reactos/sdk/lib/crt/math/amd64/asin.c

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/*
* COPYRIGHT: See COPYING in the top level directory
* PROJECT: ReactOS CRT
* FILE: lib/sdk/crt/math/amd64/asin.c
* PURPOSE: Generic C implementation of arc sine
* PROGRAMMER: Timo Kreuzer (timo.kreuzer@reactos.org)
*/
#define PRECISION 9
/*
* The arc sine can be approximated with the following row:
*
* asin(x) = a0*x + a1*x^3 + a2*x^5 + a3*x^7 + a4*x^9 + ...
*
* To reduce the number of multiplications the formula is transformed to
*
* asin(x) = x * (1 + x^2*(a1 + x^2*(a2 + x^2*(a3 + ...) ) ) )
*
* The coefficients are:
* a0 = 1
* a1 = (1/2*3)
* a2 = (3*1/4*2*5)
* a3 = (5*3*1/6*4*2*7)
* a4 = (7*5*3*1/8*6*4*2*9)
* a5 = (9*7*5*3*1/10*8*6*4*2*11)
* ...
*/
double
asin(double x)
{
double x2, result;
/* Check range */
if ((x > 1.) || (x < -1.)) return NaN;
/* Calculate the square of x */
x2 = (x * x);
/* Start with 0, compiler will optimize this away */
result = 0;
result += (15*13*11*9*7*5*3*1./(16*14*12*10*8*6*4*2*17));
result *= x2;
result += (13*11*9*7*5*3*1./(14*12*10*8*6*4*2*15));
result *= x2;
result += (11*9*7*5*3*1./(12*10*8*6*4*2*13));
result *= x2;
result += (9*7*5*3*1./(10*8*6*4*2*11));
result *= x2;
result += (7*5*3*1./(8*6*4*2*9));
result *= x2;
result += (5*3*1./(6*4*2*7));
result *= x2;
result += (3*1./(4*2*5));
result *= x2;
result += (1./(2*3));
result *= x2;
result += 1.;
result *= x;
return result;
}