font_types/
fixed.rs

1//! fixed-point numerical types
2
3use std::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Sub, SubAssign};
4
5// shared between Fixed, F26Dot6, F2Dot14, F4Dot12, F6Dot10
6macro_rules! fixed_impl {
7    ($name:ident, $bits:literal, $fract_bits:literal, $ty:ty) => {
8        #[derive(Copy, Clone, PartialEq, Eq, PartialOrd, Ord, Hash, Default)]
9        #[cfg_attr(feature = "serde", derive(serde::Serialize, serde::Deserialize))]
10        #[cfg_attr(feature = "bytemuck", derive(bytemuck::AnyBitPattern, bytemuck::NoUninit))]
11        #[repr(transparent)]
12        #[doc = concat!(stringify!($bits), "-bit signed fixed point number with ", stringify!($fract_bits), " bits of fraction." )]
13        pub struct $name($ty);
14        impl $name {
15            /// Minimum value.
16            pub const MIN: Self = Self(<$ty>::MIN);
17
18            /// Maximum value.
19            pub const MAX: Self = Self(<$ty>::MAX);
20
21            /// This type's smallest representable value
22            pub const EPSILON: Self = Self(1);
23
24            /// Representation of 0.0.
25            pub const ZERO: Self = Self(0);
26
27            /// Representation of 1.0.
28            pub const ONE: Self = Self(1 << $fract_bits);
29
30            /// Representation of -1.0.
31            pub const NEG_ONE: Self = Self((!0 << $fract_bits) as $ty);
32
33            const INT_MASK: $ty = !0 << $fract_bits;
34            const ROUND: $ty = 1 << ($fract_bits - 1);
35            const FRACT_BITS: usize = $fract_bits;
36
37            /// Creates a new fixed point value from the underlying bit representation.
38            #[inline(always)]
39            pub const fn from_bits(bits: $ty) -> Self {
40                Self(bits)
41            }
42
43            /// Returns the underlying bit representation of the value.
44            #[inline(always)]
45            pub const fn to_bits(self) -> $ty {
46                self.0
47            }
48
49            //TODO: is this actually useful?
50            /// Returns the nearest integer value.
51            #[inline(always)]
52            pub const fn round(self) -> Self {
53                Self(self.0.wrapping_add(Self::ROUND) & Self::INT_MASK)
54            }
55
56            /// Returns the absolute value of the number.
57            #[inline(always)]
58            pub const fn abs(self) -> Self {
59                Self(self.0.abs())
60            }
61
62            /// Returns the largest integer less than or equal to the number.
63            #[inline(always)]
64            pub const fn floor(self) -> Self {
65                Self(self.0 & Self::INT_MASK)
66            }
67
68            /// Returns the fractional part of the number.
69            #[inline(always)]
70            pub const fn fract(self) -> Self {
71                Self(self.0 - self.floor().0)
72            }
73
74            /// Wrapping addition.
75            #[inline(always)]
76            pub fn wrapping_add(self, other: Self) -> Self {
77                Self(self.0.wrapping_add(other.0))
78            }
79
80            /// Saturating addition.
81            #[inline(always)]
82            pub const fn saturating_add(self, other: Self) -> Self {
83                Self(self.0.saturating_add(other.0))
84            }
85
86            /// Checked addition.
87            #[inline(always)]
88            pub fn checked_add(self, other: Self) -> Option<Self> {
89                self.0.checked_add(other.0).map(|inner| Self(inner))
90            }
91
92            /// Wrapping substitution.
93            #[inline(always)]
94            pub const fn wrapping_sub(self, other: Self) -> Self {
95                Self(self.0.wrapping_sub(other.0))
96            }
97
98            /// Saturating substitution.
99            #[inline(always)]
100            pub const fn saturating_sub(self, other: Self) -> Self {
101                Self(self.0.saturating_sub(other.0))
102            }
103
104            /// The representation of this number as a big-endian byte array.
105            #[inline(always)]
106            pub const fn to_be_bytes(self) -> [u8; $bits / 8] {
107                self.0.to_be_bytes()
108            }
109        }
110
111        impl Add for $name {
112            type Output = Self;
113            #[inline(always)]
114            fn add(self, other: Self) -> Self {
115                Self(self.0.wrapping_add(other.0))
116            }
117        }
118
119        impl AddAssign for $name {
120            #[inline(always)]
121            fn add_assign(&mut self, other: Self) {
122                *self = *self + other;
123            }
124        }
125
126        impl Sub for $name {
127            type Output = Self;
128            #[inline(always)]
129            fn sub(self, other: Self) -> Self {
130                Self(self.0.wrapping_sub(other.0))
131            }
132        }
133
134        impl SubAssign for $name {
135            #[inline(always)]
136            fn sub_assign(&mut self, other: Self) {
137                *self = *self - other;
138            }
139        }
140    };
141}
142
143/// Implements multiplication and division operators for fixed types.
144macro_rules! fixed_mul_div {
145    ($ty:ty) => {
146        impl $ty {
147            /// Multiplies `self` by `a` and divides the product by `b`.
148            // This one is specifically not always inlined due to size and
149            // frequency of use. We leave it to compiler discretion.
150            #[inline]
151            pub const fn mul_div(&self, a: Self, b: Self) -> Self {
152                let mut sign = 1;
153                let mut su = self.0 as u64;
154                let mut au = a.0 as u64;
155                let mut bu = b.0 as u64;
156                if self.0 < 0 {
157                    su = 0u64.wrapping_sub(su);
158                    sign = -1;
159                }
160                if a.0 < 0 {
161                    au = 0u64.wrapping_sub(au);
162                    sign = -sign;
163                }
164                if b.0 < 0 {
165                    bu = 0u64.wrapping_sub(bu);
166                    sign = -sign;
167                }
168                let result = if bu > 0 {
169                    su.wrapping_mul(au).wrapping_add(bu >> 1) / bu
170                } else {
171                    0x7FFFFFFF
172                };
173                Self(if sign < 0 {
174                    (result as i32).wrapping_neg()
175                } else {
176                    result as i32
177                })
178            }
179        }
180
181        impl Mul for $ty {
182            type Output = Self;
183            #[inline(always)]
184            fn mul(self, other: Self) -> Self::Output {
185                let ab = self.0 as i64 * other.0 as i64;
186                Self(((ab + 0x8000 - i64::from(ab < 0)) >> 16) as i32)
187            }
188        }
189
190        impl MulAssign for $ty {
191            #[inline(always)]
192            fn mul_assign(&mut self, rhs: Self) {
193                *self = *self * rhs;
194            }
195        }
196
197        impl Div for $ty {
198            type Output = Self;
199            #[inline(always)]
200            fn div(self, other: Self) -> Self::Output {
201                let mut sign = 1;
202                let mut a = self.0;
203                let mut b = other.0;
204                if a < 0 {
205                    a = -a;
206                    sign = -1;
207                }
208                if b < 0 {
209                    b = -b;
210                    sign = -sign;
211                }
212                let q = if b == 0 {
213                    0x7FFFFFFF
214                } else {
215                    ((((a as u64) << 16) + ((b as u64) >> 1)) / (b as u64)) as u32
216                };
217                Self(if sign < 0 {
218                    (q as i32).wrapping_neg()
219                } else {
220                    q as i32
221                })
222            }
223        }
224
225        impl DivAssign for $ty {
226            #[inline(always)]
227            fn div_assign(&mut self, rhs: Self) {
228                *self = *self / rhs;
229            }
230        }
231
232        impl Neg for $ty {
233            type Output = Self;
234            #[inline(always)]
235            fn neg(self) -> Self {
236                Self(-self.0)
237            }
238        }
239    };
240}
241
242/// impl float conversion methods.
243///
244/// We convert to different float types in order to ensure we can roundtrip
245/// without floating point error.
246macro_rules! float_conv {
247    ($name:ident, $to:ident, $from:ident, $ty:ty) => {
248        impl $name {
249            #[doc = concat!("Creates a fixed point value from a", stringify!($ty), ".")]
250            ///
251            /// This operation is lossy; the float will be rounded to the nearest
252            /// representable value.
253            #[inline(always)]
254            pub fn $from(x: $ty) -> Self {
255                // When x is positive: 1.0 - 0.5 =  0.5
256                // When x is negative: 0.0 - 0.5 = -0.5
257                let frac = (x.is_sign_positive() as u8 as $ty) - 0.5;
258                Self((x * Self::ONE.0 as $ty + frac) as _)
259            }
260
261            #[doc = concat!("Returns the value as an ", stringify!($ty), ".")]
262            ///
263            /// This operation is lossless: all representable values can be
264            /// round-tripped.
265            #[inline(always)]
266            pub fn $to(self) -> $ty {
267                let int = ((self.0 & Self::INT_MASK) >> Self::FRACT_BITS) as $ty;
268                let fract = (self.0 & !Self::INT_MASK) as $ty / Self::ONE.0 as $ty;
269                int + fract
270            }
271        }
272
273        //hack: we can losslessly go to float, so use those fmt impls
274        impl std::fmt::Display for $name {
275            fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
276                self.$to().fmt(f)
277            }
278        }
279
280        impl std::fmt::Debug for $name {
281            fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
282                self.$to().fmt(f)
283            }
284        }
285    };
286}
287
288fixed_impl!(F2Dot14, 16, 14, i16);
289fixed_impl!(F4Dot12, 16, 12, i16);
290fixed_impl!(F6Dot10, 16, 10, i16);
291fixed_impl!(Fixed, 32, 16, i32);
292fixed_impl!(F26Dot6, 32, 6, i32);
293fixed_mul_div!(Fixed);
294fixed_mul_div!(F26Dot6);
295float_conv!(F2Dot14, to_f32, from_f32, f32);
296float_conv!(F4Dot12, to_f32, from_f32, f32);
297float_conv!(F6Dot10, to_f32, from_f32, f32);
298float_conv!(Fixed, to_f64, from_f64, f64);
299float_conv!(F26Dot6, to_f64, from_f64, f64);
300crate::newtype_scalar!(F2Dot14, [u8; 2]);
301crate::newtype_scalar!(F4Dot12, [u8; 2]);
302crate::newtype_scalar!(F6Dot10, [u8; 2]);
303crate::newtype_scalar!(Fixed, [u8; 4]);
304
305impl Fixed {
306    /// Creates a 16.16 fixed point value from a 32 bit integer.
307    #[inline(always)]
308    pub const fn from_i32(i: i32) -> Self {
309        Self(i << 16)
310    }
311
312    /// Converts a 16.16 fixed point value to a 32 bit integer, rounding off
313    /// the fractional bits.
314    #[inline(always)]
315    pub const fn to_i32(self) -> i32 {
316        self.0.wrapping_add(0x8000) >> 16
317    }
318
319    /// Converts a 16.16 to 26.6 fixed point value.
320    #[inline(always)]
321    pub const fn to_f26dot6(self) -> F26Dot6 {
322        F26Dot6(self.0.wrapping_add(0x200) >> 10)
323    }
324
325    /// Converts a 16.16 to 2.14 fixed point value.
326    ///
327    /// This specific conversion is defined by the spec:
328    /// <https://learn.microsoft.com/en-us/typography/opentype/spec/otvaroverview#coordinate-scales-and-normalization>
329    ///
330    /// "5. Convert the final, normalized 16.16 coordinate value to 2.14 by this method: add 0x00000002,
331    /// and sign-extend shift to the right by 2."
332    #[inline(always)]
333    pub const fn to_f2dot14(self) -> F2Dot14 {
334        F2Dot14((self.0.wrapping_add(2) >> 2) as _)
335    }
336
337    /// Converts a 16.16 fixed point value to a single precision floating
338    /// point value.
339    ///
340    /// This operation is lossy. Use `to_f64()` for a lossless conversion.
341    #[inline(always)]
342    pub fn to_f32(self) -> f32 {
343        const SCALE_FACTOR: f32 = 1.0 / 65536.0;
344        self.0 as f32 * SCALE_FACTOR
345    }
346}
347
348impl From<i32> for Fixed {
349    fn from(value: i32) -> Self {
350        Self::from_i32(value)
351    }
352}
353
354impl F26Dot6 {
355    /// Creates a 26.6 fixed point value from a 32 bit integer.
356    #[inline(always)]
357    pub const fn from_i32(i: i32) -> Self {
358        Self(i << 6)
359    }
360
361    /// Converts a 26.6 fixed point value to a 32 bit integer, rounding off
362    /// the fractional bits.
363    #[inline(always)]
364    pub const fn to_i32(self) -> i32 {
365        self.0.wrapping_add(32) >> 6
366    }
367
368    /// Converts a 26.6 fixed point value to a single precision floating
369    /// point value.
370    ///
371    /// This operation is lossy. Use `to_f64()` for a lossless conversion.
372    #[inline(always)]
373    pub fn to_f32(self) -> f32 {
374        const SCALE_FACTOR: f32 = 1.0 / 64.0;
375        self.0 as f32 * SCALE_FACTOR
376    }
377}
378
379impl F2Dot14 {
380    /// Converts a 2.14 to 16.16 fixed point value.
381    #[inline(always)]
382    pub const fn to_fixed(self) -> Fixed {
383        Fixed(self.0 as i32 * 4)
384    }
385}
386
387#[cfg(test)]
388mod tests {
389    #![allow(overflowing_literals)] // we want to specify byte values directly
390    use super::*;
391
392    #[test]
393    fn f2dot14_floats() {
394        // Examples from https://docs.microsoft.com/en-us/typography/opentype/spec/otff#data-types
395        assert_eq!(F2Dot14(0x7fff), F2Dot14::from_f32(1.999939));
396        assert_eq!(F2Dot14(0x7000), F2Dot14::from_f32(1.75));
397        assert_eq!(F2Dot14(0x0001), F2Dot14::from_f32(0.0000610356));
398        assert_eq!(F2Dot14(0x0000), F2Dot14::from_f32(0.0));
399        assert_eq!(F2Dot14(0xffff), F2Dot14::from_f32(-0.000061));
400        assert_eq!(F2Dot14(0x8000), F2Dot14::from_f32(-2.0));
401    }
402
403    #[test]
404    fn roundtrip_f2dot14() {
405        for i in i16::MIN..=i16::MAX {
406            let val = F2Dot14(i);
407            assert_eq!(val, F2Dot14::from_f32(val.to_f32()));
408        }
409    }
410
411    #[test]
412    fn round_f2dot14() {
413        assert_eq!(F2Dot14(0x7000).round(), F2Dot14::from_f32(-2.0));
414        assert_eq!(F2Dot14(0x1F00).round(), F2Dot14::from_f32(0.0));
415        assert_eq!(F2Dot14(0x2000).round(), F2Dot14::from_f32(1.0));
416    }
417
418    #[test]
419    fn round_fixed() {
420        //TODO: make good test cases
421        assert_eq!(Fixed(0x0001_7FFE).round(), Fixed(0x0001_0000));
422        assert_eq!(Fixed(0x0001_7FFF).round(), Fixed(0x0001_0000));
423        assert_eq!(Fixed(0x0001_8000).round(), Fixed(0x0002_0000));
424    }
425
426    // disabled because it's slow; these were just for my edification anyway
427    //#[test]
428    //fn roundtrip_fixed() {
429    //for i in i32::MIN..=i32::MAX {
430    //let val = Fixed(i);
431    //assert_eq!(val, Fixed::from_f64(val.to_f64()));
432    //}
433    //}
434
435    #[test]
436    fn fixed_floats() {
437        assert_eq!(Fixed(0x7fff_0000), Fixed::from_f64(32767.));
438        assert_eq!(Fixed(0x7000_0001), Fixed::from_f64(28672.00001525879));
439        assert_eq!(Fixed(0x0001_0000), Fixed::from_f64(1.0));
440        assert_eq!(Fixed(0x0000_0000), Fixed::from_f64(0.0));
441        assert_eq!(
442            Fixed(i32::from_be_bytes([0xff; 4])),
443            Fixed::from_f64(-0.000015259)
444        );
445        assert_eq!(Fixed(0x7fff_ffff), Fixed::from_f64(32768.0));
446    }
447
448    // We lost the f64::round() intrinsic when dropping std and the
449    // alternative implementation was very slightly incorrect, throwing
450    // off some tests. This makes sure we match.
451    #[test]
452    fn fixed_floats_rounding() {
453        fn with_round_intrinsic(x: f64) -> Fixed {
454            Fixed((x * 65536.0).round() as i32)
455        }
456        // These particular values were tripping up tests
457        let inputs = [0.05, 0.6, 0.2, 0.4, 0.67755];
458        for input in inputs {
459            assert_eq!(Fixed::from_f64(input), with_round_intrinsic(input));
460            // Test negated values as well for good measure
461            assert_eq!(Fixed::from_f64(-input), with_round_intrinsic(-input));
462        }
463    }
464
465    #[test]
466    fn fixed_to_int() {
467        assert_eq!(Fixed::from_f64(1.0).to_i32(), 1);
468        assert_eq!(Fixed::from_f64(1.5).to_i32(), 2);
469        assert_eq!(F26Dot6::from_f64(1.0).to_i32(), 1);
470        assert_eq!(F26Dot6::from_f64(1.5).to_i32(), 2);
471    }
472
473    #[test]
474    fn fixed_from_int() {
475        assert_eq!(Fixed::from_i32(1000).to_bits(), 1000 << 16);
476        assert_eq!(F26Dot6::from_i32(1000).to_bits(), 1000 << 6);
477    }
478
479    #[test]
480    fn fixed_to_f26dot6() {
481        assert_eq!(Fixed::from_f64(42.5).to_f26dot6(), F26Dot6::from_f64(42.5));
482    }
483
484    #[test]
485    fn fixed_muldiv() {
486        assert_eq!(
487            Fixed::from_f64(0.5) * Fixed::from_f64(2.0),
488            Fixed::from_f64(1.0)
489        );
490        assert_eq!(
491            Fixed::from_f64(0.5) / Fixed::from_f64(2.0),
492            Fixed::from_f64(0.25)
493        );
494    }
495
496    // OSS Fuzz caught panic with overflow in fixed point division.
497    // See <https://oss-fuzz.com/testcase-detail/5666843647082496> and
498    // <https://issues.oss-fuzz.com/issues/443104630>
499    #[test]
500    fn fixed_div_neg_overflow() {
501        let a = Fixed::from_f64(-92.5);
502        let b = Fixed::from_f64(0.0028228759765625);
503        // Just don't panic with overflow
504        let _ = a / b;
505    }
506
507    #[test]
508    fn fixed_mul_div_neg_overflow() {
509        let a = Fixed::from_f64(-92.5);
510        let b = Fixed::from_f64(0.0028228759765625);
511        // Just don't panic with overflow
512        let _ = a.mul_div(Fixed::ONE, b);
513    }
514}
font_types/fixed.rs

font_types/
fixed.rs
