPSILON); assert_biteq!((-largest_subnormal).next_down(), -smallest_normal); assert_biteq!((-tiny).next_down(), -tiny_up); assert_biteq!((-0.0f64).next_down(), -tiny); assert_biteq!((0.0f64).next_down(), -tiny); assert_biteq!(tiny.next_down(), 0.0f64); assert_biteq!(tiny_up.next_down(), tiny); assert_biteq!(smallest_normal.next_down(), largest_subnormal); assert_biteq!((1.0 + f64::EPSILON).next_down(), 1.0f64); assert_biteq!(f64::MAX.next_down(), max_down); assert_biteq!(f64::INFINITY.next_down(), f64::MAX); let nan0 = f64::NAN; let nan1 = f64::from_bits(f64::NAN.to_bits() ^ NAN_MASK1); let nan2 = f64::from_bits(f64::NAN.to_bits() ^ NAN_MASK2); assert_biteq!(nan0.next_down(), nan0); assert_biteq!(nan1.next_down(), nan1); assert_biteq!(nan2.next_down(), nan2); } // FIXME(#140515): mingw has an incorrect fma https://sourceforge.net/p/mingw-w64/bugs/848/ #[cfg_attr(all(target_os = "windows", target_env = "gnu", not(target_abi = "llvm")), ignore)] #[test] fn test_mul_add() { let nan: f64 = f64::NAN; let inf: f64 = f64::INFINITY; let neg_inf: f64 = f64::NEG_INFINITY; assert_biteq!(12.3f64.mul_add(4.5, 6.7), 62.050000000000004); assert_biteq!((-12.3f64).mul_add(-4.5, -6.7), 48.650000000000006); assert_biteq!(0.0f64.mul_add(8.9, 1.2), 1.2); assert_biteq!(3.4f64.mul_add(-0.0, 5.6), 5.6); assert!(nan.mul_add(7.8, 9.0).is_nan()); assert_biteq!(inf.mul_add(7.8, 9.0), inf); assert_biteq!(neg_inf.mul_add(7.8, 9.0), neg_inf); assert_biteq!(8.9f64.mul_add(inf, 3.2), inf); assert_biteq!((-3.2f64).mul_add(2.4, neg_inf), neg_inf); } #[test] fn test_recip() { let nan: f64 = f64::NAN; let inf: f64 = f64::INFINITY; let neg_inf: f64 = f64::NEG_INFINITY; assert_biteq!(1.0f64.recip(), 1.0); assert_biteq!(2.0f64.recip(), 0.5); assert_biteq!((-0.4f64).recip(), -2.5); assert_biteq!(0.0f64.recip(), inf); assert!(nan.recip().is_nan()); assert_biteq!(inf.recip(), 0.0); assert_biteq!(neg_inf.recip(), -0.0); } #[test] fn test_powi() { let nan: f64 = f64::NAN; let inf: f64 = f64::INFINITY; let neg_inf: f64 = f64::NEG_INFINITY; assert_approx_eq!(1.0f64.powi(1), 1.0); assert_approx_eq!((-3.1f64).powi(2), 9.61); assert_approx_eq!(5.9f64.powi(-2), 0.028727); assert_biteq!(8.3f64.powi(0), 1.0); assert!(nan.powi(2).is_nan()); assert_biteq!(inf.powi(3), inf); assert_biteq!(neg_inf.powi(2), inf); } #[test] fn test_sqrt_domain() { assert!(f64::NAN.sqrt().is_nan()); assert!(f64::NEG_INFINITY.sqrt().is_nan()); assert!((-1.0f64).sqrt().is_nan()); assert_biteq!((-0.0f64).sqrt(), -0.0); assert_biteq!(0.0f64.sqrt(), 0.0); assert_biteq!(1.0f64.sqrt(), 1.0); assert_biteq!(f64::INFINITY.sqrt(), f64::INFINITY); } #[test] fn test_to_degrees() { let pi: f64 = consts::PI; let nan: f64 = f64::NAN; let inf: f64 = f64::INFINITY; let neg_inf: f64 = f64::NEG_INFINITY; assert_biteq!(0.0f64.to_degrees(), 0.0); assert_approx_eq!((-5.8f64).to_degrees(), -332.315521); assert_biteq!(pi.to_degrees(), 180.0); assert!(nan.to_degrees().is_nan()); assert_biteq!(inf.to_degrees(), inf); assert_biteq!(neg_inf.to_degrees(), neg_inf); } #[test] fn test_to_radians() { let pi: f64 = consts::PI; let nan: f64 = f64::NAN; let inf: f64 = f64::INFINITY; let neg_inf: f64 = f64::NEG_INFINITY; assert_biteq!(0.0f64.to_radians(), 0.0); assert_approx_eq!(154.6f64.to_radians(), 2.698279); assert_approx_eq!((-332.31f64).to_radians(), -5.799903); assert_biteq!(180.0f64.to_radians(), pi); assert!(nan.to_radians().is_nan()); assert_biteq!(inf.to_radians(), inf); assert_biteq!(neg_inf.to_radians(), neg_inf); } #[test] fn test_float_bits_conv() { assert_eq!((1f64).to_bits(), 0x3ff0000000000000); assert_eq!((12.5f64).to_bits(), 0x4029000000000000); assert_eq!((1337f64).to_bits(), 0x4094e40000000000); assert_eq!((-14.25f64).to_bits(), 0xc02c800000000000); assert_biteq!(f64::from_bits(0x3ff0000000000000), 1.0); assert_biteq!(f64::from_bits(0x4029000000000000), 12.5); assert_biteq!(f64::from_bits(0x4094e40000000000), 1337.0); assert_biteq!(f64::from_bits(0xc02c800000000000), -14.25); // Check that NaNs roundtrip their bits regardless of signaling-ness let masked_nan1 = f64::NAN.to_bits() ^ NAN_MASK1; let masked_nan2 = f64::NAN.to_bits() ^ NAN_MASK2; assert!(f64::from_bits(masked_nan1).is_nan()); assert!(f64::from_bits(masked_nan2).is_nan()); assert_eq!(f64::from_bits(masked_nan1).to_bits(), masked_nan1); assert_eq!(f64::from_bits(masked_nan2).to_bits(), masked_nan2); } #[test] #[should_panic] fn test_clamp_min_greater_than_max() { let _ = 1.0f64.clamp(3.0, 1.0); } #[test] #[should_panic] fn test_clamp_min_is_nan() { let _ = 1.0f64.clamp(f64::NAN, 1.0); } #[test] #[should_panic] fn test_clamp_max_is_nan() { let _ = 1.0f64.clamp(3.0, f64::NAN); } #[test] fn test_total_cmp() { use core::cmp::Ordering; fn quiet_bit_mask() -> u64 { 1 << (f64::MANTISSA_DIGITS - 2) } fn min_subnorm() -> f64 { f64::MIN_POSITIVE / f64::powf(2.0, f64::MANTISSA_DIGITS as f64 - 1.0) } fn max_subnorm() -> f64 { f64::MIN_POSITIVE - min_subnorm() } fn q_nan() -> f64 { f64::from_bits(f64::NAN.to_bits() | quiet_bit_mask()) } fn s_nan() -> f64 { f64::from_bits((f64::NAN.to_bits() & !quiet_bit_mask()) + 42) } assert_eq!(Ordering::Equal, (-q_nan()).total_cmp(&-q_nan())); assert_eq!(Ordering::Equal, (-s_nan()).total_cmp(&-s_nan())); assert_eq!(Ordering::Equal, (-f64::INFINITY).total_cmp(&-f64::INFINITY)); assert_eq!(Ordering::Equal, (-f64::MAX).total_cmp(&-f64::MAX)); assert_eq!(Ordering::Equal, (-2.5_f64).total_cmp(&-2.5)); assert_eq!(Ordering::Equal, (-1.0_f64).total_cmp(&-1.0)); assert_eq!(Ordering::Equal, (-1.5_f64).total_cmp(&-1.5)); assert_eq!(Ordering::Equal, (-0.5_f64).total_cmp(&-0.5)); assert_eq!(Ordering::Equal, (-f64::MIN_POSITIVE).total_cmp(&-f64::MIN_POSITIVE)); assert_eq!(Ordering::Equal, (-max_subnorm()).total_cmp(&-max_subnorm())); assert_eq!(Ordering::Equal, (-min_subnorm()).total_cmp(&-min_subnorm())); assert_eq!(Ordering::Equal, (-0.0_f64).total_cmp(&-0.0)); assert_eq!(Ordering::Equal, 0.0_f64.total_cmp(&0.0)); assert_eq!(Ordering::Equal, min_subnorm().total_cmp(&min_subnorm())); assert_eq!(Ordering::Equal, max_subnorm().total_cmp(&max_subnorm())); assert_eq!(Ordering::Equal, f64::MIN_POSITIVE.total_cmp(&f64::MIN_POSITIVE)); assert_eq!(Ordering::Equal, 0.5_f64.total_cmp(&0.5)); assert_eq!(Ordering::Equal, 1.0_f64.total_cmp(&1.0)); assert_eq!(Ordering::Equal, 1.5_f64.total_cmp(&1.5)); assert_eq!(Ordering::Equal, 2.5_f64.total_cmp(&2.5)); assert_eq!(Ordering::Equal, f64::MAX.total_cmp(&f64::MAX)); assert_eq!(Ordering::Equal, f64::INFINITY.total_cmp(&f64::INFINITY)); assert_eq!(Ordering::Equal, s_nan().total_cmp(&s_nan())); assert_eq!(Ordering::Equal, q_nan().total_cmp(&q_nan())); assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&-s_nan())); assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&-f64::INFINITY)); assert_eq!(Ordering::Less, (-f64::INFINITY).total_cmp(&-f64::MAX)); assert_eq!(Ordering::Less, (-f64::MAX).total_cmp(&-2.5)); assert_eq!(Ordering::Less, (-2.5_f64).total_cmp(&-1.5)); assert_eq!(Ordering::Less, (-1.5_f64).total_cmp(&-1.0)); assert_eq!(Ordering::Less, (-1.0_f64).total_cmp(&-0.5)); assert_eq!(Ordering::Less, (-0.5_f64).total_cmp(&-f64::MIN_POSITIVE)); assert_eq!(Ordering::Less, (-f64::MIN_POSITIVE).total_cmp(&-max_subnorm())); assert_eq!(Ordering::Less, (-max_subnorm()).total_cmp(&-min_subnorm())); assert_eq!(Ordering::Less, (-min_subnorm()).total_cmp(&-0.0)); assert_eq!(Ordering::Less, (-0.0_f64).total_cmp(&0.0)); assert_eq!(Ordering::Less, 0.0_f64.total_cmp(&min_subnorm())); assert_eq!(Ordering::Less, min_subnorm().total_cmp(&max_subnorm())); assert_eq!(Ordering::Less, max_subnorm().total_cmp(&f64::MIN_POSITIVE)); assert_eq!(Ordering::Less, f64::MIN_POSITIVE.total_cmp(&0.5)); assert_eq!(Ordering::Less, 0.5_f64.total_cmp(&1.0)); assert_eq!(Ordering::Less, 1.0_f64.total_cmp(&1.5)); assert_eq!(Ordering::Less, 1.5_f64.total_cmp(&2.5)); assert_eq!(Ordering::Less, 2.5_f64.total_cmp(&f64::MAX)); assert_eq!(Ordering::Less, f64::MAX.total_cmp(&f64::INFINITY)); assert_eq!(Ordering::Less, f64::INFINITY.total_cmp(&s_nan())); assert_eq!(Ordering::Less, s_nan().total_cmp(&q_nan())); assert_eq!(Ordering::Greater, (-s_nan()).total_cmp(&-q_nan())); assert_eq!(Ordering::Greater, (-f64::INFINITY).total_cmp(&-s_nan())); assert_eq!(Ordering::Greater, (-f64::MAX).total_cmp(&-f64::INFINITY)); assert_eq!(Ordering::Greater, (-2.5_f64).total_cmp(&-f64::MAX)); assert_eq!(Ordering::Greater, (-1.5_f64).total_cmp(&-2.5)); assert_eq!(Ordering::Greater, (-1.0_f64).total_cmp(&-1.5)); assert_eq!(Ordering::Greater, (-0.5_f64).total_cmp(&-1.0)); assert_eq!(Ordering::Greater, (-f64::MIN_POSITIVE).total_cmp(&-0.5)); assert_eq!(Ordering::Greater, (-max_subnorm()).total_cmp(&-f64::MIN_POSITIVE)); assert_eq!(Ordering::Greater, (-min_subnorm()).total_cmp(&-max_subnorm())); assert_eq!(Ordering::Greater, (-0.0_f64).total_cmp(&-min_subnorm())); assert_eq!(Ordering::Greater, 0.0_f64.total_cmp(&-0.0)); assert_eq!(Ordering::Greater, min_subnorm().total_cmp(&0.0)); assert_eq!(Ordering::Greater, max_subnorm().total_cmp(&min_subnorm())); assert_eq!(Ordering::Greater, f64::MIN_POSITIVE.total_cmp(&max_subnorm())); assert_eq!(Ordering::Greater, 0.5_f64.total_cmp(&f64::MIN_POSITIVE)); assert_eq!(Ordering::Greater, 1.0_f64.total_cmp(&0.5)); assert_eq!(Ordering::Greater, 1.5_f64.total_cmp(&1.0)); assert_eq!(Ordering::Greater, 2.5_f64.total_cmp(&1.5)); assert_eq!(Ordering::Greater, f64::MAX.total_cmp(&2.5)); assert_eq!(Ordering::Greater, f64::INFINITY.total_cmp(&f64::MAX)); assert_eq!(Ordering::Greater, s_nan().total_cmp(&f64::INFINITY)); assert_eq!(Ordering::Greater, q_nan().total_cmp(&s_nan())); assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&-s_nan())); assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&-f64::INFINITY)); assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&-f64::MAX)); assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&-2.5)); assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&-1.5)); assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&-1.0)); assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&-0.5)); assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&-f64::MIN_POSITIVE)); assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&-max_subnorm())); assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&-min_subnorm())); assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&-0.0)); assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&0.0)); assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&min_subnorm())); assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&max_subnorm())); assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&f64::MIN_POSITIVE)); assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&0.5)); assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&1.0)); assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&1.5)); assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&2.5)); assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&f64::MAX)); assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&f64::INFINITY)); assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&s_nan())); assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&-f64::INFINITY)); assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&-f64::MAX)); assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&-2.5)); assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&-1.5)); assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&-1.0)); assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&-0.5)); assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&-f64::MIN_POSITIVE)); assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&-max_subnorm())); assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&-min_subnorm())); assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&-0.0)); assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&0.0)); assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&min_subnorm())); assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&max_subnorm())); assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&f64::MIN_POSITIVE)); assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&0.5)); assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&1.0)); assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&1.5)); assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&2.5)); assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&f64::MAX)); assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&f64::INFINITY)); assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&s_nan())); } #[test] fn test_algebraic() { let a: f64 = 123.0; let b: f64 = 456.0; // Check that individual operations match their primitive counterparts. // // This is a check of current implementations and does NOT imply any form of // guarantee about future behavior. The compiler reserves the right to make // these operations inexact matches in the future. let eps = if cfg!(miri) { 1e-6 } else { 0.0 }; assert_approx_eq!(a.algebraic_add(b), a + b, eps); assert_approx_eq!(a.algebraic_sub(b), a - b, eps); assert_approx_eq!(a.algebraic_mul(b), a * b, eps); assert_approx_eq!(a.algebraic_div(b), a / b, eps); assert_approx_eq!(a.algebraic_rem(b), a % b, eps); }