use rustc_apfloat::ppc::DoubleDouble; use rustc_apfloat::{Category, Float, Round}; use std::cmp::Ordering; #[test] fn ppc_double_double() { let test = DoubleDouble::ZERO; let expected = "0x0p+0".parse::().unwrap(); assert!(test.is_zero()); assert!(!test.is_negative()); assert!(test.bitwise_eq(expected)); assert_eq!(0, test.to_bits()); let test = -DoubleDouble::ZERO; let expected = "-0x0p+0".parse::().unwrap(); assert!(test.is_zero()); assert!(test.is_negative()); assert!(test.bitwise_eq(expected)); assert_eq!(0x8000000000000000, test.to_bits()); let test = "1.0".parse::().unwrap(); assert_eq!(0x3ff0000000000000, test.to_bits()); // LDBL_MAX let test = "1.79769313486231580793728971405301e+308".parse::().unwrap(); assert_eq!(0x7c8ffffffffffffe_7fefffffffffffff, test.to_bits()); // LDBL_MIN let test = "2.00416836000897277799610805135016e-292".parse::().unwrap(); assert_eq!(0x0000000000000000_0360000000000000, test.to_bits()); } #[test] fn ppc_double_double_add_special() { let data = [ // (1 + 0) + (-1 + 0) = Category::Zero (0x3ff0000000000000, 0xbff0000000000000, Category::Zero, Round::NearestTiesToEven), // LDBL_MAX + (1.1 >> (1023 - 106) + 0)) = Category::Infinity ( 0x7c8ffffffffffffe_7fefffffffffffff, 0x7948000000000000, Category::Infinity, Round::NearestTiesToEven, ), // FIXME: change the 4th 0x75effffffffffffe to 0x75efffffffffffff when // DoubleDouble's fallback is gone. // LDBL_MAX + (1.011111... >> (1023 - 106) + (1.1111111...0 >> (1023 - // 160))) = Category::Normal ( 0x7c8ffffffffffffe_7fefffffffffffff, 0x75effffffffffffe_7947ffffffffffff, Category::Normal, Round::NearestTiesToEven, ), // LDBL_MAX + (1.1 >> (1023 - 106) + 0)) = Category::Infinity ( 0x7c8ffffffffffffe_7fefffffffffffff, 0x7c8ffffffffffffe_7fefffffffffffff, Category::Infinity, Round::NearestTiesToEven, ), // NaN + (1 + 0) = Category::NaN (0x7ff8000000000000, 0x3ff0000000000000, Category::NaN, Round::NearestTiesToEven), ]; for (op1, op2, expected, round) in data { { let mut a1 = DoubleDouble::from_bits(op1); let a2 = DoubleDouble::from_bits(op2); a1 = a1.add_r(a2, round).value; assert_eq!(expected, a1.category(), "{:#x} + {:#x}", op1, op2); } { let a1 = DoubleDouble::from_bits(op1); let mut a2 = DoubleDouble::from_bits(op2); a2 = a2.add_r(a1, round).value; assert_eq!(expected, a2.category(), "{:#x} + {:#x}", op2, op1); } } } #[test] fn ppc_double_double_add() { let data = [ // (1 + 0) + (1e-105 + 0) = (1 + 1e-105) ( 0x3ff0000000000000, 0x3960000000000000, 0x3960000000000000_3ff0000000000000, Round::NearestTiesToEven, ), // (1 + 0) + (1e-106 + 0) = (1 + 1e-106) ( 0x3ff0000000000000, 0x3950000000000000, 0x3950000000000000_3ff0000000000000, Round::NearestTiesToEven, ), // (1 + 1e-106) + (1e-106 + 0) = (1 + 1e-105) ( 0x3950000000000000_3ff0000000000000, 0x3950000000000000, 0x3960000000000000_3ff0000000000000, Round::NearestTiesToEven, ), // (1 + 0) + (epsilon + 0) = (1 + epsilon) ( 0x3ff0000000000000, 0x0000000000000001, 0x0000000000000001_3ff0000000000000, Round::NearestTiesToEven, ), // FIXME: change 0xf950000000000000 to 0xf940000000000000, when // DoubleDouble's fallback is gone. // (DBL_MAX - 1 << (1023 - 105)) + (1 << (1023 - 53) + 0) = DBL_MAX + // 1.11111... << (1023 - 52) ( 0xf950000000000000_7fefffffffffffff, 0x7c90000000000000, 0x7c8ffffffffffffe_7fefffffffffffff, Round::NearestTiesToEven, ), // FIXME: change 0xf950000000000000 to 0xf940000000000000, when // DoubleDouble's fallback is gone. // (1 << (1023 - 53) + 0) + (DBL_MAX - 1 << (1023 - 105)) = DBL_MAX + // 1.11111... << (1023 - 52) ( 0x7c90000000000000, 0xf950000000000000_7fefffffffffffff, 0x7c8ffffffffffffe_7fefffffffffffff, Round::NearestTiesToEven, ), ]; for (op1, op2, expected, round) in data { { let mut a1 = DoubleDouble::from_bits(op1); let a2 = DoubleDouble::from_bits(op2); a1 = a1.add_r(a2, round).value; assert_eq!(expected, a1.to_bits(), "{:#x} + {:#x}", op1, op2); } { let a1 = DoubleDouble::from_bits(op1); let mut a2 = DoubleDouble::from_bits(op2); a2 = a2.add_r(a1, round).value; assert_eq!(expected, a2.to_bits(), "{:#x} + {:#x}", op2, op1); } } } #[test] fn ppc_double_double_subtract() { let data = [ // (1 + 0) - (-1e-105 + 0) = (1 + 1e-105) ( 0x3ff0000000000000, 0xb960000000000000, 0x3960000000000000_3ff0000000000000, Round::NearestTiesToEven, ), // (1 + 0) - (-1e-106 + 0) = (1 + 1e-106) ( 0x3ff0000000000000, 0xb950000000000000, 0x3950000000000000_3ff0000000000000, Round::NearestTiesToEven, ), ]; for (op1, op2, expected, round) in data { let mut a1 = DoubleDouble::from_bits(op1); let a2 = DoubleDouble::from_bits(op2); a1 = a1.sub_r(a2, round).value; assert_eq!(expected, a1.to_bits(), "{:#x} - {:#x}", op1, op2); } } #[test] fn ppc_double_double_multiply_special() { let data = [ // Category::NaN * Category::NaN = Category::NaN (0x7ff8000000000000, 0x7ff8000000000000, Category::NaN, Round::NearestTiesToEven), // Category::NaN * Category::Zero = Category::NaN (0x7ff8000000000000, 0, Category::NaN, Round::NearestTiesToEven), // Category::NaN * Category::Infinity = Category::NaN (0x7ff8000000000000, 0x7ff0000000000000, Category::NaN, Round::NearestTiesToEven), // Category::NaN * Category::Normal = Category::NaN (0x7ff8000000000000, 0x3ff0000000000000, Category::NaN, Round::NearestTiesToEven), // Category::Infinity * Category::Infinity = Category::Infinity (0x7ff0000000000000, 0x7ff0000000000000, Category::Infinity, Round::NearestTiesToEven), // Category::Infinity * Category::Zero = Category::NaN (0x7ff0000000000000, 0, Category::NaN, Round::NearestTiesToEven), // Category::Infinity * Category::Normal = Category::Infinity (0x7ff0000000000000, 0x3ff0000000000000, Category::Infinity, Round::NearestTiesToEven), // Category::Zero * Category::Zero = Category::Zero (0, 0, Category::Zero, Round::NearestTiesToEven), // Category::Zero * Category::Normal = Category::Zero (0, 0x3ff0000000000000, Category::Zero, Round::NearestTiesToEven), ]; for (op1, op2, expected, round) in data { { let mut a1 = DoubleDouble::from_bits(op1); let a2 = DoubleDouble::from_bits(op2); a1 = a1.mul_r(a2, round).value; assert_eq!(expected, a1.category(), "{:#x} * {:#x}", op1, op2); } { let a1 = DoubleDouble::from_bits(op1); let mut a2 = DoubleDouble::from_bits(op2); a2 = a2.mul_r(a1, round).value; assert_eq!(expected, a2.category(), "{:#x} * {:#x}", op2, op1); } } } #[test] fn ppc_double_double_multiply() { let data = [ // 1/3 * 3 = 1.0 ( 0x3c75555555555556_3fd5555555555555, 0x4008000000000000, 0x3ff0000000000000, Round::NearestTiesToEven, ), // (1 + epsilon) * (1 + 0) = Category::Zero ( 0x0000000000000001_3ff0000000000000, 0x3ff0000000000000, 0x0000000000000001_3ff0000000000000, Round::NearestTiesToEven, ), // (1 + epsilon) * (1 + epsilon) = 1 + 2 * epsilon ( 0x0000000000000001_3ff0000000000000, 0x0000000000000001_3ff0000000000000, 0x0000000000000002_3ff0000000000000, Round::NearestTiesToEven, ), // -(1 + epsilon) * (1 + epsilon) = -1 ( 0x0000000000000001_bff0000000000000, 0x0000000000000001_3ff0000000000000, 0xbff0000000000000, Round::NearestTiesToEven, ), // (0.5 + 0) * (1 + 2 * epsilon) = 0.5 + epsilon ( 0x3fe0000000000000, 0x0000000000000002_3ff0000000000000, 0x0000000000000001_3fe0000000000000, Round::NearestTiesToEven, ), // (0.5 + 0) * (1 + epsilon) = 0.5 ( 0x3fe0000000000000, 0x0000000000000001_3ff0000000000000, 0x3fe0000000000000, Round::NearestTiesToEven, ), // __LDBL_MAX__ * (1 + 1 << 106) = inf ( 0x7c8ffffffffffffe_7fefffffffffffff, 0x3950000000000000_3ff0000000000000, 0x7ff0000000000000, Round::NearestTiesToEven, ), // __LDBL_MAX__ * (1 + 1 << 107) > __LDBL_MAX__, but not inf, yes =_=||| ( 0x7c8ffffffffffffe_7fefffffffffffff, 0x3940000000000000_3ff0000000000000, 0x7c8fffffffffffff_7fefffffffffffff, Round::NearestTiesToEven, ), // __LDBL_MAX__ * (1 + 1 << 108) = __LDBL_MAX__ ( 0x7c8ffffffffffffe_7fefffffffffffff, 0x3930000000000000_3ff0000000000000, 0x7c8ffffffffffffe_7fefffffffffffff, Round::NearestTiesToEven, ), ]; for (op1, op2, expected, round) in data { { let mut a1 = DoubleDouble::from_bits(op1); let a2 = DoubleDouble::from_bits(op2); a1 = a1.mul_r(a2, round).value; assert_eq!(expected, a1.to_bits(), "{:#x} * {:#x}", op1, op2); } { let a1 = DoubleDouble::from_bits(op1); let mut a2 = DoubleDouble::from_bits(op2); a2 = a2.mul_r(a1, round).value; assert_eq!(expected, a2.to_bits(), "{:#x} * {:#x}", op2, op1); } } } #[test] fn ppc_double_double_divide() { // FIXME: Only a sanity check for now. Add more edge cases when the // double-double algorithm is implemented. let data = [ // 1 / 3 = 1/3 ( 0x3ff0000000000000, 0x4008000000000000, 0x3c75555555555556_3fd5555555555555, Round::NearestTiesToEven, ), ]; for (op1, op2, expected, round) in data { let mut a1 = DoubleDouble::from_bits(op1); let a2 = DoubleDouble::from_bits(op2); a1 = a1.div_r(a2, round).value; assert_eq!(expected, a1.to_bits(), "{:#x} / {:#x}", op1, op2); } } #[test] fn ppc_double_double_remainder() { let data = [ // ieee_rem(3.0 + 3.0 << 53, 1.25 + 1.25 << 53) = (0.5 + 0.5 << 53) ( 0x3cb8000000000000_4008000000000000, 0x3ca4000000000000_3ff4000000000000, 0x3c90000000000000_3fe0000000000000, ), // ieee_rem(3.0 + 3.0 << 53, 1.75 + 1.75 << 53) = (-0.5 - 0.5 << 53) ( 0x3cb8000000000000_4008000000000000, 0x3cac000000000000_3ffc000000000000, 0xbc90000000000000_bfe0000000000000, ), ]; for (op1, op2, expected) in data { let a1 = DoubleDouble::from_bits(op1); let a2 = DoubleDouble::from_bits(op2); let result = a1.ieee_rem(a2).value; assert_eq!(expected, result.to_bits(), "ieee_rem({:#x}, {:#x})", op1, op2); } } #[test] fn ppc_double_double_mod() { let data = [ // mod(3.0 + 3.0 << 53, 1.25 + 1.25 << 53) = (0.5 + 0.5 << 53) ( 0x3cb8000000000000_4008000000000000, 0x3ca4000000000000_3ff4000000000000, 0x3c90000000000000_3fe0000000000000, ), // mod(3.0 + 3.0 << 53, 1.75 + 1.75 << 53) = (1.25 + 1.25 << 53) // 0xbc98000000000000 doesn't seem right, but it's what we currently have. // FIXME: investigate ( 0x3cb8000000000000_4008000000000000, 0x3cac000000000000_3ffc000000000000, 0xbc98000000000000_3ff4000000000001, ), ]; for (op1, op2, expected) in data { let a1 = DoubleDouble::from_bits(op1); let a2 = DoubleDouble::from_bits(op2); let r = (a1 % a2).value; assert_eq!(expected, r.to_bits(), "fmod({:#x}, {:#x})", op1, op2); } } #[test] fn ppc_double_double_fma() { // Sanity check for now. let mut a = "2".parse::().unwrap(); a = a.mul_add("3".parse::().unwrap(), "4".parse::().unwrap()).value; assert_eq!(Some(Ordering::Equal), "10".parse::().unwrap().partial_cmp(&a)); } #[test] fn ppc_double_double_round_to_integral() { { let a = "1.5".parse::().unwrap(); let a = a.round_to_integral(Round::NearestTiesToEven).value; assert_eq!(Some(Ordering::Equal), "2".parse::().unwrap().partial_cmp(&a)); } { let a = "2.5".parse::().unwrap(); let a = a.round_to_integral(Round::NearestTiesToEven).value; assert_eq!(Some(Ordering::Equal), "2".parse::().unwrap().partial_cmp(&a)); } } #[test] fn ppc_double_double_compare() { let data = [ // (1 + 0) = (1 + 0) (0x3ff0000000000000, 0x3ff0000000000000, Some(Ordering::Equal)), // (1 + 0) < (1.00...1 + 0) (0x3ff0000000000000, 0x3ff0000000000001, Some(Ordering::Less)), // (1.00...1 + 0) > (1 + 0) (0x3ff0000000000001, 0x3ff0000000000000, Some(Ordering::Greater)), // (1 + 0) < (1 + epsilon) (0x3ff0000000000000, 0x0000000000000001_3ff0000000000001, Some(Ordering::Less)), // NaN != NaN (0x7ff8000000000000, 0x7ff8000000000000, None), // (1 + 0) != NaN (0x3ff0000000000000, 0x7ff8000000000000, None), // Inf = Inf (0x7ff0000000000000, 0x7ff0000000000000, Some(Ordering::Equal)), ]; for (op1, op2, expected) in data { let a1 = DoubleDouble::from_bits(op1); let a2 = DoubleDouble::from_bits(op2); assert_eq!(expected, a1.partial_cmp(&a2), "compare({:#x}, {:#x})", op1, op2,); } } #[test] fn ppc_double_double_bitwise_eq() { let data = [ // (1 + 0) = (1 + 0) (0x3ff0000000000000, 0x3ff0000000000000, true), // (1 + 0) != (1.00...1 + 0) (0x3ff0000000000000, 0x3ff0000000000001, false), // NaN = NaN (0x7ff8000000000000, 0x7ff8000000000000, true), // NaN != NaN with a different bit pattern (0x7ff8000000000000, 0x3ff0000000000000_7ff8000000000000, false), // Inf = Inf (0x7ff0000000000000, 0x7ff0000000000000, true), ]; for (op1, op2, expected) in data { let a1 = DoubleDouble::from_bits(op1); let a2 = DoubleDouble::from_bits(op2); assert_eq!(expected, a1.bitwise_eq(a2), "{:#x} = {:#x}", op1, op2); } } #[test] fn ppc_double_double_change_sign() { let float = DoubleDouble::from_bits(0xbcb0000000000000_400f000000000000); { let actual = float.copy_sign("1".parse::().unwrap()); assert_eq!(0xbcb0000000000000_400f000000000000, actual.to_bits()); } { let actual = float.copy_sign("-1".parse::().unwrap()); assert_eq!(0x3cb0000000000000_c00f000000000000, actual.to_bits()); } } #[test] fn ppc_double_double_factories() { assert_eq!(0, DoubleDouble::ZERO.to_bits()); assert_eq!(0x7c8ffffffffffffe_7fefffffffffffff, DoubleDouble::largest().to_bits()); assert_eq!(0x0000000000000001, DoubleDouble::SMALLEST.to_bits()); assert_eq!(0x0360000000000000, DoubleDouble::smallest_normalized().to_bits()); assert_eq!(0x0000000000000000_8000000000000000, (-DoubleDouble::ZERO).to_bits()); assert_eq!(0xfc8ffffffffffffe_ffefffffffffffff, (-DoubleDouble::largest()).to_bits()); assert_eq!(0x0000000000000000_8000000000000001, (-DoubleDouble::SMALLEST).to_bits()); assert_eq!( 0x0000000000000000_8360000000000000, (-DoubleDouble::smallest_normalized()).to_bits() ); assert!(DoubleDouble::SMALLEST.is_smallest()); assert!(DoubleDouble::largest().is_largest()); } #[test] fn ppc_double_double_is_denormal() { assert!(DoubleDouble::SMALLEST.is_denormal()); assert!(!DoubleDouble::largest().is_denormal()); assert!(!DoubleDouble::smallest_normalized().is_denormal()); { // (4 + 3) is not normalized let data = 0x4008000000000000_4010000000000000; assert!(DoubleDouble::from_bits(data).is_denormal()); } } #[test] fn ppc_double_double_exact_inverse() { assert!( "2.0" .parse::() .unwrap() .get_exact_inverse() .unwrap() .bitwise_eq("0.5".parse::().unwrap()) ); } #[test] fn ppc_double_double_scalbn() { // 3.0 + 3.0 << 53 let input = 0x3cb8000000000000_4008000000000000; let result = DoubleDouble::from_bits(input).scalbn(1); // 6.0 + 6.0 << 53 assert_eq!(0x3cc8000000000000_4018000000000000, result.to_bits()); } #[test] fn ppc_double_double_frexp() { // 3.0 + 3.0 << 53 let input = 0x3cb8000000000000_4008000000000000; let mut exp = 0; // 0.75 + 0.75 << 53 let result = DoubleDouble::from_bits(input).frexp(&mut exp); assert_eq!(2, exp); assert_eq!(0x3c98000000000000_3fe8000000000000, result.to_bits()); }