/* e_rem_pio2f.c -- float version of e_rem_pio2.c

 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.

 */

/*

 * ====================================================

 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.

 *

 * Developed at SunPro, a Sun Microsystems, Inc. business.

 * Permission to use, copy, modify, and distribute this

 * software is freely granted, provided that this notice

 * is preserved.

 * ====================================================

 */

#if defined(LIBM_SCCS) && !defined(lint)

static char rcsid[] = "$NetBSD: e_rem_pio2f.c,v 1.5 1995/05/10 20:46:03 jtc Exp $";

#endif

/* __ieee754_rem_pio2f(x,y)

 *

 * return the remainder of x rem pi/2 in y[0]+y[1]

 * use __kernel_rem_pio2f()

 */

#include <math.h>

#include <math_private.h>

/*

 * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi

 */

static const int32_t two_over_pi[] = {

0xA2, 0xF9, 0x83, 0x6E, 0x4E, 0x44, 0x15, 0x29, 0xFC,

0x27, 0x57, 0xD1, 0xF5, 0x34, 0xDD, 0xC0, 0xDB, 0x62,

0x95, 0x99, 0x3C, 0x43, 0x90, 0x41, 0xFE, 0x51, 0x63,

0xAB, 0xDE, 0xBB, 0xC5, 0x61, 0xB7, 0x24, 0x6E, 0x3A,

0x42, 0x4D, 0xD2, 0xE0, 0x06, 0x49, 0x2E, 0xEA, 0x09,

0xD1, 0x92, 0x1C, 0xFE, 0x1D, 0xEB, 0x1C, 0xB1, 0x29,

0xA7, 0x3E, 0xE8, 0x82, 0x35, 0xF5, 0x2E, 0xBB, 0x44,

0x84, 0xE9, 0x9C, 0x70, 0x26, 0xB4, 0x5F, 0x7E, 0x41,

0x39, 0x91, 0xD6, 0x39, 0x83, 0x53, 0x39, 0xF4, 0x9C,

0x84, 0x5F, 0x8B, 0xBD, 0xF9, 0x28, 0x3B, 0x1F, 0xF8,

0x97, 0xFF, 0xDE, 0x05, 0x98, 0x0F, 0xEF, 0x2F, 0x11,

0x8B, 0x5A, 0x0A, 0x6D, 0x1F, 0x6D, 0x36, 0x7E, 0xCF,

0x27, 0xCB, 0x09, 0xB7, 0x4F, 0x46, 0x3F, 0x66, 0x9E,

0x5F, 0xEA, 0x2D, 0x75, 0x27, 0xBA, 0xC7, 0xEB, 0xE5,

0xF1, 0x7B, 0x3D, 0x07, 0x39, 0xF7, 0x8A, 0x52, 0x92,

0xEA, 0x6B, 0xFB, 0x5F, 0xB1, 0x1F, 0x8D, 0x5D, 0x08,

0x56, 0x03, 0x30, 0x46, 0xFC, 0x7B, 0x6B, 0xAB, 0xF0,

0xCF, 0xBC, 0x20, 0x9A, 0xF4, 0x36, 0x1D, 0xA9, 0xE3,

0x91, 0x61, 0x5E, 0xE6, 0x1B, 0x08, 0x65, 0x99, 0x85,

0x5F, 0x14, 0xA0, 0x68, 0x40, 0x8D, 0xFF, 0xD8, 0x80,

0x4D, 0x73, 0x27, 0x31, 0x06, 0x06, 0x15, 0x56, 0xCA,

0x73, 0xA8, 0xC9, 0x60, 0xE2, 0x7B, 0xC0, 0x8C, 0x6B,

};

/* This array is like the one in e_rem_pio2.c, but the numbers are

   single precision and the last 8 bits are forced to 0.  */

static const int32_t npio2_hw[] = {

0x3fc90f00, 0x40490f00, 0x4096cb00, 0x40c90f00, 0x40fb5300, 0x4116cb00,

0x412fed00, 0x41490f00, 0x41623100, 0x417b5300, 0x418a3a00, 0x4196cb00,

0x41a35c00, 0x41afed00, 0x41bc7e00, 0x41c90f00, 0x41d5a000, 0x41e23100,

0x41eec200, 0x41fb5300, 0x4203f200, 0x420a3a00, 0x42108300, 0x4216cb00,

0x421d1400, 0x42235c00, 0x4229a500, 0x422fed00, 0x42363600, 0x423c7e00,

0x4242c700, 0x42490f00

};

/*

 * invpio2:  24 bits of 2/pi

 * pio2_1:   first  17 bit of pi/2

 * pio2_1t:  pi/2 - pio2_1

 * pio2_2:   second 17 bit of pi/2

 * pio2_2t:  pi/2 - (pio2_1+pio2_2)

 * pio2_3:   third  17 bit of pi/2

 * pio2_3t:  pi/2 - (pio2_1+pio2_2+pio2_3)

 */

static const float

zero =  0.0000000000e+00, /* 0x00000000 */

half =  5.0000000000e-01, /* 0x3f000000 */

two8 =  2.5600000000e+02, /* 0x43800000 */

invpio2 =  6.3661980629e-01, /* 0x3f22f984 */

pio2_1  =  1.5707855225e+00, /* 0x3fc90f80 */

pio2_1t =  1.0804334124e-05, /* 0x37354443 */

pio2_2  =  1.0804273188e-05, /* 0x37354400 */

pio2_2t =  6.0770999344e-11, /* 0x2e85a308 */

pio2_3  =  6.0770943833e-11, /* 0x2e85a300 */

pio2_3t =  6.1232342629e-17; /* 0x248d3132 */

int32_t __ieee754_rem_pio2f(float x, float *y)

{

	float z,w,t,r,fn;

	float tx[3];

	int32_t e0,i,j,nx,n,ix,hx;

	GET_FLOAT_WORD(hx,x);

	ix = hx&0x7fffffff;

	if(ix<=0x3f490fd8)   /* |x| ~<= pi/4 , no need for reduction */

	    {y[0] = x; y[1] = 0; return 0;}

	if(ix<0x4016cbe4) {  /* |x| < 3pi/4, special case with n=+-1 */

	    if(hx>0) {

		z = x - pio2_1;

		if((ix&0xffffffc0)!=0x3fc90fc0) { /* 24+24 bit pi OK */

		    y[0] = z - pio2_1t;

		    y[1] = (z-y[0])-pio2_1t;

		} else {		/* near pi/2, use 24+24+24 bit pi */

		    z -= pio2_2;

		    y[0] = z - pio2_2t;

		    y[1] = (z-y[0])-pio2_2t;

		}

		return 1;

	    } else {	/* negative x */

		z = x + pio2_1;

		if((ix&0xffffffc0)!=0x3fc90fc0) { /* 24+24 bit pi OK */

		    y[0] = z + pio2_1t;

		    y[1] = (z-y[0])+pio2_1t;

		} else {		/* near pi/2, use 24+24+24 bit pi */

		    z += pio2_2;

		    y[0] = z + pio2_2t;

		    y[1] = (z-y[0])+pio2_2t;

		}

		return -1;

	    }

	}

	if(ix<=0x43490f80) { /* |x| ~<= 2^7*(pi/2), medium size */

	    t  = fabsf(x);

	    n  = (int32_t) (t*invpio2+half);

	    fn = (float)n;

	    r  = t-fn*pio2_1;

	    w  = fn*pio2_1t;	/* 1st round good to 40 bit */

	    if(n<32&&(int32_t)(ix&0xffffff00)!=npio2_hw[n-1]) {

		y[0] = r-w;	/* quick check no cancellation */

	    } else {

	        uint32_t high;

	        j  = ix>>23;

	        y[0] = r-w;

		GET_FLOAT_WORD(high,y[0]);

	        i = j-((high>>23)&0xff);

	        if(i>8) {  /* 2nd iteration needed, good to 57 */

		    t  = r;

		    w  = fn*pio2_2;

		    r  = t-w;

		    w  = fn*pio2_2t-((t-r)-w);

		    y[0] = r-w;

		    GET_FLOAT_WORD(high,y[0]);

		    i = j-((high>>23)&0xff);

		    if(i>25)  {	/* 3rd iteration need, 74 bits acc */

			t  = r;	/* will cover all possible cases */

			w  = fn*pio2_3;

			r  = t-w;

			w  = fn*pio2_3t-((t-r)-w);

			y[0] = r-w;

		    }

		}

	    }

	    y[1] = (r-y[0])-w;

	    if(hx<0) 	{y[0] = -y[0]; y[1] = -y[1]; return -n;}

	    else	 return n;

	}

    /*

     * all other (large) arguments

     */

	if(ix>=0x7f800000) {		/* x is inf or NaN */

	    y[0]=y[1]=x-x; return 0;

	}

    /* set z = scalbn(|x|,ilogb(x)-7) */

	e0 	= (ix>>23)-134;		/* e0 = ilogb(z)-7; */

	SET_FLOAT_WORD(z, ix - ((int32_t)(e0<<23)));

	for(i=0;i<2;i++) {

		tx[i] = (float)((int32_t)(z));

		z     = (z-tx[i])*two8;

	}

	tx[2] = z;

	nx = 3;

	while(tx[nx-1]==zero) nx--;	/* skip zero term */

	n  =  __kernel_rem_pio2f(tx,y,e0,nx,2,two_over_pi);

	if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}

	return n;

}