/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunSoft, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice 
 * is preserved.
 * ====================================================
 *
 * Optimized by Bruce D. Evans.
 */

/* __ieee754_rem_pio2(x,y)
 * 
 * return the remainder of x rem pi/2 in y[0]+y[1] 
 * use __kernel_rem_pio2()
 */

#include <float.h>

#include "math.h"
#include "math_private.h"

/*
 * invpio2:  53 bits of 2/pi
 * pio2_1:   first  33 bit of pi/2
 * pio2_1t:  pi/2 - pio2_1
 * pio2_2:   second 33 bit of pi/2
 * pio2_2t:  pi/2 - (pio2_1+pio2_2)
 * pio2_3:   third  33 bit of pi/2
 * pio2_3t:  pi/2 - (pio2_1+pio2_2+pio2_3)
 */

static const double
zero =  0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
two24 =  1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
invpio2 =  6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
pio2_1  =  1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
pio2_1t =  6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
pio2_2  =  6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
pio2_2t =  2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
pio2_3  =  2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
pio2_3t =  8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */

#ifdef INLINE_REM_PIO2
static __always_inline
#endif
int
__ieee754_rem_pio2(double x, double *y)
{
        double z,w,t,r,fn;
        double tx[3],ty[2];
        int32_t e0,i,j,nx,n,ix,hx;
        u_int32_t low;

        GET_HIGH_WORD(hx,x);            /* high word of x */
        ix = hx&0x7fffffff;
#if 0 /* Must be handled in caller. */
        if(ix<=0x3fe921fb)   /* |x| ~<= pi/4 , no need for reduction */
            {y[0] = x; y[1] = 0; return 0;}
#endif
        if (ix <= 0x400f6a7a) {         /* |x| ~<= 5pi/4 */
            if ((ix & 0xfffff) == 0x921fb)  /* |x| ~= pi/2 or 2pi/2 */
                goto medium;            /* cancellation -- use medium case */
            if (ix <= 0x4002d97c) {     /* |x| ~<= 3pi/4 */
                if (hx > 0) {
                    z = x - pio2_1;     /* one round good to 85 bits */
                    y[0] = z - pio2_1t;
                    y[1] = (z-y[0])-pio2_1t;
                    return 1;
                } else {
                    z = x + pio2_1;
                    y[0] = z + pio2_1t;
                    y[1] = (z-y[0])+pio2_1t;
                    return -1;
                }
            } else {
                if (hx > 0) {
                    z = x - 2*pio2_1;
                    y[0] = z - 2*pio2_1t;
                    y[1] = (z-y[0])-2*pio2_1t;
                    return 2;
                } else {
                    z = x + 2*pio2_1;
                    y[0] = z + 2*pio2_1t;
                    y[1] = (z-y[0])+2*pio2_1t;
                    return -2;
                }
            }
        }
        if (ix <= 0x401c463b) {         /* |x| ~<= 9pi/4 */
            if (ix <= 0x4015fdbc) {     /* |x| ~<= 7pi/4 */
                if (ix == 0x4012d97c)   /* |x| ~= 3pi/2 */
                    goto medium;
                if (hx > 0) {
                    z = x - 3*pio2_1;
                    y[0] = z - 3*pio2_1t;
                    y[1] = (z-y[0])-3*pio2_1t;
                    return 3;
                } else {
                    z = x + 3*pio2_1;
                    y[0] = z + 3*pio2_1t;
                    y[1] = (z-y[0])+3*pio2_1t;
                    return -3;
                }
            } else {
                if (ix == 0x401921fb)   /* |x| ~= 4pi/2 */
                    goto medium;
                if (hx > 0) {
                    z = x - 4*pio2_1;
                    y[0] = z - 4*pio2_1t;
                    y[1] = (z-y[0])-4*pio2_1t;
                    return 4;
                } else {
                    z = x + 4*pio2_1;
                    y[0] = z + 4*pio2_1t;
                    y[1] = (z-y[0])+4*pio2_1t;
                    return -4;
                }
            }
        }
        if(ix<0x413921fb) {     /* |x| ~< 2^20*(pi/2), medium size */
medium:
            fn = rnint((double_t)x*invpio2);
            n  = irint(fn);
            r  = x-fn*pio2_1;
            w  = fn*pio2_1t;    /* 1st round good to 85 bit */
            {
                u_int32_t high;
                j  = ix>>20;
                y[0] = r-w; 
                GET_HIGH_WORD(high,y[0]);
                i = j-((high>>20)&0x7ff);
                if(i>16) {  /* 2nd iteration needed, good to 118 */
                    t  = r;
                    w  = fn*pio2_2;     
                    r  = t-w;
                    w  = fn*pio2_2t-((t-r)-w);  
                    y[0] = r-w;
                    GET_HIGH_WORD(high,y[0]);
                    i = j-((high>>20)&0x7ff);
                    if(i>49)  { /* 3rd iteration need, 151 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;
            return n;
        }
    /* 
     * all other (large) arguments
     */
        if(ix>=0x7ff00000) {            /* x is inf or NaN */
            y[0]=y[1]=x-x; return 0;
        }
    /* set z = scalbn(|x|,ilogb(x)-23) */
        GET_LOW_WORD(low,x);
        e0      = (ix>>20)-1046;        /* e0 = ilogb(z)-23; */
        INSERT_WORDS(z, ix - ((int32_t)((u_int32_t)e0<<20)), low);
        for(i=0;i<2;i++) {
                tx[i] = (double)((int32_t)(z));
                z     = (z-tx[i])*two24;
        }
        tx[2] = z;
        nx = 3;
        while(tx[nx-1]==zero) nx--;     /* skip zero term */
        n  =  __kernel_rem_pio2(tx,ty,e0,nx,1);
        if(hx<0) {y[0] = -ty[0]; y[1] = -ty[1]; return -n;}
        y[0] = ty[0]; y[1] = ty[1]; return n;
}