// Adapted from
https://github.com/Alexhuszagh/rust-lexical.
use crate::lexical::float::ExtendedFloat;
use crate::lexical::rounding::round_nearest_tie_even;
use std::{f32, f64};
// NORMALIZE
fn check_normalize(mant: u64, exp: i32, shift: u32, r_mant: u64, r_exp: i32) {
let mut x = ExtendedFloat { mant, exp };
assert_eq!(x.normalize(), shift);
assert_eq!(
x,
ExtendedFloat {
mant: r_mant,
exp: r_exp
}
);
}
#[test]
fn normalize_test() {
// F32
// 0
check_normalize(0, 0, 0, 0, 0);
// min value
check_normalize(1, -149, 63, 9223372036854775808, -212);
// 1.0e-40
check_normalize(71362, -149, 47, 10043308644012916736, -196);
// 1.0e-20
check_normalize(12379400, -90, 40, 13611294244890214400, -130);
// 1.0
check_normalize(8388608, -23, 40, 9223372036854775808, -63);
// 1e20
check_normalize(11368684, 43, 40, 12500000250510966784, 3);
// max value
check_normalize(16777213, 104, 40, 18446740775174668288, 64);
// F64
// min value
check_normalize(1, -1074, 63, 9223372036854775808, -1137);
// 1.0e-250
check_normalize(6448907850777164, -883, 11, 13207363278391631872, -894);
// 1.0e-150
check_normalize(7371020360979573, -551, 11, 15095849699286165504, -562);
// 1.0e-45
check_normalize(6427752177035961, -202, 11, 13164036458569648128, -213);
// 1.0e-40
check_normalize(4903985730770844, -185, 11, 10043362776618688512, -196);
// 1.0e-20
check_normalize(6646139978924579, -119, 11, 13611294676837537792, -130);
// 1.0
check_normalize(4503599627370496, -52, 11, 9223372036854775808, -63);
// 1e20
check_normalize(6103515625000000, 14, 11, 12500000000000000000, 3);
// 1e40
check_normalize(8271806125530277, 80, 11, 16940658945086007296, 69);
// 1e150
check_normalize(5503284107318959, 446, 11, 11270725851789228032, 435);
// 1e250
check_normalize(6290184345309700, 778, 11, 12882297539194265600, 767);
// max value
check_normalize(9007199254740991, 971, 11, 18446744073709549568, 960);
}
// ROUND
fn check_round_to_f32(mant: u64, exp: i32, r_mant: u64, r_exp: i32) {
let mut x = ExtendedFloat { mant, exp };
x.round_to_native::<f32, _>(round_nearest_tie_even);
assert_eq!(
x,
ExtendedFloat {
mant: r_mant,
exp: r_exp
}
);
}
#[test]
fn round_to_f32_test() {
// This is lossy, so some of these values are **slightly** rounded.
// underflow
check_round_to_f32(9223372036854775808, -213, 0, -149);
// min value
check_round_to_f32(9223372036854775808, -212, 1, -149);
// 1.0e-40
check_round_to_f32(10043308644012916736, -196, 71362, -149);
// 1.0e-20
check_round_to_f32(13611294244890214400, -130, 12379400, -90);
// 1.0
check_round_to_f32(9223372036854775808, -63, 8388608, -23);
// 1e20
check_round_to_f32(12500000250510966784, 3, 11368684, 43);
// max value
check_round_to_f32(18446740775174668288, 64, 16777213, 104);
// overflow
check_round_to_f32(18446740775174668288, 65, 16777213, 105);
}
fn check_round_to_f64(mant: u64, exp: i32, r_mant: u64, r_exp: i32) {
let mut x = ExtendedFloat { mant, exp };
x.round_to_native::<f64, _>(round_nearest_tie_even);
assert_eq!(
x,
ExtendedFloat {
mant: r_mant,
exp: r_exp
}
);
}
#[test]
fn round_to_f64_test() {
// This is lossy, so some of these values are **slightly** rounded.
// underflow
check_round_to_f64(9223372036854775808, -1138, 0, -1074);
// min value
check_round_to_f64(9223372036854775808, -1137, 1, -1074);
// 1.0e-250
check_round_to_f64(15095849699286165504, -562, 7371020360979573, -551);
// 1.0e-150
check_round_to_f64(15095849699286165504, -562, 7371020360979573, -551);
// 1.0e-45
check_round_to_f64(13164036458569648128, -213, 6427752177035961, -202);
// 1.0e-40
check_round_to_f64(10043362776618688512, -196, 4903985730770844, -185);
// 1.0e-20
check_round_to_f64(13611294676837537792, -130, 6646139978924579, -119);
// 1.0
check_round_to_f64(9223372036854775808, -63, 4503599627370496, -52);
// 1e20
check_round_to_f64(12500000000000000000, 3, 6103515625000000, 14);
// 1e40
check_round_to_f64(16940658945086007296, 69, 8271806125530277, 80);
// 1e150
check_round_to_f64(11270725851789228032, 435, 5503284107318959, 446);
// 1e250
check_round_to_f64(12882297539194265600, 767, 6290184345309700, 778);
// max value
check_round_to_f64(18446744073709549568, 960, 9007199254740991, 971);
// Bug fixes
// 1.2345e-308
check_round_to_f64(10234494226754558294, -1086, 2498655817078750, -1074);
}
fn assert_normalized_eq(mut x: ExtendedFloat, mut y: ExtendedFloat) {
x.normalize();
y.normalize();
assert_eq!(x, y);
}
#[test]
fn from_float() {
let values: [f32; 26] = [
1e-40, 2e-40, 1e-35, 2e-35, 1e-30, 2e-30, 1e-25, 2e-25, 1e-20, 2e-20, 1e-15, 2e-15, 1e-10,
2e-10, 1e-5, 2e-5, 1.0, 2.0, 1e5, 2e5, 1e10, 2e10, 1e15, 2e15, 1e20, 2e20,
];
for value in &values {
assert_normalized_eq(
ExtendedFloat::from_float(*value),
ExtendedFloat::from_float(*value as f64),
);
}
}
// TO
// Sample of interesting numbers to check during standard test builds.
const INTEGERS: [u64; 32] = [
0, // 0x0
1, // 0x1
7, // 0x7
15, // 0xF
112, // 0x70
119, // 0x77
127, // 0x7F
240, // 0xF0
247, // 0xF7
255, // 0xFF
2032, // 0x7F0
2039, // 0x7F7
2047, // 0x7FF
4080, // 0xFF0
4087, // 0xFF7
4095, // 0xFFF
65520, // 0xFFF0
65527, // 0xFFF7
65535, // 0xFFFF
1048560, // 0xFFFF0
1048567, // 0xFFFF7
1048575, // 0xFFFFF
16777200, // 0xFFFFF0
16777207, // 0xFFFFF7
16777215, // 0xFFFFFF
268435440, // 0xFFFFFF0
268435447, // 0xFFFFFF7
268435455, // 0xFFFFFFF
4294967280, // 0xFFFFFFF0
4294967287, // 0xFFFFFFF7
4294967295, // 0xFFFFFFFF
18446744073709551615, // 0xFFFFFFFFFFFFFFFF
];
#[test]
fn to_f32_test() {
// underflow
let x = ExtendedFloat {
mant: 9223372036854775808,
exp: -213,
};
assert_eq!(x.into_float::<f32>(), 0.0);
// min value
let x = ExtendedFloat {
mant: 9223372036854775808,
exp: -212,
};
assert_eq!(x.into_float::<f32>(), 1e-45);
// 1.0e-40
let x = ExtendedFloat {
mant: 10043308644012916736,
exp: -196,
};
assert_eq!(x.into_float::<f32>(), 1e-40);
// 1.0e-20
let x = ExtendedFloat {
mant: 13611294244890214400,
exp: -130,
};
assert_eq!(x.into_float::<f32>(), 1e-20);
// 1.0
let x = ExtendedFloat {
mant: 9223372036854775808,
exp: -63,
};
assert_eq!(x.into_float::<f32>(), 1.0);
// 1e20
let x = ExtendedFloat {
mant: 12500000250510966784,
exp: 3,
};
assert_eq!(x.into_float::<f32>(), 1e20);
// max value
let x = ExtendedFloat {
mant: 18446740775174668288,
exp: 64,
};
assert_eq!(x.into_float::<f32>(), 3.402823e38);
// almost max, high exp
let x = ExtendedFloat {
mant: 1048575,
exp: 108,
};
assert_eq!(x.into_float::<f32>(), 3.4028204e38);
// max value + 1
let x = ExtendedFloat {
mant: 16777216,
exp: 104,
};
assert_eq!(x.into_float::<f32>(), f32::INFINITY);
// max value + 1
let x = ExtendedFloat {
mant: 1048576,
exp: 108,
};
assert_eq!(x.into_float::<f32>(), f32::INFINITY);
// 1e40
let x = ExtendedFloat {
mant: 16940658945086007296,
exp: 69,
};
assert_eq!(x.into_float::<f32>(), f32::INFINITY);
// Integers.
for int in &INTEGERS {
let fp = ExtendedFloat { mant: *int, exp: 0 };
assert_eq!(fp.into_float::<f32>(), *int as f32, "{:?} as f32", *int);
}
}
#[test]
fn to_f64_test() {
// underflow
let x = ExtendedFloat {
mant: 9223372036854775808,
exp: -1138,
};
assert_eq!(x.into_float::<f64>(), 0.0);
// min value
let x = ExtendedFloat {
mant: 9223372036854775808,
exp: -1137,
};
assert_eq!(x.into_float::<f64>(), 5e-324);
// 1.0e-250
let x = ExtendedFloat {
mant: 13207363278391631872,
exp: -894,
};
assert_eq!(x.into_float::<f64>(), 1e-250);
// 1.0e-150
let x = ExtendedFloat {
mant: 15095849699286165504,
exp: -562,
};
assert_eq!(x.into_float::<f64>(), 1e-150);
// 1.0e-45
let x = ExtendedFloat {
mant: 13164036458569648128,
exp: -213,
};
assert_eq!(x.into_float::<f64>(), 1e-45);
// 1.0e-40
let x = ExtendedFloat {
mant: 10043362776618688512,
exp: -196,
};
assert_eq!(x.into_float::<f64>(), 1e-40);
// 1.0e-20
let x = ExtendedFloat {
mant: 13611294676837537792,
exp: -130,
};
assert_eq!(x.into_float::<f64>(), 1e-20);
// 1.0
let x = ExtendedFloat {
mant: 9223372036854775808,
exp: -63,
};
assert_eq!(x.into_float::<f64>(), 1.0);
// 1e20
let x = ExtendedFloat {
mant: 12500000000000000000,
exp: 3,
};
assert_eq!(x.into_float::<f64>(), 1e20);
// 1e40
let x = ExtendedFloat {
mant: 16940658945086007296,
exp: 69,
};
assert_eq!(x.into_float::<f64>(), 1e40);
// 1e150
let x = ExtendedFloat {
mant: 11270725851789228032,
exp: 435,
};
assert_eq!(x.into_float::<f64>(), 1e150);
// 1e250
let x = ExtendedFloat {
mant: 12882297539194265600,
exp: 767,
};
assert_eq!(x.into_float::<f64>(), 1e250);
// max value
let x = ExtendedFloat {
mant: 9007199254740991,
exp: 971,
};
assert_eq!(x.into_float::<f64>(), 1.7976931348623157e308);
// max value
let x = ExtendedFloat {
mant: 18446744073709549568,
exp: 960,
};
assert_eq!(x.into_float::<f64>(), 1.7976931348623157e308);
// overflow
let x = ExtendedFloat {
mant: 9007199254740992,
exp: 971,
};
assert_eq!(x.into_float::<f64>(), f64::INFINITY);
// overflow
let x = ExtendedFloat {
mant: 18446744073709549568,
exp: 961,
};
assert_eq!(x.into_float::<f64>(), f64::INFINITY);
// Underflow
// Adapted from failures in strtod.
let x = ExtendedFloat {
exp: -1139,
mant: 18446744073709550712,
};
assert_eq!(x.into_float::<f64>(), 0.0);
let x = ExtendedFloat {
exp: -1139,
mant: 18446744073709551460,
};
assert_eq!(x.into_float::<f64>(), 0.0);
let x = ExtendedFloat {
exp: -1138,
mant: 9223372036854776103,
};
assert_eq!(x.into_float::<f64>(), 5e-324);
// Integers.
for int in &INTEGERS {
let fp = ExtendedFloat { mant: *int, exp: 0 };
assert_eq!(fp.into_float::<f64>(), *int as f64, "{:?} as f64", *int);
}
}
// OPERATIONS
fn check_mul(a: ExtendedFloat, b: ExtendedFloat, c: ExtendedFloat) {
let r = a.mul(&b);
assert_eq!(r, c);
}
#[test]
fn mul_test() {
// Normalized (64-bit mantissa)
let a = ExtendedFloat {
mant: 13164036458569648128,
exp: -213,
};
let b = ExtendedFloat {
mant: 9223372036854775808,
exp: -62,
};
let c = ExtendedFloat {
mant: 6582018229284824064,
exp: -211,
};
check_mul(a, b, c);
// Check with integers
// 64-bit mantissa
let mut a = ExtendedFloat { mant: 10, exp: 0 };
let mut b = ExtendedFloat { mant: 10, exp: 0 };
a.normalize();
b.normalize();
assert_eq!(a.mul(&b).into_float::<f64>(), 100.0);
// Check both values need high bits set.
let a = ExtendedFloat {
mant: 1 << 32,
exp: -31,
};
let b = ExtendedFloat {
mant: 1 << 32,
exp: -31,
};
assert_eq!(a.mul(&b).into_float::<f64>(), 4.0);
// Check both values need high bits set.
let a = ExtendedFloat {
mant: 10 << 31,
exp: -31,
};
let b = ExtendedFloat {
mant: 10 << 31,
exp: -31,
};
assert_eq!(a.mul(&b).into_float::<f64>(), 100.0);
}
fn check_imul(mut a: ExtendedFloat, b: ExtendedFloat, c: ExtendedFloat) {
a.imul(&b);
assert_eq!(a, c);
}
#[test]
fn imul_test() {
// Normalized (64-bit mantissa)
let a = ExtendedFloat {
mant: 13164036458569648128,
exp: -213,
};
let b = ExtendedFloat {
mant: 9223372036854775808,
exp: -62,
};
let c = ExtendedFloat {
mant: 6582018229284824064,
exp: -211,
};
check_imul(a, b, c);
// Check with integers
// 64-bit mantissa
let mut a = ExtendedFloat { mant: 10, exp: 0 };
let mut b = ExtendedFloat { mant: 10, exp: 0 };
a.normalize();
b.normalize();
a.imul(&b);
assert_eq!(a.into_float::<f64>(), 100.0);
// Check both values need high bits set.
let mut a = ExtendedFloat {
mant: 1 << 32,
exp: -31,
};
let b = ExtendedFloat {
mant: 1 << 32,
exp: -31,
};
a.imul(&b);
assert_eq!(a.into_float::<f64>(), 4.0);
// Check both values need high bits set.
let mut a = ExtendedFloat {
mant: 10 << 31,
exp: -31,
};
let b = ExtendedFloat {
mant: 10 << 31,
exp: -31,
};
a.imul(&b);
assert_eq!(a.into_float::<f64>(), 100.0);
}
