PrimNum PrimInt PrimFloat strawman

/// Primitive number constants
trait PrimNumConstants {
    const ZERO: Self;
    const ONE: Self;

    fn zero() -> Self;  // make const?
    fn one() -> Self;
}


/// Primitive number information
trait PrimNumInfo {
    fn is_signed() -> bool;
    fn is_unsigned() -> bool;
    fn is_floating_point() -> bool;
    fn is_integer() -> bool;
    fn bit_width() -> u32;
}

/// Primitive number bounds
trait PrimNumBounds {
    fn min_value() -> Self;
    fn max_value() -> Self;
    fn min_positive_value() -> Self;
    fn epsilon() -> Self;
}

/// Primitive number checked arithmetic
trait PrimNumCheckedArithmetic {
    fn checked_add(&self, &Self) -> Option<Self>;
    fn checked_sub(&self, &Self) -> Option<Self>;
    fn checked_div(&self, &Self) -> Option<Self>;
    fn checked_mul(&self, &Self) -> Option<Self>;
    fn checked_neg(&self, &Self) -> Option<Self>;
}

/// Primitive number unchecked arithmetic
trait PrimNumUncheckedArithmetic {
    unsafe fn unchecked_add(&self, &Self) -> Self;
    unsafe fn unchecked_sub(&self, &Self) -> Self;
    unsafe fn unchecked_div(&self, &Self) -> Self;
    unsafe fn unchecked_mul(&self, &Self) -> Self;
    unsafe fn unchecked_neg(&self, &Self) -> Self;
}

/// Primitive number total ordering
trait PrimNumTotalOrder {
    fn less_than(&self, &Self) -> bool;
    fn equal(&self, &Self) -> bool;
}

/// Primitive number partial ordering
trait PrimNumPartialOrder {
    fn less_than(&self, &Self) -> bool;
    fn equal(&self, &Self) -> bool;
}

/// Primitive number
trait PrimNum
    : PrimNumInfo
    + PrimNumBounds
    + PrimNumCheckedArithmetic
    + PrimNumUncheckedArithmetic
{
    fn abs(&self) -> Self;
    fn abs_sub(&self, &Self) -> Self;
    fn signum(&self) -> Self;
    fn is_positive(&self) -> Self;
    fn is_negative(&self) -> Self;
    fn max(&self, &Self) -> &Self;
    fn min(&self, &Self) -> &Self;

    fn div_rem(&self, &Self) -> (Self, Self);
}

/// Primitive integer
trait PrimInt : PrimNum + PrimNumTotalOrder {
    type Signed : PrimInt;
    type Unsigned : PrimInt;
    fn div_floor(&self, &Self) -> Self;
    fn mod_floor(&self, &Self) -> Self;
    fn gcd(&self, &Self) -> Self;
    fn lcd(&self, &Self) -> Self;
    fn is_multiple_of(&self) -> bool;
    fn is_even(&self) -> bool;
    fn is_odd(&self) -> bool;
    fn div_mod_floor(&self, &Self) -> (Self, Self)
    fn logical_shr(self, u32) -> Self;
    fn logical_shl(self, u32) -> Self;
    fn arithmetic_shr(self, u32) -> Self;
    fn arithemtic_shl(self, u32) -> Self;
}

/// Primitive bit integer
trait PrimBitInt : PrimInt {
    fn count_ones(&self) -> u32;
    fn count_zeros(&self) -> u32;
    fn leading_zeros(&self) -> u32;
    fn trailing_zeros(&self) -> u32;
    fn leading_ones(&self) -> u32;
    fn trailing_ones(&self) -> u32;
    fn rotate_left(&self, &u32) -> Self;
    fn rotate_right(&self, &u32) -> Self;
    fn signed_shr(&self, &u32) -> Self;
    fn signed_shl(&self, &u32) -> Self;
    fn unsigned_shr(&self, &u32) -> Self;
    fn unsigned_shl(&self, &u32) -> Self;
    fn swap_bytes(&self) -> Self;
    fn from_be(&self) -> Self;
    fn from_le(&self) -> Self;
    fn to_be(&self) -> Self;
    fn to_le(&self) -> Self;
    fn ipow(self, mut u32) -> Self;
    fn to_unsigned(&self) -> Self::Unsigned;
    fn to_signed(&self) -> Self::Unsigned;
    fn parity(&self) -> u32;
    fn reset_least_significant_one(self) -> Self;
    fn set_least_significant_zero(self) -> Self;
    fn isolate_least_significant_one(self) -> Self;
    fn isolate_least_significant_zero(self) -> Self;
    fn reset_trailing_ones(self) -> Self;
    fn reset_trailing_zeros(self) -> Self;
    fn mask_trailing_zeros(self) -> Self;
    fn mask_trailing_ones(self) -> Self;
    fn mask_trailing_zeros_and_least_significant_one(self) -> Self;
    fn mask_trailing_ones_and_least_significant_zero(self) -> Self;
    fn reverse_bit_groups(self, u32, u32) -> Self;
    fn reverse_bits(self) -> Self;
    fn reverse_bit_pairs(self) -> Self;
    fn reverse_bit_nibbles(self) -> Self;
    fn reverse_byte_groups(self, u32, u32) -> Self;
    fn reverse_bytes(self) -> Self;
    fn set_bit(self, bit: u32) -> Self;
    fn reset_bit(self, bit: u32) -> Self;
    fn flip_bit(self, bit: u32) -> Self;
    fn test_bit(self, bit: u32) -> bool;
    fn reset_bits_geq(self, bit: u32) -> Self;
    fn reset_bits_leq(self, bit: u32) -> Self;
    fn set_bits_geq(self, bit: u32) -> Self;
    fn set_bits_leq(self, bit: u32) -> Self;
    fn flip_bits_geq(self, bit: u32) -> Self;
    fn flip_bits_leq(self, bit: u32) -> Self;
    fn is_pow2(self) -> bool;
    fn ceil_pow2(self)-> Self;
    fn floor_pow2(self) -> Self;
    fn is_aligned(self, alignment: u32) -> bool;
    fn align_up(self, alignment: u32) -> Self;
    fn align_down(self, alignment: u32) -> Self;
        fn outer_perfect_shuffle(self) -> Self;
    fn outer_perfect_unshuffle(self) -> Self;
    fn inner_perfect_shuffle(self) -> Self;
    fn inner_perfect_unshuffle(self) -> Self;
    fn parallel_bits_deposit(self, Self) -> Self;
    fn parallel_bits_extract(self, Self) -> Self;
}

/// Primitive signed integer (implemented only for signed ints)
trait PrimSignedInt : PrimBitInt {
    
}

/// Primitive unsigned integer (implemented only for unsigned ints)
trait PrimUnsignedInt : PrimBitInt {
    
}

/// Primitive float
trait PrimFloat : PrimNum + PrimNumPartialOrder {
    fn rounding_error() -> Self;
    fn positive_infinity() -> Self;
    fn negative_infinity() -> Self;
    fn quiet_nan() -> Self;
    fn signaling_nan() -> Self;
    fn nan() -> Self;
    fn is_nan(&self) -> bool;
    fn is_quiet_nan(&self) -> bool;
    fn is_signaling_nan(&self) -> bool;
    fn positive_zero() -> Self;
    fn negative_zero() -> Self;
    fn is_infinite(&self) -> bool;
    fn is_finite(&self) -> bool;
    fn is_positive_infinite(&self) -> bool;
    fn is_negative_infinite(&self) -> bool;
    fn is_normal(&self) -> bool;
    fn classify(&self) -> FpClass; // Normal, sub-normal, zero, infinite, nan
    fn floor(&self) -> Self;
    fn ceil(&self) -> Self;
    fn round(&self) -> Self;
    fn truncate(&self) -> Self;
    fn fractional(&self) -> Self;
    fn mul_add(&self, &Self, &Self) -> Self;
    fn reciprocal(&self) -> Self;
    fn ipow(&self, &i32) -> Self;
    fn upow(&self, &u32) -> Self;
    fn pow(&self, &Self) -> Self;
    fn sqrt(&self) -> Self;
    fn exp(&self) -> Self;
    fn exp2(&self) -> Self;
    fn ln(&self) -> Self;
    fn log(&self, Self) -> Self;
    fn log2(&self) -> Self;
    fn log10(&self) -> Self;
        fn cbrt(&self) -> Self;
    fn hypot(&self, &Self) -> Self;
    fn sin(&self) -> Self;
    fn cos(&self) -> Self;
    fn tan(&self) -> Self;
    fn asin(&self) -> Self;
    fn acos(&self) -> Self;
    fn atan(&self) -> Self;
    fn atan2(&self) -> Self;
    fn sin_cos(&self) -> Self;
    fn exp_m1(&self) -> Self;
    fn ln_1p(&self) -> Self;
    fn sinh(&self) -> Self;
    fn cosh(&self) -> Self;
    fn tanh(&self) -> Self;
    fn asinh(&self) -> Self;
    fn acosh(&self) -> Self;
    fn atanh(&self) -> Self;
    fn integer_decode(&self) -> (u64, i16, i8);

    fn fdim(&self, &Self) -> Self;  // fdim C++11

    fn erf(&self) -> Self;
    fn erfc(&self) -> Self;
    fn gamma(&self) -> Self;
    fn times_pow2(&self, Self) -> Self;
    fn times_pow_radix(&self, Self) -> Self;
    fn ilog_base(&self) -> i32;
    fn log_base(&self) -> Self;

    fn next_after(&self, &Self) -> Self;
    fn next_toward(&self, &Self) -> Self;

    fn is_unordered(&self, &Self) -> bool;

    // From Special Mathematical Functions
    fn beta(&self, &Self) -> Self;
    fn riemann_zeta(&self, &Self) -> Self;
       // Elliptic integrals
    fn elliptic_int_1st_complete(&self) -> Self;
    fn elliptic_int_2nd_complete(&self) -> Self;
    fn elliptic_int_3rd_complete(&self) -> Self;
    fn elliptic_int_1st_incomplete(&self) -> Self;
    fn elliptic_int_2nd_incomplete(&self) -> Self;
    fn elliptic_int_3rd_incomplete(&self) -> Self;

    fn exp_int(&self, ...) -> Self;

    // Cylindrical bessel functions
    fn cylindrical_bessel_1st(&self, ) -> Self;
    fn cylindrical_bessel_regular_modified(&self, ) -> Self;
    fn cylindrical_bessel_irregular_modified(&self, ) -> Self;
    fn cylindrical_bessel_neumann(&self, ) -> Self;

    // Spherical functions
    fn spherical_bessel_1st(&self, ) -> Self;
    fn spherical_associated_legendre(&self, ) -> Self;
    fn spherical_neumann(&self, ) -> Self;


    // Polynomials
    fn associated_laguerre(u32, u32) -> Self;
    fn associated_legendre(u32, u32) -> Self;

    fn hermite(&self, ...) -> Self;
    fn legendre(&self, ...) -> Self;
    fn laguerre(&self, ...) -> Self;
}