poly_l2.c

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/*---------------------------------------------------------------------------+
 |  poly_l2.c                                                                |
 |                                                                           |
 | Compute the base 2 log of a FPU_REG, using a polynomial approximation.    |
 |                                                                           |
 | Copyright (C) 1992,1993,1994,1997                                         |
 |                  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"

static void log2_kernel(FPU_REG const *arg, u_char argsign,
            Xsig * accum_result, long int *expon);

/*--- poly_l2() -------------------------------------------------------------+
 |   Base 2 logarithm by a polynomial approximation.                         |
 +---------------------------------------------------------------------------*/
void poly_l2(FPU_REG *st0_ptr, FPU_REG *st1_ptr, u_char st1_sign)
{
    long int exponent, expon, expon_expon;
    Xsig accumulator, expon_accum, yaccum;
    u_char sign, argsign;
    FPU_REG x;
    int tag;

    exponent = exponent16(st0_ptr);

    /* From st0_ptr, make a number > sqrt(2)/2 and < sqrt(2) */
    if (st0_ptr->sigh > (unsigned)0xb504f334) {
        /* Treat as  sqrt(2)/2 < st0_ptr < 1 */
        significand(&x) = -significand(st0_ptr);
        setexponent16(&x, -1);
        exponent++;
        argsign = SIGN_NEG;
    } else {
        /* Treat as  1 <= st0_ptr < sqrt(2) */
        x.sigh = st0_ptr->sigh - 0x80000000;
        x.sigl = st0_ptr->sigl;
        setexponent16(&x, 0);
        argsign = SIGN_POS;
    }
    tag = FPU_normalize_nuo(&x);

    if (tag == TAG_Zero) {
        expon = 0;
        accumulator.msw = accumulator.midw = accumulator.lsw = 0;
    } else {
        log2_kernel(&x, argsign, &accumulator, &expon);
    }

    if (exponent < 0) {
        sign = SIGN_NEG;
        exponent = -exponent;
    } else
        sign = SIGN_POS;
    expon_accum.msw = exponent;
    expon_accum.midw = expon_accum.lsw = 0;
    if (exponent) {
        expon_expon = 31 + norm_Xsig(&expon_accum);
        shr_Xsig(&accumulator, expon_expon - expon);

        if (sign ^ argsign)
            negate_Xsig(&accumulator);
        add_Xsig_Xsig(&accumulator, &expon_accum);
    } else {
        expon_expon = expon;
        sign = argsign;
    }

    yaccum.lsw = 0;
    XSIG_LL(yaccum) = significand(st1_ptr);
    mul_Xsig_Xsig(&accumulator, &yaccum);

    expon_expon += round_Xsig(&accumulator);

    if (accumulator.msw == 0) {
        FPU_copy_to_reg1(&CONST_Z, TAG_Zero);
        return;
    }

    significand(st1_ptr) = XSIG_LL(accumulator);
    setexponent16(st1_ptr, expon_expon + exponent16(st1_ptr) + 1);

    tag = FPU_round(st1_ptr, 1, 0, FULL_PRECISION, sign ^ st1_sign);
    FPU_settagi(1, tag);

    set_precision_flag_up();    /* 80486 appears to always do this */

    return;

}

/*--- poly_l2p1() -----------------------------------------------------------+
 |   Base 2 logarithm by a polynomial approximation.                         |
 |   log2(x+1)                                                               |
 +---------------------------------------------------------------------------*/
int poly_l2p1(u_char sign0, u_char sign1,
          FPU_REG * st0_ptr, FPU_REG * st1_ptr, FPU_REG * dest)
{
    u_char tag;
    long int exponent;
    Xsig accumulator, yaccum;

    if (exponent16(st0_ptr) < 0) {
        log2_kernel(st0_ptr, sign0, &accumulator, &exponent);

        yaccum.lsw = 0;
        XSIG_LL(yaccum) = significand(st1_ptr);
        mul_Xsig_Xsig(&accumulator, &yaccum);

        exponent += round_Xsig(&accumulator);

        exponent += exponent16(st1_ptr) + 1;
        if (exponent < EXP_WAY_UNDER)
            exponent = EXP_WAY_UNDER;

        significand(dest) = XSIG_LL(accumulator);
        setexponent16(dest, exponent);

        tag = FPU_round(dest, 1, 0, FULL_PRECISION, sign0 ^ sign1);
        FPU_settagi(1, tag);

        if (tag == TAG_Valid)
            set_precision_flag_up();    /* 80486 appears to always do this */
    } else {
        /* The magnitude of st0_ptr is far too large. */

        if (sign0 != SIGN_POS) {
            /* Trying to get the log of a negative number. */
#ifdef PECULIAR_486     /* Stupid 80486 doesn't worry about log(negative). */
            changesign(st1_ptr);
#else
            if (arith_invalid(1) < 0)
                return 1;
#endif /* PECULIAR_486 */
        }

        /* 80486 appears to do this */
        if (sign0 == SIGN_NEG)
            set_precision_flag_down();
        else
            set_precision_flag_up();
    }

    if (exponent(dest) <= EXP_UNDER)
        EXCEPTION(EX_Underflow);

    return 0;

}

#undef HIPOWER
#define HIPOWER 10
static const unsigned long long logterms[HIPOWER] = {
    0x2a8eca5705fc2ef0LL,
    0xf6384ee1d01febceLL,
    0x093bb62877cdf642LL,
    0x006985d8a9ec439bLL,
    0x0005212c4f55a9c8LL,
    0x00004326a16927f0LL,
    0x0000038d1d80a0e7LL,
    0x0000003141cc80c6LL,
    0x00000002b1668c9fLL,
    0x000000002c7a46aaLL
};

static const unsigned long leadterm = 0xb8000000;

/*--- log2_kernel() ---------------------------------------------------------+
 |   Base 2 logarithm by a polynomial approximation.                         |
 |   log2(x+1)                                                               |
 +---------------------------------------------------------------------------*/
static void log2_kernel(FPU_REG const *arg, u_char argsign, Xsig *accum_result,
            long int *expon)
{
    long int exponent, adj;
    unsigned long long Xsq;
    Xsig accumulator, Numer, Denom, argSignif, arg_signif;

    exponent = exponent16(arg);
    Numer.lsw = Denom.lsw = 0;
    XSIG_LL(Numer) = XSIG_LL(Denom) = significand(arg);
    if (argsign == SIGN_POS) {
        shr_Xsig(&Denom, 2 - (1 + exponent));
        Denom.msw |= 0x80000000;
        div_Xsig(&Numer, &Denom, &argSignif);
    } else {
        shr_Xsig(&Denom, 1 - (1 + exponent));
        negate_Xsig(&Denom);
        if (Denom.msw & 0x80000000) {
            div_Xsig(&Numer, &Denom, &argSignif);
            exponent++;
        } else {
            /* Denom must be 1.0 */
            argSignif.lsw = Numer.lsw;
            argSignif.midw = Numer.midw;
            argSignif.msw = Numer.msw;
        }
    }

#ifndef PECULIAR_486
    /* Should check here that  |local_arg|  is within the valid range */
    if (exponent >= -2) {
        if ((exponent > -2) || (argSignif.msw > (unsigned)0xafb0ccc0)) {
            /* The argument is too large */
        }
    }
#endif /* PECULIAR_486 */

    arg_signif.lsw = argSignif.lsw;
    XSIG_LL(arg_signif) = XSIG_LL(argSignif);
    adj = norm_Xsig(&argSignif);
    accumulator.lsw = argSignif.lsw;
    XSIG_LL(accumulator) = XSIG_LL(argSignif);
    mul_Xsig_Xsig(&accumulator, &accumulator);
    shr_Xsig(&accumulator, 2 * (-1 - (1 + exponent + adj)));
    Xsq = XSIG_LL(accumulator);
    if (accumulator.lsw & 0x80000000)
        Xsq++;

    accumulator.msw = accumulator.midw = accumulator.lsw = 0;
    /* Do the basic fixed point polynomial evaluation */
    polynomial_Xsig(&accumulator, &Xsq, logterms, HIPOWER - 1);

    mul_Xsig_Xsig(&accumulator, &argSignif);
    shr_Xsig(&accumulator, 6 - adj);

    mul32_Xsig(&arg_signif, leadterm);
    add_two_Xsig(&accumulator, &arg_signif, &exponent);

    *expon = exponent + 1;
    accum_result->lsw = accumulator.lsw;
    accum_result->midw = accumulator.midw;
    accum_result->msw = accumulator.msw;

}