numeric.c

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			result = 1;			/* NAN > non-NAN */
	}
	else if (NUMERIC_IS_NAN(num2))
	{
		result = -1;			/* non-NAN < NAN */
	}
	else
	{
		result = cmp_var_common(NUMERIC_DIGITS(num1), NUMERIC_NDIGITS(num1),
								num1->n_weight, NUMERIC_SIGN(num1),
								NUMERIC_DIGITS(num2), NUMERIC_NDIGITS(num2),
								num2->n_weight, NUMERIC_SIGN(num2));
	}

	return result;
}

Datum
hash_numeric(PG_FUNCTION_ARGS)
{
	Numeric		key = PG_GETARG_NUMERIC(0);
	Datum		digit_hash;
	Datum		result;
	int			weight;
	int			start_offset;
	int			end_offset;
	int			i;
	int			hash_len;

	/* If it's NaN, don't try to hash the rest of the fields */
	if (NUMERIC_IS_NAN(key))
		PG_RETURN_UINT32(0);

	weight = key->n_weight;
	start_offset = 0;
	end_offset = 0;

	/*
	 * Omit any leading or trailing zeros from the input to the hash. The
	 * numeric implementation *should* guarantee that leading and trailing
	 * zeros are suppressed, but we're paranoid. Note that we measure the
	 * starting and ending offsets in units of NumericDigits, not bytes.
	 */
	for (i = 0; i < NUMERIC_NDIGITS(key); i++)
	{
		if (NUMERIC_DIGITS(key)[i] != (NumericDigit) 0)
			break;

		start_offset++;

		/*
		 * The weight is effectively the # of digits before the decimal point,
		 * so decrement it for each leading zero we skip.
		 */
		weight--;
	}

	/*
	 * If there are no non-zero digits, then the value of the number is zero,
	 * regardless of any other fields.
	 */
	if (NUMERIC_NDIGITS(key) == start_offset)
		PG_RETURN_UINT32(-1);

	for (i = NUMERIC_NDIGITS(key) - 1; i >= 0; i--)
	{
		if (NUMERIC_DIGITS(key)[i] != (NumericDigit) 0)
			break;

		end_offset++;
	}

	/* If we get here, there should be at least one non-zero digit */
	Assert(start_offset + end_offset < NUMERIC_NDIGITS(key));

	/*
	 * Note that we don't hash on the Numeric's scale, since two numerics can
	 * compare equal but have different scales. We also don't hash on the
	 * sign, although we could: since a sign difference implies inequality,
	 * this shouldn't affect correctness.
	 */
	hash_len = NUMERIC_NDIGITS(key) - start_offset - end_offset;
	digit_hash = hash_any((unsigned char *) (NUMERIC_DIGITS(key) + start_offset),
						  hash_len * sizeof(NumericDigit));

	/* Mix in the weight, via XOR */
	result = digit_hash ^ weight;

	PG_RETURN_DATUM(result);
}


/* ----------------------------------------------------------------------
 *
 * Basic arithmetic functions
 *
 * ----------------------------------------------------------------------
 */


/*
 * numeric_add() -
 *
 *	Add two numerics
 */
Datum
numeric_add(PG_FUNCTION_ARGS)
{
	Numeric		num1 = PG_GETARG_NUMERIC(0);
	Numeric		num2 = PG_GETARG_NUMERIC(1);
	NumericVar	arg1;
	NumericVar	arg2;
	NumericVar	result;
	Numeric		res;

	/*
	 * Handle NaN
	 */
	if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2))
		PG_RETURN_NUMERIC(make_result(&const_nan));

	/*
	 * Unpack the values, let add_var() compute the result and return it.
	 */
	init_var(&arg1);
	init_var(&arg2);
	init_var(&result);

	set_var_from_num(num1, &arg1);
	set_var_from_num(num2, &arg2);

	add_var(&arg1, &arg2, &result);

	res = make_result(&result);

	free_var(&arg1);
	free_var(&arg2);
	free_var(&result);

	PG_RETURN_NUMERIC(res);
}


/*
 * numeric_sub() -
 *
 *	Subtract one numeric from another
 */
Datum
numeric_sub(PG_FUNCTION_ARGS)
{
	Numeric		num1 = PG_GETARG_NUMERIC(0);
	Numeric		num2 = PG_GETARG_NUMERIC(1);
	NumericVar	arg1;
	NumericVar	arg2;
	NumericVar	result;
	Numeric		res;

	/*
	 * Handle NaN
	 */
	if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2))
		PG_RETURN_NUMERIC(make_result(&const_nan));

	/*
	 * Unpack the values, let sub_var() compute the result and return it.
	 */
	init_var(&arg1);
	init_var(&arg2);
	init_var(&result);

	set_var_from_num(num1, &arg1);
	set_var_from_num(num2, &arg2);

	sub_var(&arg1, &arg2, &result);

	res = make_result(&result);

	free_var(&arg1);
	free_var(&arg2);
	free_var(&result);

	PG_RETURN_NUMERIC(res);
}


/*
 * numeric_mul() -
 *
 *	Calculate the product of two numerics
 */
Datum
numeric_mul(PG_FUNCTION_ARGS)
{
	Numeric		num1 = PG_GETARG_NUMERIC(0);
	Numeric		num2 = PG_GETARG_NUMERIC(1);
	NumericVar	arg1;
	NumericVar	arg2;
	NumericVar	result;
	Numeric		res;

	/*
	 * Handle NaN
	 */
	if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2))
		PG_RETURN_NUMERIC(make_result(&const_nan));

	/*
	 * Unpack the values, let mul_var() compute the result and return it.
	 * Unlike add_var() and sub_var(), mul_var() will round its result. In the
	 * case of numeric_mul(), which is invoked for the * operator on numerics,
	 * we request exact representation for the product (rscale = sum(dscale of
	 * arg1, dscale of arg2)).
	 */
	init_var(&arg1);
	init_var(&arg2);
	init_var(&result);

	set_var_from_num(num1, &arg1);
	set_var_from_num(num2, &arg2);

	mul_var(&arg1, &arg2, &result, arg1.dscale + arg2.dscale);

	res = make_result(&result);

	free_var(&arg1);
	free_var(&arg2);
	free_var(&result);

	PG_RETURN_NUMERIC(res);
}


/*
 * numeric_div() -
 *
 *	Divide one numeric into another
 */
Datum
numeric_div(PG_FUNCTION_ARGS)
{
	Numeric		num1 = PG_GETARG_NUMERIC(0);
	Numeric		num2 = PG_GETARG_NUMERIC(1);
	NumericVar	arg1;
	NumericVar	arg2;
	NumericVar	result;
	Numeric		res;
	int			rscale;

	/*
	 * Handle NaN
	 */
	if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2))
		PG_RETURN_NUMERIC(make_result(&const_nan));

	/*
	 * Unpack the arguments
	 */
	init_var(&arg1);
	init_var(&arg2);
	init_var(&result);

	set_var_from_num(num1, &arg1);
	set_var_from_num(num2, &arg2);

	/*
	 * Select scale for division result
	 */
	rscale = select_div_scale(&arg1, &arg2);

	/*
	 * Do the divide and return the result
	 */
	div_var(&arg1, &arg2, &result, rscale, true);

	res = make_result(&result);

	free_var(&arg1);
	free_var(&arg2);
	free_var(&result);

	PG_RETURN_NUMERIC(res);
}


/*
 * numeric_mod() -
 *
 *	Calculate the modulo of two numerics
 */
Datum
numeric_mod(PG_FUNCTION_ARGS)
{
	Numeric		num1 = PG_GETARG_NUMERIC(0);
	Numeric		num2 = PG_GETARG_NUMERIC(1);
	Numeric		res;
	NumericVar	arg1;
	NumericVar	arg2;
	NumericVar	result;

	if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2))
		PG_RETURN_NUMERIC(make_result(&const_nan));

	init_var(&arg1);
	init_var(&arg2);
	init_var(&result);

	set_var_from_num(num1, &arg1);
	set_var_from_num(num2, &arg2);

	mod_var(&arg1, &arg2, &result);

	res = make_result(&result);

	free_var(&result);
	free_var(&arg2);
	free_var(&arg1);

	PG_RETURN_NUMERIC(res);
}


/*
 * numeric_inc() -
 *
 *	Increment a number by one
 */
Datum
numeric_inc(PG_FUNCTION_ARGS)
{
	Numeric		num = PG_GETARG_NUMERIC(0);
	NumericVar	arg;
	Numeric		res;

	/*
	 * Handle NaN
	 */
	if (NUMERIC_IS_NAN(num))
		PG_RETURN_NUMERIC(make_result(&const_nan));

	/*
	 * Compute the result and return it
	 */
	init_var(&arg);

	set_var_from_num(num, &arg);

	add_var(&arg, &const_one, &arg);

	res = make_result(&arg);

	free_var(&arg);

	PG_RETURN_NUMERIC(res);
}


/*
 * numeric_smaller() -
 *
 *	Return the smaller of two numbers
 */
Datum
numeric_smaller(PG_FUNCTION_ARGS)
{
	Numeric		num1 = PG_GETARG_NUMERIC(0);
	Numeric		num2 = PG_GETARG_NUMERIC(1);

	/*
	 * Use cmp_numerics so that this will agree with the comparison operators,
	 * particularly as regards comparisons involving NaN.
	 */
	if (cmp_numerics(num1, num2) < 0)
		PG_RETURN_NUMERIC(num1);
	else
		PG_RETURN_NUMERIC(num2);
}


/*
 * numeric_larger() -
 *
 *	Return the larger of two numbers
 */
Datum
numeric_larger(PG_FUNCTION_ARGS)
{
	Numeric		num1 = PG_GETARG_NUMERIC(0);
	Numeric		num2 = PG_GETARG_NUMERIC(1);

	/*
	 * Use cmp_numerics so that this will agree with the comparison operators,
	 * particularly as regards comparisons involving NaN.
	 */
	if (cmp_numerics(num1, num2) > 0)
		PG_RETURN_NUMERIC(num1);
	else
		PG_RETURN_NUMERIC(num2);
}


/* ----------------------------------------------------------------------
 *
 * Advanced math functions
 *
 * ----------------------------------------------------------------------
 */

/*
 * numeric_fac()
 *
 * Compute factorial
 */
Datum
numeric_fac(PG_FUNCTION_ARGS)
{
	int64		num = PG_GETARG_INT64(0);
	Numeric		res;
	NumericVar	fact;
	NumericVar	result;

	if (num <= 1)
	{
		res = make_result(&const_one);
		PG_RETURN_NUMERIC(res);
	}
	/* Fail immediately if the result would overflow */
	if (num > 32177)
		ereport(ERROR,
				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
				 errmsg("value overflows numeric format")));

	init_var(&fact);
	init_var(&result);

	int8_to_numericvar(num, &result);

	for (num = num - 1; num > 1; num--)
	{
		/* this loop can take awhile, so allow it to be interrupted */
		CHECK_FOR_INTERRUPTS();

		int8_to_numericvar(num, &fact);

		mul_var(&result, &fact, &result, 0);
	}

	res = make_result(&result);

	free_var(&fact);
	free_var(&result);

	PG_RETURN_NUMERIC(res);
}


/*
 * numeric_sqrt() -
 *
 *	Compute the square root of a numeric.
 */
Datum
numeric_sqrt(PG_FUNCTION_ARGS)
{
	Numeric		num = PG_GETARG_NUMERIC(0);
	Numeric		res;
	NumericVar	arg;
	NumericVar	result;
	int			sweight;
	int			rscale;

	/*
	 * Handle NaN
	 */
	if (NUMERIC_IS_NAN(num))
		PG_RETURN_NUMERIC(make_result(&const_nan));

	/*
	 * Unpack the argument and determine the result scale.	We choose a scale
	 * to give at least NUMERIC_MIN_SIG_DIGITS significant digits; but in any
	 * case not less than the input's dscale.
	 */
	init_var(&arg);
	init_var(&result);

	set_var_from_num(num, &arg);

	/* Assume the input was normalized, so arg.weight is accurate */
	sweight = (arg.weight + 1) * DEC_DIGITS / 2 - 1;

	rscale = NUMERIC_MIN_SIG_DIGITS - sweight;
	rscale = Max(rscale, arg.dscale);
	rscale = Max(rscale, NUMERIC_MIN_DISPLAY_SCALE);
	rscale = Min(rscale, NUMERIC_MAX_DISPLAY_SCALE);

	/*
	 * Let sqrt_var() do the calculation and return the result.
	 */
	sqrt_var(&arg, &result, rscale);

	res = make_result(&result);

	free_var(&result);
	free_var(&arg);

	PG_RETURN_NUMERIC(res);
}


/*
 * numeric_exp() -
 *
 *	Raise e to the power of x
 */
Datum
numeric_exp(PG_FUNCTION_ARGS)
{
	Numeric		num = PG_GETARG_NUMERIC(0);
	Numeric		res;
	NumericVar	arg;
	NumericVar	result;
	int			rscale;
	double		val;

	/*
	 * Handle NaN
	 */
	if (NUMERIC_IS_NAN(num))
		PG_RETURN_NUMERIC(make_result(&const_nan));

	/*
	 * Unpack the argument and determine the result scale.	We choose a scale
	 * to give at least NUMERIC_MIN_SIG_DIGITS significant digits; but in any
	 * case not less than the input's dscale.
	 */
	init_var(&arg);
	init_var(&result);

	set_var_from_num(num, &arg);

	/* convert input to float8, ignoring overflow */
	val = numericvar_to_double_no_overflow(&arg);

	/*
	 * log10(result) = num * log10(e), so this is approximately the decimal
	 * weight of the result:
	 */
	val *= 0.434294481903252;

	/* limit to something that won't cause integer overflow */
	val = Max(val, -NUMERIC_MAX_RESULT_SCALE);
	val = Min(val, NUMERIC_MAX_RESULT_SCALE);

	rscale = NUMERIC_MIN_SIG_DIGITS - (int) val;
	rscale = Max(rscale, arg.dscale);
	rscale = Max(rscale, NUMERIC_MIN_DISPLAY_SCALE);
	rscale = Min(rscale, NUMERIC_MAX_DISPLAY_SCALE);

	/*
	 * Let exp_var() do the calculation and return the result.
	 */
	exp_var(&arg, &result, rscale);

	res = make_result(&result);

	free_var(&result);
	free_var(&arg);