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p_tan.c
85 lines (79 loc) · 1.89 KB
/
p_tan.c
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#include <pal.h>
static const PTYPE pi_4 = PCONST(M_PI) / PCONST(4.0);
static const PTYPE pi_2 = PCONST(M_PI) / PCONST(2.0);
static const PTYPE pi = PCONST(M_PI);
/*
* 0 <= x <= pi/4
* tan x / x = 1 + a2 * x^2 + a4 * x^4 + ... + a12 * x^12 + e(x)
* |e(x)| <= 2 * 10^-8
*/
static inline PTYPE __p_tan_pi_4(const PTYPE x)
{
const PTYPE a2 = PCONST(0.3333314036);
const PTYPE a4 = PCONST(0.1333923995);
const PTYPE a6 = PCONST(0.0533740603);
const PTYPE a8 = PCONST(0.0245650893);
const PTYPE a10 = PCONST(0.0029005250);
const PTYPE a12 = PCONST(0.0095168091);
PTYPE x2, tanx_x;
x2 = x * x;
tanx_x = PCONST(1.0) + x2 * (a2 + x2 * (a4 + x2 * (a6 + x2 * (a8 + x2 * (a10 + x2 * a12)))));
return tanx_x * x;
}
/*
* 0 <= x <= pi/2
* x = x' + pi/4
* tan x = tan(x' + pi/4) = (tan x' + 1) / (1 - tan x')
*/
static inline PTYPE __p_tan_pi_2(const PTYPE x)
{
PTYPE x_, tanx_;
if (x <= pi_4)
return __p_tan_pi_4(x);
x_ = x - pi_4;
tanx_ = __p_tan_pi_4(x_);
return (tanx_ + PCONST(1.0)) / (PCONST(1.0) - tanx_);
}
/*
* 0 <= x <= pi
* x = x' + pi/2
* tan x = tan (x' + pi/2) = -1 / tan x'
*/
static inline PTYPE __p_tan_pi(const PTYPE x)
{
PTYPE x_;
if (x <= pi_2)
return __p_tan_pi_2(x);
x_ = x - pi_2;
return PCONST(-1.0) / __p_tan_pi_2(x_);
}
/* 0 <= x <= 2pi */
static inline PTYPE _p_tan(const PTYPE x)
{
if (x <= pi)
return __p_tan_pi(x);
else
return __p_tan_pi(x - pi);
}
/**
*
* Calculates the tangent of the input vector 'a'.
* Angles are specified in radians.
* Input is assumed to be bound to [0, 2pi].
*
* @param a Pointer to input vector
*
* @param c Pointer to output vector
*
* @param n Size of 'a' and 'c' vector.
*
* @return None
*
*/
void PSYM(p_tan)(const PTYPE *a, PTYPE *c, int n)
{
int i;
for (i = 0; i < n; i++) {
c[i] = _p_tan(a[i]);
}
}