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/* 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.

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

 */

#ifndef lint

static char rcsid[] = "$\Id: e_rem_pio2f.c,v 1.3 1995/05/30 05:48:38 rgrimes 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

 */

#ifdef __STDC__

static const int32_t two_over_pi[] = {

#else

static int32_t two_over_pi[] = {

#endif

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.  */

#ifdef __STDC__

static const int32_t npio2_hw[] = {

#else

static int32_t npio2_hw[] = {

#endif

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)

 */

#ifdef __STDC__

static const float

#else

static float

#endif

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 */

#ifdef __STDC__

        int32_t __ieee754_rem_pio2f(float x, float *y)

#else

        int32_t __ieee754_rem_pio2f(x,y)

        float x,y[];

#endif

{

        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&0xfffffff0)!=0x3fc90fd0) { /* 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&0xfffffff0)!=0x3fc90fd0) { /* 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&&(ix&0xffffff00)!=npio2_hw[n-1]) {

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

            } else {

                u_int32_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;

}