poly_tan.c

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/*---------------------------------------------------------------------------+
 |  poly_tan.c                                                               |
 |                                                                           |
 | Compute the tan of a FPU_REG, using a polynomial approximation.           |
 |                                                                           |
 | Copyright (C) 1992,1993,1994,1997,1999                                    |
 |                       W. Metzenthen, 22 Parker St, Ormond, Vic 3163,      |
 |                       Australia.  E-mail   [email protected]            |
 |                                                                           |
 |                                                                           |
 +---------------------------------------------------------------------------*/

#include "exception.h"
#include "reg_constant.h"
#include "fpu_emu.h"
#include "fpu_system.h"
#include "control_w.h"
#include "poly.h"

#define HiPOWERop   3   /* odd poly, positive terms */
static const unsigned long long oddplterm[HiPOWERop] = {
    0x0000000000000000LL,
    0x0051a1cf08fca228LL,
    0x0000000071284ff7LL
};

#define HiPOWERon   2   /* odd poly, negative terms */
static const unsigned long long oddnegterm[HiPOWERon] = {
    0x1291a9a184244e80LL,
    0x0000583245819c21LL
};

#define HiPOWERep   2   /* even poly, positive terms */
static const unsigned long long evenplterm[HiPOWERep] = {
    0x0e848884b539e888LL,
    0x00003c7f18b887daLL
};

#define HiPOWERen   2   /* even poly, negative terms */
static const unsigned long long evennegterm[HiPOWERen] = {
    0xf1f0200fd51569ccLL,
    0x003afb46105c4432LL
};

static const unsigned long long twothirds = 0xaaaaaaaaaaaaaaabLL;

/*--- poly_tan() ------------------------------------------------------------+
 |                                                                           |
 +---------------------------------------------------------------------------*/
void poly_tan(FPU_REG *st0_ptr)
{
    long int exponent;
    int invert;
    Xsig argSq, argSqSq, accumulatoro, accumulatore, accum,
        argSignif, fix_up;
    unsigned long adj;

    exponent = exponent(st0_ptr);

#ifdef PARANOID
    if (signnegative(st0_ptr)) {    /* Can't hack a number < 0.0 */
        arith_invalid(0);
        return;
    }           /* Need a positive number */
#endif /* PARANOID */

    /* Split the problem into two domains, smaller and larger than pi/4 */
    if ((exponent == 0)
        || ((exponent == -1) && (st0_ptr->sigh > 0xc90fdaa2))) {
        /* The argument is greater than (approx) pi/4 */
        invert = 1;
        accum.lsw = 0;
        XSIG_LL(accum) = significand(st0_ptr);

        if (exponent == 0) {
            /* The argument is >= 1.0 */
            /* Put the binary point at the left. */
            XSIG_LL(accum) <<= 1;
        }
        /* pi/2 in hex is: 1.921fb54442d18469 898CC51701B839A2 52049C1 */
        XSIG_LL(accum) = 0x921fb54442d18469LL - XSIG_LL(accum);
        /* This is a special case which arises due to rounding. */
        if (XSIG_LL(accum) == 0xffffffffffffffffLL) {
            FPU_settag0(TAG_Valid);
            significand(st0_ptr) = 0x8a51e04daabda360LL;
            setexponent16(st0_ptr,
                      (0x41 + EXTENDED_Ebias) | SIGN_Negative);
            return;
        }

        argSignif.lsw = accum.lsw;
        XSIG_LL(argSignif) = XSIG_LL(accum);
        exponent = -1 + norm_Xsig(&argSignif);
    } else {
        invert = 0;
        argSignif.lsw = 0;
        XSIG_LL(accum) = XSIG_LL(argSignif) = significand(st0_ptr);

        if (exponent < -1) {
            /* shift the argument right by the required places */
            if (FPU_shrx(&XSIG_LL(accum), -1 - exponent) >=
                0x80000000U)
                XSIG_LL(accum)++;   /* round up */
        }
    }

    XSIG_LL(argSq) = XSIG_LL(accum);
    argSq.lsw = accum.lsw;
    mul_Xsig_Xsig(&argSq, &argSq);
    XSIG_LL(argSqSq) = XSIG_LL(argSq);
    argSqSq.lsw = argSq.lsw;
    mul_Xsig_Xsig(&argSqSq, &argSqSq);

    /* Compute the negative terms for the numerator polynomial */
    accumulatoro.msw = accumulatoro.midw = accumulatoro.lsw = 0;
    polynomial_Xsig(&accumulatoro, &XSIG_LL(argSqSq), oddnegterm,
            HiPOWERon - 1);
    mul_Xsig_Xsig(&accumulatoro, &argSq);
    negate_Xsig(&accumulatoro);
    /* Add the positive terms */
    polynomial_Xsig(&accumulatoro, &XSIG_LL(argSqSq), oddplterm,
            HiPOWERop - 1);

    /* Compute the positive terms for the denominator polynomial */
    accumulatore.msw = accumulatore.midw = accumulatore.lsw = 0;
    polynomial_Xsig(&accumulatore, &XSIG_LL(argSqSq), evenplterm,
            HiPOWERep - 1);
    mul_Xsig_Xsig(&accumulatore, &argSq);
    negate_Xsig(&accumulatore);
    /* Add the negative terms */
    polynomial_Xsig(&accumulatore, &XSIG_LL(argSqSq), evennegterm,
            HiPOWERen - 1);
    /* Multiply by arg^2 */
    mul64_Xsig(&accumulatore, &XSIG_LL(argSignif));
    mul64_Xsig(&accumulatore, &XSIG_LL(argSignif));
    /* de-normalize and divide by 2 */
    shr_Xsig(&accumulatore, -2 * (1 + exponent) + 1);
    negate_Xsig(&accumulatore); /* This does 1 - accumulator */

    /* Now find the ratio. */
    if (accumulatore.msw == 0) {
        /* accumulatoro must contain 1.0 here, (actually, 0) but it
           really doesn't matter what value we use because it will
           have negligible effect in later calculations
         */
        XSIG_LL(accum) = 0x8000000000000000LL;
        accum.lsw = 0;
    } else {
        div_Xsig(&accumulatoro, &accumulatore, &accum);
    }

    /* Multiply by 1/3 * arg^3 */
    mul64_Xsig(&accum, &XSIG_LL(argSignif));
    mul64_Xsig(&accum, &XSIG_LL(argSignif));
    mul64_Xsig(&accum, &XSIG_LL(argSignif));
    mul64_Xsig(&accum, &twothirds);
    shr_Xsig(&accum, -2 * (exponent + 1));

    /* tan(arg) = arg + accum */
    add_two_Xsig(&accum, &argSignif, &exponent);

    if (invert) {
        /* We now have the value of tan(pi_2 - arg) where pi_2 is an
           approximation for pi/2
         */
        /* The next step is to fix the answer to compensate for the
           error due to the approximation used for pi/2
         */

        /* This is (approx) delta, the error in our approx for pi/2
           (see above). It has an exponent of -65
         */
        XSIG_LL(fix_up) = 0x898cc51701b839a2LL;
        fix_up.lsw = 0;

        if (exponent == 0)
            adj = 0xffffffff;   /* We want approx 1.0 here, but
                           this is close enough. */
        else if (exponent > -30) {
            adj = accum.msw >> -(exponent + 1); /* tan */
            adj = mul_32_32(adj, adj);  /* tan^2 */
        } else
            adj = 0;
        adj = mul_32_32(0x898cc517, adj);   /* delta * tan^2 */

        fix_up.msw += adj;
        if (!(fix_up.msw & 0x80000000)) {   /* did fix_up overflow ? */
            /* Yes, we need to add an msb */
            shr_Xsig(&fix_up, 1);
            fix_up.msw |= 0x80000000;
            shr_Xsig(&fix_up, 64 + exponent);
        } else
            shr_Xsig(&fix_up, 65 + exponent);

        add_two_Xsig(&accum, &fix_up, &exponent);

        /* accum now contains tan(pi/2 - arg).
           Use tan(arg) = 1.0 / tan(pi/2 - arg)
         */
        accumulatoro.lsw = accumulatoro.midw = 0;
        accumulatoro.msw = 0x80000000;
        div_Xsig(&accumulatoro, &accum, &accum);
        exponent = -exponent - 1;
    }

    /* Transfer the result */
    round_Xsig(&accum);
    FPU_settag0(TAG_Valid);
    significand(st0_ptr) = XSIG_LL(accum);
    setexponent16(st0_ptr, exponent + EXTENDED_Ebias);  /* Result is positive. */

}