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use crate::core::integer::*;
use crate::core::undefined::*;
use crate::{Circle, CircleConstants, Integer, Scalar, ScalarConstants};
use core::ops::*;
use i256::I256;
use num_traits::{AsPrimitive, WrappingAdd, WrappingMul, WrappingNeg, WrappingSub};
#[allow(private_bounds)]
impl<
F: Integer
+ FullInt
+ Shl<isize, Output = F>
+ Shr<isize, Output = F>
+ Shl<F, Output = F>
+ Shr<F, Output = F>
+ Shl<E, Output = F>
+ Shr<E, Output = F>
+ WrappingNeg
+ WrappingAdd
+ WrappingMul
+ WrappingSub,
E: Integer
+ FullInt
+ Shl<isize, Output = E>
+ Shr<isize, Output = E>
+ Shl<E, Output = E>
+ Shr<E, Output = E>
+ Shl<F, Output = E>
+ Shr<F, Output = E>
+ WrappingNeg
+ WrappingAdd
+ WrappingMul
+ WrappingSub,
> Scalar<F, E>
where
Circle<F, E>: CircleConstants,
Scalar<F, E>: ScalarConstants,
u8: AsPrimitive<F>,
u16: AsPrimitive<F>,
u32: AsPrimitive<F>,
u64: AsPrimitive<F>,
u128: AsPrimitive<F>,
usize: AsPrimitive<F>,
i8: AsPrimitive<F>,
i16: AsPrimitive<F>,
i32: AsPrimitive<F>,
i64: AsPrimitive<F>,
i128: AsPrimitive<F>,
isize: AsPrimitive<F>,
I256: From<F>,
u8: AsPrimitive<E>,
u16: AsPrimitive<E>,
u32: AsPrimitive<E>,
u64: AsPrimitive<E>,
u128: AsPrimitive<E>,
usize: AsPrimitive<E>,
i8: AsPrimitive<E>,
i16: AsPrimitive<E>,
i32: AsPrimitive<E>,
i64: AsPrimitive<E>,
i128: AsPrimitive<E>,
isize: AsPrimitive<E>,
I256: From<E>,
{
/// Adds this Scalar to a Circle
///
/// # Description
///
/// Performs addition between a Scalar and a Circle, adding the Scalar value to the real component of the Circle while leaving the imaginary component unchanged (except for normalization). Returns a finite Circle unless the result exceeds representable range, in which case it may return an exploded or vanished Circle.
///
/// Addition process:
/// 0. Checks for any escaped (vanished, exploded, infinity, or undefined) values and handles these first
/// 1. Checks for Zeros and returns the appropriate result
/// 2. Aligns fractions by shifting the smaller value right based on exponent difference
/// 3. Adds the Scalar to the real component of the Circle
/// 4. Normalizes result and adjusts exponent, considering both components
/// 5. Escapes for underflow if necessary, overflow is naturally handled by escaped exponent alignment
///
/// # Returns
///
/// - `[℘ ]` ➔ `[℘ ]` First undefined state encountered
/// - `[∞]` + `[∞]` ➔ `[℘ ↑+↑]` Undefined exploded plus exploded state
/// - `[∞]` + `[#]` ➔ `[℘ ↑+]` Undefined exploded plus finite state
/// - `[#]` + `[∞]` ➔ `[℘ +↑]` Undefined finite plus exploded state
/// - `[↑]` + `[↑]` ➔ `[℘ ↑+↑]` Undefined exploded plus exploded state
/// - `[↑]` + `[#]` ➔ `[℘ ↑+]` Undefined exploded plus finite state
/// - `[#]` + `[↑]` ➔ `[℘ +↑]` Undefined finite plus exploded state
/// - `[↓]` + `[↓]` ➔ `[℘ ↓+↓]` Undefined vanished plus vanished state
/// - `[↓]` + `[#]` ➔ `[#]` The Circle unchanged
/// - `[#]` + `[↓]` ➔ `[#]` The Scalar as real part, unchanged imaginary
/// - `[0]` + `[#]` ➔ `[#]` The Circle unchanged
/// - `[#]` + `[0]` ➔ `[#, 0i]` The Scalar as real part, zero imaginary
/// - `[#]` + `[#]` ➔ `[#]` or `[↑]` or `[↓]` A finite, exploded or vanished Circle
///
/// # Examples
///
/// ```rust
/// use spirix::{Scalar, Circle, ScalarF5E3, CircleF5E3};
///
/// // Adding a Scalar to a Circle let a = Scalar::<i32, i8>::from(3_i32); let b = CircleF5E3::from((4_i32, 2_i32)); let sum = a + b; assert!(sum.r() == 7_i32); assert!(sum.i() == 2_i32);
///
/// // Adding with Zero assert!(ScalarF5E3::ZERO + b == b);
///
/// // Adding with infinity stays infinite let infinity: ScalarF5E3 = ScalarF5E3::ONE / 0_i32; assert!((infinity + b).is_infinite());
///
/// // Addition with vanished values let tiny: ScalarF5E3 = ScalarF5E3::MIN_POS / 5_i32; assert!(tiny.vanished()); assert!((tiny + b) == b);
///
/// // Addition with exploded values let huge: ScalarF5E3 = ScalarF5E3::MAX * 5_i32; assert!(huge.exploded()); assert!((huge + b).is_undefined());
///
/// // Adding two exploded values let huge_circle: CircleF5E3 = CircleF5E3::MAX * 3_i32; assert!((huge + huge_circle).is_undefined());
/// ```
pub(crate) fn scalar_add_circle(&self, circle: &Circle<F, E>) -> Circle<F, E> {
if self.is_normal() && circle.is_normal() {
// AMBIG=0 unified pipeline. self is Scalar (N0); convert fraction to N1 before sign_extend; Scalar's imaginary contribution is 0.
let self_is_big = self.exponent.into_unsigned() > circle.exponent.into_unsigned();
let (big_exp, small_exp) = if self_is_big {
(self.exponent, circle.exponent)
} else {
(circle.exponent, self.exponent)
};
let exp_diff = big_exp.wrapping_sub(&small_exp);
let frac_bits_e: E = Self::fraction_bits().as_();
if exp_diff.into_unsigned() >= frac_bits_e.into_unsigned() {
return if self_is_big {
Circle {
real: (self.fraction >> 1isize) ^ F::min_value(),
imaginary: F::zero(),
exponent: self.exponent,
}
} else {
*circle
};
}
let shift: isize = exp_diff.saturate();
let scalar_n1 = (self.fraction >> 1isize) ^ F::min_value();
let (big_r, big_i, small_r, small_i) = if self_is_big {
(
scalar_n1.sign_extend().w_shl(shift),
F::zero().sign_extend(),
circle.real.sign_extend(),
circle.imaginary.sign_extend(),
)
} else {
(
circle.real.sign_extend().w_shl(shift),
circle.imaginary.sign_extend().w_shl(shift),
scalar_n1.sign_extend(),
F::zero().sign_extend(),
)
};
let result_r = big_r.w_add(small_r);
let result_i = big_i.w_add(small_i);
if result_r.w_is_zero() && result_i.w_is_zero() {
return Circle::<F, E>::ZERO;
}
let leading_r = result_r.leading_same();
let leading_i = result_i.leading_same();
let leading = leading_r.min(leading_i);
let fb = Self::fraction_bits();
let delta: isize = fb.wrapping_sub(leading).wrapping_add(1);
let delta_e: E = delta.as_();
let offset = small_exp.wrapping_add(&delta_e);
let shl_amount = leading.wrapping_sub(fb).wrapping_sub(1);
let canonical_r = if shl_amount >= 0 {
result_r.w_shl(shl_amount)
} else {
result_r.w_shr(shl_amount.wrapping_neg())
};
let canonical_i = if shl_amount >= 0 {
result_i.w_shl(shl_amount)
} else {
result_i.w_shr(shl_amount.wrapping_neg())
};
return Circle::<F, E> {
real: canonical_r.deflate(),
imaginary: canonical_i.deflate(),
exponent: offset,
};
}
// Escape-class handling (at least one operand is non-normal). Mirrors scalar_add_scalar's order: undefined → INFINITY-absorbs → zero identity → escape combinations.
{
if self.is_undefined() {
return Circle {
real: self.fraction,
imaginary: self.fraction,
exponent: self.exponent,
};
}
if circle.is_undefined() {
return *circle;
}
// [∞] absorbs.
if self.is_infinite() || circle.is_infinite() {
return Circle::<F, E>::INFINITY;
}
// Zero identity.
if self.is_zero() {
return *circle;
}
if circle.is_zero() {
return Circle::<F, E>::from_ri(*self, Scalar::<F, E>::ZERO);
}
if self.exploded() && circle.exploded() {
return Circle {
real: TRANSFINITE_PLUS_TRANSFINITE.prefix.sa(),
imaginary: TRANSFINITE_PLUS_TRANSFINITE.prefix.sa(),
exponent: Self::ambiguous_exponent(),
};
}
if self.vanished() && circle.vanished() {
return Circle {
real: VANISHED_PLUS_VANISHED.prefix.sa(),
imaginary: VANISHED_PLUS_VANISHED.prefix.sa(),
exponent: Self::ambiguous_exponent(),
};
}
// Self exploded: exp + van = exp; exp + normal = [℘].
if self.exploded() {
if circle.vanished() {
return Circle::<F, E>::from_ri(*self, Scalar::<F, E>::ZERO);
}
return Circle {
real: TRANSFINITE_PLUS_FINITE.prefix.sa(),
imaginary: TRANSFINITE_PLUS_FINITE.prefix.sa(),
exponent: Self::ambiguous_exponent(),
};
}
// Circle exploded: van + exp = exp; normal + exp = [℘].
if circle.exploded() {
if self.vanished() {
return *circle;
}
return Circle {
real: FINITE_PLUS_TRANSFINITE.prefix.sa(),
imaginary: FINITE_PLUS_TRANSFINITE.prefix.sa(),
exponent: Self::ambiguous_exponent(),
};
}
// Single vanished (other is normal — zero/exp/inf/undef already handled).
if self.vanished() {
return *circle;
}
if circle.vanished() {
return Circle::<F, E>::from_ri(*self, Scalar::<F, E>::ZERO);
}
// Fallthrough — at least one non-normal but no class matched (shouldn't reach).
Circle::<F, E>::from_ri(*self, Scalar::<F, E>::ZERO)
}
}
}