/* origin: FreeBSD /usr/src/lib/msun/src/e_rem_pio2.c */
/*
 * ====================================================
 * 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.
 */
/* __rem_pio2(x,y)
 *
 * return the remainder of x rem pi/2 in y[0]+y[1]
 * use __rem_pio2_large() for large x
 */

#include "libm.h"

#if FLT_EVAL_METHOD==0 || FLT_EVAL_METHOD==1
#define EPS DBL_EPSILON
#elif FLT_EVAL_METHOD==2
#define EPS LDBL_EPSILON
#endif

/*
 * 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
toint   = 1.5/EPS,
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 */

/* caller must handle the case when reduction is not needed: |x| ~<= pi/4 */
int __rem_pio2(double x, double *y)
{
        union {double f; uint64_t i;} u = {x};
        double_t z,w,t,r,fn;
        double tx[3],ty[2];
        uint32_t ix;
        int sign, n, ex, ey, i;

        sign = u.i>>63;
        ix = u.i>>32 & 0x7fffffff;
        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 (!sign) {
                                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 (!sign) {
                                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 (!sign) {
                                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 (!sign) {
                                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:
                /* rint(x/(pi/2)), Assume round-to-nearest. */
                fn = (double_t)x*invpio2 + toint - toint;
                n = (int32_t)fn;
                r = x - fn*pio2_1;
                w = fn*pio2_1t;  /* 1st round, good to 85 bits */
                y[0] = r - w;
                u.f = y[0];
                ey = u.i>>52 & 0x7ff;
                ex = ix>>20;
                if (ex - ey > 16) { /* 2nd round, good to 118 bits */
                        t = r;
                        w = fn*pio2_2;
                        r = t - w;
                        w = fn*pio2_2t - ((t-r)-w);
                        y[0] = r - w;
                        u.f = y[0];
                        ey = u.i>>52 & 0x7ff;
                        if (ex - ey > 49) {  /* 3rd round, good to 151 bits, covers all cases */
                                t = r;
                                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) */
        u.f = x;
        u.i &= (uint64_t)-1>>12;
        u.i |= (uint64_t)(0x3ff + 23)<<52;
        z = u.f;
        for (i=0; i < 2; i++) {
                tx[i] = (double)(int32_t)z;
                z     = (z-tx[i])*0x1p24;
        }
        tx[i] = z;
        /* skip zero terms, first term is non-zero */
        while (tx[i] == 0.0)
                i--;
        n = __rem_pio2_large(tx,ty,(int)(ix>>20)-(0x3ff+23),i+1,1);
        if (sign) {
                y[0] = -ty[0];
                y[1] = -ty[1];
                return -n;
        }
        y[0] = ty[0];
        y[1] = ty[1];
        return n;
}