/* 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/ld128/e_rem_pio2l.h 336545 2018-07-20 12:42:24Z bde $");
#endif

/* 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 <machine/ieee.h>

#include "math.h"
#include "math_private.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 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[5],ty[3];
       int64_t n;
       int e0,ex,i,j,nx;
       int16_t expsign, expsign1;

       u.extu_ld = x;
       ex = u.extu_exp;
       expsign = u.extu_exp | (u.extu_sign << 15);
       if (ex < BIAS + 45 || (ex == BIAS + 45 &&
           u.extu_frach < 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 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>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.extu_ld = y[0];
                   ex1 = u2.extu_exp;
                   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.extu_ld = x;
       e0 = ex - BIAS - 23;            /* e0 = ilogb(|x|)-23; */
       expsign1 = ex - e0;
       u1.extu_exp = expsign1;
       u1.extu_sign = expsign1 >> 15;
       z = u1.extu_ld;
       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;
}