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use crate::core::integer::{FullInt, IntConvert};
use crate::core::undefined::*;
use crate::{
Circle, CircleConstants, ExponentConstants, FractionConstants, Integer, Scalar, ScalarConstants,
};
use i256::I256;
use num_traits::{AsPrimitive, WrappingAdd, WrappingMul, WrappingNeg, WrappingSub};
use core::ops::*;
#[allow(private_bounds)]
impl<
F: Integer
+ FractionConstants
+ 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
+ ExponentConstants
+ 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>,
{
/// Raises a scalar to a complex power.
///
/// Implements s^z (scalar raised to complex power) using the formula:
/// s^z = exp(z * ln(s))
///
/// # Special Cases:
/// - Undefined or escaped values return appropriate undefined states
/// - 0^0 returns the ZERO_POWER_ZERO undefined state
/// - 0^z returns 0 if z has a positive real part
/// - 0^z returns ZERO_NEGATIVE_POWER undefined state if z has a negative real part
/// - Negative scalar bases return NEGATIVE_POWER undefined state (for complex exponents)
///
/// # Parameters:
/// - `self`: The scalar base
/// - `exp`: The complex exponent
///
/// # Returns:
/// - A complex number representing s^z
pub(crate) fn scalar_power_circle(&self, exp: &Circle<F, E>) -> Circle<F, E> {
if !self.is_normal() || !exp.is_normal() {
if self.is_undefined() {
return Circle {
real: self.fraction,
imaginary: self.fraction,
exponent: self.exponent,
};
}
if exp.is_undefined() {
return *exp;
}
if self.is_zero() {
if exp.real.is_positive() {
return Circle::<F, E>::ZERO;
}
let prefix: F = NEGLIGIBLE_POWER.prefix.sa();
return Circle {
real: prefix,
imaginary: prefix,
exponent: E::AMBIGUOUS_EXPONENT,
};
}
if self.exploded() {
let prefix: F = TRANSFINITE_POWER.prefix.sa();
return Circle {
real: prefix,
imaginary: prefix,
exponent: E::AMBIGUOUS_EXPONENT,
};
}
if self.vanished() {
let prefix: F = NEGLIGIBLE_POWER.prefix.sa();
return Circle {
real: prefix,
imaginary: prefix,
exponent: E::AMBIGUOUS_EXPONENT,
};
}
if exp.exploded() {
let prefix: F = POWER_TRANSFINITE.prefix.sa();
return Circle {
real: prefix,
imaginary: prefix,
exponent: E::AMBIGUOUS_EXPONENT,
};
}
let prefix: F = POWER_NEGLIGIBLE.prefix.sa();
return Circle {
real: prefix,
imaginary: prefix,
exponent: E::AMBIGUOUS_EXPONENT,
};
}
if self.fraction.is_negative() {
let prefix: F = NEGATIVE_POWER.prefix.sa();
return Circle {
real: prefix,
imaginary: prefix,
exponent: E::AMBIGUOUS_EXPONENT,
};
}
// Check if exponent is real and integer for exact computation
if exp.i().is_zero() && exp.r().is_integer() {
return Circle::from(self.integer_power(&exp.r()));
}
(exp * self.ln()).exp()
}
/// Computes the logarithm of a scalar with a complex base.
///
/// Implements log_z(s) (logarithm of scalar s with complex base z) using:
/// log_z(s) = ln(s) / ln(z)
///
/// # Special Cases:
/// - Undefined or escaped values return appropriate undefined states
/// - Exploded or vanished values return appropriate undefined states
/// - log_z(0) returns ZERO_LOG undefined state
/// - log_0(s) returns LOG_ZERO undefined state
/// - log_z(negative) returns NEGATIVE_LOG undefined state
///
/// # Parameters:
/// - `self`: The scalar number to take the logarithm of
/// - `base`: The complex base of the logarithm
///
/// # Returns:
/// - A complex number representing log_z(s)
pub(crate) fn scalar_logarithm_circle(&self, base: &Circle<F, E>) -> Circle<F, E> {
if !self.is_normal() || !base.is_normal() {
if self.is_undefined() {
return Circle {
real: self.fraction,
imaginary: self.fraction,
exponent: self.exponent,
};
}
if base.is_undefined() {
return *base;
}
if self.is_zero() {
let prefix: F = NEGLIGIBLE_LOG.prefix.sa();
return Circle {
real: prefix,
imaginary: prefix,
exponent: E::AMBIGUOUS_EXPONENT,
};
}
if base.is_zero() {
let prefix: F = LOG_NEGLIGIBLE.prefix.sa();
return Circle {
real: prefix,
imaginary: prefix,
exponent: E::AMBIGUOUS_EXPONENT,
};
}
if self.exploded() {
let prefix: F = TRANSFINITE_LOG.prefix.sa();
return Circle {
real: prefix,
imaginary: prefix,
exponent: E::AMBIGUOUS_EXPONENT,
};
}
if self.vanished() {
let prefix: F = NEGLIGIBLE_LOG.prefix.sa();
return Circle {
real: prefix,
imaginary: prefix,
exponent: E::AMBIGUOUS_EXPONENT,
};
}
if base.exploded() {
let prefix: F = LOG_TRANSFINITE.prefix.sa();
return Circle {
real: prefix,
imaginary: prefix,
exponent: E::AMBIGUOUS_EXPONENT,
};
}
if base.vanished() {
let prefix: F = LOG_NEGLIGIBLE.prefix.sa();
return Circle {
real: prefix,
imaginary: prefix,
exponent: E::AMBIGUOUS_EXPONENT,
};
}
}
if self.fraction.is_negative() {
let prefix: F = NEGATIVE_LOG.prefix.sa();
return Circle {
real: prefix,
imaginary: prefix,
exponent: E::AMBIGUOUS_EXPONENT,
};
}
self.ln() / base.ln()
}
}