/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans.
 *
 * 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.
 */

/* ld128 version of __ieee754_rem_pio2l(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"
#include "fpmath.h"

#define BIAS    (LDBL_MAX_EXP - 1)

/*
 * XXX need to verify that nonzero integer multiples of pi/2 within the
 * range get no closer to a long double than 2**-140, or that
 * ilogb(x) + ilogb(min_delta) < 45 - -140.
 */
/*
 * invpio2:  113 bits of 2/pi
 * pio2_1:   first  68 bits of pi/2
 * pio2_1t:  pi/2 - pio2_1
 * pio2_2:   second 68 bits of pi/2
 * pio2_2t:  pi/2 - (pio2_1+pio2_2)
 * pio2_3:   third  68 bits 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 */

static const long double
invpio2 =  6.3661977236758134307553505349005747e-01L,   /*  0x145f306dc9c882a53f84eafa3ea6a.0p-113 */
pio2_1  =  1.5707963267948966192292994253909555e+00L,   /*  0x1921fb54442d18469800000000000.0p-112 */
pio2_1t =  2.0222662487959507323996846200947577e-21L,   /*  0x13198a2e03707344a4093822299f3.0p-181 */
pio2_2  =  2.0222662487959507323994779168837751e-21L,   /*  0x13198a2e03707344a400000000000.0p-181 */
pio2_2t =  2.0670321098263988236496903051604844e-43L,   /*  0x127044533e63a0105df531d89cd91.0p-254 */
pio2_3  =  2.0670321098263988236499468110329591e-43L,   /*  0x127044533e63a0105e00000000000.0p-254 */
pio2_3t = -2.5650587247459238361625433492959285e-65L;   /* -0x159c4ec64ddaeb5f78671cbfb2210.0p-327 */

static __always_inline int
__ieee754_rem_pio2l(long double x, long double *y)
{
        union IEEEl2bits u,u1;
        long double z,w,t,r,fn;
        double tx[5],ty[3];
        int64_t n;
        int e0,ex,i,j,nx;
        int16_t expsign;

        u.e = x;
        expsign = u.xbits.expsign;
        ex = expsign & 0x7fff;
        if (ex < BIAS + 45 || ex == BIAS + 45 &&
            u.bits.manh < 0x921fb54442d1LL) {
            /* |x| ~< 2^45*(pi/2), medium size */
            /* TODO: use only double precision for fn, as in expl(). */
            fn = rnintl(x * invpio2);
            n  = i64rint(fn);
            r  = x-fn*pio2_1;
            w  = fn*pio2_1t;    /* 1st round good to 180 bit */
            {
                union IEEEl2bits u2;
                int ex1;
                j  = ex;
                y[0] = r-w; 
                u2.e = y[0];
                ex1 = u2.xbits.expsign & 0x7fff;
                i = j-ex1;
                if(i>51) {  /* 2nd iteration needed, good to 248 */
                    t  = r;
                    w  = fn*pio2_2;     
                    r  = t-w;
                    w  = fn*pio2_2t-((t-r)-w);  
                    y[0] = r-w;
                    u2.e = y[0];
                    ex1 = u2.xbits.expsign & 0x7fff;
                    i = j-ex1;
                    if(i>119) { /* 3rd iteration need, 316 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(ex==0x7fff) {                /* x is inf or NaN */
            y[0]=y[1]=x-x; return 0;
        }
    /* set z = scalbn(|x|,ilogb(x)-23) */
        u1.e = x;
        e0 = ex - BIAS - 23;            /* e0 = ilogb(|x|)-23; */
        u1.xbits.expsign = ex - e0;
        z = u1.e;
        for(i=0;i<4;i++) {
                tx[i] = (double)((int32_t)(z));
                z     = (z-tx[i])*two24;
        }
        tx[4] = z;
        nx = 5;
        while(tx[nx-1]==zero) nx--;     /* skip zero term */
        n  =  __kernel_rem_pio2(tx,ty,e0,nx,3);
        t = (long double)ty[2] + ty[1];
        r = t + ty[0];
        w = ty[0] - (r - t);
        if(expsign<0) {y[0] = -r; y[1] = -w; return -n;}
        y[0] = r; y[1] = w; return n;
}