/***
*sincos.c - sine and cosine
*
*	Copyright (c) 1991-1991, Microsoft Corporation.	All rights reserved.
*
*Purpose:
*
*Revision History:
*   8-15-91	GDP	written
*   9-29-91	GDP	added missing ABS() for cosine
*  12-26-91	GDP	IEEE exceptions support
*  03-11-91	GDP	use 66 significant bits for representing pi
*			support FP_TLOSS, use _frnd for rounding
*******************************************************************************/
#include <math.h>
#include <trans.h>

static double _sincos(double x, double y, double sin);

/* constants */
static double const EPS = 1.05367121277235079465e-8; /* 2^(-53/2) */
static double const PI	   = 3.14159265358979323846;
static double const PI2	   = 1.57079632679489661923; /* pi/2 */
static double const PI_INV = 0.31830988618379067154; /* 1/pi */
static double const YMAX   = 2.2e8; /* approx. pi * 2 ^(t/2), where t=53 */

//
// The sum of C1 and C2 is a representation of PI with 66 bits in the
// significand (same as x87). (PI = 4 * 0.c90fdaa2 2168c234 c h)
//

static _dbl _C1	 = {SET_DBL (0x400921fb, 0x54400000)};
static _dbl _C2	 = {SET_DBL (0x3de0b461, 0x1a600000)};
#define C1  (_C1.dbl)
#define C2  (_C2.dbl)

/* constants for the polynomial approximation of sin, cos */
static double const r1 = -0.16666666666666665052e+0;
static double const r2 =  0.83333333333331650314e-2;
static double const r3 = -0.19841269841201840457e-3;
static double const r4 =  0.27557319210152756119e-5;
static double const r5 = -0.25052106798274584544e-7;
static double const r6 =  0.16058936490371589114e-9;
static double const r7 = -0.76429178068910467734e-12;
static double const r8 =  0.27204790957888846175e-14;

#define R(g)  ((((((((r8 * (g) + r7) * (g) + r6) * (g) + r5) * (g) + r4) \
			 * (g) + r3) * (g) + r2) * (g) + r1) * (g))


/***
*double sin(double x) - sine
*
*Purpose:
*   Compute the sine of a number.
*   The algorithm (reduction / polynomial approximation) is
*   taken from Cody & Waite.
*
*Entry:
*
*Exit:
*
*Exceptions:
*   I, P
*   if x is denormal: return x
*******************************************************************************/
double sin (double x)
{
    unsigned int savedcw;
    double result;
    double sign,y;

    /* save user fp control word */
    savedcw = _maskfp();

    if (IS_D_SPECIAL(x)){
	switch(_sptype(x)) {
	case T_PINF:
	case T_NINF:
	    return _except1(FP_I,OP_SIN,x,QNAN_SIN1,savedcw);
	case T_QNAN:
	    return _handle_qnan1(OP_SIN, x, savedcw);
	default: //T_SNAN
	    return _except1(FP_I,OP_SIN,x,_s2qnan(x),savedcw);
	}
    }

    if (x == 0.0) {
	// no P exception
	RETURN(savedcw,x);
    }

    if (x < 0) {
	sign = -1;
	y = -x;
    }
    else {
	sign = 1;
	y = x;
    }
    if (y >= YMAX) {

	// The argument is too large to produce a meaningful result,
	// so this is treated as an invalid operation.
	// We also set the (extra) FP_TLOSS flag for matherr
	// support

	return _except1(FP_TLOSS | FP_I,OP_SIN,x,QNAN_SIN2,savedcw);
    }

    result = _sincos(x,y,sign);

    RETURN_INEXACT1(OP_SIN,x,result,savedcw);
}


/***
*double cos(double x) - cosine
*
*Purpose:
*   Compute the cosine of a number.
*   The algorithm (reduction / polynomial approximation) is
*   taken from Cody & Waite.
*
*Entry:
*
*Exit:
*
*Exceptions:
*   P, I
*   if x is denormal: return 1
*******************************************************************************/

double cos (double x)
{
    unsigned int savedcw;
    double result,y;

    /* save user fp control word */
    savedcw = _maskfp();

    if (IS_D_SPECIAL(x)){
	switch(_sptype(x)) {
	case T_PINF:
	case T_NINF:
	    return _except1(FP_I,OP_COS,x,QNAN_COS1,savedcw);
	case T_QNAN:
	    return _handle_qnan1(OP_COS,x, savedcw);
	default: //T_SNAN
	    return _except1(FP_I,OP_COS,x,_s2qnan(x),savedcw);
	}
    }

    /* this will handle small arguments */
    if (ABS(x) < EPS) {
	if (x == 0.0) {
	    RETURN(savedcw,1.0);
	}
	result = 1.0;
    }

    else {
	y = ABS(x) + PI2;
	if (y >= YMAX) {

	    // The argument is too large to produce a meaningful result,
	    // so this is treated as an invalid operation.
	    // We also set the (extra) FP_TLOSS flag for matherr
	    // support

	    return _except1(FP_TLOSS | FP_I,OP_COS,x,QNAN_COS2,savedcw);
	}

	result = _sincos(x,y,1.0);
    }

    RETURN_INEXACT1(OP_COS,x,result,savedcw);
}



/***
*double _sincos(double x, double y,double sign) - cos sin helper
*
*Purpose:
*   Help computing sin or cos of a valid, within correct range
*   number.
*   The algorithm (reduction / polynomial approximation) is
*   taken from Cody & Waite.
*
*Entry:
*
*Exit:
*
*Exceptions:
*
*******************************************************************************/

static double _sincos(double x, double y, double sign)
{
    unsigned long n;
    double xn,f,g,r,result;

    xn = _frnd(y * PI_INV);
    n = (int) xn;

    if (n & 0x1) {
	/* n is odd */
	sign = -sign;
    }
    if (ABS(x) != y) {
	/* cosine wanted */
	xn -= .5;
    }

    /* assume there is a guard digit for addition */
    f = (ABS(x) - xn * C1) - xn * C2;
    if (ABS(f) < EPS)
	result = f;
    else {
	g = f*f;
	r = R(g);
	result = f + f*r;
    }
    result *= sign;

    return result;
}
