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/llvm-project/commit/462a31f5a5abb905869ea93cc49b096079b11aa4>
4//! * `llvm/include/llvm/ADT/APFloat.h` -> `Float` and `FloatConvert` traits
5//! * `llvm/lib/Support/APFloat.cpp` -> `ieee` and `ppc` modules
6//! * `llvm/unittests/ADT/APFloatTest.cpp` -> `tests` directory
7//!
8//! The port contains no unsafe code, global state, or side-effects in general,
9//! and the only allocations are in the conversion to/from decimal strings.
10//!
11//! Most of the API and the testcases are intact in some form or another,
12//! with some ergonomic changes, such as idiomatic short names, returning
13//! new values instead of mutating the receiver, and having separate method
14//! variants that take a non-default rounding mode (with the suffix `_r`).
15//! Comments have been preserved where possible, only slightly adapted.
16//!
17//! Instead of keeping a pointer to a configuration struct and inspecting it
18//! dynamically on every operation, types (e.g. `ieee::Double`), traits
19//! (e.g. `ieee::Semantics`) and associated constants are employed for
20//! increased type safety and performance.
21//!
22//! On-heap bigints are replaced everywhere (except in decimal conversion),
23//! with short arrays of `type Limb = u128` elements (instead of `u64`),
24//! This allows fitting the largest supported significands in one integer
25//! (`ieee::Quad` and `ppc::Fallback` use slightly less than 128 bits).
26//! All of the functions in the `ieee::sig` module operate on slices.
27//!
28//! # Note
29//!
30//! This API is completely unstable and subject to change.
31
32#![no_std]
33#![deny(warnings)]
34#![forbid(unsafe_code)]
35
36#[macro_use]
37extern crate bitflags;
38
39extern crate alloc;
40
41use core::cmp::Ordering;
42use core::fmt;
43use core::ops::{Add, Div, Mul, Neg, Rem, Sub};
44use core::ops::{AddAssign, DivAssign, MulAssign, RemAssign, SubAssign};
45use core::str::FromStr;
46
47bitflags! {
48 /// IEEE-754R 7: Default exception handling.
49 ///
50 /// UNDERFLOW or OVERFLOW are always returned or-ed with INEXACT.
51 ///
52 /// APFloat models this behavior specified by IEEE-754:
53 /// "For operations producing results in floating-point format, the default
54 /// result of an operation that signals the invalid operation exception
55 /// shall be a quiet NaN."
56 #[must_use]
57 #[derive(Copy, Clone, PartialEq, Eq, PartialOrd, Ord, Debug)]
58 pub struct Status: u8 {
59 const OK = 0x00;
60 const INVALID_OP = 0x01;
61 const DIV_BY_ZERO = 0x02;
62 const OVERFLOW = 0x04;
63 const UNDERFLOW = 0x08;
64 const INEXACT = 0x10;
65 }
66}
67
68/// The result of a computation consisting of the output value and the exceptions, if any.
69#[must_use]
70#[derive(Copy, Clone, PartialEq, Eq, PartialOrd, Ord, Debug)]
71pub struct StatusAnd<T> {
72 pub status: Status,
73 pub value: T,
74}
75
76impl Status {
77 /// Add a value to this status to create a [`StatusAnd`].
78 pub fn and<T>(self, value: T) -> StatusAnd<T> {
79 StatusAnd { status: self, value }
80 }
81}
82
83impl<T> StatusAnd<T> {
84 /// Keep the existing status but apply a transformation to `value`.
85 pub fn map<F: FnOnce(T) -> U, U>(self, f: F) -> StatusAnd<U> {
86 StatusAnd {
87 status: self.status,
88 value: f(self.value),
89 }
90 }
91}
92
93impl<T: core::fmt::Debug> StatusAnd<T> {
94 /// Extract the inner value if there were no errors. If there were errors, panic.
95 pub fn unwrap(self) -> T {
96 assert_eq!(self.status, Status::OK, "called `StatusAnd::unwrap()` on an error value. Value: {:?}", self.value);
97 self.value
98 }
99}
100
101#[macro_export]
102macro_rules! unpack {
103 ($status:ident|=, $e:expr) => {
104 match $e {
105 $crate::StatusAnd { status, value } => {
106 $status |= status;
107 value
108 }
109 }
110 };
111 ($status:ident=, $e:expr) => {
112 match $e {
113 $crate::StatusAnd { status, value } => {
114 $status = status;
115 value
116 }
117 }
118 };
119}
120
121/// Category of internally-represented number.
122#[derive(Copy, Clone, PartialEq, Eq, Debug)]
123pub enum Category {
124 Infinity,
125 NaN,
126 Normal,
127 Zero,
128}
129
130/// IEEE-754R 4.3: Rounding-direction attributes.
131#[derive(Copy, Clone, PartialEq, Eq, Debug)]
132pub enum Round {
133 NearestTiesToEven,
134 TowardPositive,
135 TowardNegative,
136 TowardZero,
137 NearestTiesToAway,
138}
139
140impl Neg for Round {
141 type Output = Round;
142 #[inline]
143 fn neg(self) -> Round {
144 match self {
145 Round::TowardPositive => Round::TowardNegative,
146 Round::TowardNegative => Round::TowardPositive,
147 Round::NearestTiesToEven | Round::TowardZero | Round::NearestTiesToAway => self,
148 }
149 }
150}
151
152/// A signed type to represent a floating point number's unbiased exponent.
153pub type ExpInt = i32;
154
155// \c ilogb error results.
156pub const IEK_INF: ExpInt = ExpInt::max_value();
157pub const IEK_NAN: ExpInt = ExpInt::min_value();
158pub const IEK_ZERO: ExpInt = ExpInt::min_value() + 1;
159
160/// An error which can occur when parsing a floating point number from a string.
161#[derive(Copy, Clone, PartialEq, Eq, Debug)]
162pub struct ParseError(pub &'static str);
163
164/// A self-contained host- and target-independent arbitrary-precision
165/// floating-point software implementation.
166///
167/// `apfloat` uses significand bignum integer arithmetic as provided by functions
168/// in the `ieee::sig`.
169///
170/// Written for clarity rather than speed, in particular with a view to use in
171/// the front-end of a cross compiler so that target arithmetic can be correctly
172/// performed on the host. Performance should nonetheless be reasonable,
173/// particularly for its intended use. It may be useful as a base
174/// implementation for a run-time library during development of a faster
175/// target-specific one.
176///
177/// All 5 rounding modes in the IEEE-754R draft are handled correctly for all
178/// implemented operations. Currently implemented operations are add, subtract,
179/// multiply, divide, fused-multiply-add, conversion-to-float,
180/// conversion-to-integer and conversion-from-integer. New rounding modes
181/// (e.g. away from zero) can be added with three or four lines of code.
182///
183/// Four formats are built-in: IEEE single precision, double precision,
184/// quadruple precision, and x87 80-bit extended double (when operating with
185/// full extended precision). Adding a new format that obeys IEEE semantics
186/// only requires adding two lines of code: a declaration and definition of the
187/// format.
188///
189/// All operations return the status of that operation as an exception bit-mask,
190/// so multiple operations can be done consecutively with their results or-ed
191/// together. The returned status can be useful for compiler diagnostics; e.g.,
192/// inexact, underflow and overflow can be easily diagnosed on constant folding,
193/// and compiler optimizers can determine what exceptions would be raised by
194/// folding operations and optimize, or perhaps not optimize, accordingly.
195///
196/// At present, underflow tininess is detected after rounding; it should be
197/// straight forward to add support for the before-rounding case too.
198///
199/// The library reads hexadecimal floating point numbers as per C99, and
200/// correctly rounds if necessary according to the specified rounding mode.
201/// Syntax is required to have been validated by the caller.
202///
203/// It also reads decimal floating point numbers and correctly rounds according
204/// to the specified rounding mode.
205///
206/// Non-zero finite numbers are represented internally as a sign bit, a 16-bit
207/// signed exponent, and the significand as an array of integer limbs. After
208/// normalization of a number of precision P the exponent is within the range of
209/// the format, and if the number is not denormal the P-th bit of the
210/// significand is set as an explicit integer bit. For denormals the most
211/// significant bit is shifted right so that the exponent is maintained at the
212/// format's minimum, so that the smallest denormal has just the least
213/// significant bit of the significand set. The sign of zeros and infinities
214/// is significant; the exponent and significand of such numbers is not stored,
215/// but has a known implicit (deterministic) value: 0 for the significands, 0
216/// for zero exponent, all 1 bits for infinity exponent. For NaNs the sign and
217/// significand are deterministic, although not really meaningful, and preserved
218/// in non-conversion operations. The exponent is implicitly all 1 bits.
219///
220/// `apfloat` does not provide any exception handling beyond default exception
221/// handling. We represent Signaling NaNs via IEEE-754R 2008 6.2.1 should clause
222/// by encoding Signaling NaNs with the first bit of its trailing significand as
223/// 0.
224///
225/// Future work
226/// ===========
227///
228/// Some features that may or may not be worth adding:
229///
230/// Optional ability to detect underflow tininess before rounding.
231///
232/// New formats: x87 in single and double precision mode (IEEE apart from
233/// extended exponent range) (hard).
234///
235/// New operations: sqrt, nexttoward.
236///
237pub trait Float:
238 Copy
239 + Default
240 + FromStr<Err = ParseError>
241 + PartialOrd
242 + fmt::Display
243 + Neg<Output = Self>
244 + AddAssign
245 + SubAssign
246 + MulAssign
247 + DivAssign
248 + RemAssign
249 + Add<Output = StatusAnd<Self>>
250 + Sub<Output = StatusAnd<Self>>
251 + Mul<Output = StatusAnd<Self>>
252 + Div<Output = StatusAnd<Self>>
253 + Rem<Output = StatusAnd<Self>>
254{
255 /// Total number of bits in the in-memory format.
256 const BITS: usize;
257
258 /// Number of bits in the significand. This includes the integer bit.
259 const PRECISION: usize;
260
261 /// The largest E such that 2^E is representable; this matches the
262 /// definition of IEEE 754.
263 const MAX_EXP: ExpInt;
264
265 /// The smallest E such that 2^E is a normalized number; this
266 /// matches the definition of IEEE 754.
267 const MIN_EXP: ExpInt;
268
269 /// Positive Zero.
270 const ZERO: Self;
271
272 /// Positive Infinity.
273 const INFINITY: Self;
274
275 /// NaN (Not a Number).
276 // FIXME(eddyb) provide a default when qnan becomes const fn.
277 const NAN: Self;
278
279 /// Factory for QNaN values.
280 // FIXME(eddyb) should be const fn.
281 fn qnan(payload: Option<u128>) -> Self;
282
283 /// Factory for SNaN values.
284 // FIXME(eddyb) should be const fn.
285 fn snan(payload: Option<u128>) -> Self;
286
287 /// Largest finite number.
288 // FIXME(eddyb) should be const (but FloatPair::largest is nontrivial).
289 fn largest() -> Self;
290
291 /// Smallest (by magnitude) finite number.
292 /// Might be denormalized, which implies a relative loss of precision.
293 const SMALLEST: Self;
294
295 /// Smallest (by magnitude) normalized finite number.
296 // FIXME(eddyb) should be const (but FloatPair::smallest_normalized is nontrivial).
297 fn smallest_normalized() -> Self;
298
299 // Arithmetic
300
301 fn add_r(self, rhs: Self, round: Round) -> StatusAnd<Self>;
302 fn sub_r(self, rhs: Self, round: Round) -> StatusAnd<Self> {
303 self.add_r(-rhs, round)
304 }
305 fn mul_r(self, rhs: Self, round: Round) -> StatusAnd<Self>;
306 fn mul_add_r(self, multiplicand: Self, addend: Self, round: Round) -> StatusAnd<Self>;
307 fn mul_add(self, multiplicand: Self, addend: Self) -> StatusAnd<Self> {
308 self.mul_add_r(multiplicand, addend, Round::NearestTiesToEven)
309 }
310 fn div_r(self, rhs: Self, round: Round) -> StatusAnd<Self>;
311 /// IEEE remainder.
312 fn ieee_rem(self, rhs: Self) -> StatusAnd<Self>;
313 /// C fmod, or llvm frem.
314 fn c_fmod(self, rhs: Self) -> StatusAnd<Self>;
315 fn round_to_integral(self, round: Round) -> StatusAnd<Self>;
316
317 /// IEEE-754R 2008 5.3.1: nextUp.
318 fn next_up(self) -> StatusAnd<Self>;
319
320 /// IEEE-754R 2008 5.3.1: nextDown.
321 ///
322 /// *NOTE* since nextDown(x) = -nextUp(-x), we only implement nextUp with
323 /// appropriate sign switching before/after the computation.
324 fn next_down(self) -> StatusAnd<Self> {
325 (-self).next_up().map(|r| -r)
326 }
327
328 fn abs(self) -> Self {
329 if self.is_negative() {
330 -self
331 } else {
332 self
333 }
334 }
335 fn copy_sign(self, rhs: Self) -> Self {
336 if self.is_negative() != rhs.is_negative() {
337 -self
338 } else {
339 self
340 }
341 }
342
343 // Conversions
344 fn from_bits(input: u128) -> Self;
345 fn from_i128_r(input: i128, round: Round) -> StatusAnd<Self> {
346 if input < 0 {
347 Self::from_u128_r(input.wrapping_neg() as u128, -round).map(|r| -r)
348 } else {
349 Self::from_u128_r(input as u128, round)
350 }
351 }
352 fn from_i128(input: i128) -> StatusAnd<Self> {
353 Self::from_i128_r(input, Round::NearestTiesToEven)
354 }
355 fn from_u128_r(input: u128, round: Round) -> StatusAnd<Self>;
356 fn from_u128(input: u128) -> StatusAnd<Self> {
357 Self::from_u128_r(input, Round::NearestTiesToEven)
358 }
359 fn from_str_r(s: &str, round: Round) -> Result<StatusAnd<Self>, ParseError>;
360 fn to_bits(self) -> u128;
361
362 /// Convert a floating point number to an integer according to the
363 /// rounding mode. In case of an invalid operation exception,
364 /// deterministic values are returned, namely zero for NaNs and the
365 /// minimal or maximal value respectively for underflow or overflow.
366 /// If the rounded value is in range but the floating point number is
367 /// not the exact integer, the C standard doesn't require an inexact
368 /// exception to be raised. IEEE-854 does require it so we do that.
369 ///
370 /// Note that for conversions to integer type the C standard requires
371 /// round-to-zero to always be used.
372 ///
373 /// The *is_exact output tells whether the result is exact, in the sense
374 /// that converting it back to the original floating point type produces
375 /// the original value. This is almost equivalent to result==Status::OK,
376 /// except for negative zeroes.
377 fn to_i128_r(self, width: usize, round: Round, is_exact: &mut bool) -> StatusAnd<i128> {
378 let status;
379 if self.is_negative() {
380 if self.is_zero() {
381 // Negative zero can't be represented as an int.
382 *is_exact = false;
383 }
384 let r = unpack!(status=, (-self).to_u128_r(width, -round, is_exact));
385
386 // Check for values that don't fit in the signed integer.
387 if r > (1 << (width - 1)) {
388 // Return the most negative integer for the given width.
389 *is_exact = false;
390 Status::INVALID_OP.and(-1 << (width - 1))
391 } else {
392 status.and(r.wrapping_neg() as i128)
393 }
394 } else {
395 // Positive case is simpler, can pretend it's a smaller unsigned
396 // integer, and `to_u128` will take care of all the edge cases.
397 self.to_u128_r(width - 1, round, is_exact).map(|r| r as i128)
398 }
399 }
400 fn to_i128(self, width: usize) -> StatusAnd<i128> {
401 self.to_i128_r(width, Round::TowardZero, &mut true)
402 }
403 fn to_u128_r(self, width: usize, round: Round, is_exact: &mut bool) -> StatusAnd<u128>;
404 fn to_u128(self, width: usize) -> StatusAnd<u128> {
405 self.to_u128_r(width, Round::TowardZero, &mut true)
406 }
407
408 fn cmp_abs_normal(self, rhs: Self) -> Ordering;
409
410 /// Bitwise comparison for equality (QNaNs compare equal, 0!=-0).
411 fn bitwise_eq(self, rhs: Self) -> bool;
412
413 // IEEE-754R 5.7.2 General operations.
414
415 /// Implements IEEE minNum semantics. Returns the smaller of the 2 arguments if
416 /// both are not NaN. If either argument is a NaN, returns the other argument.
417 fn min(self, other: Self) -> Self {
418 if self.is_nan() {
419 other
420 } else if other.is_nan() {
421 self
422 } else if other < self {
423 other
424 } else {
425 self
426 }
427 }
428
429 /// Implements IEEE maxNum semantics. Returns the larger of the 2 arguments if
430 /// both are not NaN. If either argument is a NaN, returns the other argument.
431 fn max(self, other: Self) -> Self {
432 if self.is_nan() {
433 other
434 } else if other.is_nan() {
435 self
436 } else if self < other {
437 other
438 } else {
439 self
440 }
441 }
442
443 /// Implements IEEE 754-2018 minimum semantics. Returns the smaller of 2
444 /// arguments, propagating NaNs and treating -0 as less than +0.
445 fn minimum(self, other: Self) -> Self {
446 if self.is_nan() {
447 self
448 } else if other.is_nan() {
449 other
450 } else if self.is_zero() && other.is_zero() && self.is_negative() != other.is_negative() {
451 if self.is_negative() {
452 self
453 } else {
454 other
455 }
456 } else if other < self {
457 other
458 } else {
459 self
460 }
461 }
462
463 /// Implements IEEE 754-2018 maximum semantics. Returns the larger of 2
464 /// arguments, propagating NaNs and treating -0 as less than +0.
465 fn maximum(self, other: Self) -> Self {
466 if self.is_nan() {
467 self
468 } else if other.is_nan() {
469 other
470 } else if self.is_zero() && other.is_zero() && self.is_negative() != other.is_negative() {
471 if self.is_negative() {
472 other
473 } else {
474 self
475 }
476 } else if self < other {
477 other
478 } else {
479 self
480 }
481 }
482
483 /// IEEE-754R isSignMinus: Returns true if and only if the current value is
484 /// negative.
485 ///
486 /// This applies to zeros and NaNs as well.
487 fn is_negative(self) -> bool;
488
489 /// IEEE-754R isNormal: Returns true if and only if the current value is normal.
490 ///
491 /// This implies that the current value of the float is not zero, subnormal,
492 /// infinite, or NaN following the definition of normality from IEEE-754R.
493 fn is_normal(self) -> bool {
494 !self.is_denormal() && self.is_finite_non_zero()
495 }
496
497 /// Returns true if and only if the current value is zero, subnormal, or
498 /// normal.
499 ///
500 /// This means that the value is not infinite or NaN.
501 fn is_finite(self) -> bool {
502 !self.is_nan() && !self.is_infinite()
503 }
504
505 /// Returns true if and only if the float is plus or minus zero.
506 fn is_zero(self) -> bool {
507 self.category() == Category::Zero
508 }
509
510 /// IEEE-754R isSubnormal(): Returns true if and only if the float is a
511 /// denormal.
512 fn is_denormal(self) -> bool;
513
514 /// IEEE-754R isInfinite(): Returns true if and only if the float is infinity.
515 fn is_infinite(self) -> bool {
516 self.category() == Category::Infinity
517 }
518
519 /// Returns true if and only if the float is a quiet or signaling NaN.
520 fn is_nan(self) -> bool {
521 self.category() == Category::NaN
522 }
523
524 /// Returns true if and only if the float is a signaling NaN.
525 fn is_signaling(self) -> bool;
526
527 // Simple Queries
528
529 fn category(self) -> Category;
530 fn is_non_zero(self) -> bool {
531 !self.is_zero()
532 }
533 fn is_finite_non_zero(self) -> bool {
534 self.is_finite() && !self.is_zero()
535 }
536 fn is_pos_zero(self) -> bool {
537 self.is_zero() && !self.is_negative()
538 }
539 fn is_neg_zero(self) -> bool {
540 self.is_zero() && self.is_negative()
541 }
542 fn is_pos_infinity(self) -> bool {
543 self.is_infinite() && !self.is_negative()
544 }
545 fn is_neg_infinity(self) -> bool {
546 self.is_infinite() && self.is_negative()
547 }
548
549 /// Returns true if and only if the number has the smallest possible non-zero
550 /// magnitude in the current semantics.
551 fn is_smallest(self) -> bool {
552 Self::SMALLEST.copy_sign(self).bitwise_eq(self)
553 }
554
555 /// Returns true if this is the smallest (by magnitude) normalized finite
556 /// number in the given semantics.
557 fn is_smallest_normalized(self) -> bool {
558 Self::smallest_normalized().copy_sign(self).bitwise_eq(self)
559 }
560
561 /// Returns true if and only if the number has the largest possible finite
562 /// magnitude in the current semantics.
563 fn is_largest(self) -> bool {
564 Self::largest().copy_sign(self).bitwise_eq(self)
565 }
566
567 /// Returns true if and only if the number is an exact integer.
568 fn is_integer(self) -> bool {
569 // This could be made more efficient; I'm going for obviously correct.
570 if !self.is_finite() {
571 return false;
572 }
573 self.round_to_integral(Round::TowardZero).value.bitwise_eq(self)
574 }
575
576 /// If this value has an exact multiplicative inverse, return it.
577 fn get_exact_inverse(self) -> Option<Self>;
578
579 /// Returns the exponent of the internal representation of the Float.
580 ///
581 /// Because the radix of Float is 2, this is equivalent to floor(log2(x)).
582 /// For special Float values, this returns special error codes:
583 ///
584 /// NaN -> \c IEK_NAN
585 /// 0 -> \c IEK_ZERO
586 /// Inf -> \c IEK_INF
587 ///
588 fn ilogb(self) -> ExpInt;
589
590 /// Returns: self * 2^exp for integral exponents.
591 fn scalbn_r(self, exp: ExpInt, round: Round) -> Self;
592 fn scalbn(self, exp: ExpInt) -> Self {
593 self.scalbn_r(exp, Round::NearestTiesToEven)
594 }
595
596 /// Equivalent of C standard library function.
597 ///
598 /// While the C standard says exp is an unspecified value for infinity and nan,
599 /// this returns INT_MAX for infinities, and INT_MIN for NaNs (see `ilogb`).
600 fn frexp_r(self, exp: &mut ExpInt, round: Round) -> Self;
601 fn frexp(self, exp: &mut ExpInt) -> Self {
602 self.frexp_r(exp, Round::NearestTiesToEven)
603 }
604}
605
606/// Convert between floating point types.
607pub trait FloatConvert<T: Float>: Float {
608 /// Convert a value of one floating point type to another.
609 /// The return value corresponds to the IEEE754 exceptions. *loses_info
610 /// records whether the transformation lost information, i.e. whether
611 /// converting the result back to the original type will produce the
612 /// original value (this is almost the same as return value==Status::OK,
613 /// but there are edge cases where this is not so).
614 fn convert_r(self, round: Round, loses_info: &mut bool) -> StatusAnd<T>;
615
616 /// Convert with default [`NearestTiesToEven`](Round::NearestTiesToEven) rounding.
617 fn convert(self, loses_info: &mut bool) -> StatusAnd<T> {
618 self.convert_r(Round::NearestTiesToEven, loses_info)
619 }
620}
621
622macro_rules! float_common_impls {
623 ($ty:ident<$t:tt>) => {
624 impl<$t> Default for $ty<$t>
625 where
626 Self: Float,
627 {
628 #[inline]
629 fn default() -> Self {
630 Self::ZERO
631 }
632 }
633
634 impl<$t> ::core::str::FromStr for $ty<$t>
635 where
636 Self: Float,
637 {
638 type Err = ParseError;
639 #[inline]
640 fn from_str(s: &str) -> Result<Self, ParseError> {
641 Self::from_str_r(s, Round::NearestTiesToEven).map(|x| x.value)
642 }
643 }
644
645 // Rounding ties to the nearest even, by default.
646
647 impl<$t> ::core::ops::Add for $ty<$t>
648 where
649 Self: Float,
650 {
651 type Output = StatusAnd<Self>;
652 #[inline]
653 fn add(self, rhs: Self) -> StatusAnd<Self> {
654 self.add_r(rhs, Round::NearestTiesToEven)
655 }
656 }
657
658 impl<$t> ::core::ops::Sub for $ty<$t>
659 where
660 Self: Float,
661 {
662 type Output = StatusAnd<Self>;
663 #[inline]
664 fn sub(self, rhs: Self) -> StatusAnd<Self> {
665 self.sub_r(rhs, Round::NearestTiesToEven)
666 }
667 }
668
669 impl<$t> ::core::ops::Mul for $ty<$t>
670 where
671 Self: Float,
672 {
673 type Output = StatusAnd<Self>;
674 #[inline]
675 fn mul(self, rhs: Self) -> StatusAnd<Self> {
676 self.mul_r(rhs, Round::NearestTiesToEven)
677 }
678 }
679
680 impl<$t> ::core::ops::Div for $ty<$t>
681 where
682 Self: Float,
683 {
684 type Output = StatusAnd<Self>;
685 #[inline]
686 fn div(self, rhs: Self) -> StatusAnd<Self> {
687 self.div_r(rhs, Round::NearestTiesToEven)
688 }
689 }
690
691 impl<$t> ::core::ops::Rem for $ty<$t>
692 where
693 Self: Float,
694 {
695 type Output = StatusAnd<Self>;
696 #[inline]
697 fn rem(self, rhs: Self) -> StatusAnd<Self> {
698 self.c_fmod(rhs)
699 }
700 }
701
702 impl<$t> ::core::ops::AddAssign for $ty<$t>
703 where
704 Self: Float,
705 {
706 #[inline]
707 fn add_assign(&mut self, rhs: Self) {
708 *self = (*self + rhs).value;
709 }
710 }
711
712 impl<$t> ::core::ops::SubAssign for $ty<$t>
713 where
714 Self: Float,
715 {
716 #[inline]
717 fn sub_assign(&mut self, rhs: Self) {
718 *self = (*self - rhs).value;
719 }
720 }
721
722 impl<$t> ::core::ops::MulAssign for $ty<$t>
723 where
724 Self: Float,
725 {
726 #[inline]
727 fn mul_assign(&mut self, rhs: Self) {
728 *self = (*self * rhs).value;
729 }
730 }
731
732 impl<$t> ::core::ops::DivAssign for $ty<$t>
733 where
734 Self: Float,
735 {
736 #[inline]
737 fn div_assign(&mut self, rhs: Self) {
738 *self = (*self / rhs).value;
739 }
740 }
741
742 impl<$t> ::core::ops::RemAssign for $ty<$t>
743 where
744 Self: Float,
745 {
746 #[inline]
747 fn rem_assign(&mut self, rhs: Self) {
748 *self = (*self % rhs).value;
749 }
750 }
751 };
752}
753
754pub mod ieee;
755pub mod ppc;
756