1 // Copyright 2017 The Rust Project Developers. See the COPYRIGHT
2 // file at the top-level directory of this distribution and at
3 // http://rust-lang.org/COPYRIGHT.
5 // Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
6 // http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
7 // <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
8 // option. This file may not be copied, modified, or distributed
9 // except according to those terms.
11 //! Port of LLVM's APFloat software floating-point implementation from the
12 //! following C++ sources (please update commit hash when backporting):
13 //! https://github.com/llvm-mirror/llvm/tree/23efab2bbd424ed13495a420ad8641cb2c6c28f9
14 //! * `include/llvm/ADT/APFloat.h` -> `Float` and `FloatConvert` traits
15 //! * `lib/Support/APFloat.cpp` -> `ieee` and `ppc` modules
16 //! * `unittests/ADT/APFloatTest.cpp` -> `tests` directory
18 //! The port contains no unsafe code, global state, or side-effects in general,
19 //! and the only allocations are in the conversion to/from decimal strings.
21 //! Most of the API and the testcases are intact in some form or another,
22 //! with some ergonomic changes, such as idiomatic short names, returning
23 //! new values instead of mutating the receiver, and having separate method
24 //! variants that take a non-default rounding mode (with the suffix `_r`).
25 //! Comments have been preserved where possible, only slightly adapted.
27 //! Instead of keeping a pointer to a configuration struct and inspecting it
28 //! dynamically on every operation, types (e.g. `ieee::Double`), traits
29 //! (e.g. `ieee::Semantics`) and associated constants are employed for
30 //! increased type safety and performance.
32 //! On-heap bigints are replaced everywhere (except in decimal conversion),
33 //! with short arrays of `type Limb = u128` elements (instead of `u64`),
34 //! This allows fitting the largest supported significands in one integer
35 //! (`ieee::Quad` and `ppc::Fallback` use slightly less than 128 bits).
36 //! All of the functions in the `ieee::sig` module operate on slices.
40 //! This API is completely unstable and subject to change.
42 #![crate_name = "rustc_apfloat"]
43 #![doc(html_logo_url = "https://www.rust-lang.org/logos/rust-logo-128x128-blk-v2.png",
44 html_favicon_url = "https://doc.rust-lang.org/favicon.ico",
45 html_root_url = "https://doc.rust-lang.org/nightly/")]
47 #![forbid(unsafe_code)]
50 #![feature(i128_type)]
53 extern crate rustc_bitflags;
55 use std::cmp::Ordering;
57 use std::ops::{Neg, Add, Sub, Mul, Div, Rem};
58 use std::ops::{AddAssign, SubAssign, MulAssign, DivAssign, RemAssign, BitOrAssign};
59 use std::str::FromStr;
62 /// IEEE-754R 7: Default exception handling.
64 /// UNDERFLOW or OVERFLOW are always returned or-ed with INEXACT.
69 const INVALID_OP = 0x01,
70 const DIV_BY_ZERO = 0x02,
71 const OVERFLOW = 0x04,
72 const UNDERFLOW = 0x08,
77 impl BitOrAssign for Status {
78 fn bitor_assign(&mut self, rhs: Self) {
84 #[derive(Copy, Clone, PartialEq, Eq, PartialOrd, Ord, Debug)]
85 pub struct StatusAnd<T> {
91 pub fn and<T>(self, value: T) -> StatusAnd<T> {
99 impl<T> StatusAnd<T> {
100 fn map<F: FnOnce(T) -> U, U>(self, f: F) -> StatusAnd<U> {
103 value: f(self.value),
109 macro_rules! unpack {
110 ($status:ident|=, $e:expr) => {
112 $crate::StatusAnd { status, value } => {
118 ($status:ident=, $e:expr) => {
120 $crate::StatusAnd { status, value } => {
128 /// Category of internally-represented number.
129 #[derive(Copy, Clone, PartialEq, Eq, Debug)]
137 /// IEEE-754R 4.3: Rounding-direction attributes.
138 #[derive(Copy, Clone, PartialEq, Eq, Debug)]
149 fn neg(self) -> Round {
151 Round::TowardPositive => Round::TowardNegative,
152 Round::TowardNegative => Round::TowardPositive,
153 Round::NearestTiesToEven | Round::TowardZero | Round::NearestTiesToAway => self,
158 /// A signed type to represent a floating point number's unbiased exponent.
159 pub type ExpInt = i16;
161 // \c ilogb error results.
162 pub const IEK_INF: ExpInt = ExpInt::max_value();
163 pub const IEK_NAN: ExpInt = ExpInt::min_value();
164 pub const IEK_ZERO: ExpInt = ExpInt::min_value() + 1;
166 #[derive(Copy, Clone, PartialEq, Eq, Debug)]
167 pub struct ParseError(pub &'static str);
169 /// A self-contained host- and target-independent arbitrary-precision
170 /// floating-point software implementation.
172 /// `apfloat` uses significand bignum integer arithmetic as provided by functions
173 /// in the `ieee::sig`.
175 /// Written for clarity rather than speed, in particular with a view to use in
176 /// the front-end of a cross compiler so that target arithmetic can be correctly
177 /// performed on the host. Performance should nonetheless be reasonable,
178 /// particularly for its intended use. It may be useful as a base
179 /// implementation for a run-time library during development of a faster
180 /// target-specific one.
182 /// All 5 rounding modes in the IEEE-754R draft are handled correctly for all
183 /// implemented operations. Currently implemented operations are add, subtract,
184 /// multiply, divide, fused-multiply-add, conversion-to-float,
185 /// conversion-to-integer and conversion-from-integer. New rounding modes
186 /// (e.g. away from zero) can be added with three or four lines of code.
188 /// Four formats are built-in: IEEE single precision, double precision,
189 /// quadruple precision, and x87 80-bit extended double (when operating with
190 /// full extended precision). Adding a new format that obeys IEEE semantics
191 /// only requires adding two lines of code: a declaration and definition of the
194 /// All operations return the status of that operation as an exception bit-mask,
195 /// so multiple operations can be done consecutively with their results or-ed
196 /// together. The returned status can be useful for compiler diagnostics; e.g.,
197 /// inexact, underflow and overflow can be easily diagnosed on constant folding,
198 /// and compiler optimizers can determine what exceptions would be raised by
199 /// folding operations and optimize, or perhaps not optimize, accordingly.
201 /// At present, underflow tininess is detected after rounding; it should be
202 /// straight forward to add support for the before-rounding case too.
204 /// The library reads hexadecimal floating point numbers as per C99, and
205 /// correctly rounds if necessary according to the specified rounding mode.
206 /// Syntax is required to have been validated by the caller.
208 /// It also reads decimal floating point numbers and correctly rounds according
209 /// to the specified rounding mode.
211 /// Non-zero finite numbers are represented internally as a sign bit, a 16-bit
212 /// signed exponent, and the significand as an array of integer limbs. After
213 /// normalization of a number of precision P the exponent is within the range of
214 /// the format, and if the number is not denormal the P-th bit of the
215 /// significand is set as an explicit integer bit. For denormals the most
216 /// significant bit is shifted right so that the exponent is maintained at the
217 /// format's minimum, so that the smallest denormal has just the least
218 /// significant bit of the significand set. The sign of zeros and infinities
219 /// is significant; the exponent and significand of such numbers is not stored,
220 /// but has a known implicit (deterministic) value: 0 for the significands, 0
221 /// for zero exponent, all 1 bits for infinity exponent. For NaNs the sign and
222 /// significand are deterministic, although not really meaningful, and preserved
223 /// in non-conversion operations. The exponent is implicitly all 1 bits.
225 /// `apfloat` does not provide any exception handling beyond default exception
226 /// handling. We represent Signaling NaNs via IEEE-754R 2008 6.2.1 should clause
227 /// by encoding Signaling NaNs with the first bit of its trailing significand as
233 /// Some features that may or may not be worth adding:
235 /// Optional ability to detect underflow tininess before rounding.
237 /// New formats: x87 in single and double precision mode (IEEE apart from
238 /// extended exponent range) (hard).
240 /// New operations: sqrt, nexttoward.
245 + FromStr<Err = ParseError>
254 + Add<Output = StatusAnd<Self>>
255 + Sub<Output = StatusAnd<Self>>
256 + Mul<Output = StatusAnd<Self>>
257 + Div<Output = StatusAnd<Self>>
258 + Rem<Output = StatusAnd<Self>> {
259 /// Total number of bits in the in-memory format.
262 /// Number of bits in the significand. This includes the integer bit.
263 const PRECISION: usize;
265 /// The largest E such that 2^E is representable; this matches the
266 /// definition of IEEE 754.
267 const MAX_EXP: ExpInt;
269 /// The smallest E such that 2^E is a normalized number; this
270 /// matches the definition of IEEE 754.
271 const MIN_EXP: ExpInt;
276 /// Positive Infinity.
277 const INFINITY: Self;
279 /// NaN (Not a Number).
280 // FIXME(eddyb) provide a default when qnan becomes const fn.
283 /// Factory for QNaN values.
284 // FIXME(eddyb) should be const fn.
285 fn qnan(payload: Option<u128>) -> Self;
287 /// Factory for SNaN values.
288 // FIXME(eddyb) should be const fn.
289 fn snan(payload: Option<u128>) -> Self;
291 /// Largest finite number.
292 // FIXME(eddyb) should be const (but FloatPair::largest is nontrivial).
293 fn largest() -> Self;
295 /// Smallest (by magnitude) finite number.
296 /// Might be denormalized, which implies a relative loss of precision.
297 const SMALLEST: Self;
299 /// Smallest (by magnitude) normalized finite number.
300 // FIXME(eddyb) should be const (but FloatPair::smallest_normalized is nontrivial).
301 fn smallest_normalized() -> Self;
305 fn add_r(self, rhs: Self, round: Round) -> StatusAnd<Self>;
306 fn sub_r(self, rhs: Self, round: Round) -> StatusAnd<Self> {
307 self.add_r(-rhs, round)
309 fn mul_r(self, rhs: Self, round: Round) -> StatusAnd<Self>;
310 fn mul_add_r(self, multiplicand: Self, addend: Self, round: Round) -> StatusAnd<Self>;
311 fn mul_add(self, multiplicand: Self, addend: Self) -> StatusAnd<Self> {
312 self.mul_add_r(multiplicand, addend, Round::NearestTiesToEven)
314 fn div_r(self, rhs: Self, round: Round) -> StatusAnd<Self>;
316 // This is not currently correct in all cases.
317 fn ieee_rem(self, rhs: Self) -> StatusAnd<Self> {
321 v = unpack!(status=, v / rhs);
322 if status == Status::DIV_BY_ZERO {
323 return status.and(self);
326 assert!(Self::PRECISION < 128);
329 let x = unpack!(status=, v.to_i128_r(128, Round::NearestTiesToEven, &mut false));
330 if status == Status::INVALID_OP {
331 return status.and(self);
335 let mut v = unpack!(status=, Self::from_i128(x));
336 assert_eq!(status, Status::OK); // should always work
339 v = unpack!(status=, v * rhs);
340 assert_eq!(status - Status::INEXACT, Status::OK); // should not overflow or underflow
343 v = unpack!(status=, self - v);
344 assert_eq!(status - Status::INEXACT, Status::OK); // likewise
347 status.and(v.copy_sign(self)) // IEEE754 requires this
352 /// C fmod, or llvm frem.
353 fn c_fmod(self, rhs: Self) -> StatusAnd<Self>;
354 fn round_to_integral(self, round: Round) -> StatusAnd<Self>;
356 /// IEEE-754R 2008 5.3.1: nextUp.
357 fn next_up(self) -> StatusAnd<Self>;
359 /// IEEE-754R 2008 5.3.1: nextDown.
361 /// *NOTE* since nextDown(x) = -nextUp(-x), we only implement nextUp with
362 /// appropriate sign switching before/after the computation.
363 fn next_down(self) -> StatusAnd<Self> {
364 (-self).next_up().map(|r| -r)
367 fn abs(self) -> Self {
368 if self.is_negative() { -self } else { self }
370 fn copy_sign(self, rhs: Self) -> Self {
371 if self.is_negative() != rhs.is_negative() {
379 fn from_bits(input: u128) -> Self;
380 fn from_i128_r(input: i128, round: Round) -> StatusAnd<Self> {
382 Self::from_u128_r(-input as u128, -round).map(|r| -r)
384 Self::from_u128_r(input as u128, round)
387 fn from_i128(input: i128) -> StatusAnd<Self> {
388 Self::from_i128_r(input, Round::NearestTiesToEven)
390 fn from_u128_r(input: u128, round: Round) -> StatusAnd<Self>;
391 fn from_u128(input: u128) -> StatusAnd<Self> {
392 Self::from_u128_r(input, Round::NearestTiesToEven)
394 fn from_str_r(s: &str, round: Round) -> Result<StatusAnd<Self>, ParseError>;
395 fn to_bits(self) -> u128;
397 /// Convert a floating point number to an integer according to the
398 /// rounding mode. In case of an invalid operation exception,
399 /// deterministic values are returned, namely zero for NaNs and the
400 /// minimal or maximal value respectively for underflow or overflow.
401 /// If the rounded value is in range but the floating point number is
402 /// not the exact integer, the C standard doesn't require an inexact
403 /// exception to be raised. IEEE-854 does require it so we do that.
405 /// Note that for conversions to integer type the C standard requires
406 /// round-to-zero to always be used.
408 /// The *is_exact output tells whether the result is exact, in the sense
409 /// that converting it back to the original floating point type produces
410 /// the original value. This is almost equivalent to result==Status::OK,
411 /// except for negative zeroes.
412 fn to_i128_r(self, width: usize, round: Round, is_exact: &mut bool) -> StatusAnd<i128> {
414 if self.is_negative() {
416 // Negative zero can't be represented as an int.
419 let r = unpack!(status=, (-self).to_u128_r(width, -round, is_exact));
421 // Check for values that don't fit in the signed integer.
422 if r > (1 << (width - 1)) {
423 // Return the most negative integer for the given width.
425 Status::INVALID_OP.and(-1 << (width - 1))
427 status.and(r.wrapping_neg() as i128)
430 // Positive case is simpler, can pretend it's a smaller unsigned
431 // integer, and `to_u128` will take care of all the edge cases.
432 self.to_u128_r(width - 1, round, is_exact).map(
437 fn to_i128(self, width: usize) -> StatusAnd<i128> {
438 self.to_i128_r(width, Round::TowardZero, &mut true)
440 fn to_u128_r(self, width: usize, round: Round, is_exact: &mut bool) -> StatusAnd<u128>;
441 fn to_u128(self, width: usize) -> StatusAnd<u128> {
442 self.to_u128_r(width, Round::TowardZero, &mut true)
445 fn cmp_abs_normal(self, rhs: Self) -> Ordering;
447 /// Bitwise comparison for equality (QNaNs compare equal, 0!=-0).
448 fn bitwise_eq(self, rhs: Self) -> bool;
450 // IEEE-754R 5.7.2 General operations.
452 /// Implements IEEE minNum semantics. Returns the smaller of the 2 arguments if
453 /// both are not NaN. If either argument is a NaN, returns the other argument.
454 fn min(self, other: Self) -> Self {
457 } else if other.is_nan() {
459 } else if other.partial_cmp(&self) == Some(Ordering::Less) {
466 /// Implements IEEE maxNum semantics. Returns the larger of the 2 arguments if
467 /// both are not NaN. If either argument is a NaN, returns the other argument.
468 fn max(self, other: Self) -> Self {
471 } else if other.is_nan() {
473 } else if self.partial_cmp(&other) == Some(Ordering::Less) {
480 /// IEEE-754R isSignMinus: Returns true if and only if the current value is
483 /// This applies to zeros and NaNs as well.
484 fn is_negative(self) -> bool;
486 /// IEEE-754R isNormal: Returns true if and only if the current value is normal.
488 /// This implies that the current value of the float is not zero, subnormal,
489 /// infinite, or NaN following the definition of normality from IEEE-754R.
490 fn is_normal(self) -> bool {
491 !self.is_denormal() && self.is_finite_non_zero()
494 /// Returns true if and only if the current value is zero, subnormal, or
497 /// This means that the value is not infinite or NaN.
498 fn is_finite(self) -> bool {
499 !self.is_nan() && !self.is_infinite()
502 /// Returns true if and only if the float is plus or minus zero.
503 fn is_zero(self) -> bool {
504 self.category() == Category::Zero
507 /// IEEE-754R isSubnormal(): Returns true if and only if the float is a
509 fn is_denormal(self) -> bool;
511 /// IEEE-754R isInfinite(): Returns true if and only if the float is infinity.
512 fn is_infinite(self) -> bool {
513 self.category() == Category::Infinity
516 /// Returns true if and only if the float is a quiet or signaling NaN.
517 fn is_nan(self) -> bool {
518 self.category() == Category::NaN
521 /// Returns true if and only if the float is a signaling NaN.
522 fn is_signaling(self) -> bool;
526 fn category(self) -> Category;
527 fn is_non_zero(self) -> bool {
530 fn is_finite_non_zero(self) -> bool {
531 self.is_finite() && !self.is_zero()
533 fn is_pos_zero(self) -> bool {
534 self.is_zero() && !self.is_negative()
536 fn is_neg_zero(self) -> bool {
537 self.is_zero() && self.is_negative()
540 /// Returns true if and only if the number has the smallest possible non-zero
541 /// magnitude in the current semantics.
542 fn is_smallest(self) -> bool {
543 Self::SMALLEST.copy_sign(self).bitwise_eq(self)
546 /// Returns true if and only if the number has the largest possible finite
547 /// magnitude in the current semantics.
548 fn is_largest(self) -> bool {
549 Self::largest().copy_sign(self).bitwise_eq(self)
552 /// Returns true if and only if the number is an exact integer.
553 fn is_integer(self) -> bool {
554 // This could be made more efficient; I'm going for obviously correct.
555 if !self.is_finite() {
558 self.round_to_integral(Round::TowardZero).value.bitwise_eq(
563 /// If this value has an exact multiplicative inverse, return it.
564 fn get_exact_inverse(self) -> Option<Self>;
566 /// Returns the exponent of the internal representation of the Float.
568 /// Because the radix of Float is 2, this is equivalent to floor(log2(x)).
569 /// For special Float values, this returns special error codes:
571 /// NaN -> \c IEK_NAN
573 /// Inf -> \c IEK_INF
575 fn ilogb(self) -> ExpInt;
577 /// Returns: self * 2^exp for integral exponents.
578 fn scalbn_r(self, exp: ExpInt, round: Round) -> Self;
579 fn scalbn(self, exp: ExpInt) -> Self {
580 self.scalbn_r(exp, Round::NearestTiesToEven)
583 /// Equivalent of C standard library function.
585 /// While the C standard says exp is an unspecified value for infinity and nan,
586 /// this returns INT_MAX for infinities, and INT_MIN for NaNs (see `ilogb`).
587 fn frexp_r(self, exp: &mut ExpInt, round: Round) -> Self;
588 fn frexp(self, exp: &mut ExpInt) -> Self {
589 self.frexp_r(exp, Round::NearestTiesToEven)
593 pub trait FloatConvert<T: Float>: Float {
594 /// Convert a value of one floating point type to another.
595 /// The return value corresponds to the IEEE754 exceptions. *loses_info
596 /// records whether the transformation lost information, i.e. whether
597 /// converting the result back to the original type will produce the
598 /// original value (this is almost the same as return value==Status::OK,
599 /// but there are edge cases where this is not so).
600 fn convert_r(self, round: Round, loses_info: &mut bool) -> StatusAnd<T>;
601 fn convert(self, loses_info: &mut bool) -> StatusAnd<T> {
602 self.convert_r(Round::NearestTiesToEven, loses_info)
607 macro_rules! float_common_impls {
608 ($ty:ident<$t:tt>) => {
609 impl<$t> Default for $ty<$t> where Self: Float {
610 fn default() -> Self {
615 impl<$t> ::std::str::FromStr for $ty<$t> where Self: Float {
616 type Err = ParseError;
617 fn from_str(s: &str) -> Result<Self, ParseError> {
618 Self::from_str_r(s, Round::NearestTiesToEven).map(|x| x.value)
622 // Rounding ties to the nearest even, by default.
624 impl<$t> ::std::ops::Add for $ty<$t> where Self: Float {
625 type Output = StatusAnd<Self>;
626 fn add(self, rhs: Self) -> StatusAnd<Self> {
627 self.add_r(rhs, Round::NearestTiesToEven)
631 impl<$t> ::std::ops::Sub for $ty<$t> where Self: Float {
632 type Output = StatusAnd<Self>;
633 fn sub(self, rhs: Self) -> StatusAnd<Self> {
634 self.sub_r(rhs, Round::NearestTiesToEven)
638 impl<$t> ::std::ops::Mul for $ty<$t> where Self: Float {
639 type Output = StatusAnd<Self>;
640 fn mul(self, rhs: Self) -> StatusAnd<Self> {
641 self.mul_r(rhs, Round::NearestTiesToEven)
645 impl<$t> ::std::ops::Div for $ty<$t> where Self: Float {
646 type Output = StatusAnd<Self>;
647 fn div(self, rhs: Self) -> StatusAnd<Self> {
648 self.div_r(rhs, Round::NearestTiesToEven)
652 impl<$t> ::std::ops::Rem for $ty<$t> where Self: Float {
653 type Output = StatusAnd<Self>;
654 fn rem(self, rhs: Self) -> StatusAnd<Self> {
659 impl<$t> ::std::ops::AddAssign for $ty<$t> where Self: Float {
660 fn add_assign(&mut self, rhs: Self) {
661 *self = (*self + rhs).value;
665 impl<$t> ::std::ops::SubAssign for $ty<$t> where Self: Float {
666 fn sub_assign(&mut self, rhs: Self) {
667 *self = (*self - rhs).value;
671 impl<$t> ::std::ops::MulAssign for $ty<$t> where Self: Float {
672 fn mul_assign(&mut self, rhs: Self) {
673 *self = (*self * rhs).value;
677 impl<$t> ::std::ops::DivAssign for $ty<$t> where Self: Float {
678 fn div_assign(&mut self, rhs: Self) {
679 *self = (*self / rhs).value;
683 impl<$t> ::std::ops::RemAssign for $ty<$t> where Self: Float {
684 fn rem_assign(&mut self, rhs: Self) {
685 *self = (*self % rhs).value;