dmake: do not set MAKEFLAGS=k

[unleashed/tickless.git] / usr / src / lib / libm / common / C / __rem_pio2m.c

/*
 * CDDL HEADER START
 *
 * The contents of this file are subject to the terms of the
 * Common Development and Distribution License (the "License").
 * You may not use this file except in compliance with the License.
 *
 * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
 * or http://www.opensolaris.org/os/licensing.
 * See the License for the specific language governing permissions
 * and limitations under the License.
 *
 * When distributing Covered Code, include this CDDL HEADER in each
 * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
 * If applicable, add the following below this CDDL HEADER, with the
 * fields enclosed by brackets "[]" replaced with your own identifying
 * information: Portions Copyright [yyyy] [name of copyright owner]
 *
 * CDDL HEADER END
 */
/*
 * Copyright 2011 Nexenta Systems, Inc.  All rights reserved.
 */
/*
 * Copyright 2005 Sun Microsystems, Inc.  All rights reserved.
 * Use is subject to license terms.
 */

/*
 * int __rem_pio2m(x,y,e0,nx,prec,ipio2)
 * double x[],y[]; int e0,nx,prec; const int ipio2[];
 *
 * __rem_pio2m return the last three digits of N with
 *              y = x - N*pi/2
 * so that |y| < pi/4.
 *
 * 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[].
 * Here PI could as well be a machine value pi.
 *
 * 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 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
 *              precsion, 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 interger 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 or 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 3,4,4,
 *              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 indicats q[] is >= 0.5, hence
 *              it also indicates the *sign* of the result.
 *
 */

#include "libm.h"

#if defined(__i386) && !defined(__amd64)
extern int __swapRP(int);
#endif

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

static const double pio2[] = {
        1.57079625129699707031e+00,
        7.54978941586159635335e-08,
        5.39030252995776476554e-15,
        3.28200341580791294123e-22,
        1.27065575308067607349e-29,
        1.22933308981111328932e-36,
        2.73370053816464559624e-44,
        2.16741683877804819444e-51,
};

static const double
        zero    = 0.0,
        one     = 1.0,
        half    = 0.5,
        eight   = 8.0,
        eighth  = 0.125,
        two24   = 16777216.0,
        twon24  = 5.960464477539062500E-8;

int
__rem_pio2m(double *x, double *y, int e0, int nx, int prec, const int *ipio2)
{
        int     jz, jx, jv, jp, jk, carry, n, iq[20];
        int     i, j, k, m, q0, ih;
        double  z, fw, f[20], fq[20], q[20];
#if defined(__i386) && !defined(__amd64)
        int     rp;

        rp = __swapRP(fp_extended);
#endif

        /* initialize jk */
        jp = jk = init_jk[prec];

        /* 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 = zero; 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)((int)(twon24 * z));
                iq[i] = (int)(z - two24 * fw);
                z = q[j-1] + fw;
        }

        /* compute n */
        z = scalbn(z, q0);              /* actual value of z */
        z -= eight * floor(z * eighth); /* trim off integer >= 8 */
        n = (int)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 >= half) {
                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 */
                        /* set k to no. of terms needed */
                        for (k = 1; iq[jk-k] == 0; k++)
                                ;

                        /* add q[jz+1] to q[jz+k] */
                        for (i = jz + 1; i <= jz + k; i++) {
                                f[jx+i] = (double)ipio2[jv+i];
                                for (j = 0, fw = zero; j <= jx; j++)
                                        fw += x[j] * f[jx+i-j];
                                q[i] = fw;
                        }
                        jz += k;
                        goto recompute;
                }
        }

        /* cut out zero terms */
        if (z == zero) {
                jz -= 1;
                q0 -= 24;
                while (iq[jz] == 0) {
                        jz--;
                        q0 -= 24;
                }
        } else {                /* break z into 24-bit if neccessary */
                z = scalbn(z, -q0);
                if (z >= two24) {
                        fw = (double)((int)(twon24 * z));
                        iq[jz] = (int)(z - two24 * fw);
                        jz += 1;
                        q0 += 24;
                        iq[jz] = (int)fw;
                } else {
                        iq[jz] = (int)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 = zero, 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 = zero;
                for (i = jz; i >= 0; i--)
                        fw += fq[i];
                y[0] = (ih == 0)? fw : -fw;
                break;

        case 1:
        case 2:
                fw = zero;
                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;

        default:
                for (i = jz; i > 0; i--) {
                        fw = fq[i-1] + fq[i];
                        fq[i] += fq[i-1] - fw;
                        fq[i-1] = fw;
                }
                for (i = jz; i > 1; i--) {
                        fw = fq[i-1] + fq[i];
                        fq[i] += fq[i-1] - fw;
                        fq[i-1] = fw;
                }
                for (fw = zero, 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;
                }
        }

#if defined(__i386) && !defined(__amd64)
        (void) __swapRP(rp);
#endif
        return (n & 7);
}