Struct fixed::FixedI32[][src]

#[repr(transparent)]
pub struct FixedI32<Frac> { /* fields omitted */ }
Expand description

A 32-bit signed number with Frac fractional bits.

The number has 32 bits, of which f = Frac are fractional bits and 32 − f are integer bits. The value x can lie in the range −231/2f ≤ x < 231/2f. The difference between successive numbers is constant throughout the range: Δ = 1/2f.

For FixedI32<U0>, f = 0 and Δ = 1, and the fixed-point number behaves like an i32 with the value lying in the range −231 ≤ x < 231. For FixedI32<U32>, f = 32 and Δ = 1/232, and the value lies in the range −1/2 ≤ x < 1/2.

Frac is an Unsigned as provided by the typenum crate; the plan is to to have a major version 2 with const generics instead when the Rust compiler support for them is powerful enough.

FixedI32<Frac> has the same size, alignment and ABI as i32; it is #[repr(transparent)] with i32 as the only non-zero-sized field.

Examples

use fixed::{types::extra::U3, FixedI32};
let eleven = FixedI32::<U3>::from_num(11);
assert_eq!(eleven, FixedI32::<U3>::from_bits(11 << 3));
assert_eq!(eleven, 11);
assert_eq!(eleven.to_string(), "11");
let two_point_75 = eleven / 4;
assert_eq!(two_point_75, FixedI32::<U3>::from_bits(11 << 1));
assert_eq!(two_point_75, 2.75);
assert_eq!(two_point_75.to_string(), "2.8");

Implementations

The implementation of items in this block is independent of the number of fractional bits Frac.

Zero.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::ZERO, Fix::from_bits(0));

The difference between any two successive representable numbers, Δ.

If the number has f = Frac fractional bits, then Δ = 1/2f.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::DELTA, Fix::from_bits(1));
// binary 0.0001 is decimal 0.0625
assert_eq!(Fix::DELTA, 0.0625);

The smallest value that can be represented.

If the number has f = Frac fractional bits, then the minimum is −231/2f.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::MIN, Fix::from_bits(i32::MIN));

The largest value that can be represented.

If the number has f = Frac fractional bits, then the maximum is (231 − 1)/2f.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::MAX, Fix::from_bits(i32::MAX));

true because the FixedI32 type is signed.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert!(Fix::IS_SIGNED);

Creates a fixed-point number that has a bitwise representation identical to the given integer.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
// 0010.0000 == 2
assert_eq!(Fix::from_bits(0b10_0000), 2);

Creates an integer that has a bitwise representation identical to the given fixed-point number.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
// 2 is 0010.0000
assert_eq!(Fix::from_num(2).to_bits(), 0b10_0000);

Converts a fixed-point number from big endian to the target’s endianness.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let f = Fix::from_bits(0x1234_5678);
if cfg!(target_endian = "big") {
    assert_eq!(Fix::from_be(f), f);
} else {
    assert_eq!(Fix::from_be(f), f.swap_bytes());
}

Converts a fixed-point number from little endian to the target’s endianness.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let f = Fix::from_bits(0x1234_5678);
if cfg!(target_endian = "little") {
    assert_eq!(Fix::from_le(f), f);
} else {
    assert_eq!(Fix::from_le(f), f.swap_bytes());
}

Converts self to big endian from the target’s endianness.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let f = Fix::from_bits(0x1234_5678);
if cfg!(target_endian = "big") {
    assert_eq!(f.to_be(), f);
} else {
    assert_eq!(f.to_be(), f.swap_bytes());
}

Converts self to little endian from the target’s endianness.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let f = Fix::from_bits(0x1234_5678);
if cfg!(target_endian = "little") {
    assert_eq!(f.to_le(), f);
} else {
    assert_eq!(f.to_le(), f.swap_bytes());
}

Reverses the byte order of the fixed-point number.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let f = Fix::from_bits(0x1234_5678);
let swapped = Fix::from_bits(0x7856_3412);
assert_eq!(f.swap_bytes(), swapped);

Creates a fixed-point number from its representation as a byte array in big endian.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(
    Fix::from_be_bytes([0x12, 0x34, 0x56, 0x78]),
    Fix::from_bits(0x1234_5678)
);

Creates a fixed-point number from its representation as a byte array in little endian.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(
    Fix::from_le_bytes([0x78, 0x56, 0x34, 0x12]),
    Fix::from_bits(0x1234_5678)
);

Creates a fixed-point number from its representation as a byte array in native endian.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(
    if cfg!(target_endian = "big") {
        Fix::from_ne_bytes([0x12, 0x34, 0x56, 0x78])
    } else {
        Fix::from_ne_bytes([0x78, 0x56, 0x34, 0x12])
    },
    Fix::from_bits(0x1234_5678)
);

Returns the memory representation of this fixed-point number as a byte array in big-endian byte order.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let val = Fix::from_bits(0x1234_5678);
assert_eq!(
    val.to_be_bytes(),
    [0x12, 0x34, 0x56, 0x78]
);

Returns the memory representation of this fixed-point number as a byte array in little-endian byte order.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let val = Fix::from_bits(0x1234_5678);
assert_eq!(
    val.to_le_bytes(),
    [0x78, 0x56, 0x34, 0x12]
);

Returns the memory representation of this fixed-point number as a byte array in native byte order.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let val = Fix::from_bits(0x1234_5678);
assert_eq!(
    val.to_ne_bytes(),
    if cfg!(target_endian = "big") {
        [0x12, 0x34, 0x56, 0x78]
    } else {
        [0x78, 0x56, 0x34, 0x12]
    }
);

Returns the number of ones in the binary representation.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let f = Fix::from_bits(0b11_0010);
assert_eq!(f.count_ones(), 3);

Returns the number of zeros in the binary representation.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let f = Fix::from_bits(!0b11_0010);
assert_eq!(f.count_zeros(), 3);

Returns the number of leading ones in the binary representation.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let all_ones = !Fix::ZERO;
let f = all_ones - Fix::from_bits(0b10_0000);
assert_eq!(f.leading_ones(), 32 - 6);

Returns the number of leading zeros in the binary representation.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let f = Fix::from_bits(0b10_0000);
assert_eq!(f.leading_zeros(), 32 - 6);

Returns the number of trailing ones in the binary representation.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let f = Fix::from_bits(0b101_1111);
assert_eq!(f.trailing_ones(), 5);

Returns the number of trailing zeros in the binary representation.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let f = Fix::from_bits(0b10_0000);
assert_eq!(f.trailing_zeros(), 5);

Returns the number of bits required to represent the value.

The number of bits required includes an initial one for negative numbers, and an initial zero for non-negative numbers.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(-3).signed_bits(), 7);      // “_101.0000”
assert_eq!(Fix::from_num(-1).signed_bits(), 5);      // “___1.0000”
assert_eq!(Fix::from_num(-0.0625).signed_bits(), 1); // “____.___1”
assert_eq!(Fix::from_num(0).signed_bits(), 1);       // “____.___0”
assert_eq!(Fix::from_num(0.0625).signed_bits(), 2);  // “____.__01”
assert_eq!(Fix::from_num(1).signed_bits(), 6);       // “__01.0000”
assert_eq!(Fix::from_num(3).signed_bits(), 7);       // “_011.0000”

Reverses the order of the bits of the fixed-point number.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let bits = 0x1234_5678_i32;
let rev_bits = bits.reverse_bits();
assert_eq!(Fix::from_bits(bits).reverse_bits(), Fix::from_bits(rev_bits));

Shifts to the left by n bits, wrapping the truncated bits to the right end.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let bits: i32 = (0b111 << (32 - 3)) | 0b1010;
let rot = 0b1010111;
assert_eq!(bits.rotate_left(3), rot);
assert_eq!(Fix::from_bits(bits).rotate_left(3), Fix::from_bits(rot));

Shifts to the right by n bits, wrapping the truncated bits to the left end.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let bits: i32 = 0b1010111;
let rot = (0b111 << (32 - 3)) | 0b1010;
assert_eq!(bits.rotate_right(3), rot);
assert_eq!(Fix::from_bits(bits).rotate_right(3), Fix::from_bits(rot));

Returns true if the number is zero.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert!(Fix::ZERO.is_zero());
assert!(!Fix::from_num(5).is_zero());

Returns true if the number is > 0.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert!(Fix::from_num(5).is_positive());
assert!(!Fix::ZERO.is_positive());
assert!(!Fix::from_num(-5).is_positive());

Returns true if the number is < 0.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert!(!Fix::from_num(5).is_negative());
assert!(!Fix::ZERO.is_negative());
assert!(Fix::from_num(-5).is_negative());

Multiplies two fixed-point numbers and returns a wider type to retain all precision.

If self has f fractional bits and 32 − f integer bits, and rhs has g fractional bits and 32 − g integer bits, then the returned fixed-point number will have f + g fractional bits and 64 − f − g integer bits.

Examples

use fixed::{
    types::extra::{U2, U4},
    FixedI32,
};
// decimal: 1.25 × 1.0625 = 1.328_125
// binary: 1.01 × 1.0001 == 1.010101
let a = FixedI32::<U2>::from_num(1.25);
let b = FixedI32::<U4>::from_num(1.0625);
assert_eq!(a.wide_mul(b), 1.328_125);

Multiply and add. Returns self × mul + add.

For some cases, the product self × mul would overflow on its own, but the final result self × mul + add is representable; in these cases this method returns the correct result without overflow.

The mul parameter can have a fixed-point type like self but with a different number of fractional bits.

Panics

When debug assertions are enabled, this method panics if the result overflows. When debug assertions are not enabled, the wrapped value can be returned, but it is not considered a breaking change if in the future it panics; if wrapping is required use wrapping_mul_add instead.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(
    Fix::from_num(4).mul_add(Fix::from_num(0.5), Fix::from_num(3)),
    Fix::from_num(5)
);
// MAX × 1.5 − MAX = MAX / 2, which does not overflow
assert_eq!(Fix::MAX.mul_add(Fix::from_num(1.5), -Fix::MAX), Fix::MAX / 2);

Remainder for Euclidean division.

Panics

Panics if the divisor is zero.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(7.5).rem_euclid(Fix::from_num(2)), Fix::from_num(1.5));
assert_eq!(Fix::from_num(-7.5).rem_euclid(Fix::from_num(2)), Fix::from_num(0.5));

Returns the absolute value.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let five = Fix::from_num(5);
let minus_five = Fix::from_num(-5);
assert_eq!(five.abs(), five);
assert_eq!(minus_five.abs(), five);

Returns the absolute value using an unsigned type without any wrapping or panicking.

Examples

use fixed::{types::extra::U4, FixedI32, FixedU32};
type Fix = FixedI32<U4>;
type UFix = FixedU32<U4>;
assert_eq!(Fix::from_num(-5).unsigned_abs(), UFix::from_num(5));
// min_as_unsigned has only highest bit set
let min_as_unsigned = UFix::ONE << (UFix::INT_NBITS - 1);
assert_eq!(Fix::MIN.unsigned_abs(), min_as_unsigned);

Returns the distance from self to other.

The distance is the absolute value of the difference.

Panics

When debug assertions are enabled, this method panics if the result overflows. When debug assertions are not enabled, the wrapped value can be returned, but it is not considered a breaking change if in the future it panics; if wrapping is required use wrapping_dist instead.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::ONE.dist(Fix::from_num(5)), Fix::from_num(4));
assert_eq!(Fix::from_num(-1).dist(Fix::from_num(2)), Fix::from_num(3));

Returns the distance from self to other using an unsigned type without any wrapping or panicking.

The distance is the absolute value of the difference.

Examples

use fixed::{types::extra::U4, FixedI32, FixedU32};
type Fix = FixedI32<U4>;
type UFix = FixedU32<U4>;
assert_eq!(Fix::from_num(-1).unsigned_dist(Fix::from_num(2)), UFix::from_num(3));
assert_eq!(Fix::MIN.unsigned_dist(Fix::MAX), UFix::MAX);

Returns the mean of self and other.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(3).mean(Fix::from_num(4)), Fix::from_num(3.5));
assert_eq!(Fix::from_num(-3).mean(Fix::from_num(4)), Fix::from_num(0.5));

Bitwise NOT. Usable in constant context.

This is equivalent to the ! operator and Not::not, but can also be used in constant context. Unless required in constant context, use the operator or trait instead.

Planned deprecation

This method will be deprecated when the ! operator and the Not trait are usable in constant context.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
const A: Fix = Fix::from_bits(0x3E);
const NOT_A: Fix = A.const_not();
assert_eq!(NOT_A, !A);

Bitwise AND. Usable in constant context.

This is equivalent to the & operator and BitAnd::bitand, but can also be used in constant context. Unless required in constant context, use the operator or trait instead.

Planned deprecation

This method will be deprecated when the & operator and the BitAnd trait are usable in constant context.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
const A: Fix = Fix::from_bits(0x3E);
const B: Fix = Fix::from_bits(0x55);
const A_BITAND_B: Fix = A.const_bitand(B);
assert_eq!(A_BITAND_B, A & B);

Bitwise OR. Usable in constant context.

This is equivalent to the | operator and BitOr::bitor, but can also be used in constant context. Unless required in constant context, use the operator or trait instead.

Planned deprecation

This method will be deprecated when the | operator and the BitOr trait are usable in constant context.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
const A: Fix = Fix::from_bits(0x3E);
const B: Fix = Fix::from_bits(0x55);
const A_BITOR_B: Fix = A.const_bitor(B);
assert_eq!(A_BITOR_B, A | B);

Bitwise XOR. Usable in constant context.

This is equivalent to the ^ operator and BitXor::bitxor, but can also be used in constant context. Unless required in constant context, use the operator or trait instead.

Planned deprecation

This method will be deprecated when the ^ operator and the BitXor trait are usable in constant context.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
const A: Fix = Fix::from_bits(0x3E);
const B: Fix = Fix::from_bits(0x55);
const A_BITXOR_B: Fix = A.const_bitxor(B);
assert_eq!(A_BITXOR_B, A ^ B);

Checked negation. Returns the negated value, or None on overflow.

Overflow can only occur when negating the minimum value.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(5).checked_neg(), Some(Fix::from_num(-5)));
assert_eq!(Fix::MIN.checked_neg(), None);

Checked addition. Returns the sum, or None on overflow.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!((Fix::MAX - Fix::ONE).checked_add(Fix::ONE), Some(Fix::MAX));
assert_eq!(Fix::MAX.checked_add(Fix::ONE), None);

Checked subtraction. Returns the difference, or None on overflow.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!((Fix::MIN + Fix::ONE).checked_sub(Fix::ONE), Some(Fix::MIN));
assert_eq!(Fix::MIN.checked_sub(Fix::ONE), None);

Checked remainder. Returns the remainder, or None if the divisor is zero.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(1.5).checked_rem(Fix::ONE), Some(Fix::from_num(0.5)));
assert_eq!(Fix::from_num(1.5).checked_rem(Fix::ZERO), None);

Checked multiply and add. Returns self × mul + add, or None on overflow.

For some cases, the product self × mul would overflow on its own, but the final result self × mul + add is representable; in these cases this method returns the correct result without overflow.

The mul parameter can have a fixed-point type like self but with a different number of fractional bits.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(
    Fix::from_num(4).checked_mul_add(Fix::from_num(0.5), Fix::from_num(3)),
    Some(Fix::from_num(5))
);
assert_eq!(Fix::MAX.checked_mul_add(Fix::ONE, Fix::ZERO), Some(Fix::MAX));
assert_eq!(Fix::MAX.checked_mul_add(Fix::ONE, Fix::DELTA), None);
// MAX × 1.5 − MAX = MAX / 2, which does not overflow
assert_eq!(Fix::MAX.checked_mul_add(Fix::from_num(1.5), -Fix::MAX), Some(Fix::MAX / 2));

Checked multiplication by an integer. Returns the product, or None on overflow.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::MAX.checked_mul_int(1), Some(Fix::MAX));
assert_eq!(Fix::MAX.checked_mul_int(2), None);

Checked division by an integer. Returns the quotient, or None if the divisor is zero or if the division results in overflow.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::MAX.checked_div_int(1), Some(Fix::MAX));
assert_eq!(Fix::ONE.checked_div_int(0), None);
assert_eq!(Fix::MIN.checked_div_int(-1), None);

Checked remainder for Euclidean division. Returns the remainder, or None if the divisor is zero.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let num = Fix::from_num(7.5);
assert_eq!(num.checked_rem_euclid(Fix::from_num(2)), Some(Fix::from_num(1.5)));
assert_eq!(num.checked_rem_euclid(Fix::ZERO), None);
assert_eq!((-num).checked_rem_euclid(Fix::from_num(2)), Some(Fix::from_num(0.5)));

Checked shift left. Returns the shifted number, or None if rhs ≥ 32.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!((Fix::ONE / 2).checked_shl(3), Some(Fix::from_num(4)));
assert_eq!((Fix::ONE / 2).checked_shl(32), None);

Checked shift right. Returns the shifted number, or None if rhs ≥ 32.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(4).checked_shr(3), Some(Fix::ONE / 2));
assert_eq!(Fix::from_num(4).checked_shr(32), None);

Checked absolute value. Returns the absolute value, or None on overflow.

Overflow can only occur when trying to find the absolute value of the minimum value.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(-5).checked_abs(), Some(Fix::from_num(5)));
assert_eq!(Fix::MIN.checked_abs(), None);

Checked distance. Returns the distance from self to other, or None on overflow.

The distance is the absolute value of the difference.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::ONE.checked_dist(Fix::from_num(5)), Some(Fix::from_num(4)));
assert_eq!(Fix::MIN.checked_dist(Fix::ZERO), None);

Saturating negation. Returns the negated value, saturating on overflow.

Overflow can only occur when negating the minimum value.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(5).saturating_neg(), Fix::from_num(-5));
assert_eq!(Fix::MIN.saturating_neg(), Fix::MAX);

Saturating addition. Returns the sum, saturating on overflow.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(3).saturating_add(Fix::from_num(2)), Fix::from_num(5));
assert_eq!(Fix::MAX.saturating_add(Fix::ONE), Fix::MAX);

Saturating subtraction. Returns the difference, saturating on overflow.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::ONE.saturating_sub(Fix::from_num(3)), Fix::from_num(-2));
assert_eq!(Fix::MIN.saturating_sub(Fix::ONE), Fix::MIN);

Saturating multiply and add. Returns self × mul + add, saturating on overflow.

For some cases, the product self × mul would overflow on its own, but the final result self × mul + add is representable; in these cases this method returns the correct result without overflow.

The mul parameter can have a fixed-point type like self but with a different number of fractional bits.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(
    Fix::from_num(4).saturating_mul_add(Fix::from_num(0.5), Fix::from_num(3)),
    Fix::from_num(5)
);
let half_max = Fix::MAX / 2;
assert_eq!(half_max.saturating_mul_add(Fix::from_num(3), half_max), Fix::MAX);
assert_eq!(half_max.saturating_mul_add(Fix::from_num(-5), half_max), Fix::MIN);
// MAX × 1.5 − MAX = MAX / 2, which does not overflow
assert_eq!(Fix::MAX.saturating_mul_add(Fix::from_num(1.5), -Fix::MAX), half_max);

Saturating multiplication by an integer. Returns the product, saturating on overflow.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(3).saturating_mul_int(2), Fix::from_num(6));
assert_eq!(Fix::MAX.saturating_mul_int(2), Fix::MAX);

Saturating absolute value. Returns the absolute value, saturating on overflow.

Overflow can only occur when trying to find the absolute value of the minimum value.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(-5).saturating_abs(), Fix::from_num(5));
assert_eq!(Fix::MIN.saturating_abs(), Fix::MAX);

Saturating distance. Returns the distance from self to other, saturating on overflow.

The distance is the absolute value of the difference.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::ONE.saturating_dist(Fix::from_num(5)), Fix::from_num(4));
assert_eq!(Fix::MIN.saturating_dist(Fix::MAX), Fix::MAX);

Wrapping negation. Returns the negated value, wrapping on overflow.

Overflow can only occur when negating the minimum value.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(5).wrapping_neg(), Fix::from_num(-5));
assert_eq!(Fix::MIN.wrapping_neg(), Fix::MIN);

Wrapping addition. Returns the sum, wrapping on overflow.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let one_minus_delta = Fix::ONE - Fix::DELTA;
assert_eq!(Fix::from_num(3).wrapping_add(Fix::from_num(2)), Fix::from_num(5));
assert_eq!(Fix::MAX.wrapping_add(Fix::ONE), Fix::MIN + one_minus_delta);

Wrapping subtraction. Returns the difference, wrapping on overflow.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let one_minus_delta = Fix::ONE - Fix::DELTA;
assert_eq!(Fix::from_num(3).wrapping_sub(Fix::from_num(5)), Fix::from_num(-2));
assert_eq!(Fix::MIN.wrapping_sub(Fix::ONE), Fix::MAX - one_minus_delta);

Wrapping multiply and add. Returns self × mul + add, wrapping on overflow.

The mul parameter can have a fixed-point type like self but with a different number of fractional bits.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(
    Fix::from_num(4).wrapping_mul_add(Fix::from_num(0.5), Fix::from_num(3)),
    Fix::from_num(5)
);
assert_eq!(Fix::MAX.wrapping_mul_add(Fix::ONE, Fix::from_num(0)), Fix::MAX);
assert_eq!(Fix::MAX.wrapping_mul_add(Fix::ONE, Fix::from_bits(1)), Fix::MIN);
let wrapped = Fix::MAX.wrapping_mul_int(4);
assert_eq!(Fix::MAX.wrapping_mul_add(Fix::from_num(3), Fix::MAX), wrapped);

Wrapping multiplication by an integer. Returns the product, wrapping on overflow.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(3).wrapping_mul_int(2), Fix::from_num(6));
let wrapped = Fix::from_bits(!0 << 2);
assert_eq!(Fix::MAX.wrapping_mul_int(4), wrapped);

Wrapping division by an integer. Returns the quotient, wrapping on overflow.

Overflow can only occur when dividing the minimum value by −1.

Panics

Panics if the divisor is zero.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
// 1.5 is binary 1.1
let one_point_5 = Fix::from_bits(0b11 << (4 - 1));
assert_eq!(Fix::from_num(3).wrapping_div_int(2), one_point_5);
assert_eq!(Fix::MIN.wrapping_div_int(-1), Fix::MIN);

Wrapping shift left. Wraps rhs if rhs ≥ 32, then shifts and returns the number.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!((Fix::ONE / 2).wrapping_shl(3), Fix::from_num(4));
assert_eq!((Fix::ONE / 2).wrapping_shl(3 + 32), Fix::from_num(4));

Wrapping shift right. Wraps rhs if rhs ≥ 32, then shifts and returns the number.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!((Fix::from_num(4)).wrapping_shr(3), Fix::ONE / 2);
assert_eq!((Fix::from_num(4)).wrapping_shr(3 + 32), Fix::ONE / 2);

Wrapping absolute value. Returns the absolute value, wrapping on overflow.

Overflow can only occur when trying to find the absolute value of the minimum value.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(-5).wrapping_abs(), Fix::from_num(5));
assert_eq!(Fix::MIN.wrapping_abs(), Fix::MIN);

Wrapping distance. Returns the distance from self to other, wrapping on overflow.

The distance is the absolute value of the difference.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::ONE.wrapping_dist(Fix::from_num(5)), Fix::from_num(4));
assert_eq!(Fix::MIN.wrapping_dist(Fix::MAX), -Fix::DELTA);

Unwrapped negation. Returns the negated value, panicking on overflow.

Overflow can only occur when negating the minimum value.

Panics

Panics if the result does not fit.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(5).unwrapped_neg(), Fix::from_num(-5));

The following panics because of overflow.

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let _overflow = Fix::MIN.unwrapped_neg();

Unwrapped addition. Returns the sum, panicking on overflow.

Panics

Panics if the result does not fit.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(3).unwrapped_add(Fix::from_num(2)), Fix::from_num(5));

The following panics because of overflow.

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let _overflow = Fix::MAX.unwrapped_add(Fix::DELTA);

Unwrapped subtraction. Returns the difference, panicking on overflow.

Panics

Panics if the result does not fit.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(3).unwrapped_sub(Fix::from_num(5)), Fix::from_num(-2));

The following panics because of overflow.

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let _overflow = Fix::MIN.unwrapped_sub(Fix::DELTA);

Unwrapped remainder. Returns the remainder, panicking if the divisor is zero.

Panics

Panics if the divisor is zero.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(1.5).unwrapped_rem(Fix::ONE), Fix::from_num(0.5));

The following panics because the divisor is zero.

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let _divisor_is_zero = Fix::from_num(1.5).unwrapped_rem(Fix::ZERO);

Unwrapped multiply and add. Returns self × mul + add, panicking on overflow.

For some cases, the product self × mul would overflow on its own, but the final result self × mul + add is representable; in these cases this method returns the correct result without overflow.

The mul parameter can have a fixed-point type like self but with a different number of fractional bits.

Panics

Panics if the result does not fit.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(
    Fix::from_num(4).unwrapped_mul_add(Fix::from_num(0.5), Fix::from_num(3)),
    Fix::from_num(5)
);
// MAX × 1.5 − MAX = MAX / 2, which does not overflow
assert_eq!(Fix::MAX.unwrapped_mul_add(Fix::from_num(1.5), -Fix::MAX), Fix::MAX / 2);

The following panics because of overflow.

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let _overflow = Fix::MAX.unwrapped_mul_add(Fix::ONE, Fix::DELTA);

Unwrapped multiplication by an integer. Returns the product, panicking on overflow.

Panics

Panics if the result does not fit.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(3).unwrapped_mul_int(2), Fix::from_num(6));

The following panics because of overflow.

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let _overflow = Fix::MAX.unwrapped_mul_int(4);

Unwrapped division by an integer. Returns the quotient, panicking on overflow.

Overflow can only occur when dividing the minimum value by −1.

Panics

Panics if the divisor is zero or if the division results in overflow.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
// 1.5 is binary 1.1
let one_point_5 = Fix::from_bits(0b11 << (4 - 1));
assert_eq!(Fix::from_num(3).unwrapped_div_int(2), one_point_5);

The following panics because the divisor is zero.

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let _divisor_is_zero = Fix::from_num(3).unwrapped_div_int(0);

The following panics because of overflow.

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let _overflow = Fix::MIN.unwrapped_div_int(-1);

Unwrapped remainder for Euclidean division. Returns the remainder, panicking if the divisor is zero.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let num = Fix::from_num(7.5);
assert_eq!(num.unwrapped_rem_euclid(Fix::from_num(2)), Fix::from_num(1.5));

The following panics because the divisor is zero.

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let _divisor_is_zero = Fix::from_num(3).unwrapped_rem_euclid(Fix::ZERO);

Unwrapped shift left. Panics if rhs ≥ 32.

Panics

Panics if rhs ≥ 32.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!((Fix::ONE / 2).unwrapped_shl(3), Fix::from_num(4));

The following panics because of overflow.

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let _overflow = Fix::ONE.unwrapped_shl(32);

Unwrapped shift right. Panics if rhs ≥ 32.

Panics

Panics if rhs ≥ 32.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!((Fix::from_num(4)).unwrapped_shr(3), Fix::ONE / 2);

The following panics because of overflow.

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let _overflow = Fix::ONE.unwrapped_shr(32);

Unwrapped absolute value. Returns the absolute value, panicking on overflow.

Overflow can only occur when trying to find the absolute value of the minimum value.

Panics

Panics if the result does not fit.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(-5).unwrapped_abs(), Fix::from_num(5));

The following panics because of overflow.

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let _overflow = Fix::MIN.unwrapped_abs();

Unwrapped distance. Returns the distance from self to other, panicking on overflow.

The distance is the absolute value of the difference.

Panics

Panics if the result does not fit.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::ONE.unwrapped_dist(Fix::from_num(5)), Fix::from_num(4));

The following panics because of overflow.

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let _overflow = Fix::MIN.unwrapped_dist(Fix::ZERO);

Overflowing negation.

Returns a tuple of the negated value and a bool indicating whether an overflow has occurred. On overflow, the wrapped value is returned.

Overflow can only occur when negating the minimum value.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(5).overflowing_neg(), (Fix::from_num(-5), false));
assert_eq!(Fix::MIN.overflowing_neg(), (Fix::MIN, true));

Overflowing addition.

Returns a tuple of the sum and a bool indicating whether an overflow has occurred. On overflow, the wrapped value is returned.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let one_minus_delta = Fix::ONE - Fix::DELTA;
assert_eq!(Fix::from_num(3).overflowing_add(Fix::from_num(2)), (Fix::from_num(5), false));
assert_eq!(Fix::MAX.overflowing_add(Fix::ONE), (Fix::MIN + one_minus_delta, true));

Overflowing subtraction.

Returns a tuple of the difference and a bool indicating whether an overflow has occurred. On overflow, the wrapped value is returned.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let one_minus_delta = Fix::ONE - Fix::DELTA;
assert_eq!(Fix::from_num(3).overflowing_sub(Fix::from_num(5)), (Fix::from_num(-2), false));
assert_eq!(Fix::MIN.overflowing_sub(Fix::ONE), (Fix::MAX - one_minus_delta, true));

Overflowing multiply and add.

Returns a tuple of self × mul + add and a bool indicating whether an overflow has occurred. On overflow, the wrapped value is returned.

For some cases, the product self × mul would overflow on its own, but the final result self × mul + add is representable; in these cases this method returns the correct result without overflow.

The mul parameter can have a fixed-point type like self but with a different number of fractional bits.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(
    Fix::MAX.overflowing_mul_add(Fix::ONE, Fix::ZERO),
    (Fix::MAX, false)
);
assert_eq!(
    Fix::MAX.overflowing_mul_add(Fix::ONE, Fix::DELTA),
    (Fix::MIN, true)
);
assert_eq!(
    Fix::MAX.overflowing_mul_add(Fix::from_num(3), Fix::MAX),
    Fix::MAX.overflowing_mul_int(4)
);
// MAX × 1.5 − MAX = MAX / 2, which does not overflow
assert_eq!(
    Fix::MAX.overflowing_mul_add(Fix::from_num(1.5), -Fix::MAX),
    (Fix::MAX / 2, false)
);

Overflowing multiplication by an integer.

Returns a tuple of the product and a bool indicating whether an overflow has occurred. On overflow, the wrapped value is returned.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(3).overflowing_mul_int(2), (Fix::from_num(6), false));
let wrapped = Fix::from_bits(!0 << 2);
assert_eq!(Fix::MAX.overflowing_mul_int(4), (wrapped, true));

Overflowing division by an integer.

Returns a tuple of the quotient and a bool indicating whether an overflow has occurred. On overflow, the wrapped value is returned. Overflow can only occur when dividing the minimum value by −1.

Panics

Panics if the divisor is zero.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
// 1.5 is binary 1.1
let one_point_5 = Fix::from_bits(0b11 << (4 - 1));
assert_eq!(Fix::from_num(3).overflowing_div_int(2), (one_point_5, false));
assert_eq!(Fix::MIN.overflowing_div_int(-1), (Fix::MIN, true));

Overflowing shift left.

Returns a tuple of the shifted value and a bool indicating whether an overflow has occurred. Overflow occurs when rhs ≥ 32. On overflow rhs is wrapped before the shift operation.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!((Fix::ONE / 2).overflowing_shl(3), (Fix::from_num(4), false));
assert_eq!((Fix::ONE / 2).overflowing_shl(3 + 32), (Fix::from_num(4), true));

Overflowing shift right.

Returns a tuple of the shifted value and a bool indicating whether an overflow has occurred. Overflow occurs when rhs ≥ 32. On overflow rhs is wrapped before the shift operation.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!((Fix::from_num(4)).overflowing_shr(3), (Fix::ONE / 2, false));
assert_eq!((Fix::from_num(4)).overflowing_shr(3 + 32), (Fix::ONE / 2, true));

Overflowing absolute value.

Returns a tuple of the absolute value and a bool indicating whether an overflow has occurred. On overflow, the wrapped value is returned.

Overflow can only occur when trying to find the absolute value of the minimum value.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(-5).overflowing_abs(), (Fix::from_num(5), false));
assert_eq!(Fix::MIN.overflowing_abs(), (Fix::MIN, true));

Overflowing distance.

Returns a tuple of the distance from self to other and a bool indicating whether an overflow has occurred. On overflow, the wrapped value is returned.

The distance is the absolute value of the difference.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(
    Fix::ONE.overflowing_dist(Fix::from_num(5)),
    (Fix::from_num(4), false)
);
assert_eq!(
    Fix::MIN.overflowing_dist(Fix::MAX),
    (-Fix::DELTA, true)
);

The implementation of items in this block depends on the number of fractional bits Frac.

The number of integer bits.

Examples

use fixed::{types::extra::U6, FixedI32};
type Fix = FixedI32<U6>;
assert_eq!(Fix::INT_NBITS, 32 - 6);

The number of fractional bits.

Examples

use fixed::{types::extra::U6, FixedI32};
type Fix = FixedI32<U6>;
assert_eq!(Fix::FRAC_NBITS, 6);

Creates a fixed-point number from another number.

The other number can be:

  • Another fixed-point number. Any extra fractional bits are discarded, which rounds towards −∞.
  • An integer of type i8, i16, i32, i64, i128, isize, u8, u16, u32, u64, u128, or usize.
  • A floating-point number of type f16, bf16, f32, f64 or F128Bits. For this conversion, the method rounds to the nearest, with ties rounding to even.
  • Any other number src for which ToFixed is implemented, in which case this method returns src.to_fixed().

Panics

For floating-point numbers, panics if the value is not finite.

When debug assertions are enabled, panics if the value does not fit. When debug assertions are not enabled, the wrapped value can be returned, but it is not considered a breaking change if in the future it panics; if wrapping is required use wrapping_from_num instead.

Examples

use fixed::{types::extra::U4, types::I16F16, FixedI32};
type Fix = FixedI32<U4>;

// 1.75 is 1.11 in binary
let src = I16F16::from_bits(0b111 << (16 - 2));
assert_eq!(Fix::from_num(src), Fix::from_bits(0b111 << (4 - 2)));

assert_eq!(Fix::from_num(3i32), Fix::from_bits(3 << 4));
assert_eq!(Fix::from_num(-3i64), Fix::from_bits(-3 << 4));

assert_eq!(Fix::from_num(1.75f32), Fix::from_bits(0b111 << (4 - 2)));
assert_eq!(Fix::from_num(-1.75f64), Fix::from_bits(-0b111 << (4-2)));

Converts a fixed-point number to another number.

The other number can be:

  • Another fixed-point number. Any extra fractional bits are discarded, which rounds towards −∞.
  • An integer of type i8, i16, i32, i64, i128, isize, u8, u16, u32, u64, u128, or usize. Any fractional bits are discarded, which rounds towards −∞.
  • A floating-point number of type f16, bf16, f32, f64 or F128Bits. For this conversion, the method rounds to the nearest, with ties rounding to even.
  • Any other type Dst for which FromFixed is implemented, in which case this method returns Dst::from_fixed(self).

Panics

When debug assertions are enabled, panics if the value does not fit. When debug assertions are not enabled, the wrapped value can be returned, but it is not considered a breaking change if in the future it panics; if wrapping is required use wrapping_to_num instead.

Examples

use fixed::{types::extra::U4, types::I30F2, FixedI32};
type Fix = FixedI32<U4>;

// 1.75 is 1.11 in binary
let src = Fix::from_bits(0b111 << (4 - 2));
assert_eq!(src.to_num::<I30F2>(), I30F2::from_bits(0b111));
// src >> 2 is 0.0111, which for I30F2 is truncated to 0.01
assert_eq!((src >> 2u32).to_num::<I30F2>(), I30F2::from_bits(0b1));

// 2.5 is 10.1 in binary
let two_point_5 = Fix::from_bits(0b101 << (4 - 1));
assert_eq!(two_point_5.to_num::<i32>(), 2);
assert_eq!((-two_point_5).to_num::<i64>(), -3);

// 1.625 is 1.101 in binary
let one_point_625 = Fix::from_bits(0b1101 << (4 - 3));
assert_eq!(one_point_625.to_num::<f32>(), 1.625f32);
assert_eq!((-one_point_625).to_num::<f64>(), -1.625f64);

Creates a fixed-point number from another number if it fits, otherwise returns None.

The other number can be:

  • Another fixed-point number. Any extra fractional bits are discarded, which rounds towards −∞.
  • An integer of type i8, i16, i32, i64, i128, isize, u8, u16, u32, u64, u128, or usize.
  • A floating-point number of type f16, bf16, f32, f64 or F128Bits. For this conversion, the method rounds to the nearest, with ties rounding to even.
  • Any other number src for which ToFixed is implemented, in which case this method returns src.checked_to_fixed().

Examples

use fixed::{
    types::extra::{U2, U4},
    types::I16F16,
    FixedI32,
};
type Fix = FixedI32<U4>;

// 1.75 is 1.11 in binary
let src = I16F16::from_bits(0b111 << (16 - 2));
assert_eq!(Fix::checked_from_num(src), Some(Fix::from_bits(0b111 << (4 - 2))));
let too_large = FixedI32::<U2>::MAX;
assert!(Fix::checked_from_num(too_large).is_none());

assert_eq!(Fix::checked_from_num(3), Some(Fix::from_bits(3 << 4)));
let too_large = i32::MAX;
assert!(Fix::checked_from_num(too_large).is_none());
let too_small = i32::MIN;
assert!(Fix::checked_from_num(too_small).is_none());

// 1.75 is 1.11 in binary
let expected = Fix::from_bits(0b111 << (4 - 2));
assert_eq!(Fix::checked_from_num(1.75f32), Some(expected));
assert_eq!(Fix::checked_from_num(-1.75f64), Some(-expected));
assert!(Fix::checked_from_num(2e38).is_none());
assert!(Fix::checked_from_num(std::f64::NAN).is_none());

Converts a fixed-point number to another number if it fits, otherwise returns None.

The other number can be:

  • Another fixed-point number. Any extra fractional bits are discarded, which rounds towards −∞.
  • An integer of type i8, i16, i32, i64, i128, isize, u8, u16, u32, u64, u128, or usize. Any fractional bits are discarded, which rounds towards −∞.
  • A floating-point number of type f16, bf16, f32, f64 or F128Bits. For this conversion, the method rounds to the nearest, with ties rounding to even.
  • Any other type Dst for which FromFixed is implemented, in which case this method returns Dst::checked_from_fixed(self).

Examples

use fixed::{
    types::extra::{U0, U4, U6},
    types::I16F16,
    FixedI32,
};
type Fix = FixedI32<U4>;

// 1.75 is 1.11 in binary
let src = Fix::from_bits(0b111 << (4 - 2));
let expected = I16F16::from_bits(0b111 << (16 - 2));
assert_eq!(src.checked_to_num::<I16F16>(), Some(expected));
type TooFewIntBits = FixedI32<U6>;
assert!(Fix::MAX.checked_to_num::<TooFewIntBits>().is_none());

// 2.5 is 10.1 in binary
let two_point_5 = Fix::from_bits(0b101 << (4 - 1));
assert_eq!(two_point_5.checked_to_num::<i32>(), Some(2));
assert_eq!((-two_point_5).checked_to_num::<i64>(), Some(-3));
type AllInt = FixedI32<U0>;
assert!(AllInt::from_bits(-1).checked_to_num::<u32>().is_none());

// 1.625 is 1.101 in binary
let one_point_625 = Fix::from_bits(0b1101 << (4 - 3));
assert_eq!(one_point_625.checked_to_num::<f32>(), Some(1.625f32));

Creates a fixed-point number from another number, saturating if it does not fit.

The other number can be:

  • Another fixed-point number. Any extra fractional bits are discarded, which rounds towards −∞.
  • An integer of type i8, i16, i32, i64, i128, isize, u8, u16, u32, u64, u128, or usize.
  • A floating-point number of type f16, bf16, f32, f64 or F128Bits. For this conversion, the method rounds to the nearest, with ties rounding to even.
  • Any other number src for which ToFixed is implemented, in which case this method returns src.saturating_to_fixed().

Panics

This method panics if the value is a floating-point NaN.

Examples

use fixed::{
    types::extra::{U2, U4},
    types::I16F16,
    FixedI32,
};
type Fix = FixedI32<U4>;

// 1.75 is 1.11 in binary
let src = I16F16::from_bits(0b111 << (16 - 2));
assert_eq!(Fix::saturating_from_num(src), Fix::from_bits(0b111 << (4 - 2)));
let too_large = FixedI32::<U2>::MAX;
assert_eq!(Fix::saturating_from_num(too_large), Fix::MAX);

assert_eq!(Fix::saturating_from_num(3), Fix::from_bits(3 << 4));
let too_small = i32::MIN;
assert_eq!(Fix::saturating_from_num(too_small), Fix::MIN);

// 1.75 is 1.11 in binary
let expected = Fix::from_bits(0b111 << (4 - 2));
assert_eq!(Fix::saturating_from_num(1.75f32), expected);
assert_eq!(Fix::saturating_from_num(-1.75f64), -expected);
assert_eq!(Fix::saturating_from_num(2e38), Fix::MAX);
assert_eq!(Fix::saturating_from_num(std::f64::NEG_INFINITY), Fix::MIN);

Converts a fixed-point number to another number, saturating the value if it does not fit.

The other number can be:

  • Another fixed-point number. Any extra fractional bits are discarded, which rounds towards −∞.
  • An integer of type i8, i16, i32, i64, i128, isize, u8, u16, u32, u64, u128, or usize. Any fractional bits are discarded, which rounds towards −∞.
  • A floating-point number of type f16, bf16, f32, f64 or F128Bits. For this conversion, the method rounds to the nearest, with ties rounding to even.
  • Any other type Dst for which FromFixed is implemented, in which case this method returns Dst::saturating_from_fixed(self).

Examples

use fixed::{
    types::extra::{U0, U4, U6},
    types::I16F16,
    FixedI32,
};
type Fix = FixedI32<U4>;

// 1.75 is 1.11 in binary
let src = Fix::from_bits(0b111 << (4 - 2));
let expected = I16F16::from_bits(0b111 << (16 - 2));
assert_eq!(src.saturating_to_num::<I16F16>(), expected);
type TooFewIntBits = FixedI32<U6>;
let saturated = Fix::MAX.saturating_to_num::<TooFewIntBits>();
assert_eq!(saturated, TooFewIntBits::MAX);

// 2.5 is 10.1 in binary
let two_point_5 = Fix::from_bits(0b101 << (4 - 1));
assert_eq!(two_point_5.saturating_to_num::<i32>(), 2);
type AllInt = FixedI32<U0>;
assert_eq!(AllInt::from_bits(-1).saturating_to_num::<u32>(), 0);

// 1.625 is 1.101 in binary
let one_point_625 = Fix::from_bits(0b1101 << (4 - 3));
assert_eq!(one_point_625.saturating_to_num::<f32>(), 1.625f32);

Creates a fixed-point number from another number, wrapping the value on overflow.

The other number can be:

  • Another fixed-point number. Any extra fractional bits are discarded, which rounds towards −∞.
  • An integer of type i8, i16, i32, i64, i128, isize, u8, u16, u32, u64, u128, or usize.
  • A floating-point number of type f16, bf16, f32, f64 or F128Bits. For this conversion, the method rounds to the nearest, with ties rounding to even.
  • Any other number src for which ToFixed is implemented, in which case this method returns src.wrapping_to_fixed().

Panics

For floating-point numbers, panics if the value is not finite.

Examples

use fixed::{
    types::extra::{U0, U4},
    types::I16F16,
    FixedI32,
};
type Fix = FixedI32<U4>;

// 1.75 is 1.11 in binary
let src = I16F16::from_bits(0b111 << (16 - 2));
assert_eq!(Fix::wrapping_from_num(src), Fix::from_bits(0b111 << (4 - 2)));
// integer 0b1101 << (32 - 7) will wrap to fixed-point 1010...
let too_large = FixedI32::<U0>::from_bits(0b1101 << (32 - 7));
let wrapped = Fix::from_bits(0b1010 << (32 - 4));
assert_eq!(Fix::wrapping_from_num(too_large), wrapped);

// integer 0b1101 << (32 - 7) will wrap to fixed-point 1010...
let large: i32 = 0b1101 << (32 - 7);
let wrapped = Fix::from_bits(0b1010 << (32 - 4));
assert_eq!(Fix::wrapping_from_num(large), wrapped);

// 1.75 is 1.11 in binary
let expected = Fix::from_bits(0b111 << (4 - 2));
assert_eq!(Fix::wrapping_from_num(1.75f32), expected);
// 1.75 << (32 - 4) wraps to binary 11000...
let large = 1.75 * 2f32.powi(32 - 4);
let wrapped = Fix::from_bits(0b1100 << (32 - 4));
assert_eq!(Fix::wrapping_from_num(large), wrapped);

Converts a fixed-point number to another number, wrapping the value on overflow.

The other number can be:

  • Another fixed-point number. Any extra fractional bits are discarded, which rounds towards −∞.
  • An integer of type i8, i16, i32, i64, i128, isize, u8, u16, u32, u64, u128, or usize. Any fractional bits are discarded, which rounds towards −∞.
  • A floating-point number of type f16, bf16, f32, f64 or F128Bits. For this conversion, the method rounds to the nearest, with ties rounding to even.
  • Any other type Dst for which FromFixed is implemented, in which case this method returns Dst::wrapping_from_fixed(self).

Examples

use fixed::{
    types::extra::{U0, U4, U6},
    types::I16F16,
    FixedI32,
};
type Fix = FixedI32<U4>;

// 1.75 is 1.11 in binary
let src = Fix::from_bits(0b111 << (4 - 2));
let expected = I16F16::from_bits(0b111 << (16 - 2));
assert_eq!(src.wrapping_to_num::<I16F16>(), expected);
type TooFewIntBits = FixedI32<U6>;
let wrapped = TooFewIntBits::from_bits(Fix::MAX.to_bits() << 2);
assert_eq!(Fix::MAX.wrapping_to_num::<TooFewIntBits>(), wrapped);

// 2.5 is 10.1 in binary
let two_point_5 = Fix::from_bits(0b101 << (4 - 1));
assert_eq!(two_point_5.wrapping_to_num::<i32>(), 2);
type AllInt = FixedI32<U0>;
assert_eq!(AllInt::from_bits(-1).wrapping_to_num::<u32>(), u32::MAX);

// 1.625 is 1.101 in binary
let one_point_625 = Fix::from_bits(0b1101 << (4 - 3));
assert_eq!(one_point_625.wrapping_to_num::<f32>(), 1.625f32);

Creates a fixed-point number from another number, panicking on overflow.

The other number can be:

  • Another fixed-point number. Any extra fractional bits are discarded, which rounds towards −∞.
  • An integer of type i8, i16, i32, i64, i128, isize, u8, u16, u32, u64, u128, or usize.
  • A floating-point number of type f16, bf16, f32, f64 or F128Bits. For this conversion, the method rounds to the nearest, with ties rounding to even.
  • Any other number src for which ToFixed is implemented, in which case this method returns src.unwrapped_to_fixed().

Panics

Panics if the value does not fit.

For floating-point numbers, also panics if the value is not finite.

Examples

use fixed::{
    types::{extra::U4, I16F16},
    FixedI32,
};
type Fix = FixedI32<U4>;

// 1.75 is 1.11 in binary
let src = I16F16::from_bits(0b111 << (16 - 2));
assert_eq!(Fix::unwrapped_from_num(src), Fix::from_bits(0b111 << (4 - 2)));

The following panics because of overflow.

use fixed::{
    types::extra::{U0, U4},
    FixedI32,
};
type Fix = FixedI32<U4>;
let too_large = FixedI32::<U0>::from_bits(0b1101 << (32 - 7));
let _overflow = Fix::unwrapped_from_num(too_large);

Converts a fixed-point number to another number, panicking on overflow.

The other number can be:

  • Another fixed-point number. Any extra fractional bits are discarded, which rounds towards −∞.
  • An integer of type i8, i16, i32, i64, i128, isize, u8, u16, u32, u64, u128, or usize. Any fractional bits are discarded, which rounds towards −∞.
  • A floating-point number of type f16, bf16, f32, f64 or F128Bits. For this conversion, the method rounds to the nearest, with ties rounding to even.
  • Any other type Dst for which FromFixed is implemented, in which case this method returns Dst::unwrapped_from_fixed(self).

Panics

Panics if the value does not fit.

Examples

use fixed::{
    types::{extra::U4, I16F16},
    FixedI32,
};
type Fix = FixedI32<U4>;

// 1.75 is 1.11 in binary
let src = Fix::from_bits(0b111 << (4 - 2));
let expected = I16F16::from_bits(0b111 << (16 - 2));
assert_eq!(src.unwrapped_to_num::<I16F16>(), expected);

The following panics because of overflow.

use fixed::{
    types::extra::{U4, U6},
    FixedI32,
};
type Fix = FixedI32<U4>;
type TooFewIntBits = FixedI32<U6>;
let _overflow = Fix::MAX.unwrapped_to_num::<TooFewIntBits>();

Creates a fixed-point number from another number.

Returns a tuple of the fixed-point number and a bool indicating whether an overflow has occurred. On overflow, the wrapped value is returned.

The other number can be:

  • Another fixed-point number. Any extra fractional bits are discarded, which rounds towards −∞.
  • An integer of type i8, i16, i32, i64, i128, isize, u8, u16, u32, u64, u128, or usize.
  • A floating-point number of type f16, bf16, f32, f64 or F128Bits. For this conversion, the method rounds to the nearest, with ties rounding to even.
  • Any other number src for which ToFixed is implemented, in which case this method returns src.overflowing_to_fixed().

Panics

For floating-point numbers, panics if the value is not finite.

Examples

use fixed::{
    types::extra::{U0, U4},
    types::I16F16,
    FixedI32,
};
type Fix = FixedI32<U4>;

// 1.75 is 1.11 in binary
let src = I16F16::from_bits(0b111 << (16 - 2));
let expected = Fix::from_bits(0b111 << (4 - 2));
assert_eq!(Fix::overflowing_from_num(src), (expected, false));
// integer 0b1101 << (32 - 7) will wrap to fixed-point 1010...
let too_large = FixedI32::<U0>::from_bits(0b1101 << (32 - 7));
let wrapped = Fix::from_bits(0b1010 << (32 - 4));
assert_eq!(Fix::overflowing_from_num(too_large), (wrapped, true));

assert_eq!(Fix::overflowing_from_num(3), (Fix::from_bits(3 << 4), false));
// integer 0b1101 << (32 - 7) will wrap to fixed-point 1010...
let large: i32 = 0b1101 << (32 - 7);
let wrapped = Fix::from_bits(0b1010 << (32 - 4));
assert_eq!(Fix::overflowing_from_num(large), (wrapped, true));

// 1.75 is 1.11 in binary
let expected = Fix::from_bits(0b111 << (4 - 2));
assert_eq!(Fix::overflowing_from_num(1.75f32), (expected, false));
// 1.75 << (32 - 4) wraps to binary 11000...
let large = 1.75 * 2f32.powi(32 - 4);
let wrapped = Fix::from_bits(0b1100 << (32 - 4));
assert_eq!(Fix::overflowing_from_num(large), (wrapped, true));

Converts a fixed-point number to another number.

Returns a tuple of the number and a bool indicating whether an overflow has occurred. On overflow, the wrapped value is returned.

The other number can be:

  • Another fixed-point number. Any extra fractional bits are discarded, which rounds towards −∞.
  • An integer of type i8, i16, i32, i64, i128, isize, u8, u16, u32, u64, u128, or usize. Any fractional bits are discarded, which rounds towards −∞.
  • A floating-point number of type f16, bf16, f32, f64 or F128Bits. For this conversion, the method rounds to the nearest, with ties rounding to even.
  • Any other type Dst for which FromFixed is implemented, in which case this method returns Dst::overflowing_from_fixed(self).

Examples

use fixed::{
    types::extra::{U0, U4, U6},
    types::I16F16,
    FixedI32,
};
type Fix = FixedI32<U4>;

// 1.75 is 1.11 in binary
let src = Fix::from_bits(0b111 << (4 - 2));
let expected = I16F16::from_bits(0b111 << (16 - 2));
assert_eq!(src.overflowing_to_num::<I16F16>(), (expected, false));
type TooFewIntBits = FixedI32<U6>;
let wrapped = TooFewIntBits::from_bits(Fix::MAX.to_bits() << 2);
assert_eq!(Fix::MAX.overflowing_to_num::<TooFewIntBits>(), (wrapped, true));

// 2.5 is 10.1 in binary
let two_point_5 = Fix::from_bits(0b101 << (4 - 1));
assert_eq!(two_point_5.overflowing_to_num::<i32>(), (2, false));
let does_not_fit = FixedI32::<U0>::from_bits(-1);
let wrapped = 1u32.wrapping_neg();
assert_eq!(does_not_fit.overflowing_to_num::<u32>(), (wrapped, true));

// 1.625 is 1.101 in binary
let one_point_625 = Fix::from_bits(0b1101 << (4 - 3));
assert_eq!(one_point_625.overflowing_to_num::<f32>(), (1.625f32, false));

Parses a string slice containing binary digits to return a fixed-point number.

Rounding is to the nearest, with ties rounded to even.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
// 1.75 is 1.11 in binary
let f = Fix::from_str_binary("1.11");
let check = Fix::from_bits(0b111 << (4 - 2));
assert_eq!(f, Ok(check));
let neg = Fix::from_str_binary("-1.11");
assert_eq!(neg, Ok(-check));

Parses a string slice containing octal digits to return a fixed-point number.

Rounding is to the nearest, with ties rounded to even.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
// 1.75 is 1.11 in binary, 1.6 in octal
let f = Fix::from_str_octal("1.6");
let check = Fix::from_bits(0b111 << (4 - 2));
assert_eq!(f, Ok(check));
let neg = Fix::from_str_octal("-1.6");
assert_eq!(neg, Ok(-check));

Parses a string slice containing hexadecimal digits to return a fixed-point number.

Rounding is to the nearest, with ties rounded to even.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
// 1.75 is 1.11 in binary, 1.C in hexadecimal
let f = Fix::from_str_hex("1.C");
let check = Fix::from_bits(0b111 << (4 - 2));
assert_eq!(f, Ok(check));
let neg = Fix::from_str_hex("-1.C");
assert_eq!(neg, Ok(-check));

Parses a string slice containing decimal digits to return a fixed-point number, saturating on overflow.

Rounding is to the nearest, with ties rounded to even.

Examples

use fixed::types::I8F8;
assert_eq!(I8F8::saturating_from_str("9999"), Ok(I8F8::MAX));
assert_eq!(I8F8::saturating_from_str("-9999"), Ok(I8F8::MIN));

Parses a string slice containing binary digits to return a fixed-point number, saturating on overflow.

Rounding is to the nearest, with ties rounded to even.

Examples

use fixed::types::I8F8;
assert_eq!(I8F8::saturating_from_str_binary("101100111000"), Ok(I8F8::MAX));
assert_eq!(I8F8::saturating_from_str_binary("-101100111000"), Ok(I8F8::MIN));

Parses a string slice containing octal digits to return a fixed-point number, saturating on overflow.

Rounding is to the nearest, with ties rounded to even.

Examples

use fixed::types::I8F8;
assert_eq!(I8F8::saturating_from_str_octal("7777"), Ok(I8F8::MAX));
assert_eq!(I8F8::saturating_from_str_octal("-7777"), Ok(I8F8::MIN));

Prases a string slice containing hexadecimal digits to return a fixed-point number, saturating on overflow.

Rounding is to the nearest, with ties rounded to even.

Examples

use fixed::types::I8F8;
assert_eq!(I8F8::saturating_from_str_hex("FFFF"), Ok(I8F8::MAX));
assert_eq!(I8F8::saturating_from_str_hex("-FFFF"), Ok(I8F8::MIN));

Parses a string slice containing decimal digits to return a fixed-point number, wrapping on overflow.

Rounding is to the nearest, with ties rounded to even.

Examples

use fixed::types::I8F8;
// 9999.5 = 15.5 + 256 × n
assert_eq!(I8F8::wrapping_from_str("9999.5"), Ok(I8F8::from_num(15.5)));
assert_eq!(I8F8::wrapping_from_str("-9999.5"), Ok(I8F8::from_num(-15.5)));

Parses a string slice containing binary digits to return a fixed-point number, wrapping on overflow.

Rounding is to the nearest, with ties rounded to even.

Examples

use fixed::types::I8F8;
let check = I8F8::from_bits(0b1110001 << (8 - 1));
assert_eq!(I8F8::wrapping_from_str_binary("101100111000.1"), Ok(check));
assert_eq!(I8F8::wrapping_from_str_binary("-101100111000.1"), Ok(-check));

Parses a string slice containing octal digits to return a fixed-point number, wrapping on overflow.

Rounding is to the nearest, with ties rounded to even.

Examples

use fixed::types::I8F8;
let check = I8F8::from_bits(0o1654 << (8 - 3));
assert_eq!(I8F8::wrapping_from_str_octal("7165.4"), Ok(check));
assert_eq!(I8F8::wrapping_from_str_octal("-7165.4"), Ok(-check));

Parses a string slice containing hexadecimal digits to return a fixed-point number, wrapping on overflow.

Rounding is to the nearest, with ties rounded to even.

Examples

use fixed::types::I8F8;
let check = I8F8::from_bits(0xFFE);
assert_eq!(I8F8::wrapping_from_str_hex("C0F.FE"), Ok(check));
assert_eq!(I8F8::wrapping_from_str_hex("-C0F.FE"), Ok(-check));

Parses a string slice containing decimal digits to return a fixed-point number.

Returns a tuple of the fixed-point number and a bool indicating whether an overflow has occurred. On overflow, the wrapped value is returned.

Rounding is to the nearest, with ties rounded to even.

Examples

use fixed::types::I8F8;
assert_eq!(I8F8::overflowing_from_str("99.5"), Ok((I8F8::from_num(99.5), false)));
// 9999.5 = 15.5 + 256 × n
assert_eq!(I8F8::overflowing_from_str("-9999.5"), Ok((I8F8::from_num(-15.5), true)));

Parses a string slice containing binary digits to return a fixed-point number.

Returns a tuple of the fixed-point number and a bool indicating whether an overflow has occurred. On overflow, the wrapped value is returned.

Rounding is to the nearest, with ties rounded to even.

Examples

use fixed::types::I8F8;
let check = I8F8::from_bits(0b1110001 << (8 - 1));
assert_eq!(I8F8::overflowing_from_str_binary("111000.1"), Ok((check, false)));
assert_eq!(I8F8::overflowing_from_str_binary("-101100111000.1"), Ok((-check, true)));

Parses a string slice containing octal digits to return a fixed-point number.

Returns a tuple of the fixed-point number and a bool indicating whether an overflow has occurred. On overflow, the wrapped value is returned.

Rounding is to the nearest, with ties rounded to even.

Examples

use fixed::types::I8F8;
let check = I8F8::from_bits(0o1654 << (8 - 3));
assert_eq!(I8F8::overflowing_from_str_octal("165.4"), Ok((check, false)));
assert_eq!(I8F8::overflowing_from_str_octal("-7165.4"), Ok((-check, true)));

Parses a string slice containing hexadecimal digits to return a fixed-point number.

Returns a tuple of the fixed-point number and a bool indicating whether an overflow has occurred. On overflow, the wrapped value is returned.

Rounding is to the nearest, with ties rounded to even.

Examples

use fixed::types::I8F8;
let check = I8F8::from_bits(0xFFE);
assert_eq!(I8F8::overflowing_from_str_hex("F.FE"), Ok((check, false)));
assert_eq!(I8F8::overflowing_from_str_hex("-C0F.FE"), Ok((-check, true)));

Returns the integer part.

Note that since the numbers are stored in two’s complement, negative numbers with non-zero fractional parts will be rounded towards −∞, except in the case where there are no integer bits, that is FixedI32<U32>, where the return value is always zero.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
// 0010.0000
let two = Fix::from_num(2);
// 0010.0100
let two_and_quarter = two + two / 8;
assert_eq!(two_and_quarter.int(), two);
// 1101.0000
let three = Fix::from_num(3);
// 1101.1100
assert_eq!((-two_and_quarter).int(), -three);

Returns the fractional part.

Note that since the numbers are stored in two’s complement, the returned fraction will be non-negative for negative numbers, except in the case where there are no integer bits, that is FixedI32<U32> where the return value is always equal to self.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
// 0000.0100
let quarter = Fix::ONE / 4;
// 0010.0100
let two_and_quarter = quarter * 9;
assert_eq!(two_and_quarter.frac(), quarter);
// 0000.1100
let three_quarters = quarter * 3;
// 1101.1100
assert_eq!((-two_and_quarter).frac(), three_quarters);

Rounds to the next integer towards 0.

Note that for negative numbers, this is different from truncating/discarding the fractional bits. This is because in two’s-complement representations, the value of all the bits except for the most significant bit is positive; discarding positive bits would round towards −∞ unlike this method which rounds towards zero.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(2.1).round_to_zero(), Fix::from_num(2));
assert_eq!(Fix::from_num(2.9).round_to_zero(), Fix::from_num(2));
assert_eq!(Fix::from_num(-2.1).round_to_zero(), Fix::from_num(-2));
assert_eq!(Fix::from_num(-2.9).round_to_zero(), Fix::from_num(-2));

Rounds to the next integer towards +∞.

Panics

When debug assertions are enabled, panics if the result does not fit. When debug assertions are not enabled, the wrapped result can be returned, but it is not considered a breaking change if in the future it panics; if wrapping is required use wrapping_ceil instead.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(2.5).ceil(), Fix::from_num(3));
assert_eq!(Fix::from_num(-2.5).ceil(), Fix::from_num(-2));

Rounds to the next integer towards −∞.

Panics

When debug assertions are enabled, panics if the result does not fit. When debug assertions are not enabled, the wrapped result can be returned, but it is not considered a breaking change if in the future it panics; if wrapping is required use wrapping_floor instead.

Overflow can only occur when there are zero integer bits.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(2.5).floor(), Fix::from_num(2));
assert_eq!(Fix::from_num(-2.5).floor(), Fix::from_num(-3));

Rounds to the nearest integer, with ties rounded away from zero.

Panics

When debug assertions are enabled, panics if the result does not fit. When debug assertions are not enabled, the wrapped result can be returned, but it is not considered a breaking change if in the future it panics; if wrapping is required use wrapping_round instead.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(2.5).round(), Fix::from_num(3));
assert_eq!(Fix::from_num(-2.5).round(), Fix::from_num(-3));

Rounds to the nearest integer, with ties rounded to even.

Panics

When debug assertions are enabled, panics if the result does not fit. When debug assertions are not enabled, the wrapped result can be returned, but it is not considered a breaking change if in the future it panics; if wrapping is required use wrapping_round_ties_to_even instead.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(2.5).round_ties_to_even(), Fix::from_num(2));
assert_eq!(Fix::from_num(3.5).round_ties_to_even(), Fix::from_num(4));

Checked ceil. Rounds to the next integer towards +∞, returning None on overflow.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(2.5).checked_ceil(), Some(Fix::from_num(3)));
assert_eq!(Fix::from_num(-2.5).checked_ceil(), Some(Fix::from_num(-2)));
assert!(Fix::MAX.checked_ceil().is_none());

Checked floor. Rounds to the next integer towards −∞.Returns None on overflow.

Overflow can only occur when there are zero integer bits.

Examples

use fixed::{
    types::extra::{U4, U32},
    FixedI32,
};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(2.5).checked_floor(), Some(Fix::from_num(2)));
assert_eq!(Fix::from_num(-2.5).checked_floor(), Some(Fix::from_num(-3)));
type AllFrac = FixedI32<U32>;
assert!(AllFrac::MIN.checked_floor().is_none());

Checked round. Rounds to the nearest integer, with ties rounded away from zero, returning None on overflow.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(2.5).checked_round(), Some(Fix::from_num(3)));
assert_eq!(Fix::from_num(-2.5).checked_round(), Some(Fix::from_num(-3)));
assert!(Fix::MAX.checked_round().is_none());

Checked round. Rounds to the nearest integer, with ties rounded to even, returning None on overflow.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(2.5).checked_round_ties_to_even(), Some(Fix::from_num(2)));
assert_eq!(Fix::from_num(3.5).checked_round_ties_to_even(), Some(Fix::from_num(4)));
assert!(Fix::MAX.checked_round_ties_to_even().is_none());

Saturating ceil. Rounds to the next integer towards +∞, saturating on overflow.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(2.5).saturating_ceil(), Fix::from_num(3));
assert_eq!(Fix::from_num(-2.5).saturating_ceil(), Fix::from_num(-2));
assert_eq!(Fix::MAX.saturating_ceil(), Fix::MAX);

Saturating floor. Rounds to the next integer towards −∞, saturating on overflow.

Overflow can only occur when there are zero integer bits.

Examples

use fixed::{
    types::extra::{U4, U32},
    FixedI32,
};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(2.5).saturating_floor(), Fix::from_num(2));
assert_eq!(Fix::from_num(-2.5).saturating_floor(), Fix::from_num(-3));
type AllFrac = FixedI32<U32>;
assert_eq!(AllFrac::MIN.saturating_floor(), AllFrac::MIN);

Saturating round. Rounds to the nearest integer, with ties rounded away from zero, and saturating on overflow.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(2.5).saturating_round(), Fix::from_num(3));
assert_eq!(Fix::from_num(-2.5).saturating_round(), Fix::from_num(-3));
assert_eq!(Fix::MAX.saturating_round(), Fix::MAX);

Saturating round. Rounds to the nearest integer, with ties rounded to even, and saturating on overflow.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(2.5).saturating_round_ties_to_even(), Fix::from_num(2));
assert_eq!(Fix::from_num(3.5).saturating_round_ties_to_even(), Fix::from_num(4));
assert_eq!(Fix::MAX.saturating_round_ties_to_even(), Fix::MAX);

Wrapping ceil. Rounds to the next integer towards +∞, wrapping on overflow.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(2.5).wrapping_ceil(), Fix::from_num(3));
assert_eq!(Fix::from_num(-2.5).wrapping_ceil(), Fix::from_num(-2));
assert_eq!(Fix::MAX.wrapping_ceil(), Fix::MIN);

Wrapping floor. Rounds to the next integer towards −∞, wrapping on overflow.

Overflow can only occur when there are zero integer bits.

Examples

use fixed::{
    types::extra::{U4, U32},
    FixedI32,
};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(2.5).wrapping_floor(), Fix::from_num(2));
assert_eq!(Fix::from_num(-2.5).wrapping_floor(), Fix::from_num(-3));
type AllFrac = FixedI32<U32>;
assert_eq!(AllFrac::MIN.wrapping_floor(), AllFrac::ZERO);

Wrapping round. Rounds to the next integer to the nearest, with ties rounded away from zero, and wrapping on overflow.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(2.5).wrapping_round(), Fix::from_num(3));
assert_eq!(Fix::from_num(-2.5).wrapping_round(), Fix::from_num(-3));
assert_eq!(Fix::MAX.wrapping_round(), Fix::MIN);

Wrapping round. Rounds to the next integer to the nearest, with ties rounded to even, and wrapping on overflow.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(2.5).wrapping_round_ties_to_even(), Fix::from_num(2));
assert_eq!(Fix::from_num(3.5).wrapping_round_ties_to_even(), Fix::from_num(4));
assert_eq!(Fix::MAX.wrapping_round_ties_to_even(), Fix::MIN);

Unwrapped ceil. Rounds to the next integer towards +∞, panicking on overflow.

Panics

Panics if the result does not fit.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(2.5).unwrapped_ceil(), Fix::from_num(3));
assert_eq!(Fix::from_num(-2.5).unwrapped_ceil(), Fix::from_num(-2));

The following panics because of overflow.

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let _overflow = Fix::MAX.unwrapped_ceil();

Unwrapped floor. Rounds to the next integer towards −∞, panicking on overflow.

Overflow can only occur when there are zero integer bits.

Panics

Panics if the result does not fit.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(2.5).unwrapped_floor(), Fix::from_num(2));
assert_eq!(Fix::from_num(-2.5).unwrapped_floor(), Fix::from_num(-3));

The following panics because of overflow.

use fixed::{types::extra::U32, FixedI32};
type AllFrac = FixedI32<U32>;
let _overflow = AllFrac::MIN.unwrapped_floor();

Unwrapped round. Rounds to the next integer to the nearest, with ties rounded away from zero, and panicking on overflow.

Panics

Panics if the result does not fit.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(2.5).unwrapped_round(), Fix::from_num(3));
assert_eq!(Fix::from_num(-2.5).unwrapped_round(), Fix::from_num(-3));

The following panics because of overflow.

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let _overflow = Fix::MAX.unwrapped_round();

Unwrapped round. Rounds to the next integer to the nearest, with ties rounded to even, and panicking on overflow.

Panics

Panics if the result does not fit.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(2.5).unwrapped_round_ties_to_even(), Fix::from_num(2));
assert_eq!(Fix::from_num(3.5).unwrapped_round_ties_to_even(), Fix::from_num(4));

The following panics because of overflow.

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let _overflow = Fix::MAX.unwrapped_round_ties_to_even();

Overflowing ceil. Rounds to the next integer towards +∞.

Returns a tuple of the fixed-point number and a bool, indicating whether an overflow has occurred. On overflow, the wrapped value is returned.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(2.5).overflowing_ceil(), (Fix::from_num(3), false));
assert_eq!(Fix::from_num(-2.5).overflowing_ceil(), (Fix::from_num(-2), false));
assert_eq!(Fix::MAX.overflowing_ceil(), (Fix::MIN, true));

Overflowing floor. Rounds to the next integer towards −∞.

Returns a tuple of the fixed-point number and a bool, indicating whether an overflow has occurred. On overflow, the wrapped value isreturned. Overflow can only occur when there are zero integer bits.

Examples

use fixed::{
    types::extra::{U4, U32},
    FixedI32,
};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(2.5).overflowing_floor(), (Fix::from_num(2), false));
assert_eq!(Fix::from_num(-2.5).overflowing_floor(), (Fix::from_num(-3), false));
type AllFrac = FixedI32<U32>;
assert_eq!(AllFrac::MIN.overflowing_floor(), (AllFrac::ZERO, true));

Overflowing round. Rounds to the next integer to the nearest, with ties rounded away from zero.

Returns a tuple of the fixed-point number and a bool indicating whether an overflow has occurred. On overflow, the wrapped value is returned.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(2.5).overflowing_round(), (Fix::from_num(3), false));
assert_eq!(Fix::from_num(-2.5).overflowing_round(), (Fix::from_num(-3), false));
assert_eq!(Fix::MAX.overflowing_round(), (Fix::MIN, true));

Overflowing round. Rounds to the next integer to the nearest, with ties rounded to even.

Returns a tuple of the fixed-point number and a bool indicating whether an overflow has occurred. On overflow, the wrapped value is returned.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(2.5).overflowing_round_ties_to_even(), (Fix::from_num(2), false));
assert_eq!(Fix::from_num(3.5).overflowing_round_ties_to_even(), (Fix::from_num(4), false));
assert_eq!(Fix::MAX.overflowing_round_ties_to_even(), (Fix::MIN, true));

Integer base-2 logarithm, rounded down.

Panics

Panics if the fixed-point number is ≤ 0.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(4).int_log2(), 2);
assert_eq!(Fix::from_num(3.9375).int_log2(), 1);
assert_eq!(Fix::from_num(0.25).int_log2(), -2);
assert_eq!(Fix::from_num(0.1875).int_log2(), -3);

Integer base-10 logarithm, rounded down.

Panics

Panics if the fixed-point number is ≤ 0.

Examples

use fixed::{
    types::extra::{U2, U6},
    FixedI32,
};
assert_eq!(FixedI32::<U2>::from_num(10).int_log10(), 1);
assert_eq!(FixedI32::<U2>::from_num(9.75).int_log10(), 0);
assert_eq!(FixedI32::<U6>::from_num(0.109375).int_log10(), -1);
assert_eq!(FixedI32::<U6>::from_num(0.09375).int_log10(), -2);

Checked integer base-2 logarithm, rounded down. Returns the logarithm or None if the fixed-point number is ≤ 0.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::ZERO.checked_int_log2(), None);
assert_eq!(Fix::from_num(4).checked_int_log2(), Some(2));
assert_eq!(Fix::from_num(3.9375).checked_int_log2(), Some(1));
assert_eq!(Fix::from_num(0.25).checked_int_log2(), Some(-2));
assert_eq!(Fix::from_num(0.1875).checked_int_log2(), Some(-3));

Checked integer base-10 logarithm, rounded down. Returns the logarithm or None if the fixed-point number is ≤ 0.

Examples

use fixed::{
    types::extra::{U2, U6},
    FixedI32,
};
assert_eq!(FixedI32::<U2>::ZERO.checked_int_log10(), None);
assert_eq!(FixedI32::<U2>::from_num(10).checked_int_log10(), Some(1));
assert_eq!(FixedI32::<U2>::from_num(9.75).checked_int_log10(), Some(0));
assert_eq!(FixedI32::<U6>::from_num(0.109375).checked_int_log10(), Some(-1));
assert_eq!(FixedI32::<U6>::from_num(0.09375).checked_int_log10(), Some(-2));

Returns a number representing the sign of self.

Panics

When debug assertions are enabled, this method panics

  • if the value is positive and the fixed-point number has zero or one integer bits such that it cannot hold the value 1.
  • if the value is negative and the fixed-point number has zero integer bits, such that it cannot hold the value −1.

When debug assertions are not enabled, the wrapped value can be returned in those cases, but it is not considered a breaking change if in the future it panics; using this method when 1 and −1 cannot be represented is almost certainly a bug.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(5).signum(), 1);
assert_eq!(Fix::ZERO.signum(), 0);
assert_eq!(Fix::from_num(-5).signum(), -1);

Returns the reciprocal (inverse) of the fixed-point number, 1/self.

Panics

Panics if the fixed-point number is zero.

When debug assertions are enabled, this method also panics if the reciprocal overflows. When debug assertions are not enabled, the wrapped value can be returned, but it is not considered a breaking change if in the future it panics; if wrapping is required use wrapping_recip instead.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(2).recip(), Fix::from_num(0.5));

Euclidean division.

Panics

Panics if the divisor is zero.

When debug assertions are enabled, this method also panics if the division overflows. When debug assertions are not enabled, the wrapped value can be returned, but it is not considered a breaking change if in the future it panics; if wrapping is required use wrapping_div_euclid instead.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(7.5).div_euclid(Fix::from_num(2)), Fix::from_num(3));
assert_eq!(Fix::from_num(-7.5).div_euclid(Fix::from_num(2)), Fix::from_num(-4));

Euclidean division by an integer.

Panics

Panics if the divisor is zero.

When debug assertions are enabled, this method also panics if the division overflows. Overflow can only occur when dividing the minimum value by −1. When debug assertions are not enabled, the wrapped value can be returned, but it is not considered a breaking change if in the future it panics; if wrapping is required use wrapping_div_euclid_int instead.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(7.5).div_euclid_int(2), Fix::from_num(3));
assert_eq!(Fix::from_num(-7.5).div_euclid_int(2), Fix::from_num(-4));

Multiply and accumulate. Adds (a × b) to self.

For some cases, the product a × b would overflow on its own, but the final result self + a × b is representable; in these cases this method saves the correct result without overflow.

The a and b parameters can have a fixed-point type like self but with a different number of fractional bits.

Panics

When debug assertions are enabled, this method panics if the result overflows. When debug assertions are not enabled, the wrapped value can be returned, but it is not considered a breaking change if in the future it panics; if wrapping is required use wrapping_mul_acc instead.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let mut acc = Fix::from_num(3);
acc.mul_acc(Fix::from_num(4), Fix::from_num(0.5));
assert_eq!(acc, 5);

// MAX × 1.5 − MAX = MAX / 2, which does not overflow
acc = -Fix::MAX;
acc.mul_acc(Fix::MAX, Fix::from_num(1.5));
assert_eq!(acc, Fix::MAX / 2);

Remainder for Euclidean division by an integer.

Panics

Panics if the divisor is zero.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(7.5).rem_euclid_int(2), Fix::from_num(1.5));
assert_eq!(Fix::from_num(-7.5).rem_euclid_int(2), Fix::from_num(0.5));

Checked signum. Returns a number representing the sign of self, or None on overflow.

Overflow can only occur

  • if the value is positive and the fixed-point number has zero or one integer bits such that it cannot hold the value 1.
  • if the value is negative and the fixed-point number has zero integer bits, such that it cannot hold the value −1.

Examples

use fixed::{
    types::extra::{U4, U31, U32},
    FixedI32,
};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(5).checked_signum(), Some(Fix::ONE));
assert_eq!(Fix::ZERO.checked_signum(), Some(Fix::ZERO));
assert_eq!(Fix::from_num(-5).checked_signum(), Some(Fix::from_num(-1)));

type OneIntBit = FixedI32<U31>;
type ZeroIntBits = FixedI32<U32>;
assert_eq!(OneIntBit::from_num(0.5).checked_signum(), None);
assert_eq!(ZeroIntBits::from_num(0.25).checked_signum(), None);
assert_eq!(ZeroIntBits::from_num(-0.5).checked_signum(), None);

Checked multiplication. Returns the product, or None on overflow.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::MAX.checked_mul(Fix::ONE), Some(Fix::MAX));
assert_eq!(Fix::MAX.checked_mul(Fix::from_num(2)), None);

Checked division. Returns the quotient, or None if the divisor is zero or on overflow.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::MAX.checked_div(Fix::ONE), Some(Fix::MAX));
assert_eq!(Fix::MAX.checked_div(Fix::ONE / 2), None);

Checked reciprocal. Returns the reciprocal, or None if self is zero or on overflow.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(2).checked_recip(), Some(Fix::from_num(0.5)));
assert_eq!(Fix::ZERO.checked_recip(), None);

Checked Euclidean division. Returns the quotient, or None if the divisor is zero or on overflow.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(7.5).checked_div_euclid(Fix::from_num(2)), Some(Fix::from_num(3)));
assert_eq!(Fix::from_num(7.5).checked_div_euclid(Fix::ZERO), None);
assert_eq!(Fix::MAX.checked_div_euclid(Fix::from_num(0.25)), None);
assert_eq!(Fix::from_num(-7.5).checked_div_euclid(Fix::from_num(2)), Some(Fix::from_num(-4)));

Checked multiply and accumulate. Adds (a × b) to self, or returns None on overflow.

Like all other checked methods, this method wraps the successful return value in an Option. Since the unchecked mul_acc method does not return a value, which is equivalent to returning (), this method wraps () into Some(()) on success.

When overflow occurs, self is not modified and retains its previous value.

For some cases, the product a × b would overflow on its own, but the final result self + a × b is representable; in these cases this method saves the correct result without overflow.

The a and b parameters can have a fixed-point type like self but with a different number of fractional bits.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let mut acc = Fix::from_num(3);
let check = acc.checked_mul_acc(Fix::from_num(4), Fix::from_num(0.5));
assert_eq!(check, Some(()));
assert_eq!(acc, 5);

acc = Fix::DELTA;
let check = acc.checked_mul_acc(Fix::MAX, Fix::ONE);
assert_eq!(check, None);
// acc is unchanged on error
assert_eq!(acc, Fix::DELTA);

// MAX × 1.5 − MAX = MAX / 2, which does not overflow
acc = -Fix::MAX;
let check = acc.checked_mul_acc(Fix::MAX, Fix::from_num(1.5));
assert_eq!(check, Some(()));
assert_eq!(acc, Fix::MAX / 2);

Checked fixed-point remainder for division by an integer. Returns the remainder, or None if the divisor is zero.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(3.75).checked_rem_int(2), Some(Fix::from_num(1.75)));
assert_eq!(Fix::from_num(3.75).checked_rem_int(0), None);
assert_eq!(Fix::from_num(-3.75).checked_rem_int(2), Some(Fix::from_num(-1.75)));

Checked Euclidean division by an integer. Returns the quotient, or None if the divisor is zero or if the division results in overflow.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(7.5).checked_div_euclid_int(2), Some(Fix::from_num(3)));
assert_eq!(Fix::from_num(7.5).checked_div_euclid_int(0), None);
assert_eq!(Fix::MIN.checked_div_euclid_int(-1), None);

Checked remainder for Euclidean division by an integer. Returns the remainder, or None if the divisor is zero or if the remainder results in overflow.

Examples

use fixed::{types::extra::U28, FixedI32};
type Fix = FixedI32<U28>;
assert_eq!(Fix::from_num(7.5).checked_rem_euclid_int(2), Some(Fix::from_num(1.5)));
assert_eq!(Fix::from_num(7.5).checked_rem_euclid_int(0), None);
assert_eq!(Fix::from_num(-7.5).checked_rem_euclid_int(2), Some(Fix::from_num(0.5)));
// −8 ≤ Fix < 8, so the answer 12.5 overflows
assert_eq!(Fix::from_num(-7.5).checked_rem_euclid_int(20), None);

Saturating signum. Returns a number representing the sign of self, saturating on overflow.

Overflow can only occur

  • if the value is positive and the fixed-point number has zero or one integer bits such that it cannot hold the value 1.
  • if the value is negative and the fixed-point number has zero integer bits, such that it cannot hold the value −1.

Examples

use fixed::{
    types::extra::{U4, U31, U32},
    FixedI32,
};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(5).saturating_signum(), 1);
assert_eq!(Fix::ZERO.saturating_signum(), 0);
assert_eq!(Fix::from_num(-5).saturating_signum(), -1);

type OneIntBit = FixedI32<U31>;
type ZeroIntBits = FixedI32<U32>;
assert_eq!(OneIntBit::from_num(0.5).saturating_signum(), OneIntBit::MAX);
assert_eq!(ZeroIntBits::from_num(0.25).saturating_signum(), ZeroIntBits::MAX);
assert_eq!(ZeroIntBits::from_num(-0.5).saturating_signum(), ZeroIntBits::MIN);

Saturating multiplication. Returns the product, saturating on overflow.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(3).saturating_mul(Fix::from_num(2)), Fix::from_num(6));
assert_eq!(Fix::MAX.saturating_mul(Fix::from_num(2)), Fix::MAX);

Saturating division. Returns the quotient, saturating on overflow.

Panics

Panics if the divisor is zero.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let one_half = Fix::ONE / 2;
assert_eq!(Fix::ONE.saturating_div(Fix::from_num(2)), one_half);
assert_eq!(Fix::MAX.saturating_div(one_half), Fix::MAX);

Saturating reciprocal. Returns the reciprocal, saturating on overflow.

Panics

Panics if the fixed-point number is zero.

Examples

use fixed::{types::extra::U31, FixedI32};
// only one integer bit
type Fix = FixedI32<U31>;
assert_eq!(Fix::from_num(0.25).saturating_recip(), Fix::MAX);
assert_eq!(Fix::from_num(-0.25).saturating_recip(), Fix::MIN);

Saturating Euclidean division. Returns the quotient, saturating on overflow.

Panics

Panics if the divisor is zero.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(7.5).saturating_div_euclid(Fix::from_num(2)), Fix::from_num(3));
assert_eq!(Fix::MAX.saturating_div_euclid(Fix::from_num(0.25)), Fix::MAX);
assert_eq!(Fix::from_num(-7.5).saturating_div_euclid(Fix::from_num(2)), Fix::from_num(-4));
assert_eq!(Fix::MIN.saturating_div_euclid(Fix::from_num(0.25)), Fix::MIN);

Saturating Euclidean division by an integer. Returns the quotient, saturating on overflow.

Overflow can only occur when dividing the minimum value by −1.

Panics

Panics if the divisor is zero.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(7.5).saturating_div_euclid_int(2), Fix::from_num(3));
assert_eq!(Fix::from_num(-7.5).saturating_div_euclid_int(2), Fix::from_num(-4));
assert_eq!(Fix::MIN.saturating_div_euclid_int(-1), Fix::MAX);

Saturating multiply and accumulate. Adds (a × b) to self, saturating on overflow.

For some cases, the product a × b would overflow on its own, but the final result self + a × b is representable; in these cases this method saves the correct result without overflow.

The a and b parameters can have a fixed-point type like self but with a different number of fractional bits.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let mut acc = Fix::from_num(3);
acc.saturating_mul_acc(Fix::from_num(4), Fix::from_num(0.5));
assert_eq!(acc, 5);

acc = Fix::MAX / 2;
acc.saturating_mul_acc(Fix::MAX / 2, Fix::from_num(3));
assert_eq!(acc, Fix::MAX);

// MAX × 1.5 − MAX = MAX / 2, which does not overflow
acc = -Fix::MAX;
acc.saturating_mul_acc(Fix::MAX, Fix::from_num(1.5));
assert_eq!(acc, Fix::MAX / 2);

Saturating remainder for Euclidean division by an integer. Returns the remainder, saturating on overflow.

Panics

Panics if the divisor is zero.

Examples

use fixed::{types::extra::U28, FixedI32};
type Fix = FixedI32<U28>;
assert_eq!(Fix::from_num(7.5).saturating_rem_euclid_int(2), Fix::from_num(1.5));
assert_eq!(Fix::from_num(-7.5).saturating_rem_euclid_int(2), Fix::from_num(0.5));
// −8 ≤ Fix < 8, so the answer 12.5 saturates
assert_eq!(Fix::from_num(-7.5).saturating_rem_euclid_int(20), Fix::MAX);

Wrapping signum. Returns a number representing the sign of self, wrapping on overflow.

Overflow can only occur

  • if the value is positive and the fixed-point number has zero or one integer bits such that it cannot hold the value 1.
  • if the value is negative and the fixed-point number has zero integer bits, such that it cannot hold the value −1.

Examples

use fixed::{
    types::extra::{U4, U31, U32},
    FixedI32,
};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(5).wrapping_signum(), 1);
assert_eq!(Fix::ZERO.wrapping_signum(), 0);
assert_eq!(Fix::from_num(-5).wrapping_signum(), -1);

type OneIntBit = FixedI32<U31>;
type ZeroIntBits = FixedI32<U32>;
assert_eq!(OneIntBit::from_num(0.5).wrapping_signum(), -1);
assert_eq!(ZeroIntBits::from_num(0.25).wrapping_signum(), 0);
assert_eq!(ZeroIntBits::from_num(-0.5).wrapping_signum(), 0);

Wrapping multiplication. Returns the product, wrapping on overflow.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(3).wrapping_mul(Fix::from_num(2)), Fix::from_num(6));
let wrapped = Fix::from_bits(!0 << 2);
assert_eq!(Fix::MAX.wrapping_mul(Fix::from_num(4)), wrapped);

Wrapping division. Returns the quotient, wrapping on overflow.

Panics

Panics if the divisor is zero.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let one_point_5 = Fix::from_bits(0b11 << (4 - 1));
assert_eq!(Fix::from_num(3).wrapping_div(Fix::from_num(2)), one_point_5);
let quarter = Fix::ONE / 4;
let wrapped = Fix::from_bits(!0 << 2);
assert_eq!(Fix::MAX.wrapping_div(quarter), wrapped);

Wrapping reciprocal. Returns the reciprocal, wrapping on overflow.

Panics

Panics if the fixed-point number is zero.

Examples

use fixed::{types::extra::U31, FixedI32};
// only one integer bit
type Fix = FixedI32<U31>;
assert_eq!(Fix::from_num(0.25).wrapping_recip(), Fix::ZERO);

Wrapping Euclidean division. Returns the quotient, wrapping on overflow.

Panics

Panics if the divisor is zero.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(7.5).wrapping_div_euclid(Fix::from_num(2)), Fix::from_num(3));
let wrapped = Fix::MAX.wrapping_mul_int(4).round_to_zero();
assert_eq!(Fix::MAX.wrapping_div_euclid(Fix::from_num(0.25)), wrapped);

Wrapping Euclidean division by an integer. Returns the quotient, wrapping on overflow.

Overflow can only occur when dividing the minimum value by −1.

Panics

Panics if the divisor is zero.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(7.5).wrapping_div_euclid_int(2), Fix::from_num(3));
assert_eq!(Fix::from_num(-7.5).wrapping_div_euclid_int(2), Fix::from_num(-4));
let wrapped = Fix::MIN.round_to_zero();
assert_eq!(Fix::MIN.wrapping_div_euclid_int(-1), wrapped);

Wrapping multiply and accumulate. Adds (a × b) to self, wrapping on overflow.

The a and b parameters can have a fixed-point type like self but with a different number of fractional bits.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let mut acc = Fix::from_num(3);
acc.wrapping_mul_acc(Fix::from_num(4), Fix::from_num(0.5));
assert_eq!(acc, 5);

acc = Fix::MAX;
acc.wrapping_mul_acc(Fix::MAX, Fix::from_num(3));
assert_eq!(acc, Fix::MAX.wrapping_mul_int(4));

Wrapping remainder for Euclidean division by an integer. Returns the remainder, wrapping on overflow.

Note that while remainder for Euclidean division cannot be negative, the wrapped value can be negative.

Panics

Panics if the divisor is zero.

Examples

use fixed::{types::extra::U28, FixedI32};
type Fix = FixedI32<U28>;
assert_eq!(Fix::from_num(7.5).wrapping_rem_euclid_int(2), Fix::from_num(1.5));
assert_eq!(Fix::from_num(-7.5).wrapping_rem_euclid_int(2), Fix::from_num(0.5));
// −8 ≤ Fix < 8, so the answer 12.5 wraps to −3.5
assert_eq!(Fix::from_num(-7.5).wrapping_rem_euclid_int(20), Fix::from_num(-3.5));

Unwrapped signum. Returns a number representing the sign of self, panicking on overflow.

Overflow can only occur

  • if the value is positive and the fixed-point number has zero or one integer bits such that it cannot hold the value 1.
  • if the value is negative and the fixed-point number has zero integer bits, such that it cannot hold the value −1.

Panics

Panics if the result does not fit.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(5).unwrapped_signum(), 1);
assert_eq!(Fix::ZERO.unwrapped_signum(), 0);
assert_eq!(Fix::from_num(-5).unwrapped_signum(), -1);

The following panics because of overflow.

use fixed::{types::extra::U31, FixedI32};
type OneIntBit = FixedI32<U31>;
let _overflow = OneIntBit::from_num(0.5).unwrapped_signum();

Unwrapped multiplication. Returns the product, panicking on overflow.

Panics

Panics if the result does not fit.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(3).unwrapped_mul(Fix::from_num(2)), Fix::from_num(6));

The following panics because of overflow.

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let _overflow = Fix::MAX.unwrapped_mul(Fix::from_num(4));

Unwrapped division. Returns the quotient, panicking on overflow.

Panics

Panics if the divisor is zero or if the division results in overflow.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let one_point_5 = Fix::from_bits(0b11 << (4 - 1));
assert_eq!(Fix::from_num(3).unwrapped_div(Fix::from_num(2)), one_point_5);

The following panics because of overflow.

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let quarter = Fix::ONE / 4;
let _overflow = Fix::MAX.unwrapped_div(quarter);

Unwrapped reciprocal. Returns the reciprocal, panicking on overflow.

Panics

Panics if the fixed-point number is zero or on overflow.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(0.25).unwrapped_recip(), Fix::from_num(4));

Unwrapped Euclidean division. Returns the quotient, panicking on overflow.

Panics

Panics if the divisor is zero or if the division results in overflow.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(7.5).unwrapped_div_euclid(Fix::from_num(2)), Fix::from_num(3));

The following panics because of overflow.

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let _overflow = Fix::MAX.unwrapped_div_euclid(Fix::from_num(0.25));

Unwrapped multiply and accumulate. Adds (a × b) to self, panicking on overflow.

For some cases, the product a × b would overflow on its own, but the final result self + a × b is representable; in these cases this method saves the correct result without overflow.

The a and b parameters can have a fixed-point type like self but with a different number of fractional bits.

Panics

Panics if the result does not fit.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let mut acc = Fix::from_num(3);
acc.unwrapped_mul_acc(Fix::from_num(4), Fix::from_num(0.5));
assert_eq!(acc, 5);

// MAX × 1.5 − MAX = MAX / 2, which does not overflow
acc = -Fix::MAX;
acc.unwrapped_mul_acc(Fix::MAX, Fix::from_num(1.5));
assert_eq!(acc, Fix::MAX / 2);

The following panics because of overflow.

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let mut acc = Fix::DELTA;
acc.unwrapped_mul_acc(Fix::MAX, Fix::ONE);

Unwrapped fixed-point remainder for division by an integer. Returns the remainder, panicking if the divisor is zero.

Panics

Panics if the divisor is zero.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(3.75).unwrapped_rem_int(2), Fix::from_num(1.75));

The following panics because the divisor is zero.

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let _divisor_is_zero = Fix::from_num(3.75).unwrapped_rem_int(0);

Unwrapped Euclidean division by an integer. Returns the quotient, panicking on overflow.

Overflow can only occur when dividing the minimum value by −1.

Panics

Panics if the divisor is zero or if the division results in overflow.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(7.5).unwrapped_div_euclid_int(2), Fix::from_num(3));
assert_eq!(Fix::from_num(-7.5).unwrapped_div_euclid_int(2), Fix::from_num(-4));

The following panics because of overflow.

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let _overflow = Fix::MIN.unwrapped_div_euclid_int(-1);

Unwrapped remainder for Euclidean division by an integer. Returns the remainder, panicking on overflow.

Note that while remainder for Euclidean division cannot be negative, the wrapped value can be negative.

Panics

Panics if the divisor is zero or if the division results in overflow.

Examples

use fixed::{types::extra::U28, FixedI32};
type Fix = FixedI32<U28>;
assert_eq!(Fix::from_num(7.5).unwrapped_rem_euclid_int(2), Fix::from_num(1.5));
assert_eq!(Fix::from_num(-7.5).unwrapped_rem_euclid_int(2), Fix::from_num(0.5));

The following panics because of overflow.

use fixed::{types::extra::U28, FixedI32};
type Fix = FixedI32<U28>;
// −8 ≤ Fix < 8, so the answer 12.5 overflows
let _overflow = Fix::from_num(-7.5).unwrapped_rem_euclid_int(20);

Overflowing signum.

Returns a tuple of the signum and a bool indicating whether an overflow has occurred. On overflow, the wrapped value is returned.

Overflow can only occur

  • if the value is positive and the fixed-point number has zero or one integer bits such that it cannot hold the value 1.
  • if the value is negative and the fixed-point number has zero integer bits, such that it cannot hold the value −1.

Examples

use fixed::{
    types::extra::{U4, U31, U32},
    FixedI32,
};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(5).overflowing_signum(), (Fix::ONE, false));
assert_eq!(Fix::ZERO.overflowing_signum(), (Fix::ZERO, false));
assert_eq!(Fix::from_num(-5).overflowing_signum(), (Fix::from_num(-1), false));

type OneIntBit = FixedI32<U31>;
type ZeroIntBits = FixedI32<U32>;
assert_eq!(OneIntBit::from_num(0.5).overflowing_signum(), (OneIntBit::from_num(-1), true));
assert_eq!(ZeroIntBits::from_num(0.25).overflowing_signum(), (ZeroIntBits::ZERO, true));
assert_eq!(ZeroIntBits::from_num(-0.5).overflowing_signum(), (ZeroIntBits::ZERO, true));

Overflowing multiplication.

Returns a tuple of the product and a bool indicating whether an overflow has occurred. On overflow, the wrapped value is returned.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(3).overflowing_mul(Fix::from_num(2)), (Fix::from_num(6), false));
let wrapped = Fix::from_bits(!0 << 2);
assert_eq!(Fix::MAX.overflowing_mul(Fix::from_num(4)), (wrapped, true));

Overflowing division.

Returns a tuple of the quotient and a bool indicating whether an overflow has occurred. On overflow, the wrapped value is returned.

Panics

Panics if the divisor is zero.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let one_point_5 = Fix::from_bits(0b11 << (4 - 1));
assert_eq!(Fix::from_num(3).overflowing_div(Fix::from_num(2)), (one_point_5, false));
let quarter = Fix::ONE / 4;
let wrapped = Fix::from_bits(!0 << 2);
assert_eq!(Fix::MAX.overflowing_div(quarter), (wrapped, true));

Overflowing reciprocal.

Returns a tuple of the reciprocal and a bool indicating whether an overflow has occurred. On overflow, the wrapped value is returned.

Panics

Panics if the fixed-point number is zero.

Examples

use fixed::{
    types::extra::{U4, U31},
    FixedI32,
};
type Fix = FixedI32<U4>;
// only one integer bit
type Small = FixedI32<U31>;
assert_eq!(Fix::from_num(0.25).overflowing_recip(), (Fix::from_num(4), false));
assert_eq!(Small::from_num(0.25).overflowing_recip(), (Small::ZERO, true));

Overflowing Euclidean division.

Returns a tuple of the quotient and a bool indicating whether an overflow has occurred. On overflow, the wrapped value is returned.

Panics

Panics if the divisor is zero.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let check = Fix::from_num(3);
assert_eq!(Fix::from_num(7.5).overflowing_div_euclid(Fix::from_num(2)), (check, false));
let wrapped = Fix::MAX.wrapping_mul_int(4).round_to_zero();
assert_eq!(Fix::MAX.overflowing_div_euclid(Fix::from_num(0.25)), (wrapped, true));

Overflowing Euclidean division by an integer.

Returns a tuple of the quotient and a bool indicating whether an overflow has occurred. On overflow, the wrapped value is returned. Overflow can only occur when dividing the minimum value by −1.

Panics

Panics if the divisor is zero.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::from_num(7.5).overflowing_div_euclid_int(2), (Fix::from_num(3), false));
assert_eq!(Fix::from_num(-7.5).overflowing_div_euclid_int(2), (Fix::from_num(-4), false));
let wrapped = Fix::MIN.round_to_zero();
assert_eq!(Fix::MIN.overflowing_div_euclid_int(-1), (wrapped, true));

Overflowing multiply and accumulate. Adds (a × b) to self, wrapping and returning true if overflow occurs.

For some cases, the product a × b would overflow on its own, but the final result self + a × b is representable; in these cases this method saves the correct result without overflow.

The a and b parameters can have a fixed-point type like self but with a different number of fractional bits.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
let mut acc = Fix::from_num(3);
assert!(!acc.overflowing_mul_acc(Fix::from_num(4), Fix::from_num(0.5)));
assert_eq!(acc, 5);

acc = Fix::MAX;
assert!(acc.overflowing_mul_acc(Fix::MAX, Fix::from_num(3)));
assert_eq!(acc, Fix::MAX.wrapping_mul_int(4));

// MAX × 1.5 − MAX = MAX / 2, which does not overflow
acc = -Fix::MAX;
assert!(!acc.overflowing_mul_acc(Fix::MAX, Fix::from_num(1.5)));
assert_eq!(acc, Fix::MAX / 2);

Remainder for Euclidean division by an integer.

Returns a tuple of the remainder and a bool indicating whether an overflow has occurred. On overflow, the wrapped value is returned.

Note that while remainder for Euclidean division cannot be negative, the wrapped value can be negative.

Panics

Panics if the divisor is zero.

Examples

use fixed::{types::extra::U28, FixedI32};
type Fix = FixedI32<U28>;
assert_eq!(Fix::from_num(7.5).overflowing_rem_euclid_int(2), (Fix::from_num(1.5), false));
assert_eq!(Fix::from_num(-7.5).overflowing_rem_euclid_int(2), (Fix::from_num(0.5), false));
// −8 ≤ Fix < 8, so the answer 12.5 wraps to −3.5
assert_eq!(Fix::from_num(-7.5).overflowing_rem_euclid_int(20), (Fix::from_num(-3.5), true));

This block contains constants in the range 0 < x < 0.5.

Examples

use fixed::{consts, types::extra::U32, FixedI32};
type Fix = FixedI32<U32>;
assert_eq!(Fix::LOG10_2, Fix::from_num(consts::LOG10_2));

1/τ = 0.159154…

2/τ = 0.318309…

π/8 = 0.392699…

1/π = 0.318309…

log10 2 = 0.301029…

log10 e = 0.434294…

This block contains constants in the range 0.5 ≤ x < 1.

These constants are not representable in signed fixed-point numbers with less than 1 integer bit.

Examples

use fixed::{consts, types::extra::U31, FixedI32};
type Fix = FixedI32<U31>;
assert_eq!(Fix::LN_2, Fix::from_num(consts::LN_2));
assert!(0.5 <= Fix::LN_2 && Fix::LN_2 < 1);

The following example fails to compile, since the maximum representable value with 32 fractional bits and 0 integer bits is < 0.5.

use fixed::{consts, types::extra::U32, FixedI32};
type Fix = FixedI32<U32>;
let _ = Fix::LN_2;

τ/8 = 0.785398…

τ/12 = 0.523598…

4/τ = 0.636619…

π/4 = 0.785398…

π/6 = 0.523598…

2/π = 0.636619…

1/√π = 0.564189…

1/√2 = 0.707106…

1/√3 = 0.577350…

ln 2 = 0.693147…

The golden ratio conjugate, Φ = 1/φ = 0.618033…

The Euler-Mascheroni constant, γ = 0.577215…

Catalan’s constant = 0.915965…

This block contains constants in the range 1 ≤ x < 2.

These constants are not representable in signed fixed-point numbers with less than 2 integer bits.

Examples

use fixed::{consts, types::extra::U30, FixedI32};
type Fix = FixedI32<U30>;
assert_eq!(Fix::LOG2_E, Fix::from_num(consts::LOG2_E));
assert!(1 <= Fix::LOG2_E && Fix::LOG2_E < 2);

The following example fails to compile, since the maximum representable value with 31 fractional bits and 1 integer bit is < 1.

use fixed::{consts, types::extra::U31, FixedI32};
type Fix = FixedI32<U31>;
let _ = Fix::LOG2_E;

One.

Examples

use fixed::{types::extra::U4, FixedI32};
type Fix = FixedI32<U4>;
assert_eq!(Fix::ONE, Fix::from_num(1));

τ/4 = 1.57079…

τ/6 = 1.04719…

π/2 = 1.57079…

π/3 = 1.04719…

√π = 1.77245…

2/√π = 1.12837…

√2 = 1.41421…

√3 = 1.73205…

√e = 1.64872…

log2 e = 1.44269…

The golden ratio, φ = 1.61803…

√φ = 1.27201…

This block contains constants in the range 2 ≤ x < 4.

These constants are not representable in signed fixed-point numbers with less than 3 integer bits.

Examples

use fixed::{consts, types::extra::U29, FixedI32};
type Fix = FixedI32<U29>;
assert_eq!(Fix::E, Fix::from_num(consts::E));
assert!(2 <= Fix::E && Fix::E < 4);

The following example fails to compile, since the maximum representable value with 30 fractional bits and 2 integer bits is < 2.

use fixed::{consts, types::extra::U30, FixedI32};
type Fix = FixedI32<U30>;
let _ = Fix::E;

τ/2 = 3.14159…

τ/3 = 2.09439…

Archimedes’ constant, π = 3.14159…

Euler’s number, e = 2.71828…

log2 10 = 3.32192…

ln 10 = 2.30258…

This block contains constants in the range 4 ≤ x < 8.

These constants are not representable in signed fixed-point numbers with less than 4 integer bits.

Examples

use fixed::{consts, types::extra::U28, FixedI32};
type Fix = FixedI32<U28>;
assert_eq!(Fix::TAU, Fix::from_num(consts::TAU));
assert!(4 <= Fix::TAU && Fix::TAU < 8);

The following example fails to compile, since the maximum representable value with 29 fractional bits and 3 integer bits is < 4.

use fixed::{consts, types::extra::U29, FixedI32};
type Fix = FixedI32<U29>;
let _ = Fix::TAU;

A turn, τ = 6.28318…

Trait Implementations

The resulting type after applying the + operator.

Performs the + operation. Read more

The resulting type after applying the + operator.

Performs the + operation. Read more

The resulting type after applying the + operator.

Performs the + operation. Read more

The resulting type after applying the + operator.

Performs the + operation. Read more

Performs the += operation. Read more

Performs the += operation. Read more

Generate an arbitrary value of Self from the given unstructured data. Read more

Get a size hint for how many bytes out of an Unstructured this type needs to construct itself. Read more

Generate an arbitrary value of Self from the entirety of the given unstructured data. Read more

Formats the value using the given formatter.

The resulting type after applying the & operator.

Performs the & operation. Read more

The resulting type after applying the & operator.

Performs the & operation. Read more

The resulting type after applying the & operator.

Performs the & operation. Read more

The resulting type after applying the & operator.

Performs the & operation. Read more

Performs the &= operation. Read more

Performs the &= operation. Read more

The resulting type after applying the | operator.

Performs the | operation. Read more

The resulting type after applying the | operator.

Performs the | operation. Read more

The resulting type after applying the | operator.

Performs the | operation. Read more

The resulting type after applying the | operator.

Performs the | operation. Read more

Performs the |= operation. Read more

Performs the |= operation. Read more

The resulting type after applying the ^ operator.

Performs the ^ operation. Read more

The resulting type after applying the ^ operator.

Performs the ^ operation. Read more

The resulting type after applying the ^ operator.

Performs the ^ operation. Read more

The resulting type after applying the ^ operator.

Performs the ^ operation. Read more

Performs the ^= operation. Read more

Performs the ^= operation. Read more

returns the smallest finite number this type can represent

returns the largest finite number this type can represent

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Adds two numbers, checking for overflow. If overflow happens, None is returned. Read more

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Casts the value.

Divides two numbers, checking for underflow, overflow and division by zero. If any of that happens, None is returned. Read more

Multiplies two numbers, checking for underflow or overflow. If underflow or overflow happens, None is returned. Read more

Negates a number, returning None for results that can’t be represented, like signed MIN values that can’t be positive, or non-zero unsigned values that can’t be negative. Read more

Finds the remainder of dividing two numbers, checking for underflow, overflow and division by zero. If any of that happens, None is returned. Read more

Checked shift left. Computes self << rhs, returning None if rhs is larger than or equal to the number of bits in self. Read more

Checked shift right. Computes self >> rhs, returning None if rhs is larger than or equal to the number of bits in self. Read more

Subtracts two numbers, checking for underflow. If underflow happens, None is returned. Read more

Returns a copy of the value. Read more

Performs copy-assignment from source. Read more

Formats the value using the given formatter. Read more

Returns the “default value” for a type. Read more

Deserialize this value from the given Serde deserializer. Read more

Formats the value using the given formatter. Read more

The resulting type after applying the / operator.

Performs the / operation. Read more

The resulting type after applying the / operator.

Performs the / operation. Read more

The resulting type after applying the / operator.

Performs the / operation. Read more

The resulting type after applying the / operator.

Performs the / operation. Read more

The resulting type after applying the / operator.

Performs the / operation. Read more

The resulting type after applying the / operator.

Performs the / operation. Read more

The resulting type after applying the / operator.

Performs the / operation. Read more

The resulting type after applying the / operator.

Performs the / operation. Read more

Performs the /= operation. Read more

Performs the /= operation. Read more

Performs the /= operation. Read more

Performs the /= operation. Read more

The primitive integer underlying type. Read more

The non-zero wrapped version of Bits. Read more

A byte array with the same size as the type. Read more

The number of fractional bits as a compile-time Unsigned as provided by the typenum crate. Read more

An unsigned fixed-point number type with the same number of integer and fractional bits as Self. Read more

An unsigned fixed-point number type with the same number of integer and fractional bits as Self. Read more

Zero. Read more

The difference between any two successive representable numbers, Δ. Read more

The smallest value that can be represented. Read more

The largest value that can be represented. Read more

true if the type is signed. Read more

The number of integer bits. Read more

The number of fractional bits. Read more

Creates a fixed-point number that has a bitwise representation identical to the given integer. Read more

Creates an integer that has a bitwise representation identical to the given fixed-point number. Read more

Converts a fixed-point number from big endian to the target’s endianness. Read more

Converts a fixed-point number from little endian to the target’s endianness. Read more

Converts this fixed-point number to big endian from the target’s endianness. Read more

Converts this fixed-point number to little endian from the target’s endianness. Read more

Reverses the byte order of the fixed-point number. Read more

Creates a fixed-point number from its representation as a byte array in big endian. Read more

Creates a fixed-point number from its representation as a byte array in little endian. Read more

Creates a fixed-point number from its representation as a byte array in native endian. Read more

Returns the memory representation of this fixed-point number as a byte array in big-endian byte order. Read more

Returns the memory representation of this fixed-point number as a byte array in little-endian byte order. Read more

Returns the memory representation of this fixed-point number as a byte array in native byte order. Read more

Creates a fixed-point number from another number. Read more

Converts a fixed-point number to another number. Read more

Creates a fixed-point number from another number if it fits, otherwise returns None. Read more

Converts a fixed-point number to another number if it fits, otherwise returns None. Read more

Creates a fixed-point number from another number, saturating the value if it does not fit. Read more

Converts a fixed-point number to another number, saturating the value if it does not fit. Read more

Creates a fixed-point number from another number, wrapping the value on overflow. Read more

Converts a fixed-point number to another number, wrapping the value on overflow. Read more

Creates a fixed-point number from another number, panicking on overflow. Read more

Converts a fixed-point number to another number, panicking on overflow. Read more

Creates a fixed-point number from another number. Read more

Converts a fixed-point number to another number. Read more

Parses a string slice containing binary digits to return a fixed-point number. Read more

Parses a string slice containing octal digits to return a fixed-point number. Read more

Parses a string slice containing hexadecimal digits to return a fixed-point number. Read more

Parses a string slice containing decimal digits to return a fixed-point number, saturating on overflow. Read more

Parses a string slice containing binary digits to return a fixed-point number, saturating on overflow. Read more

Parses a string slice containing octal digits to return a fixed-point number, saturating on overflow. Read more

Parses a string slice containing hexadecimal digits to return a fixed-point number, saturating on overflow. Read more

Parses a string slice containing decimal digits to return a fixed-point number, wrapping on overflow. Read more

Parses a string slice containing binary digits to return a fixed-point number, wrapping on overflow. Read more

Parses a string slice containing octal digits to return a fixed-point number, wrapping on overflow. Read more

Parses a string slice containing hexadecimal digits to return a fixed-point number, wrapping on overflow. Read more

Parses a string slice containing decimal digits to return a fixed-point number. Read more

Parses a string slice containing binary digits to return a fixed-point number. Read more

Parses a string slice containing octal digits to return a fixed-point number. Read more

Parses a string slice containing hexadecimal digits to return a fixed-point number. Read more

Returns the integer part. Read more

Returns the fractional part. Read more

Rounds to the next integer towards +∞. Read more

Rounds to the next integer towards −∞. Read more

Rounds to the next integer towards 0. Read more

Rounds to the nearest integer, with ties rounded away from zero. Read more

Rounds to the nearest integer, with ties rounded to even. Read more

Checked ceil. Rounds to the next integer towards +∞, returning None on overflow. Read more

Checked floor. Rounds to the next integer towards −∞, returning None on overflow. Read more

Checked round. Rounds to the nearest integer, with ties rounded away from zero, returning None on overflow. Read more

Checked round. Rounds to the nearest integer, with ties rounded to even, returning None on overflow. Read more

Saturating ceil. Rounds to the next integer towards +∞, saturating on overflow. Read more

Saturating floor. Rounds to the next integer towards −∞, saturating on overflow. Read more

Saturating round. Rounds to the nearest integer, with ties rounded away from zero, and saturating on overflow. Read more

Saturating round. Rounds to the nearest integer, with ties rounded to_even, and saturating on overflow. Read more

Wrapping ceil. Rounds to the next integer towards +∞, wrapping on overflow. Read more

Wrapping floor. Rounds to the next integer towards −∞, wrapping on overflow. Read more

Wrapping round. Rounds to the next integer to the nearest, with ties rounded away from zero, and wrapping on overflow. Read more

Wrapping round. Rounds to the next integer to the nearest, with ties rounded to even, and wrapping on overflow. Read more

Unwrapped ceil. Rounds to the next integer towards +∞, panicking on overflow. Read more

Unwrapped floor. Rounds to the next integer towards −∞, panicking on overflow. Read more

Unwrapped round. Rounds to the next integer to the nearest, with ties rounded away from zero, and panicking on overflow. Read more

Unwrapped round. Rounds to the next integer to the nearest, with ties rounded to even, and panicking on overflow. Read more

Overflowing ceil. Rounds to the next integer towards +∞. Read more

Overflowing floor. Rounds to the next integer towards −∞. Read more

Overflowing round. Rounds to the next integer to the nearest, with ties rounded away from zero. Read more

Overflowing round. Rounds to the next integer to the nearest, with ties rounded to even. Read more

Returns the number of ones in the binary representation. Read more

Returns the number of zeros in the binary representation. Read more

Returns the number of leading ones in the binary representation. Read more

Returns the number of leading zeros in the binary representation. Read more

Returns the number of trailing ones in the binary representation. Read more

Returns the number of trailing zeros in the binary representation. Read more

Integer base-2 logarithm, rounded down. Read more

Integer base-10 logarithm, rounded down. Read more

Checked integer base-2 logarithm, rounded down. Returns the logarithm or None if the fixed-point number is ≤ 0. Read more

Checked integer base-10 logarithm, rounded down. Returns the logarithm or None if the fixed-point number is ≤ 0. Read more

Reverses the order of the bits of the fixed-point number. Read more

Shifts to the left by n bits, wrapping the truncated bits to the right end. Read more

Shifts to the right by n bits, wrapping the truncated bits to the left end. Read more

Returns true if the number is zero. Read more

Returns the distance from self to other. Read more

Returns the mean of self and other. Read more

Returns the reciprocal. Read more

Multiply and add. Returns self × mul + add. Read more

Multiply and accumulate. Adds (a × b) to self. Read more

Euclidean division by an integer. Read more

Remainder for Euclidean division. Read more

Euclidean division by an integer. Read more

Remainder for Euclidean division by an integer. Read more

Checked negation. Returns the negated value, or None on overflow. Read more

Checked addition. Returns the sum, or None on overflow. Read more

Checked subtraction. Returns the difference, or None on overflow. Read more

Checked multiplication. Returns the product, or None on overflow. Read more

Checked division. Returns the quotient, or None if the divisor is zero or on overflow. Read more

Checked remainder. Returns the remainder, or None if the divisor is zero. Read more

Checked reciprocal. Returns the reciprocal, or None if self is zero or on overflow. Read more

Checked multiply and add. Returns self × mul + add, or None on overflow. Read more

Checked multiply and accumulate. Adds (a × b) to self, or returns None on overflow. Read more

Checked remainder for Euclidean division. Returns the remainder, or None if the divisor is zero or the division results in overflow. Read more

Checked remainder for Euclidean division. Returns the remainder, or None if the divisor is zero. Read more

Checked multiplication by an integer. Returns the product, or None on overflow. Read more

Checked division by an integer. Returns the quotient, or None if the divisor is zero or if the division results in overflow. Read more

Checked fixed-point remainder for division by an integer. Returns the remainder, or None if the divisor is zero or if the division results in overflow. Read more

Checked Euclidean division by an integer. Returns the quotient, or None if the divisor is zero or if the division results in overflow. Read more

Checked remainder for Euclidean division by an integer. Returns the remainder, or None if the divisor is zero or if the remainder results in overflow. Read more

Checked shift left. Returns the shifted number, or None if rhs ≥ the number of bits. Read more

Checked shift right. Returns the shifted number, or None if rhs ≥ the number of bits. Read more

Checked distance. Returns the distance from self to other, or None on overflow. Read more

Saturated negation. Returns the negated value, saturating on overflow. Read more

Saturating addition. Returns the sum, saturating on overflow. Read more

Saturating subtraction. Returns the difference, saturating on overflow. Read more