fixed

• The crate now requires rustc version 1.93.0 or later.
  • The unchecked_neg method was added to all signed fixed-point numbers and to the FixedSigned trait.
  • The following methods were added to all fixed-point numbers and to the Fixed trait:
    • unchecked_shl, unchecked_shr

• The crate now requires rustc version 1.85.0 or later.
  • All methods starting with unwrapped_ were renamed to start with strict_. The old method names are deprecated.
  • The Unwrapped wrapper was renamed to Strict. The old name is deprecated.
  • Bug fix: the compat-readonly-static optional feature was added to fix an issue on some platforms where statics are readonly (issue 74, merge request 14).
  • Bug fix: some numbers were being formatted incorrectly when using a defined precision (merge request 15).
  • The [az crate] dependency was updated to version 1.3.
  • The new defmt optional feature was added to support logging using the [defmt crate] (issue 70).
  • For the experimental feature num-traits, the following traits were implemented for all fixed-point numbers:
    • Euclid, CheckedEuclid

• The crate now requires rustc version 1.83.0 or later.
  • The following methods were added to all fixed-point numbers, to the Fixed trait, and to the Saturating, Wrapping and Unwrapped wrappers:
    • unbounded_shl, unbounded_shr
    • from_ascii, from_ascii_binary, from_ascii_octal, from_ascii_hex
    • saturating_from_ascii, saturating_from_ascii_binary, saturating_from_ascii_octal, saturating_from_ascii_hex
    • wrapping_from_ascii, wrapping_from_ascii_binary, wrapping_from_ascii_octal, wrapping_from_ascii_hex
    • unwrapped_from_ascii, unwrapped_from_ascii_binary, unwrapped_from_ascii_octal, unwrapped_from_ascii_hex
    • overflowing_from_ascii, overflowing_from_ascii_binary, overflowing_from_ascii_octal, overflowing_from_ascii_hex
  • The cast_unsigned method was added to all signed fixed-point numbers, to their Saturating, Wrapping and Unwrapped wrappers, and to the Fixed trait.
  • The cast_signed method was added to all unsigned fixed-point numbers, to their Saturating, Wrapping and Unwrapped wrappers, and to the Fixed trait.
  • The following methods are now usable in constant context:
    • mul_acc, checked_mul_acc, saturating_mul_acc, wrapping_mul_acc, unwrapped_mul_acc, overflowing_mul_acc
  • Now ParseFixedError implements [Error] even when the std optional feature is disabled.

• The crate now requires rustc version 1.79.0 or later.
  • The following methods were added to all fixed-point numbers and to the Fixed trait:
    • unchecked_add, unchecked_sub, unchecked_mul_int
  • For all fixed-point numbers and the Fixed trait, the following methods were renamed. The old method names are deprecated.
    • round_ties_to_even renamed to round_ties_even
    • checked_round_ties_to_even renamed to checked_round_ties_even
    • saturating_round_ties_to_even renamed to saturating_round_ties_even
    • wrapping_round_ties_to_even renamed to wrapping_round_ties_even
    • unwrapped_round_ties_to_even renamed to unwrapped_round_ties_even
    • overflowing_round_ties_to_even renamed to overflowing_round_ties_even
  • The following constants were added to the consts module and as associated constants to fixed-point types:
    • SQRT_2PI, FRAC_1_SQRT_2PI
  • The experimental feature nightly-float was added.
  • For the experimental feature num-traits, the following traits were implemented for all fixed-point numbers:
    • ConstZero, ConstOne
    • ToBytes, FromBytes

• The hypot method was added to all fixed-point numbers, to the Fixed trait, and to the Saturating, Wrapping and Unwrapped wrappers.
  • The following methods were added to all fixed-point numbers and to the Fixed trait:
    • checked_hypot, saturating_hypot, wrapping_hypot, unwrapped_hypot, overflowing_hypot
    • saturating_sqrt, wrapping_sqrt, unwrapped_sqrt, overflowing_sqrt

• The sqrt method was added to all fixed-point numbers, to the Fixed trait, and to the Saturating, Wrapping and Unwrapped wrappers.
  • The checked_sqrt method was added to all fixed-point numbers and to the Fixed trait.

• Bug fix: formatting numbers with [LowerExp] and [UpperExp] was producing incorrect output when rounding incremented a zero in the middle of a string, for example format!("{:.2e}", I16F16::lit("9.099")).

• Bug fix: formatting numbers with [LowerExp] and [UpperExp] was producing incorrect output for very small numbers, for example format!("{:e}", I16F16::DELTA).
  • Bug fix: formatting numbers with [LowerExp] and [UpperExp] was panicking for some cases of positive exponents and small precision, for example format!("{:.1e}", I16F16::from_num(1001)).
  • Bug fix: formatting numbers with [LowerExp] and [UpperExp] was producing incorrect output when rounding adds a more significant digit, for example format!("{:.1e}", I16F16::lit("0.999")).
  • The experimental borsh feature was promoted to an optional feature, and the optional [borsh crate] dependency was updated to version 1.0.

• The crate now requires rustc version 1.71.0 or later.
  • The saturating_div_int method was added to all fixed-point numbers and to the Fixed trait.
  • The Saturating wrapper was added.

• Bug fix: comparison of signed and unsigned numbers where the signed number was wider than the unsigned number was truncating bits from the signed number (issue 57).
  • The [half crate] dependency is now satisfied by version 1.8 as well as [version 2][half-2].

• String parsing of binary, octal and hexadecimal strings now supports base-2 exponents starting with the separator “p” or “P”.
  • Bug fix: int_log10, int_log, checked_int_log10 and checked_int_log were panicking or returning incorrect values for fixed-point numbers with no integer bits.

• The errors from the [lit][f-l-1-22] method have been improved.
  • The track_caller attribute is now applied to many more inline functions that can panic.

• String parsing now supports an optional exponent for all supported radices.
  • The lit method was added to all fixed-point numbers. This is useful to write fixed-point numbers literally in code and also works in constant context.
  • All fixed-point numbers now implement [LowerExp] and [UpperExp].
  • The Fixed and FixedBits traits now have the added supertraits [Binary], [Octal], [LowerHex], [UpperHex], [LowerExp] and [UpperExp].
  • The Wrapping and Unwrapped wrappers now implement [Binary], [Octal], [LowerHex], [UpperHex], [LowerExp] and [UpperExp].
  • The implementation of [Debug] for fixed-point numbers now has more relaxed constraints on the fractional bits generic parameter: now Frac only needs to implement Unsigned.

• Comparisons involving fixed-point numbers now have more relaxed constraints on the fractional bits generic parameter: now Frac only needs to implement Unsigned.
  • Better code should now be generated when comparing a fixed-point number to another fixed-point number.
  • The following methods were added to the F128 struct:
    • min, max
    • clamp

• The TRY_ONE associated constant was added to the Fixed trait.
  • The TRY_NEG_ONE associated constant was added to the FixedSigned trait.
  • The const_from_fixed and const_from_int methods were added to all fixed-point numbers.
  • The const_fixed_from_int macro is now deprecated.
  • The following associated constants were added to the F128 struct:
    • DIGITS
    • MIN_10_EXP, MAX_10_EXP
  • F128 now implements [From] for conversions from [f64], [f32], f16 and bf16.
  • The <code>fixed::f128::consts</code> module was added with F128 basic mathematical constants.

• Bug fix: comparison of and conversion from subnormal floating-point numbers to fixed-point numbers were off by a factor of 2.
  • The following associated constants were added to the FixedBits trait:
    • MIN, MAX
    • IS_SIGNED, BITS
  • FixedEquiv is now a supertrait of the FixedBits trait.
  • FixedBits now has more supertraits from the [num-traits crate] if the num-traits experimental feature is enabled.

• Bug fix: checked division methods were panicking when dividing MIN by <code>-DELTA</code> for fixed-point numbers with zero integer bits, that is when all bits are fractional bits (issue 51).
  • The following methods were added to all fixed-point numbers, to the Fixed trait, and to the Wrapping and Unwrapped wrappers:
    • int_log, checked_int_log
  • The F128 struct was added to replace the F128Bits struct which is now deprecated. F128 has standard floating-point ordering and various classification methods and associated constants.
  • The from_str_dec method was added to the Unwrapped wrapper.
  • The Contiguous trait from the [bytemuck crate] was implemented for all fixed-point numbers, added as a supertrait to the Fixed trait, and implemented for the Wrapping and Unwrapped wrappers.

• The [half crate] dependency was updated to version 2.
  • The inherent from_str method was added as a const function to all fixed-point numbers so that it can be use in constant context.
  • The following methods are now const functions:
    • saturating_from_str, wrapping_from_str, overflowing_from_str
    • from_str_binary, saturating_from_str_binary, wrapping_from_str_binary, overflowing_from_str_binary
    • from_str_octal, saturating_from_str_octal, wrapping_from_str_octal, overflowing_from_str_octal
    • from_str_hex, saturating_from_str_hex, wrapping_from_str_hex, overflowing_from_str_hex
    • checked_div, saturating_div, wrapping_div, unwrapped_div, overflowing_div
    • recip, checked_recip, saturating_recip, wrapping_recip, unwrapped_recip, overflowing_recip
    • checked_rem_int, unwrapped_rem_int
    • div_euclid, checked_div_euclid, saturating_div_euclid, wrapping_div_euclid, unwrapped_div_euclid, overflowing_div_euclid
    • div_euclid_int, checked_div_euclid_int, saturating_div_euclid_int, wrapping_div_euclid_int, unwrapped_div_euclid_int, overflowing_div_euclid_int
    • rem_euclid_int, checked_rem_euclid_int, saturating_rem_euclid_int, wrapping_rem_euclid_int, unwrapped_rem_euclid_int, overflowing_rem_euclid_int
    • lerp, checked_lerp, saturating_lerp, wrapping_lerp, unwrapped_lerp, overflowing_lerp
    • inv_lerp, checked_inv_lerp, saturating_inv_lerp, wrapping_inv_lerp, unwrapped_inv_lerp, overflowing_inv_lerp
  • The following methods were added to all fixed-point numbers and to the Fixed trait:
    • unwrapped_from_str, unwrapped_from_str_binary, unwrapped_from_str_octal, unwrapped_from_str_hex
  • Bug fix: The following methods were not panicking on all errors as required for the Unwrapped wrapper:
    • <code><Unwrapped<F> as [FromStr][FromStr]>::[from_str][FromStr::from_str]</code>
    • <code>Unwrapped<F>::from_str_binary</code>
    • <code>Unwrapped<F>::from_str_octal</code>
    • <code>Unwrapped<F>::from_str_hex</code>

• Cargo.toml now includes the [rust-version] field ([merge request 11]).

• The crate now requires rustc version 1.61.0 or later.
  • The NEG_ONE constant was added to all signed fixed-point numbers that can represent the value −1.
  • The add_prod method was added to all fixed-point numbers, to the Fixed trait, and to the Wrapping and Unwrapped wrappers.
  • The following methods were added to all fixed-point numbers and to the Fixed trait:
    • checked_add_prod, saturating_add_prod, wrapping_add_prod, unwrapped_add_prod, overflowing_add_prod
  • The following methods are now const functions:
    • int, frac, round_to_zero
    • ceil, checked_ceil, saturating_ceil, wrapping_ceil, unwrapped_ceil, overflowing_ceil
    • floor, checked_floor, saturating_floor, wrapping_floor, unwrapped_floor, overflowing_floor
    • round, checked_round, saturating_round, wrapping_round, unwrapped_round, overflowing_round
    • round_ties_to_even, checked_round_ties_to_even, saturating_round_ties_to_even, wrapping_round_ties_to_even, unwrapped_round_ties_to_even, overflowing_round_ties_to_even
    • int_log2, checked_int_log2, int_log10, checked_int_log2
    • wide_mul, wide_mul_unsigned, wide_mul_signed
    • wide_div, wide_sdiv, wide_div_unsigned, wide_sdiv_signed
    • checked_mul, saturating_mul, wrapping_mul, unwrapped_mul, overflowing_mul
    • mul_add, checked_mul_add, saturating_mul_add, wrapping_mul_add, unwrapped_mul_add, overflowing_mul_add
    • signum, checked_signum, saturating_signum, wrapping_signum, unwrapped_signum, overflowing_signum

• The following methods were added to all fixed-point signed numbers up to 64 bits wide: * wide_mul_unsigned * wide_sdiv * wide_div_unsigned
  • The following methods were added to all fixed-point unsigned numbers up to 64 bits wide:
    • wide_mul_signed
    • wide_sdiv_signed

• The next_multiple_of method was added to all fixed-point numbers, to the Fixed trait, and to the Wrapping and Unwrapped wrappers.
  • The following methods were added to all fixed-point numbers and to the Fixed trait:
    • abs_diff
    • checked_next_multiple_of, saturating_next_multiple_of, wrapping_next_multiple_of, unwrapped_next_multiple_of, overflowing_next_multiple_of
  • The following methods were added to all signed fixed-point numbers, to the FixedSigned trait, and to the Wrapping and Unwrapped wrappers for signed numbers:
    • add_unsigned, sub_unsigned
    • checked_add_unsigned, saturating_add_unsigned, wrapping_add_unsigned, unwrapped_add_unsigned, overflowing_add_unsigned
    • checked_sub_unsigned, saturating_sub_unsigned, wrapping_sub_unsigned, unwrapped_sub_unsigned, overflowing_sub_unsigned
  • The following methods were added to all unsigned fixed-point numbers, to the FixedUnsigned trait, and to the Wrapping and Unwrapped wrappers for unsigned numbers:
    • add_signed, sub_signed
    • checked_add_signed, saturating_add_signed, wrapping_add_signed, unwrapped_add_signed, overflowing_add_signed
    • checked_sub_signed, saturating_sub_signed, wrapping_sub_signed, unwrapped_sub_signed, overflowing_sub_signed
  • Supertraits were added to <code>Fixed::Bits</code> and to <code>Fixed::NonZeroBits</code> in order to allow conversions and operations in generic functions.
  • The [az crate] dependency was updated to version 1.2.

• The [const_fixed_from_int][cffi-1-13] macro now accepts a visibility qualifier ([merge request 10]).

• The [AddAssign], [SubAssign], [MulAssign], [DivAssign], [RemAssign], [BitAndAssign], [BitOrAssign] and [BitXorAssign] traits for <code>Wrapping<F></code> and <code>Unwrapped<F></code> are now also implemented with F as the type of the right-hand side operand.
  • Bug fix: compilation with certain flags was hanging for the thumbv6m target because of a rustc/LLVM issue. This version should not trigger the rustc/LLVM issue (issue 45).

• The crate now requires rustc version 1.57.0 or later.
  • The wide_div method was added to all fixed-point numbers up to 64 bits wide ([issue 25]).
  • The following methods are now const functions:
    • unwrapped_neg, unwrapped_add, unwrapped_sub
    • unwrapped_mul_int
    • unwrapped_shl, unwrapped_shr
    • unwrapped_abs, unwrapped_dist
    • unwrapped_next_power_of_two

• The following methods were added to all fixed-point numbers, to the Fixed trait, and to the Wrapping and Unwrapped wrappers: * lerp * inv_lerp
  • The following methods were added to all fixed-point numbers and to the Fixed trait:
    • checked_lerp, saturating_lerp, wrapping_lerp, unwrapped_lerp, overflowing_lerp
    • checked_inv_lerp, saturating_inv_lerp, wrapping_inv_lerp, unwrapped_inv_lerp, overflowing_inv_lerp
  • The [typenum crate] dependency was updated to version 1.14.
  • The LeEqU8, LeEqU16, LeEqU32, LeEqU64 and LeEqU128 traits no longer have a direct 'static constraint, as it is a constraint of their supertrait Unsigned since typenum version 1.14. This fixes a potential compatibility issue introduced in version 1.9.0.
  • An experimental feature was added to enable serialization using the [borsh crate] (merge request 9).

• The crate now requires rustc version 1.53.0 or later.
  • <code>{[Div][Div],[DivAssign][DivAssign],[Rem][Rem],[RemAssign][RemAssign]}<[NonZeroU32][NonZeroU32]></code> are now implemented for FixedU32, and similar for all other unsigned fixed-point numbers.
  • <code>{[Rem][Rem],[RemAssign][RemAssign]}<[NonZeroI32][NonZeroI32]></code> are now implemented for FixedI32, and similar for all other signed fixed-point numbers.
  • The new arbitrary optional feature was added to implement the Arbitrary trait provided by the [arbitrary crate] for all fixed-point numbers (issue 37).

• Fixed-point numbers can now be formatted as hexadecimal with [Debug] similarly to primitive integers, for example formatting with {:X?} will produce upper-case hexadecimal fixed-point numbers.
  • The following methods were added to all fixed-point numbers, to the Fixed trait, and to the Wrapping and Unwrapped wrappers:
    • is_zero
    • dist
  • The following methods were added to all fixed-point numbers and to the Fixed trait:
    • checked_dist, saturating_dist, wrapping_dist, unwrapped_dist, overflowing_dist
  • The unsigned_dist method was added to all signed fixed-point types and to the FixedSigned trait.
  • The following associated types and provided methods were added to the Fixed trait:
    • Signed, Unsigned
    • get_signed, get_unsigned
    • get_signed_mut, get_unsigned_mut
  • The new trait FixedEquiv was added.
  • The following traits from the [bytemuck crate] were implemented for all fixed-point numbers, added as supertraits to the Fixed trait, and implemented for the Wrapping and Unwrapped wrappers (issue 31).
    • Zeroable, Pod
    • TransparentWrapper

Compatibility notes

• Now the [Debug] implementation for Wrapping outputs the value only without “Wrapping()”, and the [Debug] implementation for Unwrapped outputs the value only without “Unwrapped()”.
• The LeEqU8, LeEqU16, LeEqU32, LeEqU64 and LeEqU128 traits now have a 'static constraint. This should have no practical side effects, since these traits are a convenience feature and already have the Unsigned marker trait as a supertrait, and the types that implement Unsigned are 'static.
• The FixedOptionalFeatures trait was not sealed, which was as an oversight. Now it is sealed, and the documentation explicitly states that the trait should not be used directly.

• The following constants and method were added to all fixed-point numbers, to the Fixed trait, and to the Wrapping and Unwrapped wrappers: * ZERO, DELTA * mul_acc
  • The ONE constant was added to all fixed-point numbers that can represent the value 1.
  • The following methods were added to all fixed-point numbers and to the Fixed trait:
    • checked_mul_acc, saturating_mul_acc, wrapping_mul_acc, unwrapped_mul_acc, overflowing_mul_acc
    • saturating_div_euclid_int, saturating_rem_euclid_int
    • unwrapped_rem, unwrapped_rem_euclid
    • unwrapped_rem_int
  • The following methods are now const functions:
    • checked_rem
    • rem_euclid, checked_rem_euclid
    • checked_div_int, wrapping_div_int, unwrapped_div_int, overflowing_div_int
  • The following methods were added to all fixed-point numbers:
    • const_not
    • const_bitand, const_bitor, const_bitxor
  • Many methods were marked with the must_use attribute.

• The crate now requires rustc version 1.50.0 or later.
  • The following methods are now const functions:
    • next_power_of_two, checked_next_power_of_two, wrapping_next_power_of_two
  • The following constant and methods were added to all fixed-point numbers, to the Fixed trait, and to the Wrapping and Unwrapped wrappers:
    • IS_SIGNED
    • from_be, from_le
    • to_be, to_le
    • swap_bytes
    • reverse_bits
    • mean
  • The following methods were added to the Wrapping and Unwrapped wrappers:
    • from_be_bytes, from_le_bytes, from_ne_bytes
    • to_be_bytes, to_le_bytes, to_ne_bytes
  • The following methods were added to all unsigned fixed-point types, to the FixedUnsigned trait, and to the Wrapping and Unwrapped wrappers for unsigned numbers:
    • significant_bits
    • highest_one
  • The signed_bits method was added to all signed fixed-point types, to the FixedSigned trait, and to the Wrapping and Unwrapped wrappers for signed numbers.
  • The following constants, which are available in other programming language standard libraries, were added to the consts module and as associated constants to fixed-point types:
    • SQRT_PI (Go), FRAC_1_SQRT_PI (C++)
    • SQRT_3 (C++), FRAC_1_SQRT_3 (C++)
    • SQRT_E (Go)
    • SQRT_PHI (Go)
    • GAMMA (C++)
    • CATALAN (Julia)
  • [Sum] and [Product] are now supertraits of the Fixed trait.
  • The F128Bits type was added to support conversions and comparisons between fixed-point numbers and binary128 floating-point numbers.
  • The features that previously required the az and f16 optional features are now always provided. The az and f16 optional features are now deprecated and have no effect.
  • For the experimental feature num-traits, the following traits were implemented for all fixed-point numbers:
    • OverflowingAdd, OverflowingSub, OverflowingMul

• The crate now requires rustc version 1.47.0 or later.
  • The optional [az crate] dependency was updated to version 1.1.
  • The unsigned_abs method was added to all signed fixed-point types and to the FixedSigned trait.
  • The following methods are now const functions:
    • checked_neg, checked_add, checked_sub, checked_mul_int, checked_shl, checked_shr, checked_abs
  • The unwrapped_to_fixed method was added to the ToFixed trait.
  • The unwrapped_from_fixed method was added to the FromFixed trait.

• The wide_mul method was added to all fixed-point numbers up to 64 bits wide (issue 25).
  • Unwrapped methods for arithmetic together with the Unwrapped wrapper were added. Unwrapped methods panic on overflow, even when debug assertions are disabled, similar to how wrapping methods will wrap around even when debug assertions are enabled. (This was previously an experimental feature unwrapped.)
  • The serde-str feature was added. (This was previously an experimental feature.)
  • For the experimental feature num-traits, some missing supertraits were added to FixedOptionalFeatures.
  • Bug fix: multiplication of FixedI128 was panicking when multiplying some large negative numbers (issue 26).

• The following methods were added to all fixed-point types, to the Fixed trait, and to the Wrapping wrapper: * recip, checked_recip, saturating_recip, wrapping_recip, overflowing_recip
  • For the experimental feature num-traits, the following traits were implemented where applicable (issue 23):
    • Num
    • Signed, Unsigned
    • Inv
    • MulAdd, MulAddAssign
    • FloatConst
    • ToPrimitive, FromPrimitive
  • For the experimental feature serde-str, serialization in human-readable formats was made more convenient to write manually (issue 24). This makes it incompatible with the version in 1.3.0.

• The [MulAssign] implementation on fixed-point numbers now accepts an rhs fixed-point number with a different number of fractional bits from self.
  • The following methods were added to all fixed-point types, to the Fixed trait, and to the Wrapping wrapper:
    • mul_add, checked_mul_add, saturating_mul_add, wrapping_mul_add, overflowing_mul_add
  • The new experimental feature unwrapped was added, providing arithmetic methods that panic on overflow even when debug assertions are disabled.
  • The new experimental feature serde-str was added, which makes serialization use the number’s value in human-readable formats.

• The const_fixed_from_int! macro was added to make it easy to define constant fixed-point numbers using integer expressions (issue 20).

• The new experimental feature num-traits was added to implement some traits, and to also add the relevant traits as supertraits to the FixedOptionalFeatures trait (issue 18).

• The crate now requires rustc version 1.44.0 or later.
  • The following methods are now const functions:
    • from_be_bytes, from_le_bytes, from_ne_bytes
    • to_be_bytes, to_le_bytes, to_ne_bytes
  • All deprecated items were removed.

• The LosslessTryFrom and LosslessTryInto traits were added.
  • The following methods were added to all fixed-point types, to the Fixed trait, and to the Wrapping wrapper:
    • leading_ones, trailing_ones
  • The following method was added to unsigned fixed-point types and to the FixedUnsigned trait:
    • wrapping_next_power_of_two
  • The PHI and FRAC_1_PHI constants were added to the consts module and as associated constants to fixed-point types.

• The following methods were added to signed fixed-point types and to the FixedSigned trait: * checked_signum, saturating_signum, wrapping_signum, overflowing_signum
  • The LossyFrom and LossyInto traits were added to the prelude.
  • Casts deprecated in version 0.3.1 of the az crate were marked as deprecated.

• Bug fix: an incorrect result could be given when comparing a signed fixed-point number of type FixedI to a number that would overflow by exactly one bit when converting to FixedI.
  • The following associated constants were added to all fixed-point types, to the Fixed trait, and to the Wrapping wrapper:
    • MIN, MAX
  • The following associated constants were added to the Fixed trait and to the Wrapping wrapper:
    • INT_NBITS, FRAC_NBITS
  • The following methods were added to all fixed-point types and to the Fixed trait:
    • int_log2, int_log10
    • checked_int_log2, checked_int_log10
  • The following methods were added to the Wrapping wrapper:
    • int_log2, int_log10
  • The constants in the consts module were also added as associated constants to fixed-point types that can represent them.
  • The following methods were deprecated:
    • min_value, max_value
    • int_nbits, frac_nbits

• Bug fix: rem_euclid_int and its checked versions were handling overflow incorrectly.

• Bug fix: round_to_zero was returning incorrect results for negative whole number operands.
  • Bug fix: all remainder operations with a fixed-point LHS and an integer RHS were giving an incorrect answer (https://gitlab.com/tspiteri/fixed/issues/13).
  • Bug fix: Euclidean division operations by integers were giving an incorrect answer.
  • Rem and RemAssign were implemented for fixed-point numbers.
  • The following methods were added to all fixed-point types and to the Fixed trait:
    • checked_rem
    • div_euclid, rem_euclid
    • checked_div_euclid, checked_rem_euclid
    • saturating_div_euclid
    • wrapping_div_euclid
    • overflowing_div_euclid
  • The following methods were added to the Wrapping wrapper:
    • div_euclid, rem_euclid
    • div_euclid_int, rem_euclid_int
  • The following methods were deprecated:
    • wrapping_rem_int, overflowing_rem_int

• Wrapping now supports serialization. (Thanks: Shane Pearman)