slvm/float/float_56.rs
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729
//! This module contains F56, a 7-byte struct that represents a 56-bit floating point number.
//! The SLVM uses 8-byte Values but the first byte stores the type of the Value so 7 bytes remain for the float.
//! Check out value.rs to see how the F56 is one of the enum variants of the Value struct.
//!
//! There are open questions about the benefits of using F56 over f32 that will depend on some peformance benchmarking.
//! f32 is simpler and faster.
//! Additionally, there are questions about whether to impl the Eq and Hash Traits <https://github.com/sl-sh-dev/sl-sh/issues/125>
use std::fmt::{Display, Formatter};
use std::hash::{Hash, Hasher};
use std::str::FromStr;
#[allow(rustdoc::broken_intra_doc_links)]
/// The F56 struct represents a 56-bit floating point number using 7 bytes.
/// Most operations on F56 are done by converting to f64, performing the operation, and then converting back to F56
///
/// F56 uses 1 bit for the sign, 10 bits for the exponent, and 45 bits for the mantissa.
/// Compared to f32, it has +2 exponent bits and +22 mantissa bits.
/// Compared to f64, it has -1 exponent bit and -7 mantissa bits.
/// Byte 0 Byte 1 Byte 2 Byte 3 Byte 4 Byte 5 Byte 6
/// [sEEEEEEE][EEEmmmmm][mmmmmmmm][mmmmmmmm][mmmmmmmm][mmmmmmmm][mmmmmmmm]]
///
/// Exponent bits range from 0 to 1023
/// they represent -511 to +512 but are stored biased by +511
/// the exponent of -511 is reserved for the number 0 and subnormal numbers
/// the exponent of +512 is reserved for infinity and NaN
/// so normal exponents range from -510 to +511
///
/// smallest positive subnormal value is 8.48e-168 (2^-555)
/// smallest positive normal value is 2.98e-154 (2^-510)
/// maximum finite value is 1.34e154
///
/// A f64 number like 1.00000000001 with 12 decimal digits will be 1.000000000001
/// A f64 number like 1.000000000001 with 13 decimal digits will be converted to 1.0
#[derive(Copy, Clone)]
pub struct F56(pub [u8; 7]);
impl Eq for F56 {}
impl PartialEq for F56 {
fn eq(&self, other: &Self) -> bool {
self.strictest_equal(other) // appropriate for `identical?` comparison
}
}
impl Hash for F56 {
// In order to use F56 as a key in a hash map, we need to ensure:
// If a == b then hash(a) == hash(b)
fn hash<H: Hasher>(&self, state: &mut H) {
state.write_u64(self.hash_for_strictest_equal())
}
}
impl std::fmt::Debug for F56 {
fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
write!(f, "F56({:?})", self.0)
}
}
impl Display for F56 {
fn fmt(&self, f: &mut Formatter<'_>) -> std::fmt::Result {
// write!(f, "{}", f64::from(*self))
write!(f, "{}", F56::round_f64_to_f56_precision(f64::from(*self)))
}
}
impl From<f64> for F56 {
fn from(f: f64) -> F56 {
let f64_bytes = f.to_be_bytes();
let f64_word = u64::from_be_bytes(f64_bytes);
let f64_sign: u8 = (f64_word >> 63) as u8; // first bit
let f64_biased_exponent: u16 = ((f64_word >> 52) & 0b111_1111_1111) as u16; // first 11 bits after the sign bit
let true_exponent: i16 = f64_biased_exponent as i16 - 1023i16; // remove the bias of 2^10-1
let f64_mantissa = f64_word & 0x000f_ffff_ffff_ffff; // everything after first 12 bits
let mut f56_mantissa = f64_mantissa >> 7; // we lose 7 bits in mantissa
if F56::ROUNDUP_ENABLED {
let round_up_bit = f64_mantissa & 0b0100_0000u64 > 0; // the highest bit we lost (7th bit from the end)
f56_mantissa += if round_up_bit { 1 } else { 0 }; // round up if the 7th bit is 1
}
let f56_biased_exponent = match f64_biased_exponent {
0b111_1111_1111 => {
// Special case meaning the f64 is NaN or Infinity
// NaN's mantissa has at least one [1]
// Infinity's mantissa is all [0]s
// We need to make sure that the lost bits from the f64 mantissa don't change it from NaN to Infinity
if f64_mantissa == 0u64 {
f56_mantissa = 0u64; // mantissa must be all [0]s to represent Infinity
} else {
f56_mantissa = 0b11_1111_1111u64; // mantissa must be all [1]s to represent NaN
}
0b11_1111_1111u64 // 10 bits of all 1s
}
0b000_0000_0000 => {
// Special case meaning the f64 is 0 or subnormal
// in both cases the f56 will be 0
// F56 cannot represent any numbers that are subnormal in F64
// The smallest positive F56 number is 8e-168 and F64 subnormals start at 1e-308
f56_mantissa = 0u64;
0b00_0000_0000u64
}
_ if true_exponent > 511 => {
// TOO LARGE TO PROPERLY REPRESENT
// standard behavior converting from f64 to f32 is to represent this as Infinity rather than panicking
f56_mantissa = 0u64; // mantissa must be all [0]s to represent Infinity
0b11_1111_1111u64 // exponent for Infinity
}
_ if true_exponent < -510 => {
// This will be either a subnormal or 0
// Requires a subnormal f56 which will lose precision as we near 8.48e-168
// to calculate a 45 bit subnormal mantissa as 0.fraction,
// take the 45 bits and treat them like an unsigned int and then divide by 2^45
// value of subnormal f56 = value of f64
// value of subnormal f56 = 2^-510 * 0.fraction
// value of f64 = 2^-510 * (u45 / 2^45)
// value of f64 * 2^555 = u45
// multiplying the f64 by 2^555 can be done by adding 555 to the exponent
// we can do this safely because the max biased exponent is 2047
// and we know that the current biased exponent is < 513 (corresponding to true exponent of -510)
let new_f64_exponent = (f64_biased_exponent + 555) as u64;
let new_f64_word = (f64_sign as u64) << 63 | new_f64_exponent << 52 | f64_mantissa;
let new_f64 = f64::from_bits(new_f64_word);
let u45 = new_f64 as u64; // we only care about the integer part
f56_mantissa = u45; // mantissa is set to u45
0b00_0000_0000u64 // exponent is set to 0
}
_ => {
// Generic case
(true_exponent + 511) as u64 // add in the bias for F56
}
};
let f56_sign: u64 = f64_sign as u64;
let word = f56_sign << 55 | f56_biased_exponent << 45 | f56_mantissa;
let f56_bytes = word.to_be_bytes();
F56([
f56_bytes[1],
f56_bytes[2],
f56_bytes[3],
f56_bytes[4],
f56_bytes[5],
f56_bytes[6],
f56_bytes[7],
])
}
}
impl From<f32> for F56 {
fn from(f: f32) -> F56 {
f64::from(f).into()
}
}
impl From<F56> for f64 {
fn from(f: F56) -> f64 {
// f64 has 1 sign bit, 11 exponent bits, and 52 mantissa bits
// f56 has 1 sign bit, 10 exponent bits, and 45 mantissa bits
let bytes7 = f.0;
let f56_word = u64::from_be_bytes([
0, bytes7[0], bytes7[1], bytes7[2], bytes7[3], bytes7[4], bytes7[5], bytes7[6],
]);
let f56_sign: u8 = (f56_word >> 55) as u8; // first bit
let f56_biased_exponent: u16 = (f56_word >> 45) as u16 & 0x3FF; // first 10 bits after the sign bit
let f56_mantissa: u64 = f56_word & 0x1FFF_FFFF_FFFF; // the rightmost 45 bits
let true_exponent = f56_biased_exponent as i16 - 511; // remove the bias of 2^9-1
let f64_biased_exponent: u64 = match f56_biased_exponent {
// NaN or Infinity
// Either way the f64 will also have an exponent of all [1]s
0b11_1111_1111 => 0b111_1111_1111_u64,
// Zero
_ if f56_biased_exponent == 0b00_0000_0000 && f56_mantissa == 0u64 => {
0b000_0000_0000_u64
}
// Subnormal
_ if f56_biased_exponent == 0b00_0000_0000 && f56_mantissa > 0u64 => {
// the f56's exponent is actually representing -510 instead of 0
// note that -510 exponent would also represented by 0x1
// which is why we only need to add 1022 instead of 1023 to bias this for f64
(true_exponent + 1022) as u64
}
// Generic case
_ => {
(true_exponent + 1023) as u64 // add in the bias for F64
}
};
let f64_sign = f56_sign as u64;
let f64_mantissa = f56_mantissa << 7_u64; // we add 7 bits in mantissa, but they're all zeros
let word: u64 = f64_sign << 63 | f64_biased_exponent << 52 | f64_mantissa;
f64::from_be_bytes(word.to_be_bytes())
}
}
impl From<F56> for f32 {
fn from(f: F56) -> f32 {
f64::from(f) as f32
}
}
impl FromStr for F56 {
type Err = std::num::ParseFloatError;
fn from_str(s: &str) -> Result<Self, Self::Err> {
f64::from_str(s).map(F56::from)
}
}
impl F56 {
// Largest finite F56, roughly 1.34e154
pub const MAX: F56 = F56([0x7F, 0xDF, 0xff, 0xff, 0xff, 0xff, 0xff]);
// Smallest positive normal F56, roughly 2.98e-154
pub const MIN_POSITIVE: F56 = F56([0x00, 0b0010_0000, 0x00, 0x00, 0x00, 0x00, 0x00]);
// Smallest positive subnormal F56, roughly 8.48e-168
pub const MIN_POSITIVE_SUBNORMAL: F56 = F56([0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01]);
// Minimum numer of decimal digits of precision (experimentally derived)
// for comparison, f32 has 6-9 decimal digits of precision and f64 has 15-17. I believe F56 has 12-14
pub const DIGITS: usize = 12;
// Cutoff for relative difference between an f64 and the F56's approximation
pub const EPSILON: f64 = 1e-10;
// When converting from f64 to F56 we truncate 7 bits of the mantissa
// We could round up if the 7th bit is 1, but this is might cause issues.
// Mantissas like 0xFFFF_FFFF_... can catastrophically round to 0x0000_0000_...
pub const ROUNDUP_ENABLED: bool = false;
}
impl F56 {
pub fn round_f64_to_7_sig_figs(raw_f64: f64) -> f64 {
if raw_f64.is_nan() || raw_f64.is_infinite() || raw_f64 == 0.0 {
return raw_f64;
}
let orig_exponent_value = raw_f64.abs().log10().floor() as i32; // the number after 'e' in scientific notation
let target_exponent_value = 2; // exponent that we will shift this number to
let scale_factor = 10f64.powi(target_exponent_value - orig_exponent_value);
let scaled_and_rounded = (raw_f64 * scale_factor).round();
scaled_and_rounded / scale_factor
}
pub fn round_f64_to_f56_precision(raw_f64: f64) -> f64 {
if raw_f64.is_nan() || raw_f64.is_infinite() || raw_f64 == 0.0 {
return raw_f64;
}
// round to a max of F56::DIGITS sig figs
let orig_exponent_value = raw_f64.abs().log10().floor() as i32; // the number after 'e' in scientific notation
let target_exponent_value = F56::DIGITS as i32 - 1; // exponent that we will shift this number to
let scale_factor = 10f64.powi(target_exponent_value - orig_exponent_value);
let scaled_and_rounded = (raw_f64 * scale_factor).round();
scaled_and_rounded / scale_factor
}
/// Returns true if the two F56s's decimal forms are equal to 7 significant figures
/// This is a lenient type of equality suitable for human use
/// It preserves transitivity, reflexivity, and symmetry
/// It meets the requirements of the Eq trait
pub fn roughly_equal_using_rounding_sig_figs(&self, other: &F56) -> bool {
println!("Rounding two numbers to 7 sig figs, {} and {}", self, other);
let self_as_f64 = f64::from(*self);
let other_as_f64 = f64::from(*other);
// NaNs are considered equal, deviating from IEEE 754 floats, but allowing us to use this as a hash key
if self_as_f64.is_nan() && other_as_f64.is_nan() {
return true;
}
F56::round_f64_to_7_sig_figs(self_as_f64) == F56::round_f64_to_7_sig_figs(other_as_f64)
}
/// Returns true if the relative difference between the two F56s is less than F56::EPSILON
/// This is a lenient type of equality suitable for human use
/// It preserves reflexivity, and symmetry but not transitivity
/// It does not meet the requirements of the Eq trait
/// The relative difference is the absolute difference divided by the larger of the two numbers
pub fn roughly_equal_using_relative_difference(&self, other: &F56) -> bool {
if self == other {
return true;
}
let self_as_f64 = f64::from(*self);
let other_as_f64 = f64::from(*other);
if self_as_f64.is_nan() && other_as_f64.is_nan() {
return true;
}
if self_as_f64.is_infinite() && other_as_f64.is_infinite() {
return self_as_f64.is_sign_positive() == other_as_f64.is_sign_positive();
}
let larger = self_as_f64.abs().max(other_as_f64.abs());
if larger == 0.0 {
return true;
}
let relative_difference = (self_as_f64 - other_as_f64).abs() / larger;
relative_difference < F56::EPSILON
}
/// Returns true if the two F56s are bitwise identical
pub fn strictest_equal(&self, other: &F56) -> bool {
self.0 == other.0
}
pub fn hash_for_strictest_equal(&self) -> u64 {
u64::from_be_bytes([
0, self.0[0], self.0[1], self.0[2], self.0[3], self.0[4], self.0[5], self.0[6],
])
}
/// Returns true if the two F56s are bitwise identical OR if they are both NaN or both 0
pub fn strictly_equal_except_nan_and_0(&self, other: &F56) -> bool {
// if the bit patterns are identical, then they are equal
if self.0 == other.0 {
return true;
}
// if both are 0 or -0 return true
if self.0 == [0, 0, 0, 0, 0, 0, 0] && other.0 == [0x80, 0, 0, 0, 0, 0, 0] {
return true;
}
if self.0 == [0x80, 0, 0, 0, 0, 0, 0] && other.0 == [0, 0, 0, 0, 0, 0, 0] {
return true;
}
// if both are NaN return true
if self.is_nan() && other.is_nan() {
return true;
}
false
}
pub fn hash_for_strictly_equal_except_nan_and_0(&self) -> u64 {
let f56_word = u64::from_be_bytes([
0, self.0[0], self.0[1], self.0[2], self.0[3], self.0[4], self.0[5], self.0[6],
]);
// Special Case 1: Convert any 0 to the same bit pattern
if f56_word == 0x0080000000000000u64 {
return 0x0000000000000000u64;
}
// Special Case 2: Convert any NaN to the same bit pattern
if self.is_nan() {
return 0x7FF8000000000001u64;
}
f56_word
}
/// Returns true if the F56 is NaN. Note that there are many bit patterns that represent NaN
pub fn is_nan(&self) -> bool {
let bytes7 = self.0;
let f56_word = u64::from_be_bytes([
0, bytes7[0], bytes7[1], bytes7[2], bytes7[3], bytes7[4], bytes7[5], bytes7[6],
]);
let f56_biased_exponent: u16 = (f56_word >> 45) as u16 & 0x3FF; // first 10 bits after the sign bit
let f56_mantissa: u64 = f56_word & 0x1FFF_FFFF_FFFF; // the rightmost 45 bits
// all 1s in the exponent and a nonzero mantissa means NaN
f56_biased_exponent == 0b11_1111_1111 && f56_mantissa > 0u64
}
}
#[cfg(test)]
mod tests {
use crate::float::F56;
const MAXIMUM_ACCEPTABLE_RELATIVE_DIFFERENCE: f64 = 1e-10;
pub fn log_f32(f: f32) -> String {
let bytes = f.to_be_bytes();
let word = u32::from_be_bytes([bytes[0], bytes[1], bytes[2], bytes[3]]);
let f32_biased_exponent: u8 = (word >> 23) as u8; // first 8 bits after the sign bit
let mut true_exponent: i16 = (f32_biased_exponent as i16) - 127; // remove the bias of 2^7-1
if f32_biased_exponent == 0 {
true_exponent = 0;
}
let f32_mantissa = word & 0x007f_ffff; // everything after first 9 bits
// print the f32 in scientific notation, the true exponent in decimal, and the mantissa in decimal, and the hex word
format!(
"f32: {:.5e}, true exponent: {}, mantissa: {:016x}, word: {:016x}",
f, true_exponent, f32_mantissa, word
)
}
pub fn log_f56(f: F56) -> String {
let bytes7 = f.0;
let word = u64::from_be_bytes([
0, bytes7[0], bytes7[1], bytes7[2], bytes7[3], bytes7[4], bytes7[5], bytes7[6],
]);
let f56_biased_exponent: u16 = ((word >> 45) as u16) & 0x3FF; // first 10 bits after the sign bit
let f56_mantissa = word & 0x1FFFF_FFFF_FFFF; // everything after first 10 bits
let mut true_exponent = f56_biased_exponent as i16 - 511; // remove the bias of 2^9-1
if f56_biased_exponent == 0 {
true_exponent = 0;
}
format!(
"f56: {:.5e}, true exponent: {}, mantissa: {:016x}, word: {:016x}",
f64::from(f),
true_exponent,
f56_mantissa,
word
)
}
pub fn log_f64(f: f64) -> String {
let bytes = f.to_be_bytes();
let word = u64::from_be_bytes([
bytes[0], bytes[1], bytes[2], bytes[3], bytes[4], bytes[5], bytes[6], bytes[7],
]);
let f64_biased_exponent: i16 = ((word & 0x7ff0_0000_0000_0000) >> 52) as i16; // first 11 bits after the sign bit
let mut true_exponent: i16 = f64_biased_exponent - 1023; // remove the bias of 2^10-1
if f64_biased_exponent == 0 {
true_exponent = 0;
}
let f64_mantissa = word & 0x001f_ffff_ffff_ffff; // everything after first 11 bits
format!(
"f64: {:.5e}, true exponent: {}, mantissa: {:016x}, word: {:016x}",
f, true_exponent, f64_mantissa, word
)
}
fn debug(orig_f64: f64, index: usize) {
println!("index: {}", index);
println!("original f64 : {}", log_f64(orig_f64));
println!("f64 -> f32 : {}", log_f32(orig_f64 as f32));
println!("f64 -> f32 -> f64 : {}", log_f64((orig_f64 as f32) as f64));
println!("f64 -> f56 : {}", log_f56(F56::from(orig_f64)));
println!(
"f64 -> f56 -> f64 : {}",
log_f64(f64::from(F56::from(orig_f64)))
);
let f32_diff = (f64::from(orig_f64 as f32) - orig_f64).abs();
let f32_relative_difference = f32_diff / orig_f64.abs();
if f32_relative_difference > 0.0 {
println!("f32 relative difference {:.5e}", f32_relative_difference);
}
let f56_diff: f64 = (f64::from(F56::from(orig_f64)) - orig_f64).abs();
let f56_relative_difference = f56_diff / orig_f64.abs();
if f56_relative_difference > 0.0 {
println!("f56 relative difference {:.5e}", f56_relative_difference);
}
println!("")
}
fn get_regular_f64_values() -> [f64; 15] {
[
0_f64,
0.0,
1.0,
2.0,
2.5123,
3.0,
4.0,
5.0,
6.0,
7.0,
8.0,
9.0,
10.0,
-1.0,
-0.33333333333333333333333333333,
]
}
fn get_variety_f64_values() -> [f64; 133] {
[
399.999_999_999_58527_f64,
399.999_999_999_585_f64,
399.999_999_999_58_f64,
399.999_999_999_6_f64,
399.999_999_999_f64,
0.000_000_012_312_312_412_412_312_3_f64,
0.000_000_012_312_312_452_57_f64,
399_999_999.999_58_f64,
399_999_999_999_600_000_000_000_000_000_000_0_f64,
399_999_999_999_600_000_000_000_000_000_000_0_f64,
0x0000_0000_0000_0000u64 as f64,
0x0000_0000_0000_0001u64 as f64,
0x8000_0000_0000_0000u64 as f64,
0x7FFF_FFFF_FFFF_FFFFu64 as f64,
0x7FFF_FFFF_FFFF_FFFEu64 as f64,
0xFFFF_FFFF_FFFF_FFFFu64 as f64,
0x7000_0000_0000_0000u64 as f64,
0xDEAD_BEEF_DEAD_BEEFu64 as f64,
0x1234_5678_9ABC_DEF0u64 as f64,
0x1111_1111_1111_1111u64 as f64,
0x2222_2222_2222_2222u64 as f64,
0x3333_3333_3333_3333u64 as f64,
0x4444_4444_4444_4444u64 as f64,
0x5555_5555_5555_5555u64 as f64,
0x6666_6666_6666_6666u64 as f64,
0x7777_7777_7777_7777u64 as f64,
0x8888_8888_8888_8888u64 as f64,
0x9999_9999_9999_9999u64 as f64,
0xAAAA_AAAA_AAAA_AAAAu64 as f64,
0xBBBB_BBBB_BBBB_BBBBu64 as f64,
0xCCCC_CCCC_CCCC_CCCCu64 as f64,
0xDDDD_DDDD_DDDD_DDDDu64 as f64,
0xEEEE_EEEE_EEEE_EEEEu64 as f64,
0xFFFF_FFFF_FFFF_FFFEu64 as f64,
0xFFF0_0000_0000_0001u64 as f64,
0xDEAD_BEEF_DEAD_BEEFu64 as f64,
0x1234_5678_9ABC_DEF0u64 as f64,
0x1111_1111_1111_1111u64 as f64,
0x2222_2222_2222_2222u64 as f64,
0x3333_3333_3333_3333u64 as f64,
0x4444_4444_4444_4444u64 as f64,
0x5555_5555_5555_5555u64 as f64,
0x6666_6666_6666_6666u64 as f64,
0x7777_7777_7777_7777u64 as f64,
0x8888_8888_8888_8888u64 as f64,
0x9999_9999_9999_9999u64 as f64,
0xAAAA_AAAA_AAAA_AAAAu64 as f64,
0xBBBB_BBBB_BBBB_BBBBu64 as f64,
0xCCCC_CCCC_CCCC_CCCCu64 as f64,
0xDDDD_DDDD_DDDD_DDDDu64 as f64,
0xEEEE_EEEE_EEEE_EEEEu64 as f64,
2.3,
23.0,
230.0,
2300.0,
23000.0,
230000.0,
23e5,
23e6,
2.3e5,
0.23,
0.023,
0.0023,
0.00023,
0.000023,
0.0000023,
0.23e-5,
-1234567890123456789012345678901.0,
-1.1412314e108,
-3.33e55,
-1e44,
-1337.1337,
-222.2,
-0.0,
-0.1,
0.0,
0.1,
0.01,
0.001,
0.249,
0.999,
1.0,
1.001,
1.01,
1.1,
1.999,
2.0,
2.2345,
3.0,
3.33333333333333333333333333333333,
4.0,
4.44,
5.0,
5.1,
6.0,
6.2,
7.0,
8.0,
9.0,
10.0,
100.0,
234.432,
420.69,
1234.0,
12345.0,
123456.0,
1234567.0,
12345678.0,
123456789.0,
1234567890.0,
12345678901.0,
123456789012.0,
1234567890123.0,
12345678901234.0,
123456789012345.0,
1234567890123456.0,
12345678901234567.0,
123456789012345678.0,
1234567890123456789.0,
12345678901234567890.0,
123456789012345678901.0,
1234567890123456789012.0,
12345678901234567890123.0,
123456789012345678901234.0,
1234567890123456789012345.0,
12345678901234567890123456.0,
123456789012345678901234567.0,
1234567890123456789012345678.0,
12345678901234567890123456789.0,
123456789012345678901234567890.0,
123456789012345678901234567890.1,
999.999e99,
1e100,
]
}
fn get_edge_case_f64_values() -> [f64; 39] {
[
f64::MIN,
f64::MAX,
f64::MIN_POSITIVE,
f64::INFINITY,
f64::NEG_INFINITY,
f64::NAN,
-0.0,
f32::MIN_POSITIVE as f64, // 42
f32::MIN_POSITIVE as f64 / 3.0,
f32::MIN_POSITIVE as f64 / 7e5,
f32::MIN_POSITIVE as f64 / 7e6,
f32::MIN_POSITIVE as f64 / 7e7,
f32::MIN_POSITIVE as f64 / 7e8,
f32::MIN_POSITIVE as f64 / 4.123e14,
f32::MAX as f64,
f32::MAX as f64 * 3.0,
f32::MAX as f64 + 99.0,
f64::MIN_POSITIVE,
f64::MIN_POSITIVE / 2.0,
f64::MIN_POSITIVE / 10.0,
f64::MIN,
f64::MAX,
f64::INFINITY,
f64::NEG_INFINITY,
f64::NAN,
F56::EPSILON,
F56::EPSILON / 3.0,
8.4e-168,
8.4e-169,
8.4e-170,
0xFFFF_FFFF_FFFF_FFFEu64 as f64,
0xFFF0_0000_0000_0001u64 as f64,
0x0000_0000_0000_0000u64 as f64,
0x0000_0000_0000_0001u64 as f64,
0x8000_0000_0000_0000u64 as f64,
0x7FFF_FFFF_FFFF_FFFFu64 as f64,
0x7FFF_FFFF_FFFF_FFFEu64 as f64,
0xFFFF_FFFF_FFFF_FFFFu64 as f64,
0x7000_0000_0000_0000u64 as f64,
]
}
fn relative_difference(a: f64, b: f64) -> f64 {
(a - b).abs() / b.abs()
}
// TODO: test the F56::MAX, F56::MIN_POSITIVE, F56::MIN_POSITIVE_SUBNORMAL cases
#[test]
fn f56_strings_match_f64_strings() {
let string_test_closure = |f64_value: &f64| {
let f64_string = format!("{}", f64_value);
let f56_value = F56::from(*f64_value);
let f56_string = format!("{}", f56_value);
if f56_string == f64_string {
return;
}
println!("f64: {} not quite equal\nF56: {}", f64_string, f56_string);
// let abs: f64 = f64_value.abs();
if f64_value.abs() > f64::from(F56::MAX) && f56_string.contains("inf") {
println!("But F56 is expected to be infinite if f64 is outside of its range. {:.0e} > {:.0e}\n", f64_value, f64::from(F56::MAX));
return;
}
if f64_value.abs() < F56::MIN_POSITIVE_SUBNORMAL.into() && f64::from(f56_value) == 0.0 {
println!(
"But F56 is expected to be 0 if f64 is outside of its range. {:.0e} < {:.0e}\n",
f64_value,
f64::from(F56::MIN_POSITIVE_SUBNORMAL)
);
return;
}
let f56_string_to_f64_value = f56_string.parse::<f64>().unwrap();
let f64_string_to_f64_value = f64_string.parse::<f64>().unwrap();
let relative_difference =
relative_difference(f56_string_to_f64_value, f64_string_to_f64_value);
if relative_difference < MAXIMUM_ACCEPTABLE_RELATIVE_DIFFERENCE {
println!(
"But the relative difference of {} is acceptably below the maximum {}\n",
relative_difference, MAXIMUM_ACCEPTABLE_RELATIVE_DIFFERENCE,
);
return;
}
// Failing this test case
debug(*f64_value, 0);
assert_eq!(
f64_string, f56_string,
"f64(left) and f56(right) string values must be equal"
);
};
println!("\n\n\n\nRegular f64 values");
for f in get_regular_f64_values().iter() {
string_test_closure(f);
}
println!("\n\n\n\nVariety f64 values");
for f in get_variety_f64_values().iter() {
string_test_closure(f);
}
println!("\n\n\n\nEdge case f64 values");
for f in get_edge_case_f64_values().iter() {
string_test_closure(f);
}
}
#[test]
fn f56_operations() {
let op1 = "1.1".parse::<F56>().unwrap();
let op2 = "1.3".parse::<F56>().unwrap();
let target = "2.4".parse::<F56>().unwrap();
let op1_f64 = f64::from(op1);
let op2_f64 = f64::from(op2);
let target_f64 = f64::from(target);
let calculated_f64 = op1_f64 + op2_f64;
assert_eq!(calculated_f64, target_f64);
// Test > on the edge of F56 precision
let op1 = "1.0000000000001".parse::<F56>().unwrap();
let op2 = "1.00000000000001".parse::<F56>().unwrap();
let gt = f64::from(op1) > f64::from(op2);
assert!(gt);
// Test < on numbers too precise for F56
let op1 = "1.000000000000001".parse::<F56>().unwrap(); // 16 digits (rounds to 1.0)
let op2 = "1.00000000000001".parse::<F56>().unwrap(); // 15 digits (rounds to 1.0)
let lt = f64::from(op1) < f64::from(op2);
let gt = f64::from(op1) > f64::from(op2);
assert_eq!(op1, op2);
assert!(!lt);
assert!(!gt);
// Test < on numbers straddling precision boundary
let op1 = "1.000000000001".parse::<F56>().unwrap(); // 13 digits (rounds to 1.0)
let op2 = "1.00000000001".parse::<F56>().unwrap(); // 12 digits (stays at 1.000000000001)
let lt = f64::from(op1) < f64::from(op2);
let gt = f64::from(op1) > f64::from(op2);
assert!(lt);
assert!(!gt);
assert_ne!(op1, op2);
// Test op1 - op2 > 0 instead of op1 > op2
let lt = (f64::from(op1) - f64::from(op2)) < 0.0;
let gt = (f64::from(op1) - f64::from(op2)) > 0.0;
assert!(lt);
assert!(!gt);
assert_ne!((f64::from(op1) - f64::from(op2)), 0.0);
}
}