1 //! Port of LLVM's APFloat software floating-point implementation from the
2 //! following C++ sources (please update commit hash when backporting):
3 //! <https://github.com/llvm-mirror/llvm/tree/23efab2bbd424ed13495a420ad8641cb2c6c28f9>
5 //! * `include/llvm/ADT/APFloat.h` -> `Float` and `FloatConvert` traits
6 //! * `lib/Support/APFloat.cpp` -> `ieee` and `ppc` modules
7 //! * `unittests/ADT/APFloatTest.cpp` -> `tests` directory
9 //! The port contains no unsafe code, global state, or side-effects in general,
10 //! and the only allocations are in the conversion to/from decimal strings.
12 //! Most of the API and the testcases are intact in some form or another,
13 //! with some ergonomic changes, such as idiomatic short names, returning
14 //! new values instead of mutating the receiver, and having separate method
15 //! variants that take a non-default rounding mode (with the suffix `_r`).
16 //! Comments have been preserved where possible, only slightly adapted.
18 //! Instead of keeping a pointer to a configuration struct and inspecting it
19 //! dynamically on every operation, types (e.g., `ieee::Double`), traits
20 //! (e.g., `ieee::Semantics`) and associated constants are employed for
21 //! increased type safety and performance.
23 //! On-heap bigints are replaced everywhere (except in decimal conversion),
24 //! with short arrays of `type Limb = u128` elements (instead of `u64`),
25 //! This allows fitting the largest supported significands in one integer
26 //! (`ieee::Quad` and `ppc::Fallback` use slightly less than 128 bits).
27 //! All of the functions in the `ieee::sig` module operate on slices.
31 //! This API is completely unstable and subject to change.
33 #![doc(html_logo_url = "https://www.rust-lang.org/logos/rust-logo-128x128-blk-v2.png",
34 html_favicon_url = "https://doc.rust-lang.org/favicon.ico",
35 html_root_url = "https://doc.rust-lang.org/nightly/")]
36 #![forbid(unsafe_code)]
40 // See librustc_cratesio_shim/Cargo.toml for a comment explaining this.
41 #[allow(unused_extern_crates)]
42 extern crate rustc_cratesio_shim;
45 extern crate bitflags;
46 extern crate smallvec;
48 use std::cmp::Ordering;
50 use std::ops::{Neg, Add, Sub, Mul, Div, Rem};
51 use std::ops::{AddAssign, SubAssign, MulAssign, DivAssign, RemAssign};
52 use std::str::FromStr;
55 /// IEEE-754R 7: Default exception handling.
57 /// UNDERFLOW or OVERFLOW are always returned or-ed with INEXACT.
59 pub struct Status: u8 {
61 const INVALID_OP = 0x01;
62 const DIV_BY_ZERO = 0x02;
63 const OVERFLOW = 0x04;
64 const UNDERFLOW = 0x08;
70 #[derive(Copy, Clone, PartialEq, Eq, PartialOrd, Ord, Debug)]
71 pub struct StatusAnd<T> {
77 pub fn and<T>(self, value: T) -> StatusAnd<T> {
85 impl<T> StatusAnd<T> {
86 pub fn map<F: FnOnce(T) -> U, U>(self, f: F) -> StatusAnd<U> {
96 ($status:ident|=, $e:expr) => {
98 $crate::StatusAnd { status, value } => {
104 ($status:ident=, $e:expr) => {
106 $crate::StatusAnd { status, value } => {
114 /// Category of internally-represented number.
115 #[derive(Copy, Clone, PartialEq, Eq, Debug)]
123 /// IEEE-754R 4.3: Rounding-direction attributes.
124 #[derive(Copy, Clone, PartialEq, Eq, Debug)]
135 fn neg(self) -> Round {
137 Round::TowardPositive => Round::TowardNegative,
138 Round::TowardNegative => Round::TowardPositive,
139 Round::NearestTiesToEven | Round::TowardZero | Round::NearestTiesToAway => self,
144 /// A signed type to represent a floating point number's unbiased exponent.
145 pub type ExpInt = i16;
147 // \c ilogb error results.
148 pub const IEK_INF: ExpInt = ExpInt::max_value();
149 pub const IEK_NAN: ExpInt = ExpInt::min_value();
150 pub const IEK_ZERO: ExpInt = ExpInt::min_value() + 1;
152 #[derive(Copy, Clone, PartialEq, Eq, Debug)]
153 pub struct ParseError(pub &'static str);
155 /// A self-contained host- and target-independent arbitrary-precision
156 /// floating-point software implementation.
158 /// `apfloat` uses significand bignum integer arithmetic as provided by functions
159 /// in the `ieee::sig`.
161 /// Written for clarity rather than speed, in particular with a view to use in
162 /// the front-end of a cross compiler so that target arithmetic can be correctly
163 /// performed on the host. Performance should nonetheless be reasonable,
164 /// particularly for its intended use. It may be useful as a base
165 /// implementation for a run-time library during development of a faster
166 /// target-specific one.
168 /// All 5 rounding modes in the IEEE-754R draft are handled correctly for all
169 /// implemented operations. Currently implemented operations are add, subtract,
170 /// multiply, divide, fused-multiply-add, conversion-to-float,
171 /// conversion-to-integer and conversion-from-integer. New rounding modes
172 /// (e.g., away from zero) can be added with three or four lines of code.
174 /// Four formats are built-in: IEEE single precision, double precision,
175 /// quadruple precision, and x87 80-bit extended double (when operating with
176 /// full extended precision). Adding a new format that obeys IEEE semantics
177 /// only requires adding two lines of code: a declaration and definition of the
180 /// All operations return the status of that operation as an exception bit-mask,
181 /// so multiple operations can be done consecutively with their results or-ed
182 /// together. The returned status can be useful for compiler diagnostics; e.g.,
183 /// inexact, underflow and overflow can be easily diagnosed on constant folding,
184 /// and compiler optimizers can determine what exceptions would be raised by
185 /// folding operations and optimize, or perhaps not optimize, accordingly.
187 /// At present, underflow tininess is detected after rounding; it should be
188 /// straight forward to add support for the before-rounding case too.
190 /// The library reads hexadecimal floating point numbers as per C99, and
191 /// correctly rounds if necessary according to the specified rounding mode.
192 /// Syntax is required to have been validated by the caller.
194 /// It also reads decimal floating point numbers and correctly rounds according
195 /// to the specified rounding mode.
197 /// Non-zero finite numbers are represented internally as a sign bit, a 16-bit
198 /// signed exponent, and the significand as an array of integer limbs. After
199 /// normalization of a number of precision P the exponent is within the range of
200 /// the format, and if the number is not denormal the P-th bit of the
201 /// significand is set as an explicit integer bit. For denormals the most
202 /// significant bit is shifted right so that the exponent is maintained at the
203 /// format's minimum, so that the smallest denormal has just the least
204 /// significant bit of the significand set. The sign of zeros and infinities
205 /// is significant; the exponent and significand of such numbers is not stored,
206 /// but has a known implicit (deterministic) value: 0 for the significands, 0
207 /// for zero exponent, all 1 bits for infinity exponent. For NaNs the sign and
208 /// significand are deterministic, although not really meaningful, and preserved
209 /// in non-conversion operations. The exponent is implicitly all 1 bits.
211 /// `apfloat` does not provide any exception handling beyond default exception
212 /// handling. We represent Signaling NaNs via IEEE-754R 2008 6.2.1 should clause
213 /// by encoding Signaling NaNs with the first bit of its trailing significand
219 /// Some features that may or may not be worth adding:
221 /// Optional ability to detect underflow tininess before rounding.
223 /// New formats: x87 in single and double precision mode (IEEE apart from
224 /// extended exponent range) (hard).
226 /// New operations: sqrt, nexttoward.
231 + FromStr<Err = ParseError>
240 + Add<Output = StatusAnd<Self>>
241 + Sub<Output = StatusAnd<Self>>
242 + Mul<Output = StatusAnd<Self>>
243 + Div<Output = StatusAnd<Self>>
244 + Rem<Output = StatusAnd<Self>> {
245 /// Total number of bits in the in-memory format.
248 /// Number of bits in the significand. This includes the integer bit.
249 const PRECISION: usize;
251 /// The largest E such that 2<sup>E</sup> is representable; this matches the
252 /// definition of IEEE 754.
253 const MAX_EXP: ExpInt;
255 /// The smallest E such that 2<sup>E</sup> is a normalized number; this
256 /// matches the definition of IEEE 754.
257 const MIN_EXP: ExpInt;
262 /// Positive Infinity.
263 const INFINITY: Self;
265 /// NaN (Not a Number).
266 // FIXME(eddyb) provide a default when qnan becomes const fn.
269 /// Factory for QNaN values.
270 // FIXME(eddyb) should be const fn.
271 fn qnan(payload: Option<u128>) -> Self;
273 /// Factory for SNaN values.
274 // FIXME(eddyb) should be const fn.
275 fn snan(payload: Option<u128>) -> Self;
277 /// Largest finite number.
278 // FIXME(eddyb) should be const (but FloatPair::largest is nontrivial).
279 fn largest() -> Self;
281 /// Smallest (by magnitude) finite number.
282 /// Might be denormalized, which implies a relative loss of precision.
283 const SMALLEST: Self;
285 /// Smallest (by magnitude) normalized finite number.
286 // FIXME(eddyb) should be const (but FloatPair::smallest_normalized is nontrivial).
287 fn smallest_normalized() -> Self;
291 fn add_r(self, rhs: Self, round: Round) -> StatusAnd<Self>;
292 fn sub_r(self, rhs: Self, round: Round) -> StatusAnd<Self> {
293 self.add_r(-rhs, round)
295 fn mul_r(self, rhs: Self, round: Round) -> StatusAnd<Self>;
296 fn mul_add_r(self, multiplicand: Self, addend: Self, round: Round) -> StatusAnd<Self>;
297 fn mul_add(self, multiplicand: Self, addend: Self) -> StatusAnd<Self> {
298 self.mul_add_r(multiplicand, addend, Round::NearestTiesToEven)
300 fn div_r(self, rhs: Self, round: Round) -> StatusAnd<Self>;
302 // This is not currently correct in all cases.
303 fn ieee_rem(self, rhs: Self) -> StatusAnd<Self> {
307 v = unpack!(status=, v / rhs);
308 if status == Status::DIV_BY_ZERO {
309 return status.and(self);
312 assert!(Self::PRECISION < 128);
315 let x = unpack!(status=, v.to_i128_r(128, Round::NearestTiesToEven, &mut false));
316 if status == Status::INVALID_OP {
317 return status.and(self);
321 let mut v = unpack!(status=, Self::from_i128(x));
322 assert_eq!(status, Status::OK); // should always work
325 v = unpack!(status=, v * rhs);
326 assert_eq!(status - Status::INEXACT, Status::OK); // should not overflow or underflow
329 v = unpack!(status=, self - v);
330 assert_eq!(status - Status::INEXACT, Status::OK); // likewise
333 status.and(v.copy_sign(self)) // IEEE754 requires this
338 /// C fmod, or llvm frem.
339 fn c_fmod(self, rhs: Self) -> StatusAnd<Self>;
340 fn round_to_integral(self, round: Round) -> StatusAnd<Self>;
342 /// IEEE-754R 2008 5.3.1: nextUp.
343 fn next_up(self) -> StatusAnd<Self>;
345 /// IEEE-754R 2008 5.3.1: nextDown.
347 /// *NOTE* since nextDown(x) = -nextUp(-x), we only implement nextUp with
348 /// appropriate sign switching before/after the computation.
349 fn next_down(self) -> StatusAnd<Self> {
350 (-self).next_up().map(|r| -r)
353 fn abs(self) -> Self {
354 if self.is_negative() { -self } else { self }
356 fn copy_sign(self, rhs: Self) -> Self {
357 if self.is_negative() != rhs.is_negative() {
365 fn from_bits(input: u128) -> Self;
366 fn from_i128_r(input: i128, round: Round) -> StatusAnd<Self> {
368 Self::from_u128_r(input.wrapping_neg() as u128, -round).map(|r| -r)
370 Self::from_u128_r(input as u128, round)
373 fn from_i128(input: i128) -> StatusAnd<Self> {
374 Self::from_i128_r(input, Round::NearestTiesToEven)
376 fn from_u128_r(input: u128, round: Round) -> StatusAnd<Self>;
377 fn from_u128(input: u128) -> StatusAnd<Self> {
378 Self::from_u128_r(input, Round::NearestTiesToEven)
380 fn from_str_r(s: &str, round: Round) -> Result<StatusAnd<Self>, ParseError>;
381 fn to_bits(self) -> u128;
383 /// Convert a floating point number to an integer according to the
384 /// rounding mode. In case of an invalid operation exception,
385 /// deterministic values are returned, namely zero for NaNs and the
386 /// minimal or maximal value respectively for underflow or overflow.
387 /// If the rounded value is in range but the floating point number is
388 /// not the exact integer, the C standard doesn't require an inexact
389 /// exception to be raised. IEEE-854 does require it so we do that.
391 /// Note that for conversions to integer type the C standard requires
392 /// round-to-zero to always be used.
394 /// The *is_exact output tells whether the result is exact, in the sense
395 /// that converting it back to the original floating point type produces
396 /// the original value. This is almost equivalent to result==Status::OK,
397 /// except for negative zeroes.
398 fn to_i128_r(self, width: usize, round: Round, is_exact: &mut bool) -> StatusAnd<i128> {
400 if self.is_negative() {
402 // Negative zero can't be represented as an int.
405 let r = unpack!(status=, (-self).to_u128_r(width, -round, is_exact));
407 // Check for values that don't fit in the signed integer.
408 if r > (1 << (width - 1)) {
409 // Return the most negative integer for the given width.
411 Status::INVALID_OP.and(-1 << (width - 1))
413 status.and(r.wrapping_neg() as i128)
416 // Positive case is simpler, can pretend it's a smaller unsigned
417 // integer, and `to_u128` will take care of all the edge cases.
418 self.to_u128_r(width - 1, round, is_exact).map(
423 fn to_i128(self, width: usize) -> StatusAnd<i128> {
424 self.to_i128_r(width, Round::TowardZero, &mut true)
426 fn to_u128_r(self, width: usize, round: Round, is_exact: &mut bool) -> StatusAnd<u128>;
427 fn to_u128(self, width: usize) -> StatusAnd<u128> {
428 self.to_u128_r(width, Round::TowardZero, &mut true)
431 fn cmp_abs_normal(self, rhs: Self) -> Ordering;
433 /// Bitwise comparison for equality (QNaNs compare equal, 0!=-0).
434 fn bitwise_eq(self, rhs: Self) -> bool;
436 // IEEE-754R 5.7.2 General operations.
438 /// Implements IEEE minNum semantics. Returns the smaller of the 2 arguments if
439 /// both are not NaN. If either argument is a NaN, returns the other argument.
440 fn min(self, other: Self) -> Self {
443 } else if other.is_nan() {
445 } else if other.partial_cmp(&self) == Some(Ordering::Less) {
452 /// Implements IEEE maxNum semantics. Returns the larger of the 2 arguments if
453 /// both are not NaN. If either argument is a NaN, returns the other argument.
454 fn max(self, other: Self) -> Self {
457 } else if other.is_nan() {
459 } else if self.partial_cmp(&other) == Some(Ordering::Less) {
466 /// IEEE-754R isSignMinus: Returns true if and only if the current value is
469 /// This applies to zeros and NaNs as well.
470 fn is_negative(self) -> bool;
472 /// IEEE-754R isNormal: Returns true if and only if the current value is normal.
474 /// This implies that the current value of the float is not zero, subnormal,
475 /// infinite, or NaN following the definition of normality from IEEE-754R.
476 fn is_normal(self) -> bool {
477 !self.is_denormal() && self.is_finite_non_zero()
480 /// Returns true if and only if the current value is zero, subnormal, or
483 /// This means that the value is not infinite or NaN.
484 fn is_finite(self) -> bool {
485 !self.is_nan() && !self.is_infinite()
488 /// Returns true if and only if the float is plus or minus zero.
489 fn is_zero(self) -> bool {
490 self.category() == Category::Zero
493 /// IEEE-754R isSubnormal(): Returns true if and only if the float is a
495 fn is_denormal(self) -> bool;
497 /// IEEE-754R isInfinite(): Returns true if and only if the float is infinity.
498 fn is_infinite(self) -> bool {
499 self.category() == Category::Infinity
502 /// Returns true if and only if the float is a quiet or signaling NaN.
503 fn is_nan(self) -> bool {
504 self.category() == Category::NaN
507 /// Returns true if and only if the float is a signaling NaN.
508 fn is_signaling(self) -> bool;
512 fn category(self) -> Category;
513 fn is_non_zero(self) -> bool {
516 fn is_finite_non_zero(self) -> bool {
517 self.is_finite() && !self.is_zero()
519 fn is_pos_zero(self) -> bool {
520 self.is_zero() && !self.is_negative()
522 fn is_neg_zero(self) -> bool {
523 self.is_zero() && self.is_negative()
526 /// Returns true if and only if the number has the smallest possible non-zero
527 /// magnitude in the current semantics.
528 fn is_smallest(self) -> bool {
529 Self::SMALLEST.copy_sign(self).bitwise_eq(self)
532 /// Returns true if and only if the number has the largest possible finite
533 /// magnitude in the current semantics.
534 fn is_largest(self) -> bool {
535 Self::largest().copy_sign(self).bitwise_eq(self)
538 /// Returns true if and only if the number is an exact integer.
539 fn is_integer(self) -> bool {
540 // This could be made more efficient; I'm going for obviously correct.
541 if !self.is_finite() {
544 self.round_to_integral(Round::TowardZero).value.bitwise_eq(
549 /// If this value has an exact multiplicative inverse, return it.
550 fn get_exact_inverse(self) -> Option<Self>;
552 /// Returns the exponent of the internal representation of the Float.
554 /// Because the radix of Float is 2, this is equivalent to floor(log2(x)).
555 /// For special Float values, this returns special error codes:
557 /// NaN -> \c IEK_NAN
559 /// Inf -> \c IEK_INF
561 fn ilogb(self) -> ExpInt;
563 /// Returns: self * 2<sup>exp</sup> for integral exponents.
564 fn scalbn_r(self, exp: ExpInt, round: Round) -> Self;
565 fn scalbn(self, exp: ExpInt) -> Self {
566 self.scalbn_r(exp, Round::NearestTiesToEven)
569 /// Equivalent of C standard library function.
571 /// While the C standard says exp is an unspecified value for infinity and nan,
572 /// this returns INT_MAX for infinities, and INT_MIN for NaNs (see `ilogb`).
573 fn frexp_r(self, exp: &mut ExpInt, round: Round) -> Self;
574 fn frexp(self, exp: &mut ExpInt) -> Self {
575 self.frexp_r(exp, Round::NearestTiesToEven)
579 pub trait FloatConvert<T: Float>: Float {
580 /// Convert a value of one floating point type to another.
581 /// The return value corresponds to the IEEE754 exceptions. *loses_info
582 /// records whether the transformation lost information, i.e., whether
583 /// converting the result back to the original type will produce the
584 /// original value (this is almost the same as return value==Status::OK,
585 /// but there are edge cases where this is not so).
586 fn convert_r(self, round: Round, loses_info: &mut bool) -> StatusAnd<T>;
587 fn convert(self, loses_info: &mut bool) -> StatusAnd<T> {
588 self.convert_r(Round::NearestTiesToEven, loses_info)
592 macro_rules! float_common_impls {
593 ($ty:ident<$t:tt>) => {
594 impl<$t> Default for $ty<$t> where Self: Float {
595 fn default() -> Self {
600 impl<$t> ::std::str::FromStr for $ty<$t> where Self: Float {
601 type Err = ParseError;
602 fn from_str(s: &str) -> Result<Self, ParseError> {
603 Self::from_str_r(s, Round::NearestTiesToEven).map(|x| x.value)
607 // Rounding ties to the nearest even, by default.
609 impl<$t> ::std::ops::Add for $ty<$t> where Self: Float {
610 type Output = StatusAnd<Self>;
611 fn add(self, rhs: Self) -> StatusAnd<Self> {
612 self.add_r(rhs, Round::NearestTiesToEven)
616 impl<$t> ::std::ops::Sub for $ty<$t> where Self: Float {
617 type Output = StatusAnd<Self>;
618 fn sub(self, rhs: Self) -> StatusAnd<Self> {
619 self.sub_r(rhs, Round::NearestTiesToEven)
623 impl<$t> ::std::ops::Mul for $ty<$t> where Self: Float {
624 type Output = StatusAnd<Self>;
625 fn mul(self, rhs: Self) -> StatusAnd<Self> {
626 self.mul_r(rhs, Round::NearestTiesToEven)
630 impl<$t> ::std::ops::Div for $ty<$t> where Self: Float {
631 type Output = StatusAnd<Self>;
632 fn div(self, rhs: Self) -> StatusAnd<Self> {
633 self.div_r(rhs, Round::NearestTiesToEven)
637 impl<$t> ::std::ops::Rem for $ty<$t> where Self: Float {
638 type Output = StatusAnd<Self>;
639 fn rem(self, rhs: Self) -> StatusAnd<Self> {
644 impl<$t> ::std::ops::AddAssign for $ty<$t> where Self: Float {
645 fn add_assign(&mut self, rhs: Self) {
646 *self = (*self + rhs).value;
650 impl<$t> ::std::ops::SubAssign for $ty<$t> where Self: Float {
651 fn sub_assign(&mut self, rhs: Self) {
652 *self = (*self - rhs).value;
656 impl<$t> ::std::ops::MulAssign for $ty<$t> where Self: Float {
657 fn mul_assign(&mut self, rhs: Self) {
658 *self = (*self * rhs).value;
662 impl<$t> ::std::ops::DivAssign for $ty<$t> where Self: Float {
663 fn div_assign(&mut self, rhs: Self) {
664 *self = (*self / rhs).value;
668 impl<$t> ::std::ops::RemAssign for $ty<$t> where Self: Float {
669 fn rem_assign(&mut self, rhs: Self) {
670 *self = (*self % rhs).value;