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added exponentiation approximations

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Ahmet Inan 2019-02-27 18:54:39 +01:00
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README.md
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@ -66,6 +66,10 @@ Normalizers for [periodic](https://en.wikipedia.org/wiki/Periodic_function) sign
[atan](https://en.wikipedia.org/wiki/Inverse_trigonometric_functions) and [atan2](https://en.wikipedia.org/wiki/Atan2). [atan](https://en.wikipedia.org/wiki/Inverse_trigonometric_functions) and [atan2](https://en.wikipedia.org/wiki/Atan2).
### [exp.hh](exp.hh)
[Exponentiation](https://en.wikipedia.org/wiki/Exponentiation) approximations.
### [cordic.hh](cordic.hh) ### [cordic.hh](cordic.hh)
When working on a device where multiplication is expensive, the [CORDIC](https://en.wikipedia.org/wiki/CORDIC) comes in handy for computing [trigonometric functions](https://en.wikipedia.org/wiki/Trigonometric_functions). When working on a device where multiplication is expensive, the [CORDIC](https://en.wikipedia.org/wiki/CORDIC) comes in handy for computing [trigonometric functions](https://en.wikipedia.org/wiki/Trigonometric_functions).

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exp.hh Normal file
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/*
Exponentiation approximations
Constants below lifted from the Cephes Mathematical Library:
https://www.netlib.org/cephes/cmath.tgz
Copyright 2018 Ahmet Inan <inan@aicodix.de>
*/
#pragma once
namespace DSP {
template <typename TYPE>
TYPE ldexp(TYPE x, int n)
{
int a = n < 0 ? -n : n;
int a8 = a / 8;
int ar = a - a8 * 8;
TYPE t = 1 << a8;
t *= t;
t *= t;
t *= t;
t *= 1 << ar;
return n < 0 ? x / t : x * t;
}
template <typename TYPE>
TYPE exp10(TYPE x)
{
static constexpr TYPE
LOG210 = 3.32192809488736234787e0,
LG102A = 3.01025390625000000000E-1,
LG102B = 4.60503898119521373889E-6,
P0 = 4.09962519798587023075E-2,
P1 = 1.17452732554344059015E1,
P2 = 4.06717289936872725516E2,
P3 = 2.39423741207388267439E3,
Q0 = 8.50936160849306532625E1,
Q1 = 1.27209271178345121210E3,
Q2 = 2.07960819286001865907E3;
TYPE i = nearbyint(x * LOG210);
x -= i * LG102A;
x -= i * LG102B;
TYPE xx = x * x;
TYPE py = x * (xx * (xx * (xx * P0 + P1) + P2) + P3);
TYPE qy = xx * (xx * (xx + Q0) + Q1) + Q2;
TYPE pq = TYPE(1) + TYPE(2) * py / (qy - py);
return ldexp(pq, (int)i);
}
}