/* From: @(#)e_rem_pio2.c 1.4 95/01/18 */
/*
* ====================================================
* 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.
*/

#include <sys/cdefs.h>
#if 0
__FBSDID("$FreeBSD: head/lib/msun/ld80/e_rem_pio2l.h 336545 2018-07-20 12:42:24Z bde $");
#endif

/* 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 <machine/ieee.h>

#include "math.h"
#include "math_private.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 inline __always_inline int
__ieee754_rem_pio2l(long double x, long double *y)
{
       union ieee_ext_u u, u1;
       long double z,w,t,r,fn;
       double tx[3],ty[2];
       int e0,ex,i,j,nx,n;
       int16_t expsign, expsign1;

       u.extu_ld = x;
       ex = u.extu_exp;
       expsign = GET_EXPSIGN(&u);
       if (ex < BIAS + 25 || (ex == BIAS + 25 && u.extu_frach < 0xc90fdaa2U)) {
           /* |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 ieee_ext_u u2;
               int ex1;
               j  = ex;
               y[0] = r-w;
               u2.extu_ld = y[0];
               ex1 = u2.extu_exp;
               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.extu_ld = y[0];
                   ex1 = u2.extu_exp;
                   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.extu_ld = x;
       e0 = ex - BIAS - 23;            /* e0 = ilogb(|x|)-23; */
       expsign1 = ex - e0;
       SET_EXPSIGN(&u1, expsign1);
       z = u1.extu_ld;
       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;
}