Tcl Source Code

	 */

	TclGetIntFromObj(interp, incrPtr, &type1);
	Tcl_AddErrorInfo(interp, "\n    (reading increment)");
	return TCL_ERROR;
    }

    if ((type1 != TCL_NUMBER_BIG) && (type2 != TCL_NUMBER_BIG)) {
	Tcl_WideInt w1, w2, sum;

	TclGetWideIntFromObj(NULL, valuePtr, &w1);
	TclGetWideIntFromObj(NULL, incrPtr, &w2);
	sum = w1 + w2;

	/*
	 * Check for overflow.
	 */

	if (!Overflowing(w1, w2, sum)) {
................................................................................

    contextPtr->index = PTR2INT(data[2]);
    contextPtr->skip = PTR2INT(data[3]);
    contextPtr->oPtr->flags |= FILTER_HANDLING;
    return result;
}
 





















































































/*
 *----------------------------------------------------------------------
 *
 * ExecuteExtendedBinaryMathOp, ExecuteExtendedUnaryMathOp --
 *
 *	These functions do advanced math for binary and unary operators
 *	respectively, so that the main TEBC code does not bear the cost of
................................................................................

    int type1, type2;
    ClientData ptr1, ptr2;
    double d1, d2, dResult;
    Tcl_WideInt w1, w2, wResult;
    mp_int big1, big2, bigResult, bigRemainder;
    Tcl_Obj *objResultPtr;
    int invalid, numPos, zero;
    long shift;

    (void) GetNumberFromObj(NULL, valuePtr, &ptr1, &type1);
    (void) GetNumberFromObj(NULL, value2Ptr, &ptr2, &type2);

    switch (opcode) {
    case INST_MOD:
................................................................................
	    if (w1 == 0) {
		/*
		 * 0 % (non-zero) always yields remainder of 0.
		 */

		return constants[0];
	    }
	    if (type2 != TCL_NUMBER_BIG) {
		Tcl_WideInt wQuotient, wRemainder;
		Tcl_GetWideIntFromObj(NULL, value2Ptr, &w2);
		wQuotient = w1 / w2;

		/*
		 * Force Tcl's integer division rules.
		 * TODO: examine for logic simplification
		 */

................................................................................
	    }
	    shift = (int)(*((const Tcl_WideInt *)ptr2));

	    /*
	     * Handle shifts within the native wide range.
	     */

	    if ((type1 != TCL_NUMBER_BIG)
		    && ((size_t)shift < CHAR_BIT*sizeof(Tcl_WideInt))) {
		TclGetWideIntFromObj(NULL, valuePtr, &w1);
		if (!((w1>0 ? w1 : ~w1)
			& -(((Tcl_WideInt)1)
			<< (CHAR_BIT*sizeof(Tcl_WideInt) - 1 - shift)))) {
		    WIDE_RESULT(w1 << shift);
		}
	    }
	} else {
................................................................................

	Tcl_TakeBignumFromObj(NULL, valuePtr, &big1);

	mp_init(&bigResult);
	if (opcode == INST_LSHIFT) {
	    mp_mul_2d(&big1, shift, &bigResult);
	} else {
	    mp_init(&bigRemainder);
	    mp_div_2d(&big1, shift, &bigResult, &bigRemainder);
	    if (mp_isneg(&bigRemainder)) {
		/*
		 * Convert to Tcl's integer division rules.
		 */

		mp_sub_d(&bigResult, 1, &bigResult);
	    }
	    mp_clear(&bigRemainder);
	}
	mp_clear(&big1);
	BIG_RESULT(&bigResult);
    }

    case INST_BITOR:
    case INST_BITXOR:
    case INST_BITAND:
	if ((type1 == TCL_NUMBER_BIG) || (type2 == TCL_NUMBER_BIG)) {
	    mp_int *First, *Second;

	    Tcl_TakeBignumFromObj(NULL, valuePtr, &big1);
	    Tcl_TakeBignumFromObj(NULL, value2Ptr, &big2);

	    /*
	     * Count how many positive arguments we have. If only one of the
	     * arguments is negative, store it in 'Second'.
	     */

	    if (!mp_isneg(&big1)) {
		numPos = 1 + !mp_isneg(&big2);
		First = &big1;
		Second = &big2;
	    } else {
		First = &big2;
		Second = &big1;
		numPos = (!mp_isneg(First));
	    }
	    mp_init(&bigResult);

	    switch (opcode) {
	    case INST_BITAND:
		switch (numPos) {
		case 2:
		    /*
		     * Both arguments positive, base case.
		     */

		    mp_and(First, Second, &bigResult);
		    break;
		case 1:
		    /*
		     * First is positive; second negative:
		     * P & N = P & ~~N = P&~(-N-1) = P & (P ^ (-N-1))
		     */

		    mp_neg(Second, Second);
		    mp_sub_d(Second, 1, Second);
		    mp_xor(First, Second, &bigResult);
		    mp_and(First, &bigResult, &bigResult);
		    break;
		case 0:
		    /*
		     * Both arguments negative:
		     * a & b = ~ (~a | ~b) = -(-a-1|-b-1)-1
		     */

		    mp_neg(First, First);
		    mp_sub_d(First, 1, First);
		    mp_neg(Second, Second);
		    mp_sub_d(Second, 1, Second);
		    mp_or(First, Second, &bigResult);
		    mp_neg(&bigResult, &bigResult);
		    mp_sub_d(&bigResult, 1, &bigResult);
		    break;
		}
		break;

	    case INST_BITOR:
		switch (numPos) {
		case 2:
		    /*
		     * Both arguments positive, base case.
		     */

		    mp_or(First, Second, &bigResult);
		    break;
		case 1:
		    /*
		     * First is positive; second negative:
		     * N|P = ~(~N&~P) = ~((-N-1)&~P) = -((-N-1)&((-N-1)^P))-1
		     */

		    mp_neg(Second, Second);
		    mp_sub_d(Second, 1, Second);
		    mp_xor(First, Second, &bigResult);
		    mp_and(Second, &bigResult, &bigResult);
		    mp_neg(&bigResult, &bigResult);
		    mp_sub_d(&bigResult, 1, &bigResult);
		    break;
		case 0:
		    /*
		     * Both arguments negative:
		     * a | b = ~ (~a & ~b) = -(-a-1&-b-1)-1
		     */

		    mp_neg(First, First);
		    mp_sub_d(First, 1, First);
		    mp_neg(Second, Second);
		    mp_sub_d(Second, 1, Second);
		    mp_and(First, Second, &bigResult);
		    mp_neg(&bigResult, &bigResult);
		    mp_sub_d(&bigResult, 1, &bigResult);
		    break;
		}
		break;

	    case INST_BITXOR:
		switch (numPos) {
		case 2:
		    /*
		     * Both arguments positive, base case.
		     */

		    mp_xor(First, Second, &bigResult);
		    break;
		case 1:
		    /*
		     * First is positive; second negative:
		     * P^N = ~(P^~N) = -(P^(-N-1))-1
		     */

		    mp_neg(Second, Second);
		    mp_sub_d(Second, 1, Second);
		    mp_xor(First, Second, &bigResult);
		    mp_neg(&bigResult, &bigResult);
		    mp_sub_d(&bigResult, 1, &bigResult);
		    break;
		case 0:
		    /*
		     * Both arguments negative:
		     * a ^ b = (~a ^ ~b) = (-a-1^-b-1)
		     */

		    mp_neg(First, First);
		    mp_sub_d(First, 1, First);
		    mp_neg(Second, Second);
		    mp_sub_d(Second, 1, Second);
		    mp_xor(First, Second, &bigResult);
		    break;
		}
		break;
	    }

	    mp_clear(&big1);
	    mp_clear(&big2);
	    BIG_RESULT(&bigResult);
	}

	if ((type1 == TCL_NUMBER_INT) || (type2 == TCL_NUMBER_INT)) {
	    TclGetWideIntFromObj(NULL, valuePtr, &w1);
	    TclGetWideIntFromObj(NULL, value2Ptr, &w2);

	    switch (opcode) {
	    case INST_BITAND:
		wResult = w1 & w2;
		break;
	    case INST_BITOR:
		wResult = w1 | w2;
		break;
	    case INST_BITXOR:
		wResult = w1 ^ w2;
		break;
	    default:
		/* Unused, here to silence compiler warning. */
		wResult = 0;
	    }
	    WIDE_RESULT(wResult);
	}
	w1 = *((const Tcl_WideInt *)ptr1);
	w2 = *((const Tcl_WideInt *)ptr2);

	switch (opcode) {
	case INST_BITAND:
	    wResult = w1 & w2;
	    break;
................................................................................

	    if (d1==0.0 && d2<0.0) {
		return EXPONENT_OF_ZERO;
	    }
	    dResult = pow(d1, d2);
	    goto doubleResult;
	}
	w2 = 0;
	if (type2 == TCL_NUMBER_INT) {
	    w2 = *((const Tcl_WideInt *) ptr2);
	    if (w2 == 0) {
		/*
		 * Anything to the zero power is 1.
		 */

................................................................................
	    } else if (w2 == 1) {
		/*
		 * Anything to the first power is itself
		 */

		return NULL;
	    }
	}

	switch (type2) {
	case TCL_NUMBER_INT:
	    w2 = *((const Tcl_WideInt *)ptr2);
	    negativeExponent = (w2 < 0);
	    oddExponent = (int) (w2 & (Tcl_WideInt)1);
	    break;
	case TCL_NUMBER_BIG:

	    Tcl_TakeBignumFromObj(NULL, value2Ptr, &big2);
	    negativeExponent = mp_isneg(&big2);
	    mp_mod_2d(&big2, 1, &big2);
	    oddExponent = !mp_iszero(&big2);
	    mp_clear(&big2);
	    break;
	}

	if (type1 == TCL_NUMBER_INT) {
	    w1 = *((const Tcl_WideInt *)ptr1);
	}
	if (negativeExponent) {
	    if (type1 == TCL_NUMBER_INT) {
		switch (w1) {
		case 0:
		    /*
		     * Zero to a negative power is div by zero error.
		     */

		    return EXPONENT_OF_ZERO;
................................................................................
		    /*
		     * 1 to any power is 1.
		     */

		    return constants[1];
		}
	    }



	    /*
	     * Integers with magnitude greater than 1 raise to a negative
	     * power yield the answer zero (see TIP 123).
	     */

	    return constants[0];
	}

	if (type1 == TCL_NUMBER_INT) {



	    switch (w1) {
	    case 0:
		/*
		 * Zero to a positive power is zero.
		 */

		return constants[0];
	    case 1:
................................................................................

		return constants[1];
	    case -1:
		if (!oddExponent) {
		    return constants[1];
		}
		WIDE_RESULT(-1);
	    }
	}

	/*
	 * We refuse to accept exponent arguments that exceed one mp_digit
	 * which means the max exponent value is 2**28-1 = 0x0fffffff =
	 * 268435455, which fits into a signed 32 bit int which is within the
	 * range of the long int type. This means any numeric Tcl_Obj value
................................................................................

	if (type2 != TCL_NUMBER_INT) {
	    Tcl_SetObjResult(interp, Tcl_NewStringObj(
		    "exponent too large", -1));
	    return GENERAL_ARITHMETIC_ERROR;
	}


	if (type1 == TCL_NUMBER_INT) {

	    if (w1 == 2) {
		/*
		 * Reduce small powers of 2 to shifts.
		 */

		if ((Tcl_WideUInt) w2 < (Tcl_WideUInt) CHAR_BIT*sizeof(Tcl_WideInt) - 1) {
		    WIDE_RESULT(((Tcl_WideInt) 1) << (int)w2);
		}
		goto overflowExpon;
	    }
	    if (w1 == -2) {
		int signum = oddExponent ? -1 : 1;

		/*
		 * Reduce small powers of 2 to shifts.
		 */

		if ((Tcl_WideUInt)w2 < CHAR_BIT*sizeof(Tcl_WideInt) - 1){
		    WIDE_RESULT(signum * (((Tcl_WideInt) 1) << (int) w2));
		}
		goto overflowExpon;
	    }
	}
	if (type1 == TCL_NUMBER_INT) {
	    w1 = *((const Tcl_WideInt *) ptr1);
	} else {
	    goto overflowExpon;
	}
	if (w2 - 2 < (long)MaxBase64Size
		&& w1 <=  MaxBase64[w2 - 2]
		&& w1 >= -MaxBase64[w2 - 2]) {
	    /*
	     * Small powers of integers whose result is wide.
	     */


	    wResult = w1 * w1;		/* b**2 */
	    switch (w2) {
	    case 2:
		break;
	    case 3:
		wResult *= w1;		/* b**3 */
		break;
	    case 4:
		wResult *= wResult;	/* b**4 */
		break;
	    case 5:
		wResult *= wResult;	/* b**4 */
		wResult *= w1;		/* b**5 */
		break;
	    case 6:
		wResult *= w1;		/* b**3 */
		wResult *= wResult;	/* b**6 */
		break;
	    case 7:
		wResult *= w1;		/* b**3 */
		wResult *= wResult;	/* b**6 */
		wResult *= w1;		/* b**7 */
		break;
	    case 8:
		wResult *= wResult;	/* b**4 */
		wResult *= wResult;	/* b**8 */
		break;
	    case 9:
		wResult *= wResult;	/* b**4 */
		wResult *= wResult;	/* b**8 */
		wResult *= w1;		/* b**9 */
		break;
	    case 10:
		wResult *= wResult;	/* b**4 */
		wResult *= w1;		/* b**5 */
		wResult *= wResult;	/* b**10 */
		break;
	    case 11:
		wResult *= wResult;	/* b**4 */
		wResult *= w1;		/* b**5 */
		wResult *= wResult;	/* b**10 */
		wResult *= w1;		/* b**11 */
		break;
	    case 12:
		wResult *= w1;		/* b**3 */
		wResult *= wResult;	/* b**6 */
		wResult *= wResult;	/* b**12 */
		break;
	    case 13:
		wResult *= w1;		/* b**3 */
		wResult *= wResult;	/* b**6 */
		wResult *= wResult;	/* b**12 */
		wResult *= w1;		/* b**13 */
		break;
	    case 14:
		wResult *= w1;		/* b**3 */
		wResult *= wResult;	/* b**6 */
		wResult *= w1;		/* b**7 */
		wResult *= wResult;	/* b**14 */
		break;
	    case 15:
		wResult *= w1;		/* b**3 */
		wResult *= wResult;	/* b**6 */
		wResult *= w1;		/* b**7 */
		wResult *= wResult;	/* b**14 */
		wResult *= w1;		/* b**15 */
		break;
	    case 16:
		wResult *= wResult;	/* b**4 */
		wResult *= wResult;	/* b**8 */
		wResult *= wResult;	/* b**16 */
		break;
	    }
	    WIDE_RESULT(wResult);
	}

	/*
	 * Handle cases of powers > 16 that still fit in a 64-bit word by
	 * doing table lookup.
	 */
................................................................................
	    if (TclIsNaN(dResult)) {
		TclExprFloatError(interp, dResult);
		return GENERAL_ARITHMETIC_ERROR;
	    }
#endif
	    DOUBLE_RESULT(dResult);
	}
	if ((type1 != TCL_NUMBER_BIG) && (type2 != TCL_NUMBER_BIG)) {
	    TclGetWideIntFromObj(NULL, valuePtr, &w1);
	    TclGetWideIntFromObj(NULL, value2Ptr, &w2);

	    switch (opcode) {
	    case INST_ADD:
		wResult = w1 + w2;
		if ((type1 == TCL_NUMBER_INT) || (type2 == TCL_NUMBER_INT))
		{
		    /*

	 */

	TclGetIntFromObj(interp, incrPtr, &type1);
	Tcl_AddErrorInfo(interp, "\n    (reading increment)");
	return TCL_ERROR;
    }

    if ((type1 == TCL_NUMBER_INT) && (type2 == TCL_NUMBER_INT)) {
	Tcl_WideInt w1, w2, sum;

	w1 = *((const Tcl_WideInt *)ptr1);
	w2 = *((const Tcl_WideInt *)ptr2);
	sum = w1 + w2;

	/*
	 * Check for overflow.
	 */

	if (!Overflowing(w1, w2, sum)) {
................................................................................

    contextPtr->index = PTR2INT(data[2]);
    contextPtr->skip = PTR2INT(data[3]);
    contextPtr->oPtr->flags |= FILTER_HANDLING;
    return result;
}
 
/*
 * WidePwrSmallExpon --
 *
 * Helper to calculate small powers of integers whose result is wide.
 */
static inline Tcl_WideInt
WidePwrSmallExpon(Tcl_WideInt w1, Tcl_WideInt exponent) {

    Tcl_WideInt wResult;

    wResult = w1 * w1;		/* b**2 */
    switch (exponent) {
    case 2:
	break;
    case 3:
	wResult *= w1;		/* b**3 */
	break;
    case 4:
	wResult *= wResult;	/* b**4 */
	break;
    case 5:
	wResult *= wResult;	/* b**4 */
	wResult *= w1;		/* b**5 */
	break;
    case 6:
	wResult *= w1;		/* b**3 */
	wResult *= wResult;	/* b**6 */
	break;
    case 7:
	wResult *= w1;		/* b**3 */
	wResult *= wResult;	/* b**6 */
	wResult *= w1;		/* b**7 */
	break;
    case 8:
	wResult *= wResult;	/* b**4 */
	wResult *= wResult;	/* b**8 */
	break;
    case 9:
	wResult *= wResult;	/* b**4 */
	wResult *= wResult;	/* b**8 */
	wResult *= w1;		/* b**9 */
	break;
    case 10:
	wResult *= wResult;	/* b**4 */
	wResult *= w1;		/* b**5 */
	wResult *= wResult;	/* b**10 */
	break;
    case 11:
	wResult *= wResult;	/* b**4 */
	wResult *= w1;		/* b**5 */
	wResult *= wResult;	/* b**10 */
	wResult *= w1;		/* b**11 */
	break;
    case 12:
	wResult *= w1;		/* b**3 */
	wResult *= wResult;	/* b**6 */
	wResult *= wResult;	/* b**12 */
	break;
    case 13:
	wResult *= w1;		/* b**3 */
	wResult *= wResult;	/* b**6 */
	wResult *= wResult;	/* b**12 */
	wResult *= w1;		/* b**13 */
	break;
    case 14:
	wResult *= w1;		/* b**3 */
	wResult *= wResult;	/* b**6 */
	wResult *= w1;		/* b**7 */
	wResult *= wResult;	/* b**14 */
	break;
    case 15:
	wResult *= w1;		/* b**3 */
	wResult *= wResult;	/* b**6 */
	wResult *= w1;		/* b**7 */
	wResult *= wResult;	/* b**14 */
	wResult *= w1;		/* b**15 */
	break;
    case 16:
	wResult *= wResult;	/* b**4 */
	wResult *= wResult;	/* b**8 */
	wResult *= wResult;	/* b**16 */
	break;
    }
    return wResult;
}
/*
 *----------------------------------------------------------------------
 *
 * ExecuteExtendedBinaryMathOp, ExecuteExtendedUnaryMathOp --
 *
 *	These functions do advanced math for binary and unary operators
 *	respectively, so that the main TEBC code does not bear the cost of
................................................................................

    int type1, type2;
    ClientData ptr1, ptr2;
    double d1, d2, dResult;
    Tcl_WideInt w1, w2, wResult;
    mp_int big1, big2, bigResult, bigRemainder;
    Tcl_Obj *objResultPtr;
    int invalid, zero;
    long shift;

    (void) GetNumberFromObj(NULL, valuePtr, &ptr1, &type1);
    (void) GetNumberFromObj(NULL, value2Ptr, &ptr2, &type2);

    switch (opcode) {
    case INST_MOD:
................................................................................
	    if (w1 == 0) {
		/*
		 * 0 % (non-zero) always yields remainder of 0.
		 */

		return constants[0];
	    }
	    if (type2 == TCL_NUMBER_INT) {
		Tcl_WideInt wQuotient, wRemainder;
		w2 = *((const Tcl_WideInt *)ptr2);
		wQuotient = w1 / w2;

		/*
		 * Force Tcl's integer division rules.
		 * TODO: examine for logic simplification
		 */

................................................................................
	    }
	    shift = (int)(*((const Tcl_WideInt *)ptr2));

	    /*
	     * Handle shifts within the native wide range.
	     */

	    if ((type1 == TCL_NUMBER_INT)
		    && ((size_t)shift < CHAR_BIT*sizeof(Tcl_WideInt))) {
		w1 = *((const Tcl_WideInt *)ptr1);
		if (!((w1>0 ? w1 : ~w1)
			& -(((Tcl_WideInt)1)
			<< (CHAR_BIT*sizeof(Tcl_WideInt) - 1 - shift)))) {
		    WIDE_RESULT(w1 << shift);
		}
	    }
	} else {
................................................................................

	Tcl_TakeBignumFromObj(NULL, valuePtr, &big1);

	mp_init(&bigResult);
	if (opcode == INST_LSHIFT) {
	    mp_mul_2d(&big1, shift, &bigResult);
	} else {

	    mp_tc_div_2d(&big1, shift, &bigResult);








	}
	mp_clear(&big1);
	BIG_RESULT(&bigResult);
    }

    case INST_BITOR:
    case INST_BITXOR:
    case INST_BITAND:
	if ((type1 != TCL_NUMBER_INT) || (type2 != TCL_NUMBER_INT)) {


	    Tcl_TakeBignumFromObj(NULL, valuePtr, &big1);
	    Tcl_TakeBignumFromObj(NULL, value2Ptr, &big2);















	    mp_init(&bigResult);

	    switch (opcode) {
	    case INST_BITAND:






























		mp_tc_and(&big1, &big2, &bigResult);

		break;



	    case INST_BITOR:


















		mp_tc_or(&big1, &big2, &bigResult);

		break;

















	    case INST_BITXOR:

















		mp_tc_xor(&big1, &big2, &bigResult);















		break;
	    }

	    mp_clear(&big1);
	    mp_clear(&big2);
	    BIG_RESULT(&bigResult);
	}





















	w1 = *((const Tcl_WideInt *)ptr1);
	w2 = *((const Tcl_WideInt *)ptr2);

	switch (opcode) {
	case INST_BITAND:
	    wResult = w1 & w2;
	    break;
................................................................................

	    if (d1==0.0 && d2<0.0) {
		return EXPONENT_OF_ZERO;
	    }
	    dResult = pow(d1, d2);
	    goto doubleResult;
	}
	w1 = w2 = 0; /* to silence compiler warning (maybe-uninitialized) */
	if (type2 == TCL_NUMBER_INT) {
	    w2 = *((const Tcl_WideInt *) ptr2);
	    if (w2 == 0) {
		/*
		 * Anything to the zero power is 1.
		 */

................................................................................
	    } else if (w2 == 1) {
		/*
		 * Anything to the first power is itself
		 */

		return NULL;
	    }





	    negativeExponent = (w2 < 0);
	    oddExponent = (int) (w2 & (Tcl_WideInt)1);


	} else {
	    Tcl_TakeBignumFromObj(NULL, value2Ptr, &big2);
	    negativeExponent = mp_isneg(&big2);
	    mp_mod_2d(&big2, 1, &big2);
	    oddExponent = !mp_iszero(&big2);
	    mp_clear(&big2);

	}

	if (type1 == TCL_NUMBER_INT) {
	    w1 = *((const Tcl_WideInt *)ptr1);

	    if (negativeExponent) {

		switch (w1) {
		case 0:
		    /*
		     * Zero to a negative power is div by zero error.
		     */

		    return EXPONENT_OF_ZERO;
................................................................................
		    /*
		     * 1 to any power is 1.
		     */

		    return constants[1];
		}
	    }
	}
	if (negativeExponent) {

	    /*
	     * Integers with magnitude greater than 1 raise to a negative
	     * power yield the answer zero (see TIP 123).
	     */

	    return constants[0];
	}

	if (type1 != TCL_NUMBER_INT) {
	    goto overflowExpon;
	}

	switch (w1) {
	    case 0:
		/*
		 * Zero to a positive power is zero.
		 */

		return constants[0];
	    case 1:
................................................................................

		return constants[1];
	    case -1:
		if (!oddExponent) {
		    return constants[1];
		}
		WIDE_RESULT(-1);

	}

	/*
	 * We refuse to accept exponent arguments that exceed one mp_digit
	 * which means the max exponent value is 2**28-1 = 0x0fffffff =
	 * 268435455, which fits into a signed 32 bit int which is within the
	 * range of the long int type. This means any numeric Tcl_Obj value
................................................................................

	if (type2 != TCL_NUMBER_INT) {
	    Tcl_SetObjResult(interp, Tcl_NewStringObj(
		    "exponent too large", -1));
	    return GENERAL_ARITHMETIC_ERROR;
	}

	/* From here (up to overflowExpon) w1 and exponent w2 are wide-int's. */
	assert(type1 == TCL_NUMBER_INT && type2 == TCL_NUMBER_INT);

	if (w1 == 2) {
	    /*
	     * Reduce small powers of 2 to shifts.
	     */

	    if ((Tcl_WideUInt) w2 < (Tcl_WideUInt) CHAR_BIT*sizeof(Tcl_WideInt) - 1) {
		WIDE_RESULT(((Tcl_WideInt) 1) << (int)w2);
	    }
	    goto overflowExpon;
	}
	if (w1 == -2) {
	    int signum = oddExponent ? -1 : 1;

	    /*
	     * Reduce small powers of 2 to shifts.
	     */

	    if ((Tcl_WideUInt)w2 < CHAR_BIT*sizeof(Tcl_WideInt) - 1){
		WIDE_RESULT(signum * (((Tcl_WideInt) 1) << (int) w2));
	    }






	    goto overflowExpon;
	}
	if (w2 - 2 < (long)MaxBase64Size
		&& w1 <=  MaxBase64[w2 - 2]
		&& w1 >= -MaxBase64[w2 - 2]) {
	    /*
	     * Small powers of integers whose result is wide.
	     */
	    wResult = WidePwrSmallExpon(w1, w2);










































































	    WIDE_RESULT(wResult);
	}

	/*
	 * Handle cases of powers > 16 that still fit in a 64-bit word by
	 * doing table lookup.
	 */
................................................................................
	    if (TclIsNaN(dResult)) {
		TclExprFloatError(interp, dResult);
		return GENERAL_ARITHMETIC_ERROR;
	    }
#endif
	    DOUBLE_RESULT(dResult);
	}
	if ((type1 == TCL_NUMBER_INT) && (type2 == TCL_NUMBER_INT)) {
	    w1 = *((const Tcl_WideInt *)ptr1);
	    w2 = *((const Tcl_WideInt *)ptr2);

	    switch (opcode) {
	    case INST_ADD:
		wResult = w1 + w2;
		if ((type1 == TCL_NUMBER_INT) || (type2 == TCL_NUMBER_INT))
		{
		    /*

    0, /* 66 */
    TclBN_mp_expt_d_ex, /* 67 */
    TclBN_mp_set_long_long, /* 68 */
    TclBN_mp_get_long_long, /* 69 */
    TclBN_mp_set_long, /* 70 */
    TclBN_mp_get_long, /* 71 */
    TclBN_mp_get_int, /* 72 */




};

static const TclStubHooks tclStubHooks = {
    &tclPlatStubs,
    &tclIntStubs,
    &tclIntPlatStubs
};

    0, /* 66 */
    TclBN_mp_expt_d_ex, /* 67 */
    TclBN_mp_set_long_long, /* 68 */
    TclBN_mp_get_long_long, /* 69 */
    TclBN_mp_set_long, /* 70 */
    TclBN_mp_get_long, /* 71 */
    TclBN_mp_get_int, /* 72 */
    TclBN_mp_tc_and, /* 73 */
    TclBN_mp_tc_or, /* 74 */
    TclBN_mp_tc_xor, /* 75 */
    TclBN_mp_tc_div_2d, /* 76 */
};

static const TclStubHooks tclStubHooks = {
    &tclPlatStubs,
    &tclIntStubs,
    &tclIntPlatStubs
};

}
declare 71 {
    unsigned long TclBN_mp_get_long(const mp_int *a)
}
declare 72 {
    unsigned long TclBN_mp_get_int(const mp_int *a)
}
















# Local Variables:
# mode: tcl
# End:

}
declare 71 {
    unsigned long TclBN_mp_get_long(const mp_int *a)
}
declare 72 {
    unsigned long TclBN_mp_get_int(const mp_int *a)
}

# Added in libtommath 1.1.0
declare 73 {
    int TclBN_mp_tc_and(const mp_int *a, const mp_int *b, mp_int *c)
}
declare 74 {
    int TclBN_mp_tc_or(const mp_int *a, const mp_int *b, mp_int *c)
}
declare 75 {
    int TclBN_mp_tc_xor(const mp_int *a, const mp_int *b, mp_int *c)
}
declare 76 {
    int TclBN_mp_tc_div_2d(const mp_int *a, int b, mp_int *c)
}


# Local Variables:
# mode: tcl
# End:

#define mp_set_long TclBN_mp_set_long
#define mp_set_long_long TclBN_mp_set_long_long
#define mp_shrink TclBN_mp_shrink
#define mp_sqr TclBN_mp_sqr
#define mp_sqrt TclBN_mp_sqrt
#define mp_sub TclBN_mp_sub
#define mp_sub_d TclBN_mp_sub_d




#define mp_to_unsigned_bin TclBN_mp_to_unsigned_bin
#define mp_to_unsigned_bin_n TclBN_mp_to_unsigned_bin_n
#define mp_toom_mul TclBN_mp_toom_mul
#define mp_toom_sqr TclBN_mp_toom_sqr
#define mp_toradix_n TclBN_mp_toradix_n
#define mp_unsigned_bin_size TclBN_mp_unsigned_bin_size
#define mp_xor TclBN_mp_xor
................................................................................
EXTERN Tcl_WideUInt	TclBN_mp_get_long_long(const mp_int *a);
/* 70 */
EXTERN int		TclBN_mp_set_long(mp_int *a, unsigned long i);
/* 71 */
EXTERN unsigned long	TclBN_mp_get_long(const mp_int *a);
/* 72 */
EXTERN unsigned long	TclBN_mp_get_int(const mp_int *a);












typedef struct TclTomMathStubs {
    int magic;
    void *hooks;

    int (*tclBN_epoch) (void); /* 0 */
    int (*tclBN_revision) (void); /* 1 */
................................................................................
    void (*reserved66)(void);
    int (*tclBN_mp_expt_d_ex) (const mp_int *a, mp_digit b, mp_int *c, int fast); /* 67 */
    int (*tclBN_mp_set_long_long) (mp_int *a, Tcl_WideUInt i); /* 68 */
    Tcl_WideUInt (*tclBN_mp_get_long_long) (const mp_int *a); /* 69 */
    int (*tclBN_mp_set_long) (mp_int *a, unsigned long i); /* 70 */
    unsigned long (*tclBN_mp_get_long) (const mp_int *a); /* 71 */
    unsigned long (*tclBN_mp_get_int) (const mp_int *a); /* 72 */




} TclTomMathStubs;

extern const TclTomMathStubs *tclTomMathStubsPtr;

#ifdef __cplusplus
}
#endif
................................................................................
	(tclTomMathStubsPtr->tclBN_mp_get_long_long) /* 69 */
#define TclBN_mp_set_long \
	(tclTomMathStubsPtr->tclBN_mp_set_long) /* 70 */
#define TclBN_mp_get_long \
	(tclTomMathStubsPtr->tclBN_mp_get_long) /* 71 */
#define TclBN_mp_get_int \
	(tclTomMathStubsPtr->tclBN_mp_get_int) /* 72 */









#endif /* defined(USE_TCL_STUBS) */

/* !END!: Do not edit above this line. */

#undef TCL_STORAGE_CLASS
#define TCL_STORAGE_CLASS DLLIMPORT

#endif /* _TCLINTDECLS */

#define mp_set_long TclBN_mp_set_long
#define mp_set_long_long TclBN_mp_set_long_long
#define mp_shrink TclBN_mp_shrink
#define mp_sqr TclBN_mp_sqr
#define mp_sqrt TclBN_mp_sqrt
#define mp_sub TclBN_mp_sub
#define mp_sub_d TclBN_mp_sub_d
#define mp_tc_and TclBN_mp_tc_and
#define mp_tc_div_2d TclBN_mp_tc_div_2d
#define mp_tc_or TclBN_mp_tc_or
#define mp_tc_xor TclBN_mp_tc_xor
#define mp_to_unsigned_bin TclBN_mp_to_unsigned_bin
#define mp_to_unsigned_bin_n TclBN_mp_to_unsigned_bin_n
#define mp_toom_mul TclBN_mp_toom_mul
#define mp_toom_sqr TclBN_mp_toom_sqr
#define mp_toradix_n TclBN_mp_toradix_n
#define mp_unsigned_bin_size TclBN_mp_unsigned_bin_size
#define mp_xor TclBN_mp_xor
................................................................................
EXTERN Tcl_WideUInt	TclBN_mp_get_long_long(const mp_int *a);
/* 70 */
EXTERN int		TclBN_mp_set_long(mp_int *a, unsigned long i);
/* 71 */
EXTERN unsigned long	TclBN_mp_get_long(const mp_int *a);
/* 72 */
EXTERN unsigned long	TclBN_mp_get_int(const mp_int *a);
/* 73 */
EXTERN int		TclBN_mp_tc_and(const mp_int *a, const mp_int *b,
				mp_int *c);
/* 74 */
EXTERN int		TclBN_mp_tc_or(const mp_int *a, const mp_int *b,
				mp_int *c);
/* 75 */
EXTERN int		TclBN_mp_tc_xor(const mp_int *a, const mp_int *b,
				mp_int *c);
/* 76 */
EXTERN int		TclBN_mp_tc_div_2d(const mp_int *a, int b, mp_int *c);

typedef struct TclTomMathStubs {
    int magic;
    void *hooks;

    int (*tclBN_epoch) (void); /* 0 */
    int (*tclBN_revision) (void); /* 1 */
................................................................................
    void (*reserved66)(void);
    int (*tclBN_mp_expt_d_ex) (const mp_int *a, mp_digit b, mp_int *c, int fast); /* 67 */
    int (*tclBN_mp_set_long_long) (mp_int *a, Tcl_WideUInt i); /* 68 */
    Tcl_WideUInt (*tclBN_mp_get_long_long) (const mp_int *a); /* 69 */
    int (*tclBN_mp_set_long) (mp_int *a, unsigned long i); /* 70 */
    unsigned long (*tclBN_mp_get_long) (const mp_int *a); /* 71 */
    unsigned long (*tclBN_mp_get_int) (const mp_int *a); /* 72 */
    int (*tclBN_mp_tc_and) (const mp_int *a, const mp_int *b, mp_int *c); /* 73 */
    int (*tclBN_mp_tc_or) (const mp_int *a, const mp_int *b, mp_int *c); /* 74 */
    int (*tclBN_mp_tc_xor) (const mp_int *a, const mp_int *b, mp_int *c); /* 75 */
    int (*tclBN_mp_tc_div_2d) (const mp_int *a, int b, mp_int *c); /* 76 */
} TclTomMathStubs;

extern const TclTomMathStubs *tclTomMathStubsPtr;

#ifdef __cplusplus
}
#endif
................................................................................
	(tclTomMathStubsPtr->tclBN_mp_get_long_long) /* 69 */
#define TclBN_mp_set_long \
	(tclTomMathStubsPtr->tclBN_mp_set_long) /* 70 */
#define TclBN_mp_get_long \
	(tclTomMathStubsPtr->tclBN_mp_get_long) /* 71 */
#define TclBN_mp_get_int \
	(tclTomMathStubsPtr->tclBN_mp_get_int) /* 72 */
#define TclBN_mp_tc_and \
	(tclTomMathStubsPtr->tclBN_mp_tc_and) /* 73 */
#define TclBN_mp_tc_or \
	(tclTomMathStubsPtr->tclBN_mp_tc_or) /* 74 */
#define TclBN_mp_tc_xor \
	(tclTomMathStubsPtr->tclBN_mp_tc_xor) /* 75 */
#define TclBN_mp_tc_div_2d \
	(tclTomMathStubsPtr->tclBN_mp_tc_div_2d) /* 76 */

#endif /* defined(USE_TCL_STUBS) */

/* !END!: Do not edit above this line. */

#undef TCL_STORAGE_CLASS
#define TCL_STORAGE_CLASS DLLIMPORT

#endif /* _TCLINTDECLS */

    if (code == TCL_OK) {
	if (numType == TCL_NUMBER_INT) {
	    /* objPtr holds an integer in the signed wide range */
	    *widePtr = *(Tcl_WideInt *)cd;
	    return TCL_OK;
	}
	if (numType == TCL_NUMBER_BIG) {
	    /* objPtr holds an integer outside the signed wide range */
	    /* Truncate to the signed wide range. */
	    if (mp_isneg((mp_int *)cd)) {
		*widePtr = WIDE_MIN;
	    } else {
		*widePtr = WIDE_MAX;
	    }
	    return TCL_OK;
	}
	/* Must be a double -> not a valid index */
	goto parseError;
    }

    /* objPtr does not hold a number, check the end+/- format... */
    if (GetEndOffsetFromObj(objPtr, endValue, widePtr) == TCL_OK) {
	return TCL_OK;
    }

    if (code == TCL_OK) {
	if (numType == TCL_NUMBER_INT) {
	    /* objPtr holds an integer in the signed wide range */
	    *widePtr = *(Tcl_WideInt *)cd;
	    return TCL_OK;
	}
	if (numType != TCL_NUMBER_BIG) {
	    /* Must be a double -> not a valid index */
	    goto parseError;
	}

	/* objPtr holds an integer outside the signed wide range */
	/* Truncate to the signed wide range. */
	*widePtr = mp_isneg((mp_int *)cd) ? WIDE_MIN : WIDE_MAX;
    return TCL_OK;



    }

    /* objPtr does not hold a number, check the end+/- format... */
    if (GetEndOffsetFromObj(objPtr, endValue, widePtr) == TCL_OK) {
	return TCL_OK;
    }

LibTomMath is licensed under DUAL licensing terms.

Choose and use the license of your needs.

[LICENSE #1]

LibTomMath is public domain.  As should all quality software be.

Tom St Denis

[/LICENSE #1]

[LICENSE #2]

            DO WHAT THE FUCK YOU WANT TO PUBLIC LICENSE
                    Version 2, December 2004

 Copyright (C) 2004 Sam Hocevar <sam@hocevar.net>

 Everyone is permitted to copy and distribute verbatim or modified
 copies of this license document, and changing it is allowed as long
 as the name is changed.

            DO WHAT THE FUCK YOU WANT TO PUBLIC LICENSE
   TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION

  0. You just DO WHAT THE FUCK YOU WANT TO. 

[/LICENSE #2]

                          The LibTom license

This is free and unencumbered software released into the public domain.

Anyone is free to copy, modify, publish, use, compile, sell, or
distribute this software, either in source code form or as a compiled
binary, for any purpose, commercial or non-commercial, and by any
means.

In jurisdictions that recognize copyright laws, the author or authors
of this software dedicate any and all copyright interest in the
software to the public domain. We make this dedication for the benefit
of the public at large and to the detriment of our heirs and
successors. We intend this dedication to be an overt act of
relinquishment in perpetuity of all present and future rights to this
software under copyright law.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR
OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
OTHER DEALINGS IN THE SOFTWARE.

For more information, please refer to <http://unlicense.org/>

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

static const struct {
   int code;
   const char *msg;
} msgs[] = {
   { MP_OKAY, "Successful" },

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

static const struct {
   int code;
   const char *msg;
} msgs[] = {
   { MP_OKAY, "Successful" },

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* computes the modular inverse via binary extended euclidean algorithm,
 * that is c = 1/a mod b
 *
 * Based on slow invmod except this is optimized for the case where b is
 * odd as per HAC Note 14.64 on pp. 610

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* computes the modular inverse via binary extended euclidean algorithm,
 * that is c = 1/a mod b
 *
 * Based on slow invmod except this is optimized for the case where b is
 * odd as per HAC Note 14.64 on pp. 610

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* computes xR**-1 == x (mod N) via Montgomery Reduction
 *
 * This is an optimized implementation of montgomery_reduce
 * which uses the comba method to quickly calculate the columns of the
 * reduction.

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* computes xR**-1 == x (mod N) via Montgomery Reduction
 *
 * This is an optimized implementation of montgomery_reduce
 * which uses the comba method to quickly calculate the columns of the
 * reduction.

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* Fast (comba) multiplier
 *
 * This is the fast column-array [comba] multiplier.  It is
 * designed to compute the columns of the product first
 * then handle the carries afterwards.  This has the effect

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* Fast (comba) multiplier
 *
 * This is the fast column-array [comba] multiplier.  It is
 * designed to compute the columns of the product first
 * then handle the carries afterwards.  This has the effect

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* this is a modified version of fast_s_mul_digs that only produces
 * output digits *above* digs.  See the comments for fast_s_mul_digs
 * to see how it works.
 *
 * This is used in the Barrett reduction since for one of the multiplications

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* this is a modified version of fast_s_mul_digs that only produces
 * output digits *above* digs.  See the comments for fast_s_mul_digs
 * to see how it works.
 *
 * This is used in the Barrett reduction since for one of the multiplications

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* the jist of squaring...
 * you do like mult except the offset of the tmpx [one that
 * starts closer to zero] can't equal the offset of tmpy.
 * So basically you set up iy like before then you min it with
 * (ty-tx) so that it never happens.  You double all those

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* the jist of squaring...
 * you do like mult except the offset of the tmpx [one that
 * starts closer to zero] can't equal the offset of tmpy.
 * So basically you set up iy like before then you min it with
 * (ty-tx) so that it never happens.  You double all those

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* computes a = 2**b
 *
 * Simple algorithm which zeroes the int, grows it then just sets one bit
 * as required.
 */

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* computes a = 2**b
 *
 * Simple algorithm which zeroes the int, grows it then just sets one bit
 * as required.
 */

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* b = |a|
 *
 * Simple function copies the input and fixes the sign to positive
 */
int mp_abs(const mp_int *a, mp_int *b)

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* b = |a|
 *
 * Simple function copies the input and fixes the sign to positive
 */
int mp_abs(const mp_int *a, mp_int *b)

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* high level addition (handles signs) */
int mp_add(const mp_int *a, const mp_int *b, mp_int *c)
{
   int     sa, sb, res;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* high level addition (handles signs) */
int mp_add(const mp_int *a, const mp_int *b, mp_int *c)
{
   int     sa, sb, res;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* single digit addition */
int mp_add_d(const mp_int *a, mp_digit b, mp_int *c)
{
   int     res, ix, oldused;
   mp_digit *tmpa, *tmpc, mu;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* single digit addition */
int mp_add_d(const mp_int *a, mp_digit b, mp_int *c)
{
   int     res, ix, oldused;
   mp_digit *tmpa, *tmpc, mu;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* d = a + b (mod c) */
int mp_addmod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d)
{
   int     res;
   mp_int  t;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* d = a + b (mod c) */
int mp_addmod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d)
{
   int     res;
   mp_int  t;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* AND two ints together */
int mp_and(const mp_int *a, const mp_int *b, mp_int *c)
{
   int     res, ix, px;
   mp_int  t;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* AND two ints together */
int mp_and(const mp_int *a, const mp_int *b, mp_int *c)
{
   int     res, ix, px;
   mp_int  t;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* trim unused digits
 *
 * This is used to ensure that leading zero digits are
 * trimed and the leading "used" digit will be non-zero
 * Typically very fast.  Also fixes the sign if there

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* trim unused digits
 *
 * This is used to ensure that leading zero digits are
 * trimed and the leading "used" digit will be non-zero
 * Typically very fast.  Also fixes the sign if there

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* clear one (frees)  */
void mp_clear(mp_int *a)
{
   int i;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* clear one (frees)  */
void mp_clear(mp_int *a)
{
   int i;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

#include <stdarg.h>

void mp_clear_multi(mp_int *mp, ...)
{
   mp_int *next_mp = mp;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

#include <stdarg.h>

void mp_clear_multi(mp_int *mp, ...)
{
   mp_int *next_mp = mp;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* compare two ints (signed)*/
int mp_cmp(const mp_int *a, const mp_int *b)
{
   /* compare based on sign */
   if (a->sign != b->sign) {

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* compare two ints (signed)*/
int mp_cmp(const mp_int *a, const mp_int *b)
{
   /* compare based on sign */
   if (a->sign != b->sign) {

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* compare a digit */
int mp_cmp_d(const mp_int *a, mp_digit b)
{
   /* compare based on sign */
   if (a->sign == MP_NEG) {

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* compare a digit */
int mp_cmp_d(const mp_int *a, mp_digit b)
{
   /* compare based on sign */
   if (a->sign == MP_NEG) {

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* compare maginitude of two ints (unsigned) */
int mp_cmp_mag(const mp_int *a, const mp_int *b)
{
   int     n;
   mp_digit *tmpa, *tmpb;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* compare maginitude of two ints (unsigned) */
int mp_cmp_mag(const mp_int *a, const mp_int *b)
{
   int     n;
   mp_digit *tmpa, *tmpb;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

static const int lnz[16] = {
   4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0
};

/* Counts the number of lsbs which are zero before the first zero bit */

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

static const int lnz[16] = {
   4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0
};

/* Counts the number of lsbs which are zero before the first zero bit */

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* b = ~a */
int mp_complement(const mp_int *a, mp_int *b)
{
   int res = mp_neg(a, b);
   return (res == MP_OKAY) ? mp_sub_d(b, 1uL, b) : res;
}
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* b = ~a */
int mp_complement(const mp_int *a, mp_int *b)
{
   int res = mp_neg(a, b);
   return (res == MP_OKAY) ? mp_sub_d(b, 1uL, b) : res;
}
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* copy, b = a */
int mp_copy(const mp_int *a, mp_int *b)
{
   int     res, n;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* copy, b = a */
int mp_copy(const mp_int *a, mp_int *b)
{
   int     res, n;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* returns the number of bits in an int */
int mp_count_bits(const mp_int *a)
{
   int     r;
   mp_digit q;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* returns the number of bits in an int */
int mp_count_bits(const mp_int *a)
{
   int     r;
   mp_digit q;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

#ifdef BN_MP_DIV_SMALL

/* slower bit-bang division... also smaller */
int mp_div(const mp_int *a, const mp_int *b, mp_int *c, mp_int *d)
{

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

#ifdef BN_MP_DIV_SMALL

/* slower bit-bang division... also smaller */
int mp_div(const mp_int *a, const mp_int *b, mp_int *c, mp_int *d)
{

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* b = a/2 */
int mp_div_2(const mp_int *a, mp_int *b)
{
   int     x, res, oldused;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* b = a/2 */
int mp_div_2(const mp_int *a, mp_int *b)
{
   int     x, res, oldused;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* shift right by a certain bit count (store quotient in c, optional remainder in d) */
int mp_div_2d(const mp_int *a, int b, mp_int *c, mp_int *d)
{
   mp_digit D, r, rr;
   int     x, res;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* shift right by a certain bit count (store quotient in c, optional remainder in d) */
int mp_div_2d(const mp_int *a, int b, mp_int *c, mp_int *d)
{
   mp_digit D, r, rr;
   int     x, res;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* divide by three (based on routine from MPI and the GMP manual) */
int mp_div_3(const mp_int *a, mp_int *c, mp_digit *d)
{
   mp_int   q;
   mp_word  w, t;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* divide by three (based on routine from MPI and the GMP manual) */
int mp_div_3(const mp_int *a, mp_int *c, mp_digit *d)
{
   mp_int   q;
   mp_word  w, t;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* single digit division (based on routine from MPI) */
int mp_div_d(const mp_int *a, mp_digit b, mp_int *c, mp_digit *d)
{
   mp_int  q;
   mp_word w;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* single digit division (based on routine from MPI) */
int mp_div_d(const mp_int *a, mp_digit b, mp_int *c, mp_digit *d)
{
   mp_int  q;
   mp_word w;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* determines if a number is a valid DR modulus */
int mp_dr_is_modulus(const mp_int *a)
{
   int ix;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* determines if a number is a valid DR modulus */
int mp_dr_is_modulus(const mp_int *a)
{
   int ix;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* reduce "x" in place modulo "n" using the Diminished Radix algorithm.
 *
 * Based on algorithm from the paper
 *
 * "Generating Efficient Primes for Discrete Log Cryptosystems"

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* reduce "x" in place modulo "n" using the Diminished Radix algorithm.
 *
 * Based on algorithm from the paper
 *
 * "Generating Efficient Primes for Discrete Log Cryptosystems"

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* determines the setup value */
void mp_dr_setup(const mp_int *a, mp_digit *d)
{
   /* the casts are required if DIGIT_BIT is one less than
    * the number of bits in a mp_digit [e.g. DIGIT_BIT==31]

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* determines the setup value */
void mp_dr_setup(const mp_int *a, mp_digit *d)
{
   /* the casts are required if DIGIT_BIT is one less than
    * the number of bits in a mp_digit [e.g. DIGIT_BIT==31]

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* swap the elements of two integers, for cases where you can't simply swap the
 * mp_int pointers around
 */
void mp_exch(mp_int *a, mp_int *b)
{

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* swap the elements of two integers, for cases where you can't simply swap the
 * mp_int pointers around
 */
void mp_exch(mp_int *a, mp_int *b)
{

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* based on gmp's mpz_export.
 * see http://gmplib.org/manual/Integer-Import-and-Export.html
 */
int mp_export(void *rop, size_t *countp, int order, size_t size,
              int endian, size_t nails, const mp_int *op)

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* based on gmp's mpz_export.
 * see http://gmplib.org/manual/Integer-Import-and-Export.html
 */
int mp_export(void *rop, size_t *countp, int order, size_t size,
              int endian, size_t nails, const mp_int *op)

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* wrapper function for mp_expt_d_ex() */
int mp_expt_d(const mp_int *a, mp_digit b, mp_int *c)
{
   return mp_expt_d_ex(a, b, c, 0);
}

#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* wrapper function for mp_expt_d_ex() */
int mp_expt_d(const mp_int *a, mp_digit b, mp_int *c)
{
   return mp_expt_d_ex(a, b, c, 0);
}

#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* calculate c = a**b  using a square-multiply algorithm */
int mp_expt_d_ex(const mp_int *a, mp_digit b, mp_int *c, int fast)
{
   int     res;
   unsigned int x;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* calculate c = a**b  using a square-multiply algorithm */
int mp_expt_d_ex(const mp_int *a, mp_digit b, mp_int *c, int fast)
{
   int     res;
   unsigned int x;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */


/* this is a shell function that calls either the normal or Montgomery
 * exptmod functions.  Originally the call to the montgomery code was
 * embedded in the normal function but that wasted alot of stack space
 * for nothing (since 99% of the time the Montgomery code would be called)

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */


/* this is a shell function that calls either the normal or Montgomery
 * exptmod functions.  Originally the call to the montgomery code was
 * embedded in the normal function but that wasted alot of stack space
 * for nothing (since 99% of the time the Montgomery code would be called)

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* computes Y == G**X mod P, HAC pp.616, Algorithm 14.85
 *
 * Uses a left-to-right k-ary sliding window to compute the modular exponentiation.
 * The value of k changes based on the size of the exponent.
 *
................................................................................
      mp_set(&res, 1uL);
      if ((err = mp_mod(G, P, &M[1])) != MP_OKAY) {
         goto LBL_RES;
      }
   }

   /* compute the value at M[1<<(winsize-1)] by squaring M[1] (winsize-1) times */
   if ((err = mp_copy(&M[1], &M[1 << (winsize - 1)])) != MP_OKAY) {
      goto LBL_RES;
   }

   for (x = 0; x < (winsize - 1); x++) {
      if ((err = mp_sqr(&M[1 << (winsize - 1)], &M[1 << (winsize - 1)])) != MP_OKAY) {
         goto LBL_RES;
      }
      if ((err = redux(&M[1 << (winsize - 1)], P, mp)) != MP_OKAY) {
         goto LBL_RES;
      }
   }

   /* create upper table */
   for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
      if ((err = mp_mul(&M[x - 1], &M[1], &M[x])) != MP_OKAY) {

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* computes Y == G**X mod P, HAC pp.616, Algorithm 14.85
 *
 * Uses a left-to-right k-ary sliding window to compute the modular exponentiation.
 * The value of k changes based on the size of the exponent.
 *
................................................................................
      mp_set(&res, 1uL);
      if ((err = mp_mod(G, P, &M[1])) != MP_OKAY) {
         goto LBL_RES;
      }
   }

   /* compute the value at M[1<<(winsize-1)] by squaring M[1] (winsize-1) times */
   if ((err = mp_copy(&M[1], &M[(size_t)1 << (winsize - 1)])) != MP_OKAY) {
      goto LBL_RES;
   }

   for (x = 0; x < (winsize - 1); x++) {
      if ((err = mp_sqr(&M[(size_t)1 << (winsize - 1)], &M[(size_t)1 << (winsize - 1)])) != MP_OKAY) {
         goto LBL_RES;
      }
      if ((err = redux(&M[(size_t)1 << (winsize - 1)], P, mp)) != MP_OKAY) {
         goto LBL_RES;
      }
   }

   /* create upper table */
   for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
      if ((err = mp_mul(&M[x - 1], &M[1], &M[x])) != MP_OKAY) {

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* Extended euclidean algorithm of (a, b) produces
   a*u1 + b*u2 = u3
 */
int mp_exteuclid(const mp_int *a, const mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3)
{

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* Extended euclidean algorithm of (a, b) produces
   a*u1 + b*u2 = u3
 */
int mp_exteuclid(const mp_int *a, const mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3)
{

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

#ifndef LTM_NO_FILE
/* read a bigint from a file stream in ASCII */
int mp_fread(mp_int *a, int radix, FILE *stream)
{
   int err, ch, neg, y;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

#ifndef LTM_NO_FILE
/* read a bigint from a file stream in ASCII */
int mp_fread(mp_int *a, int radix, FILE *stream)
{
   int err, ch, neg, y;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

#ifndef LTM_NO_FILE
int mp_fwrite(const mp_int *a, int radix, FILE *stream)
{
   char *buf;
   int err, len, x;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

#ifndef LTM_NO_FILE
int mp_fwrite(const mp_int *a, int radix, FILE *stream)
{
   char *buf;
   int err, len, x;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* Greatest Common Divisor using the binary method */
int mp_gcd(const mp_int *a, const mp_int *b, mp_int *c)
{
   mp_int  u, v;
   int     k, u_lsb, v_lsb, res;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* Greatest Common Divisor using the binary method */
int mp_gcd(const mp_int *a, const mp_int *b, mp_int *c)
{
   mp_int  u, v;
   int     k, u_lsb, v_lsb, res;

#include "tommath_private.h"
#ifdef BN_MP_GET_BIT_C

/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense
 */

/* Checks the bit at position b and returns MP_YES
   if the bit is 1, MP_NO if it is 0 and MP_VAL
   in case of error */
int mp_get_bit(const mp_int *a, int b)
{
   int limb;
   mp_digit bit, isset;

   if (b < 0) {
      return MP_VAL;
   }

   limb = b / DIGIT_BIT;

   /*
    * Zero is a special value with the member "used" set to zero.
    * Needs to be tested before the check for the upper boundary
    * otherwise (limb >= a->used) would be true for a = 0
    */

   if (mp_iszero(a) != MP_NO) {
      return MP_NO;
   }

   if (limb >= a->used) {
      return MP_VAL;
   }

   bit = (mp_digit)(1) << (b % DIGIT_BIT);

   isset = a->dp[limb] & bit;
   return (isset != 0u) ? MP_YES : MP_NO;
}

#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

#include "tommath_private.h"
#ifdef BN_MP_GET_DOUBLE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense
 */

double mp_get_double(const mp_int *a)
{
   int i;
   double d = 0.0, fac = 1.0;
   for (i = 0; i < DIGIT_BIT; ++i) {
      fac *= 2.0;
   }
   for (i = USED(a); i --> 0;) {
      d = (d * fac) + (double)DIGIT(a, i);
   }
   return (mp_isneg(a) != MP_NO) ? -d : d;
}
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* get the lower 32-bits of an mp_int */
unsigned long mp_get_int(const mp_int *a)
{
   int i;
   mp_min_u32 res;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* get the lower 32-bits of an mp_int */
unsigned long mp_get_int(const mp_int *a)
{
   int i;
   mp_min_u32 res;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* get the lower unsigned long of an mp_int, platform dependent */
unsigned long mp_get_long(const mp_int *a)
{
   int i;
   unsigned long res;
................................................................................
   while (--i >= 0) {
      res = (res << DIGIT_BIT) | DIGIT(a, i);
   }
#endif
   return res;
}
#endif

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* get the lower unsigned long of an mp_int, platform dependent */
unsigned long mp_get_long(const mp_int *a)
{
   int i;
   unsigned long res;
................................................................................
   while (--i >= 0) {
      res = (res << DIGIT_BIT) | DIGIT(a, i);
   }
#endif
   return res;
}
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* get the lower unsigned long long of an mp_int, platform dependent */
Tcl_WideUInt mp_get_long_long(const mp_int *a)
{
   int i;
   Tcl_WideUInt res;
................................................................................
   while (--i >= 0) {
      res = (res << DIGIT_BIT) | DIGIT(a, i);
   }
#endif
   return res;
}
#endif

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* get the lower unsigned long long of an mp_int, platform dependent */
Tcl_WideUInt mp_get_long_long(const mp_int *a)
{
   int i;
   Tcl_WideUInt res;
................................................................................
   while (--i >= 0) {
      res = (res << DIGIT_BIT) | DIGIT(a, i);
   }
#endif
   return res;
}
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* grow as required */
int mp_grow(mp_int *a, int size)
{
   int     i;
   mp_digit *tmp;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* grow as required */
int mp_grow(mp_int *a, int size)
{
   int     i;
   mp_digit *tmp;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* based on gmp's mpz_import.
 * see http://gmplib.org/manual/Integer-Import-and-Export.html
 */
int mp_import(mp_int *rop, size_t count, int order, size_t size,
              int endian, size_t nails, const void *op)

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* based on gmp's mpz_import.
 * see http://gmplib.org/manual/Integer-Import-and-Export.html
 */
int mp_import(mp_int *rop, size_t count, int order, size_t size,
              int endian, size_t nails, const void *op)

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* init a new mp_int */
int mp_init(mp_int *a)
{
   int i;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* init a new mp_int */
int mp_init(mp_int *a)
{
   int i;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* creates "a" then copies b into it */
int mp_init_copy(mp_int *a, const mp_int *b)
{
   int     res;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* creates "a" then copies b into it */
int mp_init_copy(mp_int *a, const mp_int *b)
{
   int     res;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

#include <stdarg.h>

int mp_init_multi(mp_int *mp, ...)
{
   mp_err res = MP_OKAY;      /* Assume ok until proven otherwise */

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

#include <stdarg.h>

int mp_init_multi(mp_int *mp, ...)
{
   mp_err res = MP_OKAY;      /* Assume ok until proven otherwise */

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* initialize and set a digit */
int mp_init_set(mp_int *a, mp_digit b)
{
   int err;
   if ((err = mp_init(a)) != MP_OKAY) {

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* initialize and set a digit */
int mp_init_set(mp_int *a, mp_digit b)
{
   int err;
   if ((err = mp_init(a)) != MP_OKAY) {

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* initialize and set a digit */
int mp_init_set_int(mp_int *a, unsigned long b)
{
   int err;
   if ((err = mp_init(a)) != MP_OKAY) {

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* initialize and set a digit */
int mp_init_set_int(mp_int *a, unsigned long b)
{
   int err;
   if ((err = mp_init(a)) != MP_OKAY) {

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* init an mp_init for a given size */
int mp_init_size(mp_int *a, int size)
{
   int x;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* init an mp_init for a given size */
int mp_init_size(mp_int *a, int size)
{
   int x;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* hac 14.61, pp608 */
int mp_invmod(const mp_int *a, const mp_int *b, mp_int *c)
{
   /* b cannot be negative and has to be >1 */
   if ((b->sign == MP_NEG) || (mp_cmp_d(b, 1uL) != MP_GT)) {

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* hac 14.61, pp608 */
int mp_invmod(const mp_int *a, const mp_int *b, mp_int *c)
{
   /* b cannot be negative and has to be >1 */
   if ((b->sign == MP_NEG) || (mp_cmp_d(b, 1uL) != MP_GT)) {

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* hac 14.61, pp608 */
int mp_invmod_slow(const mp_int *a, const mp_int *b, mp_int *c)
{
   mp_int  x, y, u, v, A, B, C, D;
   int     res;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* hac 14.61, pp608 */
int mp_invmod_slow(const mp_int *a, const mp_int *b, mp_int *c)
{
   mp_int  x, y, u, v, A, B, C, D;
   int     res;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* Check if remainders are possible squares - fast exclude non-squares */
static const char rem_128[128] = {
   0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
   0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
   1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* Check if remainders are possible squares - fast exclude non-squares */
static const char rem_128[128] = {
   0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
   0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
   1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* computes the jacobi c = (a | n) (or Legendre if n is prime)
 * HAC pp. 73 Algorithm 2.149
 * HAC is wrong here, as the special case of (0 | 1) is not
 * handled correctly.
 */
int mp_jacobi(const mp_int *a, const mp_int *n, int *c)
{
   mp_int  a1, p1;
   int     k, s, r, res;
   mp_digit residue;

   /* if a < 0 return MP_VAL */
   if (mp_isneg(a) == MP_YES) {
      return MP_VAL;
   }

   /* if n <= 0 return MP_VAL */
   if (mp_cmp_d(n, 0uL) != MP_GT) {
      return MP_VAL;
   }

   /* step 1. handle case of a == 0 */
   if (mp_iszero(a) == MP_YES) {
      /* special case of a == 0 and n == 1 */
      if (mp_cmp_d(n, 1uL) == MP_EQ) {
         *c = 1;
      } else {
         *c = 0;

      }
      return MP_OKAY;
   }

   /* step 2.  if a == 1, return 1 */
   if (mp_cmp_d(a, 1uL) == MP_EQ) {
      *c = 1;
      return MP_OKAY;
   }

   /* default */
   s = 0;

   /* step 3.  write a = a1 * 2**k  */
   if ((res = mp_init_copy(&a1, a)) != MP_OKAY) {
      return res;
   }

   if ((res = mp_init(&p1)) != MP_OKAY) {
      goto LBL_A1;
   }

   /* divide out larger power of two */
   k = mp_cnt_lsb(&a1);
   if ((res = mp_div_2d(&a1, k, &a1, NULL)) != MP_OKAY) {
      goto LBL_P1;
   }

   /* step 4.  if e is even set s=1 */
   if (((unsigned)k & 1u) == 0u) {
      s = 1;
   } else {
      /* else set s=1 if p = 1/7 (mod 8) or s=-1 if p = 3/5 (mod 8) */
      residue = n->dp[0] & 7u;

      if ((residue == 1u) || (residue == 7u)) {
         s = 1;
      } else if ((residue == 3u) || (residue == 5u)) {
         s = -1;
      }
   }

   /* step 5.  if p == 3 (mod 4) *and* a1 == 3 (mod 4) then s = -s */
   if (((n->dp[0] & 3u) == 3u) && ((a1.dp[0] & 3u) == 3u)) {
      s = -s;
   }

   /* if a1 == 1 we're done */
   if (mp_cmp_d(&a1, 1uL) == MP_EQ) {
      *c = s;
   } else {
      /* n1 = n mod a1 */
      if ((res = mp_mod(n, &a1, &p1)) != MP_OKAY) {
         goto LBL_P1;
      }
      if ((res = mp_jacobi(&p1, &a1, &r)) != MP_OKAY) {
         goto LBL_P1;
      }
      *c = s * r;
   }

   /* done */
   res = MP_OKAY;
LBL_P1:
   mp_clear(&p1);
LBL_A1:
   mp_clear(&a1);
   return res;
}
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* computes the jacobi c = (a | n) (or Legendre if n is prime)
 * Kept for legacy reasons, please use mp_kronecker() instead


 */
int mp_jacobi(const mp_int *a, const mp_int *n, int *c)
{




   /* if a < 0 return MP_VAL */
   if (mp_isneg(a) == MP_YES) {
      return MP_VAL;
   }

   /* if n <= 0 return MP_VAL */
   if (mp_cmp_d(n, 0uL) != MP_GT) {
      return MP_VAL;
   }








   return mp_kronecker(a, n, c);
}




































































#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* c = |a| * |b| using Karatsuba Multiplication using
 * three half size multiplications
 *
 * Let B represent the radix [e.g. 2**DIGIT_BIT] and
 * let n represent half of the number of digits in

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* c = |a| * |b| using Karatsuba Multiplication using
 * three half size multiplications
 *
 * Let B represent the radix [e.g. 2**DIGIT_BIT] and
 * let n represent half of the number of digits in

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* Karatsuba squaring, computes b = a*a using three
 * half size squarings
 *
 * See comments of karatsuba_mul for details.  It
 * is essentially the same algorithm but merely

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* Karatsuba squaring, computes b = a*a using three
 * half size squarings
 *
 * See comments of karatsuba_mul for details.  It
 * is essentially the same algorithm but merely

#include "tommath_private.h"
#ifdef BN_MP_KRONECKER_C

/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense
 */

/*
   Kronecker symbol (a|p)
   Straightforward implementation of algorithm 1.4.10 in
   Henri Cohen: "A Course in Computational Algebraic Number Theory"

   @book{cohen2013course,
     title={A course in computational algebraic number theory},
     author={Cohen, Henri},
     volume={138},
     year={2013},
     publisher={Springer Science \& Business Media}
    }
 */
int mp_kronecker(const mp_int *a, const mp_int *p, int *c)
{
   mp_int a1, p1, r;

   int e = MP_OKAY;
   int v, k;

   static const int table[8] = {0, 1, 0, -1, 0, -1, 0, 1};

   if (mp_iszero(p) != MP_NO) {
      if ((a->used == 1) && (a->dp[0] == 1u)) {
         *c = 1;
         return e;
      } else {
         *c = 0;
         return e;
      }
   }

   if ((mp_iseven(a) != MP_NO) && (mp_iseven(p) != MP_NO)) {
      *c = 0;
      return e;
   }

   if ((e = mp_init_copy(&a1, a)) != MP_OKAY) {
      return e;
   }
   if ((e = mp_init_copy(&p1, p)) != MP_OKAY) {
      goto LBL_KRON_0;
   }

   v = mp_cnt_lsb(&p1);
   if ((e = mp_div_2d(&p1, v, &p1, NULL)) != MP_OKAY) {
      goto LBL_KRON_1;
   }

   if ((v & 0x1) == 0) {
      k = 1;
   } else {
      k = table[a->dp[0] & 7u];
   }

   if (p1.sign == MP_NEG) {
      p1.sign = MP_ZPOS;
      if (a1.sign == MP_NEG) {
         k = -k;
      }
   }

   if ((e = mp_init(&r)) != MP_OKAY) {
      goto LBL_KRON_1;
   }

   for (;;) {
      if (mp_iszero(&a1) != MP_NO) {
         if (mp_cmp_d(&p1, 1uL) == MP_EQ) {
            *c = k;
            goto LBL_KRON;
         } else {
            *c = 0;
            goto LBL_KRON;
         }
      }

      v = mp_cnt_lsb(&a1);
      if ((e = mp_div_2d(&a1, v, &a1, NULL)) != MP_OKAY) {
         goto LBL_KRON;
      }

      if ((v & 0x1) == 1) {
         k = k * table[p1.dp[0] & 7u];
      }

      if (a1.sign == MP_NEG) {
         /*
          * Compute k = (-1)^((a1)*(p1-1)/4) * k
          * a1.dp[0] + 1 cannot overflow because the MSB
          * of the type mp_digit is not set by definition
          */
         if (((a1.dp[0] + 1u) & p1.dp[0] & 2u) != 0u) {
            k = -k;
         }
      } else {
         /* compute k = (-1)^((a1-1)*(p1-1)/4) * k */
         if ((a1.dp[0] & p1.dp[0] & 2u) != 0u) {
            k = -k;
         }
      }

      if ((e = mp_copy(&a1, &r)) != MP_OKAY) {
         goto LBL_KRON;
      }
      r.sign = MP_ZPOS;
      if ((e = mp_mod(&p1, &r, &a1)) != MP_OKAY) {
         goto LBL_KRON;
      }
      if ((e = mp_copy(&r, &p1)) != MP_OKAY) {
         goto LBL_KRON;
      }
   }

LBL_KRON:
   mp_clear(&r);
LBL_KRON_1:
   mp_clear(&p1);
LBL_KRON_0:
   mp_clear(&a1);

   return e;
}

#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* computes least common multiple as |a*b|/(a, b) */
int mp_lcm(const mp_int *a, const mp_int *b, mp_int *c)
{
   int     res;
   mp_int  t1, t2;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* computes least common multiple as |a*b|/(a, b) */
int mp_lcm(const mp_int *a, const mp_int *b, mp_int *c)
{
   int     res;
   mp_int  t1, t2;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* shift left a certain amount of digits */
int mp_lshd(mp_int *a, int b)
{
   int     x, res;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* shift left a certain amount of digits */
int mp_lshd(mp_int *a, int b)
{
   int     x, res;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* c = a mod b, 0 <= c < b if b > 0, b < c <= 0 if b < 0 */
int mp_mod(const mp_int *a, const mp_int *b, mp_int *c)
{
   mp_int  t;
   int     res;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* c = a mod b, 0 <= c < b if b > 0, b < c <= 0 if b < 0 */
int mp_mod(const mp_int *a, const mp_int *b, mp_int *c)
{
   mp_int  t;
   int     res;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* calc a value mod 2**b */
int mp_mod_2d(const mp_int *a, int b, mp_int *c)
{
   int     x, res;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* calc a value mod 2**b */
int mp_mod_2d(const mp_int *a, int b, mp_int *c)
{
   int     x, res;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

int mp_mod_d(const mp_int *a, mp_digit b, mp_digit *c)
{
   return mp_div_d(a, b, NULL, c);
}
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

int mp_mod_d(const mp_int *a, mp_digit b, mp_digit *c)
{
   return mp_div_d(a, b, NULL, c);
}
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/*
 * shifts with subtractions when the result is greater than b.
 *
 * The method is slightly modified to shift B unconditionally upto just under
 * the leading bit of b.  This saves alot of multiple precision shifting.

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/*
 * shifts with subtractions when the result is greater than b.
 *
 * The method is slightly modified to shift B unconditionally upto just under
 * the leading bit of b.  This saves alot of multiple precision shifting.

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* computes xR**-1 == x (mod N) via Montgomery Reduction */
int mp_montgomery_reduce(mp_int *x, const mp_int *n, mp_digit rho)
{
   int     ix, res, digs;
   mp_digit mu;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* computes xR**-1 == x (mod N) via Montgomery Reduction */
int mp_montgomery_reduce(mp_int *x, const mp_int *n, mp_digit rho)
{
   int     ix, res, digs;
   mp_digit mu;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* setups the montgomery reduction stuff */
int mp_montgomery_setup(const mp_int *n, mp_digit *rho)
{
   mp_digit x, b;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* setups the montgomery reduction stuff */
int mp_montgomery_setup(const mp_int *n, mp_digit *rho)
{
   mp_digit x, b;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* high level multiplication (handles sign) */
int mp_mul(const mp_int *a, const mp_int *b, mp_int *c)
{
   int     res, neg;
   neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* high level multiplication (handles sign) */
int mp_mul(const mp_int *a, const mp_int *b, mp_int *c)
{
   int     res, neg;
   neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* b = a*2 */
int mp_mul_2(const mp_int *a, mp_int *b)
{
   int     x, res, oldused;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* b = a*2 */
int mp_mul_2(const mp_int *a, mp_int *b)
{
   int     x, res, oldused;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* shift left by a certain bit count */
int mp_mul_2d(const mp_int *a, int b, mp_int *c)
{
   mp_digit d;
   int      res;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* shift left by a certain bit count */
int mp_mul_2d(const mp_int *a, int b, mp_int *c)
{
   mp_digit d;
   int      res;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* multiply by a digit */
int mp_mul_d(const mp_int *a, mp_digit b, mp_int *c)
{
   mp_digit u, *tmpa, *tmpc;
   mp_word  r;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* multiply by a digit */
int mp_mul_d(const mp_int *a, mp_digit b, mp_int *c)
{
   mp_digit u, *tmpa, *tmpc;
   mp_word  r;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* d = a * b (mod c) */
int mp_mulmod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d)
{
   int     res;
   mp_int  t;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* d = a * b (mod c) */
int mp_mulmod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d)
{
   int     res;
   mp_int  t;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* wrapper function for mp_n_root_ex()
 * computes c = (a)**(1/b) such that (c)**b <= a and (c+1)**b > a
 */
int mp_n_root(const mp_int *a, mp_digit b, mp_int *c)
{

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* wrapper function for mp_n_root_ex()
 * computes c = (a)**(1/b) such that (c)**b <= a and (c+1)**b > a
 */
int mp_n_root(const mp_int *a, mp_digit b, mp_int *c)
{

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* find the n'th root of an integer
 *
 * Result found such that (c)**b <= a and (c+1)**b > a
 *
 * This algorithm uses Newton's approximation

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* find the n'th root of an integer
 *
 * Result found such that (c)**b <= a and (c+1)**b > a
 *
 * This algorithm uses Newton's approximation

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* b = -a */
int mp_neg(const mp_int *a, mp_int *b)
{
   int     res;
   if (a != b) {

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* b = -a */
int mp_neg(const mp_int *a, mp_int *b)
{
   int     res;
   if (a != b) {

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* OR two ints together */
int mp_or(const mp_int *a, const mp_int *b, mp_int *c)
{
   int     res, ix, px;
   mp_int  t;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* OR two ints together */
int mp_or(const mp_int *a, const mp_int *b, mp_int *c)
{
   int     res, ix, px;
   mp_int  t;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* performs one Fermat test.
 *
 * If "a" were prime then b**a == b (mod a) since the order of
 * the multiplicative sub-group would be phi(a) = a-1.  That means
 * it would be the same as b**(a mod (a-1)) == b**1 == b (mod a).

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* performs one Fermat test.
 *
 * If "a" were prime then b**a == b (mod a) since the order of
 * the multiplicative sub-group would be phi(a) = a-1.  That means
 * it would be the same as b**(a mod (a-1)) == b**1 == b (mod a).

#include "tommath_private.h"
#ifdef BN_MP_PRIME_FROBENIUS_UNDERWOOD_C

/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense
 */

/*
 *  See file bn_mp_prime_is_prime.c or the documentation in doc/bn.tex for the details
 */
#ifndef LTM_USE_FIPS_ONLY

#ifdef MP_8BIT
/*
 * floor of positive solution of
 * (2^16)-1 = (a+4)*(2*a+5)
 * TODO: Both values are smaller than N^(1/4), would have to use a bigint
 *       for a instead but any a biger than about 120 are already so rare that
 *       it is possible to ignore them and still get enough pseudoprimes.
 *       But it is still a restriction of the set of available pseudoprimes
 *       which makes this implementation less secure if used stand-alone.
 */
#define LTM_FROBENIUS_UNDERWOOD_A 177
#else
#define LTM_FROBENIUS_UNDERWOOD_A 32764
#endif
int mp_prime_frobenius_underwood(const mp_int *N, int *result)
{
   mp_int T1z, T2z, Np1z, sz, tz;

   int a, ap2, length, i, j, isset;
   int e;

   *result = MP_NO;

   if ((e = mp_init_multi(&T1z, &T2z, &Np1z, &sz, &tz, NULL)) != MP_OKAY) {
      return e;
   }

   for (a = 0; a < LTM_FROBENIUS_UNDERWOOD_A; a++) {
      /* TODO: That's ugly! No, really, it is! */
      if ((a==2) || (a==4) || (a==7) || (a==8) || (a==10) ||
          (a==14) || (a==18) || (a==23) || (a==26) || (a==28)) {
         continue;
      }
      /* (32764^2 - 4) < 2^31, no bigint for >MP_8BIT needed) */
      if ((e = mp_set_long(&T1z, (unsigned long)a)) != MP_OKAY) {
         goto LBL_FU_ERR;
      }

      if ((e = mp_sqr(&T1z, &T1z)) != MP_OKAY) {
         goto LBL_FU_ERR;
      }

      if ((e = mp_sub_d(&T1z, 4uL, &T1z)) != MP_OKAY) {
         goto LBL_FU_ERR;
      }

      if ((e = mp_kronecker(&T1z, N, &j)) != MP_OKAY) {
         goto LBL_FU_ERR;
      }

      if (j == -1) {
         break;
      }

      if (j == 0) {
         /* composite */
         goto LBL_FU_ERR;
      }
   }
   /* Tell it a composite and set return value accordingly */
   if (a >= LTM_FROBENIUS_UNDERWOOD_A) {
      e = MP_ITER;
      goto LBL_FU_ERR;
   }
   /* Composite if N and (a+4)*(2*a+5) are not coprime */
   if ((e = mp_set_long(&T1z, (unsigned long)((a+4)*((2*a)+5)))) != MP_OKAY) {
      goto LBL_FU_ERR;
   }

   if ((e = mp_gcd(N, &T1z, &T1z)) != MP_OKAY) {
      goto LBL_FU_ERR;
   }

   if (!((T1z.used == 1) && (T1z.dp[0] == 1u))) {
      goto LBL_FU_ERR;
   }

   ap2 = a + 2;
   if ((e = mp_add_d(N, 1uL, &Np1z)) != MP_OKAY) {
      goto LBL_FU_ERR;
   }

   mp_set(&sz, 1uL);
   mp_set(&tz, 2uL);
   length = mp_count_bits(&Np1z);

   for (i = length - 2; i >= 0; i--) {
      /*
       * temp = (sz*(a*sz+2*tz))%N;
       * tz   = ((tz-sz)*(tz+sz))%N;
       * sz   = temp;
       */
      if ((e = mp_mul_2(&tz, &T2z)) != MP_OKAY) {
         goto LBL_FU_ERR;
      }

      /* a = 0 at about 50% of the cases (non-square and odd input) */
      if (a != 0) {
         if ((e = mp_mul_d(&sz, (mp_digit)a, &T1z)) != MP_OKAY) {
            goto LBL_FU_ERR;
         }
         if ((e = mp_add(&T1z, &T2z, &T2z)) != MP_OKAY) {
            goto LBL_FU_ERR;
         }
      }

      if ((e = mp_mul(&T2z, &sz, &T1z)) != MP_OKAY) {
         goto LBL_FU_ERR;
      }
      if ((e = mp_sub(&tz, &sz, &T2z)) != MP_OKAY) {
         goto LBL_FU_ERR;
      }
      if ((e = mp_add(&sz, &tz, &sz)) != MP_OKAY) {
         goto LBL_FU_ERR;
      }
      if ((e = mp_mul(&sz, &T2z, &tz)) != MP_OKAY) {
         goto LBL_FU_ERR;
      }
      if ((e = mp_mod(&tz, N, &tz)) != MP_OKAY) {
         goto LBL_FU_ERR;
      }
      if ((e = mp_mod(&T1z, N, &sz)) != MP_OKAY) {
         goto LBL_FU_ERR;
      }
      if ((isset = mp_get_bit(&Np1z, i)) == MP_VAL) {
         e = isset;
         goto LBL_FU_ERR;
      }
      if (isset == MP_YES) {
         /*
          *  temp = (a+2) * sz + tz
          *  tz   = 2 * tz - sz
          *  sz   = temp
          */
         if (a == 0) {
            if ((e = mp_mul_2(&sz, &T1z)) != MP_OKAY) {
               goto LBL_FU_ERR;
            }
         } else {
            if ((e = mp_mul_d(&sz, (mp_digit)ap2, &T1z)) != MP_OKAY) {
               goto LBL_FU_ERR;
            }
         }
         if ((e = mp_add(&T1z, &tz, &T1z)) != MP_OKAY) {
            goto LBL_FU_ERR;
         }
         if ((e = mp_mul_2(&tz, &T2z)) != MP_OKAY) {
            goto LBL_FU_ERR;
         }
         if ((e = mp_sub(&T2z, &sz, &tz)) != MP_OKAY) {
            goto LBL_FU_ERR;
         }
         mp_exch(&sz, &T1z);
      }
   }

   if ((e = mp_set_long(&T1z, (unsigned long)((2 * a) + 5))) != MP_OKAY) {
      goto LBL_FU_ERR;
   }
   if ((e = mp_mod(&T1z, N, &T1z)) != MP_OKAY) {
      goto LBL_FU_ERR;
   }
   if ((mp_iszero(&sz) != MP_NO) && (mp_cmp(&tz, &T1z) == MP_EQ)) {
      *result = MP_YES;
      goto LBL_FU_ERR;
   }

LBL_FU_ERR:
   mp_clear_multi(&tz, &sz, &Np1z, &T2z, &T1z, NULL);
   return e;
}

#endif
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* determines if an integers is divisible by one
 * of the first PRIME_SIZE primes or not
 *
 * sets result to 0 if not, 1 if yes
 */

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* determines if an integers is divisible by one
 * of the first PRIME_SIZE primes or not
 *
 * sets result to 0 if not, 1 if yes
 */

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */


/* performs a variable number of rounds of Miller-Rabin
 *

 * Probability of error after t rounds is no more than





 *
 * Sets result to 1 if probably prime, 0 otherwise
 */

int mp_prime_is_prime(const mp_int *a, int t, int *result)
{
   mp_int  b;
   int     ix, err, res;


   /* default to no */
   *result = MP_NO;

   /* valid value of t? */
   if ((t <= 0) || (t > PRIME_SIZE)) {
      return MP_VAL;
   }


























   /* is the input equal to one of the primes in the table? */
   for (ix = 0; ix < PRIME_SIZE; ix++) {
      if (mp_cmp_d(a, ltm_prime_tab[ix]) == MP_EQ) {
         *result = 1;
         return MP_OKAY;
      }
   }







   /* first perform trial division */
   if ((err = mp_prime_is_divisible(a, &res)) != MP_OKAY) {
      return err;
   }

   /* return if it was trivially divisible */
   if (res == MP_YES) {
      return MP_OKAY;
   }

   /* now perform the miller-rabin rounds */


   if ((err = mp_init(&b)) != MP_OKAY) {
      return err;
   }

   for (ix = 0; ix < t; ix++) {
      /* set the prime */
      mp_set(&b, ltm_prime_tab[ix]);











      if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
         goto LBL_B;
      }





















      if (res == MP_NO) {
         goto LBL_B;
      }



   }





























































































































































































































   /* passed the test */
   *result = MP_YES;
LBL_B:
   mp_clear(&b);
   return err;
}

#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* portable integer log of two with small footprint */
static unsigned int s_floor_ilog2(int value)

{
   unsigned int r = 0;
   while ((value >>= 1) != 0) {
      r++;
   }
   return r;
}




int mp_prime_is_prime(const mp_int *a, int t, int *result)
{
   mp_int  b;
   int     ix, err, res, p_max = 0, size_a, len;
   unsigned int fips_rand, mask;

   /* default to no */
   *result = MP_NO;

   /* valid value of t? */
   if (t > PRIME_SIZE) {
      return MP_VAL;
   }

   /* Some shortcuts */
   /* N > 3 */
   if (a->used == 1) {
      if ((a->dp[0] == 0u) || (a->dp[0] == 1u)) {
         *result = 0;
         return MP_OKAY;
      }
      if (a->dp[0] == 2u) {
         *result = 1;
         return MP_OKAY;
      }
   }

   /* N must be odd */
   if (mp_iseven(a) == MP_YES) {
      return MP_OKAY;
   }
   /* N is not a perfect square: floor(sqrt(N))^2 != N */
   if ((err = mp_is_square(a, &res)) != MP_OKAY) {
      return err;
   }
   if (res != 0) {
      return MP_OKAY;
   }

   /* is the input equal to one of the primes in the table? */
   for (ix = 0; ix < PRIME_SIZE; ix++) {
      if (mp_cmp_d(a, ltm_prime_tab[ix]) == MP_EQ) {
         *result = MP_YES;
         return MP_OKAY;
      }
   }
#ifdef MP_8BIT
   /* The search in the loop above was exhaustive in this case */
   if (a->used == 1 && PRIME_SIZE >= 31) {
      return MP_OKAY;
   }
#endif

   /* first perform trial division */
   if ((err = mp_prime_is_divisible(a, &res)) != MP_OKAY) {
      return err;
   }

   /* return if it was trivially divisible */
   if (res == MP_YES) {
      return MP_OKAY;
   }

   /*
       Run the Miller-Rabin test with base 2 for the BPSW test.
    */
   if ((err = mp_init_set(&b, 2uL)) != MP_OKAY) {
      return err;
   }



   if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
      goto LBL_B;
   }
   if (res == MP_NO) {
      goto LBL_B;
   }
   /*
      Rumours have it that Mathematica does a second M-R test with base 3.
      Other rumours have it that their strong L-S test is slightly different.
      It does not hurt, though, beside a bit of extra runtime.
   */
   b.dp[0]++;
   if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
      goto LBL_B;
   }
   if (res == MP_NO) {
      goto LBL_B;
   }

   /*
    * Both, the Frobenius-Underwood test and the the Lucas-Selfridge test are quite
    * slow so if speed is an issue, define LTM_USE_FIPS_ONLY to use M-R tests with
    * bases 2, 3 and t random bases.
    */
#ifndef LTM_USE_FIPS_ONLY
   if (t >= 0) {
      /*
       * Use a Frobenius-Underwood test instead of the Lucas-Selfridge test for
       * MP_8BIT (It is unknown if the Lucas-Selfridge test works with 16-bit
       * integers but the necesssary analysis is on the todo-list).
       */
#if defined (MP_8BIT) || defined (LTM_USE_FROBENIUS_TEST)
      err = mp_prime_frobenius_underwood(a, &res);
      if (err != MP_OKAY && err != MP_ITER) {
         goto LBL_B;
      }
      if (res == MP_NO) {
         goto LBL_B;
      }
#else
      if ((err = mp_prime_strong_lucas_selfridge(a, &res)) != MP_OKAY) {
         goto LBL_B;
      }
      if (res == MP_NO) {
         goto LBL_B;
      }
#endif
   }
#endif

   /* run at least one Miller-Rabin test with a random base */
   if (t == 0) {
      t = 1;
   }

   /*
      abs(t) extra rounds of M-R to extend the range of primes it can find if t < 0.
      Only recommended if the input range is known to be < 3317044064679887385961981

      It uses the bases for a deterministic M-R test if input < 3317044064679887385961981
      The caller has to check the size.

      Not for cryptographic use because with known bases strong M-R pseudoprimes can
      be constructed. Use at least one M-R test with a random base (t >= 1).

      The 1119 bit large number

      80383745745363949125707961434194210813883768828755814583748891752229742737653\
      33652186502336163960045457915042023603208766569966760987284043965408232928738\
      79185086916685732826776177102938969773947016708230428687109997439976544144845\
      34115587245063340927902227529622941498423068816854043264575340183297861112989\
      60644845216191652872597534901

      has been constructed by F. Arnault (F. Arnault, "Rabin-Miller primality test:
      composite numbers which pass it.",  Mathematics of Computation, 1995, 64. Jg.,
      Nr. 209, S. 355-361), is a semiprime with the two factors

      40095821663949960541830645208454685300518816604113250877450620473800321707011\
      96242716223191597219733582163165085358166969145233813917169287527980445796800\
      452592031836601

      20047910831974980270915322604227342650259408302056625438725310236900160853505\
      98121358111595798609866791081582542679083484572616906958584643763990222898400\
      226296015918301

      and it is a strong pseudoprime to all forty-six prime M-R bases up to 200

      It does not fail the strong Bailley-PSP test as implemented here, it is just
      given as an example, if not the reason to use the BPSW-test instead of M-R-tests
      with a sequence of primes 2...n.

   */
   if (t < 0) {
      t = -t;
      /*
          Sorenson, Jonathan; Webster, Jonathan (2015).
           "Strong Pseudoprimes to Twelve Prime Bases".
       */
      /* 0x437ae92817f9fc85b7e5 = 318665857834031151167461 */
      if ((err =   mp_read_radix(&b, "437ae92817f9fc85b7e5", 16)) != MP_OKAY) {
         goto LBL_B;
      }

      if (mp_cmp(a, &b) == MP_LT) {
         p_max = 12;
      } else {
         /* 0x2be6951adc5b22410a5fd = 3317044064679887385961981 */
         if ((err = mp_read_radix(&b, "2be6951adc5b22410a5fd", 16)) != MP_OKAY) {
            goto LBL_B;
         }

         if (mp_cmp(a, &b) == MP_LT) {
            p_max = 13;
         } else {
            err = MP_VAL;
            goto LBL_B;
         }
      }

      /* for compatibility with the current API (well, compatible within a sign's width) */
      if (p_max < t) {
         p_max = t;
      }

      if (p_max > PRIME_SIZE) {
         err = MP_VAL;
         goto LBL_B;
      }
      /* we did bases 2 and 3  already, skip them */
      for (ix = 2; ix < p_max; ix++) {
         mp_set(&b, ltm_prime_tab[ix]);
         if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
            goto LBL_B;
         }
         if (res == MP_NO) {
            goto LBL_B;
         }
      }
   }
   /*
       Do "t" M-R tests with random bases between 3 and "a".
       See Fips 186.4 p. 126ff
   */
   else if (t > 0) {
      /*
       * The mp_digit's have a defined bit-size but the size of the
       * array a.dp is a simple 'int' and this library can not assume full
       * compliance to the current C-standard (ISO/IEC 9899:2011) because
       * it gets used for small embeded processors, too. Some of those MCUs
       * have compilers that one cannot call standard compliant by any means.
       * Hence the ugly type-fiddling in the following code.
       */
      size_a = mp_count_bits(a);
      mask = (1u << s_floor_ilog2(size_a)) - 1u;
      /*
         Assuming the General Rieman hypothesis (never thought to write that in a
         comment) the upper bound can be lowered to  2*(log a)^2.
         E. Bach, "Explicit bounds for primality testing and related problems,"
         Math. Comp. 55 (1990), 355-380.

            size_a = (size_a/10) * 7;
            len = 2 * (size_a * size_a);

         E.g.: a number of size 2^2048 would be reduced to the upper limit

            floor(2048/10)*7 = 1428
            2 * 1428^2       = 4078368

         (would have been ~4030331.9962 with floats and natural log instead)
         That number is smaller than 2^28, the default bit-size of mp_digit.
      */

      /*
        How many tests, you might ask? Dana Jacobsen of Math::Prime::Util fame
        does exactly 1. In words: one. Look at the end of _GMP_is_prime() in
        Math-Prime-Util-GMP-0.50/primality.c if you do not believe it.

        The function mp_rand() goes to some length to use a cryptographically
        good PRNG. That also means that the chance to always get the same base
        in the loop is non-zero, although very low.
        If the BPSW test and/or the addtional Frobenious test have been
        performed instead of just the Miller-Rabin test with the bases 2 and 3,
        a single extra test should suffice, so such a very unlikely event
        will not do much harm.

        To preemptivly answer the dangling question: no, a witness does not
        need to be prime.
      */
      for (ix = 0; ix < t; ix++) {
         /* mp_rand() guarantees the first digit to be non-zero */
         if ((err = mp_rand(&b, 1)) != MP_OKAY) {
            goto LBL_B;
         }
         /*
          * Reduce digit before casting because mp_digit might be bigger than
          * an unsigned int and "mask" on the other side is most probably not.
          */
         fips_rand = (unsigned int)(b.dp[0] & (mp_digit) mask);
#ifdef MP_8BIT
         /*
          * One 8-bit digit is too small, so concatenate two if the size of
          * unsigned int allows for it.
          */
         if ((sizeof(unsigned int) * CHAR_BIT)/2 >= (sizeof(mp_digit) * CHAR_BIT)) {
            if ((err = mp_rand(&b, 1)) != MP_OKAY) {
               goto LBL_B;
            }
            fips_rand <<= sizeof(mp_digit) * CHAR_BIT;
            fips_rand |= (unsigned int) b.dp[0];
            fips_rand &= mask;
         }
#endif
         if (fips_rand > ((unsigned int) INT_MAX - DIGIT_BIT)) {
            len = INT_MAX / DIGIT_BIT;
         }
         else {
            len = (((int)fips_rand + DIGIT_BIT) / DIGIT_BIT);
         }
         /*  Unlikely. */
         if (len < 0) {
            ix--;
            continue;
         }
         /*
          * As mentioned above, one 8-bit digit is too small and
          * although it can only happen in the unlikely case that
          * an "unsigned int" is smaller than 16 bit a simple test
          * is cheap and the correction even cheaper.
          */
#ifdef MP_8BIT
         /* All "a" < 2^8 have been caught before */
         if (len == 1) {
            len++;
         }
#endif
         if ((err = mp_rand(&b, len)) != MP_OKAY) {
            goto LBL_B;
         }
         /*
          * That number might got too big and the witness has to be
          * smaller than or equal to "a"
          */
         len = mp_count_bits(&b);
         if (len > size_a) {
            len = len - size_a;
            if ((err = mp_div_2d(&b, len, &b, NULL)) != MP_OKAY) {
               goto LBL_B;
            }
         }

         /* Although the chance for b <= 3 is miniscule, try again. */
         if (mp_cmp_d(&b, 3uL) != MP_GT) {
            ix--;
            continue;
         }
         if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
            goto LBL_B;
         }
         if (res == MP_NO) {
            goto LBL_B;
         }
      }
   }

   /* passed the test */
   *result = MP_YES;
LBL_B:
   mp_clear(&b);
   return err;
}

#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* Miller-Rabin test of "a" to the base of "b" as described in
 * HAC pp. 139 Algorithm 4.24
 *
 * Sets result to 0 if definitely composite or 1 if probably prime.
 * Randomly the chance of error is no more than 1/4 and often

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* Miller-Rabin test of "a" to the base of "b" as described in
 * HAC pp. 139 Algorithm 4.24
 *
 * Sets result to 0 if definitely composite or 1 if probably prime.
 * Randomly the chance of error is no more than 1/4 and often

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* finds the next prime after the number "a" using "t" trials
 * of Miller-Rabin.
 *
 * bbs_style = 1 means the prime must be congruent to 3 mod 4
 */
int mp_prime_next_prime(mp_int *a, int t, int bbs_style)
{
   int      err, res = MP_NO, x, y;
   mp_digit res_tab[PRIME_SIZE], step, kstep;
   mp_int   b;

   /* ensure t is valid */
   if ((t <= 0) || (t > PRIME_SIZE)) {
      return MP_VAL;
   }

   /* force positive */
   a->sign = MP_ZPOS;

   /* simple algo if a is less than the largest prime in the table */
   if (mp_cmp_d(a, ltm_prime_tab[PRIME_SIZE-1]) == MP_LT) {
      /* find which prime it is bigger than */
      for (x = PRIME_SIZE - 2; x >= 0; x--) {
................................................................................
      }

      /* if didn't pass sieve and step == MAX then skip test */
      if ((y == 1) && (step >= (((mp_digit)1 << DIGIT_BIT) - kstep))) {
         continue;
      }

      /* is this prime? */
      for (x = 0; x < t; x++) {
         mp_set(&b, ltm_prime_tab[x]);
         if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
            goto LBL_ERR;
         }
         if (res == MP_NO) {
            break;
         }
      }

      if (res == MP_YES) {
         break;
      }
   }

   err = MP_OKAY;
LBL_ERR:

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* finds the next prime after the number "a" using "t" trials
 * of Miller-Rabin.
 *
 * bbs_style = 1 means the prime must be congruent to 3 mod 4
 */
int mp_prime_next_prime(mp_int *a, int t, int bbs_style)
{
   int      err, res = MP_NO, x, y;
   mp_digit res_tab[PRIME_SIZE], step, kstep;
   mp_int   b;






   /* force positive */
   a->sign = MP_ZPOS;

   /* simple algo if a is less than the largest prime in the table */
   if (mp_cmp_d(a, ltm_prime_tab[PRIME_SIZE-1]) == MP_LT) {
      /* find which prime it is bigger than */
      for (x = PRIME_SIZE - 2; x >= 0; x--) {
................................................................................
      }

      /* if didn't pass sieve and step == MAX then skip test */
      if ((y == 1) && (step >= (((mp_digit)1 << DIGIT_BIT) - kstep))) {
         continue;
      }

      if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY) {



         goto LBL_ERR;
      }





      if (res == MP_YES) {
         break;
      }
   }

   err = MP_OKAY;
LBL_ERR:

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */


static const struct {
   int k, t;
} sizes[] = {



   {   128,    28 },


   {   256,    16 },
   {   384,    10 },
   {   512,     7 },
   {   640,     6 },
   {   768,     5 },
   {   896,     4 },
   {  1024,     4 }


};

/* returns # of RM trials required for a given bit size */
int mp_prime_rabin_miller_trials(int size)
{
   int x;

   for (x = 0; x < (int)(sizeof(sizes)/(sizeof(sizes[0]))); x++) {
      if (sizes[x].k == size) {
         return sizes[x].t;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */


static const struct {
   int k, t;
} sizes[] = {
   {    80,    -1 }, /* Use deterministic algorithm for size <= 80 bits */
   {    81,    39 },
   {    96,    37 },
   {   128,    32 },
   {   160,    27 },
   {   192,    21 },
   {   256,    16 },
   {   384,    10 },
   {   512,     7 },
   {   640,     6 },
   {   768,     5 },
   {   896,     4 },
   {  1024,     4 },
   {  2048,     2 },
   {  4096,     1 },
};

/* returns # of RM trials required for a given bit size and max. error of 2^(-96)*/
int mp_prime_rabin_miller_trials(int size)
{
   int x;

   for (x = 0; x < (int)(sizeof(sizes)/(sizeof(sizes[0]))); x++) {
      if (sizes[x].k == size) {
         return sizes[x].t;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* makes a truly random prime of a given size (bits),
 *
 * Flags are as follows:
 *
 *   LTM_PRIME_BBS      - make prime congruent to 3 mod 4

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* makes a truly random prime of a given size (bits),
 *
 * Flags are as follows:
 *
 *   LTM_PRIME_BBS      - make prime congruent to 3 mod 4

#include "tommath_private.h"
#ifdef BN_MP_PRIME_STRONG_LUCAS_SELFRIDGE_C

/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense
 */

/*
 *  See file bn_mp_prime_is_prime.c or the documentation in doc/bn.tex for the details
 */
#ifndef LTM_USE_FIPS_ONLY

/*
 *  8-bit is just too small. You can try the Frobenius test
 *  but that frobenius test can fail, too, for the same reason.
 */
#ifndef MP_8BIT

/*
 * multiply bigint a with int d and put the result in c
 * Like mp_mul_d() but with a signed long as the small input
 */
static int s_mp_mul_si(const mp_int *a, long d, mp_int *c)
{
   mp_int t;
   int err, neg = 0;

   if ((err = mp_init(&t)) != MP_OKAY) {
      return err;
   }
   if (d < 0) {
      neg = 1;
      d = -d;
   }

   /*
    * mp_digit might be smaller than a long, which excludes
    * the use of mp_mul_d() here.
    */
   if ((err = mp_set_long(&t, (unsigned long) d)) != MP_OKAY) {
      goto LBL_MPMULSI_ERR;
   }
   if ((err = mp_mul(a, &t, c)) != MP_OKAY) {
      goto LBL_MPMULSI_ERR;
   }
   if (neg ==  1) {
      c->sign = (a->sign == MP_NEG) ? MP_ZPOS: MP_NEG;
   }
LBL_MPMULSI_ERR:
   mp_clear(&t);
   return err;
}
/*
    Strong Lucas-Selfridge test.
    returns MP_YES if it is a strong L-S prime, MP_NO if it is composite

    Code ported from  Thomas Ray Nicely's implementation of the BPSW test
    at http://www.trnicely.net/misc/bpsw.html

    Freeware copyright (C) 2016 Thomas R. Nicely <http://www.trnicely.net>.
    Released into the public domain by the author, who disclaims any legal
    liability arising from its use

    The multi-line comments are made by Thomas R. Nicely and are copied verbatim.
    Additional comments marked "CZ" (without the quotes) are by the code-portist.

    (If that name sounds familiar, he is the guy who found the fdiv bug in the
     Pentium (P5x, I think) Intel processor)
*/
int mp_prime_strong_lucas_selfridge(const mp_int *a, int *result)
{
   /* CZ TODO: choose better variable names! */
   mp_int Dz, gcd, Np1, Uz, Vz, U2mz, V2mz, Qmz, Q2mz, Qkdz, T1z, T2z, T3z, T4z, Q2kdz;
   /* CZ TODO: Some of them need the full 32 bit, hence the (temporary) exclusion of MP_8BIT */
   int32_t D, Ds, J, sign, P, Q, r, s, u, Nbits;
   int e;
   int isset, oddness;

   *result = MP_NO;
   /*
   Find the first element D in the sequence {5, -7, 9, -11, 13, ...}
   such that Jacobi(D,N) = -1 (Selfridge's algorithm). Theory
   indicates that, if N is not a perfect square, D will "nearly
   always" be "small." Just in case, an overflow trap for D is
   included.
   */

   if ((e = mp_init_multi(&Dz, &gcd, &Np1, &Uz, &Vz, &U2mz, &V2mz, &Qmz, &Q2mz, &Qkdz, &T1z, &T2z, &T3z, &T4z, &Q2kdz,
                          NULL)) != MP_OKAY) {
      return e;
   }

   D = 5;
   sign = 1;

   for (;;) {
      Ds   = sign * D;
      sign = -sign;
      if ((e = mp_set_long(&Dz, (unsigned long)D)) != MP_OKAY) {
         goto LBL_LS_ERR;
      }
      if ((e = mp_gcd(a, &Dz, &gcd)) != MP_OKAY) {
         goto LBL_LS_ERR;
      }
      /* if 1 < GCD < N then N is composite with factor "D", and
         Jacobi(D,N) is technically undefined (but often returned
         as zero). */
      if ((mp_cmp_d(&gcd, 1uL) == MP_GT) && (mp_cmp(&gcd, a) == MP_LT)) {
         goto LBL_LS_ERR;
      }
      if (Ds < 0) {
         Dz.sign = MP_NEG;
      }
      if ((e = mp_kronecker(&Dz, a, &J)) != MP_OKAY) {
         goto LBL_LS_ERR;
      }

      if (J == -1) {
         break;
      }
      D += 2;

      if (D > (INT_MAX - 2)) {
         e = MP_VAL;
         goto LBL_LS_ERR;
      }
   }



   P = 1;              /* Selfridge's choice */
   Q = (1 - Ds) / 4;   /* Required so D = P*P - 4*Q */

   /* NOTE: The conditions (a) N does not divide Q, and
      (b) D is square-free or not a perfect square, are included by
      some authors; e.g., "Prime numbers and computer methods for
      factorization," Hans Riesel (2nd ed., 1994, Birkhauser, Boston),
      p. 130. For this particular application of Lucas sequences,
      these conditions were found to be immaterial. */

   /* Now calculate N - Jacobi(D,N) = N + 1 (even), and calculate the
      odd positive integer d and positive integer s for which
      N + 1 = 2^s*d (similar to the step for N - 1 in Miller's test).
      The strong Lucas-Selfridge test then returns N as a strong
      Lucas probable prime (slprp) if any of the following
      conditions is met: U_d=0, V_d=0, V_2d=0, V_4d=0, V_8d=0,
      V_16d=0, ..., etc., ending with V_{2^(s-1)*d}=V_{(N+1)/2}=0
      (all equalities mod N). Thus d is the highest index of U that
      must be computed (since V_2m is independent of U), compared
      to U_{N+1} for the standard Lucas-Selfridge test; and no
      index of V beyond (N+1)/2 is required, just as in the
      standard Lucas-Selfridge test. However, the quantity Q^d must
      be computed for use (if necessary) in the latter stages of
      the test. The result is that the strong Lucas-Selfridge test
      has a running time only slightly greater (order of 10 %) than
      that of the standard Lucas-Selfridge test, while producing
      only (roughly) 30 % as many pseudoprimes (and every strong
      Lucas pseudoprime is also a standard Lucas pseudoprime). Thus
      the evidence indicates that the strong Lucas-Selfridge test is
      more effective than the standard Lucas-Selfridge test, and a
      Baillie-PSW test based on the strong Lucas-Selfridge test
      should be more reliable. */

   if ((e = mp_add_d(a, 1uL, &Np1)) != MP_OKAY) {
      goto LBL_LS_ERR;
   }
   s = mp_cnt_lsb(&Np1);

   /* CZ
    * This should round towards zero because
    * Thomas R. Nicely used GMP's mpz_tdiv_q_2exp()
    * and mp_div_2d() is equivalent. Additionally:
    * dividing an even number by two does not produce
    * any leftovers.
    */
   if ((e = mp_div_2d(&Np1, s, &Dz, NULL)) != MP_OKAY) {
      goto LBL_LS_ERR;
   }
   /* We must now compute U_d and V_d. Since d is odd, the accumulated
      values U and V are initialized to U_1 and V_1 (if the target
      index were even, U and V would be initialized instead to U_0=0
      and V_0=2). The values of U_2m and V_2m are also initialized to
      U_1 and V_1; the FOR loop calculates in succession U_2 and V_2,
      U_4 and V_4, U_8 and V_8, etc. If the corresponding bits
      (1, 2, 3, ...) of t are on (the zero bit having been accounted
      for in the initialization of U and V), these values are then
      combined with the previous totals for U and V, using the
      composition formulas for addition of indices. */

   mp_set(&Uz, 1uL);    /* U=U_1 */
   mp_set(&Vz, (mp_digit)P);    /* V=V_1 */
   mp_set(&U2mz, 1uL);  /* U_1 */
   mp_set(&V2mz, (mp_digit)P);  /* V_1 */

   if (Q < 0) {
      Q = -Q;
      if ((e = mp_set_long(&Qmz, (unsigned long)Q)) != MP_OKAY) {
         goto LBL_LS_ERR;
      }
      if ((e = mp_mul_2(&Qmz, &Q2mz)) != MP_OKAY) {
         goto LBL_LS_ERR;
      }
      /* Initializes calculation of Q^d */
      if ((e = mp_set_long(&Qkdz, (unsigned long)Q)) != MP_OKAY) {
         goto LBL_LS_ERR;
      }
      Qmz.sign = MP_NEG;
      Q2mz.sign = MP_NEG;
      Qkdz.sign = MP_NEG;
      Q = -Q;
   } else {
      if ((e = mp_set_long(&Qmz, (unsigned long)Q)) != MP_OKAY) {
         goto LBL_LS_ERR;
      }
      if ((e = mp_mul_2(&Qmz, &Q2mz)) != MP_OKAY) {
         goto LBL_LS_ERR;
      }
      /* Initializes calculation of Q^d */
      if ((e = mp_set_long(&Qkdz, (unsigned long)Q)) != MP_OKAY) {
         goto LBL_LS_ERR;
      }
   }

   Nbits = mp_count_bits(&Dz);

   for (u = 1; u < Nbits; u++) { /* zero bit off, already accounted for */
      /* Formulas for doubling of indices (carried out mod N). Note that
       * the indices denoted as "2m" are actually powers of 2, specifically
       * 2^(ul-1) beginning each loop and 2^ul ending each loop.
       *
       * U_2m = U_m*V_m
       * V_2m = V_m*V_m - 2*Q^m
       */

      if ((e = mp_mul(&U2mz, &V2mz, &U2mz)) != MP_OKAY) {
         goto LBL_LS_ERR;
      }
      if ((e = mp_mod(&U2mz, a, &U2mz)) != MP_OKAY) {
         goto LBL_LS_ERR;
      }
      if ((e = mp_sqr(&V2mz, &V2mz)) != MP_OKAY) {
         goto LBL_LS_ERR;
      }
      if ((e = mp_sub(&V2mz, &Q2mz, &V2mz)) != MP_OKAY) {
         goto LBL_LS_ERR;
      }
      if ((e = mp_mod(&V2mz, a, &V2mz)) != MP_OKAY) {
         goto LBL_LS_ERR;
      }
      /* Must calculate powers of Q for use in V_2m, also for Q^d later */
      if ((e = mp_sqr(&Qmz, &Qmz)) != MP_OKAY) {
         goto LBL_LS_ERR;
      }
      /* prevents overflow */ /* CZ  still necessary without a fixed prealloc'd mem.? */
      if ((e = mp_mod(&Qmz, a, &Qmz)) != MP_OKAY) {
         goto LBL_LS_ERR;
      }
      if ((e = mp_mul_2(&Qmz, &Q2mz)) != MP_OKAY) {
         goto LBL_LS_ERR;
      }
      if ((isset = mp_get_bit(&Dz, u)) == MP_VAL) {
         e = isset;
         goto LBL_LS_ERR;
      }
      if (isset == MP_YES) {
         /* Formulas for addition of indices (carried out mod N);
          *
          * U_(m+n) = (U_m*V_n + U_n*V_m)/2
          * V_(m+n) = (V_m*V_n + D*U_m*U_n)/2
          *
          * Be careful with division by 2 (mod N)!
          */
         if ((e = mp_mul(&U2mz, &Vz, &T1z)) != MP_OKAY) {
            goto LBL_LS_ERR;
         }
         if ((e = mp_mul(&Uz, &V2mz, &T2z)) != MP_OKAY) {
            goto LBL_LS_ERR;
         }
         if ((e = mp_mul(&V2mz, &Vz, &T3z)) != MP_OKAY) {
            goto LBL_LS_ERR;
         }
         if ((e = mp_mul(&U2mz, &Uz, &T4z)) != MP_OKAY) {
            goto LBL_LS_ERR;
         }
         if ((e = s_mp_mul_si(&T4z, (long)Ds, &T4z)) != MP_OKAY) {
            goto LBL_LS_ERR;
         }
         if ((e = mp_add(&T1z, &T2z, &Uz)) != MP_OKAY) {
            goto LBL_LS_ERR;
         }
         if (mp_isodd(&Uz) != MP_NO) {
            if ((e = mp_add(&Uz, a, &Uz)) != MP_OKAY) {
               goto LBL_LS_ERR;
            }
         }
         /* CZ
          * This should round towards negative infinity because
          * Thomas R. Nicely used GMP's mpz_fdiv_q_2exp().
          * But mp_div_2() does not do so, it is truncating instead.
          */
         oddness = mp_isodd(&Uz);
         if ((e = mp_div_2(&Uz, &Uz)) != MP_OKAY) {
            goto LBL_LS_ERR;
         }
         if ((Uz.sign == MP_NEG) && (oddness != MP_NO)) {
            if ((e = mp_sub_d(&Uz, 1uL, &Uz)) != MP_OKAY) {
               goto LBL_LS_ERR;
            }
         }
         if ((e = mp_add(&T3z, &T4z, &Vz)) != MP_OKAY) {
            goto LBL_LS_ERR;
         }
         if (mp_isodd(&Vz) != MP_NO) {
            if ((e = mp_add(&Vz, a, &Vz)) != MP_OKAY) {
               goto LBL_LS_ERR;
            }
         }
         oddness = mp_isodd(&Vz);
         if ((e = mp_div_2(&Vz, &Vz)) != MP_OKAY) {
            goto LBL_LS_ERR;
         }
         if ((Vz.sign == MP_NEG) && (oddness != MP_NO)) {
            if ((e = mp_sub_d(&Vz, 1uL, &Vz)) != MP_OKAY) {
               goto LBL_LS_ERR;
            }
         }
         if ((e = mp_mod(&Uz, a, &Uz)) != MP_OKAY) {
            goto LBL_LS_ERR;
         }
         if ((e = mp_mod(&Vz, a, &Vz)) != MP_OKAY) {
            goto LBL_LS_ERR;
         }
         /* Calculating Q^d for later use */
         if ((e = mp_mul(&Qkdz, &Qmz, &Qkdz)) != MP_OKAY) {
            goto LBL_LS_ERR;
         }
         if ((e = mp_mod(&Qkdz, a, &Qkdz)) != MP_OKAY) {
            goto LBL_LS_ERR;
         }
      }
   }

   /* If U_d or V_d is congruent to 0 mod N, then N is a prime or a
      strong Lucas pseudoprime. */
   if ((mp_iszero(&Uz) != MP_NO) || (mp_iszero(&Vz) != MP_NO)) {
      *result = MP_YES;
      goto LBL_LS_ERR;
   }

   /* NOTE: Ribenboim ("The new book of prime number records," 3rd ed.,
      1995/6) omits the condition V0 on p.142, but includes it on
      p. 130. The condition is NECESSARY; otherwise the test will
      return false negatives---e.g., the primes 29 and 2000029 will be
      returned as composite. */

   /* Otherwise, we must compute V_2d, V_4d, V_8d, ..., V_{2^(s-1)*d}
      by repeated use of the formula V_2m = V_m*V_m - 2*Q^m. If any of
      these are congruent to 0 mod N, then N is a prime or a strong
      Lucas pseudoprime. */

   /* Initialize 2*Q^(d*2^r) for V_2m */
   if ((e = mp_mul_2(&Qkdz, &Q2kdz)) != MP_OKAY) {
      goto LBL_LS_ERR;
   }

   for (r = 1; r < s; r++) {
      if ((e = mp_sqr(&Vz, &Vz)) != MP_OKAY) {
         goto LBL_LS_ERR;
      }
      if ((e = mp_sub(&Vz, &Q2kdz, &Vz)) != MP_OKAY) {
         goto LBL_LS_ERR;
      }
      if ((e = mp_mod(&Vz, a, &Vz)) != MP_OKAY) {
         goto LBL_LS_ERR;
      }
      if (mp_iszero(&Vz) != MP_NO) {
         *result = MP_YES;
         goto LBL_LS_ERR;
      }
      /* Calculate Q^{d*2^r} for next r (final iteration irrelevant). */
      if (r < (s - 1)) {
         if ((e = mp_sqr(&Qkdz, &Qkdz)) != MP_OKAY) {
            goto LBL_LS_ERR;
         }
         if ((e = mp_mod(&Qkdz, a, &Qkdz)) != MP_OKAY) {
            goto LBL_LS_ERR;
         }
         if ((e = mp_mul_2(&Qkdz, &Q2kdz)) != MP_OKAY) {
            goto LBL_LS_ERR;
         }
      }
   }
LBL_LS_ERR:
   mp_clear_multi(&Q2kdz, &T4z, &T3z, &T2z, &T1z, &Qkdz, &Q2mz, &Qmz, &V2mz, &U2mz, &Vz, &Uz, &Np1, &gcd, &Dz, NULL);
   return e;
}
#endif
#endif
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* returns size of ASCII reprensentation */
int mp_radix_size(const mp_int *a, int radix, int *size)
{
   int     res, digs;
   mp_int  t;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* returns size of ASCII reprensentation */
int mp_radix_size(const mp_int *a, int radix, int *size)
{
   int     res, digs;
   mp_int  t;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* chars used in radix conversions */
const char *const mp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/";
const unsigned char mp_s_rmap_reverse[] = {
   0xff, 0xff, 0xff, 0x3e, 0xff, 0xff, 0xff, 0x3f, /* ()*+,-./ */
   0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, /* 01234567 */

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* chars used in radix conversions */
const char *const mp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/";
const unsigned char mp_s_rmap_reverse[] = {
   0xff, 0xff, 0xff, 0x3e, 0xff, 0xff, 0xff, 0x3f, /* ()*+,-./ */
   0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, /* 01234567 */

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* First the OS-specific special cases
 * - *BSD
 * - Windows
 */
#if defined(__FreeBSD__) || defined(__OpenBSD__) || defined(__NetBSD__) || defined(__DragonFly__)
................................................................................
   if (ret == MP_OKAY) return ret;
#endif

   return ret;
}

/* makes a pseudo-random int of a given size */
static int s_gen_random(mp_digit *r)
{
   int ret = s_rand_digit(r);
   *r &= MP_MASK;
   return ret;
}

int mp_rand(mp_int *a, int digits)
................................................................................
   mp_zero(a);
   if (digits <= 0) {
      return MP_OKAY;
   }

   /* first place a random non-zero digit */
   do {
      if (s_gen_random(&d) != MP_OKAY) {
         return MP_VAL;
      }
   } while (d == 0u);

   if ((res = mp_add_d(a, d, a)) != MP_OKAY) {
      return res;
   }

   while (--digits > 0) {
      if ((res = mp_lshd(a, 1)) != MP_OKAY) {
         return res;
      }

      if (s_gen_random(&d) != MP_OKAY) {
         return MP_VAL;
      }
      if ((res = mp_add_d(a, d, a)) != MP_OKAY) {
         return res;
      }
   }

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* First the OS-specific special cases
 * - *BSD
 * - Windows
 */
#if defined(__FreeBSD__) || defined(__OpenBSD__) || defined(__NetBSD__) || defined(__DragonFly__)
................................................................................
   if (ret == MP_OKAY) return ret;
#endif

   return ret;
}

/* makes a pseudo-random int of a given size */
int mp_rand_digit(mp_digit *r)
{
   int ret = s_rand_digit(r);
   *r &= MP_MASK;
   return ret;
}

int mp_rand(mp_int *a, int digits)
................................................................................
   mp_zero(a);
   if (digits <= 0) {
      return MP_OKAY;
   }

   /* first place a random non-zero digit */
   do {
      if (mp_rand_digit(&d) != MP_OKAY) {
         return MP_VAL;
      }
   } while (d == 0u);

   if ((res = mp_add_d(a, d, a)) != MP_OKAY) {
      return res;
   }

   while (--digits > 0) {
      if ((res = mp_lshd(a, 1)) != MP_OKAY) {
         return res;
      }

      if (mp_rand_digit(&d) != MP_OKAY) {
         return MP_VAL;
      }
      if ((res = mp_add_d(a, d, a)) != MP_OKAY) {
         return res;
      }
   }

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* read a string [ASCII] in a given radix */
int mp_read_radix(mp_int *a, const char *str, int radix)
{
   int     y, res, neg;
   unsigned pos;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* read a string [ASCII] in a given radix */
int mp_read_radix(mp_int *a, const char *str, int radix)
{
   int     y, res, neg;
   unsigned pos;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* read signed bin, big endian, first byte is 0==positive or 1==negative */
int mp_read_signed_bin(mp_int *a, const unsigned char *b, int c)
{
   int     res;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* read signed bin, big endian, first byte is 0==positive or 1==negative */
int mp_read_signed_bin(mp_int *a, const unsigned char *b, int c)
{
   int     res;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* reads a unsigned char array, assumes the msb is stored first [big endian] */
int mp_read_unsigned_bin(mp_int *a, const unsigned char *b, int c)
{
   int     res;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* reads a unsigned char array, assumes the msb is stored first [big endian] */
int mp_read_unsigned_bin(mp_int *a, const unsigned char *b, int c)
{
   int     res;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* reduces x mod m, assumes 0 < x < m**2, mu is
 * precomputed via mp_reduce_setup.
 * From HAC pp.604 Algorithm 14.42
 */
int mp_reduce(mp_int *x, const mp_int *m, const mp_int *mu)

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* reduces x mod m, assumes 0 < x < m**2, mu is
 * precomputed via mp_reduce_setup.
 * From HAC pp.604 Algorithm 14.42
 */
int mp_reduce(mp_int *x, const mp_int *m, const mp_int *mu)

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* reduces a modulo n where n is of the form 2**p - d */
int mp_reduce_2k(mp_int *a, const mp_int *n, mp_digit d)
{
   mp_int q;
   int    p, res;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* reduces a modulo n where n is of the form 2**p - d */
int mp_reduce_2k(mp_int *a, const mp_int *n, mp_digit d)
{
   mp_int q;
   int    p, res;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* reduces a modulo n where n is of the form 2**p - d
   This differs from reduce_2k since "d" can be larger
   than a single digit.
*/
int mp_reduce_2k_l(mp_int *a, const mp_int *n, const mp_int *d)

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* reduces a modulo n where n is of the form 2**p - d
   This differs from reduce_2k since "d" can be larger
   than a single digit.
*/
int mp_reduce_2k_l(mp_int *a, const mp_int *n, const mp_int *d)

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* determines the setup value */
int mp_reduce_2k_setup(const mp_int *a, mp_digit *d)
{
   int res, p;
   mp_int tmp;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* determines the setup value */
int mp_reduce_2k_setup(const mp_int *a, mp_digit *d)
{
   int res, p;
   mp_int tmp;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* determines the setup value */
int mp_reduce_2k_setup_l(const mp_int *a, mp_int *d)
{
   int    res;
   mp_int tmp;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* determines the setup value */
int mp_reduce_2k_setup_l(const mp_int *a, mp_int *d)
{
   int    res;
   mp_int tmp;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* determines if mp_reduce_2k can be used */
int mp_reduce_is_2k(const mp_int *a)
{
   int ix, iy, iw;
   mp_digit iz;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* determines if mp_reduce_2k can be used */
int mp_reduce_is_2k(const mp_int *a)
{
   int ix, iy, iw;
   mp_digit iz;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* determines if reduce_2k_l can be used */
int mp_reduce_is_2k_l(const mp_int *a)
{
   int ix, iy;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* determines if reduce_2k_l can be used */
int mp_reduce_is_2k_l(const mp_int *a)
{
   int ix, iy;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* pre-calculate the value required for Barrett reduction
 * For a given modulus "b" it calulates the value required in "a"
 */
int mp_reduce_setup(mp_int *a, const mp_int *b)
{

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* pre-calculate the value required for Barrett reduction
 * For a given modulus "b" it calulates the value required in "a"
 */
int mp_reduce_setup(mp_int *a, const mp_int *b)
{

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* shift right a certain amount of digits */
void mp_rshd(mp_int *a, int b)
{
   int     x;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* shift right a certain amount of digits */
void mp_rshd(mp_int *a, int b)
{
   int     x;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* set to a digit */
void mp_set(mp_int *a, mp_digit b)
{
   mp_zero(a);
   a->dp[0] = b & MP_MASK;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* set to a digit */
void mp_set(mp_int *a, mp_digit b)
{
   mp_zero(a);
   a->dp[0] = b & MP_MASK;

#include "tommath_private.h"
#ifdef BN_MP_SET_DOUBLE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense
 */

#if defined(__STDC_IEC_559__) || defined(__GCC_IEC_559)
int mp_set_double(mp_int *a, double b)
{
   uint64_t frac;
   int exp, res;
   union {
      double   dbl;
      uint64_t bits;
   } cast;
   cast.dbl = b;

   exp = (int)((unsigned)(cast.bits >> 52) & 0x7FFU);
   frac = (cast.bits & ((1ULL << 52) - 1ULL)) | (1ULL << 52);

   if (exp == 0x7FF) { /* +-inf, NaN */
      return MP_VAL;
   }
   exp -= 1023 + 52;

   res = mp_set_long_long(a, frac);
   if (res != MP_OKAY) {
      return res;
   }

   res = (exp < 0) ? mp_div_2d(a, -exp, a, NULL) : mp_mul_2d(a, exp, a);
   if (res != MP_OKAY) {
      return res;
   }

   if (((cast.bits >> 63) != 0ULL) && (mp_iszero(a) == MP_NO)) {
      SIGN(a) = MP_NEG;
   }

   return MP_OKAY;
}
#else
/* pragma message() not supported by several compilers (in mostly older but still used versions) */
#  ifdef _MSC_VER
#    pragma message("mp_set_double implementation is only available on platforms with IEEE754 floating point format")
#  else
#    warning "mp_set_double implementation is only available on platforms with IEEE754 floating point format"
#  endif
#endif
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* set a 32-bit const */
int mp_set_int(mp_int *a, unsigned long b)
{
   int     x, res;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* set a 32-bit const */
int mp_set_int(mp_int *a, unsigned long b)
{
   int     x, res;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* set a platform dependent unsigned long int */
MP_SET_XLONG(mp_set_long, unsigned long)
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* set a platform dependent unsigned long int */
MP_SET_XLONG(mp_set_long, unsigned long)
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* set a platform dependent unsigned long long int */
MP_SET_XLONG(mp_set_long_long, Tcl_WideUInt)
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* set a platform dependent unsigned long long int */
MP_SET_XLONG(mp_set_long_long, Tcl_WideUInt)
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* shrink a bignum */
int mp_shrink(mp_int *a)
{
   mp_digit *tmp;
   int used = 1;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* shrink a bignum */
int mp_shrink(mp_int *a)
{
   mp_digit *tmp;
   int used = 1;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* get the size for an signed equivalent */
int mp_signed_bin_size(const mp_int *a)
{
   return 1 + mp_unsigned_bin_size(a);
}
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* get the size for an signed equivalent */
int mp_signed_bin_size(const mp_int *a)
{
   return 1 + mp_unsigned_bin_size(a);
}
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* computes b = a*a */
int mp_sqr(const mp_int *a, mp_int *b)
{
   int     res;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* computes b = a*a */
int mp_sqr(const mp_int *a, mp_int *b)
{
   int     res;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* c = a * a (mod b) */
int mp_sqrmod(const mp_int *a, const mp_int *b, mp_int *c)
{
   int     res;
   mp_int  t;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* c = a * a (mod b) */
int mp_sqrmod(const mp_int *a, const mp_int *b, mp_int *c)
{
   int     res;
   mp_int  t;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

#ifndef NO_FLOATING_POINT
#include <math.h>
#endif

/* this function is less generic than mp_n_root, simpler and faster */

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

#ifndef NO_FLOATING_POINT
#include <math.h>
#endif

/* this function is less generic than mp_n_root, simpler and faster */

#include "tommath_private.h"
#ifdef BN_MP_SQRTMOD_PRIME_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library is free for all purposes without any express
 * guarantee it works.



 */

/* Tonelli-Shanks algorithm
 * https://en.wikipedia.org/wiki/Tonelli%E2%80%93Shanks_algorithm
 * https://gmplib.org/list-archives/gmp-discuss/2013-April/005300.html
 *
 */
................................................................................

cleanup:
   mp_clear_multi(&t1, &C, &Q, &S, &Z, &M, &T, &R, &two, NULL);
   return res;
}

#endif

#include "tommath_private.h"
#ifdef BN_MP_SQRTMOD_PRIME_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense
 */

/* Tonelli-Shanks algorithm
 * https://en.wikipedia.org/wiki/Tonelli%E2%80%93Shanks_algorithm
 * https://gmplib.org/list-archives/gmp-discuss/2013-April/005300.html
 *
 */
................................................................................

cleanup:
   mp_clear_multi(&t1, &C, &Q, &S, &Z, &M, &T, &R, &two, NULL);
   return res;
}

#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* high level subtraction (handles signs) */
int mp_sub(const mp_int *a, const mp_int *b, mp_int *c)
{
   int     sa, sb, res;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* high level subtraction (handles signs) */
int mp_sub(const mp_int *a, const mp_int *b, mp_int *c)
{
   int     sa, sb, res;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* single digit subtraction */
int mp_sub_d(const mp_int *a, mp_digit b, mp_int *c)
{
   mp_digit *tmpa, *tmpc, mu;
   int       res, ix, oldused;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* single digit subtraction */
int mp_sub_d(const mp_int *a, mp_digit b, mp_int *c)
{
   mp_digit *tmpa, *tmpc, mu;
   int       res, ix, oldused;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* d = a - b (mod c) */
int mp_submod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d)
{
   int     res;
   mp_int  t;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* d = a - b (mod c) */
int mp_submod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d)
{
   int     res;
   mp_int  t;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* two complement and */
int mp_tc_and(const mp_int *a, const mp_int *b, mp_int *c)
{
   int res = MP_OKAY, bits;
   int as = mp_isneg(a), bs = mp_isneg(b);
   mp_int *mx = NULL, _mx, acpy, bcpy;

   if ((as != MP_NO) || (bs != MP_NO)) {
      bits = MAX(mp_count_bits(a), mp_count_bits(b));


      res = mp_init_set_int(&_mx, 1uL);
      if (res != MP_OKAY) {
         goto end;
      }

      mx = &_mx;
      res = mp_mul_2d(mx, bits + 1, mx);

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* two complement and */
int mp_tc_and(const mp_int *a, const mp_int *b, mp_int *c)
{
   int res = MP_OKAY, bits, abits, bbits;
   int as = mp_isneg(a), bs = mp_isneg(b);
   mp_int *mx = NULL, _mx, acpy, bcpy;

   if ((as != MP_NO) || (bs != MP_NO)) {
      abits = mp_count_bits(a);
      bbits = mp_count_bits(b);
      bits = MAX(abits, bbits);
      res = mp_init_set_int(&_mx, 1uL);
      if (res != MP_OKAY) {
         goto end;
      }

      mx = &_mx;
      res = mp_mul_2d(mx, bits + 1, mx);

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* two complement right shift */
int mp_tc_div_2d(const mp_int *a, int b, mp_int *c)
{
   int res;
   if (mp_isneg(a) == MP_NO) {

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* two complement right shift */
int mp_tc_div_2d(const mp_int *a, int b, mp_int *c)
{
   int res;
   if (mp_isneg(a) == MP_NO) {

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* two complement or */
int mp_tc_or(const mp_int *a, const mp_int *b, mp_int *c)
{
   int res = MP_OKAY, bits;
   int as = mp_isneg(a), bs = mp_isneg(b);
   mp_int *mx = NULL, _mx, acpy, bcpy;

   if ((as != MP_NO) || (bs != MP_NO)) {
      bits = MAX(mp_count_bits(a), mp_count_bits(b));


      res = mp_init_set_int(&_mx, 1uL);
      if (res != MP_OKAY) {
         goto end;
      }

      mx = &_mx;
      res = mp_mul_2d(mx, bits + 1, mx);

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* two complement or */
int mp_tc_or(const mp_int *a, const mp_int *b, mp_int *c)
{
   int res = MP_OKAY, bits, abits, bbits;
   int as = mp_isneg(a), bs = mp_isneg(b);
   mp_int *mx = NULL, _mx, acpy, bcpy;

   if ((as != MP_NO) || (bs != MP_NO)) {
      abits = mp_count_bits(a);
      bbits = mp_count_bits(b);
      bits = MAX(abits, bbits);
      res = mp_init_set_int(&_mx, 1uL);
      if (res != MP_OKAY) {
         goto end;
      }

      mx = &_mx;
      res = mp_mul_2d(mx, bits + 1, mx);

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* two complement xor */
int mp_tc_xor(const mp_int *a, const mp_int *b, mp_int *c)
{
   int res = MP_OKAY, bits;
   int as = mp_isneg(a), bs = mp_isneg(b);
   mp_int *mx = NULL, _mx, acpy, bcpy;

   if ((as != MP_NO) || (bs != MP_NO)) {
      bits = MAX(mp_count_bits(a), mp_count_bits(b));


      res = mp_init_set_int(&_mx, 1uL);
      if (res != MP_OKAY) {
         goto end;
      }

      mx = &_mx;
      res = mp_mul_2d(mx, bits + 1, mx);

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* two complement xor */
int mp_tc_xor(const mp_int *a, const mp_int *b, mp_int *c)
{
   int res = MP_OKAY, bits, abits, bbits;
   int as = mp_isneg(a), bs = mp_isneg(b);
   mp_int *mx = NULL, _mx, acpy, bcpy;

   if ((as != MP_NO) || (bs != MP_NO)) {
      abits = mp_count_bits(a);
      bbits = mp_count_bits(b);
      bits = MAX(abits, bbits);
      res = mp_init_set_int(&_mx, 1uL);
      if (res != MP_OKAY) {
         goto end;
      }

      mx = &_mx;
      res = mp_mul_2d(mx, bits + 1, mx);

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* store in signed [big endian] format */
int mp_to_signed_bin(const mp_int *a, unsigned char *b)
{
   int     res;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* store in signed [big endian] format */
int mp_to_signed_bin(const mp_int *a, unsigned char *b)
{
   int     res;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* store in signed [big endian] format */
int mp_to_signed_bin_n(const mp_int *a, unsigned char *b, unsigned long *outlen)
{
   if (*outlen < (unsigned long)mp_signed_bin_size(a)) {
      return MP_VAL;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* store in signed [big endian] format */
int mp_to_signed_bin_n(const mp_int *a, unsigned char *b, unsigned long *outlen)
{
   if (*outlen < (unsigned long)mp_signed_bin_size(a)) {
      return MP_VAL;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* store in unsigned [big endian] format */
int mp_to_unsigned_bin(const mp_int *a, unsigned char *b)
{
   int     x, res;
   mp_int  t;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* store in unsigned [big endian] format */
int mp_to_unsigned_bin(const mp_int *a, unsigned char *b)
{
   int     x, res;
   mp_int  t;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* store in unsigned [big endian] format */
int mp_to_unsigned_bin_n(const mp_int *a, unsigned char *b, unsigned long *outlen)
{
   if (*outlen < (unsigned long)mp_unsigned_bin_size(a)) {
      return MP_VAL;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* store in unsigned [big endian] format */
int mp_to_unsigned_bin_n(const mp_int *a, unsigned char *b, unsigned long *outlen)
{
   if (*outlen < (unsigned long)mp_unsigned_bin_size(a)) {
      return MP_VAL;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* multiplication using the Toom-Cook 3-way algorithm
 *
 * Much more complicated than Karatsuba but has a lower
 * asymptotic running time of O(N**1.464).  This algorithm is
 * only particularly useful on VERY large inputs

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* multiplication using the Toom-Cook 3-way algorithm
 *
 * Much more complicated than Karatsuba but has a lower
 * asymptotic running time of O(N**1.464).  This algorithm is
 * only particularly useful on VERY large inputs

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* squaring using Toom-Cook 3-way algorithm */
int mp_toom_sqr(const mp_int *a, mp_int *b)
{
   mp_int w0, w1, w2, w3, w4, tmp1, a0, a1, a2;
   int res, B;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* squaring using Toom-Cook 3-way algorithm */
int mp_toom_sqr(const mp_int *a, mp_int *b)
{
   mp_int w0, w1, w2, w3, w4, tmp1, a0, a1, a2;
   int res, B;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* stores a bignum as a ASCII string in a given radix (2..64) */
int mp_toradix(const mp_int *a, char *str, int radix)
{
   int     res, digs;
   mp_int  t;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* stores a bignum as a ASCII string in a given radix (2..64) */
int mp_toradix(const mp_int *a, char *str, int radix)
{
   int     res, digs;
   mp_int  t;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* stores a bignum as a ASCII string in a given radix (2..64)
 *
 * Stores upto maxlen-1 chars and always a NULL byte
 */
int mp_toradix_n(const mp_int *a, char *str, int radix, int maxlen)

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* stores a bignum as a ASCII string in a given radix (2..64)
 *
 * Stores upto maxlen-1 chars and always a NULL byte
 */
int mp_toradix_n(const mp_int *a, char *str, int radix, int maxlen)

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* get the size for an unsigned equivalent */
int mp_unsigned_bin_size(const mp_int *a)
{
   int     size = mp_count_bits(a);
   return (size / 8) + ((((unsigned)size & 7u) != 0u) ? 1 : 0);
}
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* get the size for an unsigned equivalent */
int mp_unsigned_bin_size(const mp_int *a)
{
   int     size = mp_count_bits(a);
   return (size / 8) + ((((unsigned)size & 7u) != 0u) ? 1 : 0);
}
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* XOR two ints together */
int mp_xor(const mp_int *a, const mp_int *b, mp_int *c)
{
   int     res, ix, px;
   mp_int  t;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* XOR two ints together */
int mp_xor(const mp_int *a, const mp_int *b, mp_int *c)
{
   int     res, ix, px;
   mp_int  t;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* set to zero */
void mp_zero(mp_int *a)
{
   int       n;
   mp_digit *tmp;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* set to zero */
void mp_zero(mp_int *a)
{
   int       n;
   mp_digit *tmp;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

const mp_digit ltm_prime_tab[] = {
   0x0002, 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013,
   0x0017, 0x001D, 0x001F, 0x0025, 0x0029, 0x002B, 0x002F, 0x0035,
   0x003B, 0x003D, 0x0043, 0x0047, 0x0049, 0x004F, 0x0053, 0x0059,
   0x0061, 0x0065, 0x0067, 0x006B, 0x006D, 0x0071, 0x007F,

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

const mp_digit ltm_prime_tab[] = {
   0x0002, 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013,
   0x0017, 0x001D, 0x001F, 0x0025, 0x0029, 0x002B, 0x002F, 0x0035,
   0x003B, 0x003D, 0x0043, 0x0047, 0x0049, 0x004F, 0x0053, 0x0059,
   0x0061, 0x0065, 0x0067, 0x006B, 0x006D, 0x0071, 0x007F,

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* reverse an array, used for radix code */
void bn_reverse(unsigned char *s, int len)
{
   int     ix, iy;
   unsigned char t;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* reverse an array, used for radix code */
void bn_reverse(unsigned char *s, int len)
{
   int     ix, iy;
   unsigned char t;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* low level addition, based on HAC pp.594, Algorithm 14.7 */
int s_mp_add(const mp_int *a, const mp_int *b, mp_int *c)
{
   const mp_int *x;
   int     olduse, res, min, max;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* low level addition, based on HAC pp.594, Algorithm 14.7 */
int s_mp_add(const mp_int *a, const mp_int *b, mp_int *c)
{
   const mp_int *x;
   int     olduse, res, min, max;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

#ifdef MP_LOW_MEM
#   define TAB_SIZE 32
#else
#   define TAB_SIZE 256
#endif
................................................................................
   if ((err = mp_mod(G, P, &M[1])) != MP_OKAY) {
      goto LBL_MU;
   }

   /* compute the value at M[1<<(winsize-1)] by squaring
    * M[1] (winsize-1) times
    */
   if ((err = mp_copy(&M[1], &M[1 << (winsize - 1)])) != MP_OKAY) {
      goto LBL_MU;
   }

   for (x = 0; x < (winsize - 1); x++) {
      /* square it */
      if ((err = mp_sqr(&M[1 << (winsize - 1)],
                        &M[1 << (winsize - 1)])) != MP_OKAY) {
         goto LBL_MU;
      }

      /* reduce modulo P */
      if ((err = redux(&M[1 << (winsize - 1)], P, &mu)) != MP_OKAY) {
         goto LBL_MU;
      }
   }

   /* create upper table, that is M[x] = M[x-1] * M[1] (mod P)
    * for x = (2**(winsize - 1) + 1) to (2**winsize - 1)
    */

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

#ifdef MP_LOW_MEM
#   define TAB_SIZE 32
#else
#   define TAB_SIZE 256
#endif
................................................................................
   if ((err = mp_mod(G, P, &M[1])) != MP_OKAY) {
      goto LBL_MU;
   }

   /* compute the value at M[1<<(winsize-1)] by squaring
    * M[1] (winsize-1) times
    */
   if ((err = mp_copy(&M[1], &M[(size_t)1 << (winsize - 1)])) != MP_OKAY) {
      goto LBL_MU;
   }

   for (x = 0; x < (winsize - 1); x++) {
      /* square it */
      if ((err = mp_sqr(&M[(size_t)1 << (winsize - 1)],
                        &M[(size_t)1 << (winsize - 1)])) != MP_OKAY) {
         goto LBL_MU;
      }

      /* reduce modulo P */
      if ((err = redux(&M[(size_t)1 << (winsize - 1)], P, &mu)) != MP_OKAY) {
         goto LBL_MU;
      }
   }

   /* create upper table, that is M[x] = M[x-1] * M[1] (mod P)
    * for x = (2**(winsize - 1) + 1) to (2**winsize - 1)
    */

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* multiplies |a| * |b| and only computes upto digs digits of result
 * HAC pp. 595, Algorithm 14.12  Modified so you can control how
 * many digits of output are created.
 */
int s_mp_mul_digs(const mp_int *a, const mp_int *b, mp_int *c, int digs)

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* multiplies |a| * |b| and only computes upto digs digits of result
 * HAC pp. 595, Algorithm 14.12  Modified so you can control how
 * many digits of output are created.
 */
int s_mp_mul_digs(const mp_int *a, const mp_int *b, mp_int *c, int digs)

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* multiplies |a| * |b| and does not compute the lower digs digits
 * [meant to get the higher part of the product]
 */
int s_mp_mul_high_digs(const mp_int *a, const mp_int *b, mp_int *c, int digs)
{

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* multiplies |a| * |b| and does not compute the lower digs digits
 * [meant to get the higher part of the product]
 */
int s_mp_mul_high_digs(const mp_int *a, const mp_int *b, mp_int *c, int digs)
{

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* low level squaring, b = a*a, HAC pp.596-597, Algorithm 14.16 */
int s_mp_sqr(const mp_int *a, mp_int *b)
{
   mp_int  t;
   int     res, ix, iy, pa;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* low level squaring, b = a*a, HAC pp.596-597, Algorithm 14.16 */
int s_mp_sqr(const mp_int *a, mp_int *b)
{
   mp_int  t;
   int     res, ix, iy, pa;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* low level subtraction (assumes |a| > |b|), HAC pp.595 Algorithm 14.9 */
int s_mp_sub(const mp_int *a, const mp_int *b, mp_int *c)
{
   int     olduse, res, min, max;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* low level subtraction (assumes |a| > |b|), HAC pp.595 Algorithm 14.9 */
int s_mp_sub(const mp_int *a, const mp_int *b, mp_int *c)
{
   int     olduse, res, min, max;

 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 */

/* Known optimal configurations

 CPU                    /Compiler     /MUL CUTOFF/SQR CUTOFF
-------------------------------------------------------------
 Intel P4 Northwood     /GCC v3.4.1   /        88/       128/LTM 0.32 ;-)

 * LibTomMath is a library that provides multiple-precision
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 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense

 */

/* Known optimal configurations

 CPU                    /Compiler     /MUL CUTOFF/SQR CUTOFF
-------------------------------------------------------------
 Intel P4 Northwood     /GCC v3.4.1   /        88/       128/LTM 0.32 ;-)

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