#[macro_use] extern crate rustc_apfloat; use core::cmp::Ordering; use rustc_apfloat::ieee::{BFloat, Double, Float8E4M3FN, Float8E5M2, Half, Quad, Single, X87DoubleExtended}; use rustc_apfloat::{Category, ExpInt, IEK_INF, IEK_NAN, IEK_ZERO}; use rustc_apfloat::{Float, FloatConvert, Round, Status}; // FIXME(eddyb) maybe include this in `rustc_apfloat` itself? macro_rules! define_for_each_float_type { ($($ty:ty),+ $(,)?) => { macro_rules! for_each_float_type { // FIXME(eddyb) use generic closures if they're ever added to Rust. (for<$ty_var:ident: Float> $e:expr) => {{ $({ type $ty_var = $ty; $e; })+ }} } } } define_for_each_float_type! { Half, Single, Double, Quad, BFloat, Float8E5M2, Float8E4M3FN, X87DoubleExtended, // NOTE(eddyb) tests for this are usually in `ppc.rs` but this works too. rustc_apfloat::ppc::DoubleDouble, } trait SingleExt { fn from_f32(input: f32) -> Self; fn to_f32(self) -> f32; } impl SingleExt for Single { fn from_f32(input: f32) -> Self { Self::from_bits(input.to_bits() as u128) } fn to_f32(self) -> f32 { f32::from_bits(self.to_bits() as u32) } } trait DoubleExt { fn from_f64(input: f64) -> Self; fn to_f64(self) -> f64; } impl DoubleExt for Double { fn from_f64(input: f64) -> Self { Self::from_bits(input.to_bits() as u128) } fn to_f64(self) -> f64 { f64::from_bits(self.to_bits() as u64) } } // NOTE(eddyb) these match the C++ `convertToFloat`/`convertToDouble` methods, // after their generalization to allow an optional lossless conversion to their // expected semantics (from e.g. `IEEEhalf`/`BFloat`, for `convertToSingle`). // FIXME(eddyb) should the methods have e.g. `_lossless_via_convert` in their names? fn assert_lossless_conversion, T: Float>(src: S) -> T { let mut loses_info = false; let status; let r = unpack!(status=, src.convert(&mut loses_info)); assert!(!status.intersects(Status::INEXACT) && !loses_info, "Unexpected imprecision"); r } trait ToF32LosslessViaConvertToSingle: FloatConvert { fn to_f32(self) -> f32 { assert_lossless_conversion(self).to_f32() } } impl ToF32LosslessViaConvertToSingle for Half {} impl ToF32LosslessViaConvertToSingle for BFloat {} impl ToF32LosslessViaConvertToSingle for Float8E5M2 {} impl ToF32LosslessViaConvertToSingle for Float8E4M3FN {} trait ToF64LosslessViaConvertToDouble: FloatConvert { fn to_f64(self) -> f64 { assert_lossless_conversion(self).to_f64() } } impl ToF64LosslessViaConvertToDouble for Single {} // HACK(eddyb) take advantage of the transitivity of "are conversions lossless". impl> ToF64LosslessViaConvertToDouble for T {} #[test] fn is_signaling() { // We test qNaN, -qNaN, +sNaN, -sNaN with and without payloads. let payload = 4; assert!(!Single::qnan(None).is_signaling()); assert!(!(-Single::qnan(None)).is_signaling()); assert!(!Single::qnan(Some(payload)).is_signaling()); assert!(!(-Single::qnan(Some(payload))).is_signaling()); assert!(Single::snan(None).is_signaling()); assert!((-Single::snan(None)).is_signaling()); assert!(Single::snan(Some(payload)).is_signaling()); assert!((-Single::snan(Some(payload))).is_signaling()); } #[test] fn next() { // 1. Test Special Cases Values. // // Test all special values for nextUp and nextDown perscribed by IEEE-754R // 2008. These are: // 1. +inf // 2. -inf // 3. largest // 4. -largest // 5. smallest // 6. -smallest // 7. qNaN // 8. sNaN // 9. +0 // 10. -0 let mut status; // nextUp(+inf) = +inf. let test = unpack!(status=, Quad::INFINITY.next_up()); let expected = Quad::INFINITY; assert_eq!(status, Status::OK); assert!(test.is_infinite()); assert!(!test.is_negative()); assert!(test.bitwise_eq(expected)); // nextDown(+inf) = -nextUp(-inf) = -(-largest) = largest let test = unpack!(status=, Quad::INFINITY.next_down()); let expected = Quad::largest(); assert_eq!(status, Status::OK); assert!(!test.is_negative()); assert!(test.bitwise_eq(expected)); // nextUp(-inf) = -largest let test = unpack!(status=, (-Quad::INFINITY).next_up()); let expected = -Quad::largest(); assert_eq!(status, Status::OK); assert!(test.is_negative()); assert!(test.bitwise_eq(expected)); // nextDown(-inf) = -nextUp(+inf) = -(+inf) = -inf. let test = unpack!(status=, (-Quad::INFINITY).next_down()); let expected = -Quad::INFINITY; assert_eq!(status, Status::OK); assert!(test.is_infinite() && test.is_negative()); assert!(test.bitwise_eq(expected)); // nextUp(largest) = +inf let test = unpack!(status=, Quad::largest().next_up()); let expected = Quad::INFINITY; assert_eq!(status, Status::OK); assert!(test.is_infinite() && !test.is_negative()); assert!(test.bitwise_eq(expected)); // nextDown(largest) = -nextUp(-largest) // = -(-largest + inc) // = largest - inc. let test = unpack!(status=, Quad::largest().next_down()); let expected = "0x1.fffffffffffffffffffffffffffep+16383".parse::().unwrap(); assert_eq!(status, Status::OK); assert!(!test.is_infinite() && !test.is_negative()); assert!(test.bitwise_eq(expected)); // nextUp(-largest) = -largest + inc. let test = unpack!(status=, (-Quad::largest()).next_up()); let expected = "-0x1.fffffffffffffffffffffffffffep+16383".parse::().unwrap(); assert_eq!(status, Status::OK); assert!(test.bitwise_eq(expected)); // nextDown(-largest) = -nextUp(largest) = -(inf) = -inf. let test = unpack!(status=, (-Quad::largest()).next_down()); let expected = -Quad::INFINITY; assert_eq!(status, Status::OK); assert!(test.is_infinite() && test.is_negative()); assert!(test.bitwise_eq(expected)); // nextUp(smallest) = smallest + inc. let test = unpack!(status=, "0x0.0000000000000000000000000001p-16382" .parse::() .unwrap() .next_up()); let expected = "0x0.0000000000000000000000000002p-16382".parse::().unwrap(); assert_eq!(status, Status::OK); assert!(test.bitwise_eq(expected)); // nextDown(smallest) = -nextUp(-smallest) = -(-0) = +0. let test = unpack!(status=, "0x0.0000000000000000000000000001p-16382" .parse::() .unwrap() .next_down()); let expected = Quad::ZERO; assert_eq!(status, Status::OK); assert!(test.is_pos_zero()); assert!(test.bitwise_eq(expected)); // nextUp(-smallest) = -0. let test = unpack!(status=, "-0x0.0000000000000000000000000001p-16382" .parse::() .unwrap() .next_up()); let expected = -Quad::ZERO; assert_eq!(status, Status::OK); assert!(test.is_neg_zero()); assert!(test.bitwise_eq(expected)); // nextDown(-smallest) = -nextUp(smallest) = -smallest - inc. let test = unpack!(status=, "-0x0.0000000000000000000000000001p-16382" .parse::() .unwrap() .next_down()); let expected = "-0x0.0000000000000000000000000002p-16382".parse::().unwrap(); assert_eq!(status, Status::OK); assert!(test.bitwise_eq(expected)); // nextUp(qNaN) = qNaN let test = unpack!(status=, Quad::qnan(None).next_up()); let expected = Quad::qnan(None); assert_eq!(status, Status::OK); assert!(test.bitwise_eq(expected)); // nextDown(qNaN) = qNaN let test = unpack!(status=, Quad::qnan(None).next_down()); let expected = Quad::qnan(None); assert_eq!(status, Status::OK); assert!(test.bitwise_eq(expected)); // nextUp(sNaN) = qNaN let test = unpack!(status=, Quad::snan(None).next_up()); let expected = Quad::qnan(None); assert_eq!(status, Status::INVALID_OP); assert!(test.bitwise_eq(expected)); // nextDown(sNaN) = qNaN let test = unpack!(status=, Quad::snan(None).next_down()); let expected = Quad::qnan(None); assert_eq!(status, Status::INVALID_OP); assert!(test.bitwise_eq(expected)); // nextUp(+0) = +smallest let test = unpack!(status=, Quad::ZERO.next_up()); let expected = Quad::SMALLEST; assert_eq!(status, Status::OK); assert!(test.bitwise_eq(expected)); // nextDown(+0) = -nextUp(-0) = -smallest let test = unpack!(status=, Quad::ZERO.next_down()); let expected = -Quad::SMALLEST; assert_eq!(status, Status::OK); assert!(test.bitwise_eq(expected)); // nextUp(-0) = +smallest let test = unpack!(status=, (-Quad::ZERO).next_up()); let expected = Quad::SMALLEST; assert_eq!(status, Status::OK); assert!(test.bitwise_eq(expected)); // nextDown(-0) = -nextUp(0) = -smallest let test = unpack!(status=, (-Quad::ZERO).next_down()); let expected = -Quad::SMALLEST; assert_eq!(status, Status::OK); assert!(test.bitwise_eq(expected)); // 2. Binade Boundary Tests. // 2a. Test denormal <-> normal binade boundaries. // * nextUp(+Largest Denormal) -> +Smallest Normal. // * nextDown(-Largest Denormal) -> -Smallest Normal. // * nextUp(-Smallest Normal) -> -Largest Denormal. // * nextDown(+Smallest Normal) -> +Largest Denormal. // nextUp(+Largest Denormal) -> +Smallest Normal. let test = unpack!(status=, "0x0.ffffffffffffffffffffffffffffp-16382" .parse::() .unwrap() .next_up()); let expected = "0x1.0000000000000000000000000000p-16382".parse::().unwrap(); assert_eq!(status, Status::OK); assert!(!test.is_denormal()); assert!(test.bitwise_eq(expected)); // nextDown(-Largest Denormal) -> -Smallest Normal. let test = unpack!(status=, "-0x0.ffffffffffffffffffffffffffffp-16382" .parse::() .unwrap() .next_down()); let expected = "-0x1.0000000000000000000000000000p-16382".parse::().unwrap(); assert_eq!(status, Status::OK); assert!(!test.is_denormal()); assert!(test.bitwise_eq(expected)); // nextUp(-Smallest Normal) -> -Largest Denormal. let test = unpack!(status=, "-0x1.0000000000000000000000000000p-16382" .parse::() .unwrap() .next_up()); let expected = "-0x0.ffffffffffffffffffffffffffffp-16382".parse::().unwrap(); assert_eq!(status, Status::OK); assert!(test.is_denormal()); assert!(test.bitwise_eq(expected)); // nextDown(+Smallest Normal) -> +Largest Denormal. let test = unpack!(status=, "+0x1.0000000000000000000000000000p-16382" .parse::() .unwrap() .next_down()); let expected = "+0x0.ffffffffffffffffffffffffffffp-16382".parse::().unwrap(); assert_eq!(status, Status::OK); assert!(test.is_denormal()); assert!(test.bitwise_eq(expected)); // 2b. Test normal <-> normal binade boundaries. // * nextUp(-Normal Binade Boundary) -> -Normal Binade Boundary + 1. // * nextDown(+Normal Binade Boundary) -> +Normal Binade Boundary - 1. // * nextUp(+Normal Binade Boundary - 1) -> +Normal Binade Boundary. // * nextDown(-Normal Binade Boundary + 1) -> -Normal Binade Boundary. // nextUp(-Normal Binade Boundary) -> -Normal Binade Boundary + 1. let test = unpack!(status=, "-0x1p+1".parse::().unwrap().next_up()); let expected = "-0x1.ffffffffffffffffffffffffffffp+0".parse::().unwrap(); assert_eq!(status, Status::OK); assert!(test.bitwise_eq(expected)); // nextDown(+Normal Binade Boundary) -> +Normal Binade Boundary - 1. let test = unpack!(status=, "0x1p+1".parse::().unwrap().next_down()); let expected = "0x1.ffffffffffffffffffffffffffffp+0".parse::().unwrap(); assert_eq!(status, Status::OK); assert!(test.bitwise_eq(expected)); // nextUp(+Normal Binade Boundary - 1) -> +Normal Binade Boundary. let test = unpack!(status=, "0x1.ffffffffffffffffffffffffffffp+0" .parse::() .unwrap() .next_up()); let expected = "0x1p+1".parse::().unwrap(); assert_eq!(status, Status::OK); assert!(test.bitwise_eq(expected)); // nextDown(-Normal Binade Boundary + 1) -> -Normal Binade Boundary. let test = unpack!(status=, "-0x1.ffffffffffffffffffffffffffffp+0" .parse::() .unwrap() .next_down()); let expected = "-0x1p+1".parse::().unwrap(); assert_eq!(status, Status::OK); assert!(test.bitwise_eq(expected)); // 2c. Test using next at binade boundaries with a direction away from the // binade boundary. Away from denormal <-> normal boundaries. // // This is to make sure that even though we are at a binade boundary, since // we are rounding away, we do not trigger the binade boundary code. Thus we // test: // * nextUp(-Largest Denormal) -> -Largest Denormal + inc. // * nextDown(+Largest Denormal) -> +Largest Denormal - inc. // * nextUp(+Smallest Normal) -> +Smallest Normal + inc. // * nextDown(-Smallest Normal) -> -Smallest Normal - inc. // nextUp(-Largest Denormal) -> -Largest Denormal + inc. let test = unpack!(status=, "-0x0.ffffffffffffffffffffffffffffp-16382" .parse::() .unwrap() .next_up()); let expected = "-0x0.fffffffffffffffffffffffffffep-16382".parse::().unwrap(); assert_eq!(status, Status::OK); assert!(test.is_denormal()); assert!(test.is_negative()); assert!(test.bitwise_eq(expected)); // nextDown(+Largest Denormal) -> +Largest Denormal - inc. let test = unpack!(status=, "0x0.ffffffffffffffffffffffffffffp-16382" .parse::() .unwrap() .next_down()); let expected = "0x0.fffffffffffffffffffffffffffep-16382".parse::().unwrap(); assert_eq!(status, Status::OK); assert!(test.is_denormal()); assert!(!test.is_negative()); assert!(test.bitwise_eq(expected)); // nextUp(+Smallest Normal) -> +Smallest Normal + inc. let test = unpack!(status=, "0x1.0000000000000000000000000000p-16382" .parse::() .unwrap() .next_up()); let expected = "0x1.0000000000000000000000000001p-16382".parse::().unwrap(); assert_eq!(status, Status::OK); assert!(!test.is_denormal()); assert!(!test.is_negative()); assert!(test.bitwise_eq(expected)); // nextDown(-Smallest Normal) -> -Smallest Normal - inc. let test = unpack!(status=, "-0x1.0000000000000000000000000000p-16382" .parse::() .unwrap() .next_down()); let expected = "-0x1.0000000000000000000000000001p-16382".parse::().unwrap(); assert_eq!(status, Status::OK); assert!(!test.is_denormal()); assert!(test.is_negative()); assert!(test.bitwise_eq(expected)); // 2d. Test values which cause our exponent to go to min exponent. This // is to ensure that guards in the code to check for min exponent // trigger properly. // * nextUp(-0x1p-16381) -> -0x1.ffffffffffffffffffffffffffffp-16382 // * nextDown(-0x1.ffffffffffffffffffffffffffffp-16382) -> // -0x1p-16381 // * nextUp(0x1.ffffffffffffffffffffffffffffp-16382) -> 0x1p-16382 // * nextDown(0x1p-16382) -> 0x1.ffffffffffffffffffffffffffffp-16382 // nextUp(-0x1p-16381) -> -0x1.ffffffffffffffffffffffffffffp-16382 let test = unpack!(status=, "-0x1p-16381".parse::().unwrap().next_up()); let expected = "-0x1.ffffffffffffffffffffffffffffp-16382".parse::().unwrap(); assert_eq!(status, Status::OK); assert!(test.bitwise_eq(expected)); // nextDown(-0x1.ffffffffffffffffffffffffffffp-16382) -> // -0x1p-16381 let test = unpack!(status=, "-0x1.ffffffffffffffffffffffffffffp-16382" .parse::() .unwrap() .next_down()); let expected = "-0x1p-16381".parse::().unwrap(); assert_eq!(status, Status::OK); assert!(test.bitwise_eq(expected)); // nextUp(0x1.ffffffffffffffffffffffffffffp-16382) -> 0x1p-16381 let test = unpack!(status=, "0x1.ffffffffffffffffffffffffffffp-16382" .parse::() .unwrap() .next_up()); let expected = "0x1p-16381".parse::().unwrap(); assert_eq!(status, Status::OK); assert!(test.bitwise_eq(expected)); // nextDown(0x1p-16381) -> 0x1.ffffffffffffffffffffffffffffp-16382 let test = unpack!(status=, "0x1p-16381".parse::().unwrap().next_down()); let expected = "0x1.ffffffffffffffffffffffffffffp-16382".parse::().unwrap(); assert_eq!(status, Status::OK); assert!(test.bitwise_eq(expected)); // 3. Now we test both denormal/normal computation which will not cause us // to go across binade boundaries. Specifically we test: // * nextUp(+Denormal) -> +Denormal. // * nextDown(+Denormal) -> +Denormal. // * nextUp(-Denormal) -> -Denormal. // * nextDown(-Denormal) -> -Denormal. // * nextUp(+Normal) -> +Normal. // * nextDown(+Normal) -> +Normal. // * nextUp(-Normal) -> -Normal. // * nextDown(-Normal) -> -Normal. // nextUp(+Denormal) -> +Denormal. let test = unpack!(status=, "0x0.ffffffffffffffffffffffff000cp-16382" .parse::() .unwrap() .next_up()); let expected = "0x0.ffffffffffffffffffffffff000dp-16382".parse::().unwrap(); assert_eq!(status, Status::OK); assert!(test.is_denormal()); assert!(!test.is_negative()); assert!(test.bitwise_eq(expected)); // nextDown(+Denormal) -> +Denormal. let test = unpack!(status=, "0x0.ffffffffffffffffffffffff000cp-16382" .parse::() .unwrap() .next_down()); let expected = "0x0.ffffffffffffffffffffffff000bp-16382".parse::().unwrap(); assert_eq!(status, Status::OK); assert!(test.is_denormal()); assert!(!test.is_negative()); assert!(test.bitwise_eq(expected)); // nextUp(-Denormal) -> -Denormal. let test = unpack!(status=, "-0x0.ffffffffffffffffffffffff000cp-16382" .parse::() .unwrap() .next_up()); let expected = "-0x0.ffffffffffffffffffffffff000bp-16382".parse::().unwrap(); assert_eq!(status, Status::OK); assert!(test.is_denormal()); assert!(test.is_negative()); assert!(test.bitwise_eq(expected)); // nextDown(-Denormal) -> -Denormal let test = unpack!(status=, "-0x0.ffffffffffffffffffffffff000cp-16382" .parse::() .unwrap() .next_down()); let expected = "-0x0.ffffffffffffffffffffffff000dp-16382".parse::().unwrap(); assert_eq!(status, Status::OK); assert!(test.is_denormal()); assert!(test.is_negative()); assert!(test.bitwise_eq(expected)); // nextUp(+Normal) -> +Normal. let test = unpack!(status=, "0x1.ffffffffffffffffffffffff000cp-16000" .parse::() .unwrap() .next_up()); let expected = "0x1.ffffffffffffffffffffffff000dp-16000".parse::().unwrap(); assert_eq!(status, Status::OK); assert!(!test.is_denormal()); assert!(!test.is_negative()); assert!(test.bitwise_eq(expected)); // nextDown(+Normal) -> +Normal. let test = unpack!(status=, "0x1.ffffffffffffffffffffffff000cp-16000" .parse::() .unwrap() .next_down()); let expected = "0x1.ffffffffffffffffffffffff000bp-16000".parse::().unwrap(); assert_eq!(status, Status::OK); assert!(!test.is_denormal()); assert!(!test.is_negative()); assert!(test.bitwise_eq(expected)); // nextUp(-Normal) -> -Normal. let test = unpack!(status=, "-0x1.ffffffffffffffffffffffff000cp-16000" .parse::() .unwrap() .next_up()); let expected = "-0x1.ffffffffffffffffffffffff000bp-16000".parse::().unwrap(); assert_eq!(status, Status::OK); assert!(!test.is_denormal()); assert!(test.is_negative()); assert!(test.bitwise_eq(expected)); // nextDown(-Normal) -> -Normal. let test = unpack!(status=, "-0x1.ffffffffffffffffffffffff000cp-16000" .parse::() .unwrap() .next_down()); let expected = "-0x1.ffffffffffffffffffffffff000dp-16000".parse::().unwrap(); assert_eq!(status, Status::OK); assert!(!test.is_denormal()); assert!(test.is_negative()); assert!(test.bitwise_eq(expected)); } #[test] fn fma() { { let mut f1 = Single::from_f32(14.5); let f2 = Single::from_f32(-14.5); let f3 = Single::from_f32(225.0); f1 = f1.mul_add(f2, f3).value; assert_eq!(14.75, f1.to_f32()); } { let val2 = Single::from_f32(2.0); let mut f1 = Single::from_f32(1.17549435e-38); let mut f2 = Single::from_f32(1.17549435e-38); f1 /= val2; f2 /= val2; let f3 = Single::from_f32(12.0); f1 = f1.mul_add(f2, f3).value; assert_eq!(12.0, f1.to_f32()); } // Test for correct zero sign when answer is exactly zero. // fma(1.0, -1.0, 1.0) -> +ve 0. { let mut f1 = Double::from_f64(1.0); let f2 = Double::from_f64(-1.0); let f3 = Double::from_f64(1.0); f1 = f1.mul_add(f2, f3).value; assert!(!f1.is_negative() && f1.is_zero()); } // Test for correct zero sign when answer is exactly zero and rounding towards // negative. // fma(1.0, -1.0, 1.0) -> +ve 0. { let mut f1 = Double::from_f64(1.0); let f2 = Double::from_f64(-1.0); let f3 = Double::from_f64(1.0); f1 = f1.mul_add_r(f2, f3, Round::TowardNegative).value; assert!(f1.is_negative() && f1.is_zero()); } // Test for correct (in this case -ve) sign when adding like signed zeros. // Test fma(0.0, -0.0, -0.0) -> -ve 0. { let mut f1 = Double::from_f64(0.0); let f2 = Double::from_f64(-0.0); let f3 = Double::from_f64(-0.0); f1 = f1.mul_add(f2, f3).value; assert!(f1.is_negative() && f1.is_zero()); } // Test -ve sign preservation when small negative results underflow. { let mut f1 = "-0x1p-1074".parse::().unwrap(); let f2 = "+0x1p-1074".parse::().unwrap(); let f3 = Double::from_f64(0.0); f1 = f1.mul_add(f2, f3).value; assert!(f1.is_negative() && f1.is_zero()); } // Test x87 extended precision case from http://llvm.org/PR20728. { let mut m1 = X87DoubleExtended::from_u128(1).value; let m2 = X87DoubleExtended::from_u128(1).value; let a = X87DoubleExtended::from_u128(3).value; let mut loses_info = false; m1 = m1.mul_add(m2, a).value; let r: Single = m1.convert(&mut loses_info).value; assert!(!loses_info); assert_eq!(4.0, r.to_f32()); } // Regression test that failed an assertion. { let mut f1 = Single::from_f32(-8.85242279E-41); let f2 = Single::from_f32(2.0); let f3 = Single::from_f32(8.85242279E-41); f1 = f1.mul_add(f2, f3).value; assert_eq!(-8.85242279E-41, f1.to_f32()); } // Test using only a single instance of APFloat. { let mut f = Double::from_f64(1.5); f = f.mul_add(f, f).value; assert_eq!(3.75, f.to_f64()); } } #[test] fn min_num() { let f1 = Double::from_f64(1.0); let f2 = Double::from_f64(2.0); let nan = Double::NAN; assert_eq!(1.0, f1.min(f2).to_f64()); assert_eq!(1.0, f2.min(f1).to_f64()); assert_eq!(1.0, f1.min(nan).to_f64()); assert_eq!(1.0, nan.min(f1).to_f64()); } #[test] fn max_num() { let f1 = Double::from_f64(1.0); let f2 = Double::from_f64(2.0); let nan = Double::NAN; assert_eq!(2.0, f1.max(f2).to_f64()); assert_eq!(2.0, f2.max(f1).to_f64()); assert_eq!(1.0, f1.max(nan).to_f64()); assert_eq!(1.0, nan.max(f1).to_f64()); } #[test] fn minimum() { let f1 = Double::from_f64(1.0); let f2 = Double::from_f64(2.0); let zp = Double::from_f64(0.0); let zn = Double::from_f64(-0.0); let nan = Double::NAN; assert_eq!(1.0, f1.minimum(f2).to_f64()); assert_eq!(1.0, f2.minimum(f1).to_f64()); assert_eq!(-0.0, zp.minimum(zn).to_f64()); assert_eq!(-0.0, zn.minimum(zp).to_f64()); assert!(f1.minimum(nan).to_f64().is_nan()); assert!(nan.minimum(f1).to_f64().is_nan()); } #[test] fn maximum() { let f1 = Double::from_f64(1.0); let f2 = Double::from_f64(2.0); let zp = Double::from_f64(0.0); let zn = Double::from_f64(-0.0); let nan = Double::NAN; assert_eq!(2.0, f1.maximum(f2).to_f64()); assert_eq!(2.0, f2.maximum(f1).to_f64()); assert_eq!(0.0, zp.maximum(zn).to_f64()); assert_eq!(0.0, zn.maximum(zp).to_f64()); assert!(f1.maximum(nan).to_f64().is_nan()); assert!(nan.maximum(f1).to_f64().is_nan()); } #[test] fn denormal() { // Test single precision { assert!(!Single::from_u128(0).value.is_denormal()); let mut t = "1.17549435082228750797e-38".parse::().unwrap(); assert!(!t.is_denormal()); t /= Single::from_u128(2).value; assert!(t.is_denormal()); } // Test double precision { assert!(!Double::from_u128(0).value.is_denormal()); let mut t = "2.22507385850720138309e-308".parse::().unwrap(); assert!(!t.is_denormal()); t /= Double::from_u128(2).value; assert!(t.is_denormal()); } // Test Intel double-ext { assert!(!X87DoubleExtended::from_u128(0).value.is_denormal()); let mut t = "3.36210314311209350626e-4932".parse::().unwrap(); assert!(!t.is_denormal()); t /= X87DoubleExtended::from_u128(2).value; assert!(t.is_denormal()); } // Test quadruple precision { assert!(!Quad::from_u128(0).value.is_denormal()); let mut t = "3.36210314311209350626267781732175260e-4932".parse::().unwrap(); assert!(!t.is_denormal()); t /= Quad::from_u128(2).value; assert!(t.is_denormal()); } } #[test] fn is_smallest_normalized() { for_each_float_type!(for test::()); fn test() { assert!(!F::ZERO.is_smallest_normalized()); assert!(!(-F::ZERO).is_smallest_normalized()); assert!(!F::INFINITY.is_smallest_normalized()); assert!(!(-F::INFINITY).is_smallest_normalized()); assert!(!F::qnan(None).is_smallest_normalized()); assert!(!F::snan(None).is_smallest_normalized()); assert!(!F::largest().is_smallest_normalized()); assert!(!(-F::largest()).is_smallest_normalized()); assert!(!F::SMALLEST.is_smallest_normalized()); assert!(!(-F::SMALLEST).is_smallest_normalized()); assert!(!F::from_bits(!0u128 >> (128 - F::BITS)).is_smallest_normalized()); let pos_smallest_normalized = F::smallest_normalized(); let neg_smallest_normalized = -F::smallest_normalized(); assert!(pos_smallest_normalized.is_smallest_normalized()); assert!(neg_smallest_normalized.is_smallest_normalized()); for mut val in [pos_smallest_normalized, neg_smallest_normalized] { let old_sign = val.is_negative(); let mut status; // Step down, make sure it's still not smallest normalized. val = unpack!(status=, val.next_down()); assert_eq!(Status::OK, status); assert_eq!(old_sign, val.is_negative()); assert!(!val.is_smallest_normalized()); assert_eq!(old_sign, val.is_negative()); // Step back up should restore it to being smallest normalized. val = unpack!(status=, val.next_up()); assert_eq!(Status::OK, status); assert!(val.is_smallest_normalized()); assert_eq!(old_sign, val.is_negative()); // Step beyond should no longer smallest normalized. val = unpack!(status=, val.next_up()); assert_eq!(Status::OK, status); assert!(!val.is_smallest_normalized()); assert_eq!(old_sign, val.is_negative()); } } } #[test] fn decimal_strings_without_null_terminators() { // Make sure that we can parse strings without null terminators. // rdar://14323230. assert_eq!("0.00"[..3].parse::().unwrap().to_f64(), 0.0); assert_eq!("0.01"[..3].parse::().unwrap().to_f64(), 0.0); assert_eq!("0.09"[..3].parse::().unwrap().to_f64(), 0.0); assert_eq!("0.095"[..4].parse::().unwrap().to_f64(), 0.09); assert_eq!("0.00e+3"[..7].parse::().unwrap().to_f64(), 0.00); assert_eq!("0e+3"[..4].parse::().unwrap().to_f64(), 0.00); } #[test] fn from_zero_decimal_string() { assert_eq!(0.0, "0".parse::().unwrap().to_f64()); assert_eq!(0.0, "+0".parse::().unwrap().to_f64()); assert_eq!(-0.0, "-0".parse::().unwrap().to_f64()); assert_eq!(0.0, "0.".parse::().unwrap().to_f64()); assert_eq!(0.0, "+0.".parse::().unwrap().to_f64()); assert_eq!(-0.0, "-0.".parse::().unwrap().to_f64()); assert_eq!(0.0, ".0".parse::().unwrap().to_f64()); assert_eq!(0.0, "+.0".parse::().unwrap().to_f64()); assert_eq!(-0.0, "-.0".parse::().unwrap().to_f64()); assert_eq!(0.0, "0.0".parse::().unwrap().to_f64()); assert_eq!(0.0, "+0.0".parse::().unwrap().to_f64()); assert_eq!(-0.0, "-0.0".parse::().unwrap().to_f64()); assert_eq!(0.0, "00000.".parse::().unwrap().to_f64()); assert_eq!(0.0, "+00000.".parse::().unwrap().to_f64()); assert_eq!(-0.0, "-00000.".parse::().unwrap().to_f64()); assert_eq!(0.0, ".00000".parse::().unwrap().to_f64()); assert_eq!(0.0, "+.00000".parse::().unwrap().to_f64()); assert_eq!(-0.0, "-.00000".parse::().unwrap().to_f64()); assert_eq!(0.0, "0000.00000".parse::().unwrap().to_f64()); assert_eq!(0.0, "+0000.00000".parse::().unwrap().to_f64()); assert_eq!(-0.0, "-0000.00000".parse::().unwrap().to_f64()); } #[test] fn from_zero_decimal_single_exponent_string() { assert_eq!(0.0, "0e1".parse::().unwrap().to_f64()); assert_eq!(0.0, "+0e1".parse::().unwrap().to_f64()); assert_eq!(-0.0, "-0e1".parse::().unwrap().to_f64()); assert_eq!(0.0, "0e+1".parse::().unwrap().to_f64()); assert_eq!(0.0, "+0e+1".parse::().unwrap().to_f64()); assert_eq!(-0.0, "-0e+1".parse::().unwrap().to_f64()); assert_eq!(0.0, "0e-1".parse::().unwrap().to_f64()); assert_eq!(0.0, "+0e-1".parse::().unwrap().to_f64()); assert_eq!(-0.0, "-0e-1".parse::().unwrap().to_f64()); assert_eq!(0.0, "0.e1".parse::().unwrap().to_f64()); assert_eq!(0.0, "+0.e1".parse::().unwrap().to_f64()); assert_eq!(-0.0, "-0.e1".parse::().unwrap().to_f64()); assert_eq!(0.0, "0.e+1".parse::().unwrap().to_f64()); assert_eq!(0.0, "+0.e+1".parse::().unwrap().to_f64()); assert_eq!(-0.0, "-0.e+1".parse::().unwrap().to_f64()); assert_eq!(0.0, "0.e-1".parse::().unwrap().to_f64()); assert_eq!(0.0, "+0.e-1".parse::().unwrap().to_f64()); assert_eq!(-0.0, "-0.e-1".parse::().unwrap().to_f64()); assert_eq!(0.0, ".0e1".parse::().unwrap().to_f64()); assert_eq!(0.0, "+.0e1".parse::().unwrap().to_f64()); assert_eq!(-0.0, "-.0e1".parse::().unwrap().to_f64()); assert_eq!(0.0, ".0e+1".parse::().unwrap().to_f64()); assert_eq!(0.0, "+.0e+1".parse::().unwrap().to_f64()); assert_eq!(-0.0, "-.0e+1".parse::().unwrap().to_f64()); assert_eq!(0.0, ".0e-1".parse::().unwrap().to_f64()); assert_eq!(0.0, "+.0e-1".parse::().unwrap().to_f64()); assert_eq!(-0.0, "-.0e-1".parse::().unwrap().to_f64()); assert_eq!(0.0, "0.0e1".parse::().unwrap().to_f64()); assert_eq!(0.0, "+0.0e1".parse::().unwrap().to_f64()); assert_eq!(-0.0, "-0.0e1".parse::().unwrap().to_f64()); assert_eq!(0.0, "0.0e+1".parse::().unwrap().to_f64()); assert_eq!(0.0, "+0.0e+1".parse::().unwrap().to_f64()); assert_eq!(-0.0, "-0.0e+1".parse::().unwrap().to_f64()); assert_eq!(0.0, "0.0e-1".parse::().unwrap().to_f64()); assert_eq!(0.0, "+0.0e-1".parse::().unwrap().to_f64()); assert_eq!(-0.0, "-0.0e-1".parse::().unwrap().to_f64()); assert_eq!(0.0, "000.0000e1".parse::().unwrap().to_f64()); assert_eq!(0.0, "+000.0000e+1".parse::().unwrap().to_f64()); assert_eq!(-0.0, "-000.0000e+1".parse::().unwrap().to_f64()); } #[test] fn from_zero_decimal_large_exponent_string() { assert_eq!(0.0, "0e1234".parse::().unwrap().to_f64()); assert_eq!(0.0, "+0e1234".parse::().unwrap().to_f64()); assert_eq!(-0.0, "-0e1234".parse::().unwrap().to_f64()); assert_eq!(0.0, "0e+1234".parse::().unwrap().to_f64()); assert_eq!(0.0, "+0e+1234".parse::().unwrap().to_f64()); assert_eq!(-0.0, "-0e+1234".parse::().unwrap().to_f64()); assert_eq!(0.0, "0e-1234".parse::().unwrap().to_f64()); assert_eq!(0.0, "+0e-1234".parse::().unwrap().to_f64()); assert_eq!(-0.0, "-0e-1234".parse::().unwrap().to_f64()); assert_eq!(0.0, "000.0000e1234".parse::().unwrap().to_f64()); assert_eq!(0.0, "000.0000e-1234".parse::().unwrap().to_f64()); } #[test] fn from_zero_hexadecimal_string() { assert_eq!(0.0, "0x0p1".parse::().unwrap().to_f64()); assert_eq!(0.0, "+0x0p1".parse::().unwrap().to_f64()); assert_eq!(-0.0, "-0x0p1".parse::().unwrap().to_f64()); assert_eq!(0.0, "0x0p+1".parse::().unwrap().to_f64()); assert_eq!(0.0, "+0x0p+1".parse::().unwrap().to_f64()); assert_eq!(-0.0, "-0x0p+1".parse::().unwrap().to_f64()); assert_eq!(0.0, "0x0p-1".parse::().unwrap().to_f64()); assert_eq!(0.0, "+0x0p-1".parse::().unwrap().to_f64()); assert_eq!(-0.0, "-0x0p-1".parse::().unwrap().to_f64()); assert_eq!(0.0, "0x0.p1".parse::().unwrap().to_f64()); assert_eq!(0.0, "+0x0.p1".parse::().unwrap().to_f64()); assert_eq!(-0.0, "-0x0.p1".parse::().unwrap().to_f64()); assert_eq!(0.0, "0x0.p+1".parse::().unwrap().to_f64()); assert_eq!(0.0, "+0x0.p+1".parse::().unwrap().to_f64()); assert_eq!(-0.0, "-0x0.p+1".parse::().unwrap().to_f64()); assert_eq!(0.0, "0x0.p-1".parse::().unwrap().to_f64()); assert_eq!(0.0, "+0x0.p-1".parse::().unwrap().to_f64()); assert_eq!(-0.0, "-0x0.p-1".parse::().unwrap().to_f64()); assert_eq!(0.0, "0x.0p1".parse::().unwrap().to_f64()); assert_eq!(0.0, "+0x.0p1".parse::().unwrap().to_f64()); assert_eq!(-0.0, "-0x.0p1".parse::().unwrap().to_f64()); assert_eq!(0.0, "0x.0p+1".parse::().unwrap().to_f64()); assert_eq!(0.0, "+0x.0p+1".parse::().unwrap().to_f64()); assert_eq!(-0.0, "-0x.0p+1".parse::().unwrap().to_f64()); assert_eq!(0.0, "0x.0p-1".parse::().unwrap().to_f64()); assert_eq!(0.0, "+0x.0p-1".parse::().unwrap().to_f64()); assert_eq!(-0.0, "-0x.0p-1".parse::().unwrap().to_f64()); assert_eq!(0.0, "0x0.0p1".parse::().unwrap().to_f64()); assert_eq!(0.0, "+0x0.0p1".parse::().unwrap().to_f64()); assert_eq!(-0.0, "-0x0.0p1".parse::().unwrap().to_f64()); assert_eq!(0.0, "0x0.0p+1".parse::().unwrap().to_f64()); assert_eq!(0.0, "+0x0.0p+1".parse::().unwrap().to_f64()); assert_eq!(-0.0, "-0x0.0p+1".parse::().unwrap().to_f64()); assert_eq!(0.0, "0x0.0p-1".parse::().unwrap().to_f64()); assert_eq!(0.0, "+0x0.0p-1".parse::().unwrap().to_f64()); assert_eq!(-0.0, "-0x0.0p-1".parse::().unwrap().to_f64()); assert_eq!(0.0, "0x00000.p1".parse::().unwrap().to_f64()); assert_eq!(0.0, "0x0000.00000p1".parse::().unwrap().to_f64()); assert_eq!(0.0, "0x.00000p1".parse::().unwrap().to_f64()); assert_eq!(0.0, "0x0.p1".parse::().unwrap().to_f64()); assert_eq!(0.0, "0x0p1234".parse::().unwrap().to_f64()); assert_eq!(-0.0, "-0x0p1234".parse::().unwrap().to_f64()); assert_eq!(0.0, "0x00000.p1234".parse::().unwrap().to_f64()); assert_eq!(0.0, "0x0000.00000p1234".parse::().unwrap().to_f64()); assert_eq!(0.0, "0x.00000p1234".parse::().unwrap().to_f64()); assert_eq!(0.0, "0x0.p1234".parse::().unwrap().to_f64()); } #[test] fn from_decimal_string() { assert_eq!(1.0, "1".parse::().unwrap().to_f64()); assert_eq!(2.0, "2.".parse::().unwrap().to_f64()); assert_eq!(0.5, ".5".parse::().unwrap().to_f64()); assert_eq!(1.0, "1.0".parse::().unwrap().to_f64()); assert_eq!(-2.0, "-2".parse::().unwrap().to_f64()); assert_eq!(-4.0, "-4.".parse::().unwrap().to_f64()); assert_eq!(-0.5, "-.5".parse::().unwrap().to_f64()); assert_eq!(-1.5, "-1.5".parse::().unwrap().to_f64()); assert_eq!(1.25e12, "1.25e12".parse::().unwrap().to_f64()); assert_eq!(1.25e+12, "1.25e+12".parse::().unwrap().to_f64()); assert_eq!(1.25e-12, "1.25e-12".parse::().unwrap().to_f64()); assert_eq!(1024.0, "1024.".parse::().unwrap().to_f64()); assert_eq!(1024.05, "1024.05000".parse::().unwrap().to_f64()); assert_eq!(0.05, ".05000".parse::().unwrap().to_f64()); assert_eq!(2.0, "2.".parse::().unwrap().to_f64()); assert_eq!(2.0e2, "2.e2".parse::().unwrap().to_f64()); assert_eq!(2.0e+2, "2.e+2".parse::().unwrap().to_f64()); assert_eq!(2.0e-2, "2.e-2".parse::().unwrap().to_f64()); assert_eq!(2.05e2, "002.05000e2".parse::().unwrap().to_f64()); assert_eq!(2.05e+2, "002.05000e+2".parse::().unwrap().to_f64()); assert_eq!(2.05e-2, "002.05000e-2".parse::().unwrap().to_f64()); assert_eq!(2.05e12, "002.05000e12".parse::().unwrap().to_f64()); assert_eq!(2.05e+12, "002.05000e+12".parse::().unwrap().to_f64()); assert_eq!(2.05e-12, "002.05000e-12".parse::().unwrap().to_f64()); assert_eq!(1.0, "1e".parse::().unwrap().to_f64()); assert_eq!(1.0, "+1e".parse::().unwrap().to_f64()); assert_eq!(-1.0, "-1e".parse::().unwrap().to_f64()); assert_eq!(1.0, "1.e".parse::().unwrap().to_f64()); assert_eq!(1.0, "+1.e".parse::().unwrap().to_f64()); assert_eq!(-1.0, "-1.e".parse::().unwrap().to_f64()); assert_eq!(0.1, ".1e".parse::().unwrap().to_f64()); assert_eq!(0.1, "+.1e".parse::().unwrap().to_f64()); assert_eq!(-0.1, "-.1e".parse::().unwrap().to_f64()); assert_eq!(1.1, "1.1e".parse::().unwrap().to_f64()); assert_eq!(1.1, "+1.1e".parse::().unwrap().to_f64()); assert_eq!(-1.1, "-1.1e".parse::().unwrap().to_f64()); assert_eq!(1.0, "1e+".parse::().unwrap().to_f64()); assert_eq!(1.0, "1e-".parse::().unwrap().to_f64()); assert_eq!(0.1, ".1e".parse::().unwrap().to_f64()); assert_eq!(0.1, ".1e+".parse::().unwrap().to_f64()); assert_eq!(0.1, ".1e-".parse::().unwrap().to_f64()); assert_eq!(1.0, "1.0e".parse::().unwrap().to_f64()); assert_eq!(1.0, "1.0e+".parse::().unwrap().to_f64()); assert_eq!(1.0, "1.0e-".parse::().unwrap().to_f64()); // These are "carefully selected" to overflow the fast log-base // calculations in the implementation. assert!("99e99999".parse::().unwrap().is_infinite()); assert!("-99e99999".parse::().unwrap().is_infinite()); assert!("1e-99999".parse::().unwrap().is_pos_zero()); assert!("-1e-99999".parse::().unwrap().is_neg_zero()); assert_eq!(2.71828, "2.71828".parse::().unwrap().to_f64()); } #[test] fn from_string_specials() { let precision = 53; let payload_bits = precision - 2; let payload_mask = (1 << payload_bits) - 1; let mut nan_payloads = [ 0, 1, 123, 0xDEADBEEF, -2i32 as u128, 1 << payload_bits, // overflow bit 1 << (payload_bits - 1), // signaling bit 1 << (payload_bits - 2), // highest possible bit ]; // Convert payload integer to decimal string representation. let nan_payload_dec_strings: Vec<_> = nan_payloads.iter().map(|payload| format!("{payload}")).collect(); // Convert payload integer to hexadecimal string representation. let nan_payload_hex_strings: Vec<_> = nan_payloads.iter().map(|payload| format!("{payload:#x}")).collect(); // Fix payloads to expected result. for payload in &mut nan_payloads { *payload &= payload_mask; } // Signaling NaN must have a non-zero payload. In case a zero payload is // requested, a default arbitrary payload is set instead. Save this payload // for testing. let snan_default_payload = Double::snan(None).to_bits() & payload_mask; // Negative sign prefix (or none - for positive). let signs = ["", "-"]; // "Signaling" prefix (or none - for "Quiet"). let nan_types = ["", "s", "S"]; let nan_strings = ["nan", "NaN"]; for nan_str in nan_strings { for type_str in nan_types { let signaling = matches!(type_str, "s" | "S"); for j in 0..nan_payloads.len() { let payload = if signaling && nan_payloads[j] == 0 { snan_default_payload } else { nan_payloads[j] }; let payload_dec = &nan_payload_dec_strings[j]; let payload_hex = &nan_payload_hex_strings[j]; for sign_str in signs { let negative = sign_str == "-"; let prefix = format!("{sign_str}{type_str}{nan_str}"); let test_strings = [ // Test without any paylod. (payload == 0).then(|| prefix.clone()), // Test with the payload as a suffix. Some(format!("{prefix}{payload_dec}")), Some(format!("{prefix}{payload_hex}")), // Test with the payload inside parentheses. Some(format!("{prefix}({payload_dec})")), Some(format!("{prefix}({payload_hex})")), ] .into_iter() .flatten(); for test_str in test_strings { let f = test_str .parse::() .map_err(|e| format!("{test_str:?}: {e:?}")) .unwrap(); assert!(f.is_nan()); assert_eq!(signaling, f.is_signaling()); assert_eq!(negative, f.is_negative()); assert_eq!(payload, f.to_bits() & payload_mask); } } } } } let inf_strings = ["inf", "INFINITY", "+Inf", "-inf", "-INFINITY", "-Inf"]; for &inf_str in &inf_strings { let negative = inf_str.starts_with('-'); let f = inf_str.parse::().unwrap(); assert!(f.is_infinite()); assert_eq!(negative, f.is_negative()); assert_eq!(0, f.to_bits() & payload_mask); } } #[test] fn from_to_string_specials() { assert_eq!("+Inf", "+Inf".parse::().unwrap().to_string()); assert_eq!("+Inf", "INFINITY".parse::().unwrap().to_string()); assert_eq!("+Inf", "inf".parse::().unwrap().to_string()); assert_eq!("-Inf", "-Inf".parse::().unwrap().to_string()); assert_eq!("-Inf", "-INFINITY".parse::().unwrap().to_string()); assert_eq!("-Inf", "-inf".parse::().unwrap().to_string()); assert_eq!("NaN", "NaN".parse::().unwrap().to_string()); assert_eq!("NaN", "nan".parse::().unwrap().to_string()); assert_eq!("NaN", "-NaN".parse::().unwrap().to_string()); assert_eq!("NaN", "-nan".parse::().unwrap().to_string()); } #[test] fn from_hexadecimal_string() { assert_eq!(1.0, "0x1p0".parse::().unwrap().to_f64()); assert_eq!(1.0, "+0x1p0".parse::().unwrap().to_f64()); assert_eq!(-1.0, "-0x1p0".parse::().unwrap().to_f64()); assert_eq!(1.0, "0x1p+0".parse::().unwrap().to_f64()); assert_eq!(1.0, "+0x1p+0".parse::().unwrap().to_f64()); assert_eq!(-1.0, "-0x1p+0".parse::().unwrap().to_f64()); assert_eq!(1.0, "0x1p-0".parse::().unwrap().to_f64()); assert_eq!(1.0, "+0x1p-0".parse::().unwrap().to_f64()); assert_eq!(-1.0, "-0x1p-0".parse::().unwrap().to_f64()); assert_eq!(2.0, "0x1p1".parse::().unwrap().to_f64()); assert_eq!(2.0, "+0x1p1".parse::().unwrap().to_f64()); assert_eq!(-2.0, "-0x1p1".parse::().unwrap().to_f64()); assert_eq!(2.0, "0x1p+1".parse::().unwrap().to_f64()); assert_eq!(2.0, "+0x1p+1".parse::().unwrap().to_f64()); assert_eq!(-2.0, "-0x1p+1".parse::().unwrap().to_f64()); assert_eq!(0.5, "0x1p-1".parse::().unwrap().to_f64()); assert_eq!(0.5, "+0x1p-1".parse::().unwrap().to_f64()); assert_eq!(-0.5, "-0x1p-1".parse::().unwrap().to_f64()); assert_eq!(3.0, "0x1.8p1".parse::().unwrap().to_f64()); assert_eq!(3.0, "+0x1.8p1".parse::().unwrap().to_f64()); assert_eq!(-3.0, "-0x1.8p1".parse::().unwrap().to_f64()); assert_eq!(3.0, "0x1.8p+1".parse::().unwrap().to_f64()); assert_eq!(3.0, "+0x1.8p+1".parse::().unwrap().to_f64()); assert_eq!(-3.0, "-0x1.8p+1".parse::().unwrap().to_f64()); assert_eq!(0.75, "0x1.8p-1".parse::().unwrap().to_f64()); assert_eq!(0.75, "+0x1.8p-1".parse::().unwrap().to_f64()); assert_eq!(-0.75, "-0x1.8p-1".parse::().unwrap().to_f64()); assert_eq!(8192.0, "0x1000.000p1".parse::().unwrap().to_f64()); assert_eq!(8192.0, "+0x1000.000p1".parse::().unwrap().to_f64()); assert_eq!(-8192.0, "-0x1000.000p1".parse::().unwrap().to_f64()); assert_eq!(8192.0, "0x1000.000p+1".parse::().unwrap().to_f64()); assert_eq!(8192.0, "+0x1000.000p+1".parse::().unwrap().to_f64()); assert_eq!(-8192.0, "-0x1000.000p+1".parse::().unwrap().to_f64()); assert_eq!(2048.0, "0x1000.000p-1".parse::().unwrap().to_f64()); assert_eq!(2048.0, "+0x1000.000p-1".parse::().unwrap().to_f64()); assert_eq!(-2048.0, "-0x1000.000p-1".parse::().unwrap().to_f64()); assert_eq!(8192.0, "0x1000p1".parse::().unwrap().to_f64()); assert_eq!(8192.0, "+0x1000p1".parse::().unwrap().to_f64()); assert_eq!(-8192.0, "-0x1000p1".parse::().unwrap().to_f64()); assert_eq!(8192.0, "0x1000p+1".parse::().unwrap().to_f64()); assert_eq!(8192.0, "+0x1000p+1".parse::().unwrap().to_f64()); assert_eq!(-8192.0, "-0x1000p+1".parse::().unwrap().to_f64()); assert_eq!(2048.0, "0x1000p-1".parse::().unwrap().to_f64()); assert_eq!(2048.0, "+0x1000p-1".parse::().unwrap().to_f64()); assert_eq!(-2048.0, "-0x1000p-1".parse::().unwrap().to_f64()); assert_eq!(16384.0, "0x10p10".parse::().unwrap().to_f64()); assert_eq!(16384.0, "+0x10p10".parse::().unwrap().to_f64()); assert_eq!(-16384.0, "-0x10p10".parse::().unwrap().to_f64()); assert_eq!(16384.0, "0x10p+10".parse::().unwrap().to_f64()); assert_eq!(16384.0, "+0x10p+10".parse::().unwrap().to_f64()); assert_eq!(-16384.0, "-0x10p+10".parse::().unwrap().to_f64()); assert_eq!(0.015625, "0x10p-10".parse::().unwrap().to_f64()); assert_eq!(0.015625, "+0x10p-10".parse::().unwrap().to_f64()); assert_eq!(-0.015625, "-0x10p-10".parse::().unwrap().to_f64()); assert_eq!(1.0625, "0x1.1p0".parse::().unwrap().to_f64()); assert_eq!(1.0, "0x1p0".parse::().unwrap().to_f64()); assert_eq!( "0x1p-150".parse::().unwrap().to_f64(), "+0x800000000000000001.p-221".parse::().unwrap().to_f64() ); assert_eq!(2251799813685248.5, "0x80000000000004000000.010p-28".parse::().unwrap().to_f64()); } #[test] fn to_string() { let to_string = |d: f64, precision: usize, width: usize| { let x = Double::from_f64(d); if precision == 0 { format!("{:1$}", x, width) } else { format!("{:2$.1$}", x, precision, width) } }; assert_eq!("10", to_string(10.0, 6, 3)); assert_eq!("1.0E+1", to_string(10.0, 6, 0)); assert_eq!("10100", to_string(1.01E+4, 5, 2)); assert_eq!("1.01E+4", to_string(1.01E+4, 4, 2)); assert_eq!("1.01E+4", to_string(1.01E+4, 5, 1)); assert_eq!("0.0101", to_string(1.01E-2, 5, 2)); assert_eq!("0.0101", to_string(1.01E-2, 4, 2)); assert_eq!("1.01E-2", to_string(1.01E-2, 5, 1)); assert_eq!("0.78539816339744828", to_string(0.78539816339744830961, 0, 3)); assert_eq!("4.9406564584124654E-324", to_string(4.9406564584124654e-324, 0, 3)); assert_eq!("873.18340000000001", to_string(873.1834, 0, 1)); assert_eq!("8.7318340000000001E+2", to_string(873.1834, 0, 0)); assert_eq!("1.7976931348623157E+308", to_string(1.7976931348623157E+308, 0, 0)); let to_string = |d: f64, precision: usize, width: usize| { let x = Double::from_f64(d); if precision == 0 { format!("{:#1$}", x, width) } else { format!("{:#2$.1$}", x, precision, width) } }; assert_eq!("10", to_string(10.0, 6, 3)); assert_eq!("1.000000e+01", to_string(10.0, 6, 0)); assert_eq!("10100", to_string(1.01E+4, 5, 2)); assert_eq!("1.0100e+04", to_string(1.01E+4, 4, 2)); assert_eq!("1.01000e+04", to_string(1.01E+4, 5, 1)); assert_eq!("0.0101", to_string(1.01E-2, 5, 2)); assert_eq!("0.0101", to_string(1.01E-2, 4, 2)); assert_eq!("1.01000e-02", to_string(1.01E-2, 5, 1)); assert_eq!("0.78539816339744828", to_string(0.78539816339744830961, 0, 3)); assert_eq!("4.94065645841246540e-324", to_string(4.9406564584124654e-324, 0, 3)); assert_eq!("873.18340000000001", to_string(873.1834, 0, 1)); assert_eq!("8.73183400000000010e+02", to_string(873.1834, 0, 0)); assert_eq!("1.79769313486231570e+308", to_string(1.7976931348623157E+308, 0, 0)); assert_eq!("NaN", X87DoubleExtended::from_bits(1 << 64).to_string()); } #[test] fn to_integer() { let mut is_exact = false; assert_eq!( Status::OK.and(10), "10".parse::() .unwrap() .to_u128_r(5, Round::TowardZero, &mut is_exact,) ); assert!(is_exact); assert_eq!( Status::INVALID_OP.and(0), "-10" .parse::() .unwrap() .to_u128_r(5, Round::TowardZero, &mut is_exact,) ); assert!(!is_exact); assert_eq!( Status::INVALID_OP.and(31), "32".parse::() .unwrap() .to_u128_r(5, Round::TowardZero, &mut is_exact,) ); assert!(!is_exact); assert_eq!( Status::INEXACT.and(7), "7.9" .parse::() .unwrap() .to_u128_r(5, Round::TowardZero, &mut is_exact,) ); assert!(!is_exact); assert_eq!( Status::OK.and(-10), "-10" .parse::() .unwrap() .to_i128_r(5, Round::TowardZero, &mut is_exact,) ); assert!(is_exact); assert_eq!( Status::INVALID_OP.and(-16), "-17" .parse::() .unwrap() .to_i128_r(5, Round::TowardZero, &mut is_exact,) ); assert!(!is_exact); assert_eq!( Status::INVALID_OP.and(15), "16".parse::() .unwrap() .to_i128_r(5, Round::TowardZero, &mut is_exact,) ); assert!(!is_exact); } #[test] fn nan() { fn nanbits_from_u128(signaling: bool, negative: bool, payload: u128) -> u128 { let x = if signaling { F::snan(Some(payload)) } else { F::qnan(Some(payload)) }; if negative { (-x).to_bits() } else { x.to_bits() } } let tests_single = [ // expected SNaN Neg payload (0x7fc00000, false, false, 0x00000000), (0xffc00000, false, true, 0x00000000), (0x7fc0ae72, false, false, 0x0000ae72), (0x7fffae72, false, false, 0xffffae72), (0x7fdaae72, false, false, 0x00daae72), (0x7fa00000, true, false, 0x00000000), (0xffa00000, true, true, 0x00000000), (0x7f80ae72, true, false, 0x0000ae72), (0x7fbfae72, true, false, 0xffffae72), (0x7f9aae72, true, false, 0x001aae72), ]; let tests_double = [ // expected SNaN Neg payload (0x7ff8000000000000, false, false, 0x0000000000000000), (0xfff8000000000000, false, true, 0x0000000000000000), (0x7ff800000000ae72, false, false, 0x000000000000ae72), (0x7fffffffffffae72, false, false, 0xffffffffffffae72), (0x7ffdaaaaaaaaae72, false, false, 0x000daaaaaaaaae72), (0x7ff4000000000000, true, false, 0x0000000000000000), (0xfff4000000000000, true, true, 0x0000000000000000), (0x7ff000000000ae72, true, false, 0x000000000000ae72), (0x7ff7ffffffffae72, true, false, 0xffffffffffffae72), (0x7ff1aaaaaaaaae72, true, false, 0x0001aaaaaaaaae72), ]; for (expected, signaling, negative, payload) in tests_single { assert_eq!(expected, nanbits_from_u128::(signaling, negative, payload)); } for (expected, signaling, negative, payload) in tests_double { assert_eq!(expected, nanbits_from_u128::(signaling, negative, payload)); } } #[test] fn string_decimal_error() { assert_eq!("Invalid string length", "".parse::().unwrap_err().0); assert_eq!("String has no digits", "+".parse::().unwrap_err().0); assert_eq!("String has no digits", "-".parse::().unwrap_err().0); assert_eq!("Invalid character in significand", "\0".parse::().unwrap_err().0); assert_eq!("Invalid character in significand", "1\0".parse::().unwrap_err().0); assert_eq!("Invalid character in significand", "1\02".parse::().unwrap_err().0); assert_eq!("Invalid character in significand", "1\02e1".parse::().unwrap_err().0); assert_eq!("Invalid character in exponent", "1e\0".parse::().unwrap_err().0); assert_eq!("Invalid character in exponent", "1e1\0".parse::().unwrap_err().0); assert_eq!("Invalid character in exponent", "1e1\02".parse::().unwrap_err().0); assert_eq!("Invalid character in significand", "1.0f".parse::().unwrap_err().0); assert_eq!("String contains multiple dots", "..".parse::().unwrap_err().0); assert_eq!("String contains multiple dots", "..0".parse::().unwrap_err().0); assert_eq!("String contains multiple dots", "1.0.0".parse::().unwrap_err().0); } #[test] fn string_decimal_significand_error() { assert_eq!("Significand has no digits", ".".parse::().unwrap_err().0); assert_eq!("Significand has no digits", "+.".parse::().unwrap_err().0); assert_eq!("Significand has no digits", "-.".parse::().unwrap_err().0); assert_eq!("Significand has no digits", "e".parse::().unwrap_err().0); assert_eq!("Significand has no digits", "+e".parse::().unwrap_err().0); assert_eq!("Significand has no digits", "-e".parse::().unwrap_err().0); assert_eq!("Significand has no digits", "e1".parse::().unwrap_err().0); assert_eq!("Significand has no digits", "+e1".parse::().unwrap_err().0); assert_eq!("Significand has no digits", "-e1".parse::().unwrap_err().0); assert_eq!("Significand has no digits", ".e1".parse::().unwrap_err().0); assert_eq!("Significand has no digits", "+.e1".parse::().unwrap_err().0); assert_eq!("Significand has no digits", "-.e1".parse::().unwrap_err().0); assert_eq!("Significand has no digits", ".e".parse::().unwrap_err().0); assert_eq!("Significand has no digits", "+.e".parse::().unwrap_err().0); assert_eq!("Significand has no digits", "-.e".parse::().unwrap_err().0); } #[test] fn string_hexadecimal_error() { assert_eq!("Invalid string", "0x".parse::().unwrap_err().0); assert_eq!("Invalid string", "+0x".parse::().unwrap_err().0); assert_eq!("Invalid string", "-0x".parse::().unwrap_err().0); assert_eq!("Hex strings require an exponent", "0x0".parse::().unwrap_err().0); assert_eq!("Hex strings require an exponent", "+0x0".parse::().unwrap_err().0); assert_eq!("Hex strings require an exponent", "-0x0".parse::().unwrap_err().0); assert_eq!("Hex strings require an exponent", "0x0.".parse::().unwrap_err().0); assert_eq!("Hex strings require an exponent", "+0x0.".parse::().unwrap_err().0); assert_eq!("Hex strings require an exponent", "-0x0.".parse::().unwrap_err().0); assert_eq!("Hex strings require an exponent", "0x.0".parse::().unwrap_err().0); assert_eq!("Hex strings require an exponent", "+0x.0".parse::().unwrap_err().0); assert_eq!("Hex strings require an exponent", "-0x.0".parse::().unwrap_err().0); assert_eq!("Hex strings require an exponent", "0x0.0".parse::().unwrap_err().0); assert_eq!("Hex strings require an exponent", "+0x0.0".parse::().unwrap_err().0); assert_eq!("Hex strings require an exponent", "-0x0.0".parse::().unwrap_err().0); assert_eq!("Invalid character in significand", "0x\0".parse::().unwrap_err().0); assert_eq!("Invalid character in significand", "0x1\0".parse::().unwrap_err().0); assert_eq!("Invalid character in significand", "0x1\02".parse::().unwrap_err().0); assert_eq!("Invalid character in significand", "0x1\02p1".parse::().unwrap_err().0); assert_eq!("Invalid character in exponent", "0x1p\0".parse::().unwrap_err().0); assert_eq!("Invalid character in exponent", "0x1p1\0".parse::().unwrap_err().0); assert_eq!("Invalid character in exponent", "0x1p1\02".parse::().unwrap_err().0); assert_eq!("Invalid character in exponent", "0x1p0f".parse::().unwrap_err().0); assert_eq!("String contains multiple dots", "0x..p1".parse::().unwrap_err().0); assert_eq!("String contains multiple dots", "0x..0p1".parse::().unwrap_err().0); assert_eq!("String contains multiple dots", "0x1.0.0p1".parse::().unwrap_err().0); } #[test] fn string_hexadecimal_significand_error() { assert_eq!("Significand has no digits", "0x.".parse::().unwrap_err().0); assert_eq!("Significand has no digits", "+0x.".parse::().unwrap_err().0); assert_eq!("Significand has no digits", "-0x.".parse::().unwrap_err().0); assert_eq!("Significand has no digits", "0xp".parse::().unwrap_err().0); assert_eq!("Significand has no digits", "+0xp".parse::().unwrap_err().0); assert_eq!("Significand has no digits", "-0xp".parse::().unwrap_err().0); assert_eq!("Significand has no digits", "0xp+".parse::().unwrap_err().0); assert_eq!("Significand has no digits", "+0xp+".parse::().unwrap_err().0); assert_eq!("Significand has no digits", "-0xp+".parse::().unwrap_err().0); assert_eq!("Significand has no digits", "0xp-".parse::().unwrap_err().0); assert_eq!("Significand has no digits", "+0xp-".parse::().unwrap_err().0); assert_eq!("Significand has no digits", "-0xp-".parse::().unwrap_err().0); assert_eq!("Significand has no digits", "0x.p".parse::().unwrap_err().0); assert_eq!("Significand has no digits", "+0x.p".parse::().unwrap_err().0); assert_eq!("Significand has no digits", "-0x.p".parse::().unwrap_err().0); assert_eq!("Significand has no digits", "0x.p+".parse::().unwrap_err().0); assert_eq!("Significand has no digits", "+0x.p+".parse::().unwrap_err().0); assert_eq!("Significand has no digits", "-0x.p+".parse::().unwrap_err().0); assert_eq!("Significand has no digits", "0x.p-".parse::().unwrap_err().0); assert_eq!("Significand has no digits", "+0x.p-".parse::().unwrap_err().0); assert_eq!("Significand has no digits", "-0x.p-".parse::().unwrap_err().0); } #[test] fn string_hexadecimal_exponent_error() { assert_eq!("Exponent has no digits", "0x1p".parse::().unwrap_err().0); assert_eq!("Exponent has no digits", "+0x1p".parse::().unwrap_err().0); assert_eq!("Exponent has no digits", "-0x1p".parse::().unwrap_err().0); assert_eq!("Exponent has no digits", "0x1p+".parse::().unwrap_err().0); assert_eq!("Exponent has no digits", "+0x1p+".parse::().unwrap_err().0); assert_eq!("Exponent has no digits", "-0x1p+".parse::().unwrap_err().0); assert_eq!("Exponent has no digits", "0x1p-".parse::().unwrap_err().0); assert_eq!("Exponent has no digits", "+0x1p-".parse::().unwrap_err().0); assert_eq!("Exponent has no digits", "-0x1p-".parse::().unwrap_err().0); assert_eq!("Exponent has no digits", "0x1.p".parse::().unwrap_err().0); assert_eq!("Exponent has no digits", "+0x1.p".parse::().unwrap_err().0); assert_eq!("Exponent has no digits", "-0x1.p".parse::().unwrap_err().0); assert_eq!("Exponent has no digits", "0x1.p+".parse::().unwrap_err().0); assert_eq!("Exponent has no digits", "+0x1.p+".parse::().unwrap_err().0); assert_eq!("Exponent has no digits", "-0x1.p+".parse::().unwrap_err().0); assert_eq!("Exponent has no digits", "0x1.p-".parse::().unwrap_err().0); assert_eq!("Exponent has no digits", "+0x1.p-".parse::().unwrap_err().0); assert_eq!("Exponent has no digits", "-0x1.p-".parse::().unwrap_err().0); assert_eq!("Exponent has no digits", "0x.1p".parse::().unwrap_err().0); assert_eq!("Exponent has no digits", "+0x.1p".parse::().unwrap_err().0); assert_eq!("Exponent has no digits", "-0x.1p".parse::().unwrap_err().0); assert_eq!("Exponent has no digits", "0x.1p+".parse::().unwrap_err().0); assert_eq!("Exponent has no digits", "+0x.1p+".parse::().unwrap_err().0); assert_eq!("Exponent has no digits", "-0x.1p+".parse::().unwrap_err().0); assert_eq!("Exponent has no digits", "0x.1p-".parse::().unwrap_err().0); assert_eq!("Exponent has no digits", "+0x.1p-".parse::().unwrap_err().0); assert_eq!("Exponent has no digits", "-0x.1p-".parse::().unwrap_err().0); assert_eq!("Exponent has no digits", "0x1.1p".parse::().unwrap_err().0); assert_eq!("Exponent has no digits", "+0x1.1p".parse::().unwrap_err().0); assert_eq!("Exponent has no digits", "-0x1.1p".parse::().unwrap_err().0); assert_eq!("Exponent has no digits", "0x1.1p+".parse::().unwrap_err().0); assert_eq!("Exponent has no digits", "+0x1.1p+".parse::().unwrap_err().0); assert_eq!("Exponent has no digits", "-0x1.1p+".parse::().unwrap_err().0); assert_eq!("Exponent has no digits", "0x1.1p-".parse::().unwrap_err().0); assert_eq!("Exponent has no digits", "+0x1.1p-".parse::().unwrap_err().0); assert_eq!("Exponent has no digits", "-0x1.1p-".parse::().unwrap_err().0); } #[test] fn exact_inverse() { // Trivial operation. assert!(Double::from_f64(2.0) .get_exact_inverse() .unwrap() .bitwise_eq(Double::from_f64(0.5))); assert!(Single::from_f32(2.0) .get_exact_inverse() .unwrap() .bitwise_eq(Single::from_f32(0.5))); assert!("2.0" .parse::() .unwrap() .get_exact_inverse() .unwrap() .bitwise_eq("0.5".parse::().unwrap())); assert!("2.0" .parse::() .unwrap() .get_exact_inverse() .unwrap() .bitwise_eq("0.5".parse::().unwrap())); // FLT_MIN assert!(Single::from_f32(1.17549435e-38) .get_exact_inverse() .unwrap() .bitwise_eq(Single::from_f32(8.5070592e+37))); // Large float, inverse is a denormal. assert!(Single::from_f32(1.7014118e38).get_exact_inverse().is_none()); // Zero assert!(Double::from_f64(0.0).get_exact_inverse().is_none()); // Denormalized float assert!(Single::from_f32(1.40129846e-45).get_exact_inverse().is_none()); } #[test] fn round_to_integral() { let t = Double::from_f64(-0.5); assert_eq!(-0.0, t.round_to_integral(Round::TowardZero).value.to_f64()); assert_eq!(-1.0, t.round_to_integral(Round::TowardNegative).value.to_f64()); assert_eq!(-0.0, t.round_to_integral(Round::TowardPositive).value.to_f64()); assert_eq!(-0.0, t.round_to_integral(Round::NearestTiesToEven).value.to_f64()); let s = Double::from_f64(3.14); assert_eq!(3.0, s.round_to_integral(Round::TowardZero).value.to_f64()); assert_eq!(3.0, s.round_to_integral(Round::TowardNegative).value.to_f64()); assert_eq!(4.0, s.round_to_integral(Round::TowardPositive).value.to_f64()); assert_eq!(3.0, s.round_to_integral(Round::NearestTiesToEven).value.to_f64()); let r = Double::largest(); assert_eq!(r.to_f64(), r.round_to_integral(Round::TowardZero).value.to_f64()); assert_eq!(r.to_f64(), r.round_to_integral(Round::TowardNegative).value.to_f64()); assert_eq!(r.to_f64(), r.round_to_integral(Round::TowardPositive).value.to_f64()); assert_eq!(r.to_f64(), r.round_to_integral(Round::NearestTiesToEven).value.to_f64()); let p = Double::ZERO.round_to_integral(Round::TowardZero).value; assert_eq!(0.0, p.to_f64()); let p = (-Double::ZERO).round_to_integral(Round::TowardZero).value; assert_eq!(-0.0, p.to_f64()); let p = Double::NAN.round_to_integral(Round::TowardZero).value; assert!(p.to_f64().is_nan()); let p = Double::INFINITY.round_to_integral(Round::TowardZero).value; assert!(p.to_f64().is_infinite() && p.to_f64() > 0.0); let p = (-Double::INFINITY).round_to_integral(Round::TowardZero).value; assert!(p.to_f64().is_infinite() && p.to_f64() < 0.0); let mut status; let p = unpack!(status=, Double::NAN.round_to_integral(Round::TowardZero)); assert!(p.is_nan()); assert!(!p.is_negative()); assert_eq!(Status::OK, status); let p = unpack!(status=, (-Double::NAN).round_to_integral(Round::TowardZero)); assert!(p.is_nan()); assert!(p.is_negative()); assert_eq!(Status::OK, status); let p = unpack!(status=, Double::snan(None).round_to_integral(Round::TowardZero)); assert!(p.is_nan()); assert!(!p.is_signaling()); assert!(!p.is_negative()); assert_eq!(Status::INVALID_OP, status); let p = unpack!(status=, (-Double::snan(None)).round_to_integral(Round::TowardZero)); assert!(p.is_nan()); assert!(!p.is_signaling()); assert!(p.is_negative()); assert_eq!(Status::INVALID_OP, status); let p = unpack!(status=, Double::INFINITY.round_to_integral(Round::TowardZero)); assert!(p.is_infinite()); assert!(!p.is_negative()); assert_eq!(Status::OK, status); let p = unpack!(status=, (-Double::INFINITY).round_to_integral(Round::TowardZero)); assert!(p.is_infinite()); assert!(p.is_negative()); assert_eq!(Status::OK, status); let p = unpack!(status=, Double::ZERO.round_to_integral(Round::TowardZero)); assert!(p.is_zero()); assert!(!p.is_negative()); assert_eq!(Status::OK, status); let p = unpack!(status=, Double::ZERO.round_to_integral(Round::TowardNegative)); assert!(p.is_zero()); assert!(!p.is_negative()); assert_eq!(Status::OK, status); let p = unpack!(status=, (-Double::ZERO).round_to_integral(Round::TowardZero)); assert!(p.is_zero()); assert!(p.is_negative()); assert_eq!(Status::OK, status); let p = unpack!(status=, (-Double::ZERO).round_to_integral(Round::TowardNegative)); assert!(p.is_zero()); assert!(p.is_negative()); assert_eq!(Status::OK, status); let p = unpack!(status=, Double::from_f64(1E-100).round_to_integral(Round::TowardNegative)); assert!(p.is_zero()); assert!(!p.is_negative()); assert_eq!(Status::INEXACT, status); let p = unpack!(status=, Double::from_f64(1E-100).round_to_integral(Round::TowardPositive)); assert_eq!(1.0, p.to_f64()); assert!(!p.is_negative()); assert_eq!(Status::INEXACT, status); let p = unpack!(status=, Double::from_f64(-1E-100).round_to_integral(Round::TowardNegative)); assert!(p.is_negative()); assert_eq!(-1.0, p.to_f64()); assert_eq!(Status::INEXACT, status); let p = unpack!(status=, Double::from_f64(-1E-100).round_to_integral(Round::TowardPositive)); assert!(p.is_zero()); assert!(p.is_negative()); assert_eq!(Status::INEXACT, status); let p = unpack!(status=, Double::from_f64(10.0).round_to_integral(Round::TowardZero)); assert_eq!(10.0, p.to_f64()); assert_eq!(Status::OK, status); let p = unpack!(status=, Double::from_f64(10.5).round_to_integral(Round::TowardZero)); assert_eq!(10.0, p.to_f64()); assert_eq!(Status::INEXACT, status); let p = unpack!(status=, Double::from_f64(10.5).round_to_integral(Round::TowardPositive)); assert_eq!(11.0, p.to_f64()); assert_eq!(Status::INEXACT, status); let p = unpack!(status=, Double::from_f64(10.5).round_to_integral(Round::TowardNegative)); assert_eq!(10.0, p.to_f64()); assert_eq!(Status::INEXACT, status); let p = unpack!(status=, Double::from_f64(10.5).round_to_integral(Round::NearestTiesToAway)); assert_eq!(11.0, p.to_f64()); assert_eq!(Status::INEXACT, status); let p = unpack!(status=, Double::from_f64(10.5).round_to_integral(Round::NearestTiesToEven)); assert_eq!(10.0, p.to_f64()); assert_eq!(Status::INEXACT, status); } #[test] fn is_integer() { let t = Double::from_f64(-0.0); assert!(t.is_integer()); let t = Double::from_f64(3.14159); assert!(!t.is_integer()); let t = Double::NAN; assert!(!t.is_integer()); let t = Double::INFINITY; assert!(!t.is_integer()); let t = -Double::INFINITY; assert!(!t.is_integer()); let t = Double::largest(); assert!(t.is_integer()); } #[test] fn largest() { assert_eq!(3.402823466e+38, Single::largest().to_f32()); assert_eq!(1.7976931348623158e+308, Double::largest().to_f64()); assert_eq!(448.0, Float8E4M3FN::largest().to_f64()); } #[test] fn smallest() { let test = Single::SMALLEST; let expected = "0x0.000002p-126".parse::().unwrap(); assert!(!test.is_negative()); assert!(test.is_finite_non_zero()); assert!(test.is_denormal()); assert!(test.bitwise_eq(expected)); let test = -Single::SMALLEST; let expected = "-0x0.000002p-126".parse::().unwrap(); assert!(test.is_negative()); assert!(test.is_finite_non_zero()); assert!(test.is_denormal()); assert!(test.bitwise_eq(expected)); let test = Quad::SMALLEST; let expected = "0x0.0000000000000000000000000001p-16382".parse::().unwrap(); assert!(!test.is_negative()); assert!(test.is_finite_non_zero()); assert!(test.is_denormal()); assert!(test.bitwise_eq(expected)); let test = -Quad::SMALLEST; let expected = "-0x0.0000000000000000000000000001p-16382".parse::().unwrap(); assert!(test.is_negative()); assert!(test.is_finite_non_zero()); assert!(test.is_denormal()); assert!(test.bitwise_eq(expected)); } #[test] fn smallest_normalized() { let test = Single::smallest_normalized(); let expected = "0x1p-126".parse::().unwrap(); assert!(!test.is_negative()); assert!(test.is_finite_non_zero()); assert!(!test.is_denormal()); assert!(test.bitwise_eq(expected)); assert!(test.is_smallest_normalized()); let test = -Single::smallest_normalized(); let expected = "-0x1p-126".parse::().unwrap(); assert!(test.is_negative()); assert!(test.is_finite_non_zero()); assert!(!test.is_denormal()); assert!(test.bitwise_eq(expected)); assert!(test.is_smallest_normalized()); let test = Double::smallest_normalized(); let expected = "0x1p-1022".parse::().unwrap(); assert!(!test.is_negative()); assert!(test.is_finite_non_zero()); assert!(!test.is_denormal()); assert!(test.bitwise_eq(expected)); assert!(test.is_smallest_normalized()); let test = -Double::smallest_normalized(); let expected = "-0x1p-1022".parse::().unwrap(); assert!(test.is_negative()); assert!(test.is_finite_non_zero()); assert!(!test.is_denormal()); assert!(test.bitwise_eq(expected)); assert!(test.is_smallest_normalized()); let test = Quad::smallest_normalized(); let expected = "0x1p-16382".parse::().unwrap(); assert!(!test.is_negative()); assert!(test.is_finite_non_zero()); assert!(!test.is_denormal()); assert!(test.bitwise_eq(expected)); assert!(test.is_smallest_normalized()); let test = -Quad::smallest_normalized(); let expected = "-0x1p-16382".parse::().unwrap(); assert!(test.is_negative()); assert!(test.is_finite_non_zero()); assert!(!test.is_denormal()); assert!(test.bitwise_eq(expected)); assert!(test.is_smallest_normalized()); } #[test] fn zero() { assert_eq!(0.0, Single::from_f32(0.0).to_f32()); assert_eq!(-0.0, Single::from_f32(-0.0).to_f32()); assert!(Single::from_f32(-0.0).is_negative()); assert_eq!(0.0, Double::from_f64(0.0).to_f64()); assert_eq!(-0.0, Double::from_f64(-0.0).to_f64()); assert!(Double::from_f64(-0.0).is_negative()); fn test(sign: bool, bits: u128) { let test = if sign { -F::ZERO } else { F::ZERO }; let pattern = if sign { "-0x0p+0" } else { "0x0p+0" }; let expected = pattern.parse::().unwrap(); assert!(test.is_zero()); assert_eq!(sign, test.is_negative()); assert!(test.bitwise_eq(expected)); assert_eq!(bits, test.to_bits()); } test::(false, 0); test::(true, 0x8000); test::(false, 0); test::(true, 0x80000000); test::(false, 0); test::(true, 0x8000000000000000); test::(false, 0); test::(true, 0x8000000000000000_0000000000000000); test::(false, 0); test::(true, 0x8000_0000000000000000); test::(false, 0); test::(true, 0x80); test::(false, 0); test::(true, 0x80); } #[test] fn copy_sign() { assert!(Double::from_f64(-42.0).bitwise_eq(Double::from_f64(42.0).copy_sign(Double::from_f64(-1.0),),)); assert!(Double::from_f64(42.0).bitwise_eq(Double::from_f64(-42.0).copy_sign(Double::from_f64(1.0),),)); assert!(Double::from_f64(-42.0).bitwise_eq(Double::from_f64(-42.0).copy_sign(Double::from_f64(-1.0),),)); assert!(Double::from_f64(42.0).bitwise_eq(Double::from_f64(42.0).copy_sign(Double::from_f64(1.0),),)); } #[test] fn convert() { let mut loses_info = false; let mut status; let test = "1.0".parse::().unwrap(); let test: Single = test.convert(&mut loses_info).value; assert_eq!(1.0, test.to_f32()); assert!(!loses_info); let mut test = "0x1p-53".parse::().unwrap(); let one = "1.0".parse::().unwrap(); test += one; let test: Double = test.convert(&mut loses_info).value; assert_eq!(1.0, test.to_f64()); assert!(loses_info); let mut test = "0x1p-53".parse::().unwrap(); let one = "1.0".parse::().unwrap(); test += one; let test: Double = test.convert(&mut loses_info).value; assert_eq!(1.0, test.to_f64()); assert!(loses_info); let test = "0xf.fffffffp+28".parse::().unwrap(); let test: Double = test.convert(&mut loses_info).value; assert_eq!(4294967295.0, test.to_f64()); assert!(!loses_info); let test = Single::snan(None); let test: X87DoubleExtended = unpack!(status=, test.convert(&mut loses_info)); // Conversion quiets the SNAN, so now 2 bits of the 64-bit significand should be set. assert!(test.bitwise_eq(X87DoubleExtended::qnan(Some(0x6000000000000000)))); assert!(!loses_info); assert_eq!(status, Status::INVALID_OP); let test = Single::qnan(None); let x87_qnan = X87DoubleExtended::qnan(None); let test: X87DoubleExtended = test.convert(&mut loses_info).value; assert!(test.bitwise_eq(x87_qnan)); assert!(!loses_info); // NOTE(eddyb) these were mistakenly noops upstream, here they're already // fixed (by instead converting from `Double` to `X87DoubleExtended`), // see also upstream issue https://github.com/llvm/llvm-project/issues/63842. let test = Double::snan(None); let test: X87DoubleExtended = test.convert(&mut loses_info).value; // Conversion quiets the SNAN, so now 2 bits of the 64-bit significand should be set. assert!(test.bitwise_eq(X87DoubleExtended::qnan(Some(0x6000000000000000)))); assert!(!loses_info); let test = Double::qnan(None); let test: X87DoubleExtended = test.convert(&mut loses_info).value; assert!(test.bitwise_eq(x87_qnan)); assert!(!loses_info); // The payload is lost in truncation, but we retain NaN by setting the quiet bit. let test = Double::snan(Some(1)); let test: Single = unpack!(status=, test.convert(&mut loses_info)); assert_eq!(0x7fc00000, test.to_bits()); assert!(loses_info); assert_eq!(status, Status::INVALID_OP); // The payload is lost in truncation. QNaN remains QNaN. let test = Double::qnan(Some(1)); let test: Single = unpack!(status=, test.convert(&mut loses_info)); assert_eq!(0x7fc00000, test.to_bits()); assert!(loses_info); assert_eq!(status, Status::OK); // Test that subnormals are handled correctly in double to float conversion let test = "0x0.0000010000000p-1022".parse::().unwrap(); let test: Single = unpack!(status=, test.convert(&mut loses_info)); assert_eq!(0.0, test.to_f32()); assert!(loses_info); let test = "0x0.0000010000001p-1022".parse::().unwrap(); let test: Single = unpack!(status=, test.convert(&mut loses_info)); assert_eq!(0.0, test.to_f32()); assert!(loses_info); let test = "-0x0.0000010000001p-1022".parse::().unwrap(); let test: Single = unpack!(status=, test.convert(&mut loses_info)); assert_eq!(0.0, test.to_f32()); assert!(loses_info); let test = "0x0.0000020000000p-1022".parse::().unwrap(); let test: Single = unpack!(status=, test.convert(&mut loses_info)); assert_eq!(0.0, test.to_f32()); assert!(loses_info); let test = "0x0.0000020000001p-1022".parse::().unwrap(); let test: Single = unpack!(status=, test.convert(&mut loses_info)); assert_eq!(0.0, test.to_f32()); assert!(loses_info); // Test subnormal conversion to bfloat let test = "0x0.01p-126".parse::().unwrap(); let test: BFloat = unpack!(status=, test.convert(&mut loses_info)); assert_eq!(0.0, test.to_f32()); assert!(loses_info); let test = "0x0.02p-126".parse::().unwrap(); let test: BFloat = unpack!(status=, test.convert(&mut loses_info)); assert_eq!(0x01, test.to_bits()); assert!(!loses_info); let test = "0x0.01p-126".parse::().unwrap(); let test: BFloat = unpack!(status=, test.convert_r(Round::NearestTiesToAway, &mut loses_info)); assert_eq!(0x01, test.to_bits()); assert!(loses_info); } #[test] fn is_negative() { let t = "0x1p+0".parse::().unwrap(); assert!(!t.is_negative()); let t = "-0x1p+0".parse::().unwrap(); assert!(t.is_negative()); assert!(!Single::INFINITY.is_negative()); assert!((-Single::INFINITY).is_negative()); assert!(!Single::ZERO.is_negative()); assert!((-Single::ZERO).is_negative()); assert!(!Single::NAN.is_negative()); assert!((-Single::NAN).is_negative()); assert!(!Single::snan(None).is_negative()); assert!((-Single::snan(None)).is_negative()); } #[test] fn is_normal() { let t = "0x1p+0".parse::().unwrap(); assert!(t.is_normal()); assert!(!Single::INFINITY.is_normal()); assert!(!Single::ZERO.is_normal()); assert!(!Single::NAN.is_normal()); assert!(!Single::snan(None).is_normal()); assert!(!"0x1p-149".parse::().unwrap().is_normal()); } #[test] fn is_finite() { let t = "0x1p+0".parse::().unwrap(); assert!(t.is_finite()); assert!(!Single::INFINITY.is_finite()); assert!(Single::ZERO.is_finite()); assert!(!Single::NAN.is_finite()); assert!(!Single::snan(None).is_finite()); assert!("0x1p-149".parse::().unwrap().is_finite()); } #[test] fn is_infinite() { let t = "0x1p+0".parse::().unwrap(); assert!(!t.is_infinite()); let pos_inf = Single::INFINITY; let neg_inf = -Single::INFINITY; assert!(pos_inf.is_infinite()); assert!(pos_inf.is_pos_infinity()); assert!(!pos_inf.is_neg_infinity()); assert!(neg_inf.is_infinite()); assert!(!neg_inf.is_pos_infinity()); assert!(neg_inf.is_neg_infinity()); assert!(!Single::ZERO.is_infinite()); assert!(!Single::NAN.is_infinite()); assert!(!Single::snan(None).is_infinite()); assert!(!"0x1p-149".parse::().unwrap().is_infinite()); } #[test] fn is_nan() { let t = "0x1p+0".parse::().unwrap(); assert!(!t.is_nan()); assert!(!Single::INFINITY.is_nan()); assert!(!Single::ZERO.is_nan()); assert!(Single::NAN.is_nan()); assert!(Single::snan(None).is_nan()); assert!(!"0x1p-149".parse::().unwrap().is_nan()); } #[test] fn is_finite_non_zero() { // Test positive/negative normal value. assert!("0x1p+0".parse::().unwrap().is_finite_non_zero()); assert!("-0x1p+0".parse::().unwrap().is_finite_non_zero()); // Test positive/negative denormal value. assert!("0x1p-149".parse::().unwrap().is_finite_non_zero()); assert!("-0x1p-149".parse::().unwrap().is_finite_non_zero()); // Test +/- Infinity. assert!(!Single::INFINITY.is_finite_non_zero()); assert!(!(-Single::INFINITY).is_finite_non_zero()); // Test +/- Zero. assert!(!Single::ZERO.is_finite_non_zero()); assert!(!(-Single::ZERO).is_finite_non_zero()); // Test +/- qNaN. +/- dont mean anything with qNaN but paranoia can't hurt in // this instance. assert!(!Single::NAN.is_finite_non_zero()); assert!(!(-Single::NAN).is_finite_non_zero()); // Test +/- sNaN. +/- dont mean anything with sNaN but paranoia can't hurt in // this instance. assert!(!Single::snan(None).is_finite_non_zero()); assert!(!(-Single::snan(None)).is_finite_non_zero()); } #[test] fn add() { // Test Special Cases against each other and normal values. let p_inf = Single::INFINITY; let m_inf = -Single::INFINITY; let p_zero = Single::ZERO; let m_zero = -Single::ZERO; let qnan = Single::NAN; let snan = "snan123".parse::().unwrap(); let p_normal_value = "0x1p+0".parse::().unwrap(); let m_normal_value = "-0x1p+0".parse::().unwrap(); let p_largest_value = Single::largest(); let m_largest_value = -Single::largest(); let p_smallest_value = Single::SMALLEST; let m_smallest_value = -Single::SMALLEST; let p_smallest_normalized = Single::smallest_normalized(); let m_smallest_normalized = -Single::smallest_normalized(); let overflow_status = Status::OVERFLOW | Status::INEXACT; let special_cases = [ (p_inf, p_inf, "inf", Status::OK, Category::Infinity), (p_inf, m_inf, "nan", Status::INVALID_OP, Category::NaN), (p_inf, p_zero, "inf", Status::OK, Category::Infinity), (p_inf, m_zero, "inf", Status::OK, Category::Infinity), (p_inf, qnan, "nan", Status::OK, Category::NaN), (p_inf, snan, "nan123", Status::INVALID_OP, Category::NaN), (p_inf, p_normal_value, "inf", Status::OK, Category::Infinity), (p_inf, m_normal_value, "inf", Status::OK, Category::Infinity), (p_inf, p_largest_value, "inf", Status::OK, Category::Infinity), (p_inf, m_largest_value, "inf", Status::OK, Category::Infinity), (p_inf, p_smallest_value, "inf", Status::OK, Category::Infinity), (p_inf, m_smallest_value, "inf", Status::OK, Category::Infinity), (p_inf, p_smallest_normalized, "inf", Status::OK, Category::Infinity), (p_inf, m_smallest_normalized, "inf", Status::OK, Category::Infinity), (m_inf, p_inf, "nan", Status::INVALID_OP, Category::NaN), (m_inf, m_inf, "-inf", Status::OK, Category::Infinity), (m_inf, p_zero, "-inf", Status::OK, Category::Infinity), (m_inf, m_zero, "-inf", Status::OK, Category::Infinity), (m_inf, qnan, "nan", Status::OK, Category::NaN), (m_inf, snan, "nan123", Status::INVALID_OP, Category::NaN), (m_inf, p_normal_value, "-inf", Status::OK, Category::Infinity), (m_inf, m_normal_value, "-inf", Status::OK, Category::Infinity), (m_inf, p_largest_value, "-inf", Status::OK, Category::Infinity), (m_inf, m_largest_value, "-inf", Status::OK, Category::Infinity), (m_inf, p_smallest_value, "-inf", Status::OK, Category::Infinity), (m_inf, m_smallest_value, "-inf", Status::OK, Category::Infinity), (m_inf, p_smallest_normalized, "-inf", Status::OK, Category::Infinity), (m_inf, m_smallest_normalized, "-inf", Status::OK, Category::Infinity), (p_zero, p_inf, "inf", Status::OK, Category::Infinity), (p_zero, m_inf, "-inf", Status::OK, Category::Infinity), (p_zero, p_zero, "0x0p+0", Status::OK, Category::Zero), (p_zero, m_zero, "0x0p+0", Status::OK, Category::Zero), (p_zero, qnan, "nan", Status::OK, Category::NaN), (p_zero, snan, "nan123", Status::INVALID_OP, Category::NaN), (p_zero, p_normal_value, "0x1p+0", Status::OK, Category::Normal), (p_zero, m_normal_value, "-0x1p+0", Status::OK, Category::Normal), (p_zero, p_largest_value, "0x1.fffffep+127", Status::OK, Category::Normal), (p_zero, m_largest_value, "-0x1.fffffep+127", Status::OK, Category::Normal), (p_zero, p_smallest_value, "0x1p-149", Status::OK, Category::Normal), (p_zero, m_smallest_value, "-0x1p-149", Status::OK, Category::Normal), (p_zero, p_smallest_normalized, "0x1p-126", Status::OK, Category::Normal), (p_zero, m_smallest_normalized, "-0x1p-126", Status::OK, Category::Normal), (m_zero, p_inf, "inf", Status::OK, Category::Infinity), (m_zero, m_inf, "-inf", Status::OK, Category::Infinity), (m_zero, p_zero, "0x0p+0", Status::OK, Category::Zero), (m_zero, m_zero, "-0x0p+0", Status::OK, Category::Zero), (m_zero, qnan, "nan", Status::OK, Category::NaN), (m_zero, snan, "nan123", Status::INVALID_OP, Category::NaN), (m_zero, p_normal_value, "0x1p+0", Status::OK, Category::Normal), (m_zero, m_normal_value, "-0x1p+0", Status::OK, Category::Normal), (m_zero, p_largest_value, "0x1.fffffep+127", Status::OK, Category::Normal), (m_zero, m_largest_value, "-0x1.fffffep+127", Status::OK, Category::Normal), (m_zero, p_smallest_value, "0x1p-149", Status::OK, Category::Normal), (m_zero, m_smallest_value, "-0x1p-149", Status::OK, Category::Normal), (m_zero, p_smallest_normalized, "0x1p-126", Status::OK, Category::Normal), (m_zero, m_smallest_normalized, "-0x1p-126", Status::OK, Category::Normal), (qnan, p_inf, "nan", Status::OK, Category::NaN), (qnan, m_inf, "nan", Status::OK, Category::NaN), (qnan, p_zero, "nan", Status::OK, Category::NaN), (qnan, m_zero, "nan", Status::OK, Category::NaN), (qnan, qnan, "nan", Status::OK, Category::NaN), (qnan, snan, "nan", Status::INVALID_OP, Category::NaN), (qnan, p_normal_value, "nan", Status::OK, Category::NaN), (qnan, m_normal_value, "nan", Status::OK, Category::NaN), (qnan, p_largest_value, "nan", Status::OK, Category::NaN), (qnan, m_largest_value, "nan", Status::OK, Category::NaN), (qnan, p_smallest_value, "nan", Status::OK, Category::NaN), (qnan, m_smallest_value, "nan", Status::OK, Category::NaN), (qnan, p_smallest_normalized, "nan", Status::OK, Category::NaN), (qnan, m_smallest_normalized, "nan", Status::OK, Category::NaN), (snan, p_inf, "nan123", Status::INVALID_OP, Category::NaN), (snan, m_inf, "nan123", Status::INVALID_OP, Category::NaN), (snan, p_zero, "nan123", Status::INVALID_OP, Category::NaN), (snan, m_zero, "nan123", Status::INVALID_OP, Category::NaN), (snan, qnan, "nan123", Status::INVALID_OP, Category::NaN), (snan, snan, "nan123", Status::INVALID_OP, Category::NaN), (snan, p_normal_value, "nan123", Status::INVALID_OP, Category::NaN), (snan, m_normal_value, "nan123", Status::INVALID_OP, Category::NaN), (snan, p_largest_value, "nan123", Status::INVALID_OP, Category::NaN), (snan, m_largest_value, "nan123", Status::INVALID_OP, Category::NaN), (snan, p_smallest_value, "nan123", Status::INVALID_OP, Category::NaN), (snan, m_smallest_value, "nan123", Status::INVALID_OP, Category::NaN), (snan, p_smallest_normalized, "nan123", Status::INVALID_OP, Category::NaN), (snan, m_smallest_normalized, "nan123", Status::INVALID_OP, Category::NaN), (p_normal_value, p_inf, "inf", Status::OK, Category::Infinity), (p_normal_value, m_inf, "-inf", Status::OK, Category::Infinity), (p_normal_value, p_zero, "0x1p+0", Status::OK, Category::Normal), (p_normal_value, m_zero, "0x1p+0", Status::OK, Category::Normal), (p_normal_value, qnan, "nan", Status::OK, Category::NaN), (p_normal_value, snan, "nan123", Status::INVALID_OP, Category::NaN), (p_normal_value, p_normal_value, "0x1p+1", Status::OK, Category::Normal), (p_normal_value, m_normal_value, "0x0p+0", Status::OK, Category::Zero), (p_normal_value, p_largest_value, "0x1.fffffep+127", Status::INEXACT, Category::Normal), (p_normal_value, m_largest_value, "-0x1.fffffep+127", Status::INEXACT, Category::Normal), (p_normal_value, p_smallest_value, "0x1p+0", Status::INEXACT, Category::Normal), (p_normal_value, m_smallest_value, "0x1p+0", Status::INEXACT, Category::Normal), (p_normal_value, p_smallest_normalized, "0x1p+0", Status::INEXACT, Category::Normal), (p_normal_value, m_smallest_normalized, "0x1p+0", Status::INEXACT, Category::Normal), (m_normal_value, p_inf, "inf", Status::OK, Category::Infinity), (m_normal_value, m_inf, "-inf", Status::OK, Category::Infinity), (m_normal_value, p_zero, "-0x1p+0", Status::OK, Category::Normal), (m_normal_value, m_zero, "-0x1p+0", Status::OK, Category::Normal), (m_normal_value, qnan, "nan", Status::OK, Category::NaN), (m_normal_value, snan, "nan123", Status::INVALID_OP, Category::NaN), (m_normal_value, p_normal_value, "0x0p+0", Status::OK, Category::Zero), (m_normal_value, m_normal_value, "-0x1p+1", Status::OK, Category::Normal), (m_normal_value, p_largest_value, "0x1.fffffep+127", Status::INEXACT, Category::Normal), (m_normal_value, m_largest_value, "-0x1.fffffep+127", Status::INEXACT, Category::Normal), (m_normal_value, p_smallest_value, "-0x1p+0", Status::INEXACT, Category::Normal), (m_normal_value, m_smallest_value, "-0x1p+0", Status::INEXACT, Category::Normal), (m_normal_value, p_smallest_normalized, "-0x1p+0", Status::INEXACT, Category::Normal), (m_normal_value, m_smallest_normalized, "-0x1p+0", Status::INEXACT, Category::Normal), (p_largest_value, p_inf, "inf", Status::OK, Category::Infinity), (p_largest_value, m_inf, "-inf", Status::OK, Category::Infinity), (p_largest_value, p_zero, "0x1.fffffep+127", Status::OK, Category::Normal), (p_largest_value, m_zero, "0x1.fffffep+127", Status::OK, Category::Normal), (p_largest_value, qnan, "nan", Status::OK, Category::NaN), (p_largest_value, snan, "nan123", Status::INVALID_OP, Category::NaN), (p_largest_value, p_normal_value, "0x1.fffffep+127", Status::INEXACT, Category::Normal), (p_largest_value, m_normal_value, "0x1.fffffep+127", Status::INEXACT, Category::Normal), (p_largest_value, p_largest_value, "inf", overflow_status, Category::Infinity), (p_largest_value, m_largest_value, "0x0p+0", Status::OK, Category::Zero), (p_largest_value, p_smallest_value, "0x1.fffffep+127", Status::INEXACT, Category::Normal), (p_largest_value, m_smallest_value, "0x1.fffffep+127", Status::INEXACT, Category::Normal), (p_largest_value, p_smallest_normalized, "0x1.fffffep+127", Status::INEXACT, Category::Normal), (p_largest_value, m_smallest_normalized, "0x1.fffffep+127", Status::INEXACT, Category::Normal), (m_largest_value, p_inf, "inf", Status::OK, Category::Infinity), (m_largest_value, m_inf, "-inf", Status::OK, Category::Infinity), (m_largest_value, p_zero, "-0x1.fffffep+127", Status::OK, Category::Normal), (m_largest_value, m_zero, "-0x1.fffffep+127", Status::OK, Category::Normal), (m_largest_value, qnan, "nan", Status::OK, Category::NaN), (m_largest_value, snan, "nan123", Status::INVALID_OP, Category::NaN), (m_largest_value, p_normal_value, "-0x1.fffffep+127", Status::INEXACT, Category::Normal), (m_largest_value, m_normal_value, "-0x1.fffffep+127", Status::INEXACT, Category::Normal), (m_largest_value, p_largest_value, "0x0p+0", Status::OK, Category::Zero), (m_largest_value, m_largest_value, "-inf", overflow_status, Category::Infinity), (m_largest_value, p_smallest_value, "-0x1.fffffep+127", Status::INEXACT, Category::Normal), (m_largest_value, m_smallest_value, "-0x1.fffffep+127", Status::INEXACT, Category::Normal), (m_largest_value, p_smallest_normalized, "-0x1.fffffep+127", Status::INEXACT, Category::Normal), (m_largest_value, m_smallest_normalized, "-0x1.fffffep+127", Status::INEXACT, Category::Normal), (p_smallest_value, p_inf, "inf", Status::OK, Category::Infinity), (p_smallest_value, m_inf, "-inf", Status::OK, Category::Infinity), (p_smallest_value, p_zero, "0x1p-149", Status::OK, Category::Normal), (p_smallest_value, m_zero, "0x1p-149", Status::OK, Category::Normal), (p_smallest_value, qnan, "nan", Status::OK, Category::NaN), (p_smallest_value, snan, "nan123", Status::INVALID_OP, Category::NaN), (p_smallest_value, p_normal_value, "0x1p+0", Status::INEXACT, Category::Normal), (p_smallest_value, m_normal_value, "-0x1p+0", Status::INEXACT, Category::Normal), (p_smallest_value, p_largest_value, "0x1.fffffep+127", Status::INEXACT, Category::Normal), (p_smallest_value, m_largest_value, "-0x1.fffffep+127", Status::INEXACT, Category::Normal), (p_smallest_value, p_smallest_value, "0x1p-148", Status::OK, Category::Normal), (p_smallest_value, m_smallest_value, "0x0p+0", Status::OK, Category::Zero), (p_smallest_value, p_smallest_normalized, "0x1.000002p-126", Status::OK, Category::Normal), (p_smallest_value, m_smallest_normalized, "-0x1.fffffcp-127", Status::OK, Category::Normal), (m_smallest_value, p_inf, "inf", Status::OK, Category::Infinity), (m_smallest_value, m_inf, "-inf", Status::OK, Category::Infinity), (m_smallest_value, p_zero, "-0x1p-149", Status::OK, Category::Normal), (m_smallest_value, m_zero, "-0x1p-149", Status::OK, Category::Normal), (m_smallest_value, qnan, "nan", Status::OK, Category::NaN), (m_smallest_value, snan, "nan123", Status::INVALID_OP, Category::NaN), (m_smallest_value, p_normal_value, "0x1p+0", Status::INEXACT, Category::Normal), (m_smallest_value, m_normal_value, "-0x1p+0", Status::INEXACT, Category::Normal), (m_smallest_value, p_largest_value, "0x1.fffffep+127", Status::INEXACT, Category::Normal), (m_smallest_value, m_largest_value, "-0x1.fffffep+127", Status::INEXACT, Category::Normal), (m_smallest_value, p_smallest_value, "0x0p+0", Status::OK, Category::Zero), (m_smallest_value, m_smallest_value, "-0x1p-148", Status::OK, Category::Normal), (m_smallest_value, p_smallest_normalized, "0x1.fffffcp-127", Status::OK, Category::Normal), (m_smallest_value, m_smallest_normalized, "-0x1.000002p-126", Status::OK, Category::Normal), (p_smallest_normalized, p_inf, "inf", Status::OK, Category::Infinity), (p_smallest_normalized, m_inf, "-inf", Status::OK, Category::Infinity), (p_smallest_normalized, p_zero, "0x1p-126", Status::OK, Category::Normal), (p_smallest_normalized, m_zero, "0x1p-126", Status::OK, Category::Normal), (p_smallest_normalized, qnan, "nan", Status::OK, Category::NaN), (p_smallest_normalized, snan, "nan123", Status::INVALID_OP, Category::NaN), (p_smallest_normalized, p_normal_value, "0x1p+0", Status::INEXACT, Category::Normal), (p_smallest_normalized, m_normal_value, "-0x1p+0", Status::INEXACT, Category::Normal), (p_smallest_normalized, p_largest_value, "0x1.fffffep+127", Status::INEXACT, Category::Normal), (p_smallest_normalized, m_largest_value, "-0x1.fffffep+127", Status::INEXACT, Category::Normal), (p_smallest_normalized, p_smallest_value, "0x1.000002p-126", Status::OK, Category::Normal), (p_smallest_normalized, m_smallest_value, "0x1.fffffcp-127", Status::OK, Category::Normal), (p_smallest_normalized, p_smallest_normalized, "0x1p-125", Status::OK, Category::Normal), (p_smallest_normalized, m_smallest_normalized, "0x0p+0", Status::OK, Category::Zero), (m_smallest_normalized, p_inf, "inf", Status::OK, Category::Infinity), (m_smallest_normalized, m_inf, "-inf", Status::OK, Category::Infinity), (m_smallest_normalized, p_zero, "-0x1p-126", Status::OK, Category::Normal), (m_smallest_normalized, m_zero, "-0x1p-126", Status::OK, Category::Normal), (m_smallest_normalized, qnan, "nan", Status::OK, Category::NaN), (m_smallest_normalized, snan, "nan123", Status::INVALID_OP, Category::NaN), (m_smallest_normalized, p_normal_value, "0x1p+0", Status::INEXACT, Category::Normal), (m_smallest_normalized, m_normal_value, "-0x1p+0", Status::INEXACT, Category::Normal), (m_smallest_normalized, p_largest_value, "0x1.fffffep+127", Status::INEXACT, Category::Normal), (m_smallest_normalized, m_largest_value, "-0x1.fffffep+127", Status::INEXACT, Category::Normal), (m_smallest_normalized, p_smallest_value, "-0x1.fffffcp-127", Status::OK, Category::Normal), (m_smallest_normalized, m_smallest_value, "-0x1.000002p-126", Status::OK, Category::Normal), (m_smallest_normalized, p_smallest_normalized, "0x0p+0", Status::OK, Category::Zero), (m_smallest_normalized, m_smallest_normalized, "-0x1p-125", Status::OK, Category::Normal), ]; for case @ &(x, y, e_result, e_status, e_category) in &special_cases[..] { let status; let result = unpack!(status=, x + y); assert_eq!(e_status, status); assert_eq!(e_category, result.category()); assert!(result.bitwise_eq(e_result.parse::().unwrap()), "result = {result:?}, case = {case:?}"); } } #[test] fn subtract() { // Test Special Cases against each other and normal values. let p_inf = Single::INFINITY; let m_inf = -Single::INFINITY; let p_zero = Single::ZERO; let m_zero = -Single::ZERO; let qnan = Single::NAN; let snan = "snan123".parse::().unwrap(); let p_normal_value = "0x1p+0".parse::().unwrap(); let m_normal_value = "-0x1p+0".parse::().unwrap(); let p_largest_value = Single::largest(); let m_largest_value = -Single::largest(); let p_smallest_value = Single::SMALLEST; let m_smallest_value = -Single::SMALLEST; let p_smallest_normalized = Single::smallest_normalized(); let m_smallest_normalized = -Single::smallest_normalized(); let overflow_status = Status::OVERFLOW | Status::INEXACT; let special_cases = [ (p_inf, p_inf, "nan", Status::INVALID_OP, Category::NaN), (p_inf, m_inf, "inf", Status::OK, Category::Infinity), (p_inf, p_zero, "inf", Status::OK, Category::Infinity), (p_inf, m_zero, "inf", Status::OK, Category::Infinity), (p_inf, qnan, "nan", Status::OK, Category::NaN), (p_inf, snan, "nan123", Status::INVALID_OP, Category::NaN), (p_inf, p_normal_value, "inf", Status::OK, Category::Infinity), (p_inf, m_normal_value, "inf", Status::OK, Category::Infinity), (p_inf, p_largest_value, "inf", Status::OK, Category::Infinity), (p_inf, m_largest_value, "inf", Status::OK, Category::Infinity), (p_inf, p_smallest_value, "inf", Status::OK, Category::Infinity), (p_inf, m_smallest_value, "inf", Status::OK, Category::Infinity), (p_inf, p_smallest_normalized, "inf", Status::OK, Category::Infinity), (p_inf, m_smallest_normalized, "inf", Status::OK, Category::Infinity), (m_inf, p_inf, "-inf", Status::OK, Category::Infinity), (m_inf, m_inf, "nan", Status::INVALID_OP, Category::NaN), (m_inf, p_zero, "-inf", Status::OK, Category::Infinity), (m_inf, m_zero, "-inf", Status::OK, Category::Infinity), (m_inf, qnan, "nan", Status::OK, Category::NaN), (m_inf, snan, "nan123", Status::INVALID_OP, Category::NaN), (m_inf, p_normal_value, "-inf", Status::OK, Category::Infinity), (m_inf, m_normal_value, "-inf", Status::OK, Category::Infinity), (m_inf, p_largest_value, "-inf", Status::OK, Category::Infinity), (m_inf, m_largest_value, "-inf", Status::OK, Category::Infinity), (m_inf, p_smallest_value, "-inf", Status::OK, Category::Infinity), (m_inf, m_smallest_value, "-inf", Status::OK, Category::Infinity), (m_inf, p_smallest_normalized, "-inf", Status::OK, Category::Infinity), (m_inf, m_smallest_normalized, "-inf", Status::OK, Category::Infinity), (p_zero, p_inf, "-inf", Status::OK, Category::Infinity), (p_zero, m_inf, "inf", Status::OK, Category::Infinity), (p_zero, p_zero, "0x0p+0", Status::OK, Category::Zero), (p_zero, m_zero, "0x0p+0", Status::OK, Category::Zero), (p_zero, qnan, "nan", Status::OK, Category::NaN), (p_zero, snan, "nan123", Status::INVALID_OP, Category::NaN), (p_zero, p_normal_value, "-0x1p+0", Status::OK, Category::Normal), (p_zero, m_normal_value, "0x1p+0", Status::OK, Category::Normal), (p_zero, p_largest_value, "-0x1.fffffep+127", Status::OK, Category::Normal), (p_zero, m_largest_value, "0x1.fffffep+127", Status::OK, Category::Normal), (p_zero, p_smallest_value, "-0x1p-149", Status::OK, Category::Normal), (p_zero, m_smallest_value, "0x1p-149", Status::OK, Category::Normal), (p_zero, p_smallest_normalized, "-0x1p-126", Status::OK, Category::Normal), (p_zero, m_smallest_normalized, "0x1p-126", Status::OK, Category::Normal), (m_zero, p_inf, "-inf", Status::OK, Category::Infinity), (m_zero, m_inf, "inf", Status::OK, Category::Infinity), (m_zero, p_zero, "-0x0p+0", Status::OK, Category::Zero), (m_zero, m_zero, "0x0p+0", Status::OK, Category::Zero), (m_zero, qnan, "nan", Status::OK, Category::NaN), (m_zero, snan, "nan123", Status::INVALID_OP, Category::NaN), (m_zero, p_normal_value, "-0x1p+0", Status::OK, Category::Normal), (m_zero, m_normal_value, "0x1p+0", Status::OK, Category::Normal), (m_zero, p_largest_value, "-0x1.fffffep+127", Status::OK, Category::Normal), (m_zero, m_largest_value, "0x1.fffffep+127", Status::OK, Category::Normal), (m_zero, p_smallest_value, "-0x1p-149", Status::OK, Category::Normal), (m_zero, m_smallest_value, "0x1p-149", Status::OK, Category::Normal), (m_zero, p_smallest_normalized, "-0x1p-126", Status::OK, Category::Normal), (m_zero, m_smallest_normalized, "0x1p-126", Status::OK, Category::Normal), (qnan, p_inf, "nan", Status::OK, Category::NaN), (qnan, m_inf, "nan", Status::OK, Category::NaN), (qnan, p_zero, "nan", Status::OK, Category::NaN), (qnan, m_zero, "nan", Status::OK, Category::NaN), (qnan, qnan, "nan", Status::OK, Category::NaN), (qnan, snan, "nan", Status::INVALID_OP, Category::NaN), (qnan, p_normal_value, "nan", Status::OK, Category::NaN), (qnan, m_normal_value, "nan", Status::OK, Category::NaN), (qnan, p_largest_value, "nan", Status::OK, Category::NaN), (qnan, m_largest_value, "nan", Status::OK, Category::NaN), (qnan, p_smallest_value, "nan", Status::OK, Category::NaN), (qnan, m_smallest_value, "nan", Status::OK, Category::NaN), (qnan, p_smallest_normalized, "nan", Status::OK, Category::NaN), (qnan, m_smallest_normalized, "nan", Status::OK, Category::NaN), (snan, p_inf, "nan123", Status::INVALID_OP, Category::NaN), (snan, m_inf, "nan123", Status::INVALID_OP, Category::NaN), (snan, p_zero, "nan123", Status::INVALID_OP, Category::NaN), (snan, m_zero, "nan123", Status::INVALID_OP, Category::NaN), (snan, qnan, "nan123", Status::INVALID_OP, Category::NaN), (snan, snan, "nan123", Status::INVALID_OP, Category::NaN), (snan, p_normal_value, "nan123", Status::INVALID_OP, Category::NaN), (snan, m_normal_value, "nan123", Status::INVALID_OP, Category::NaN), (snan, p_largest_value, "nan123", Status::INVALID_OP, Category::NaN), (snan, m_largest_value, "nan123", Status::INVALID_OP, Category::NaN), (snan, p_smallest_value, "nan123", Status::INVALID_OP, Category::NaN), (snan, m_smallest_value, "nan123", Status::INVALID_OP, Category::NaN), (snan, p_smallest_normalized, "nan123", Status::INVALID_OP, Category::NaN), (snan, m_smallest_normalized, "nan123", Status::INVALID_OP, Category::NaN), (p_normal_value, p_inf, "-inf", Status::OK, Category::Infinity), (p_normal_value, m_inf, "inf", Status::OK, Category::Infinity), (p_normal_value, p_zero, "0x1p+0", Status::OK, Category::Normal), (p_normal_value, m_zero, "0x1p+0", Status::OK, Category::Normal), (p_normal_value, qnan, "nan", Status::OK, Category::NaN), (p_normal_value, snan, "nan123", Status::INVALID_OP, Category::NaN), (p_normal_value, p_normal_value, "0x0p+0", Status::OK, Category::Zero), (p_normal_value, m_normal_value, "0x1p+1", Status::OK, Category::Normal), (p_normal_value, p_largest_value, "-0x1.fffffep+127", Status::INEXACT, Category::Normal), (p_normal_value, m_largest_value, "0x1.fffffep+127", Status::INEXACT, Category::Normal), (p_normal_value, p_smallest_value, "0x1p+0", Status::INEXACT, Category::Normal), (p_normal_value, m_smallest_value, "0x1p+0", Status::INEXACT, Category::Normal), (p_normal_value, p_smallest_normalized, "0x1p+0", Status::INEXACT, Category::Normal), (p_normal_value, m_smallest_normalized, "0x1p+0", Status::INEXACT, Category::Normal), (m_normal_value, p_inf, "-inf", Status::OK, Category::Infinity), (m_normal_value, m_inf, "inf", Status::OK, Category::Infinity), (m_normal_value, p_zero, "-0x1p+0", Status::OK, Category::Normal), (m_normal_value, m_zero, "-0x1p+0", Status::OK, Category::Normal), (m_normal_value, qnan, "nan", Status::OK, Category::NaN), (m_normal_value, snan, "nan123", Status::INVALID_OP, Category::NaN), (m_normal_value, p_normal_value, "-0x1p+1", Status::OK, Category::Normal), (m_normal_value, m_normal_value, "0x0p+0", Status::OK, Category::Zero), (m_normal_value, p_largest_value, "-0x1.fffffep+127", Status::INEXACT, Category::Normal), (m_normal_value, m_largest_value, "0x1.fffffep+127", Status::INEXACT, Category::Normal), (m_normal_value, p_smallest_value, "-0x1p+0", Status::INEXACT, Category::Normal), (m_normal_value, m_smallest_value, "-0x1p+0", Status::INEXACT, Category::Normal), (m_normal_value, p_smallest_normalized, "-0x1p+0", Status::INEXACT, Category::Normal), (m_normal_value, m_smallest_normalized, "-0x1p+0", Status::INEXACT, Category::Normal), (p_largest_value, p_inf, "-inf", Status::OK, Category::Infinity), (p_largest_value, m_inf, "inf", Status::OK, Category::Infinity), (p_largest_value, p_zero, "0x1.fffffep+127", Status::OK, Category::Normal), (p_largest_value, m_zero, "0x1.fffffep+127", Status::OK, Category::Normal), (p_largest_value, qnan, "nan", Status::OK, Category::NaN), (p_largest_value, snan, "nan123", Status::INVALID_OP, Category::NaN), (p_largest_value, p_normal_value, "0x1.fffffep+127", Status::INEXACT, Category::Normal), (p_largest_value, m_normal_value, "0x1.fffffep+127", Status::INEXACT, Category::Normal), (p_largest_value, p_largest_value, "0x0p+0", Status::OK, Category::Zero), (p_largest_value, m_largest_value, "inf", overflow_status, Category::Infinity), (p_largest_value, p_smallest_value, "0x1.fffffep+127", Status::INEXACT, Category::Normal), (p_largest_value, m_smallest_value, "0x1.fffffep+127", Status::INEXACT, Category::Normal), (p_largest_value, p_smallest_normalized, "0x1.fffffep+127", Status::INEXACT, Category::Normal), (p_largest_value, m_smallest_normalized, "0x1.fffffep+127", Status::INEXACT, Category::Normal), (m_largest_value, p_inf, "-inf", Status::OK, Category::Infinity), (m_largest_value, m_inf, "inf", Status::OK, Category::Infinity), (m_largest_value, p_zero, "-0x1.fffffep+127", Status::OK, Category::Normal), (m_largest_value, m_zero, "-0x1.fffffep+127", Status::OK, Category::Normal), (m_largest_value, qnan, "nan", Status::OK, Category::NaN), (m_largest_value, snan, "nan123", Status::INVALID_OP, Category::NaN), (m_largest_value, p_normal_value, "-0x1.fffffep+127", Status::INEXACT, Category::Normal), (m_largest_value, m_normal_value, "-0x1.fffffep+127", Status::INEXACT, Category::Normal), (m_largest_value, p_largest_value, "-inf", overflow_status, Category::Infinity), (m_largest_value, m_largest_value, "0x0p+0", Status::OK, Category::Zero), (m_largest_value, p_smallest_value, "-0x1.fffffep+127", Status::INEXACT, Category::Normal), (m_largest_value, m_smallest_value, "-0x1.fffffep+127", Status::INEXACT, Category::Normal), (m_largest_value, p_smallest_normalized, "-0x1.fffffep+127", Status::INEXACT, Category::Normal), (m_largest_value, m_smallest_normalized, "-0x1.fffffep+127", Status::INEXACT, Category::Normal), (p_smallest_value, p_inf, "-inf", Status::OK, Category::Infinity), (p_smallest_value, m_inf, "inf", Status::OK, Category::Infinity), (p_smallest_value, p_zero, "0x1p-149", Status::OK, Category::Normal), (p_smallest_value, m_zero, "0x1p-149", Status::OK, Category::Normal), (p_smallest_value, qnan, "nan", Status::OK, Category::NaN), (p_smallest_value, snan, "nan123", Status::INVALID_OP, Category::NaN), (p_smallest_value, p_normal_value, "-0x1p+0", Status::INEXACT, Category::Normal), (p_smallest_value, m_normal_value, "0x1p+0", Status::INEXACT, Category::Normal), (p_smallest_value, p_largest_value, "-0x1.fffffep+127", Status::INEXACT, Category::Normal), (p_smallest_value, m_largest_value, "0x1.fffffep+127", Status::INEXACT, Category::Normal), (p_smallest_value, p_smallest_value, "0x0p+0", Status::OK, Category::Zero), (p_smallest_value, m_smallest_value, "0x1p-148", Status::OK, Category::Normal), (p_smallest_value, p_smallest_normalized, "-0x1.fffffcp-127", Status::OK, Category::Normal), (p_smallest_value, m_smallest_normalized, "0x1.000002p-126", Status::OK, Category::Normal), (m_smallest_value, p_inf, "-inf", Status::OK, Category::Infinity), (m_smallest_value, m_inf, "inf", Status::OK, Category::Infinity), (m_smallest_value, p_zero, "-0x1p-149", Status::OK, Category::Normal), (m_smallest_value, m_zero, "-0x1p-149", Status::OK, Category::Normal), (m_smallest_value, qnan, "nan", Status::OK, Category::NaN), (m_smallest_value, snan, "nan123", Status::INVALID_OP, Category::NaN), (m_smallest_value, p_normal_value, "-0x1p+0", Status::INEXACT, Category::Normal), (m_smallest_value, m_normal_value, "0x1p+0", Status::INEXACT, Category::Normal), (m_smallest_value, p_largest_value, "-0x1.fffffep+127", Status::INEXACT, Category::Normal), (m_smallest_value, m_largest_value, "0x1.fffffep+127", Status::INEXACT, Category::Normal), (m_smallest_value, p_smallest_value, "-0x1p-148", Status::OK, Category::Normal), (m_smallest_value, m_smallest_value, "0x0p+0", Status::OK, Category::Zero), (m_smallest_value, p_smallest_normalized, "-0x1.000002p-126", Status::OK, Category::Normal), (m_smallest_value, m_smallest_normalized, "0x1.fffffcp-127", Status::OK, Category::Normal), (p_smallest_normalized, p_inf, "-inf", Status::OK, Category::Infinity), (p_smallest_normalized, m_inf, "inf", Status::OK, Category::Infinity), (p_smallest_normalized, p_zero, "0x1p-126", Status::OK, Category::Normal), (p_smallest_normalized, m_zero, "0x1p-126", Status::OK, Category::Normal), (p_smallest_normalized, qnan, "nan", Status::OK, Category::NaN), (p_smallest_normalized, snan, "nan123", Status::INVALID_OP, Category::NaN), (p_smallest_normalized, p_normal_value, "-0x1p+0", Status::INEXACT, Category::Normal), (p_smallest_normalized, m_normal_value, "0x1p+0", Status::INEXACT, Category::Normal), (p_smallest_normalized, p_largest_value, "-0x1.fffffep+127", Status::INEXACT, Category::Normal), (p_smallest_normalized, m_largest_value, "0x1.fffffep+127", Status::INEXACT, Category::Normal), (p_smallest_normalized, p_smallest_value, "0x1.fffffcp-127", Status::OK, Category::Normal), (p_smallest_normalized, m_smallest_value, "0x1.000002p-126", Status::OK, Category::Normal), (p_smallest_normalized, p_smallest_normalized, "0x0p+0", Status::OK, Category::Zero), (p_smallest_normalized, m_smallest_normalized, "0x1p-125", Status::OK, Category::Normal), (m_smallest_normalized, p_inf, "-inf", Status::OK, Category::Infinity), (m_smallest_normalized, m_inf, "inf", Status::OK, Category::Infinity), (m_smallest_normalized, p_zero, "-0x1p-126", Status::OK, Category::Normal), (m_smallest_normalized, m_zero, "-0x1p-126", Status::OK, Category::Normal), (m_smallest_normalized, qnan, "nan", Status::OK, Category::NaN), (m_smallest_normalized, snan, "nan123", Status::INVALID_OP, Category::NaN), (m_smallest_normalized, p_normal_value, "-0x1p+0", Status::INEXACT, Category::Normal), (m_smallest_normalized, m_normal_value, "0x1p+0", Status::INEXACT, Category::Normal), (m_smallest_normalized, p_largest_value, "-0x1.fffffep+127", Status::INEXACT, Category::Normal), (m_smallest_normalized, m_largest_value, "0x1.fffffep+127", Status::INEXACT, Category::Normal), (m_smallest_normalized, p_smallest_value, "-0x1.000002p-126", Status::OK, Category::Normal), (m_smallest_normalized, m_smallest_value, "-0x1.fffffcp-127", Status::OK, Category::Normal), (m_smallest_normalized, p_smallest_normalized, "-0x1p-125", Status::OK, Category::Normal), (m_smallest_normalized, m_smallest_normalized, "0x0p+0", Status::OK, Category::Zero), ]; for case @ &(x, y, e_result, e_status, e_category) in &special_cases[..] { let status; let result = unpack!(status=, x - y); assert_eq!(e_status, status); assert_eq!(e_category, result.category()); assert!(result.bitwise_eq(e_result.parse::().unwrap()), "result = {result:?}, case = {case:?}"); } } #[test] fn multiply() { // Test Special Cases against each other and normal values. let p_inf = Single::INFINITY; let m_inf = -Single::INFINITY; let p_zero = Single::ZERO; let m_zero = -Single::ZERO; let qnan = Single::NAN; let snan = "snan123".parse::().unwrap(); let p_normal_value = "0x1p+0".parse::().unwrap(); let m_normal_value = "-0x1p+0".parse::().unwrap(); let p_largest_value = Single::largest(); let m_largest_value = -Single::largest(); let p_smallest_value = Single::SMALLEST; let m_smallest_value = -Single::SMALLEST; let p_smallest_normalized = Single::smallest_normalized(); let m_smallest_normalized = -Single::smallest_normalized(); let max_quad = "0x1.ffffffffffffffffffffffffffffp+16383".parse::().unwrap(); let min_quad = "0x0.0000000000000000000000000001p-16382".parse::().unwrap(); let n_min_quad = "-0x0.0000000000000000000000000001p-16382".parse::().unwrap(); let overflow_status = Status::OVERFLOW | Status::INEXACT; let underflow_status = Status::UNDERFLOW | Status::INEXACT; let single_special_cases = [ (p_inf, p_inf, "inf", Status::OK, Category::Infinity), (p_inf, m_inf, "-inf", Status::OK, Category::Infinity), (p_inf, p_zero, "nan", Status::INVALID_OP, Category::NaN), (p_inf, m_zero, "nan", Status::INVALID_OP, Category::NaN), (p_inf, qnan, "nan", Status::OK, Category::NaN), (p_inf, snan, "nan123", Status::INVALID_OP, Category::NaN), (p_inf, p_normal_value, "inf", Status::OK, Category::Infinity), (p_inf, m_normal_value, "-inf", Status::OK, Category::Infinity), (p_inf, p_largest_value, "inf", Status::OK, Category::Infinity), (p_inf, m_largest_value, "-inf", Status::OK, Category::Infinity), (p_inf, p_smallest_value, "inf", Status::OK, Category::Infinity), (p_inf, m_smallest_value, "-inf", Status::OK, Category::Infinity), (p_inf, p_smallest_normalized, "inf", Status::OK, Category::Infinity), (p_inf, m_smallest_normalized, "-inf", Status::OK, Category::Infinity), (m_inf, p_inf, "-inf", Status::OK, Category::Infinity), (m_inf, m_inf, "inf", Status::OK, Category::Infinity), (m_inf, p_zero, "nan", Status::INVALID_OP, Category::NaN), (m_inf, m_zero, "nan", Status::INVALID_OP, Category::NaN), (m_inf, qnan, "nan", Status::OK, Category::NaN), (m_inf, snan, "nan123", Status::INVALID_OP, Category::NaN), (m_inf, p_normal_value, "-inf", Status::OK, Category::Infinity), (m_inf, m_normal_value, "inf", Status::OK, Category::Infinity), (m_inf, p_largest_value, "-inf", Status::OK, Category::Infinity), (m_inf, m_largest_value, "inf", Status::OK, Category::Infinity), (m_inf, p_smallest_value, "-inf", Status::OK, Category::Infinity), (m_inf, m_smallest_value, "inf", Status::OK, Category::Infinity), (m_inf, p_smallest_normalized, "-inf", Status::OK, Category::Infinity), (m_inf, m_smallest_normalized, "inf", Status::OK, Category::Infinity), (p_zero, p_inf, "nan", Status::INVALID_OP, Category::NaN), (p_zero, m_inf, "nan", Status::INVALID_OP, Category::NaN), (p_zero, p_zero, "0x0p+0", Status::OK, Category::Zero), (p_zero, m_zero, "-0x0p+0", Status::OK, Category::Zero), (p_zero, qnan, "nan", Status::OK, Category::NaN), (p_zero, snan, "nan123", Status::INVALID_OP, Category::NaN), (p_zero, p_normal_value, "0x0p+0", Status::OK, Category::Zero), (p_zero, m_normal_value, "-0x0p+0", Status::OK, Category::Zero), (p_zero, p_largest_value, "0x0p+0", Status::OK, Category::Zero), (p_zero, m_largest_value, "-0x0p+0", Status::OK, Category::Zero), (p_zero, p_smallest_value, "0x0p+0", Status::OK, Category::Zero), (p_zero, m_smallest_value, "-0x0p+0", Status::OK, Category::Zero), (p_zero, p_smallest_normalized, "0x0p+0", Status::OK, Category::Zero), (p_zero, m_smallest_normalized, "-0x0p+0", Status::OK, Category::Zero), (m_zero, p_inf, "nan", Status::INVALID_OP, Category::NaN), (m_zero, m_inf, "nan", Status::INVALID_OP, Category::NaN), (m_zero, p_zero, "-0x0p+0", Status::OK, Category::Zero), (m_zero, m_zero, "0x0p+0", Status::OK, Category::Zero), (m_zero, qnan, "nan", Status::OK, Category::NaN), (m_zero, snan, "nan123", Status::INVALID_OP, Category::NaN), (m_zero, p_normal_value, "-0x0p+0", Status::OK, Category::Zero), (m_zero, m_normal_value, "0x0p+0", Status::OK, Category::Zero), (m_zero, p_largest_value, "-0x0p+0", Status::OK, Category::Zero), (m_zero, m_largest_value, "0x0p+0", Status::OK, Category::Zero), (m_zero, p_smallest_value, "-0x0p+0", Status::OK, Category::Zero), (m_zero, m_smallest_value, "0x0p+0", Status::OK, Category::Zero), (m_zero, p_smallest_normalized, "-0x0p+0", Status::OK, Category::Zero), (m_zero, m_smallest_normalized, "0x0p+0", Status::OK, Category::Zero), (qnan, p_inf, "nan", Status::OK, Category::NaN), (qnan, m_inf, "nan", Status::OK, Category::NaN), (qnan, p_zero, "nan", Status::OK, Category::NaN), (qnan, m_zero, "nan", Status::OK, Category::NaN), (qnan, qnan, "nan", Status::OK, Category::NaN), (qnan, snan, "nan", Status::INVALID_OP, Category::NaN), (qnan, p_normal_value, "nan", Status::OK, Category::NaN), (qnan, m_normal_value, "nan", Status::OK, Category::NaN), (qnan, p_largest_value, "nan", Status::OK, Category::NaN), (qnan, m_largest_value, "nan", Status::OK, Category::NaN), (qnan, p_smallest_value, "nan", Status::OK, Category::NaN), (qnan, m_smallest_value, "nan", Status::OK, Category::NaN), (qnan, p_smallest_normalized, "nan", Status::OK, Category::NaN), (qnan, m_smallest_normalized, "nan", Status::OK, Category::NaN), (snan, p_inf, "nan123", Status::INVALID_OP, Category::NaN), (snan, m_inf, "nan123", Status::INVALID_OP, Category::NaN), (snan, p_zero, "nan123", Status::INVALID_OP, Category::NaN), (snan, m_zero, "nan123", Status::INVALID_OP, Category::NaN), (snan, qnan, "nan123", Status::INVALID_OP, Category::NaN), (snan, snan, "nan123", Status::INVALID_OP, Category::NaN), (snan, p_normal_value, "nan123", Status::INVALID_OP, Category::NaN), (snan, m_normal_value, "nan123", Status::INVALID_OP, Category::NaN), (snan, p_largest_value, "nan123", Status::INVALID_OP, Category::NaN), (snan, m_largest_value, "nan123", Status::INVALID_OP, Category::NaN), (snan, p_smallest_value, "nan123", Status::INVALID_OP, Category::NaN), (snan, m_smallest_value, "nan123", Status::INVALID_OP, Category::NaN), (snan, p_smallest_normalized, "nan123", Status::INVALID_OP, Category::NaN), (snan, m_smallest_normalized, "nan123", Status::INVALID_OP, Category::NaN), (p_normal_value, p_inf, "inf", Status::OK, Category::Infinity), (p_normal_value, m_inf, "-inf", Status::OK, Category::Infinity), (p_normal_value, p_zero, "0x0p+0", Status::OK, Category::Zero), (p_normal_value, m_zero, "-0x0p+0", Status::OK, Category::Zero), (p_normal_value, qnan, "nan", Status::OK, Category::NaN), (p_normal_value, snan, "nan123", Status::INVALID_OP, Category::NaN), (p_normal_value, p_normal_value, "0x1p+0", Status::OK, Category::Normal), (p_normal_value, m_normal_value, "-0x1p+0", Status::OK, Category::Normal), (p_normal_value, p_largest_value, "0x1.fffffep+127", Status::OK, Category::Normal), (p_normal_value, m_largest_value, "-0x1.fffffep+127", Status::OK, Category::Normal), (p_normal_value, p_smallest_value, "0x1p-149", Status::OK, Category::Normal), (p_normal_value, m_smallest_value, "-0x1p-149", Status::OK, Category::Normal), (p_normal_value, p_smallest_normalized, "0x1p-126", Status::OK, Category::Normal), (p_normal_value, m_smallest_normalized, "-0x1p-126", Status::OK, Category::Normal), (m_normal_value, p_inf, "-inf", Status::OK, Category::Infinity), (m_normal_value, m_inf, "inf", Status::OK, Category::Infinity), (m_normal_value, p_zero, "-0x0p+0", Status::OK, Category::Zero), (m_normal_value, m_zero, "0x0p+0", Status::OK, Category::Zero), (m_normal_value, qnan, "nan", Status::OK, Category::NaN), (m_normal_value, snan, "nan123", Status::INVALID_OP, Category::NaN), (m_normal_value, p_normal_value, "-0x1p+0", Status::OK, Category::Normal), (m_normal_value, m_normal_value, "0x1p+0", Status::OK, Category::Normal), (m_normal_value, p_largest_value, "-0x1.fffffep+127", Status::OK, Category::Normal), (m_normal_value, m_largest_value, "0x1.fffffep+127", Status::OK, Category::Normal), (m_normal_value, p_smallest_value, "-0x1p-149", Status::OK, Category::Normal), (m_normal_value, m_smallest_value, "0x1p-149", Status::OK, Category::Normal), (m_normal_value, p_smallest_normalized, "-0x1p-126", Status::OK, Category::Normal), (m_normal_value, m_smallest_normalized, "0x1p-126", Status::OK, Category::Normal), (p_largest_value, p_inf, "inf", Status::OK, Category::Infinity), (p_largest_value, m_inf, "-inf", Status::OK, Category::Infinity), (p_largest_value, p_zero, "0x0p+0", Status::OK, Category::Zero), (p_largest_value, m_zero, "-0x0p+0", Status::OK, Category::Zero), (p_largest_value, qnan, "nan", Status::OK, Category::NaN), (p_largest_value, snan, "nan123", Status::INVALID_OP, Category::NaN), (p_largest_value, p_normal_value, "0x1.fffffep+127", Status::OK, Category::Normal), (p_largest_value, m_normal_value, "-0x1.fffffep+127", Status::OK, Category::Normal), (p_largest_value, p_largest_value, "inf", overflow_status, Category::Infinity), (p_largest_value, m_largest_value, "-inf", overflow_status, Category::Infinity), (p_largest_value, p_smallest_value, "0x1.fffffep-22", Status::OK, Category::Normal), (p_largest_value, m_smallest_value, "-0x1.fffffep-22", Status::OK, Category::Normal), (p_largest_value, p_smallest_normalized, "0x1.fffffep+1", Status::OK, Category::Normal), (p_largest_value, m_smallest_normalized, "-0x1.fffffep+1", Status::OK, Category::Normal), (m_largest_value, p_inf, "-inf", Status::OK, Category::Infinity), (m_largest_value, m_inf, "inf", Status::OK, Category::Infinity), (m_largest_value, p_zero, "-0x0p+0", Status::OK, Category::Zero), (m_largest_value, m_zero, "0x0p+0", Status::OK, Category::Zero), (m_largest_value, qnan, "nan", Status::OK, Category::NaN), (m_largest_value, snan, "nan123", Status::INVALID_OP, Category::NaN), (m_largest_value, p_normal_value, "-0x1.fffffep+127", Status::OK, Category::Normal), (m_largest_value, m_normal_value, "0x1.fffffep+127", Status::OK, Category::Normal), (m_largest_value, p_largest_value, "-inf", overflow_status, Category::Infinity), (m_largest_value, m_largest_value, "inf", overflow_status, Category::Infinity), (m_largest_value, p_smallest_value, "-0x1.fffffep-22", Status::OK, Category::Normal), (m_largest_value, m_smallest_value, "0x1.fffffep-22", Status::OK, Category::Normal), (m_largest_value, p_smallest_normalized, "-0x1.fffffep+1", Status::OK, Category::Normal), (m_largest_value, m_smallest_normalized, "0x1.fffffep+1", Status::OK, Category::Normal), (p_smallest_value, p_inf, "inf", Status::OK, Category::Infinity), (p_smallest_value, m_inf, "-inf", Status::OK, Category::Infinity), (p_smallest_value, p_zero, "0x0p+0", Status::OK, Category::Zero), (p_smallest_value, m_zero, "-0x0p+0", Status::OK, Category::Zero), (p_smallest_value, qnan, "nan", Status::OK, Category::NaN), (p_smallest_value, snan, "nan123", Status::INVALID_OP, Category::NaN), (p_smallest_value, p_normal_value, "0x1p-149", Status::OK, Category::Normal), (p_smallest_value, m_normal_value, "-0x1p-149", Status::OK, Category::Normal), (p_smallest_value, p_largest_value, "0x1.fffffep-22", Status::OK, Category::Normal), (p_smallest_value, m_largest_value, "-0x1.fffffep-22", Status::OK, Category::Normal), (p_smallest_value, p_smallest_value, "0x0p+0", underflow_status, Category::Zero), (p_smallest_value, m_smallest_value, "-0x0p+0", underflow_status, Category::Zero), (p_smallest_value, p_smallest_normalized, "0x0p+0", underflow_status, Category::Zero), (p_smallest_value, m_smallest_normalized, "-0x0p+0", underflow_status, Category::Zero), (m_smallest_value, p_inf, "-inf", Status::OK, Category::Infinity), (m_smallest_value, m_inf, "inf", Status::OK, Category::Infinity), (m_smallest_value, p_zero, "-0x0p+0", Status::OK, Category::Zero), (m_smallest_value, m_zero, "0x0p+0", Status::OK, Category::Zero), (m_smallest_value, qnan, "nan", Status::OK, Category::NaN), (m_smallest_value, snan, "nan123", Status::INVALID_OP, Category::NaN), (m_smallest_value, p_normal_value, "-0x1p-149", Status::OK, Category::Normal), (m_smallest_value, m_normal_value, "0x1p-149", Status::OK, Category::Normal), (m_smallest_value, p_largest_value, "-0x1.fffffep-22", Status::OK, Category::Normal), (m_smallest_value, m_largest_value, "0x1.fffffep-22", Status::OK, Category::Normal), (m_smallest_value, p_smallest_value, "-0x0p+0", underflow_status, Category::Zero), (m_smallest_value, m_smallest_value, "0x0p+0", underflow_status, Category::Zero), (m_smallest_value, p_smallest_normalized, "-0x0p+0", underflow_status, Category::Zero), (m_smallest_value, m_smallest_normalized, "0x0p+0", underflow_status, Category::Zero), (p_smallest_normalized, p_inf, "inf", Status::OK, Category::Infinity), (p_smallest_normalized, m_inf, "-inf", Status::OK, Category::Infinity), (p_smallest_normalized, p_zero, "0x0p+0", Status::OK, Category::Zero), (p_smallest_normalized, m_zero, "-0x0p+0", Status::OK, Category::Zero), (p_smallest_normalized, qnan, "nan", Status::OK, Category::NaN), (p_smallest_normalized, snan, "nan123", Status::INVALID_OP, Category::NaN), (p_smallest_normalized, p_normal_value, "0x1p-126", Status::OK, Category::Normal), (p_smallest_normalized, m_normal_value, "-0x1p-126", Status::OK, Category::Normal), (p_smallest_normalized, p_largest_value, "0x1.fffffep+1", Status::OK, Category::Normal), (p_smallest_normalized, m_largest_value, "-0x1.fffffep+1", Status::OK, Category::Normal), (p_smallest_normalized, p_smallest_value, "0x0p+0", underflow_status, Category::Zero), (p_smallest_normalized, m_smallest_value, "-0x0p+0", underflow_status, Category::Zero), (p_smallest_normalized, p_smallest_normalized, "0x0p+0", underflow_status, Category::Zero), (p_smallest_normalized, m_smallest_normalized, "-0x0p+0", underflow_status, Category::Zero), (m_smallest_normalized, p_inf, "-inf", Status::OK, Category::Infinity), (m_smallest_normalized, m_inf, "inf", Status::OK, Category::Infinity), (m_smallest_normalized, p_zero, "-0x0p+0", Status::OK, Category::Zero), (m_smallest_normalized, m_zero, "0x0p+0", Status::OK, Category::Zero), (m_smallest_normalized, qnan, "nan", Status::OK, Category::NaN), (m_smallest_normalized, snan, "nan123", Status::INVALID_OP, Category::NaN), (m_smallest_normalized, p_normal_value, "-0x1p-126", Status::OK, Category::Normal), (m_smallest_normalized, m_normal_value, "0x1p-126", Status::OK, Category::Normal), (m_smallest_normalized, p_largest_value, "-0x1.fffffep+1", Status::OK, Category::Normal), (m_smallest_normalized, m_largest_value, "0x1.fffffep+1", Status::OK, Category::Normal), (m_smallest_normalized, p_smallest_value, "-0x0p+0", underflow_status, Category::Zero), (m_smallest_normalized, m_smallest_value, "0x0p+0", underflow_status, Category::Zero), (m_smallest_normalized, p_smallest_normalized, "-0x0p+0", underflow_status, Category::Zero), (m_smallest_normalized, m_smallest_normalized, "0x0p+0", underflow_status, Category::Zero), ]; let quad_special_cases = [ ( max_quad, min_quad, "0x1.ffffffffffffffffffffffffffffp-111", Status::OK, Category::Normal, Round::NearestTiesToEven, ), ( max_quad, min_quad, "0x1.ffffffffffffffffffffffffffffp-111", Status::OK, Category::Normal, Round::TowardPositive, ), ( max_quad, min_quad, "0x1.ffffffffffffffffffffffffffffp-111", Status::OK, Category::Normal, Round::TowardNegative, ), (max_quad, min_quad, "0x1.ffffffffffffffffffffffffffffp-111", Status::OK, Category::Normal, Round::TowardZero), ( max_quad, min_quad, "0x1.ffffffffffffffffffffffffffffp-111", Status::OK, Category::Normal, Round::NearestTiesToAway, ), ( max_quad, n_min_quad, "-0x1.ffffffffffffffffffffffffffffp-111", Status::OK, Category::Normal, Round::NearestTiesToEven, ), ( max_quad, n_min_quad, "-0x1.ffffffffffffffffffffffffffffp-111", Status::OK, Category::Normal, Round::TowardPositive, ), ( max_quad, n_min_quad, "-0x1.ffffffffffffffffffffffffffffp-111", Status::OK, Category::Normal, Round::TowardNegative, ), ( max_quad, n_min_quad, "-0x1.ffffffffffffffffffffffffffffp-111", Status::OK, Category::Normal, Round::TowardZero, ), ( max_quad, n_min_quad, "-0x1.ffffffffffffffffffffffffffffp-111", Status::OK, Category::Normal, Round::NearestTiesToAway, ), (max_quad, max_quad, "inf", overflow_status, Category::Infinity, Round::NearestTiesToEven), (max_quad, max_quad, "inf", overflow_status, Category::Infinity, Round::TowardPositive), ( max_quad, max_quad, "0x1.ffffffffffffffffffffffffffffp+16383", Status::INEXACT, Category::Normal, Round::TowardNegative, ), ( max_quad, max_quad, "0x1.ffffffffffffffffffffffffffffp+16383", Status::INEXACT, Category::Normal, Round::TowardZero, ), (max_quad, max_quad, "inf", overflow_status, Category::Infinity, Round::NearestTiesToAway), (min_quad, min_quad, "0", underflow_status, Category::Zero, Round::NearestTiesToEven), ( min_quad, min_quad, "0x0.0000000000000000000000000001p-16382", underflow_status, Category::Normal, Round::TowardPositive, ), (min_quad, min_quad, "0", underflow_status, Category::Zero, Round::TowardNegative), (min_quad, min_quad, "0", underflow_status, Category::Zero, Round::TowardZero), (min_quad, min_quad, "0", underflow_status, Category::Zero, Round::NearestTiesToAway), (min_quad, n_min_quad, "-0", underflow_status, Category::Zero, Round::NearestTiesToEven), (min_quad, n_min_quad, "-0", underflow_status, Category::Zero, Round::TowardPositive), ( min_quad, n_min_quad, "-0x0.0000000000000000000000000001p-16382", underflow_status, Category::Normal, Round::TowardNegative, ), (min_quad, n_min_quad, "-0", underflow_status, Category::Zero, Round::TowardZero), (min_quad, n_min_quad, "-0", underflow_status, Category::Zero, Round::NearestTiesToAway), ]; for case @ &(x, y, e_result, e_status, e_category) in &single_special_cases { let status; let result = unpack!(status=, x * y); assert_eq!(e_status, status); assert_eq!(e_category, result.category()); assert!(result.bitwise_eq(e_result.parse::().unwrap()), "result = {result:?}, case = {case:?}"); } for case @ &(x, y, e_result, e_status, e_category, round) in &quad_special_cases { let status; let result = unpack!(status=, x.mul_r(y, round)); assert_eq!(e_status, status); assert_eq!(e_category, result.category()); assert!(result.bitwise_eq(e_result.parse::().unwrap()), "result = {result:?}, case = {case:?}"); } } #[test] fn divide() { // Test Special Cases against each other and normal values. let p_inf = Single::INFINITY; let m_inf = -Single::INFINITY; let p_zero = Single::ZERO; let m_zero = -Single::ZERO; let qnan = Single::NAN; let snan = "snan123".parse::().unwrap(); let p_normal_value = "0x1p+0".parse::().unwrap(); let m_normal_value = "-0x1p+0".parse::().unwrap(); let p_largest_value = Single::largest(); let m_largest_value = -Single::largest(); let p_smallest_value = Single::SMALLEST; let m_smallest_value = -Single::SMALLEST; let p_smallest_normalized = Single::smallest_normalized(); let m_smallest_normalized = -Single::smallest_normalized(); let max_quad = "0x1.ffffffffffffffffffffffffffffp+16383".parse::().unwrap(); let min_quad = "0x0.0000000000000000000000000001p-16382".parse::().unwrap(); let n_min_quad = "-0x0.0000000000000000000000000001p-16382".parse::().unwrap(); let overflow_status = Status::OVERFLOW | Status::INEXACT; let underflow_status = Status::UNDERFLOW | Status::INEXACT; let single_special_cases = [ (p_inf, p_inf, "nan", Status::INVALID_OP, Category::NaN), (p_inf, m_inf, "nan", Status::INVALID_OP, Category::NaN), (p_inf, p_zero, "inf", Status::OK, Category::Infinity), (p_inf, m_zero, "-inf", Status::OK, Category::Infinity), (p_inf, qnan, "nan", Status::OK, Category::NaN), (p_inf, snan, "nan123", Status::INVALID_OP, Category::NaN), (p_inf, p_normal_value, "inf", Status::OK, Category::Infinity), (p_inf, m_normal_value, "-inf", Status::OK, Category::Infinity), (p_inf, p_largest_value, "inf", Status::OK, Category::Infinity), (p_inf, m_largest_value, "-inf", Status::OK, Category::Infinity), (p_inf, p_smallest_value, "inf", Status::OK, Category::Infinity), (p_inf, m_smallest_value, "-inf", Status::OK, Category::Infinity), (p_inf, p_smallest_normalized, "inf", Status::OK, Category::Infinity), (p_inf, m_smallest_normalized, "-inf", Status::OK, Category::Infinity), (m_inf, p_inf, "nan", Status::INVALID_OP, Category::NaN), (m_inf, m_inf, "nan", Status::INVALID_OP, Category::NaN), (m_inf, p_zero, "-inf", Status::OK, Category::Infinity), (m_inf, m_zero, "inf", Status::OK, Category::Infinity), (m_inf, qnan, "nan", Status::OK, Category::NaN), (m_inf, snan, "nan123", Status::INVALID_OP, Category::NaN), (m_inf, p_normal_value, "-inf", Status::OK, Category::Infinity), (m_inf, m_normal_value, "inf", Status::OK, Category::Infinity), (m_inf, p_largest_value, "-inf", Status::OK, Category::Infinity), (m_inf, m_largest_value, "inf", Status::OK, Category::Infinity), (m_inf, p_smallest_value, "-inf", Status::OK, Category::Infinity), (m_inf, m_smallest_value, "inf", Status::OK, Category::Infinity), (m_inf, p_smallest_normalized, "-inf", Status::OK, Category::Infinity), (m_inf, m_smallest_normalized, "inf", Status::OK, Category::Infinity), (p_zero, p_inf, "0x0p+0", Status::OK, Category::Zero), (p_zero, m_inf, "-0x0p+0", Status::OK, Category::Zero), (p_zero, p_zero, "nan", Status::INVALID_OP, Category::NaN), (p_zero, m_zero, "nan", Status::INVALID_OP, Category::NaN), (p_zero, qnan, "nan", Status::OK, Category::NaN), (p_zero, snan, "nan123", Status::INVALID_OP, Category::NaN), (p_zero, p_normal_value, "0x0p+0", Status::OK, Category::Zero), (p_zero, m_normal_value, "-0x0p+0", Status::OK, Category::Zero), (p_zero, p_largest_value, "0x0p+0", Status::OK, Category::Zero), (p_zero, m_largest_value, "-0x0p+0", Status::OK, Category::Zero), (p_zero, p_smallest_value, "0x0p+0", Status::OK, Category::Zero), (p_zero, m_smallest_value, "-0x0p+0", Status::OK, Category::Zero), (p_zero, p_smallest_normalized, "0x0p+0", Status::OK, Category::Zero), (p_zero, m_smallest_normalized, "-0x0p+0", Status::OK, Category::Zero), (m_zero, p_inf, "-0x0p+0", Status::OK, Category::Zero), (m_zero, m_inf, "0x0p+0", Status::OK, Category::Zero), (m_zero, p_zero, "nan", Status::INVALID_OP, Category::NaN), (m_zero, m_zero, "nan", Status::INVALID_OP, Category::NaN), (m_zero, qnan, "nan", Status::OK, Category::NaN), (m_zero, snan, "nan123", Status::INVALID_OP, Category::NaN), (m_zero, p_normal_value, "-0x0p+0", Status::OK, Category::Zero), (m_zero, m_normal_value, "0x0p+0", Status::OK, Category::Zero), (m_zero, p_largest_value, "-0x0p+0", Status::OK, Category::Zero), (m_zero, m_largest_value, "0x0p+0", Status::OK, Category::Zero), (m_zero, p_smallest_value, "-0x0p+0", Status::OK, Category::Zero), (m_zero, m_smallest_value, "0x0p+0", Status::OK, Category::Zero), (m_zero, p_smallest_normalized, "-0x0p+0", Status::OK, Category::Zero), (m_zero, m_smallest_normalized, "0x0p+0", Status::OK, Category::Zero), (qnan, p_inf, "nan", Status::OK, Category::NaN), (qnan, m_inf, "nan", Status::OK, Category::NaN), (qnan, p_zero, "nan", Status::OK, Category::NaN), (qnan, m_zero, "nan", Status::OK, Category::NaN), (qnan, qnan, "nan", Status::OK, Category::NaN), (qnan, snan, "nan", Status::INVALID_OP, Category::NaN), (qnan, p_normal_value, "nan", Status::OK, Category::NaN), (qnan, m_normal_value, "nan", Status::OK, Category::NaN), (qnan, p_largest_value, "nan", Status::OK, Category::NaN), (qnan, m_largest_value, "nan", Status::OK, Category::NaN), (qnan, p_smallest_value, "nan", Status::OK, Category::NaN), (qnan, m_smallest_value, "nan", Status::OK, Category::NaN), (qnan, p_smallest_normalized, "nan", Status::OK, Category::NaN), (qnan, m_smallest_normalized, "nan", Status::OK, Category::NaN), (snan, p_inf, "nan123", Status::INVALID_OP, Category::NaN), (snan, m_inf, "nan123", Status::INVALID_OP, Category::NaN), (snan, p_zero, "nan123", Status::INVALID_OP, Category::NaN), (snan, m_zero, "nan123", Status::INVALID_OP, Category::NaN), (snan, qnan, "nan123", Status::INVALID_OP, Category::NaN), (snan, snan, "nan123", Status::INVALID_OP, Category::NaN), (snan, p_normal_value, "nan123", Status::INVALID_OP, Category::NaN), (snan, m_normal_value, "nan123", Status::INVALID_OP, Category::NaN), (snan, p_largest_value, "nan123", Status::INVALID_OP, Category::NaN), (snan, m_largest_value, "nan123", Status::INVALID_OP, Category::NaN), (snan, p_smallest_value, "nan123", Status::INVALID_OP, Category::NaN), (snan, m_smallest_value, "nan123", Status::INVALID_OP, Category::NaN), (snan, p_smallest_normalized, "nan123", Status::INVALID_OP, Category::NaN), (snan, m_smallest_normalized, "nan123", Status::INVALID_OP, Category::NaN), (p_normal_value, p_inf, "0x0p+0", Status::OK, Category::Zero), (p_normal_value, m_inf, "-0x0p+0", Status::OK, Category::Zero), (p_normal_value, p_zero, "inf", Status::DIV_BY_ZERO, Category::Infinity), (p_normal_value, m_zero, "-inf", Status::DIV_BY_ZERO, Category::Infinity), (p_normal_value, qnan, "nan", Status::OK, Category::NaN), (p_normal_value, snan, "nan123", Status::INVALID_OP, Category::NaN), (p_normal_value, p_normal_value, "0x1p+0", Status::OK, Category::Normal), (p_normal_value, m_normal_value, "-0x1p+0", Status::OK, Category::Normal), (p_normal_value, p_largest_value, "0x1p-128", underflow_status, Category::Normal), (p_normal_value, m_largest_value, "-0x1p-128", underflow_status, Category::Normal), (p_normal_value, p_smallest_value, "inf", overflow_status, Category::Infinity), (p_normal_value, m_smallest_value, "-inf", overflow_status, Category::Infinity), (p_normal_value, p_smallest_normalized, "0x1p+126", Status::OK, Category::Normal), (p_normal_value, m_smallest_normalized, "-0x1p+126", Status::OK, Category::Normal), (m_normal_value, p_inf, "-0x0p+0", Status::OK, Category::Zero), (m_normal_value, m_inf, "0x0p+0", Status::OK, Category::Zero), (m_normal_value, p_zero, "-inf", Status::DIV_BY_ZERO, Category::Infinity), (m_normal_value, m_zero, "inf", Status::DIV_BY_ZERO, Category::Infinity), (m_normal_value, qnan, "nan", Status::OK, Category::NaN), (m_normal_value, snan, "nan123", Status::INVALID_OP, Category::NaN), (m_normal_value, p_normal_value, "-0x1p+0", Status::OK, Category::Normal), (m_normal_value, m_normal_value, "0x1p+0", Status::OK, Category::Normal), (m_normal_value, p_largest_value, "-0x1p-128", underflow_status, Category::Normal), (m_normal_value, m_largest_value, "0x1p-128", underflow_status, Category::Normal), (m_normal_value, p_smallest_value, "-inf", overflow_status, Category::Infinity), (m_normal_value, m_smallest_value, "inf", overflow_status, Category::Infinity), (m_normal_value, p_smallest_normalized, "-0x1p+126", Status::OK, Category::Normal), (m_normal_value, m_smallest_normalized, "0x1p+126", Status::OK, Category::Normal), (p_largest_value, p_inf, "0x0p+0", Status::OK, Category::Zero), (p_largest_value, m_inf, "-0x0p+0", Status::OK, Category::Zero), (p_largest_value, p_zero, "inf", Status::DIV_BY_ZERO, Category::Infinity), (p_largest_value, m_zero, "-inf", Status::DIV_BY_ZERO, Category::Infinity), (p_largest_value, qnan, "nan", Status::OK, Category::NaN), (p_largest_value, snan, "nan123", Status::INVALID_OP, Category::NaN), (p_largest_value, p_normal_value, "0x1.fffffep+127", Status::OK, Category::Normal), (p_largest_value, m_normal_value, "-0x1.fffffep+127", Status::OK, Category::Normal), (p_largest_value, p_largest_value, "0x1p+0", Status::OK, Category::Normal), (p_largest_value, m_largest_value, "-0x1p+0", Status::OK, Category::Normal), (p_largest_value, p_smallest_value, "inf", overflow_status, Category::Infinity), (p_largest_value, m_smallest_value, "-inf", overflow_status, Category::Infinity), (p_largest_value, p_smallest_normalized, "inf", overflow_status, Category::Infinity), (p_largest_value, m_smallest_normalized, "-inf", overflow_status, Category::Infinity), (m_largest_value, p_inf, "-0x0p+0", Status::OK, Category::Zero), (m_largest_value, m_inf, "0x0p+0", Status::OK, Category::Zero), (m_largest_value, p_zero, "-inf", Status::DIV_BY_ZERO, Category::Infinity), (m_largest_value, m_zero, "inf", Status::DIV_BY_ZERO, Category::Infinity), (m_largest_value, qnan, "nan", Status::OK, Category::NaN), (m_largest_value, snan, "nan123", Status::INVALID_OP, Category::NaN), (m_largest_value, p_normal_value, "-0x1.fffffep+127", Status::OK, Category::Normal), (m_largest_value, m_normal_value, "0x1.fffffep+127", Status::OK, Category::Normal), (m_largest_value, p_largest_value, "-0x1p+0", Status::OK, Category::Normal), (m_largest_value, m_largest_value, "0x1p+0", Status::OK, Category::Normal), (m_largest_value, p_smallest_value, "-inf", overflow_status, Category::Infinity), (m_largest_value, m_smallest_value, "inf", overflow_status, Category::Infinity), (m_largest_value, p_smallest_normalized, "-inf", overflow_status, Category::Infinity), (m_largest_value, m_smallest_normalized, "inf", overflow_status, Category::Infinity), (p_smallest_value, p_inf, "0x0p+0", Status::OK, Category::Zero), (p_smallest_value, m_inf, "-0x0p+0", Status::OK, Category::Zero), (p_smallest_value, p_zero, "inf", Status::DIV_BY_ZERO, Category::Infinity), (p_smallest_value, m_zero, "-inf", Status::DIV_BY_ZERO, Category::Infinity), (p_smallest_value, qnan, "nan", Status::OK, Category::NaN), (p_smallest_value, snan, "nan123", Status::INVALID_OP, Category::NaN), (p_smallest_value, p_normal_value, "0x1p-149", Status::OK, Category::Normal), (p_smallest_value, m_normal_value, "-0x1p-149", Status::OK, Category::Normal), (p_smallest_value, p_largest_value, "0x0p+0", underflow_status, Category::Zero), (p_smallest_value, m_largest_value, "-0x0p+0", underflow_status, Category::Zero), (p_smallest_value, p_smallest_value, "0x1p+0", Status::OK, Category::Normal), (p_smallest_value, m_smallest_value, "-0x1p+0", Status::OK, Category::Normal), (p_smallest_value, p_smallest_normalized, "0x1p-23", Status::OK, Category::Normal), (p_smallest_value, m_smallest_normalized, "-0x1p-23", Status::OK, Category::Normal), (m_smallest_value, p_inf, "-0x0p+0", Status::OK, Category::Zero), (m_smallest_value, m_inf, "0x0p+0", Status::OK, Category::Zero), (m_smallest_value, p_zero, "-inf", Status::DIV_BY_ZERO, Category::Infinity), (m_smallest_value, m_zero, "inf", Status::DIV_BY_ZERO, Category::Infinity), (m_smallest_value, qnan, "nan", Status::OK, Category::NaN), (m_smallest_value, snan, "nan123", Status::INVALID_OP, Category::NaN), (m_smallest_value, p_normal_value, "-0x1p-149", Status::OK, Category::Normal), (m_smallest_value, m_normal_value, "0x1p-149", Status::OK, Category::Normal), (m_smallest_value, p_largest_value, "-0x0p+0", underflow_status, Category::Zero), (m_smallest_value, m_largest_value, "0x0p+0", underflow_status, Category::Zero), (m_smallest_value, p_smallest_value, "-0x1p+0", Status::OK, Category::Normal), (m_smallest_value, m_smallest_value, "0x1p+0", Status::OK, Category::Normal), (m_smallest_value, p_smallest_normalized, "-0x1p-23", Status::OK, Category::Normal), (m_smallest_value, m_smallest_normalized, "0x1p-23", Status::OK, Category::Normal), (p_smallest_normalized, p_inf, "0x0p+0", Status::OK, Category::Zero), (p_smallest_normalized, m_inf, "-0x0p+0", Status::OK, Category::Zero), (p_smallest_normalized, p_zero, "inf", Status::DIV_BY_ZERO, Category::Infinity), (p_smallest_normalized, m_zero, "-inf", Status::DIV_BY_ZERO, Category::Infinity), (p_smallest_normalized, qnan, "nan", Status::OK, Category::NaN), (p_smallest_normalized, snan, "nan123", Status::INVALID_OP, Category::NaN), (p_smallest_normalized, p_normal_value, "0x1p-126", Status::OK, Category::Normal), (p_smallest_normalized, m_normal_value, "-0x1p-126", Status::OK, Category::Normal), (p_smallest_normalized, p_largest_value, "0x0p+0", underflow_status, Category::Zero), (p_smallest_normalized, m_largest_value, "-0x0p+0", underflow_status, Category::Zero), (p_smallest_normalized, p_smallest_value, "0x1p+23", Status::OK, Category::Normal), (p_smallest_normalized, m_smallest_value, "-0x1p+23", Status::OK, Category::Normal), (p_smallest_normalized, p_smallest_normalized, "0x1p+0", Status::OK, Category::Normal), (p_smallest_normalized, m_smallest_normalized, "-0x1p+0", Status::OK, Category::Normal), (m_smallest_normalized, p_inf, "-0x0p+0", Status::OK, Category::Zero), (m_smallest_normalized, m_inf, "0x0p+0", Status::OK, Category::Zero), (m_smallest_normalized, p_zero, "-inf", Status::DIV_BY_ZERO, Category::Infinity), (m_smallest_normalized, m_zero, "inf", Status::DIV_BY_ZERO, Category::Infinity), (m_smallest_normalized, qnan, "nan", Status::OK, Category::NaN), (m_smallest_normalized, snan, "nan123", Status::INVALID_OP, Category::NaN), (m_smallest_normalized, p_normal_value, "-0x1p-126", Status::OK, Category::Normal), (m_smallest_normalized, m_normal_value, "0x1p-126", Status::OK, Category::Normal), (m_smallest_normalized, p_largest_value, "-0x0p+0", underflow_status, Category::Zero), (m_smallest_normalized, m_largest_value, "0x0p+0", underflow_status, Category::Zero), (m_smallest_normalized, p_smallest_value, "-0x1p+23", Status::OK, Category::Normal), (m_smallest_normalized, m_smallest_value, "0x1p+23", Status::OK, Category::Normal), (m_smallest_normalized, p_smallest_normalized, "-0x1p+0", Status::OK, Category::Normal), (m_smallest_normalized, m_smallest_normalized, "0x1p+0", Status::OK, Category::Normal), ]; let quad_special_cases = [ (max_quad, n_min_quad, "-inf", overflow_status, Category::Infinity, Round::NearestTiesToEven), ( max_quad, n_min_quad, "-0x1.ffffffffffffffffffffffffffffp+16383", Status::INEXACT, Category::Normal, Round::TowardPositive, ), (max_quad, n_min_quad, "-inf", overflow_status, Category::Infinity, Round::TowardNegative), ( max_quad, n_min_quad, "-0x1.ffffffffffffffffffffffffffffp+16383", Status::INEXACT, Category::Normal, Round::TowardZero, ), (max_quad, n_min_quad, "-inf", overflow_status, Category::Infinity, Round::NearestTiesToAway), (min_quad, max_quad, "0", underflow_status, Category::Zero, Round::NearestTiesToEven), ( min_quad, max_quad, "0x0.0000000000000000000000000001p-16382", underflow_status, Category::Normal, Round::TowardPositive, ), (min_quad, max_quad, "0", underflow_status, Category::Zero, Round::TowardNegative), (min_quad, max_quad, "0", underflow_status, Category::Zero, Round::TowardZero), (min_quad, max_quad, "0", underflow_status, Category::Zero, Round::NearestTiesToAway), (n_min_quad, max_quad, "-0", underflow_status, Category::Zero, Round::NearestTiesToEven), (n_min_quad, max_quad, "-0", underflow_status, Category::Zero, Round::TowardPositive), ( n_min_quad, max_quad, "-0x0.0000000000000000000000000001p-16382", underflow_status, Category::Normal, Round::TowardNegative, ), (n_min_quad, max_quad, "-0", underflow_status, Category::Zero, Round::TowardZero), (n_min_quad, max_quad, "-0", underflow_status, Category::Zero, Round::NearestTiesToAway), ]; for case @ &(x, y, e_result, e_status, e_category) in &single_special_cases { let status; let result = unpack!(status=, x / y); assert_eq!(e_status, status); assert_eq!(e_category, result.category()); assert!(result.bitwise_eq(e_result.parse::().unwrap()), "result = {result:?}, case = {case:?}"); } for case @ &(x, y, e_result, e_status, e_category, round) in &quad_special_cases { let status; let result = unpack!(status=, x.div_r(y, round)); assert_eq!(e_status, status); assert_eq!(e_category, result.category()); assert!(result.bitwise_eq(e_result.parse::().unwrap()), "result = {result:?}, case = {case:?}"); } } #[test] fn operator_overloads() { // This is mostly testing that these operator overloads compile. let one = "0x1p+0".parse::().unwrap(); let two = "0x2p+0".parse::().unwrap(); assert!(two.bitwise_eq((one + one).value)); assert!(one.bitwise_eq((two - one).value)); assert!(two.bitwise_eq((one * two).value)); assert!(one.bitwise_eq((two / two).value)); } #[test] fn comparisons() { let vals = [ /* MNan */ -Single::NAN, /* MInf */ -Single::INFINITY, /* MBig */ -Single::largest(), /* MOne */ "-0x1p+0".parse::().unwrap(), /* MZer */ -Single::ZERO, /* PZer */ Single::ZERO, /* POne */ "0x1p+0".parse::().unwrap(), /* PBig */ Single::largest(), /* PInf */ Single::INFINITY, /* PNan */ Single::NAN, ]; const LT: Option = Some(Ordering::Less); const EQ: Option = Some(Ordering::Equal); const GT: Option = Some(Ordering::Greater); const UN: Option = None; // HACK(eddyb) for some reason the first row (MNan) gets formatted differently. #[rustfmt::skip] let relations = [ // -N -I -B -1 -0 +0 +1 +B +I +N /* MNan */ [UN, UN, UN, UN, UN, UN, UN, UN, UN, UN], /* MInf */ [UN, EQ, LT, LT, LT, LT, LT, LT, LT, UN], /* MBig */ [UN, GT, EQ, LT, LT, LT, LT, LT, LT, UN], /* MOne */ [UN, GT, GT, EQ, LT, LT, LT, LT, LT, UN], /* MZer */ [UN, GT, GT, GT, EQ, EQ, LT, LT, LT, UN], /* PZer */ [UN, GT, GT, GT, EQ, EQ, LT, LT, LT, UN], /* POne */ [UN, GT, GT, GT, GT, GT, EQ, LT, LT, UN], /* PBig */ [UN, GT, GT, GT, GT, GT, GT, EQ, LT, UN], /* PInf */ [UN, GT, GT, GT, GT, GT, GT, GT, EQ, UN], /* PNan */ [UN, UN, UN, UN, UN, UN, UN, UN, UN, UN], ]; for (i, &lhs) in vals.iter().enumerate() { for (j, &rhs) in vals.iter().enumerate() { let relation = lhs.partial_cmp(&rhs); assert_eq!(relation, relations[i][j]); // NOTE(eddyb) these checks have been kept from the C++ code which didn't // appear to have a concept like `Option`, but in Rust they // should be entirely redundant with the single `assert_eq!` above. match relation { LT => { assert!(!(lhs == rhs)); assert!(lhs != rhs); assert!(lhs < rhs); assert!(!(lhs > rhs)); assert!(lhs <= rhs); assert!(!(lhs >= rhs)); } EQ => { assert!(lhs == rhs); assert!(!(lhs != rhs)); assert!(!(lhs < rhs)); assert!(!(lhs > rhs)); assert!(lhs <= rhs); assert!(lhs >= rhs); } GT => { assert!(!(lhs == rhs)); assert!(lhs != rhs); assert!(!(lhs < rhs)); assert!(lhs > rhs); assert!(!(lhs <= rhs)); assert!(lhs >= rhs); } UN => { assert!(!(lhs == rhs)); assert!(lhs != rhs); assert!(!(lhs < rhs)); assert!(!(lhs > rhs)); assert!(!(lhs <= rhs)); assert!(!(lhs >= rhs)); } } } } } #[test] fn abs() { let p_inf = Single::INFINITY; let m_inf = -Single::INFINITY; let p_zero = Single::ZERO; let m_zero = -Single::ZERO; let p_qnan = Single::NAN; let m_qnan = -Single::NAN; let p_snan = Single::snan(None); let m_snan = -Single::snan(None); let p_normal_value = "0x1p+0".parse::().unwrap(); let m_normal_value = "-0x1p+0".parse::().unwrap(); let p_largest_value = Single::largest(); let m_largest_value = -Single::largest(); let p_smallest_value = Single::SMALLEST; let m_smallest_value = -Single::SMALLEST; let p_smallest_normalized = Single::smallest_normalized(); let m_smallest_normalized = -Single::smallest_normalized(); assert!(p_inf.bitwise_eq(p_inf.abs())); assert!(p_inf.bitwise_eq(m_inf.abs())); assert!(p_zero.bitwise_eq(p_zero.abs())); assert!(p_zero.bitwise_eq(m_zero.abs())); assert!(p_qnan.bitwise_eq(p_qnan.abs())); assert!(p_qnan.bitwise_eq(m_qnan.abs())); assert!(p_snan.bitwise_eq(p_snan.abs())); assert!(p_snan.bitwise_eq(m_snan.abs())); assert!(p_normal_value.bitwise_eq(p_normal_value.abs())); assert!(p_normal_value.bitwise_eq(m_normal_value.abs())); assert!(p_largest_value.bitwise_eq(p_largest_value.abs())); assert!(p_largest_value.bitwise_eq(m_largest_value.abs())); assert!(p_smallest_value.bitwise_eq(p_smallest_value.abs())); assert!(p_smallest_value.bitwise_eq(m_smallest_value.abs())); assert!(p_smallest_normalized.bitwise_eq(p_smallest_normalized.abs(),)); assert!(p_smallest_normalized.bitwise_eq(m_smallest_normalized.abs(),)); } #[test] fn neg() { let one = "1.0".parse::().unwrap(); let neg_one = "-1.0".parse::().unwrap(); let zero = Single::ZERO; let neg_zero = -Single::ZERO; let inf = Single::INFINITY; let neg_inf = -Single::INFINITY; let qnan = Single::NAN; let neg_qnan = -Single::NAN; assert!(neg_one.bitwise_eq(-one)); assert!(one.bitwise_eq(-neg_one)); assert!(neg_zero.bitwise_eq(-zero)); assert!(zero.bitwise_eq(-neg_zero)); assert!(neg_inf.bitwise_eq(-inf)); assert!(inf.bitwise_eq(-neg_inf)); assert!(neg_inf.bitwise_eq(-inf)); assert!(inf.bitwise_eq(-neg_inf)); assert!(neg_qnan.bitwise_eq(-qnan)); assert!(qnan.bitwise_eq(-neg_qnan)); } #[test] fn ilogb() { assert_eq!(-1074, Double::SMALLEST.ilogb()); assert_eq!(-1074, (-Double::SMALLEST).ilogb()); assert_eq!(-1023, "0x1.ffffffffffffep-1024".parse::().unwrap().ilogb()); assert_eq!(-1023, "0x1.ffffffffffffep-1023".parse::().unwrap().ilogb()); assert_eq!(-1023, "-0x1.ffffffffffffep-1023".parse::().unwrap().ilogb()); assert_eq!(-51, "0x1p-51".parse::().unwrap().ilogb()); assert_eq!(-1023, "0x1.c60f120d9f87cp-1023".parse::().unwrap().ilogb()); assert_eq!(-2, "0x0.ffffp-1".parse::().unwrap().ilogb()); assert_eq!(-1023, "0x1.fffep-1023".parse::().unwrap().ilogb()); assert_eq!(1023, Double::largest().ilogb()); assert_eq!(1023, (-Double::largest()).ilogb()); assert_eq!(0, "0x1p+0".parse::().unwrap().ilogb()); assert_eq!(0, "-0x1p+0".parse::().unwrap().ilogb()); assert_eq!(42, "0x1p+42".parse::().unwrap().ilogb()); assert_eq!(-42, "0x1p-42".parse::().unwrap().ilogb()); assert_eq!(IEK_INF, Single::INFINITY.ilogb()); assert_eq!(IEK_INF, (-Single::INFINITY).ilogb()); assert_eq!(IEK_ZERO, Single::ZERO.ilogb()); assert_eq!(IEK_ZERO, (-Single::ZERO).ilogb()); assert_eq!(IEK_NAN, Single::NAN.ilogb()); assert_eq!(IEK_NAN, Single::snan(None).ilogb()); assert_eq!(127, Single::largest().ilogb()); assert_eq!(127, (-Single::largest()).ilogb()); assert_eq!(-149, Single::SMALLEST.ilogb()); assert_eq!(-149, (-Single::SMALLEST).ilogb()); assert_eq!(-126, Single::smallest_normalized().ilogb()); assert_eq!(-126, (-Single::smallest_normalized()).ilogb()); } #[test] fn scalbn() { assert!("0x1p+0" .parse::() .unwrap() .bitwise_eq("0x1p+0".parse::().unwrap().scalbn(0),)); assert!("0x1p+42" .parse::() .unwrap() .bitwise_eq("0x1p+0".parse::().unwrap().scalbn(42),)); assert!("0x1p-42" .parse::() .unwrap() .bitwise_eq("0x1p+0".parse::().unwrap().scalbn(-42),)); let p_inf = Single::INFINITY; let m_inf = -Single::INFINITY; let p_zero = Single::ZERO; let m_zero = -Single::ZERO; let p_qnan = Single::NAN; let m_qnan = -Single::NAN; let snan = Single::snan(None); assert!(p_inf.bitwise_eq(p_inf.scalbn(0))); assert!(m_inf.bitwise_eq(m_inf.scalbn(0))); assert!(p_zero.bitwise_eq(p_zero.scalbn(0))); assert!(m_zero.bitwise_eq(m_zero.scalbn(0))); assert!(p_qnan.bitwise_eq(p_qnan.scalbn(0))); assert!(m_qnan.bitwise_eq(m_qnan.scalbn(0))); assert!(!snan.scalbn(0).is_signaling()); let scalbn_snan = snan.scalbn(1); assert!(scalbn_snan.is_nan() && !scalbn_snan.is_signaling()); // Make sure highest bit of payload is preserved. let payload = (1 << 50) | (1 << 49) | (1234 << 32) | 1; let snan_with_payload = Double::snan(Some(payload)); let quiet_payload = snan_with_payload.scalbn(1); assert!(quiet_payload.is_nan() && !quiet_payload.is_signaling()); assert_eq!(payload, quiet_payload.to_bits() & ((1 << 51) - 1)); assert!(p_inf.bitwise_eq("0x1p+0".parse::().unwrap().scalbn(128),)); assert!(m_inf.bitwise_eq("-0x1p+0".parse::().unwrap().scalbn(128),)); assert!(p_inf.bitwise_eq("0x1p+127".parse::().unwrap().scalbn(1),)); assert!(p_zero.bitwise_eq("0x1p-127".parse::().unwrap().scalbn(-127),)); assert!(m_zero.bitwise_eq("-0x1p-127".parse::().unwrap().scalbn(-127),)); assert!("-0x1p-149" .parse::() .unwrap() .bitwise_eq("-0x1p-127".parse::().unwrap().scalbn(-22),)); assert!(p_zero.bitwise_eq("0x1p-126".parse::().unwrap().scalbn(-24),)); let smallest_f64 = Double::SMALLEST; let neg_smallest_f64 = -Double::SMALLEST; let largest_f64 = Double::largest(); let neg_largest_f64 = -Double::largest(); let largest_denormal_f64 = "0x1.ffffffffffffep-1023".parse::().unwrap(); let neg_largest_denormal_f64 = "-0x1.ffffffffffffep-1023".parse::().unwrap(); assert!(smallest_f64.bitwise_eq("0x1p-1074".parse::().unwrap().scalbn(0),)); assert!(neg_smallest_f64.bitwise_eq("-0x1p-1074".parse::().unwrap().scalbn(0),)); assert!("0x1p+1023" .parse::() .unwrap() .bitwise_eq(smallest_f64.scalbn(2097,),)); assert!(smallest_f64.scalbn(-2097).is_pos_zero()); assert!(smallest_f64.scalbn(-2098).is_pos_zero()); assert!(smallest_f64.scalbn(-2099).is_pos_zero()); assert!("0x1p+1022" .parse::() .unwrap() .bitwise_eq(smallest_f64.scalbn(2096,),)); assert!("0x1p+1023" .parse::() .unwrap() .bitwise_eq(smallest_f64.scalbn(2097,),)); assert!(smallest_f64.scalbn(2098).is_infinite()); assert!(smallest_f64.scalbn(2099).is_infinite()); // Test for integer overflows when adding to exponent. assert!(smallest_f64.scalbn(-ExpInt::max_value()).is_pos_zero()); assert!(largest_f64.scalbn(ExpInt::max_value()).is_infinite()); assert!(largest_denormal_f64.bitwise_eq(largest_denormal_f64.scalbn(0),)); assert!(neg_largest_denormal_f64.bitwise_eq(neg_largest_denormal_f64.scalbn(0),)); assert!("0x1.ffffffffffffep-1022" .parse::() .unwrap() .bitwise_eq(largest_denormal_f64.scalbn(1))); assert!("-0x1.ffffffffffffep-1021" .parse::() .unwrap() .bitwise_eq(neg_largest_denormal_f64.scalbn(2))); assert!("0x1.ffffffffffffep+1" .parse::() .unwrap() .bitwise_eq(largest_denormal_f64.scalbn(1024))); assert!(largest_denormal_f64.scalbn(-1023).is_pos_zero()); assert!(largest_denormal_f64.scalbn(-1024).is_pos_zero()); assert!(largest_denormal_f64.scalbn(-2048).is_pos_zero()); assert!(largest_denormal_f64.scalbn(2047).is_infinite()); assert!(largest_denormal_f64.scalbn(2098).is_infinite()); assert!(largest_denormal_f64.scalbn(2099).is_infinite()); assert!("0x1.ffffffffffffep-2" .parse::() .unwrap() .bitwise_eq(largest_denormal_f64.scalbn(1021))); assert!("0x1.ffffffffffffep-1" .parse::() .unwrap() .bitwise_eq(largest_denormal_f64.scalbn(1022))); assert!("0x1.ffffffffffffep+0" .parse::() .unwrap() .bitwise_eq(largest_denormal_f64.scalbn(1023))); assert!("0x1.ffffffffffffep+1023" .parse::() .unwrap() .bitwise_eq(largest_denormal_f64.scalbn(2046))); assert!("0x1p+974" .parse::() .unwrap() .bitwise_eq(smallest_f64.scalbn(2048,),)); let random_denormal_f64 = "0x1.c60f120d9f87cp+51".parse::().unwrap(); assert!("0x1.c60f120d9f87cp-972" .parse::() .unwrap() .bitwise_eq(random_denormal_f64.scalbn(-1023))); assert!("0x1.c60f120d9f87cp-1" .parse::() .unwrap() .bitwise_eq(random_denormal_f64.scalbn(-52))); assert!("0x1.c60f120d9f87cp-2" .parse::() .unwrap() .bitwise_eq(random_denormal_f64.scalbn(-53))); assert!("0x1.c60f120d9f87cp+0" .parse::() .unwrap() .bitwise_eq(random_denormal_f64.scalbn(-51))); assert!(random_denormal_f64.scalbn(-2097).is_pos_zero()); assert!(random_denormal_f64.scalbn(-2090).is_pos_zero()); assert!("-0x1p-1073" .parse::() .unwrap() .bitwise_eq(neg_largest_f64.scalbn(-2097),)); assert!("-0x1p-1024" .parse::() .unwrap() .bitwise_eq(neg_largest_f64.scalbn(-2048),)); assert!("0x1p-1073" .parse::() .unwrap() .bitwise_eq(largest_f64.scalbn(-2097,),)); assert!("0x1p-1074" .parse::() .unwrap() .bitwise_eq(largest_f64.scalbn(-2098,),)); assert!("-0x1p-1074" .parse::() .unwrap() .bitwise_eq(neg_largest_f64.scalbn(-2098),)); assert!(neg_largest_f64.scalbn(-2099).is_neg_zero()); assert!(largest_f64.scalbn(1).is_infinite()); assert!("0x1p+0" .parse::() .unwrap() .bitwise_eq("0x1p+52".parse::().unwrap().scalbn(-52),)); assert!("0x1p-103" .parse::() .unwrap() .bitwise_eq("0x1p-51".parse::().unwrap().scalbn(-52),)); } #[test] fn frexp() { let p_zero = Double::ZERO; let m_zero = -Double::ZERO; let one = Double::from_f64(1.0); let m_one = Double::from_f64(-1.0); let largest_denormal = "0x1.ffffffffffffep-1023".parse::().unwrap(); let neg_largest_denormal = "-0x1.ffffffffffffep-1023".parse::().unwrap(); let smallest = Double::SMALLEST; let neg_smallest = -Double::SMALLEST; let largest = Double::largest(); let neg_largest = -Double::largest(); let p_inf = Double::INFINITY; let m_inf = -Double::INFINITY; let p_qnan = Double::NAN; let m_qnan = -Double::NAN; let snan = Double::snan(None); // Make sure highest bit of payload is preserved. let payload = (1 << 50) | (1 << 49) | (1234 << 32) | 1; let snan_with_payload = Double::snan(Some(payload)); let mut exp = 0; let frac = p_zero.frexp(&mut exp); assert_eq!(0, exp); assert!(frac.is_pos_zero()); let frac = m_zero.frexp(&mut exp); assert_eq!(0, exp); assert!(frac.is_neg_zero()); let frac = one.frexp(&mut exp); assert_eq!(1, exp); assert!("0x1p-1".parse::().unwrap().bitwise_eq(frac)); let frac = m_one.frexp(&mut exp); assert_eq!(1, exp); assert!("-0x1p-1".parse::().unwrap().bitwise_eq(frac)); let frac = largest_denormal.frexp(&mut exp); assert_eq!(-1022, exp); assert!("0x1.ffffffffffffep-1".parse::().unwrap().bitwise_eq(frac)); let frac = neg_largest_denormal.frexp(&mut exp); assert_eq!(-1022, exp); assert!("-0x1.ffffffffffffep-1".parse::().unwrap().bitwise_eq(frac)); let frac = smallest.frexp(&mut exp); assert_eq!(-1073, exp); assert!("0x1p-1".parse::().unwrap().bitwise_eq(frac)); let frac = neg_smallest.frexp(&mut exp); assert_eq!(-1073, exp); assert!("-0x1p-1".parse::().unwrap().bitwise_eq(frac)); let frac = largest.frexp(&mut exp); assert_eq!(1024, exp); assert!("0x1.fffffffffffffp-1".parse::().unwrap().bitwise_eq(frac)); let frac = neg_largest.frexp(&mut exp); assert_eq!(1024, exp); assert!("-0x1.fffffffffffffp-1".parse::().unwrap().bitwise_eq(frac)); let frac = p_inf.frexp(&mut exp); assert_eq!(IEK_INF, exp); assert!(frac.is_infinite() && !frac.is_negative()); let frac = m_inf.frexp(&mut exp); assert_eq!(IEK_INF, exp); assert!(frac.is_infinite() && frac.is_negative()); let frac = p_qnan.frexp(&mut exp); assert_eq!(IEK_NAN, exp); assert!(frac.is_nan()); let frac = m_qnan.frexp(&mut exp); assert_eq!(IEK_NAN, exp); assert!(frac.is_nan()); let frac = snan.frexp(&mut exp); assert_eq!(IEK_NAN, exp); assert!(frac.is_nan() && !frac.is_signaling()); let frac = snan_with_payload.frexp(&mut exp); assert_eq!(IEK_NAN, exp); assert!(frac.is_nan() && !frac.is_signaling()); assert_eq!(payload, frac.to_bits() & ((1 << 51) - 1)); let frac = "0x0.ffffp-1".parse::().unwrap().frexp(&mut exp); assert_eq!(-1, exp); assert!("0x1.fffep-1".parse::().unwrap().bitwise_eq(frac)); let frac = "0x1p-51".parse::().unwrap().frexp(&mut exp); assert_eq!(-50, exp); assert!("0x1p-1".parse::().unwrap().bitwise_eq(frac)); let frac = "0x1.c60f120d9f87cp+51".parse::().unwrap().frexp(&mut exp); assert_eq!(52, exp); assert!("0x1.c60f120d9f87cp-1".parse::().unwrap().bitwise_eq(frac)); } #[test] fn modulo() { let mut status; { let f1 = "1.5".parse::().unwrap(); let f2 = "1.0".parse::().unwrap(); let expected = "0.5".parse::().unwrap(); assert!(unpack!(status=, f1 % f2).bitwise_eq(expected)); assert_eq!(status, Status::OK); } { let f1 = "0.5".parse::().unwrap(); let f2 = "1.0".parse::().unwrap(); let expected = "0.5".parse::().unwrap(); assert!(unpack!(status=, f1 % f2).bitwise_eq(expected)); assert_eq!(status, Status::OK); } { let f1 = "0x1.3333333333333p-2".parse::().unwrap(); // 0.3 let f2 = "0x1.47ae147ae147bp-7".parse::().unwrap(); // 0.01 // 0.009999999999999983 let expected = "0x1.47ae147ae1471p-7".parse::().unwrap(); assert!(unpack!(status=, f1 % f2).bitwise_eq(expected)); assert_eq!(status, Status::OK); } { let f1 = "0x1p64".parse::().unwrap(); // 1.8446744073709552e19 let f2 = "1.5".parse::().unwrap(); let expected = "1.0".parse::().unwrap(); assert!(unpack!(status=, f1 % f2).bitwise_eq(expected)); assert_eq!(status, Status::OK); } { let f1 = "0x1p1000".parse::().unwrap(); let f2 = "0x1p-1000".parse::().unwrap(); let expected = "0.0".parse::().unwrap(); assert!(unpack!(status=, f1 % f2).bitwise_eq(expected)); assert_eq!(status, Status::OK); } { let f1 = "0.0".parse::().unwrap(); let f2 = "1.0".parse::().unwrap(); let expected = "0.0".parse::().unwrap(); assert!(unpack!(status=, f1 % f2).bitwise_eq(expected)); assert_eq!(status, Status::OK); } { let f1 = "1.0".parse::().unwrap(); let f2 = "0.0".parse::().unwrap(); assert!(unpack!(status=, f1 % f2).is_nan()); assert_eq!(status, Status::INVALID_OP); } { let f1 = "0.0".parse::().unwrap(); let f2 = "0.0".parse::().unwrap(); assert!(unpack!(status=, f1 % f2).is_nan()); assert_eq!(status, Status::INVALID_OP); } { let f1 = Double::INFINITY; let f2 = "1.0".parse::().unwrap(); assert!(unpack!(status=, f1 % f2).is_nan()); assert_eq!(status, Status::INVALID_OP); } { let f1 = "-4.0".parse::().unwrap(); let f2 = "-2.0".parse::().unwrap(); let expected = "-0.0".parse::().unwrap(); assert!(unpack!(status=, f1 % f2).bitwise_eq(expected)); assert_eq!(status, Status::OK); } { let f1 = "-4.0".parse::().unwrap(); let f2 = "2.0".parse::().unwrap(); let expected = "-0.0".parse::().unwrap(); assert!(unpack!(status=, f1 % f2).bitwise_eq(expected)); assert_eq!(status, Status::OK); } { // Test E4M3FN mod where the LHS exponent is maxExponent (8) and the RHS is // the max value whose exponent is minExponent (-6). This requires special // logic in the mod implementation to prevent overflow to NaN. let f1 = "0x1p8".parse::().unwrap(); // 256 let f2 = "0x1.ep-6".parse::().unwrap(); // 0.029296875 let expected = "0x1p-8".parse::().unwrap(); // 0.00390625 assert!(unpack!(status=, f1 % f2).bitwise_eq(expected)); assert_eq!(status, Status::OK); } } #[test] fn remainder() { // Test Special Cases against each other and normal values. let p_inf = Single::INFINITY; let m_inf = -Single::INFINITY; let p_zero = Single::ZERO; let m_zero = -Single::ZERO; let qnan = Single::NAN; let snan = "snan123".parse::().unwrap(); let p_normal_value = "0x1p+0".parse::().unwrap(); let m_normal_value = "-0x1p+0".parse::().unwrap(); let p_largest_value = Single::largest(); let m_largest_value = -Single::largest(); let p_smallest_value = Single::SMALLEST; let m_smallest_value = -Single::SMALLEST; let p_smallest_normalized = Single::smallest_normalized(); let m_smallest_normalized = -Single::smallest_normalized(); let p_val1 = "0x1.fffffep+126".parse::().unwrap(); let m_val1 = "-0x1.fffffep+126".parse::().unwrap(); let p_val2 = "0x1.fffffep-126".parse::().unwrap(); let m_val2 = "-0x1.fffffep-126".parse::().unwrap(); let p_val3 = "0x1p-125".parse::().unwrap(); let m_val3 = "-0x1p-125".parse::().unwrap(); let p_val4 = "0x1p+127".parse::().unwrap(); let m_val4 = "-0x1p+127".parse::().unwrap(); let p_val5 = "1.5".parse::().unwrap(); let m_val5 = "-1.5".parse::().unwrap(); let p_val6 = "1".parse::().unwrap(); let m_val6 = "-1".parse::().unwrap(); let special_cases = [ (p_inf, p_inf, "nan", Status::INVALID_OP, Category::NaN), (p_inf, m_inf, "nan", Status::INVALID_OP, Category::NaN), (p_inf, p_zero, "nan", Status::INVALID_OP, Category::NaN), (p_inf, m_zero, "nan", Status::INVALID_OP, Category::NaN), (p_inf, qnan, "nan", Status::OK, Category::NaN), (p_inf, snan, "nan123", Status::INVALID_OP, Category::NaN), (p_inf, p_normal_value, "nan", Status::INVALID_OP, Category::NaN), (p_inf, m_normal_value, "nan", Status::INVALID_OP, Category::NaN), (p_inf, p_largest_value, "nan", Status::INVALID_OP, Category::NaN), (p_inf, m_largest_value, "nan", Status::INVALID_OP, Category::NaN), (p_inf, p_smallest_value, "nan", Status::INVALID_OP, Category::NaN), (p_inf, m_smallest_value, "nan", Status::INVALID_OP, Category::NaN), (p_inf, p_smallest_normalized, "nan", Status::INVALID_OP, Category::NaN), (p_inf, m_smallest_normalized, "nan", Status::INVALID_OP, Category::NaN), (m_inf, p_inf, "nan", Status::INVALID_OP, Category::NaN), (m_inf, m_inf, "nan", Status::INVALID_OP, Category::NaN), (m_inf, p_zero, "nan", Status::INVALID_OP, Category::NaN), (m_inf, m_zero, "nan", Status::INVALID_OP, Category::NaN), (m_inf, qnan, "nan", Status::OK, Category::NaN), (m_inf, snan, "nan123", Status::INVALID_OP, Category::NaN), (m_inf, p_normal_value, "nan", Status::INVALID_OP, Category::NaN), (m_inf, m_normal_value, "nan", Status::INVALID_OP, Category::NaN), (m_inf, p_largest_value, "nan", Status::INVALID_OP, Category::NaN), (m_inf, m_largest_value, "nan", Status::INVALID_OP, Category::NaN), (m_inf, p_smallest_value, "nan", Status::INVALID_OP, Category::NaN), (m_inf, m_smallest_value, "nan", Status::INVALID_OP, Category::NaN), (m_inf, p_smallest_normalized, "nan", Status::INVALID_OP, Category::NaN), (m_inf, m_smallest_normalized, "nan", Status::INVALID_OP, Category::NaN), (p_zero, p_inf, "0x0p+0", Status::OK, Category::Zero), (p_zero, m_inf, "0x0p+0", Status::OK, Category::Zero), (p_zero, p_zero, "nan", Status::INVALID_OP, Category::NaN), (p_zero, m_zero, "nan", Status::INVALID_OP, Category::NaN), (p_zero, qnan, "nan", Status::OK, Category::NaN), (p_zero, snan, "nan123", Status::INVALID_OP, Category::NaN), (p_zero, p_normal_value, "0x0p+0", Status::OK, Category::Zero), (p_zero, m_normal_value, "0x0p+0", Status::OK, Category::Zero), (p_zero, p_largest_value, "0x0p+0", Status::OK, Category::Zero), (p_zero, m_largest_value, "0x0p+0", Status::OK, Category::Zero), (p_zero, p_smallest_value, "0x0p+0", Status::OK, Category::Zero), (p_zero, m_smallest_value, "0x0p+0", Status::OK, Category::Zero), (p_zero, p_smallest_normalized, "0x0p+0", Status::OK, Category::Zero), (p_zero, m_smallest_normalized, "0x0p+0", Status::OK, Category::Zero), (m_zero, p_inf, "-0x0p+0", Status::OK, Category::Zero), (m_zero, m_inf, "-0x0p+0", Status::OK, Category::Zero), (m_zero, p_zero, "nan", Status::INVALID_OP, Category::NaN), (m_zero, m_zero, "nan", Status::INVALID_OP, Category::NaN), (m_zero, qnan, "nan", Status::OK, Category::NaN), (m_zero, snan, "nan123", Status::INVALID_OP, Category::NaN), (m_zero, p_normal_value, "-0x0p+0", Status::OK, Category::Zero), (m_zero, m_normal_value, "-0x0p+0", Status::OK, Category::Zero), (m_zero, p_largest_value, "-0x0p+0", Status::OK, Category::Zero), (m_zero, m_largest_value, "-0x0p+0", Status::OK, Category::Zero), (m_zero, p_smallest_value, "-0x0p+0", Status::OK, Category::Zero), (m_zero, m_smallest_value, "-0x0p+0", Status::OK, Category::Zero), (m_zero, p_smallest_normalized, "-0x0p+0", Status::OK, Category::Zero), (m_zero, m_smallest_normalized, "-0x0p+0", Status::OK, Category::Zero), (qnan, p_inf, "nan", Status::OK, Category::NaN), (qnan, m_inf, "nan", Status::OK, Category::NaN), (qnan, p_zero, "nan", Status::OK, Category::NaN), (qnan, m_zero, "nan", Status::OK, Category::NaN), (qnan, qnan, "nan", Status::OK, Category::NaN), (qnan, snan, "nan", Status::INVALID_OP, Category::NaN), (qnan, p_normal_value, "nan", Status::OK, Category::NaN), (qnan, m_normal_value, "nan", Status::OK, Category::NaN), (qnan, p_largest_value, "nan", Status::OK, Category::NaN), (qnan, m_largest_value, "nan", Status::OK, Category::NaN), (qnan, p_smallest_value, "nan", Status::OK, Category::NaN), (qnan, m_smallest_value, "nan", Status::OK, Category::NaN), (qnan, p_smallest_normalized, "nan", Status::OK, Category::NaN), (qnan, m_smallest_normalized, "nan", Status::OK, Category::NaN), (snan, p_inf, "nan123", Status::INVALID_OP, Category::NaN), (snan, m_inf, "nan123", Status::INVALID_OP, Category::NaN), (snan, p_zero, "nan123", Status::INVALID_OP, Category::NaN), (snan, m_zero, "nan123", Status::INVALID_OP, Category::NaN), (snan, qnan, "nan123", Status::INVALID_OP, Category::NaN), (snan, snan, "nan123", Status::INVALID_OP, Category::NaN), (snan, p_normal_value, "nan123", Status::INVALID_OP, Category::NaN), (snan, m_normal_value, "nan123", Status::INVALID_OP, Category::NaN), (snan, p_largest_value, "nan123", Status::INVALID_OP, Category::NaN), (snan, m_largest_value, "nan123", Status::INVALID_OP, Category::NaN), (snan, p_smallest_value, "nan123", Status::INVALID_OP, Category::NaN), (snan, m_smallest_value, "nan123", Status::INVALID_OP, Category::NaN), (snan, p_smallest_normalized, "nan123", Status::INVALID_OP, Category::NaN), (snan, m_smallest_normalized, "nan123", Status::INVALID_OP, Category::NaN), (p_normal_value, p_inf, "0x1p+0", Status::OK, Category::Normal), (p_normal_value, m_inf, "0x1p+0", Status::OK, Category::Normal), (p_normal_value, p_zero, "nan", Status::INVALID_OP, Category::NaN), (p_normal_value, m_zero, "nan", Status::INVALID_OP, Category::NaN), (p_normal_value, qnan, "nan", Status::OK, Category::NaN), (p_normal_value, snan, "nan123", Status::INVALID_OP, Category::NaN), (p_normal_value, p_normal_value, "0x0p+0", Status::OK, Category::Zero), (p_normal_value, m_normal_value, "0x0p+0", Status::OK, Category::Zero), (p_normal_value, p_largest_value, "0x1p+0", Status::OK, Category::Normal), (p_normal_value, m_largest_value, "0x1p+0", Status::OK, Category::Normal), (p_normal_value, p_smallest_value, "0x0p+0", Status::OK, Category::Zero), (p_normal_value, m_smallest_value, "0x0p+0", Status::OK, Category::Zero), (p_normal_value, p_smallest_normalized, "0x0p+0", Status::OK, Category::Zero), (p_normal_value, m_smallest_normalized, "0x0p+0", Status::OK, Category::Zero), (m_normal_value, p_inf, "-0x1p+0", Status::OK, Category::Normal), (m_normal_value, m_inf, "-0x1p+0", Status::OK, Category::Normal), (m_normal_value, p_zero, "nan", Status::INVALID_OP, Category::NaN), (m_normal_value, m_zero, "nan", Status::INVALID_OP, Category::NaN), (m_normal_value, qnan, "nan", Status::OK, Category::NaN), (m_normal_value, snan, "nan123", Status::INVALID_OP, Category::NaN), (m_normal_value, p_normal_value, "-0x0p+0", Status::OK, Category::Zero), (m_normal_value, m_normal_value, "-0x0p+0", Status::OK, Category::Zero), (m_normal_value, p_largest_value, "-0x1p+0", Status::OK, Category::Normal), (m_normal_value, m_largest_value, "-0x1p+0", Status::OK, Category::Normal), (m_normal_value, p_smallest_value, "-0x0p+0", Status::OK, Category::Zero), (m_normal_value, m_smallest_value, "-0x0p+0", Status::OK, Category::Zero), (m_normal_value, p_smallest_normalized, "-0x0p+0", Status::OK, Category::Zero), (m_normal_value, m_smallest_normalized, "-0x0p+0", Status::OK, Category::Zero), (p_largest_value, p_inf, "0x1.fffffep+127", Status::OK, Category::Normal), (p_largest_value, m_inf, "0x1.fffffep+127", Status::OK, Category::Normal), (p_largest_value, p_zero, "nan", Status::INVALID_OP, Category::NaN), (p_largest_value, m_zero, "nan", Status::INVALID_OP, Category::NaN), (p_largest_value, qnan, "nan", Status::OK, Category::NaN), (p_largest_value, snan, "nan123", Status::INVALID_OP, Category::NaN), (p_largest_value, p_normal_value, "0x0p+0", Status::OK, Category::Zero), (p_largest_value, m_normal_value, "0x0p+0", Status::OK, Category::Zero), (p_largest_value, p_largest_value, "0x0p+0", Status::OK, Category::Zero), (p_largest_value, m_largest_value, "0x0p+0", Status::OK, Category::Zero), (p_largest_value, p_smallest_value, "0x0p+0", Status::OK, Category::Zero), (p_largest_value, m_smallest_value, "0x0p+0", Status::OK, Category::Zero), (p_largest_value, p_smallest_normalized, "0x0p+0", Status::OK, Category::Zero), (p_largest_value, m_smallest_normalized, "0x0p+0", Status::OK, Category::Zero), (m_largest_value, p_inf, "-0x1.fffffep+127", Status::OK, Category::Normal), (m_largest_value, m_inf, "-0x1.fffffep+127", Status::OK, Category::Normal), (m_largest_value, p_zero, "nan", Status::INVALID_OP, Category::NaN), (m_largest_value, m_zero, "nan", Status::INVALID_OP, Category::NaN), (m_largest_value, qnan, "nan", Status::OK, Category::NaN), (m_largest_value, snan, "nan123", Status::INVALID_OP, Category::NaN), (m_largest_value, p_normal_value, "-0x0p+0", Status::OK, Category::Zero), (m_largest_value, m_normal_value, "-0x0p+0", Status::OK, Category::Zero), (m_largest_value, p_largest_value, "-0x0p+0", Status::OK, Category::Zero), (m_largest_value, m_largest_value, "-0x0p+0", Status::OK, Category::Zero), (m_largest_value, p_smallest_value, "-0x0p+0", Status::OK, Category::Zero), (m_largest_value, m_smallest_value, "-0x0p+0", Status::OK, Category::Zero), (m_largest_value, p_smallest_normalized, "-0x0p+0", Status::OK, Category::Zero), (m_largest_value, m_smallest_normalized, "-0x0p+0", Status::OK, Category::Zero), (p_smallest_value, p_inf, "0x1p-149", Status::OK, Category::Normal), (p_smallest_value, m_inf, "0x1p-149", Status::OK, Category::Normal), (p_smallest_value, p_zero, "nan", Status::INVALID_OP, Category::NaN), (p_smallest_value, m_zero, "nan", Status::INVALID_OP, Category::NaN), (p_smallest_value, qnan, "nan", Status::OK, Category::NaN), (p_smallest_value, snan, "nan123", Status::INVALID_OP, Category::NaN), (p_smallest_value, p_normal_value, "0x1p-149", Status::OK, Category::Normal), (p_smallest_value, m_normal_value, "0x1p-149", Status::OK, Category::Normal), (p_smallest_value, p_largest_value, "0x1p-149", Status::OK, Category::Normal), (p_smallest_value, m_largest_value, "0x1p-149", Status::OK, Category::Normal), (p_smallest_value, p_smallest_value, "0x0p+0", Status::OK, Category::Zero), (p_smallest_value, m_smallest_value, "0x0p+0", Status::OK, Category::Zero), (p_smallest_value, p_smallest_normalized, "0x1p-149", Status::OK, Category::Normal), (p_smallest_value, m_smallest_normalized, "0x1p-149", Status::OK, Category::Normal), (m_smallest_value, p_inf, "-0x1p-149", Status::OK, Category::Normal), (m_smallest_value, m_inf, "-0x1p-149", Status::OK, Category::Normal), (m_smallest_value, p_zero, "nan", Status::INVALID_OP, Category::NaN), (m_smallest_value, m_zero, "nan", Status::INVALID_OP, Category::NaN), (m_smallest_value, qnan, "nan", Status::OK, Category::NaN), (m_smallest_value, snan, "nan123", Status::INVALID_OP, Category::NaN), (m_smallest_value, p_normal_value, "-0x1p-149", Status::OK, Category::Normal), (m_smallest_value, m_normal_value, "-0x1p-149", Status::OK, Category::Normal), (m_smallest_value, p_largest_value, "-0x1p-149", Status::OK, Category::Normal), (m_smallest_value, m_largest_value, "-0x1p-149", Status::OK, Category::Normal), (m_smallest_value, p_smallest_value, "-0x0p+0", Status::OK, Category::Zero), (m_smallest_value, m_smallest_value, "-0x0p+0", Status::OK, Category::Zero), (m_smallest_value, p_smallest_normalized, "-0x1p-149", Status::OK, Category::Normal), (m_smallest_value, m_smallest_normalized, "-0x1p-149", Status::OK, Category::Normal), (p_smallest_normalized, p_inf, "0x1p-126", Status::OK, Category::Normal), (p_smallest_normalized, m_inf, "0x1p-126", Status::OK, Category::Normal), (p_smallest_normalized, p_zero, "nan", Status::INVALID_OP, Category::NaN), (p_smallest_normalized, m_zero, "nan", Status::INVALID_OP, Category::NaN), (p_smallest_normalized, qnan, "nan", Status::OK, Category::NaN), (p_smallest_normalized, snan, "nan123", Status::INVALID_OP, Category::NaN), (p_smallest_normalized, p_normal_value, "0x1p-126", Status::OK, Category::Normal), (p_smallest_normalized, m_normal_value, "0x1p-126", Status::OK, Category::Normal), (p_smallest_normalized, p_largest_value, "0x1p-126", Status::OK, Category::Normal), (p_smallest_normalized, m_largest_value, "0x1p-126", Status::OK, Category::Normal), (p_smallest_normalized, p_smallest_value, "0x0p+0", Status::OK, Category::Zero), (p_smallest_normalized, m_smallest_value, "0x0p+0", Status::OK, Category::Zero), (p_smallest_normalized, p_smallest_normalized, "0x0p+0", Status::OK, Category::Zero), (p_smallest_normalized, m_smallest_normalized, "0x0p+0", Status::OK, Category::Zero), (m_smallest_normalized, p_inf, "-0x1p-126", Status::OK, Category::Normal), (m_smallest_normalized, m_inf, "-0x1p-126", Status::OK, Category::Normal), (m_smallest_normalized, p_zero, "nan", Status::INVALID_OP, Category::NaN), (m_smallest_normalized, m_zero, "nan", Status::INVALID_OP, Category::NaN), (m_smallest_normalized, qnan, "nan", Status::OK, Category::NaN), (m_smallest_normalized, snan, "nan123", Status::INVALID_OP, Category::NaN), (m_smallest_normalized, p_normal_value, "-0x1p-126", Status::OK, Category::Normal), (m_smallest_normalized, m_normal_value, "-0x1p-126", Status::OK, Category::Normal), (m_smallest_normalized, p_largest_value, "-0x1p-126", Status::OK, Category::Normal), (m_smallest_normalized, m_largest_value, "-0x1p-126", Status::OK, Category::Normal), (m_smallest_normalized, p_smallest_value, "-0x0p+0", Status::OK, Category::Zero), (m_smallest_normalized, m_smallest_value, "-0x0p+0", Status::OK, Category::Zero), (m_smallest_normalized, p_smallest_normalized, "-0x0p+0", Status::OK, Category::Zero), (m_smallest_normalized, m_smallest_normalized, "-0x0p+0", Status::OK, Category::Zero), (p_val1, p_val1, "0x0p+0", Status::OK, Category::Zero), (p_val1, m_val1, "0x0p+0", Status::OK, Category::Zero), (p_val1, p_val2, "0x0p+0", Status::OK, Category::Zero), (p_val1, m_val2, "0x0p+0", Status::OK, Category::Zero), (p_val1, p_val3, "0x0p+0", Status::OK, Category::Zero), (p_val1, m_val3, "0x0p+0", Status::OK, Category::Zero), (p_val1, p_val4, "-0x1p+103", Status::OK, Category::Normal), (p_val1, m_val4, "-0x1p+103", Status::OK, Category::Normal), (p_val1, p_val5, "0x0p+0", Status::OK, Category::Zero), (p_val1, m_val5, "0x0p+0", Status::OK, Category::Zero), (p_val1, p_val6, "0x0p+0", Status::OK, Category::Zero), (p_val1, m_val6, "0x0p+0", Status::OK, Category::Zero), (m_val1, p_val1, "-0x0p+0", Status::OK, Category::Zero), (m_val1, m_val1, "-0x0p+0", Status::OK, Category::Zero), (m_val1, p_val2, "-0x0p+0", Status::OK, Category::Zero), (m_val1, m_val2, "-0x0p+0", Status::OK, Category::Zero), (m_val1, p_val3, "-0x0p+0", Status::OK, Category::Zero), (m_val1, m_val3, "-0x0p+0", Status::OK, Category::Zero), (m_val1, p_val4, "0x1p+103", Status::OK, Category::Normal), (m_val1, m_val4, "0x1p+103", Status::OK, Category::Normal), (m_val1, p_val5, "-0x0p+0", Status::OK, Category::Zero), (m_val1, m_val5, "-0x0p+0", Status::OK, Category::Zero), (m_val1, p_val6, "-0x0p+0", Status::OK, Category::Zero), (m_val1, m_val6, "-0x0p+0", Status::OK, Category::Zero), (p_val2, p_val1, "0x1.fffffep-126", Status::OK, Category::Normal), (p_val2, m_val1, "0x1.fffffep-126", Status::OK, Category::Normal), (p_val2, p_val2, "0x0p+0", Status::OK, Category::Zero), (p_val2, m_val2, "0x0p+0", Status::OK, Category::Zero), (p_val2, p_val3, "-0x0.000002p-126", Status::OK, Category::Normal), (p_val2, m_val3, "-0x0.000002p-126", Status::OK, Category::Normal), (p_val2, p_val4, "0x1.fffffep-126", Status::OK, Category::Normal), (p_val2, m_val4, "0x1.fffffep-126", Status::OK, Category::Normal), (p_val2, p_val5, "0x1.fffffep-126", Status::OK, Category::Normal), (p_val2, m_val5, "0x1.fffffep-126", Status::OK, Category::Normal), (p_val2, p_val6, "0x1.fffffep-126", Status::OK, Category::Normal), (p_val2, m_val6, "0x1.fffffep-126", Status::OK, Category::Normal), (m_val2, p_val1, "-0x1.fffffep-126", Status::OK, Category::Normal), (m_val2, m_val1, "-0x1.fffffep-126", Status::OK, Category::Normal), (m_val2, p_val2, "-0x0p+0", Status::OK, Category::Zero), (m_val2, m_val2, "-0x0p+0", Status::OK, Category::Zero), (m_val2, p_val3, "0x0.000002p-126", Status::OK, Category::Normal), (m_val2, m_val3, "0x0.000002p-126", Status::OK, Category::Normal), (m_val2, p_val4, "-0x1.fffffep-126", Status::OK, Category::Normal), (m_val2, m_val4, "-0x1.fffffep-126", Status::OK, Category::Normal), (m_val2, p_val5, "-0x1.fffffep-126", Status::OK, Category::Normal), (m_val2, m_val5, "-0x1.fffffep-126", Status::OK, Category::Normal), (m_val2, p_val6, "-0x1.fffffep-126", Status::OK, Category::Normal), (m_val2, m_val6, "-0x1.fffffep-126", Status::OK, Category::Normal), (p_val3, p_val1, "0x1p-125", Status::OK, Category::Normal), (p_val3, m_val1, "0x1p-125", Status::OK, Category::Normal), (p_val3, p_val2, "0x0.000002p-126", Status::OK, Category::Normal), (p_val3, m_val2, "0x0.000002p-126", Status::OK, Category::Normal), (p_val3, p_val3, "0x0p+0", Status::OK, Category::Zero), (p_val3, m_val3, "0x0p+0", Status::OK, Category::Zero), (p_val3, p_val4, "0x1p-125", Status::OK, Category::Normal), (p_val3, m_val4, "0x1p-125", Status::OK, Category::Normal), (p_val3, p_val5, "0x1p-125", Status::OK, Category::Normal), (p_val3, m_val5, "0x1p-125", Status::OK, Category::Normal), (p_val3, p_val6, "0x1p-125", Status::OK, Category::Normal), (p_val3, m_val6, "0x1p-125", Status::OK, Category::Normal), (m_val3, p_val1, "-0x1p-125", Status::OK, Category::Normal), (m_val3, m_val1, "-0x1p-125", Status::OK, Category::Normal), (m_val3, p_val2, "-0x0.000002p-126", Status::OK, Category::Normal), (m_val3, m_val2, "-0x0.000002p-126", Status::OK, Category::Normal), (m_val3, p_val3, "-0x0p+0", Status::OK, Category::Zero), (m_val3, m_val3, "-0x0p+0", Status::OK, Category::Zero), (m_val3, p_val4, "-0x1p-125", Status::OK, Category::Normal), (m_val3, m_val4, "-0x1p-125", Status::OK, Category::Normal), (m_val3, p_val5, "-0x1p-125", Status::OK, Category::Normal), (m_val3, m_val5, "-0x1p-125", Status::OK, Category::Normal), (m_val3, p_val6, "-0x1p-125", Status::OK, Category::Normal), (m_val3, m_val6, "-0x1p-125", Status::OK, Category::Normal), (p_val4, p_val1, "0x1p+103", Status::OK, Category::Normal), (p_val4, m_val1, "0x1p+103", Status::OK, Category::Normal), (p_val4, p_val2, "0x0.002p-126", Status::OK, Category::Normal), (p_val4, m_val2, "0x0.002p-126", Status::OK, Category::Normal), (p_val4, p_val3, "0x0p+0", Status::OK, Category::Zero), (p_val4, m_val3, "0x0p+0", Status::OK, Category::Zero), (p_val4, p_val4, "0x0p+0", Status::OK, Category::Zero), (p_val4, m_val4, "0x0p+0", Status::OK, Category::Zero), (p_val4, p_val5, "0.5", Status::OK, Category::Normal), (p_val4, m_val5, "0.5", Status::OK, Category::Normal), (p_val4, p_val6, "0x0p+0", Status::OK, Category::Zero), (p_val4, m_val6, "0x0p+0", Status::OK, Category::Zero), (m_val4, p_val1, "-0x1p+103", Status::OK, Category::Normal), (m_val4, m_val1, "-0x1p+103", Status::OK, Category::Normal), (m_val4, p_val2, "-0x0.002p-126", Status::OK, Category::Normal), (m_val4, m_val2, "-0x0.002p-126", Status::OK, Category::Normal), (m_val4, p_val3, "-0x0p+0", Status::OK, Category::Zero), (m_val4, m_val3, "-0x0p+0", Status::OK, Category::Zero), (m_val4, p_val4, "-0x0p+0", Status::OK, Category::Zero), (m_val4, m_val4, "-0x0p+0", Status::OK, Category::Zero), (m_val4, p_val5, "-0.5", Status::OK, Category::Normal), (m_val4, m_val5, "-0.5", Status::OK, Category::Normal), (m_val4, p_val6, "-0x0p+0", Status::OK, Category::Zero), (m_val4, m_val6, "-0x0p+0", Status::OK, Category::Zero), (p_val5, p_val1, "1.5", Status::OK, Category::Normal), (p_val5, m_val1, "1.5", Status::OK, Category::Normal), (p_val5, p_val2, "0x0.00006p-126", Status::OK, Category::Normal), (p_val5, m_val2, "0x0.00006p-126", Status::OK, Category::Normal), (p_val5, p_val3, "0x0p+0", Status::OK, Category::Zero), (p_val5, m_val3, "0x0p+0", Status::OK, Category::Zero), (p_val5, p_val4, "1.5", Status::OK, Category::Normal), (p_val5, m_val4, "1.5", Status::OK, Category::Normal), (p_val5, p_val5, "0x0p+0", Status::OK, Category::Zero), (p_val5, m_val5, "0x0p+0", Status::OK, Category::Zero), (p_val5, p_val6, "-0.5", Status::OK, Category::Normal), (p_val5, m_val6, "-0.5", Status::OK, Category::Normal), (m_val5, p_val1, "-1.5", Status::OK, Category::Normal), (m_val5, m_val1, "-1.5", Status::OK, Category::Normal), (m_val5, p_val2, "-0x0.00006p-126", Status::OK, Category::Normal), (m_val5, m_val2, "-0x0.00006p-126", Status::OK, Category::Normal), (m_val5, p_val3, "-0x0p+0", Status::OK, Category::Zero), (m_val5, m_val3, "-0x0p+0", Status::OK, Category::Zero), (m_val5, p_val4, "-1.5", Status::OK, Category::Normal), (m_val5, m_val4, "-1.5", Status::OK, Category::Normal), (m_val5, p_val5, "-0x0p+0", Status::OK, Category::Zero), (m_val5, m_val5, "-0x0p+0", Status::OK, Category::Zero), (m_val5, p_val6, "0.5", Status::OK, Category::Normal), (m_val5, m_val6, "0.5", Status::OK, Category::Normal), (p_val6, p_val1, "0x1p+0", Status::OK, Category::Normal), (p_val6, m_val1, "0x1p+0", Status::OK, Category::Normal), (p_val6, p_val2, "0x0.00004p-126", Status::OK, Category::Normal), (p_val6, m_val2, "0x0.00004p-126", Status::OK, Category::Normal), (p_val6, p_val3, "0x0p+0", Status::OK, Category::Zero), (p_val6, m_val3, "0x0p+0", Status::OK, Category::Zero), (p_val6, p_val4, "0x1p+0", Status::OK, Category::Normal), (p_val6, m_val4, "0x1p+0", Status::OK, Category::Normal), (p_val6, p_val5, "-0.5", Status::OK, Category::Normal), (p_val6, m_val5, "-0.5", Status::OK, Category::Normal), (p_val6, p_val6, "0x0p+0", Status::OK, Category::Zero), (p_val6, m_val6, "0x0p+0", Status::OK, Category::Zero), (m_val6, p_val1, "-0x1p+0", Status::OK, Category::Normal), (m_val6, m_val1, "-0x1p+0", Status::OK, Category::Normal), (m_val6, p_val2, "-0x0.00004p-126", Status::OK, Category::Normal), (m_val6, m_val2, "-0x0.00004p-126", Status::OK, Category::Normal), (m_val6, p_val3, "-0x0p+0", Status::OK, Category::Zero), (m_val6, m_val3, "-0x0p+0", Status::OK, Category::Zero), (m_val6, p_val4, "-0x1p+0", Status::OK, Category::Normal), (m_val6, m_val4, "-0x1p+0", Status::OK, Category::Normal), (m_val6, p_val5, "0.5", Status::OK, Category::Normal), (m_val6, m_val5, "0.5", Status::OK, Category::Normal), (m_val6, p_val6, "-0x0p+0", Status::OK, Category::Zero), (m_val6, m_val6, "-0x0p+0", Status::OK, Category::Zero), ]; for case @ &(x, y, e_result, e_status, e_category) in &special_cases { let status; let result = unpack!(status=, x.ieee_rem(y)); assert_eq!(e_status, status); assert_eq!(e_category, result.category()); assert!(result.bitwise_eq(e_result.parse::().unwrap()), "result = {result:?}, case = {case:?}"); } let mut status; { let f1 = "0x1.3333333333333p-2".parse::().unwrap(); // 0.3 let f2 = "0x1.47ae147ae147bp-7".parse::().unwrap(); // 0.01 let expected = "-0x1.4p-56".parse::().unwrap(); assert!(unpack!(status=, f1.ieee_rem(f2)).bitwise_eq(expected)); assert_eq!(status, Status::OK); } { let f1 = "0x1p64".parse::().unwrap(); // 1.8446744073709552e19 let f2 = "1.5".parse::().unwrap(); let expected = "-0.5".parse::().unwrap(); assert!(unpack!(status=, f1.ieee_rem(f2)).bitwise_eq(expected)); assert_eq!(status, Status::OK); } { let f1 = "0x1p1000".parse::().unwrap(); let f2 = "0x1p-1000".parse::().unwrap(); let expected = "0.0".parse::().unwrap(); assert!(unpack!(status=, f1.ieee_rem(f2)).bitwise_eq(expected)); assert_eq!(status, Status::OK); } { let f1 = Double::INFINITY; let f2 = "1.0".parse::().unwrap(); assert!(unpack!(status=, f1.ieee_rem(f2)).is_nan()); assert_eq!(status, Status::INVALID_OP); } { let f1 = "-4.0".parse::().unwrap(); let f2 = "-2.0".parse::().unwrap(); let expected = "-0.0".parse::().unwrap(); assert!(unpack!(status=, f1.ieee_rem(f2)).bitwise_eq(expected)); assert_eq!(status, Status::OK); } { let f1 = "-4.0".parse::().unwrap(); let f2 = "2.0".parse::().unwrap(); let expected = "-0.0".parse::().unwrap(); assert!(unpack!(status=, f1.ieee_rem(f2)).bitwise_eq(expected)); assert_eq!(status, Status::OK); } } #[test] fn x87_largest() { assert!(X87DoubleExtended::largest().is_largest()); } #[test] fn x87_next() { assert_eq!("-1.0".parse::().unwrap().next_up().value.ilogb(), -1); } #[test] fn convert_e4m3fn_to_e5m2() { let mut status; let mut loses_info = false; let test = "1.0".parse::().unwrap(); let test: Float8E5M2 = unpack!(status=, test.convert(&mut loses_info)); assert_eq!(1.0, test.to_f32()); assert!(!loses_info); assert_eq!(status, Status::OK); let test = "0.0".parse::().unwrap(); let test: Float8E5M2 = unpack!(status=, test.convert(&mut loses_info)); assert_eq!(0.0, test.to_f32()); assert!(!loses_info); assert_eq!(status, Status::OK); let test = "0x1.2p0".parse::().unwrap(); // 1.125 let test: Float8E5M2 = unpack!(status=, test.convert(&mut loses_info)); assert_eq!(/* 0x1.0p0 */ 1.0, test.to_f32()); assert!(loses_info); assert_eq!(status, Status::INEXACT); let test = "0x1.6p0".parse::().unwrap(); // 1.375 let test: Float8E5M2 = unpack!(status=, test.convert(&mut loses_info)); assert_eq!(/* 0x1.8p0 */ 1.5, test.to_f32()); assert!(loses_info); assert_eq!(status, Status::INEXACT); // Convert E4M3 denormal to E5M2 normal. Should not be truncated, despite the // destination format having one fewer significand bit let test = "0x1.Cp-7".parse::().unwrap(); let test: Float8E5M2 = unpack!(status=, test.convert(&mut loses_info)); assert_eq!(/* 0x1.Cp-7 */ 0.013671875, test.to_f32()); assert!(!loses_info); assert_eq!(status, Status::OK); // Test convert from NaN let test = "nan".parse::().unwrap(); let test: Float8E5M2 = unpack!(status=, test.convert(&mut loses_info)); assert!(test.to_f32().is_nan()); assert!(!loses_info); assert_eq!(status, Status::OK); } #[test] fn convert_e5m2_to_e4m3fn() { let mut status; let mut loses_info = false; let test = "1.0".parse::().unwrap(); let test: Float8E4M3FN = unpack!(status=, test.convert(&mut loses_info)); assert_eq!(1.0, test.to_f32()); assert!(!loses_info); assert_eq!(status, Status::OK); let test = "0.0".parse::().unwrap(); let test: Float8E4M3FN = unpack!(status=, test.convert(&mut loses_info)); assert_eq!(0.0, test.to_f32()); assert!(!loses_info); assert_eq!(status, Status::OK); let test = "0x1.Cp8".parse::().unwrap(); // 448 let test: Float8E4M3FN = unpack!(status=, test.convert(&mut loses_info)); assert_eq!(/* 0x1.Cp8 */ 448.0, test.to_f32()); assert!(!loses_info); assert_eq!(status, Status::OK); // Test overflow let test = "0x1.0p9".parse::().unwrap(); // 512 let test: Float8E4M3FN = unpack!(status=, test.convert(&mut loses_info)); assert!(test.to_f32().is_nan()); assert!(loses_info); assert_eq!(status, Status::OVERFLOW | Status::INEXACT); // Test underflow let test = "0x1.0p-10".parse::().unwrap(); let test: Float8E4M3FN = unpack!(status=, test.convert(&mut loses_info)); assert_eq!(0., test.to_f32()); assert!(loses_info); assert_eq!(status, Status::UNDERFLOW | Status::INEXACT); // Test rounding up to smallest denormal number let test = "0x1.8p-10".parse::().unwrap(); let test: Float8E4M3FN = unpack!(status=, test.convert(&mut loses_info)); assert_eq!(/* 0x1.0p-9 */ 0.001953125, test.to_f32()); assert!(loses_info); assert_eq!(status, Status::UNDERFLOW | Status::INEXACT); // Testing inexact rounding to denormal number let test = "0x1.8p-9".parse::().unwrap(); let test: Float8E4M3FN = unpack!(status=, test.convert(&mut loses_info)); assert_eq!(/* 0x1.0p-8 */ 0.00390625, test.to_f32()); assert!(loses_info); assert_eq!(status, Status::UNDERFLOW | Status::INEXACT); let nan = "nan".parse::().unwrap(); // Testing convert from Inf let test = "inf".parse::().unwrap(); let test: Float8E4M3FN = unpack!(status=, test.convert(&mut loses_info)); assert!(test.to_f32().is_nan()); assert!(loses_info); assert_eq!(status, Status::INEXACT); assert!(test.bitwise_eq(nan)); // Testing convert from quiet NaN let test = "nan".parse::().unwrap(); let test: Float8E4M3FN = unpack!(status=, test.convert(&mut loses_info)); assert!(test.to_f32().is_nan()); assert!(loses_info); assert_eq!(status, Status::OK); assert!(test.bitwise_eq(nan)); // Testing convert from signaling NaN let test = "snan".parse::().unwrap(); let test: Float8E4M3FN = unpack!(status=, test.convert(&mut loses_info)); assert!(test.to_f32().is_nan()); assert!(loses_info); assert_eq!(status, Status::INVALID_OP); assert!(test.bitwise_eq(nan)); } #[test] fn float8e4m3fn_infinity() { let t = Float8E4M3FN::INFINITY; assert!(t.is_nan()); assert!(!t.is_infinite()); } #[test] fn float8e4m3fn_from_string() { // Exactly representable assert_eq!(448.0, "448".parse::().unwrap().to_f64()); // Round down to maximum value assert_eq!(448.0, "464".parse::().unwrap().to_f64()); // Round up, causing overflow to NaN assert!("465".parse::().unwrap().is_nan()); // Overflow without rounding assert!("480".parse::().unwrap().is_nan()); // Inf converted to NaN assert!("inf".parse::().unwrap().is_nan()); // NaN converted to NaN assert!("nan".parse::().unwrap().is_nan()); } #[test] fn float8e4m3fn_add() { let qnan = Float8E4M3FN::NAN; let from_str = |s: &str| s.parse::().unwrap(); let addition_tests = [ // Test addition operations involving NaN, overflow, and the max E4M3 // value (448) because E4M3 differs from IEEE-754 types in these regards (from_str("448"), from_str("16"), "448", Status::INEXACT, Category::Normal, Round::NearestTiesToEven), ( from_str("448"), from_str("18"), "NaN", Status::OVERFLOW | Status::INEXACT, Category::NaN, Round::NearestTiesToEven, ), ( from_str("448"), from_str("32"), "NaN", Status::OVERFLOW | Status::INEXACT, Category::NaN, Round::NearestTiesToEven, ), ( from_str("-448"), from_str("-32"), "-NaN", Status::OVERFLOW | Status::INEXACT, Category::NaN, Round::NearestTiesToEven, ), (qnan, from_str("-448"), "NaN", Status::OK, Category::NaN, Round::NearestTiesToEven), (from_str("448"), from_str("-32"), "416", Status::OK, Category::Normal, Round::NearestTiesToEven), (from_str("448"), from_str("0"), "448", Status::OK, Category::Normal, Round::NearestTiesToEven), (from_str("448"), from_str("32"), "448", Status::INEXACT, Category::Normal, Round::TowardZero), (from_str("448"), from_str("448"), "448", Status::INEXACT, Category::Normal, Round::TowardZero), ]; for case @ &(x, y, e_result, e_status, e_category, round) in &addition_tests { let status; let result = unpack!(status=, x.add_r(y, round)); assert_eq!(e_status, status); assert_eq!(e_category, result.category()); assert!(result.bitwise_eq(e_result.parse::().unwrap()), "result = {result:?}, case = {case:?}"); } } #[test] fn float8e4m3fn_divide_by_zero() { let x = "1".parse::().unwrap(); let zero = "0".parse::().unwrap(); let status; assert!(unpack!(status=, x / zero).is_nan()); assert_eq!(status, Status::DIV_BY_ZERO); } #[test] fn float8e4m3fn_next() { let mut status; // nextUp on positive numbers for i in 0..127 { let test = Float8E4M3FN::from_bits(i); let expected = Float8E4M3FN::from_bits(i + 1); assert!(unpack!(status=, test.next_up()).bitwise_eq(expected)); assert_eq!(status, Status::OK); } // nextUp on negative zero let test = -Float8E4M3FN::ZERO; let expected = Float8E4M3FN::SMALLEST; assert!(unpack!(status=, test.next_up()).bitwise_eq(expected)); assert_eq!(status, Status::OK); // nextUp on negative nonzero numbers for i in 129..255 { let test = Float8E4M3FN::from_bits(i); let expected = Float8E4M3FN::from_bits(i - 1); assert!(unpack!(status=, test.next_up()).bitwise_eq(expected)); assert_eq!(status, Status::OK); } // nextUp on NaN let test = Float8E4M3FN::qnan(None); let expected = Float8E4M3FN::qnan(None); assert!(unpack!(status=, test.next_up()).bitwise_eq(expected)); assert_eq!(status, Status::OK); // nextDown on positive nonzero finite numbers for i in 1..127 { let test = Float8E4M3FN::from_bits(i); let expected = Float8E4M3FN::from_bits(i - 1); assert!(unpack!(status=, test.next_down()).bitwise_eq(expected)); assert_eq!(status, Status::OK); } // nextDown on positive zero let test = -Float8E4M3FN::ZERO; let expected = -Float8E4M3FN::SMALLEST; assert!(unpack!(status=, test.next_down()).bitwise_eq(expected)); assert_eq!(status, Status::OK); // nextDown on negative finite numbers for i in 128..255 { let test = Float8E4M3FN::from_bits(i); let expected = Float8E4M3FN::from_bits(i + 1); assert!(unpack!(status=, test.next_down()).bitwise_eq(expected)); assert_eq!(status, Status::OK); } // nextDown on NaN let test = Float8E4M3FN::qnan(None); let expected = Float8E4M3FN::qnan(None); assert!(unpack!(status=, test.next_down()).bitwise_eq(expected)); assert_eq!(status, Status::OK); } #[test] fn float8e4m3fn_exhaustive() { // Test each of the 256 Float8E4M3FN values. for i in 0..=u8::MAX { let test = Float8E4M3FN::from_bits(i.into()); // isLargest if i == 126 || i == 254 { assert!(test.is_largest()); assert_eq!(test.abs().to_f64(), 448.); } else { assert!(!test.is_largest()); } // isSmallest if i == 1 || i == 129 { assert!(test.is_smallest()); assert_eq!(test.abs().to_f64(), /* 0x1p-9 */ 0.001953125); } else { assert!(!test.is_smallest()); } // convert to BFloat let status; let mut loses_info = false; let test2: BFloat = unpack!(status=, test.convert(&mut loses_info)); assert_eq!(status, Status::OK); assert!(!loses_info); if i == 127 || i == 255 { assert!(test2.is_nan()); } else { assert_eq!(test.to_f32(), test2.to_f32()); } // bitcastToAPInt assert_eq!(u128::from(i), test.to_bits()); } } #[test] fn float8e4m3fn_exhaustive_pair() { // Test each pair of Float8E4M3FN values. for i in 0..=u8::MAX { for j in 0..=u8::MAX { let x = Float8E4M3FN::from_bits(i.into()); let y = Float8E4M3FN::from_bits(j.into()); let mut loses_info = false; let x16: Half = x.convert(&mut loses_info).value; assert!(!loses_info); let y16: Half = y.convert(&mut loses_info).value; assert!(!loses_info); // Add let z = (x + y).value; let z16 = (x16 + y16).value; assert!(z.bitwise_eq(z16.convert(&mut loses_info).value), "i={i}, j={j}"); // Subtract let z = (x - y).value; let z16 = (x16 - y16).value; assert!(z.bitwise_eq(z16.convert(&mut loses_info).value), "i={i}, j={j}"); // Multiply let z = (x * y).value; let z16 = (x16 * y16).value; assert!(z.bitwise_eq(z16.convert(&mut loses_info).value), "i={i}, j={j}"); // Divide let z = (x / y).value; let z16 = (x16 / y16).value; assert!(z.bitwise_eq(z16.convert(&mut loses_info).value), "i={i}, j={j}"); // Mod let z = (x % y).value; let z16 = (x16 % y16).value; assert!(z.bitwise_eq(z16.convert(&mut loses_info).value), "i={i}, j={j}"); // Remainder let z = x.ieee_rem(y).value; let z16 = x16.ieee_rem(y16).value; assert!(z.bitwise_eq(z16.convert(&mut loses_info).value), "i={i}, j={j}"); } } } #[test] fn f8_to_string() { for_each_float_type!(for test::()); fn test() { if F::BITS != 8 { return; } // NOTE(eddyb) this was buggy upstream as it didn't test `F` but `Float8E5M2`, // https://github.com/llvm/llvm-project/commit/6109e70c72fc5171d25c4467fc3cfe6eb2029f50 // fixed it upstream so we've effectively backported that commit. for i in 0..=u8::MAX { let test = F::from_bits(i.into()); let str = test.to_string(); if test.is_nan() { assert_eq!(str, "NaN"); } else { assert!(test.bitwise_eq(str.parse::().unwrap())); } } } } // HACK(eddyb) C`{FLT,DBL}_TRUE_MIN` / C++ `std::numeric_limits::denorm_min` // equivalents, for the two tests below, as Rust seems to lack anything like them, // but their bit-patterns are thankfuly trivial, with the main caveat that they // can't be `const` (subnormals and NaNs are banned from CTFE `{to,from}_bits`). fn f64_smallest_subnormal() -> f64 { f64::from_bits(1) } fn f32_smallest_subnormal() -> f32 { f32::from_bits(1) } #[test] fn double_to_f64() { let d_pos_zero = Double::from_f64(0.0); assert!(Double::from_f64(d_pos_zero.to_f64()).is_pos_zero()); let d_neg_zero = Double::from_f64(-0.0); assert!(Double::from_f64(d_neg_zero.to_f64()).is_neg_zero()); let d_one = Double::from_f64(1.0); assert_eq!(1.0, d_one.to_f64()); let d_pos_largest = Double::largest(); assert_eq!(f64::MAX, d_pos_largest.to_f64()); let d_neg_largest = -Double::largest(); assert_eq!(-f64::MAX, d_neg_largest.to_f64()); let d_pos_smallest = Double::smallest_normalized(); assert_eq!(f64::MIN_POSITIVE, d_pos_smallest.to_f64()); let d_neg_smallest = -Double::smallest_normalized(); assert_eq!(-f64::MIN_POSITIVE, d_neg_smallest.to_f64()); let d_smallest_denorm = Double::SMALLEST; assert_eq!(f64_smallest_subnormal(), d_smallest_denorm.to_f64()); let d_largest_denorm = "0x0.FFFFFFFFFFFFFp-1022".parse::().unwrap(); assert_eq!(/*0x0.FFFFFFFFFFFFFp-1022*/ 2.225073858507201e-308, d_largest_denorm.to_f64()); let d_pos_inf = Double::INFINITY; assert_eq!(f64::INFINITY, d_pos_inf.to_f64()); let d_neg_inf = -Double::INFINITY; assert_eq!(-f64::INFINITY, d_neg_inf.to_f64()); let d_qnan = Double::qnan(None); assert!(d_qnan.to_f64().is_nan()); } #[test] fn single_to_f64() { let f_pos_zero = Single::from_f32(0.0); assert!(Double::from_f64(f_pos_zero.to_f64()).is_pos_zero()); let f_neg_zero = Single::from_f32(-0.0); assert!(Double::from_f64(f_neg_zero.to_f64()).is_neg_zero()); let f_one = Single::from_f32(1.0); assert_eq!(1.0, f_one.to_f64()); let f_pos_largest = Single::largest(); assert_eq!(f32::MAX as f64, f_pos_largest.to_f64()); let f_neg_largest = -Single::largest(); assert_eq!(-f32::MAX as f64, f_neg_largest.to_f64()); let f_pos_smallest = Single::smallest_normalized(); assert_eq!(f32::MIN_POSITIVE as f64, f_pos_smallest.to_f64()); let f_neg_smallest = -Single::smallest_normalized(); assert_eq!(-f32::MIN_POSITIVE as f64, f_neg_smallest.to_f64()); let f_smallest_denorm = Single::SMALLEST; assert_eq!(f32_smallest_subnormal() as f64, f_smallest_denorm.to_f64()); let f_largest_denorm = "0x0.FFFFFEp-126".parse::().unwrap(); assert_eq!(/*0x0.FFFFFEp-126*/ 1.1754942106924411e-38, f_largest_denorm.to_f64()); let f_pos_inf = Single::INFINITY; assert_eq!(f64::INFINITY, f_pos_inf.to_f64()); let f_neg_inf = -Single::INFINITY; assert_eq!(-f64::INFINITY, f_neg_inf.to_f64()); let f_qnan = Single::qnan(None); assert!(f_qnan.to_f64().is_nan()); let h_pos_zero = Half::ZERO; assert!(Double::from_f64(h_pos_zero.to_f64()).is_pos_zero()); let h_neg_zero = -Half::ZERO; assert!(Double::from_f64(h_neg_zero.to_f64()).is_neg_zero()); } #[test] fn half_to_f64() { let h_one = "1.0".parse::().unwrap(); assert_eq!(1.0, h_one.to_f64()); let h_pos_largest = Half::largest(); assert_eq!(65504.0, h_pos_largest.to_f64()); let h_neg_largest = -Half::largest(); assert_eq!(-65504.0, h_neg_largest.to_f64()); let h_pos_smallest = Half::smallest_normalized(); assert_eq!(/*0x1.p-14*/ 6.103515625e-05, h_pos_smallest.to_f64()); let h_neg_smallest = -Half::smallest_normalized(); assert_eq!(/*-0x1.p-14*/ -6.103515625e-05, h_neg_smallest.to_f64()); let h_smallest_denorm = Half::SMALLEST; assert_eq!(/*0x1.p-24*/ 5.960464477539063e-08, h_smallest_denorm.to_f64()); let h_largest_denorm = "0x1.FFCp-14".parse::().unwrap(); assert_eq!(/*0x1.FFCp-14*/ 0.00012201070785522461, h_largest_denorm.to_f64()); let h_pos_inf = Half::INFINITY; assert_eq!(f64::INFINITY, h_pos_inf.to_f64()); let h_neg_inf = -Half::INFINITY; assert_eq!(-f64::INFINITY, h_neg_inf.to_f64()); let h_qnan = Half::qnan(None); assert!(h_qnan.to_f64().is_nan()); } #[test] fn bfloat_to_f64() { let b_pos_zero = Half::ZERO; assert!(Double::from_f64(b_pos_zero.to_f64()).is_pos_zero()); let b_neg_zero = -Half::ZERO; assert!(Double::from_f64(b_neg_zero.to_f64()).is_neg_zero()); let b_one = "1.0".parse::().unwrap(); assert_eq!(1.0, b_one.to_f64()); let b_pos_largest = BFloat::largest(); assert_eq!(/*0x1.FEp127*/ 3.3895313892515355e+38, b_pos_largest.to_f64()); let b_neg_largest = -BFloat::largest(); assert_eq!(/*-0x1.FEp127*/ -3.3895313892515355e+38, b_neg_largest.to_f64()); let b_pos_smallest = BFloat::smallest_normalized(); assert_eq!(/*0x1.p-126*/ 1.1754943508222875e-38, b_pos_smallest.to_f64()); let b_neg_smallest = -BFloat::smallest_normalized(); assert_eq!(/*-0x1.p-126*/ -1.1754943508222875e-38, b_neg_smallest.to_f64()); let b_smallest_denorm = BFloat::SMALLEST; assert_eq!(/*0x1.p-133*/ 9.183549615799121e-41, b_smallest_denorm.to_f64()); let b_largest_denorm = "0x1.FCp-127".parse::().unwrap(); assert_eq!(/*0x1.FCp-127*/ 1.1663108012064884e-38, b_largest_denorm.to_f64()); let b_pos_inf = BFloat::INFINITY; assert_eq!(f64::INFINITY, b_pos_inf.to_f64()); let b_neg_inf = -BFloat::INFINITY; assert_eq!(-f64::INFINITY, b_neg_inf.to_f64()); let b_qnan = BFloat::qnan(None); assert!(b_qnan.to_f64().is_nan()); } #[test] fn float8e5m2_to_f64() { let one = "1.0".parse::().unwrap(); assert_eq!(1.0, one.to_f64()); let two = "2.0".parse::().unwrap(); assert_eq!(2.0, two.to_f64()); let pos_largest = Float8E5M2::largest(); assert_eq!(5.734400e+04, pos_largest.to_f64()); let neg_largest = -Float8E5M2::largest(); assert_eq!(-5.734400e+04, neg_largest.to_f64()); let pos_smallest = Float8E5M2::smallest_normalized(); assert_eq!(/* 0x1.p-14 */ 6.103515625e-05, pos_smallest.to_f64()); let neg_smallest = -Float8E5M2::smallest_normalized(); assert_eq!(/* -0x1.p-14 */ -6.103515625e-05, neg_smallest.to_f64()); let smallest_denorm = Float8E5M2::SMALLEST; assert!(smallest_denorm.is_denormal()); assert_eq!(/* 0x1p-16 */ 0.0000152587890625, smallest_denorm.to_f64()); let pos_inf = Float8E5M2::INFINITY; assert_eq!(f64::INFINITY, pos_inf.to_f64()); let neg_inf = -Float8E5M2::INFINITY; assert_eq!(-f64::INFINITY, neg_inf.to_f64()); let qnan = Float8E5M2::qnan(None); assert!(qnan.to_f64().is_nan()); } #[test] fn float8e4m3fn_to_f64() { let one = "1.0".parse::().unwrap(); assert_eq!(1.0, one.to_f64()); let two = "2.0".parse::().unwrap(); assert_eq!(2.0, two.to_f64()); let pos_largest = Float8E4M3FN::largest(); assert_eq!(448., pos_largest.to_f64()); let neg_largest = -Float8E4M3FN::largest(); assert_eq!(-448., neg_largest.to_f64()); let pos_smallest = Float8E4M3FN::smallest_normalized(); assert_eq!(/* 0x1.p-6 */ 0.015625, pos_smallest.to_f64()); let neg_smallest = -Float8E4M3FN::smallest_normalized(); assert_eq!(/* -0x1.p-6 */ -0.015625, neg_smallest.to_f64()); let smallest_denorm = Float8E4M3FN::SMALLEST; assert!(smallest_denorm.is_denormal()); assert_eq!(/* 0x1p-9 */ 0.001953125, smallest_denorm.to_f64()); let qnan = Float8E4M3FN::qnan(None); assert!(qnan.to_f64().is_nan()); } #[test] fn single_to_f32() { let f_pos_zero = Single::from_f32(0.0); assert!(Single::from_f32(f_pos_zero.to_f32()).is_pos_zero()); let f_neg_zero = Single::from_f32(-0.0); assert!(Single::from_f32(f_neg_zero.to_f32()).is_neg_zero()); let f_one = Single::from_f32(1.0); assert_eq!(1.0, f_one.to_f32()); let f_pos_largest = Single::largest(); assert_eq!(f32::MAX, f_pos_largest.to_f32()); let f_neg_largest = -Single::largest(); assert_eq!(-f32::MAX, f_neg_largest.to_f32()); let f_pos_smallest = Single::smallest_normalized(); assert_eq!(f32::MIN_POSITIVE, f_pos_smallest.to_f32()); let f_neg_smallest = -Single::smallest_normalized(); assert_eq!(-f32::MIN_POSITIVE, f_neg_smallest.to_f32()); let f_smallest_denorm = Single::SMALLEST; assert_eq!(f32_smallest_subnormal(), f_smallest_denorm.to_f32()); let f_largest_denorm = "0x1.FFFFFEp-126".parse::().unwrap(); assert_eq!(/*0x1.FFFFFEp-126*/ 2.3509885615147286e-38, f_largest_denorm.to_f32()); let f_pos_inf = Single::INFINITY; assert_eq!(f32::INFINITY, f_pos_inf.to_f32()); let f_neg_inf = -Single::INFINITY; assert_eq!(-f32::INFINITY, f_neg_inf.to_f32()); let f_qnan = Single::qnan(None); assert!(f_qnan.to_f32().is_nan()); } #[test] fn half_to_f32() { let h_pos_zero = Half::ZERO; assert!(Single::from_f32(h_pos_zero.to_f32()).is_pos_zero()); let h_neg_zero = -Half::ZERO; assert!(Single::from_f32(h_neg_zero.to_f32()).is_neg_zero()); let h_one = "1.0".parse::().unwrap(); assert_eq!(1.0, h_one.to_f32()); let h_pos_largest = Half::largest(); assert_eq!(/*0x1.FFCp15*/ 65504.0, h_pos_largest.to_f32()); let h_neg_largest = -Half::largest(); assert_eq!(/*-0x1.FFCp15*/ -65504.0, h_neg_largest.to_f32()); let h_pos_smallest = Half::smallest_normalized(); assert_eq!(/*0x1.p-14*/ 6.103515625e-05, h_pos_smallest.to_f32()); let h_neg_smallest = -Half::smallest_normalized(); assert_eq!(/*-0x1.p-14*/ -6.103515625e-05, h_neg_smallest.to_f32()); let h_smallest_denorm = Half::SMALLEST; assert_eq!(/*0x1.p-24*/ 5.960464477539063e-08, h_smallest_denorm.to_f32()); let h_largest_denorm = "0x1.FFCp-14".parse::().unwrap(); assert_eq!(/*0x1.FFCp-14*/ 0.00012201070785522461, h_largest_denorm.to_f32()); let h_pos_inf = Half::INFINITY; assert_eq!(f32::INFINITY, h_pos_inf.to_f32()); let h_neg_inf = -Half::INFINITY; assert_eq!(-f32::INFINITY, h_neg_inf.to_f32()); let h_qnan = Half::qnan(None); assert!(h_qnan.to_f32().is_nan()); } #[test] fn bfloat_to_f32() { let b_pos_zero = BFloat::ZERO; assert!(Single::from_f32(b_pos_zero.to_f32()).is_pos_zero()); let b_neg_zero = -BFloat::ZERO; assert!(Single::from_f32(b_neg_zero.to_f32()).is_neg_zero()); let b_one = "1.0".parse::().unwrap(); assert_eq!(1.0, b_one.to_f32()); let b_pos_largest = BFloat::largest(); assert_eq!(/*0x1.FEp127*/ 3.3895313892515355e+38, b_pos_largest.to_f32()); let b_neg_largest = -BFloat::largest(); assert_eq!(/*-0x1.FEp127*/ -3.3895313892515355e+38, b_neg_largest.to_f32()); let b_pos_smallest = BFloat::smallest_normalized(); assert_eq!(/*0x1.p-126*/ 1.1754943508222875e-38, b_pos_smallest.to_f32()); let b_neg_smallest = -BFloat::smallest_normalized(); assert_eq!(/*-0x1.p-126*/ -1.1754943508222875e-38, b_neg_smallest.to_f32()); let b_smallest_denorm = BFloat::SMALLEST; assert_eq!(/*0x1.p-133*/ 9.183549615799121e-41, b_smallest_denorm.to_f32()); let b_largest_denorm = "0x1.FCp-127".parse::().unwrap(); assert_eq!(/*0x1.FCp-127*/ 1.1663108012064884e-38, b_largest_denorm.to_f32()); let b_pos_inf = BFloat::INFINITY; assert_eq!(f32::INFINITY, b_pos_inf.to_f32()); let b_neg_inf = -BFloat::INFINITY; assert_eq!(-f32::INFINITY, b_neg_inf.to_f32()); let b_qnan = BFloat::qnan(None); assert!(b_qnan.to_f32().is_nan()); } #[test] fn float8e5m2_to_f32() { let pos_zero = Float8E5M2::ZERO; assert!(Single::from_f32(pos_zero.to_f32()).is_pos_zero()); let neg_zero = -Float8E5M2::ZERO; assert!(Single::from_f32(neg_zero.to_f32()).is_neg_zero()); let one = "1.0".parse::().unwrap(); assert_eq!(1.0, one.to_f32()); let two = "2.0".parse::().unwrap(); assert_eq!(2.0, two.to_f32()); let pos_largest = Float8E5M2::largest(); assert_eq!(5.734400e+04, pos_largest.to_f32()); let neg_largest = -Float8E5M2::largest(); assert_eq!(-5.734400e+04, neg_largest.to_f32()); let pos_smallest = Float8E5M2::smallest_normalized(); assert_eq!(/* 0x1.p-14 */ 6.103515625e-05, pos_smallest.to_f32()); let neg_smallest = -Float8E5M2::smallest_normalized(); assert_eq!(/* -0x1.p-14 */ -6.103515625e-05, neg_smallest.to_f32()); let smallest_denorm = Float8E5M2::SMALLEST; assert!(smallest_denorm.is_denormal()); assert_eq!(/* 0x1.p-16 */ 0.0000152587890625, smallest_denorm.to_f32()); let pos_inf = Float8E5M2::INFINITY; assert_eq!(f32::INFINITY, pos_inf.to_f32()); let neg_inf = -Float8E5M2::INFINITY; assert_eq!(-f32::INFINITY, neg_inf.to_f32()); let qnan = Float8E5M2::qnan(None); assert!(qnan.to_f32().is_nan()); } #[test] fn float8e4m3fn_to_f32() { let pos_zero = Float8E4M3FN::ZERO; assert!(Single::from_f32(pos_zero.to_f32()).is_pos_zero()); let neg_zero = -Float8E4M3FN::ZERO; assert!(Single::from_f32(neg_zero.to_f32()).is_neg_zero()); let one = "1.0".parse::().unwrap(); assert_eq!(1.0, one.to_f32()); let two = "2.0".parse::().unwrap(); assert_eq!(2.0, two.to_f32()); let pos_largest = Float8E4M3FN::largest(); assert_eq!(448., pos_largest.to_f32()); let neg_largest = -Float8E4M3FN::largest(); assert_eq!(-448.0, neg_largest.to_f32()); let pos_smallest = Float8E4M3FN::smallest_normalized(); assert_eq!(/* 0x1.p-6 */ 0.015625, pos_smallest.to_f32()); let neg_smallest = -Float8E4M3FN::smallest_normalized(); assert_eq!(/* -0x1.p-6 */ -0.015625, neg_smallest.to_f32()); let smallest_denorm = Float8E4M3FN::SMALLEST; assert!(smallest_denorm.is_denormal()); assert_eq!(/* 0x1.p-9 */ 0.001953125, smallest_denorm.to_f32()); let qnan = Float8E4M3FN::qnan(None); assert!(qnan.to_f32().is_nan()); }