/*
 * ====================================================
 * 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.
 */

/* ld80 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)

/*
 * invpio2:  64 bits of 2/pi
 * pio2_1:   first  39 bits of pi/2
 * pio2_1t:  pi/2 - pio2_1
 * pio2_2:   second 39 bits of pi/2
 * pio2_2t:  pi/2 - (pio2_1+pio2_2)
 * pio2_3:   third  39 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 */
pio2_1  =  1.57079632679597125389e+00,  /* 0x3FF921FB, 0x54444000 */
pio2_2  = -1.07463465549783099519e-12,  /* -0x12e7b967674000.0p-92 */
pio2_3  =  6.36831716351370313614e-25;  /*  0x18a2e037074000.0p-133 */

#if defined(__amd64__) || defined(__i386__)
/* Long double constants are slow on these arches, and broken on i386. */
static const volatile double
invpio2hi =  6.3661977236758138e-01,    /*  0x145f306dc9c883.0p-53 */
invpio2lo = -3.9356538861223811e-17,    /* -0x16b00000000000.0p-107 */
pio2_1thi = -1.0746346554971943e-12,    /* -0x12e7b9676733af.0p-92 */
pio2_1tlo =  8.8451028997905949e-29,    /*  0x1c080000000000.0p-146 */
pio2_2thi =  6.3683171635109499e-25,    /*  0x18a2e03707344a.0p-133 */
pio2_2tlo =  2.3183081793789774e-41,    /*  0x10280000000000.0p-187 */
pio2_3thi = -2.7529965190440717e-37,    /* -0x176b7ed8fbbacc.0p-174 */
pio2_3tlo = -4.2006647512740502e-54;    /* -0x19c00000000000.0p-230 */
#define invpio2 ((long double)invpio2hi + invpio2lo)
#define pio2_1t ((long double)pio2_1thi + pio2_1tlo)
#define pio2_2t ((long double)pio2_2thi + pio2_2tlo)
#define pio2_3t ((long double)pio2_3thi + pio2_3tlo)
#else
static const long double
invpio2 =  6.36619772367581343076e-01L, /*  0xa2f9836e4e44152a.0p-64 */
pio2_1t = -1.07463465549719416346e-12L, /* -0x973dcb3b399d747f.0p-103 */
pio2_2t =  6.36831716351095013979e-25L, /*  0xc51701b839a25205.0p-144 */
pio2_3t = -2.75299651904407171810e-37L; /* -0xbb5bf6c7ddd660ce.0p-185 */
#endif

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[3],ty[2];
        int e0,ex,i,j,nx,n;
        int16_t expsign;

        u.e = x;
        expsign = u.xbits.expsign;
        ex = expsign & 0x7fff;
        if (ex < BIAS + 25 || (ex == BIAS + 25 && u.bits.manh < 0xc90fdaa2)) {
            /* |x| ~< 2^25*(pi/2), medium size */
            fn = rnintl(x*invpio2);
            n  = irint(fn);
            r  = x-fn*pio2_1;
            w  = fn*pio2_1t;    /* 1st round good to 102 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>22) {  /* 2nd iteration needed, good to 141 */
                    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>61) {  /* 3rd iteration need, 180 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<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,2);
        r = (long double)ty[0] + ty[1];
        w = ty[1] - (r - ty[0]);
        if(expsign<0) {y[0] = -r; y[1] = -w; return -n;}
        y[0] = r; y[1] = w; return n;
}