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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,
> Circle<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 Circle to another Circle
///
/// # Description
///
/// Performs addition between two Circles, handling special cases according to mathematical principles. 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 abnormal Circles (Zeros, vanished, exploded or undefined) and handles these cases
/// 1. Aligns fractions by shifting the larger value left based on exponent difference
/// 2. Adds the aligned values for both real and imaginary components simultaneously
/// 3. Normalizes the result and adjusts exponent accordingly
/// 4. Escapes for underflow if necessary (vanished), 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 vanished plus vanished state
/// - `[↓]` + `[#]` or `[#]` + `[↓]` ➔ `[#]` The finite Circle
/// - `[0]` + `[#]` or `[#]` + `[0]` ➔ `[#]` The non-Zero Circle
/// - `[0]` + `[0]` ➔ `[0]` Zero
/// - `[#]` + `[#]` ➔ `[#]` or `[↑]` or `[↓]` A finite, exploded or vanished Circle
///
/// # Examples
///
/// ```rust
/// use spirix::{Circle, CircleF5E3};
///
/// // Adding finite Circles let a = Circle::<i32, i8>::from((3_i32, 4_i32)); let b = CircleF5E3::from((1_i32, 2_i32)); let sum = a + b; assert!(sum.r() == 4_i32); assert!(sum.i() == 6_i32);
///
/// // Adding with Zero assert!(a + 0_i32 == a); assert!(0_i32 + a == a);
///
/// // Adding Circles that produce Zero let pos = CircleF5E3::from((2_i32, 3_i32)); let neg = CircleF5E3::from((-2_i32, -3_i32)); assert!((pos + neg).is_zero()); assert!((neg + pos).is_zero());
///
/// // Addition with vanished Circles let tiny: CircleF5E3 = CircleF5E3::MIN_POS / 5_i32; assert!(tiny.vanished());
///
/// // Addition with exploded Circles let huge: CircleF5E3 = CircleF5E3::MAX * 5_i32; assert!(huge.exploded()); assert!((a + huge).is_undefined());
///
/// // Adding two exploded Circles assert!((huge + huge).is_undefined());
/// ```
pub(crate) fn circle_add_circle(&self, circle: &Self) -> Self {
if self.is_normal() && circle.is_normal() {
// AMBIG=0 native: dominance via unsigned-cyclic compare on stored exp (matches Scalar add/sub).
let (big, small) = if self.exponent.into_unsigned() > circle.exponent.into_unsigned() {
(self, circle)
} else {
(circle, self)
};
let exp_diff = big.exponent.wrapping_sub(&small.exponent);
// Under cmp_unsigned ordering, exp_diff (interpreted unsigned) is non-negative. If the unsigned diff exceeds FRAC_BITS, small is negligible against big.
let frac_bits_e: E = Self::fraction_bits().as_();
if exp_diff.into_unsigned() >= frac_bits_e.into_unsigned() {
return *big;
}
// AMBIG=0 native unified pipeline (mirrors Scalar add). Circle's N1 inflation is sign_extend — the explicit sign bit at MSB means widening preserves the signed value without needing the XOR mask Scalar's N0 inflate applies.
let shift: isize = exp_diff.saturate();
let big_r = big.real.sign_extend().w_shl(shift);
let big_i = big.imaginary.sign_extend().w_shl(shift);
let small_r = small.real.sign_extend();
let small_i = small.imaginary.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 Self::ZERO;
}
let leading_r = result_r.leading_same();
let leading_i = result_i.leading_same();
let leading = leading_r.min(leading_i);
// Result exp = small.exp + delta, delta ∈ [-FRAC, FRAC+1]. Delta is bounded so the only escape transition is offset landing on AMBIG = 0, which IS the exploded signal — no explicit bounds check needed. The canonical-N1 fraction shape is the same for normal and exploded outputs (Circle's exploded constants are pos_one_normal / neg_one_normal at AMBIG exp), so a single shift formula handles both.
let fb = Self::fraction_bits();
let delta: isize = fb.wrapping_sub(leading).wrapping_add(1);
let delta_e: E = delta.as_();
let offset = small.exponent.wrapping_add(&delta_e);
// Shift to canonical N1 (wide leading = FRAC + 1). Net shift relative to wide = leading - (FRAC + 1).
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 Self {
real: canonical_r.deflate(),
imaginary: canonical_i.deflate(),
exponent: offset,
};
}
// Escape-class handling (mirrors Scalar add ordering: undefined first, then infinity absorbs, then zero identity, then escape pair rules).
if self.is_undefined() {
return *self;
}
if circle.is_undefined() {
return *circle;
}
// Infinity absorbs everything. [∞] is the signless Riemann-sphere point reached only by n/0; −∞ is a no-op so [∞]−[∞] = [∞] too.
if self.is_infinite() || circle.is_infinite() {
return Self::INFINITY;
}
if self.is_zero() {
return *circle;
}
if circle.is_zero() {
return *self;
}
if self.exploded() && circle.exploded() {
return Self {
real: TRANSFINITE_PLUS_TRANSFINITE.prefix.sa(),
imaginary: TRANSFINITE_PLUS_TRANSFINITE.prefix.sa(),
exponent: Self::ambiguous_exponent(),
};
}
if self.vanished() && circle.vanished() {
return Self {
real: VANISHED_PLUS_VANISHED.prefix.sa(),
imaginary: VANISHED_PLUS_VANISHED.prefix.sa(),
exponent: Self::ambiguous_exponent(),
};
}
if self.exploded() {
if circle.vanished() {
return *self;
}
return Self {
real: TRANSFINITE_PLUS_FINITE.prefix.sa(),
imaginary: TRANSFINITE_PLUS_FINITE.prefix.sa(),
exponent: Self::ambiguous_exponent(),
};
}
if circle.exploded() {
if self.vanished() {
return *circle;
}
return Self {
real: FINITE_PLUS_TRANSFINITE.prefix.sa(),
imaginary: FINITE_PLUS_TRANSFINITE.prefix.sa(),
exponent: Self::ambiguous_exponent(),
};
}
if self.vanished() {
return *circle;
}
if circle.vanished() {
return *self;
}
*self
}
}