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use crate::core::integer::*;
use crate::core::undefined::*;
use crate::{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
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>,
{
/// Subtracts another Scalar from this Scalar
///
/// # Description
///
/// Performs subtraction between two Scalars, handling special cases according to mathematical principles. Returns a finite Scalar unless the result exceeds representable range, in which case it may return an exploded or vanished Scalar.
///
/// Subtraction process:
/// 0. Checks for any escaped Scalars (vanished, exploded or undefined) and handles these cases
/// 1. Checks for Zeros and returns the appropriate result
/// 2. Aligns fractions by shifting the smaller value right based on exponent difference
/// 3. Subtracts the aligned values
/// 4. Normalizes the result and adjusts exponent accordingly
/// 5. Escapes for underflow if necessary, overflow is naturally handled by escaped exponent alignment
///
/// # Returns
///
/// - `[℘ ]` ➔ `[℘ ]` First undefined state encountered
/// - `[↑]` - `[↑]` ➔ `[℘ ↑-↑]` Undefined exploded minus exploded state
/// - `[↑]` - `[#]` ➔ `[℘ ↑-]` Undefined exploded minus finite state
/// - `[#]` - `[↑]` ➔ `[℘ -↑]` Undefined finite minus exploded state
/// - `[↓]` - `[↓]` ➔ `[℘ ↓-↓]` Undefined vanished minus vanished state
/// - `[↓]` - `[#]` ➔ `[-#]` Negative of the finite Scalar
/// - `[#]` - `[↓]` ➔ `[#]` The finite Scalar
/// - `[0]` - `[#]` ➔ `[-#]` Negative of the Scalar
/// - `[#]` - `[0]` ➔ `[#]` The Scalar
/// - `[0]` - `[0]` ➔ `[0]` Zero
/// - `[#]` - `[#]` ➔ `[#]` or `[↑]` or `[↓]` A finite, exploded or vanished Scalar
///
/// # Examples
///
/// ```rust
/// use spirix::{Scalar, ScalarF5E3};
///
/// // Subtracting finite Scalars let a = Scalar::<i32, i8>::from(42_i32); let b = ScalarF5E3::from(12_i32); let diff = a - b; assert!(diff == 30_i32);
///
/// // Subtracting with Zero assert!(a - 0_i32 == a); assert!(0_i32 - a == -a);
///
/// // Subtraction that produces Zero let pos = ScalarF5E3::from(7_i32); assert!((pos - pos).is_zero());
///
/// // Subtraction with vanished Scalars let tiny: ScalarF5E3 = ScalarF5E3::MIN_POS / 4_i32; assert!(tiny.vanished()); assert!(a - tiny == a); // Vanished value treated as Zero
///
/// // Subtraction with exploded Scalars let huge: ScalarF5E3 = ScalarF5E3::MAX * 4_i32; assert!(huge.exploded()); assert!((a - huge).is_undefined());
///
/// // Subtracting two exploded Scalars assert!((huge - huge).is_undefined());
/// ```
pub(crate) fn scalar_subtract_scalar(&self, scalar: &Self) -> Self {
if !self.is_normal() || !scalar.is_normal() {
if self.is_undefined() {
return *self;
}
if scalar.is_undefined() {
return *scalar;
}
// Infinity absorbs everything. [∞] is signless so −[∞] is a no-op; [∞]−X and X−[∞] both yield [∞].
if self.is_infinite() || scalar.is_infinite() {
return Self::INFINITY;
}
// Zero identity: X−[0] = X and [0]−X = −X.
if scalar.is_zero() {
return *self;
}
if self.is_zero() {
return -scalar;
}
if self.exploded() && scalar.exploded() {
return Self {
fraction: TRANSFINITE_MINUS_TRANSFINITE.prefix.sa(),
exponent: Self::ambiguous_exponent(),
};
}
if self.vanished() && scalar.vanished() {
return Self {
fraction: VANISHED_MINUS_VANISHED.prefix.sa(),
exponent: Self::ambiguous_exponent(),
};
}
if self.exploded() {
if scalar.vanished() {
return *self;
}
return Self {
fraction: TRANSFINITE_MINUS_FINITE.prefix.sa(),
exponent: Self::ambiguous_exponent(),
};
}
if scalar.exploded() {
if self.vanished() {
return -scalar;
}
return Self {
fraction: FINITE_MINUS_TRANSFINITE.prefix.sa(),
exponent: Self::ambiguous_exponent(),
};
}
if self.vanished() {
return -scalar;
}
if scalar.vanished() {
return *self;
}
return *self;
}
let big_is_self = self.exponent.into_unsigned() > scalar.exponent.into_unsigned();
let (big, small) = if big_is_self {
(self, scalar)
} else {
(scalar, self)
};
let exp_diff = big.exponent.wrapping_sub(&small.exponent);
// x86 implementation note: Spirix's signless design wants to drop small only when shift ≥ FRAC. But Wide = 2*FRAC bits, and the inflated form reaches 2^FRAC magnitude at the ±1.0 boundary, so big_f<<shift ± small_f needs 2*FRAC+2 bits — one more than Rust/x86 provides at any power-of-2 width. Tightening the threshold to FRAC-1 keeps the sub in signed 2*FRAC-bit arithmetic with no sign branching. Cost: ≤1 ULP when shift == FRAC-1. In Verilog this tightening is unnecessary.
let small_lost = if big_is_self { *self } else { -scalar };
if exp_diff.is_negative() {
return small_lost;
}
let shift: isize = exp_diff.saturate();
if shift >= Self::fraction_bits().wrapping_sub(1) {
return small_lost;
}
let big_f = big.fraction.inflate(true).w_shl(shift);
let small_f = small.fraction.inflate(true);
// Pure two's complement subtract. With shift<=FRAC-2 both operands fit with room to spare, so signed wrap cannot occur regardless of sign.
let result = if big_is_self {
big_f.w_sub(small_f)
} else {
small_f.w_sub(big_f)
};
if result.w_is_zero() {
return Self {
fraction: F::zero(),
exponent: Self::ambiguous_exponent(),
};
}
let leading = result.leading_same();
let fb = Self::fraction_bits();
let delta: isize = fb.wrapping_sub(leading);
// AMBIG=0 native: view small.exponent as an unsigned cycle position via `cycle_widen` (2x widening into <E as Inflate>::Wide), add the normalization delta (sign-extended since it can be negative), and bounds-check against the cycle's normal range [min_pos, max_pos].
let small_pos = small.exponent.cycle_widen();
let delta_e: E = delta.as_();
let w_delta = delta_e.sign_extend();
let offset_pos = small_pos.w_add(w_delta);
let max_pos = Self::max_exponent().cycle_widen();
let min_pos = Self::min_exponent().cycle_widen();
if offset_pos > max_pos {
return Self {
fraction: result.w_shl(leading.wrapping_sub(1)).w_shr(fb).deflate(),
exponent: Self::ambiguous_exponent(),
};
}
if offset_pos < min_pos {
return Self {
fraction: result.w_shl(leading.wrapping_sub(2)).w_shr(fb).deflate(),
exponent: Self::ambiguous_exponent(),
};
}
let offset: E = offset_pos.deflate();
// Main path extraction: `result << L >> FRAC` composed as a net shift of (L - FRAC). Writing it directly avoids the Rust shift-overflow semantics that bite when L == wide_bits (result = -1, full sign extension).
let shl_amount = leading.wrapping_sub(fb);
let canonical = if shl_amount >= 0 {
result.w_shl(shl_amount)
} else {
result.w_shr(shl_amount.wrapping_neg())
};
Self {
fraction: canonical.deflate(),
exponent: offset,
}
}
}