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#include "quadmath-imp.h"

#include <math.h>

/* @(#)k_rem_pio2.c 5.1 93/09/24 */

/*

 * ====================================================

 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.

 *

 * Developed at SunPro, a Sun Microsystems, Inc. business.

 * Permission to use, copy, modify, and distribute this

 * software is freely granted, provided that this notice

 * is preserved.

 * ====================================================

 */

/*

 * __kernel_rem_pio2(x,y,e0,nx,prec,ipio2)

 * double x[],y[]; int e0,nx,prec; int ipio2[];

 *

 * __kernel_rem_pio2 return the last three digits of N with

 *              y = x - N*pi/2

 * so that |y| < pi/2.

 *

 * The method is to compute the integer (mod 8) and fraction parts of

 * (2/pi)*x without doing the full multiplication. In general we

 * skip the part of the product that are known to be a huge integer (

 * more accurately, = 0 mod 8 ). Thus the number of operations are

 * independent of the exponent of the input.

 *

 * (2/pi) is represented by an array of 24-bit integers in ipio2[].

 *

 * Input parameters:

 *      x[]     The input value (must be positive) is broken into nx

 *              pieces of 24-bit integers in double precision format.

 *              x[i] will be the i-th 24 bit of x. The scaled exponent

 *              of x[0] is given in input parameter e0 (i.e., x[0]*2^e0

 *              match x's up to 24 bits.

 *

 *              Example of breaking a double positive z into x[0]+x[1]+x[2]:

 *                      e0 = ilogb(z)-23

 *                      z  = scalbn(z,-e0)

 *              for i = 0,1,2

 *                      x[i] = floor(z)

 *                      z    = (z-x[i])*2**24

 *

 *

 *      y[]     ouput result in an array of double precision numbers.

 *              The dimension of y[] is:

 *                      24-bit  precision       1

 *                      53-bit  precision       2

 *                      64-bit  precision       2

 *                      113-bit precision       3

 *              The actual value is the sum of them. Thus for 113-bit

 *              precision, one may have to do something like:

 *

 *              long double t,w,r_head, r_tail;

 *              t = (long double)y[2] + (long double)y[1];

 *              w = (long double)y[0];

 *              r_head = t+w;

 *              r_tail = w - (r_head - t);

 *

 *      e0      The exponent of x[0]

 *

 *      nx      dimension of x[]

 *

 *      prec    an integer indicating the precision:

 *                      0        24  bits (single)

 *                      1       53  bits (double)

 *                      2       64  bits (extended)

 *                      3       113 bits (quad)

 *

 *      ipio2[]

 *              integer array, contains the (24*i)-th to (24*i+23)-th

 *              bit of 2/pi after binary point. The corresponding

 *              floating value is

 *

 *                      ipio2[i] * 2^(-24(i+1)).

 *

 * External function:

 *      double scalbn(), floor();

 *

 *

 * Here is the description of some local variables:

 *

 *      jk      jk+1 is the initial number of terms of ipio2[] needed

 *              in the computation. The recommended value is 2,3,4,

 *              6 for single, double, extended,and quad.

 *

 *      jz      local integer variable indicating the number of

 *              terms of ipio2[] used.

 *

 *      jx      nx - 1

 *

 *      jv      index for pointing to the suitable ipio2[] for the

 *              computation. In general, we want

 *                      ( 2^e0*x[0] * ipio2[jv-1]*2^(-24jv) )/8

 *              is an integer. Thus

 *                      e0-3-24*jv >= 0 or (e0-3)/24 >= jv

 *              Hence jv = max(0,(e0-3)/24).

 *

 *      jp      jp+1 is the number of terms in PIo2[] needed, jp = jk.

 *

 *      q[]     double array with integral value, representing the

 *              24-bits chunk of the product of x and 2/pi.

 *

 *      q0      the corresponding exponent of q[0]. Note that the

 *              exponent for q[i] would be q0-24*i.

 *

 *      PIo2[]  double precision array, obtained by cutting pi/2

 *              into 24 bits chunks.

 *

 *      f[]     ipio2[] in floating point

 *

 *      iq[]    integer array by breaking up q[] in 24-bits chunk.

 *

 *      fq[]    final product of x*(2/pi) in fq[0],..,fq[jk]

 *

 *      ih      integer. If >0 it indicates q[] is >= 0.5, hence

 *              it also indicates the *sign* of the result.

 *

 */

/*

 * Constants:

 * The hexadecimal values are the intended ones for the following

 * constants. The decimal values may be used, provided that the

 * compiler will convert from decimal to binary accurately enough

 * to produce the hexadecimal values shown.

 */

static const int init_jk[] = {2,3,4,6}; /* initial value for jk */

static const double PIo2[] = {

  1.57079625129699707031e+00, /* 0x3FF921FB, 0x40000000 */

  7.54978941586159635335e-08, /* 0x3E74442D, 0x00000000 */

  5.39030252995776476554e-15, /* 0x3CF84698, 0x80000000 */

  3.28200341580791294123e-22, /* 0x3B78CC51, 0x60000000 */

  1.27065575308067607349e-29, /* 0x39F01B83, 0x80000000 */

  1.22933308981111328932e-36, /* 0x387A2520, 0x40000000 */

  2.73370053816464559624e-44, /* 0x36E38222, 0x80000000 */

  2.16741683877804819444e-51, /* 0x3569F31D, 0x00000000 */

};

static const double

  zero   = 0.0,

  one    = 1.0,

  two24   =  1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */

  twon24  =  5.96046447753906250000e-08; /* 0x3E700000, 0x00000000 */

static int

__quadmath_kernel_rem_pio2 (double *x, double *y, int e0, int nx, int prec, const int32_t *ipio2)

{

        int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;

        double z,fw,f[20],fq[20],q[20];

    /* initialize jk*/

        jk = init_jk[prec];

        jp = jk;

    /* determine jx,jv,q0, note that 3>q0 */

        jx =  nx-1;

        jv = (e0-3)/24; if(jv<0) jv=0;

        q0 =  e0-24*(jv+1);

    /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */

        j = jv-jx; m = jx+jk;

        for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (double) ipio2[j];

    /* compute q[0],q[1],...q[jk] */

        for (i=0;i<=jk;i++) {

            for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw;

        }

        jz = jk;

recompute:

    /* distill q[] into iq[] reversingly */

        for(i=0,j=jz,z=q[jz];j>0;i++,j--) {

            fw    =  (double)((int32_t)(twon24* z));

            iq[i] =  (int32_t)(z-two24*fw);

            z     =  q[j-1]+fw;

        }

    /* compute n */

        z  = scalbn(z,q0);              /* actual value of z */

        z -= 8.0*floor(z*0.125);                /* trim off integer >= 8 */

        n  = (int32_t) z;

        z -= (double)n;

        ih = 0;

        if(q0>0) {       /* need iq[jz-1] to determine n */

            i  = (iq[jz-1]>>(24-q0)); n += i;

            iq[jz-1] -= i<<(24-q0);

            ih = iq[jz-1]>>(23-q0);

        }

        else if(q0==0) ih = iq[jz-1]>>23;

        else if(z>=0.5) ih=2;

        if(ih>0) {       /* q > 0.5 */

            n += 1; carry = 0;

            for(i=0;i<jz ;i++) { /* compute 1-q */

                j = iq[i];

                if(carry==0) {

                    if(j!=0) {

                        carry = 1; iq[i] = 0x1000000- j;

                    }

                } else  iq[i] = 0xffffff - j;

            }

            if(q0>0) {           /* rare case: chance is 1 in 12 */

                switch(q0) {

                case 1:

                   iq[jz-1] &= 0x7fffff; break;

                case 2:

                   iq[jz-1] &= 0x3fffff; break;

                }

            }

            if(ih==2) {

                z = one - z;

                if(carry!=0) z -= scalbn(one,q0);

            }

        }

    /* check if recomputation is needed */

        if(z==zero) {

            j = 0;

            for (i=jz-1;i>=jk;i--) j |= iq[i];

            if(j==0) { /* need recomputation */

                for(k=1;iq[jk-k]==0;k++);   /* k = no. of terms needed */

                for(i=jz+1;i<=jz+k;i++) {   /* add q[jz+1] to q[jz+k] */

                    f[jx+i] = (double) ipio2[jv+i];

                    for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j];

                    q[i] = fw;

                }

                jz += k;

                goto recompute;

            }

        }

    /* chop off zero terms */

        if(z==0.0) {

            jz -= 1; q0 -= 24;

            while(iq[jz]==0) { jz--; q0-=24;}

        } else { /* break z into 24-bit if necessary */

            z = scalbn(z,-q0);

            if(z>=two24) {

                fw = (double)((int32_t)(twon24*z));

                iq[jz] = (int32_t)(z-two24*fw);

                jz += 1; q0 += 24;

                iq[jz] = (int32_t) fw;

            } else iq[jz] = (int32_t) z ;

        }

    /* convert integer "bit" chunk to floating-point value */

        fw = scalbn(one,q0);

        for(i=jz;i>=0;i--) {

            q[i] = fw*(double)iq[i]; fw*=twon24;

        }

    /* compute PIo2[0,...,jp]*q[jz,...,0] */

        for(i=jz;i>=0;i--) {

            for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k];

            fq[jz-i] = fw;

        }

    /* compress fq[] into y[] */

        switch(prec) {

            case 0:

                fw = 0.0;

                for (i=jz;i>=0;i--) fw += fq[i];

                y[0] = (ih==0)? fw: -fw;

                break;

            case 1:

            case 2:

                fw = 0.0;

                for (i=jz;i>=0;i--) fw += fq[i];

                y[0] = (ih==0)? fw: -fw;

                fw = fq[0]-fw;

                for (i=1;i<=jz;i++) fw += fq[i];

                y[1] = (ih==0)? fw: -fw;

                break;

            case 3:     /* painful */

                for (i=jz;i>0;i--) {

#if __FLT_EVAL_METHOD__ != 0

                    volatile

#endif

                    double fv = (double)(fq[i-1]+fq[i]);

                    fq[i]  += fq[i-1]-fv;

                    fq[i-1] = fv;

                }

                for (i=jz;i>1;i--) {

#if __FLT_EVAL_METHOD__ != 0

                    volatile

#endif

                    double fv = (double)(fq[i-1]+fq[i]);

                    fq[i]  += fq[i-1]-fv;

                    fq[i-1] = fv;

                }

                for (fw=0.0,i=jz;i>=2;i--) fw += fq[i];

                if(ih==0) {

                    y[0] =  fq[0]; y[1] =  fq[1]; y[2] =  fw;

                } else {

                    y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;

                }

        }

        return n&7;

}

/* Quad-precision floating point argument reduction.

   Copyright (C) 1999 Free Software Foundation, Inc.

   This file is part of the GNU C Library.

   Contributed by Jakub Jelinek <jj@ultra.linux.cz>

   The GNU C Library is free software; you can redistribute it and/or

   modify it under the terms of the GNU Lesser General Public

   License as published by the Free Software Foundation; either

   version 2.1 of the License, or (at your option) any later version.

   The GNU C Library is distributed in the hope that it will be useful,

   but WITHOUT ANY WARRANTY; without even the implied warranty of

   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU

   Lesser General Public License for more details.

   You should have received a copy of the GNU Lesser General Public

   License along with the GNU C Library; if not, write to the Free

   Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA

   02111-1307 USA.  */

/*

 * Table of constants for 2/pi, 5628 hexadecimal digits of 2/pi

 */

static const int32_t two_over_pi[] = {

0xa2f983, 0x6e4e44, 0x1529fc, 0x2757d1, 0xf534dd, 0xc0db62,

0x95993c, 0x439041, 0xfe5163, 0xabdebb, 0xc561b7, 0x246e3a,

0x424dd2, 0xe00649, 0x2eea09, 0xd1921c, 0xfe1deb, 0x1cb129,

0xa73ee8, 0x8235f5, 0x2ebb44, 0x84e99c, 0x7026b4, 0x5f7e41,

0x3991d6, 0x398353, 0x39f49c, 0x845f8b, 0xbdf928, 0x3b1ff8,

0x97ffde, 0x05980f, 0xef2f11, 0x8b5a0a, 0x6d1f6d, 0x367ecf,

0x27cb09, 0xb74f46, 0x3f669e, 0x5fea2d, 0x7527ba, 0xc7ebe5,

0xf17b3d, 0x0739f7, 0x8a5292, 0xea6bfb, 0x5fb11f, 0x8d5d08,

0x560330, 0x46fc7b, 0x6babf0, 0xcfbc20, 0x9af436, 0x1da9e3,

0x91615e, 0xe61b08, 0x659985, 0x5f14a0, 0x68408d, 0xffd880,

0x4d7327, 0x310606, 0x1556ca, 0x73a8c9, 0x60e27b, 0xc08c6b,

0x47c419, 0xc367cd, 0xdce809, 0x2a8359, 0xc4768b, 0x961ca6,

0xddaf44, 0xd15719, 0x053ea5, 0xff0705, 0x3f7e33, 0xe832c2,

0xde4f98, 0x327dbb, 0xc33d26, 0xef6b1e, 0x5ef89f, 0x3a1f35,

0xcaf27f, 0x1d87f1, 0x21907c, 0x7c246a, 0xfa6ed5, 0x772d30,

0x433b15, 0xc614b5, 0x9d19c3, 0xc2c4ad, 0x414d2c, 0x5d000c,

0x467d86, 0x2d71e3, 0x9ac69b, 0x006233, 0x7cd2b4, 0x97a7b4,

0xd55537, 0xf63ed7, 0x1810a3, 0xfc764d, 0x2a9d64, 0xabd770,

0xf87c63, 0x57b07a, 0xe71517, 0x5649c0, 0xd9d63b, 0x3884a7,

0xcb2324, 0x778ad6, 0x23545a, 0xb91f00, 0x1b0af1, 0xdfce19,

0xff319f, 0x6a1e66, 0x615799, 0x47fbac, 0xd87f7e, 0xb76522,

0x89e832, 0x60bfe6, 0xcdc4ef, 0x09366c, 0xd43f5d, 0xd7de16,

0xde3b58, 0x929bde, 0x2822d2, 0xe88628, 0x4d58e2, 0x32cac6,

0x16e308, 0xcb7de0, 0x50c017, 0xa71df3, 0x5be018, 0x34132e,

0x621283, 0x014883, 0x5b8ef5, 0x7fb0ad, 0xf2e91e, 0x434a48,

0xd36710, 0xd8ddaa, 0x425fae, 0xce616a, 0xa4280a, 0xb499d3,

0xf2a606, 0x7f775c, 0x83c2a3, 0x883c61, 0x78738a, 0x5a8caf,

0xbdd76f, 0x63a62d, 0xcbbff4, 0xef818d, 0x67c126, 0x45ca55,

0x36d9ca, 0xd2a828, 0x8d61c2, 0x77c912, 0x142604, 0x9b4612,

0xc459c4, 0x44c5c8, 0x91b24d, 0xf31700, 0xad43d4, 0xe54929,

0x10d5fd, 0xfcbe00, 0xcc941e, 0xeece70, 0xf53e13, 0x80f1ec,

0xc3e7b3, 0x28f8c7, 0x940593, 0x3e71c1, 0xb3092e, 0xf3450b,

0x9c1288, 0x7b20ab, 0x9fb52e, 0xc29247, 0x2f327b, 0x6d550c,

0x90a772, 0x1fe76b, 0x96cb31, 0x4a1679, 0xe27941, 0x89dff4,

0x9794e8, 0x84e6e2, 0x973199, 0x6bed88, 0x365f5f, 0x0efdbb,

0xb49a48, 0x6ca467, 0x427271, 0x325d8d, 0xb8159f, 0x09e5bc,

0x25318d, 0x3974f7, 0x1c0530, 0x010c0d, 0x68084b, 0x58ee2c,

0x90aa47, 0x02e774, 0x24d6bd, 0xa67df7, 0x72486e, 0xef169f,

0xa6948e, 0xf691b4, 0x5153d1, 0xf20acf, 0x339820, 0x7e4bf5,

0x6863b2, 0x5f3edd, 0x035d40, 0x7f8985, 0x295255, 0xc06437,

0x10d86d, 0x324832, 0x754c5b, 0xd4714e, 0x6e5445, 0xc1090b,

0x69f52a, 0xd56614, 0x9d0727, 0x50045d, 0xdb3bb4, 0xc576ea,

0x17f987, 0x7d6b49, 0xba271d, 0x296996, 0xacccc6, 0x5414ad,

0x6ae290, 0x89d988, 0x50722c, 0xbea404, 0x940777, 0x7030f3,

0x27fc00, 0xa871ea, 0x49c266, 0x3de064, 0x83dd97, 0x973fa3,

0xfd9443, 0x8c860d, 0xde4131, 0x9d3992, 0x8c70dd, 0xe7b717,

0x3bdf08, 0x2b3715, 0xa0805c, 0x93805a, 0x921110, 0xd8e80f,

0xaf806c, 0x4bffdb, 0x0f9038, 0x761859, 0x15a562, 0xbbcb61,

0xb989c7, 0xbd4010, 0x04f2d2, 0x277549, 0xf6b6eb, 0xbb22db,

0xaa140a, 0x2f2689, 0x768364, 0x333b09, 0x1a940e, 0xaa3a51,

0xc2a31d, 0xaeedaf, 0x12265c, 0x4dc26d, 0x9c7a2d, 0x9756c0,

0x833f03, 0xf6f009, 0x8c402b, 0x99316d, 0x07b439, 0x15200c,

0x5bc3d8, 0xc492f5, 0x4badc6, 0xa5ca4e, 0xcd37a7, 0x36a9e6,

0x9492ab, 0x6842dd, 0xde6319, 0xef8c76, 0x528b68, 0x37dbfc,

0xaba1ae, 0x3115df, 0xa1ae00, 0xdafb0c, 0x664d64, 0xb705ed,

0x306529, 0xbf5657, 0x3aff47, 0xb9f96a, 0xf3be75, 0xdf9328,

0x3080ab, 0xf68c66, 0x15cb04, 0x0622fa, 0x1de4d9, 0xa4b33d,

0x8f1b57, 0x09cd36, 0xe9424e, 0xa4be13, 0xb52333, 0x1aaaf0,

0xa8654f, 0xa5c1d2, 0x0f3f0b, 0xcd785b, 0x76f923, 0x048b7b,

0x721789, 0x53a6c6, 0xe26e6f, 0x00ebef, 0x584a9b, 0xb7dac4,

0xba66aa, 0xcfcf76, 0x1d02d1, 0x2df1b1, 0xc1998c, 0x77adc3,

0xda4886, 0xa05df7, 0xf480c6, 0x2ff0ac, 0x9aecdd, 0xbc5c3f,

0x6dded0, 0x1fc790, 0xb6db2a, 0x3a25a3, 0x9aaf00, 0x9353ad,

0x0457b6, 0xb42d29, 0x7e804b, 0xa707da, 0x0eaa76, 0xa1597b,

0x2a1216, 0x2db7dc, 0xfde5fa, 0xfedb89, 0xfdbe89, 0x6c76e4,

0xfca906, 0x70803e, 0x156e85, 0xff87fd, 0x073e28, 0x336761,

0x86182a, 0xeabd4d, 0xafe7b3, 0x6e6d8f, 0x396795, 0x5bbf31,

0x48d784, 0x16df30, 0x432dc7, 0x356125, 0xce70c9, 0xb8cb30,

0xfd6cbf, 0xa200a4, 0xe46c05, 0xa0dd5a, 0x476f21, 0xd21262,

0x845cb9, 0x496170, 0xe0566b, 0x015299, 0x375550, 0xb7d51e,

0xc4f133, 0x5f6e13, 0xe4305d, 0xa92e85, 0xc3b21d, 0x3632a1,

0xa4b708, 0xd4b1ea, 0x21f716, 0xe4698f, 0x77ff27, 0x80030c,

0x2d408d, 0xa0cd4f, 0x99a520, 0xd3a2b3, 0x0a5d2f, 0x42f9b4,

0xcbda11, 0xd0be7d, 0xc1db9b, 0xbd17ab, 0x81a2ca, 0x5c6a08,

0x17552e, 0x550027, 0xf0147f, 0x8607e1, 0x640b14, 0x8d4196,

0xdebe87, 0x2afdda, 0xb6256b, 0x34897b, 0xfef305, 0x9ebfb9,

0x4f6a68, 0xa82a4a, 0x5ac44f, 0xbcf82d, 0x985ad7, 0x95c7f4,

0x8d4d0d, 0xa63a20, 0x5f57a4, 0xb13f14, 0x953880, 0x0120cc,

0x86dd71, 0xb6dec9, 0xf560bf, 0x11654d, 0x6b0701, 0xacb08c,

0xd0c0b2, 0x485551, 0x0efb1e, 0xc37295, 0x3b06a3, 0x3540c0,

0x7bdc06, 0xcc45e0, 0xfa294e, 0xc8cad6, 0x41f3e8, 0xde647c,

0xd8649b, 0x31bed9, 0xc397a4, 0xd45877, 0xc5e369, 0x13daf0,

0x3c3aba, 0x461846, 0x5f7555, 0xf5bdd2, 0xc6926e, 0x5d2eac,

0xed440e, 0x423e1c, 0x87c461, 0xe9fd29, 0xf3d6e7, 0xca7c22,

0x35916f, 0xc5e008, 0x8dd7ff, 0xe26a6e, 0xc6fdb0, 0xc10893,

0x745d7c, 0xb2ad6b, 0x9d6ecd, 0x7b723e, 0x6a11c6, 0xa9cff7,

0xdf7329, 0xbac9b5, 0x5100b7, 0x0db2e2, 0x24ba74, 0x607de5,

0x8ad874, 0x2c150d, 0x0c1881, 0x94667e, 0x162901, 0x767a9f,

0xbefdfd, 0xef4556, 0x367ed9, 0x13d9ec, 0xb9ba8b, 0xfc97c4,

0x27a831, 0xc36ef1, 0x36c594, 0x56a8d8, 0xb5a8b4, 0x0ecccf,

0x2d8912, 0x34576f, 0x89562c, 0xe3ce99, 0xb920d6, 0xaa5e6b,

0x9c2a3e, 0xcc5f11, 0x4a0bfd, 0xfbf4e1, 0x6d3b8e, 0x2c86e2,

0x84d4e9, 0xa9b4fc, 0xd1eeef, 0xc9352e, 0x61392f, 0x442138,

0xc8d91b, 0x0afc81, 0x6a4afb, 0xd81c2f, 0x84b453, 0x8c994e,

0xcc2254, 0xdc552a, 0xd6c6c0, 0x96190b, 0xb8701a, 0x649569,

0x605a26, 0xee523f, 0x0f117f, 0x11b5f4, 0xf5cbfc, 0x2dbc34,

0xeebc34, 0xcc5de8, 0x605edd, 0x9b8e67, 0xef3392, 0xb817c9,

0x9b5861, 0xbc57e1, 0xc68351, 0x103ed8, 0x4871dd, 0xdd1c2d,

0xa118af, 0x462c21, 0xd7f359, 0x987ad9, 0xc0549e, 0xfa864f,

0xfc0656, 0xae79e5, 0x362289, 0x22ad38, 0xdc9367, 0xaae855,

0x382682, 0x9be7ca, 0xa40d51, 0xb13399, 0x0ed7a9, 0x480569,

0xf0b265, 0xa7887f, 0x974c88, 0x36d1f9, 0xb39221, 0x4a827b,

0x21cf98, 0xdc9f40, 0x5547dc, 0x3a74e1, 0x42eb67, 0xdf9dfe,

0x5fd45e, 0xa4677b, 0x7aacba, 0xa2f655, 0x23882b, 0x55ba41,

0x086e59, 0x862a21, 0x834739, 0xe6e389, 0xd49ee5, 0x40fb49,

0xe956ff, 0xca0f1c, 0x8a59c5, 0x2bfa94, 0xc5c1d3, 0xcfc50f,

0xae5adb, 0x86c547, 0x624385, 0x3b8621, 0x94792c, 0x876110,

0x7b4c2a, 0x1a2c80, 0x12bf43, 0x902688, 0x893c78, 0xe4c4a8,

0x7bdbe5, 0xc23ac4, 0xeaf426, 0x8a67f7, 0xbf920d, 0x2ba365,

0xb1933d, 0x0b7cbd, 0xdc51a4, 0x63dd27, 0xdde169, 0x19949a,

0x9529a8, 0x28ce68, 0xb4ed09, 0x209f44, 0xca984e, 0x638270,

0x237c7e, 0x32b90f, 0x8ef5a7, 0xe75614, 0x08f121, 0x2a9db5,

0x4d7e6f, 0x5119a5, 0xabf9b5, 0xd6df82, 0x61dd96, 0x023616,

0x9f3ac4, 0xa1a283, 0x6ded72, 0x7a8d39, 0xa9b882, 0x5c326b,

0x5b2746, 0xed3400, 0x7700d2, 0x55f4fc, 0x4d5901, 0x8071e0,

0xe13f89, 0xb295f3, 0x64a8f1, 0xaea74b, 0x38fc4c, 0xeab2bb,

0x47270b, 0xabc3a7, 0x34ba60, 0x52dd34, 0xf8563a, 0xeb7e8a,

0x31bb36, 0x5895b7, 0x47f7a9, 0x94c3aa, 0xd39225, 0x1e7f3e,

0xd8974e, 0xbba94f, 0xd8ae01, 0xe661b4, 0x393d8e, 0xa523aa,

0x33068e, 0x1633b5, 0x3bb188, 0x1d3a9d, 0x4013d0, 0xcc1be5,

0xf862e7, 0x3bf28f, 0x39b5bf, 0x0bc235, 0x22747e, 0xa247c0,

0xd52d1f, 0x19add3, 0x9094df, 0x9311d0, 0xb42b25, 0x496db2,

0xe264b2, 0x5ef135, 0x3bc6a4, 0x1a4ad0, 0xaac92e, 0x64e886,

0x573091, 0x982cfb, 0x311b1a, 0x08728b, 0xbdcee1, 0x60e142,

0xeb641d, 0xd0bba3, 0xe559d4, 0x597b8c, 0x2a4483, 0xf332ba,

0xf84867, 0x2c8d1b, 0x2fa9b0, 0x50f3dd, 0xf9f573, 0xdb61b4,

0xfe233e, 0x6c41a6, 0xeea318, 0x775a26, 0xbc5e5c, 0xcea708,

0x94dc57, 0xe20196, 0xf1e839, 0xbe4851, 0x5d2d2f, 0x4e9555,

0xd96ec2, 0xe7d755, 0x6304e0, 0xc02e0e, 0xfc40a0, 0xbbf9b3,

0x7125a7, 0x222dfb, 0xf619d8, 0x838c1c, 0x6619e6, 0xb20d55,

0xbb5137, 0x79e809, 0xaf9149, 0x0d73de, 0x0b0da5, 0xce7f58,

0xac1934, 0x724667, 0x7a1a13, 0x9e26bc, 0x4555e7, 0x585cb5,

0x711d14, 0x486991, 0x480d60, 0x56adab, 0xd62f64, 0x96ee0c,

0x212ff3, 0x5d6d88, 0xa67684, 0x95651e, 0xab9e0a, 0x4ddefe,

0x571010, 0x836a39, 0xf8ea31, 0x9e381d, 0xeac8b1, 0xcac96b,

0x37f21e, 0xd505e9, 0x984743, 0x9fc56c, 0x0331b7, 0x3b8bf8,

0x86e56a, 0x8dc343, 0x6230e7, 0x93cfd5, 0x6a8f2d, 0x733005,

0x1af021, 0xa09fcb, 0x7415a1, 0xd56b23, 0x6ff725, 0x2f4bc7,

0xb8a591, 0x7fac59, 0x5c55de, 0x212c38, 0xb13296, 0x5cff50,

0x366262, 0xfa7b16, 0xf4d9a6, 0x2acfe7, 0xf07403, 0xd4d604,

0x6fd916, 0x31b1bf, 0xcbb450, 0x5bd7c8, 0x0ce194, 0x6bd643,

0x4fd91c, 0xdf4543, 0x5f3453, 0xe2b5aa, 0xc9aec8, 0x131485,

0xf9d2bf, 0xbadb9e, 0x76f5b9, 0xaf15cf, 0xca3182, 0x14b56d,

0xe9fe4d, 0x50fc35, 0xf5aed5, 0xa2d0c1, 0xc96057, 0x192eb6,

0xe91d92, 0x07d144, 0xaea3c6, 0x343566, 0x26d5b4, 0x3161e2,

0x37f1a2, 0x209eff, 0x958e23, 0x493798, 0x35f4a6, 0x4bdc02,

0xc2be13, 0xbe80a0, 0x0b72a3, 0x115c5f, 0x1e1bd1, 0x0db4d3,

0x869e85, 0x96976b, 0x2ac91f, 0x8a26c2, 0x3070f0, 0x041412,

0xfc9fa5, 0xf72a38, 0x9c6878, 0xe2aa76, 0x50cfe1, 0x559274,

0x934e38, 0x0a92f7, 0x5533f0, 0xa63db4, 0x399971, 0xe2b755,

0xa98a7c, 0x008f19, 0xac54d2, 0x2ea0b4, 0xf5f3e0, 0x60c849,

0xffd269, 0xae52ce, 0x7a5fdd, 0xe9ce06, 0xfb0ae8, 0xa50cce,

0xea9d3e, 0x3766dd, 0xb834f5, 0x0da090, 0x846f88, 0x4ae3d5,

0x099a03, 0x2eae2d, 0xfcb40a, 0xfb9b33, 0xe281dd, 0x1b16ba,

0xd8c0af, 0xd96b97, 0xb52dc9, 0x9c277f, 0x5951d5, 0x21ccd6,

0xb6496b, 0x584562, 0xb3baf2, 0xa1a5c4, 0x7ca2cf, 0xa9b93d,

0x7b7b89, 0x483d38,

};

static const __float128 c[] = {

/* 93 bits of pi/2 */

#define PI_2_1 c[0]

 1.57079632679489661923132169155131424e+00Q, /* 3fff921fb54442d18469898cc5100000 */

/* pi/2 - PI_2_1 */

#define PI_2_1t c[1]

 8.84372056613570112025531863263659260e-29Q, /* 3fa1c06e0e68948127044533e63a0106 */

};

int32_t

__quadmath_rem_pio2q (__float128 x, __float128 *y)

{

  __float128 z, w, t;

  double tx[8];

  int64_t exp, n, ix, hx;

  uint64_t lx;

  GET_FLT128_WORDS64 (hx, lx, x);

  ix = hx & 0x7fffffffffffffffLL;

  if (ix <= 0x3ffe921fb54442d1LL)       /* x in <-pi/4, pi/4> */