Example #1
0
floatx80 floatx80_scale(floatx80 a, floatx80 b)
{
	sbits32 aExp, bExp;
	bits64 aSig, bSig;

	// handle unsupported extended double-precision floating encodings
/*    if (floatx80_is_unsupported(a) || floatx80_is_unsupported(b))
    {
        float_raise(float_flag_invalid);
        return floatx80_default_nan;
    }*/

	aSig = extractFloatx80Frac(a);
	aExp = extractFloatx80Exp(a);
	int aSign = extractFloatx80Sign(a);
	bSig = extractFloatx80Frac(b);
	bExp = extractFloatx80Exp(b);
	int bSign = extractFloatx80Sign(b);

	if (aExp == 0x7FFF) {
		if ((bits64) (aSig<<1) || ((bExp == 0x7FFF) && (bits64) (bSig<<1)))
		{
			return propagateFloatx80NaN(a, b);
		}
		if ((bExp == 0x7FFF) && bSign) {
			float_raise(float_flag_invalid);
			return floatx80_default_nan;
		}
		if (bSig && (bExp == 0)) float_raise(float_flag_denormal);
		return a;
	}
	if (bExp == 0x7FFF) {
		if ((bits64) (bSig<<1)) return propagateFloatx80NaN(a, b);
		if ((aExp | aSig) == 0) {
			if (! bSign) {
				float_raise(float_flag_invalid);
				return floatx80_default_nan;
			}
			return a;
		}
		if (aSig && (aExp == 0)) float_raise(float_flag_denormal);
		if (bSign) return packFloatx80(aSign, 0, 0);
		return packFloatx80(aSign, 0x7FFF, U64(0x8000000000000000));
	}
	if (aExp == 0) {
		if (aSig == 0) return a;
		float_raise(float_flag_denormal);
		normalizeFloatx80Subnormal(aSig, &aExp, &aSig);
	}
	if (bExp == 0) {
		if (bSig == 0) return a;
		float_raise(float_flag_denormal);
		normalizeFloatx80Subnormal(bSig, &bExp, &bSig);
	}

	if (bExp > 0x400E) {
		/* generate appropriate overflow/underflow */
		return roundAndPackFloatx80(80, aSign,
							bSign ? -0x3FFF : 0x7FFF, aSig, 0);
	}
	if (bExp < 0x3FFF) return a;

	int shiftCount = 0x403E - bExp;
	bSig >>= shiftCount;
	sbits32 scale = bSig;
	if (bSign) scale = -scale; /* -32768..32767 */
	return
		roundAndPackFloatx80(80, aSign, aExp+scale, aSig, 0);
}
Example #2
0
int ftan(floatx80 &a, float_status_t &status)
{
    Bit64u aSig0, aSig1 = 0;
    Bit32s aExp, zExp, expDiff;
    int aSign, zSign; 
    int q = 0;

    // handle unsupported extended double-precision floating encodings
    if (floatx80_is_unsupported(a)) 
    {
        goto invalid;
    }

    aSig0 = extractFloatx80Frac(a);
    aExp = extractFloatx80Exp(a);
    aSign = extractFloatx80Sign(a);
     
    /* invalid argument */
    if (aExp == 0x7FFF) {
        if ((Bit64u) (aSig0<<1))
        {
            a = propagateFloatx80NaN(a, status);
            return 0;
        }

    invalid:
        float_raise(status, float_flag_invalid);
        a = floatx80_default_nan;
        return 0;
    }

    if (aExp == 0) {
        if (aSig0 == 0) return 0;
        float_raise(status, float_flag_denormal);
        /* handle pseudo denormals */
        if (! (aSig0 & BX_CONST64(0x8000000000000000)))
        {
            float_raise(status, float_flag_inexact | float_flag_underflow);
            return 0;
        }
        normalizeFloatx80Subnormal(aSig0, &aExp, &aSig0);
    }
    
    zSign = aSign;
    zExp = EXP_BIAS;
    expDiff = aExp - zExp;

    /* argument is out-of-range */
    if (expDiff >= 63) 
        return -1;

    float_raise(status, float_flag_inexact);

    if (expDiff < -1) {    // doesn't require reduction
        if (expDiff <= -68) {
            a = packFloatx80(aSign, aExp, aSig0);
            return 0;
        }
        zExp = aExp;
    }
    else {
        q = reduce_trig_arg(expDiff, zSign, aSig0, aSig1);
    }

    /* **************************** */
    /* argument reduction completed */
    /* **************************** */

    /* using float128 for approximation */
    float128 r = normalizeRoundAndPackFloat128(0, zExp-0x10, aSig0, aSig1, status);

    float128 sin_r = poly_sin(r, status);
    float128 cos_r = poly_cos(r, status);

    if (q & 0x1) {
        r = float128_div(cos_r, sin_r, status);
        zSign = ! zSign;
    } else {
        r = float128_div(sin_r, cos_r, status);
    }

    a = float128_to_floatx80(r, status);
    if (zSign)
        floatx80_chs(a);

    return 0;
}
Example #3
0
floatx80 fyl2xp1(floatx80 a, floatx80 b)
{
    INT32 aExp, bExp;
    UINT64 aSig, bSig, zSig0, zSig1, zSig2;
    int aSign, bSign;

    aSig = extractFloatx80Frac(a);
    aExp = extractFloatx80Exp(a);
    aSign = extractFloatx80Sign(a);
    bSig = extractFloatx80Frac(b);
    bExp = extractFloatx80Exp(b);
    bSign = extractFloatx80Sign(b);
    int zSign = aSign ^ bSign;

    if (aExp == 0x7FFF) {
        if ((UINT64) (aSig<<1)
             || ((bExp == 0x7FFF) && (UINT64) (bSig<<1)))
        {
            return propagateFloatx80NaN(a, b);
        }
        if (aSign)
        {
invalid:
			float_raise(float_flag_invalid);
			return floatx80_default_nan;
    	}
         else {
            if (bExp == 0) {
                if (bSig == 0) goto invalid;
                float_raise(float_flag_denormal);
            }
            return packFloatx80(bSign, 0x7FFF, U64(0x8000000000000000));
        }
    }
    if (bExp == 0x7FFF)
    {
        if ((UINT64) (bSig<<1))
            return propagateFloatx80NaN(a, b);

        if (aExp == 0) {
            if (aSig == 0) goto invalid;
            float_raise(float_flag_denormal);
        }

        return packFloatx80(zSign, 0x7FFF, U64(0x8000000000000000));
    }
    if (aExp == 0) {
        if (aSig == 0) {
            if (bSig && (bExp == 0)) float_raise(float_flag_denormal);
            return packFloatx80(zSign, 0, 0);
        }
        float_raise(float_flag_denormal);
        normalizeFloatx80Subnormal(aSig, &aExp, &aSig);
    }
    if (bExp == 0) {
        if (bSig == 0) return packFloatx80(zSign, 0, 0);
        float_raise(float_flag_denormal);
        normalizeFloatx80Subnormal(bSig, &bExp, &bSig);
    }

    float_raise(float_flag_inexact);

    if (aSign && aExp >= 0x3FFF)
        return a;

    if (aExp >= 0x3FFC) // big argument
    {
        return fyl2x(floatx80_add(a, floatx80_one), b);
    }

    // handle tiny argument
    if (aExp < EXP_BIAS-70)
    {
        // first order approximation, return (a*b)/ln(2)
        INT32 zExp = aExp + FLOAT_LN2INV_EXP - 0x3FFE;

	mul128By64To192(FLOAT_LN2INV_HI, FLOAT_LN2INV_LO, aSig, &zSig0, &zSig1, &zSig2);
        if (0 < (INT64) zSig0) {
            shortShift128Left(zSig0, zSig1, 1, &zSig0, &zSig1);
            --zExp;
        }

        zExp = zExp + bExp - 0x3FFE;
	mul128By64To192(zSig0, zSig1, bSig, &zSig0, &zSig1, &zSig2);
        if (0 < (INT64) zSig0) {
            shortShift128Left(zSig0, zSig1, 1, &zSig0, &zSig1);
            --zExp;
        }

        return
            roundAndPackFloatx80(80, aSign ^ bSign, zExp, zSig0, zSig1);
    }

    /* ******************************** */
    /* using float128 for approximation */
    /* ******************************** */

    shift128Right(aSig<<1, 0, 16, &zSig0, &zSig1);
    float128 x = packFloat128(aSign, aExp, zSig0, zSig1);
    x = poly_l2p1(x);
    return floatx80_mul(b, float128_to_floatx80(x));
}
Example #4
0
static floatx80 fyl2x(floatx80 a, floatx80 b)
{
    UINT64 aSig = extractFloatx80Frac(a);
    INT32 aExp = extractFloatx80Exp(a);
    int aSign = extractFloatx80Sign(a);
    UINT64 bSig = extractFloatx80Frac(b);
    INT32 bExp = extractFloatx80Exp(b);
    int bSign = extractFloatx80Sign(b);

    int zSign = bSign ^ 1;

    if (aExp == 0x7FFF) {
        if ((UINT64) (aSig<<1)
             || ((bExp == 0x7FFF) && (UINT64) (bSig<<1)))
        {
            return propagateFloatx80NaN(a, b);
        }
        if (aSign)
        {
invalid:
			float_raise(float_flag_invalid);
			return floatx80_default_nan;
    	}
        else {
            if (bExp == 0) {
                if (bSig == 0) goto invalid;
                float_raise(float_flag_denormal);
            }
            return packFloatx80(bSign, 0x7FFF, U64(0x8000000000000000));
        }
    }
    if (bExp == 0x7FFF)
    {
        if ((UINT64) (bSig<<1)) return propagateFloatx80NaN(a, b);
        if (aSign && (UINT64)(aExp | aSig)) goto invalid;
        if (aSig && (aExp == 0))
            float_raise(float_flag_denormal);
        if (aExp < 0x3FFF) {
            return packFloatx80(zSign, 0x7FFF, U64(0x8000000000000000));
        }
        if (aExp == 0x3FFF && ((UINT64) (aSig<<1) == 0)) goto invalid;
        return packFloatx80(bSign, 0x7FFF, U64(0x8000000000000000));
    }
    if (aExp == 0) {
        if (aSig == 0) {
            if ((bExp | bSig) == 0) goto invalid;
            float_raise(float_flag_divbyzero);
            return packFloatx80(zSign, 0x7FFF, U64(0x8000000000000000));
        }
        if (aSign) goto invalid;
        float_raise(float_flag_denormal);
        normalizeFloatx80Subnormal(aSig, &aExp, &aSig);
    }
    if (aSign) goto invalid;
    if (bExp == 0) {
        if (bSig == 0) {
            if (aExp < 0x3FFF) return packFloatx80(zSign, 0, 0);
            return packFloatx80(bSign, 0, 0);
        }
        float_raise(float_flag_denormal);
        normalizeFloatx80Subnormal(bSig, &bExp, &bSig);
    }
    if (aExp == 0x3FFF && ((UINT64) (aSig<<1) == 0))
        return packFloatx80(bSign, 0, 0);

    float_raise(float_flag_inexact);

    int ExpDiff = aExp - 0x3FFF;
    aExp = 0;
    if (aSig >= SQRT2_HALF_SIG) {
        ExpDiff++;
        aExp--;
    }

    /* ******************************** */
    /* using float128 for approximation */
    /* ******************************** */

    UINT64 zSig0, zSig1;
    shift128Right(aSig<<1, 0, 16, &zSig0, &zSig1);
    float128 x = packFloat128(0, aExp+0x3FFF, zSig0, zSig1);
    x = poly_l2(x);
    x = float128_add(x, int64_to_float128((INT64) ExpDiff));
    return floatx80_mul(b, float128_to_floatx80(x));
}
Example #5
0
File: fpatan.cpp Project: iver6/BA
floatx80 fpatan(floatx80 a, floatx80 b, float_status_t &status)
{
    // handle unsupported extended double-precision floating encodings
    if (floatx80_is_unsupported(a) || floatx80_is_unsupported(b)) {
        float_raise(status, float_flag_invalid);
        return floatx80_default_nan;
    }

    Bit64u aSig = extractFloatx80Frac(a);
    Bit32s aExp = extractFloatx80Exp(a);
    int aSign = extractFloatx80Sign(a);
    Bit64u bSig = extractFloatx80Frac(b);
    Bit32s bExp = extractFloatx80Exp(b);
    int bSign = extractFloatx80Sign(b);

    int zSign = aSign ^ bSign;

    if (bExp == 0x7FFF)
    {
        if ((Bit64u) (bSig<<1))
            return propagateFloatx80NaN(a, b, status);

        if (aExp == 0x7FFF) {
            if ((Bit64u) (aSig<<1))
                return propagateFloatx80NaN(a, b, status);

            if (aSign) {   /* return 3PI/4 */
                return roundAndPackFloatx80(80, bSign,
                        FLOATX80_3PI4_EXP, FLOAT_3PI4_HI, FLOAT_3PI4_LO, status);
            }
            else {         /* return  PI/4 */
                return roundAndPackFloatx80(80, bSign,
                        FLOATX80_PI4_EXP, FLOAT_PI_HI, FLOAT_PI_LO, status);
            }
        }

        if (aSig && (aExp == 0))
            float_raise(status, float_flag_denormal);

        /* return PI/2 */
        return roundAndPackFloatx80(80, bSign, FLOATX80_PI2_EXP, FLOAT_PI_HI, FLOAT_PI_LO, status);
    }
    if (aExp == 0x7FFF)
    {
        if ((Bit64u) (aSig<<1))
            return propagateFloatx80NaN(a, b, status);

        if (bSig && (bExp == 0))
            float_raise(status, float_flag_denormal);

return_PI_or_ZERO:

        if (aSign) {   /* return PI */
            return roundAndPackFloatx80(80, bSign, FLOATX80_PI_EXP, FLOAT_PI_HI, FLOAT_PI_LO, status);
        } else {       /* return  0 */
            return packFloatx80(bSign, 0, 0);
        }
    }
    if (bExp == 0)
    {
        if (bSig == 0) {
             if (aSig && (aExp == 0)) float_raise(status, float_flag_denormal);
             goto return_PI_or_ZERO;
        }

        float_raise(status, float_flag_denormal);
        normalizeFloatx80Subnormal(bSig, &bExp, &bSig);
    }
    if (aExp == 0)
    {
        if (aSig == 0)   /* return PI/2 */
            return roundAndPackFloatx80(80, bSign, FLOATX80_PI2_EXP, FLOAT_PI_HI, FLOAT_PI_LO, status);

        float_raise(status, float_flag_denormal);
        normalizeFloatx80Subnormal(aSig, &aExp, &aSig);
    }

    float_raise(status, float_flag_inexact);

    /* |a| = |b| ==> return PI/4 */
    if (aSig == bSig && aExp == bExp)
        return roundAndPackFloatx80(80, bSign, FLOATX80_PI4_EXP, FLOAT_PI_HI, FLOAT_PI_LO, status);

    /* ******************************** */
    /* using float128 for approximation */
    /* ******************************** */

    float128 a128 = normalizeRoundAndPackFloat128(0, aExp-0x10, aSig, 0, status);
    float128 b128 = normalizeRoundAndPackFloat128(0, bExp-0x10, bSig, 0, status);
    float128 x;
    int swap = 0, add_pi6 = 0, add_pi4 = 0;

    if (aExp > bExp || (aExp == bExp && aSig > bSig))
    {
        x = float128_div(b128, a128, status);
    }
    else {
        x = float128_div(a128, b128, status);
        swap = 1;
    }

    Bit32s xExp = extractFloat128Exp(x);

    if (xExp <= EXP_BIAS-40)
        goto approximation_completed;

    if (x.hi >= BX_CONST64(0x3ffe800000000000))        // 3/4 < x < 1
    {
        /*
        arctan(x) = arctan((x-1)/(x+1)) + pi/4
        */
        float128 t1 = float128_sub(x, float128_one, status);
        float128 t2 = float128_add(x, float128_one, status);
        x = float128_div(t1, t2, status);
        add_pi4 = 1;
    }
    else
    {
        /* argument correction */
        if (xExp >= 0x3FFD)                     // 1/4 < x < 3/4
        {
            /*
            arctan(x) = arctan((x*sqrt(3)-1)/(x+sqrt(3))) + pi/6
            */
            float128 t1 = float128_mul(x, float128_sqrt3, status);
            float128 t2 = float128_add(x, float128_sqrt3, status);
            x = float128_sub(t1, float128_one, status);
            x = float128_div(x, t2, status);
            add_pi6 = 1;
        }
    }

    x = poly_atan(x, status);
    if (add_pi6) x = float128_add(x, float128_pi6, status);
    if (add_pi4) x = float128_add(x, float128_pi4, status);

approximation_completed:
    if (swap) x = float128_sub(float128_pi2, x, status);
    floatx80 result = float128_to_floatx80(x, status);
    if (zSign) floatx80_chs(result);
    int rSign = extractFloatx80Sign(result);
    if (!bSign && rSign)
        return floatx80_add(result, floatx80_pi, status);
    if (bSign && !rSign)
        return floatx80_sub(result, floatx80_pi, status);
    return result;
}
Example #6
0
static floatx80 do_fprem(floatx80 a, floatx80 b, Bit64u &q, int rounding_mode, float_status_t &status)
{
    Bit32s aExp, bExp, zExp, expDiff;
    Bit64u aSig0, aSig1, bSig;
    int aSign;
    q = 0;

    // handle unsupported extended double-precision floating encodings
    if (floatx80_is_unsupported(a) || floatx80_is_unsupported(b))
    {
        float_raise(status, float_flag_invalid);
        return floatx80_default_nan;
    }

    aSig0 = extractFloatx80Frac(a);
    aExp = extractFloatx80Exp(a);
    aSign = extractFloatx80Sign(a);
    bSig = extractFloatx80Frac(b);
    bExp = extractFloatx80Exp(b);

    if (aExp == 0x7FFF) {
        if ((Bit64u) (aSig0<<1)
                || ((bExp == 0x7FFF) && (Bit64u) (bSig<<1)))
        {
            return propagateFloatx80NaN(a, b, status);
        }
        goto invalid;
    }
    if (bExp == 0x7FFF) {
        if ((Bit64u) (bSig<<1)) return propagateFloatx80NaN(a, b, status);
        return a;
    }
    if (bExp == 0) {
        if (bSig == 0) {
invalid:
            float_raise(status, float_flag_invalid);
            return floatx80_default_nan;
        }
        float_raise(status, float_flag_denormal);
        normalizeFloatx80Subnormal(bSig, &bExp, &bSig);
    }
    if (aExp == 0) {
        if ((Bit64u) (aSig0<<1) == 0) return a;
        float_raise(status, float_flag_denormal);
        normalizeFloatx80Subnormal(aSig0, &aExp, &aSig0);
    }
    expDiff = aExp - bExp;
    aSig1 = 0;

    if (expDiff >= 64) {
        int n = (expDiff & 0x1f) | 0x20;
        remainder_kernel(aSig0, bSig, n, &aSig0, &aSig1);
        zExp = aExp - n;
        q = (Bit64u) -1;
    }
    else {
        zExp = bExp;

        if (expDiff < 0) {
            if (expDiff < -1)
                return (a.fraction & BX_CONST64(0x8000000000000000)) ?
                       packFloatx80(aSign, aExp, aSig0) : a;
            shift128Right(aSig0, 0, 1, &aSig0, &aSig1);
            expDiff = 0;
        }

        if (expDiff > 0) {
            q = remainder_kernel(aSig0, bSig, expDiff, &aSig0, &aSig1);
        }
        else {
            if (bSig <= aSig0) {
                aSig0 -= bSig;
                q = 1;
            }
        }

        if (rounding_mode == float_round_nearest_even)
        {
            Bit64u term0, term1;
            shift128Right(bSig, 0, 1, &term0, &term1);

            if (! lt128(aSig0, aSig1, term0, term1))
            {
                int lt = lt128(term0, term1, aSig0, aSig1);
                int eq = eq128(aSig0, aSig1, term0, term1);

                if ((eq && (q & 1)) || lt) {
                    aSign = !aSign;
                    ++q;
                }
                if (lt) sub128(bSig, 0, aSig0, aSig1, &aSig0, &aSig1);
            }
        }
    }

    return normalizeRoundAndPackFloatx80(80, aSign, zExp, aSig0, aSig1, status);
}
Example #7
0
floatx80 floatx80_mod(floatx80 a, floatx80 b, float_status *status)
{
    flag aSign, zSign;
    int32_t aExp, bExp, expDiff;
    uint64_t aSig0, aSig1, bSig;
    uint64_t qTemp, term0, term1;

    aSig0 = extractFloatx80Frac(a);
    aExp = extractFloatx80Exp(a);
    aSign = extractFloatx80Sign(a);
    bSig = extractFloatx80Frac(b);
    bExp = extractFloatx80Exp(b);

    if (aExp == 0x7FFF) {
        if ((uint64_t) (aSig0 << 1)
            || ((bExp == 0x7FFF) && (uint64_t) (bSig << 1))) {
            return propagateFloatx80NaN(a, b, status);
        }
        goto invalid;
    }
    if (bExp == 0x7FFF) {
        if ((uint64_t) (bSig << 1)) {
            return propagateFloatx80NaN(a, b, status);
        }
        return a;
    }
    if (bExp == 0) {
        if (bSig == 0) {
        invalid:
            float_raise(float_flag_invalid, status);
            return floatx80_default_nan(status);
        }
        normalizeFloatx80Subnormal(bSig, &bExp, &bSig);
    }
    if (aExp == 0) {
        if ((uint64_t) (aSig0 << 1) == 0) {
            return a;
        }
        normalizeFloatx80Subnormal(aSig0, &aExp, &aSig0);
    }
    bSig |= LIT64(0x8000000000000000);
    zSign = aSign;
    expDiff = aExp - bExp;
    aSig1 = 0;
    if (expDiff < 0) {
        return a;
    }
    qTemp = (bSig <= aSig0);
    if (qTemp) {
        aSig0 -= bSig;
    }
    expDiff -= 64;
    while (0 < expDiff) {
        qTemp = estimateDiv128To64(aSig0, aSig1, bSig);
        qTemp = (2 < qTemp) ? qTemp - 2 : 0;
        mul64To128(bSig, qTemp, &term0, &term1);
        sub128(aSig0, aSig1, term0, term1, &aSig0, &aSig1);
        shortShift128Left(aSig0, aSig1, 62, &aSig0, &aSig1);
    }
    expDiff += 64;
    if (0 < expDiff) {
        qTemp = estimateDiv128To64(aSig0, aSig1, bSig);
        qTemp = (2 < qTemp) ? qTemp - 2 : 0;
        qTemp >>= 64 - expDiff;
        mul64To128(bSig, qTemp << (64 - expDiff), &term0, &term1);
        sub128(aSig0, aSig1, term0, term1, &aSig0, &aSig1);
        shortShift128Left(0, bSig, 64 - expDiff, &term0, &term1);
        while (le128(term0, term1, aSig0, aSig1)) {
            ++qTemp;
            sub128(aSig0, aSig1, term0, term1, &aSig0, &aSig1);
        }
    }