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