k_rem_pio2.c File Reference

#include "math_libm.h"
#include "math_private.h"
#include "SDL_assert.h"

Include dependency graph for k_rem_pio2.c:

Go to the source code of this file.

Functions
	libm_hidden_proto (scalbn)
int attribute_hidden	__kernel_rem_pio2 (x, y, int e0, int nx, int prec, ipio2)

Variables
static double	PIo2 []
static double	zero = 0.0
static double	one = 1.0
static double	two24 = 1.67772160000000000000e+07
static double	twon24 = 5.96046447753906250000e-08

Function Documentation

int attribute_hidden __kernel_rem_pio2	(	x	,
		y	,
		int	e0,
		int	nx,
		int	prec,
		ipio2
	)

Definition at line 176 of file k_rem_pio2.c.

References floor, i, j, one, scalbn, SDL_arraysize, SDL_assert, two24, twon24, and zero.

Referenced by __ieee754_rem_pio2().

{
    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 */
    SDL_assert((prec >= 0) && (prec < SDL_arraysize(init_jk)));
    jk = init_jk[prec];
    SDL_assert((jk >= 2) && (jk <= 6));
    jp = jk;

    /* determine jx,jv,q0, note that 3>q0 */
    SDL_assert(nx > 0);
    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--) {
            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 = 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;
}

libm_hidden_proto

(

scalbn

)

Definition at line 139 of file k_rem_pio2.c.

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

Variable Documentation

double one = 1.0

static

Definition at line 167 of file k_rem_pio2.c.

Referenced by __kernel_rem_pio2().

double PIo2[]

static

Initial value:

= {

    1.57079625129699707031e+00, 
    7.54978941586159635335e-08, 
    5.39030252995776476554e-15, 
    3.28200341580791294123e-22, 
    1.27065575308067607349e-29, 
    1.22933308981111328932e-36, 
    2.73370053816464559624e-44, 
    2.16741683877804819444e-51, 
}

Definition at line 150 of file k_rem_pio2.c.

double two24 = 1.67772160000000000000e+07

static

Definition at line 167 of file k_rem_pio2.c.

Referenced by __kernel_rem_pio2().

double twon24 = 5.96046447753906250000e-08

static

Definition at line 168 of file k_rem_pio2.c.

Referenced by __kernel_rem_pio2().

double zero = 0.0

static

Definition at line 167 of file k_rem_pio2.c.

Referenced by __kernel_rem_pio2().