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)]
51 #![feature(slice_patterns)]
55 extern crate rustc_bitflags;
57 use std::cmp::Ordering;
59 use std::ops::{Neg, Add, Sub, Mul, Div, Rem};
60 use std::ops::{AddAssign, SubAssign, MulAssign, DivAssign, RemAssign, BitOrAssign};
61 use std::str::FromStr;
64 /// IEEE-754R 7: Default exception handling.
66 /// UNDERFLOW or OVERFLOW are always returned or-ed with INEXACT.
71 const INVALID_OP = 0x01,
72 const DIV_BY_ZERO = 0x02,
73 const OVERFLOW = 0x04,
74 const UNDERFLOW = 0x08,
79 impl BitOrAssign for Status {
80 fn bitor_assign(&mut self, rhs: Self) {
86 #[derive(Copy, Clone, PartialEq, Eq, PartialOrd, Ord, Debug)]
87 pub struct StatusAnd<T> {
93 pub fn and<T>(self, value: T) -> StatusAnd<T> {
101 impl<T> StatusAnd<T> {
102 fn map<F: FnOnce(T) -> U, U>(self, f: F) -> StatusAnd<U> {
105 value: f(self.value),
111 macro_rules! unpack {
112 ($status:ident|=, $e:expr) => {
114 $crate::StatusAnd { status, value } => {
120 ($status:ident=, $e:expr) => {
122 $crate::StatusAnd { status, value } => {
130 /// Category of internally-represented number.
131 #[derive(Copy, Clone, PartialEq, Eq, Debug)]
139 /// IEEE-754R 4.3: Rounding-direction attributes.
140 #[derive(Copy, Clone, PartialEq, Eq, Debug)]
151 fn neg(self) -> Round {
153 Round::TowardPositive => Round::TowardNegative,
154 Round::TowardNegative => Round::TowardPositive,
155 Round::NearestTiesToEven | Round::TowardZero | Round::NearestTiesToAway => self,
160 /// A signed type to represent a floating point number's unbiased exponent.
161 pub type ExpInt = i16;
163 // \c ilogb error results.
164 pub const IEK_INF: ExpInt = ExpInt::max_value();
165 pub const IEK_NAN: ExpInt = ExpInt::min_value();
166 pub const IEK_ZERO: ExpInt = ExpInt::min_value() + 1;
168 #[derive(Copy, Clone, PartialEq, Eq, Debug)]
169 pub struct ParseError(pub &'static str);
171 /// A self-contained host- and target-independent arbitrary-precision
172 /// floating-point software implementation.
174 /// `apfloat` uses significand bignum integer arithmetic as provided by functions
175 /// in the `ieee::sig`.
177 /// Written for clarity rather than speed, in particular with a view to use in
178 /// the front-end of a cross compiler so that target arithmetic can be correctly
179 /// performed on the host. Performance should nonetheless be reasonable,
180 /// particularly for its intended use. It may be useful as a base
181 /// implementation for a run-time library during development of a faster
182 /// target-specific one.
184 /// All 5 rounding modes in the IEEE-754R draft are handled correctly for all
185 /// implemented operations. Currently implemented operations are add, subtract,
186 /// multiply, divide, fused-multiply-add, conversion-to-float,
187 /// conversion-to-integer and conversion-from-integer. New rounding modes
188 /// (e.g. away from zero) can be added with three or four lines of code.
190 /// Four formats are built-in: IEEE single precision, double precision,
191 /// quadruple precision, and x87 80-bit extended double (when operating with
192 /// full extended precision). Adding a new format that obeys IEEE semantics
193 /// only requires adding two lines of code: a declaration and definition of the
196 /// All operations return the status of that operation as an exception bit-mask,
197 /// so multiple operations can be done consecutively with their results or-ed
198 /// together. The returned status can be useful for compiler diagnostics; e.g.,
199 /// inexact, underflow and overflow can be easily diagnosed on constant folding,
200 /// and compiler optimizers can determine what exceptions would be raised by
201 /// folding operations and optimize, or perhaps not optimize, accordingly.
203 /// At present, underflow tininess is detected after rounding; it should be
204 /// straight forward to add support for the before-rounding case too.
206 /// The library reads hexadecimal floating point numbers as per C99, and
207 /// correctly rounds if necessary according to the specified rounding mode.
208 /// Syntax is required to have been validated by the caller.
210 /// It also reads decimal floating point numbers and correctly rounds according
211 /// to the specified rounding mode.
213 /// Non-zero finite numbers are represented internally as a sign bit, a 16-bit
214 /// signed exponent, and the significand as an array of integer limbs. After
215 /// normalization of a number of precision P the exponent is within the range of
216 /// the format, and if the number is not denormal the P-th bit of the
217 /// significand is set as an explicit integer bit. For denormals the most
218 /// significant bit is shifted right so that the exponent is maintained at the
219 /// format's minimum, so that the smallest denormal has just the least
220 /// significant bit of the significand set. The sign of zeros and infinities
221 /// is significant; the exponent and significand of such numbers is not stored,
222 /// but has a known implicit (deterministic) value: 0 for the significands, 0
223 /// for zero exponent, all 1 bits for infinity exponent. For NaNs the sign and
224 /// significand are deterministic, although not really meaningful, and preserved
225 /// in non-conversion operations. The exponent is implicitly all 1 bits.
227 /// `apfloat` does not provide any exception handling beyond default exception
228 /// handling. We represent Signaling NaNs via IEEE-754R 2008 6.2.1 should clause
229 /// by encoding Signaling NaNs with the first bit of its trailing significand as
235 /// Some features that may or may not be worth adding:
237 /// Optional ability to detect underflow tininess before rounding.
239 /// New formats: x87 in single and double precision mode (IEEE apart from
240 /// extended exponent range) (hard).
242 /// New operations: sqrt, nexttoward.
247 + FromStr<Err = ParseError>
256 + Add<Output = StatusAnd<Self>>
257 + Sub<Output = StatusAnd<Self>>
258 + Mul<Output = StatusAnd<Self>>
259 + Div<Output = StatusAnd<Self>>
260 + Rem<Output = StatusAnd<Self>> {
261 /// Total number of bits in the in-memory format.
264 /// Number of bits in the significand. This includes the integer bit.
265 const PRECISION: usize;
267 /// The largest E such that 2^E is representable; this matches the
268 /// definition of IEEE 754.
269 const MAX_EXP: ExpInt;
271 /// The smallest E such that 2^E is a normalized number; this
272 /// matches the definition of IEEE 754.
273 const MIN_EXP: ExpInt;
278 /// Positive Infinity.
279 const INFINITY: Self;
281 /// NaN (Not a Number).
282 // FIXME(eddyb) provide a default when qnan becomes const fn.
285 /// Factory for QNaN values.
286 // FIXME(eddyb) should be const fn.
287 fn qnan(payload: Option<u128>) -> Self;
289 /// Factory for SNaN values.
290 // FIXME(eddyb) should be const fn.
291 fn snan(payload: Option<u128>) -> Self;
293 /// Largest finite number.
294 // FIXME(eddyb) should be const (but FloatPair::largest is nontrivial).
295 fn largest() -> Self;
297 /// Smallest (by magnitude) finite number.
298 /// Might be denormalized, which implies a relative loss of precision.
299 const SMALLEST: Self;
301 /// Smallest (by magnitude) normalized finite number.
302 // FIXME(eddyb) should be const (but FloatPair::smallest_normalized is nontrivial).
303 fn smallest_normalized() -> Self;
307 fn add_r(self, rhs: Self, round: Round) -> StatusAnd<Self>;
308 fn sub_r(self, rhs: Self, round: Round) -> StatusAnd<Self> {
309 self.add_r(-rhs, round)
311 fn mul_r(self, rhs: Self, round: Round) -> StatusAnd<Self>;
312 fn mul_add_r(self, multiplicand: Self, addend: Self, round: Round) -> StatusAnd<Self>;
313 fn mul_add(self, multiplicand: Self, addend: Self) -> StatusAnd<Self> {
314 self.mul_add_r(multiplicand, addend, Round::NearestTiesToEven)
316 fn div_r(self, rhs: Self, round: Round) -> StatusAnd<Self>;
318 // This is not currently correct in all cases.
319 fn ieee_rem(self, rhs: Self) -> StatusAnd<Self> {
323 v = unpack!(status=, v / rhs);
324 if status == Status::DIV_BY_ZERO {
325 return status.and(self);
328 assert!(Self::PRECISION < 128);
331 let x = unpack!(status=, v.to_i128_r(128, Round::NearestTiesToEven, &mut false));
332 if status == Status::INVALID_OP {
333 return status.and(self);
337 let mut v = unpack!(status=, Self::from_i128(x));
338 assert_eq!(status, Status::OK); // should always work
341 v = unpack!(status=, v * rhs);
342 assert_eq!(status - Status::INEXACT, Status::OK); // should not overflow or underflow
345 v = unpack!(status=, self - v);
346 assert_eq!(status - Status::INEXACT, Status::OK); // likewise
349 status.and(v.copy_sign(self)) // IEEE754 requires this
354 /// C fmod, or llvm frem.
355 fn c_fmod(self, rhs: Self) -> StatusAnd<Self>;
356 fn round_to_integral(self, round: Round) -> StatusAnd<Self>;
358 /// IEEE-754R 2008 5.3.1: nextUp.
359 fn next_up(self) -> StatusAnd<Self>;
361 /// IEEE-754R 2008 5.3.1: nextDown.
363 /// *NOTE* since nextDown(x) = -nextUp(-x), we only implement nextUp with
364 /// appropriate sign switching before/after the computation.
365 fn next_down(self) -> StatusAnd<Self> {
366 (-self).next_up().map(|r| -r)
369 fn abs(self) -> Self {
370 if self.is_negative() { -self } else { self }
372 fn copy_sign(self, rhs: Self) -> Self {
373 if self.is_negative() != rhs.is_negative() {
381 fn from_bits(input: u128) -> Self;
382 fn from_i128_r(input: i128, round: Round) -> StatusAnd<Self> {
384 Self::from_u128_r(-input as u128, -round).map(|r| -r)
386 Self::from_u128_r(input as u128, round)
389 fn from_i128(input: i128) -> StatusAnd<Self> {
390 Self::from_i128_r(input, Round::NearestTiesToEven)
392 fn from_u128_r(input: u128, round: Round) -> StatusAnd<Self>;
393 fn from_u128(input: u128) -> StatusAnd<Self> {
394 Self::from_u128_r(input, Round::NearestTiesToEven)
396 fn from_str_r(s: &str, round: Round) -> Result<StatusAnd<Self>, ParseError>;
397 fn to_bits(self) -> u128;
399 /// Convert a floating point number to an integer according to the
400 /// rounding mode. In case of an invalid operation exception,
401 /// deterministic values are returned, namely zero for NaNs and the
402 /// minimal or maximal value respectively for underflow or overflow.
403 /// If the rounded value is in range but the floating point number is
404 /// not the exact integer, the C standard doesn't require an inexact
405 /// exception to be raised. IEEE-854 does require it so we do that.
407 /// Note that for conversions to integer type the C standard requires
408 /// round-to-zero to always be used.
410 /// The *is_exact output tells whether the result is exact, in the sense
411 /// that converting it back to the original floating point type produces
412 /// the original value. This is almost equivalent to result==Status::OK,
413 /// except for negative zeroes.
414 fn to_i128_r(self, width: usize, round: Round, is_exact: &mut bool) -> StatusAnd<i128> {
416 if self.is_negative() {
418 // Negative zero can't be represented as an int.
421 let r = unpack!(status=, (-self).to_u128_r(width, -round, is_exact));
423 // Check for values that don't fit in the signed integer.
424 if r > (1 << (width - 1)) {
425 // Return the most negative integer for the given width.
427 Status::INVALID_OP.and(-1 << (width - 1))
429 status.and(r.wrapping_neg() as i128)
432 // Positive case is simpler, can pretend it's a smaller unsigned
433 // integer, and `to_u128` will take care of all the edge cases.
434 self.to_u128_r(width - 1, round, is_exact).map(
439 fn to_i128(self, width: usize) -> StatusAnd<i128> {
440 self.to_i128_r(width, Round::TowardZero, &mut true)
442 fn to_u128_r(self, width: usize, round: Round, is_exact: &mut bool) -> StatusAnd<u128>;
443 fn to_u128(self, width: usize) -> StatusAnd<u128> {
444 self.to_u128_r(width, Round::TowardZero, &mut true)
447 fn cmp_abs_normal(self, rhs: Self) -> Ordering;
449 /// Bitwise comparison for equality (QNaNs compare equal, 0!=-0).
450 fn bitwise_eq(self, rhs: Self) -> bool;
452 // IEEE-754R 5.7.2 General operations.
454 /// Implements IEEE minNum semantics. Returns the smaller of the 2 arguments if
455 /// both are not NaN. If either argument is a NaN, returns the other argument.
456 fn min(self, other: Self) -> Self {
459 } else if other.is_nan() {
461 } else if other.partial_cmp(&self) == Some(Ordering::Less) {
468 /// Implements IEEE maxNum semantics. Returns the larger of the 2 arguments if
469 /// both are not NaN. If either argument is a NaN, returns the other argument.
470 fn max(self, other: Self) -> Self {
473 } else if other.is_nan() {
475 } else if self.partial_cmp(&other) == Some(Ordering::Less) {
482 /// IEEE-754R isSignMinus: Returns true if and only if the current value is
485 /// This applies to zeros and NaNs as well.
486 fn is_negative(self) -> bool;
488 /// IEEE-754R isNormal: Returns true if and only if the current value is normal.
490 /// This implies that the current value of the float is not zero, subnormal,
491 /// infinite, or NaN following the definition of normality from IEEE-754R.
492 fn is_normal(self) -> bool {
493 !self.is_denormal() && self.is_finite_non_zero()
496 /// Returns true if and only if the current value is zero, subnormal, or
499 /// This means that the value is not infinite or NaN.
500 fn is_finite(self) -> bool {
501 !self.is_nan() && !self.is_infinite()
504 /// Returns true if and only if the float is plus or minus zero.
505 fn is_zero(self) -> bool {
506 self.category() == Category::Zero
509 /// IEEE-754R isSubnormal(): Returns true if and only if the float is a
511 fn is_denormal(self) -> bool;
513 /// IEEE-754R isInfinite(): Returns true if and only if the float is infinity.
514 fn is_infinite(self) -> bool {
515 self.category() == Category::Infinity
518 /// Returns true if and only if the float is a quiet or signaling NaN.
519 fn is_nan(self) -> bool {
520 self.category() == Category::NaN
523 /// Returns true if and only if the float is a signaling NaN.
524 fn is_signaling(self) -> bool;
528 fn category(self) -> Category;
529 fn is_non_zero(self) -> bool {
532 fn is_finite_non_zero(self) -> bool {
533 self.is_finite() && !self.is_zero()
535 fn is_pos_zero(self) -> bool {
536 self.is_zero() && !self.is_negative()
538 fn is_neg_zero(self) -> bool {
539 self.is_zero() && self.is_negative()
542 /// Returns true if and only if the number has the smallest possible non-zero
543 /// magnitude in the current semantics.
544 fn is_smallest(self) -> bool {
545 Self::SMALLEST.copy_sign(self).bitwise_eq(self)
548 /// Returns true if and only if the number has the largest possible finite
549 /// magnitude in the current semantics.
550 fn is_largest(self) -> bool {
551 Self::largest().copy_sign(self).bitwise_eq(self)
554 /// Returns true if and only if the number is an exact integer.
555 fn is_integer(self) -> bool {
556 // This could be made more efficient; I'm going for obviously correct.
557 if !self.is_finite() {
560 self.round_to_integral(Round::TowardZero).value.bitwise_eq(
565 /// If this value has an exact multiplicative inverse, return it.
566 fn get_exact_inverse(self) -> Option<Self>;
568 /// Returns the exponent of the internal representation of the Float.
570 /// Because the radix of Float is 2, this is equivalent to floor(log2(x)).
571 /// For special Float values, this returns special error codes:
573 /// NaN -> \c IEK_NAN
575 /// Inf -> \c IEK_INF
577 fn ilogb(self) -> ExpInt;
579 /// Returns: self * 2^exp for integral exponents.
580 fn scalbn_r(self, exp: ExpInt, round: Round) -> Self;
581 fn scalbn(self, exp: ExpInt) -> Self {
582 self.scalbn_r(exp, Round::NearestTiesToEven)
585 /// Equivalent of C standard library function.
587 /// While the C standard says exp is an unspecified value for infinity and nan,
588 /// this returns INT_MAX for infinities, and INT_MIN for NaNs (see `ilogb`).
589 fn frexp_r(self, exp: &mut ExpInt, round: Round) -> Self;
590 fn frexp(self, exp: &mut ExpInt) -> Self {
591 self.frexp_r(exp, Round::NearestTiesToEven)
595 pub trait FloatConvert<T: Float>: Float {
596 /// Convert a value of one floating point type to another.
597 /// The return value corresponds to the IEEE754 exceptions. *loses_info
598 /// records whether the transformation lost information, i.e. whether
599 /// converting the result back to the original type will produce the
600 /// original value (this is almost the same as return value==Status::OK,
601 /// but there are edge cases where this is not so).
602 fn convert_r(self, round: Round, loses_info: &mut bool) -> StatusAnd<T>;
603 fn convert(self, loses_info: &mut bool) -> StatusAnd<T> {
604 self.convert_r(Round::NearestTiesToEven, loses_info)
608 macro_rules! float_common_impls {
609 ($ty:ident<$t:tt>) => {
610 impl<$t> Default for $ty<$t> where Self: Float {
611 fn default() -> Self {
616 impl<$t> ::std::str::FromStr for $ty<$t> where Self: Float {
617 type Err = ParseError;
618 fn from_str(s: &str) -> Result<Self, ParseError> {
619 Self::from_str_r(s, Round::NearestTiesToEven).map(|x| x.value)
623 // Rounding ties to the nearest even, by default.
625 impl<$t> ::std::ops::Add for $ty<$t> where Self: Float {
626 type Output = StatusAnd<Self>;
627 fn add(self, rhs: Self) -> StatusAnd<Self> {
628 self.add_r(rhs, Round::NearestTiesToEven)
632 impl<$t> ::std::ops::Sub for $ty<$t> where Self: Float {
633 type Output = StatusAnd<Self>;
634 fn sub(self, rhs: Self) -> StatusAnd<Self> {
635 self.sub_r(rhs, Round::NearestTiesToEven)
639 impl<$t> ::std::ops::Mul for $ty<$t> where Self: Float {
640 type Output = StatusAnd<Self>;
641 fn mul(self, rhs: Self) -> StatusAnd<Self> {
642 self.mul_r(rhs, Round::NearestTiesToEven)
646 impl<$t> ::std::ops::Div for $ty<$t> where Self: Float {
647 type Output = StatusAnd<Self>;
648 fn div(self, rhs: Self) -> StatusAnd<Self> {
649 self.div_r(rhs, Round::NearestTiesToEven)
653 impl<$t> ::std::ops::Rem for $ty<$t> where Self: Float {
654 type Output = StatusAnd<Self>;
655 fn rem(self, rhs: Self) -> StatusAnd<Self> {
660 impl<$t> ::std::ops::AddAssign for $ty<$t> where Self: Float {
661 fn add_assign(&mut self, rhs: Self) {
662 *self = (*self + rhs).value;
666 impl<$t> ::std::ops::SubAssign for $ty<$t> where Self: Float {
667 fn sub_assign(&mut self, rhs: Self) {
668 *self = (*self - rhs).value;
672 impl<$t> ::std::ops::MulAssign for $ty<$t> where Self: Float {
673 fn mul_assign(&mut self, rhs: Self) {
674 *self = (*self * rhs).value;
678 impl<$t> ::std::ops::DivAssign for $ty<$t> where Self: Float {
679 fn div_assign(&mut self, rhs: Self) {
680 *self = (*self / rhs).value;
684 impl<$t> ::std::ops::RemAssign for $ty<$t> where Self: Float {
685 fn rem_assign(&mut self, rhs: Self) {
686 *self = (*self % rhs).value;