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// Add this to the implementations/powers/circle_circle.rs file
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>,
{
pub(crate) fn circle_power_circle(&self, exp: &Self) -> Self {
// A purely-real exponent is the scalar-exponent op: reroute so all of circle_power_scalar's resolutions (zero base, escaped base thru the multiply chain / rotation, ∞ base) apply uniformly.
if exp.is_normal() && exp.i().is_zero() {
return self.circle_power_scalar(&exp.r());
}
if !self.is_normal() || !exp.is_normal() {
if self.is_undefined() {
return *self;
}
if exp.is_undefined() {
return *exp;
}
// z^0 = 1 for any finite z (0^0 = 1 included). The old code fell past this: a zero exponent has real = 0, so the is_positive test below sent 0^0 to ℘.
if exp.is_zero() {
return Self::ONE;
}
// Zero base, complex exponent w: 0^w = e^(w·ln 0) — magnitude by the sign of Re(w) (Circle components are plain two's complement, so the raw sign test is the right one). Re > 0 → 0, Re < 0 → ∞, Re = 0 (pure imaginary) → oscillates → ℘.
if self.is_zero() {
if exp.is_normal() {
if exp.real > F::zero() {
return Self::ZERO;
}
if exp.real < F::zero() {
return Self::INFINITY;
}
}
let prefix: F = VANISHED_POWER.prefix.sa();
return Self {
real: prefix,
imaginary: prefix,
exponent: Self::ambiguous_exponent(),
};
}
// Escaped base with a truly-complex exponent w = a+bi: the result angle contains b·ln|z| with ln|z| unknowable → ℘ regardless of a. (b = 0 was rerouted above.)
if self.exploded() {
let prefix: F = TRANSFINITE_POWER.prefix.sa();
return Self {
real: prefix,
imaginary: prefix,
exponent: Self::ambiguous_exponent(),
};
}
if self.vanished() {
let prefix: F = VANISHED_POWER.prefix.sa();
return Self {
real: prefix,
imaginary: prefix,
exponent: Self::ambiguous_exponent(),
};
}
// Infinite base (single point, no angle to lose): magnitude by sign of Re(w).
if self.is_infinite() && exp.is_normal() {
if exp.real > F::zero() {
return Self::INFINITY;
}
if exp.real < F::zero() {
return Self::ZERO;
}
}
// Normal (or ∞ with Re(w) = 0) base, non-normal exponent: transfinite exponents (exploded/∞) → ℘^⬆; vanished exponent → ℘^⬇ (was a single ℘^⬇ catch-all that mislabeled the transfinite cases).
let prefix: F = if exp.vanished() {
POWER_VANISHED.prefix.sa()
} else {
POWER_TRANSFINITE.prefix.sa()
};
return Self {
real: prefix,
imaginary: prefix,
exponent: Self::ambiguous_exponent(),
};
}
let ln_z = self.ln();
let w_ln_z = exp * ln_z;
w_ln_z.exp()
}
/// Computes the logarithm of a complex number with a complex base.
///
/// Implements log_b(z) (logarithm of complex z with complex base b) using: log_b(z) = ln(z) / ln(b)
///
/// # Special Cases:
/// - Undefined or escaped values return appropriate undefined states
/// - Exploded or vanished values return appropriate undefined states
/// - log_b(0) returns ZERO_LOG undefined state
/// - log_0(z) returns LOG_ZERO undefined state
///
/// # Parameters:
/// - `self`: The complex number to take the logarithm of
/// - `base`: The complex base of the logarithm
///
/// # Returns:
/// - A complex number representing log_b(z)
pub(crate) fn circle_logarithm_circle(&self, base: &Self) -> Self {
if !self.is_normal() || !base.is_normal() {
if self.is_undefined() {
return *self;
}
if base.is_undefined() {
return *base;
}
if self.is_zero() {
let prefix: F = NEGLIGIBLE_LOG.prefix.sa();
return Self {
real: prefix,
imaginary: prefix,
exponent: Self::ambiguous_exponent(),
};
}
if base.is_zero() {
let prefix: F = LOG_NEGLIGIBLE.prefix.sa();
return Self {
real: prefix,
imaginary: prefix,
exponent: Self::ambiguous_exponent(),
};
}
if self.exploded() {
let prefix: F = TRANSFINITE_LOG.prefix.sa();
return Self {
real: prefix,
imaginary: prefix,
exponent: Self::ambiguous_exponent(),
};
}
if self.vanished() {
let prefix: F = NEGLIGIBLE_LOG.prefix.sa();
return Self {
real: prefix,
imaginary: prefix,
exponent: Self::ambiguous_exponent(),
};
}
if base.exploded() {
let prefix: F = LOG_TRANSFINITE.prefix.sa();
return Self {
real: prefix,
imaginary: prefix,
exponent: Self::ambiguous_exponent(),
};
}
if base.vanished() {
let prefix: F = LOG_NEGLIGIBLE.prefix.sa();
return Self {
real: prefix,
imaginary: prefix,
exponent: Self::ambiguous_exponent(),
};
}
}
let ln_z = self.ln();
let ln_base = base.ln();
ln_z / ln_base
}
}