Function primitive_float_log_base 

pub fn primitive_float_log_base<T>(x: T, base: u64) -> T
where
    Float: From<T> + PartialOrd<T>,
    for<'a> T: ExactFrom<&'a Float> + RoundingFrom<&'a Float> + PrimitiveFloat,

Computes $\log_b x$, the base-$b$ logarithm of a primitive float, where $b$ is a u64 greater than 1. Using this function is more accurate than computing the logarithm using the standard library, whose log is not always correctly rounded.

The base-$b$ logarithm of any negative number is NaN.

$$ f(x,b) = \log_b x+\varepsilon. $$

• If $\log_b x$ is infinite, zero, or NaN, $\varepsilon$ may be ignored or assumed to be 0.
• If $\log_b x$ is finite and nonzero, then $|\varepsilon| < 2^{\lfloor\log_2 |\log_b x|\rfloor-p}$, where $p$ is precision of the output (typically 24 if T is a f32 and 53 if T is a f64, but less if the output is subnormal).

Special cases:

• $f(\text{NaN},b)=\text{NaN}$
• $f(\infty,b)=\infty$
• $f(-\infty,b)=\text{NaN}$
• $f(\pm0.0,b)=-\infty$
• $f(1.0,b)=0.0$
• $f(x,b)=\text{NaN}$ for $x<0$

Neither overflow nor underflow is possible.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if base is less than 2.

Examples

use malachite_base::num::basic::traits::NegativeInfinity;
use malachite_base::num::float::NiceFloat;
use malachite_float::arithmetic::log_base::primitive_float_log_base;

assert!(primitive_float_log_base(f32::NAN, 10).is_nan());
assert_eq!(
    NiceFloat(primitive_float_log_base(f32::INFINITY, 10)),
    NiceFloat(f32::INFINITY)
);
assert_eq!(
    NiceFloat(primitive_float_log_base(0.0f32, 10)),
    NiceFloat(f32::NEGATIVE_INFINITY)
);
// log_10(1000) = 3
assert_eq!(
    NiceFloat(primitive_float_log_base(1000.0f32, 10)),
    NiceFloat(3.0)
);
// log_3(9) = 2
assert_eq!(
    NiceFloat(primitive_float_log_base(9.0f32, 3)),
    NiceFloat(2.0)
);
// log_10(50)
assert_eq!(
    NiceFloat(primitive_float_log_base(50.0f32, 10)),
    NiceFloat(1.69897)
);
assert!(primitive_float_log_base(-1.0f32, 10).is_nan());