compiler_builtins\libm\src\math\support/
float_traits.rs

1#![allow(unknown_lints)] // FIXME(msrv) we shouldn't need this
2
3use core::{fmt, mem, ops};
4
5use super::int_traits::{CastFrom, Int, MinInt};
6
7/// Trait for some basic operations on floats
8// #[allow(dead_code)]
9#[allow(dead_code)] // Some constants are only used with tests
10pub trait Float:
11    Copy
12    + fmt::Debug
13    + PartialEq
14    + PartialOrd
15    + ops::AddAssign
16    + ops::MulAssign
17    + ops::Add<Output = Self>
18    + ops::Sub<Output = Self>
19    + ops::Mul<Output = Self>
20    + ops::Div<Output = Self>
21    + ops::Rem<Output = Self>
22    + ops::Neg<Output = Self>
23    + 'static
24{
25    /// A uint of the same width as the float
26    type Int: Int<OtherSign = Self::SignedInt, Unsigned = Self::Int>;
27
28    /// A int of the same width as the float
29    type SignedInt: Int
30        + MinInt<OtherSign = Self::Int, Unsigned = Self::Int>
31        + ops::Neg<Output = Self::SignedInt>;
32
33    const ZERO: Self;
34    const NEG_ZERO: Self;
35    const ONE: Self;
36    const NEG_ONE: Self;
37    const INFINITY: Self;
38    const NEG_INFINITY: Self;
39    const NAN: Self;
40    const NEG_NAN: Self;
41    const MAX: Self;
42    const MIN: Self;
43    const EPSILON: Self;
44    const PI: Self;
45    const NEG_PI: Self;
46    const FRAC_PI_2: Self;
47
48    const MIN_POSITIVE_NORMAL: Self;
49
50    /// The bitwidth of the float type
51    const BITS: u32;
52
53    /// The bitwidth of the significand
54    const SIG_BITS: u32;
55
56    /// The bitwidth of the exponent
57    const EXP_BITS: u32 = Self::BITS - Self::SIG_BITS - 1;
58
59    /// The saturated (maximum bitpattern) value of the exponent, i.e. the infinite
60    /// representation.
61    ///
62    /// This shifted fully right, use `EXP_MASK` for the shifted value.
63    const EXP_SAT: u32 = (1 << Self::EXP_BITS) - 1;
64
65    /// The exponent bias value
66    const EXP_BIAS: u32 = Self::EXP_SAT >> 1;
67
68    /// Maximum unbiased exponent value.
69    const EXP_MAX: i32 = Self::EXP_BIAS as i32;
70
71    /// Minimum *NORMAL* unbiased exponent value.
72    const EXP_MIN: i32 = -(Self::EXP_MAX - 1);
73
74    /// Minimum subnormal exponent value.
75    const EXP_MIN_SUBNORM: i32 = Self::EXP_MIN - Self::SIG_BITS as i32;
76
77    /// A mask for the sign bit
78    const SIGN_MASK: Self::Int;
79
80    /// A mask for the significand
81    const SIG_MASK: Self::Int;
82
83    /// A mask for the exponent
84    const EXP_MASK: Self::Int;
85
86    /// The implicit bit of the float format
87    const IMPLICIT_BIT: Self::Int;
88
89    /// Returns `self` transmuted to `Self::Int`
90    fn to_bits(self) -> Self::Int;
91
92    /// Returns `self` transmuted to `Self::SignedInt`
93    #[allow(dead_code)]
94    fn to_bits_signed(self) -> Self::SignedInt {
95        self.to_bits().signed()
96    }
97
98    /// Check bitwise equality.
99    #[allow(dead_code)]
100    fn biteq(self, rhs: Self) -> bool {
101        self.to_bits() == rhs.to_bits()
102    }
103
104    /// Checks if two floats have the same bit representation. *Except* for NaNs! NaN can be
105    /// represented in multiple different ways.
106    ///
107    /// This method returns `true` if two NaNs are compared. Use [`biteq`](Self::biteq) instead
108    /// if `NaN` should not be treated separately.
109    #[allow(dead_code)]
110    fn eq_repr(self, rhs: Self) -> bool {
111        if self.is_nan() && rhs.is_nan() {
112            true
113        } else {
114            self.biteq(rhs)
115        }
116    }
117
118    /// Returns true if the value is NaN.
119    fn is_nan(self) -> bool;
120
121    /// Returns true if the value is +inf or -inf.
122    fn is_infinite(self) -> bool;
123
124    /// Returns true if the sign is negative. Extracts the sign bit regardless of zero or NaN.
125    fn is_sign_negative(self) -> bool;
126
127    /// Returns true if the sign is positive. Extracts the sign bit regardless of zero or NaN.
128    fn is_sign_positive(self) -> bool {
129        !self.is_sign_negative()
130    }
131
132    /// Returns if `self` is subnormal.
133    #[allow(dead_code)]
134    fn is_subnormal(self) -> bool {
135        (self.to_bits() & Self::EXP_MASK) == Self::Int::ZERO
136    }
137
138    /// Returns the exponent, not adjusting for bias, not accounting for subnormals or zero.
139    fn ex(self) -> u32 {
140        u32::cast_from(self.to_bits() >> Self::SIG_BITS) & Self::EXP_SAT
141    }
142
143    /// Extract the exponent and adjust it for bias, not accounting for subnormals or zero.
144    fn exp_unbiased(self) -> i32 {
145        self.ex().signed() - (Self::EXP_BIAS as i32)
146    }
147
148    /// Returns the significand with no implicit bit (or the "fractional" part)
149    #[allow(dead_code)]
150    fn frac(self) -> Self::Int {
151        self.to_bits() & Self::SIG_MASK
152    }
153
154    /// Returns a `Self::Int` transmuted back to `Self`
155    fn from_bits(a: Self::Int) -> Self;
156
157    /// Constructs a `Self` from its parts. Inputs are treated as bits and shifted into position.
158    fn from_parts(negative: bool, exponent: u32, significand: Self::Int) -> Self {
159        let sign = if negative {
160            Self::Int::ONE
161        } else {
162            Self::Int::ZERO
163        };
164        Self::from_bits(
165            (sign << (Self::BITS - 1))
166                | (Self::Int::cast_from(exponent & Self::EXP_SAT) << Self::SIG_BITS)
167                | (significand & Self::SIG_MASK),
168        )
169    }
170
171    #[allow(dead_code)]
172    fn abs(self) -> Self;
173
174    /// Returns a number composed of the magnitude of self and the sign of sign.
175    fn copysign(self, other: Self) -> Self;
176
177    /// Fused multiply add, rounding once.
178    fn fma(self, y: Self, z: Self) -> Self;
179
180    /// Returns (normalized exponent, normalized significand)
181    #[allow(dead_code)]
182    fn normalize(significand: Self::Int) -> (i32, Self::Int);
183
184    /// Returns a number that represents the sign of self.
185    #[allow(dead_code)]
186    fn signum(self) -> Self {
187        if self.is_nan() {
188            self
189        } else {
190            Self::ONE.copysign(self)
191        }
192    }
193}
194
195/// Access the associated `Int` type from a float (helper to avoid ambiguous associated types).
196pub type IntTy<F> = <F as Float>::Int;
197
198macro_rules! float_impl {
199    (
200        $ty:ident,
201        $ity:ident,
202        $sity:ident,
203        $bits:expr,
204        $significand_bits:expr,
205        $from_bits:path,
206        $to_bits:path,
207        $fma_fn:ident,
208        $fma_intrinsic:ident
209    ) => {
210        impl Float for $ty {
211            type Int = $ity;
212            type SignedInt = $sity;
213
214            const ZERO: Self = 0.0;
215            const NEG_ZERO: Self = -0.0;
216            const ONE: Self = 1.0;
217            const NEG_ONE: Self = -1.0;
218            const INFINITY: Self = Self::INFINITY;
219            const NEG_INFINITY: Self = Self::NEG_INFINITY;
220            const NAN: Self = Self::NAN;
221            // NAN isn't guaranteed to be positive but it usually is. We only use this for
222            // tests.
223            const NEG_NAN: Self = $from_bits($to_bits(Self::NAN) | Self::SIGN_MASK);
224            const MAX: Self = -Self::MIN;
225            // Sign bit set, saturated mantissa, saturated exponent with last bit zeroed
226            const MIN: Self = $from_bits(Self::Int::MAX & !(1 << Self::SIG_BITS));
227            const EPSILON: Self = <$ty>::EPSILON;
228
229            // Exponent is a 1 in the LSB
230            const MIN_POSITIVE_NORMAL: Self = $from_bits(1 << Self::SIG_BITS);
231
232            const PI: Self = core::$ty::consts::PI;
233            const NEG_PI: Self = -Self::PI;
234            const FRAC_PI_2: Self = core::$ty::consts::FRAC_PI_2;
235
236            const BITS: u32 = $bits;
237            const SIG_BITS: u32 = $significand_bits;
238
239            const SIGN_MASK: Self::Int = 1 << (Self::BITS - 1);
240            const SIG_MASK: Self::Int = (1 << Self::SIG_BITS) - 1;
241            const EXP_MASK: Self::Int = !(Self::SIGN_MASK | Self::SIG_MASK);
242            const IMPLICIT_BIT: Self::Int = 1 << Self::SIG_BITS;
243
244            fn to_bits(self) -> Self::Int {
245                self.to_bits()
246            }
247            fn is_nan(self) -> bool {
248                self.is_nan()
249            }
250            fn is_infinite(self) -> bool {
251                self.is_infinite()
252            }
253            fn is_sign_negative(self) -> bool {
254                self.is_sign_negative()
255            }
256            fn from_bits(a: Self::Int) -> Self {
257                Self::from_bits(a)
258            }
259            fn abs(self) -> Self {
260                cfg_if! {
261                    // FIXME(msrv): `abs` is available in `core` starting with 1.85.
262                    if #[cfg(intrinsics_enabled)] {
263                        self.abs()
264                    } else {
265                        super::super::generic::fabs(self)
266                    }
267                }
268            }
269            fn copysign(self, other: Self) -> Self {
270                cfg_if! {
271                    // FIXME(msrv): `copysign` is available in `core` starting with 1.85.
272                    if #[cfg(intrinsics_enabled)] {
273                        self.copysign(other)
274                    } else {
275                        super::super::generic::copysign(self, other)
276                    }
277                }
278            }
279            fn fma(self, y: Self, z: Self) -> Self {
280                cfg_if! {
281                    // fma is not yet available in `core`
282                    if #[cfg(intrinsics_enabled)] {
283                        unsafe{ core::intrinsics::$fma_intrinsic(self, y, z) }
284                    } else {
285                        super::super::$fma_fn(self, y, z)
286                    }
287                }
288            }
289            fn normalize(significand: Self::Int) -> (i32, Self::Int) {
290                let shift = significand.leading_zeros().wrapping_sub(Self::EXP_BITS);
291                (
292                    1i32.wrapping_sub(shift as i32),
293                    significand << shift as Self::Int,
294                )
295            }
296        }
297    };
298}
299
300#[cfg(f16_enabled)]
301float_impl!(
302    f16,
303    u16,
304    i16,
305    16,
306    10,
307    f16::from_bits,
308    f16::to_bits,
309    fmaf16,
310    fmaf16
311);
312float_impl!(
313    f32,
314    u32,
315    i32,
316    32,
317    23,
318    f32_from_bits,
319    f32_to_bits,
320    fmaf,
321    fmaf32
322);
323float_impl!(
324    f64,
325    u64,
326    i64,
327    64,
328    52,
329    f64_from_bits,
330    f64_to_bits,
331    fma,
332    fmaf64
333);
334#[cfg(f128_enabled)]
335float_impl!(
336    f128,
337    u128,
338    i128,
339    128,
340    112,
341    f128::from_bits,
342    f128::to_bits,
343    fmaf128,
344    fmaf128
345);
346
347/* FIXME(msrv): vendor some things that are not const stable at our MSRV */
348
349/// `f32::from_bits`
350#[allow(unnecessary_transmutes)] // lint appears in newer versions of Rust
351pub const fn f32_from_bits(bits: u32) -> f32 {
352    // SAFETY: POD cast with no preconditions
353    unsafe { mem::transmute::<u32, f32>(bits) }
354}
355
356/// `f32::to_bits`
357#[allow(unnecessary_transmutes)] // lint appears in newer versions of Rust
358pub const fn f32_to_bits(x: f32) -> u32 {
359    // SAFETY: POD cast with no preconditions
360    unsafe { mem::transmute::<f32, u32>(x) }
361}
362
363/// `f64::from_bits`
364#[allow(unnecessary_transmutes)] // lint appears in newer versions of Rust
365pub const fn f64_from_bits(bits: u64) -> f64 {
366    // SAFETY: POD cast with no preconditions
367    unsafe { mem::transmute::<u64, f64>(bits) }
368}
369
370/// `f64::to_bits`
371#[allow(unnecessary_transmutes)] // lint appears in newer versions of Rust
372pub const fn f64_to_bits(x: f64) -> u64 {
373    // SAFETY: POD cast with no preconditions
374    unsafe { mem::transmute::<f64, u64>(x) }
375}
376
377/// Trait for floats twice the bit width of another integer.
378pub trait DFloat: Float {
379    /// Float that is half the bit width of the floatthis trait is implemented for.
380    type H: HFloat<D = Self>;
381
382    /// Narrow the float type.
383    fn narrow(self) -> Self::H;
384}
385
386/// Trait for floats half the bit width of another float.
387pub trait HFloat: Float {
388    /// Float that is double the bit width of the float this trait is implemented for.
389    type D: DFloat<H = Self>;
390
391    /// Widen the float type.
392    fn widen(self) -> Self::D;
393}
394
395macro_rules! impl_d_float {
396    ($($X:ident $D:ident),*) => {
397        $(
398            impl DFloat for $D {
399                type H = $X;
400
401                fn narrow(self) -> Self::H {
402                    self as $X
403                }
404            }
405        )*
406    };
407}
408
409macro_rules! impl_h_float {
410    ($($H:ident $X:ident),*) => {
411        $(
412            impl HFloat for $H {
413                type D = $X;
414
415                fn widen(self) -> Self::D {
416                    self as $X
417                }
418            }
419        )*
420    };
421}
422
423impl_d_float!(f32 f64);
424#[cfg(f16_enabled)]
425impl_d_float!(f16 f32);
426#[cfg(f128_enabled)]
427impl_d_float!(f64 f128);
428
429impl_h_float!(f32 f64);
430#[cfg(f16_enabled)]
431impl_h_float!(f16 f32);
432#[cfg(f128_enabled)]
433impl_h_float!(f64 f128);
434
435#[cfg(test)]
436mod tests {
437    use super::*;
438
439    #[test]
440    #[cfg(f16_enabled)]
441    fn check_f16() {
442        // Constants
443        assert_eq!(f16::EXP_SAT, 0b11111);
444        assert_eq!(f16::EXP_BIAS, 15);
445        assert_eq!(f16::EXP_MAX, 15);
446        assert_eq!(f16::EXP_MIN, -14);
447        assert_eq!(f16::EXP_MIN_SUBNORM, -24);
448
449        // `exp_unbiased`
450        assert_eq!(f16::FRAC_PI_2.exp_unbiased(), 0);
451        assert_eq!((1.0f16 / 2.0).exp_unbiased(), -1);
452        assert_eq!(f16::MAX.exp_unbiased(), 15);
453        assert_eq!(f16::MIN.exp_unbiased(), 15);
454        assert_eq!(f16::MIN_POSITIVE.exp_unbiased(), -14);
455        // This is a convenience method and not ldexp, `exp_unbiased` does not return correct
456        // results for zero and subnormals.
457        assert_eq!(f16::ZERO.exp_unbiased(), -15);
458        assert_eq!(f16::from_bits(0x1).exp_unbiased(), -15);
459        assert_eq!(f16::MIN_POSITIVE, f16::MIN_POSITIVE_NORMAL);
460
461        // `from_parts`
462        assert_biteq!(f16::from_parts(true, f16::EXP_BIAS, 0), -1.0f16);
463        assert_biteq!(f16::from_parts(false, 0, 1), f16::from_bits(0x1));
464    }
465
466    #[test]
467    fn check_f32() {
468        // Constants
469        assert_eq!(f32::EXP_SAT, 0b11111111);
470        assert_eq!(f32::EXP_BIAS, 127);
471        assert_eq!(f32::EXP_MAX, 127);
472        assert_eq!(f32::EXP_MIN, -126);
473        assert_eq!(f32::EXP_MIN_SUBNORM, -149);
474
475        // `exp_unbiased`
476        assert_eq!(f32::FRAC_PI_2.exp_unbiased(), 0);
477        assert_eq!((1.0f32 / 2.0).exp_unbiased(), -1);
478        assert_eq!(f32::MAX.exp_unbiased(), 127);
479        assert_eq!(f32::MIN.exp_unbiased(), 127);
480        assert_eq!(f32::MIN_POSITIVE.exp_unbiased(), -126);
481        // This is a convenience method and not ldexp, `exp_unbiased` does not return correct
482        // results for zero and subnormals.
483        assert_eq!(f32::ZERO.exp_unbiased(), -127);
484        assert_eq!(f32::from_bits(0x1).exp_unbiased(), -127);
485        assert_eq!(f32::MIN_POSITIVE, f32::MIN_POSITIVE_NORMAL);
486
487        // `from_parts`
488        assert_biteq!(f32::from_parts(true, f32::EXP_BIAS, 0), -1.0f32);
489        assert_biteq!(
490            f32::from_parts(false, 10 + f32::EXP_BIAS, 0),
491            hf32!("0x1p10")
492        );
493        assert_biteq!(f32::from_parts(false, 0, 1), f32::from_bits(0x1));
494    }
495
496    #[test]
497    fn check_f64() {
498        // Constants
499        assert_eq!(f64::EXP_SAT, 0b11111111111);
500        assert_eq!(f64::EXP_BIAS, 1023);
501        assert_eq!(f64::EXP_MAX, 1023);
502        assert_eq!(f64::EXP_MIN, -1022);
503        assert_eq!(f64::EXP_MIN_SUBNORM, -1074);
504
505        // `exp_unbiased`
506        assert_eq!(f64::FRAC_PI_2.exp_unbiased(), 0);
507        assert_eq!((1.0f64 / 2.0).exp_unbiased(), -1);
508        assert_eq!(f64::MAX.exp_unbiased(), 1023);
509        assert_eq!(f64::MIN.exp_unbiased(), 1023);
510        assert_eq!(f64::MIN_POSITIVE.exp_unbiased(), -1022);
511        // This is a convenience method and not ldexp, `exp_unbiased` does not return correct
512        // results for zero and subnormals.
513        assert_eq!(f64::ZERO.exp_unbiased(), -1023);
514        assert_eq!(f64::from_bits(0x1).exp_unbiased(), -1023);
515        assert_eq!(f64::MIN_POSITIVE, f64::MIN_POSITIVE_NORMAL);
516
517        // `from_parts`
518        assert_biteq!(f64::from_parts(true, f64::EXP_BIAS, 0), -1.0f64);
519        assert_biteq!(
520            f64::from_parts(false, 10 + f64::EXP_BIAS, 0),
521            hf64!("0x1p10")
522        );
523        assert_biteq!(f64::from_parts(false, 0, 1), f64::from_bits(0x1));
524    }
525
526    #[test]
527    #[cfg(f128_enabled)]
528    fn check_f128() {
529        // Constants
530        assert_eq!(f128::EXP_SAT, 0b111111111111111);
531        assert_eq!(f128::EXP_BIAS, 16383);
532        assert_eq!(f128::EXP_MAX, 16383);
533        assert_eq!(f128::EXP_MIN, -16382);
534        assert_eq!(f128::EXP_MIN_SUBNORM, -16494);
535
536        // `exp_unbiased`
537        assert_eq!(f128::FRAC_PI_2.exp_unbiased(), 0);
538        assert_eq!((1.0f128 / 2.0).exp_unbiased(), -1);
539        assert_eq!(f128::MAX.exp_unbiased(), 16383);
540        assert_eq!(f128::MIN.exp_unbiased(), 16383);
541        assert_eq!(f128::MIN_POSITIVE.exp_unbiased(), -16382);
542        // This is a convenience method and not ldexp, `exp_unbiased` does not return correct
543        // results for zero and subnormals.
544        assert_eq!(f128::ZERO.exp_unbiased(), -16383);
545        assert_eq!(f128::from_bits(0x1).exp_unbiased(), -16383);
546        assert_eq!(f128::MIN_POSITIVE, f128::MIN_POSITIVE_NORMAL);
547
548        // `from_parts`
549        assert_biteq!(f128::from_parts(true, f128::EXP_BIAS, 0), -1.0f128);
550        assert_biteq!(f128::from_parts(false, 0, 1), f128::from_bits(0x1));
551    }
552}