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/* Copyright (C) 1994 DJ Delorie, see COPYING.DJ for details */

/* k_rem_pio2f.c -- float version of k_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[] = "$Id: k_rem_pio2f.c,v 1.2 1994/08/18 23:06:12 jtc Exp $";

#endif

#include "math.h"

#include "math_private.h"

/* In the float version, the input parameter x contains 8 bit

   integers, not 24 bit integers.  113 bit precision is not supported.  */

#ifdef __STDC__

static const int init_jk[] = {4,7,9}; /* initial value for jk */

#else

static int init_jk[] = {4,7,9};

#endif

#ifdef __STDC__

static const float PIo2[] = {

#else

static float PIo2[] = {

#endif

  1.5703125000e+00, /* 0x3fc90000 */

  4.5776367188e-04, /* 0x39f00000 */

  2.5987625122e-05, /* 0x37da0000 */

  7.5437128544e-08, /* 0x33a20000 */

  6.0026650317e-11, /* 0x2e840000 */

  7.3896444519e-13, /* 0x2b500000 */

  5.3845816694e-15, /* 0x27c20000 */

  5.6378512969e-18, /* 0x22d00000 */

  8.3009228831e-20, /* 0x1fc40000 */

  3.2756352257e-22, /* 0x1bc60000 */

  6.3331015649e-25, /* 0x17440000 */

};

#ifdef __STDC__

static const float

#else

static float

#endif

zero   = 0.0,

one    = 1.0,

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

twon8  =  3.9062500000e-03; /* 0x3b800000 */

#ifdef __STDC__

	int __kernel_rem_pio2f(float *x, float *y, int e0, int nx, int prec, const int32_t *ipio2)

#else

	int __kernel_rem_pio2f(x,y,e0,nx,prec,ipio2)

	float x[], y[]; int e0,nx,prec; int32_t ipio2[];

#endif

{

	int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;

	float z,fw,f[20],fq[20],q[20];

    /* initialize jk*/

	jk = init_jk[prec];

	jp = jk;

    /* determine jx,jv,q0, note that 3>q0 */

	jx =  nx-1;

	jv = (e0-3)/8; if(jv<0) jv=0;

	q0 =  e0-8*(jv+1);

    /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */

	j = jv-jx; m = jx+jk;

	for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (float) ipio2[j];

    /* compute q[0],q[1],...q[jk] */

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

	    for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw;

	}

	jz = jk;

recompute:

    /* distill q[] into iq[] reversingly */

	for(i=0,j=jz,z=q[jz];j>0;i++,j--) {

	    fw    =  (float)((int32_t)(twon8* z));

	    iq[i] =  (int32_t)(z-two8*fw);

	    z     =  q[j-1]+fw;

	}

    /* compute n */

	z  = scalbnf(z,q0);		/* actual value of z */

	z -= (float)8.0*floorf(z*(float)0.125);	/* trim off integer >= 8 */

	n  = (int32_t) z;

	z -= (float)n;

	ih = 0;

	if(q0>0) {	/* need iq[jz-1] to determine n */

	    i  = (iq[jz-1]>>(8-q0)); n += i;

	    iq[jz-1] -= i<<(8-q0);

	    ih = iq[jz-1]>>(7-q0);

	}

	else if(q0==0) ih = iq[jz-1]>>8;

	else if(z>=(float)0.5) ih=2;

	if(ih>0) {	/* q > 0.5 */

	    n += 1; carry = 0;

	    for(i=0;i

		j = iq[i];

		if(carry==0) {

		    if(j!=0) {

			carry = 1; iq[i] = 0x100- j;

		    }

		} else  iq[i] = 0xff - j;

	    }

	    if(q0>0) {		/* rare case: chance is 1 in 12 */

	        switch(q0) {

	        case 1:

	    	   iq[jz-1] &= 0x7f; break;

	    	case 2:

	    	   iq[jz-1] &= 0x3f; break;

	        }

	    }

	    if(ih==2) {

		z = one - z;

		if(carry!=0) z -= scalbnf(one,q0);

	    }

	}

    /* check if recomputation is needed */

	if(z==zero) {

	    j = 0;

	    for (i=jz-1;i>=jk;i--) j |= iq[i];

	    if(j==0) { /* need recomputation */

		for(k=1;iq[jk-k]==0;k++);   /* k = no. of terms needed */

		for(i=jz+1;i<=jz+k;i++) {   /* add q[jz+1] to q[jz+k] */

		    f[jx+i] = (float) ipio2[jv+i];

		    for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j];

		    q[i] = fw;

		}

		jz += k;

		goto recompute;

	    }

	}

    /* chop off zero terms */

	if(z==(float)0.0) {

	    jz -= 1; q0 -= 8;

	    while(iq[jz]==0) { jz--; q0-=8;}

	} else { /* break z into 8-bit if necessary */

	    z = scalbnf(z,-q0);

	    if(z>=two8) {

		fw = (float)((int32_t)(twon8*z));

		iq[jz] = (int32_t)(z-two8*fw);

		jz += 1; q0 += 8;

		iq[jz] = (int32_t) fw;

	    } else iq[jz] = (int32_t) z ;

	}

    /* convert integer "bit" chunk to floating-point value */

	fw = scalbnf(one,q0);

	for(i=jz;i>=0;i--) {

	    q[i] = fw*(float)iq[i]; fw*=twon8;

	}

    /* compute PIo2[0,...,jp]*q[jz,...,0] */

	for(i=jz;i>=0;i--) {

	    for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k];

	    fq[jz-i] = fw;

	}

    /* compress fq[] into y[] */

	switch(prec) {

	    case 0:

		fw = 0.0;

		for (i=jz;i>=0;i--) fw += fq[i];

		y[0] = (ih==0)? fw: -fw;

		break;

	    case 1:

	    case 2:

		fw = 0.0;

		for (i=jz;i>=0;i--) fw += fq[i];

		y[0] = (ih==0)? fw: -fw;

		fw = fq[0]-fw;

		for (i=1;i<=jz;i++) fw += fq[i];

		y[1] = (ih==0)? fw: -fw;

		break;

	    case 3:	/* painful */

		for (i=jz;i>0;i--) {

		    fw      = fq[i-1]+fq[i];

		    fq[i]  += fq[i-1]-fw;

		    fq[i-1] = fw;

		}

		for (i=jz;i>1;i--) {

		    fw      = fq[i-1]+fq[i];

		    fq[i]  += fq[i-1]-fw;

		    fq[i-1] = fw;

		}

		for (fw=0.0,i=jz;i>=2;i--) fw += fq[i];

		if(ih==0) {

		    y[0] =  fq[0]; y[1] =  fq[1]; y[2] =  fw;

		} else {

		    y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;

		}

	}

	return n&7;

}