Improve the accuracy of numeric power() for integer exponents.
This makes the choice of result scale of numeric power() for integer exponents consistent with the choice for non-integer exponents, and with the result scale of other numeric functions. Specifically, the result scale will be at least as large as the scale of either input, and sufficient to ensure that the result has at least 16 significant digits. Formerly, the result scale was based only on the scale of the first input, without taking into account the weight of the result. For results with negative weight, that could lead to results with very few or even no non-zero significant digits (e.g., 10.0 ^ (-18) produced 0.0000000000000000). Fix this by moving responsibility for the choice of result scale into power_var_int(), which already has code to estimate the result weight. Per report by Adrian Klaver and suggested fix by Tom Lane. No back-patch -- arguably this is a bug fix, but one which is easy to work around, so it doesn't seem worth the risk of changing query results in stable branches. Discussion: https://postgr.es/m/12a40226-70ac-3a3b-3d3a-fdaf9e32d312%40aklaver.com
This commit is contained in:
Dean Rasheed
parent
7fd1ae987a
commit
40c7fcbbed
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@ -571,8 +571,8 @@ static void log_var(const NumericVar *base, const NumericVar *num,
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NumericVar *result);
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static void power_var(const NumericVar *base, const NumericVar *exp,
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NumericVar *result);
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static void power_var_int(const NumericVar *base, int exp, NumericVar *result,
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int rscale);
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static void power_var_int(const NumericVar *base, int exp, int exp_dscale,
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NumericVar *result);
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static void power_ten_int(int exp, NumericVar *result);
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static int cmp_abs(const NumericVar *var1, const NumericVar *var2);
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@ -10335,13 +10335,8 @@ power_var(const NumericVar *base, const NumericVar *exp, NumericVar *result)
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{
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if (expval64 >= PG_INT32_MIN && expval64 <= PG_INT32_MAX)
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{
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/* Okay, select rscale */
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rscale = NUMERIC_MIN_SIG_DIGITS;
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rscale = Max(rscale, base->dscale);
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rscale = Max(rscale, NUMERIC_MIN_DISPLAY_SCALE);
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rscale = Min(rscale, NUMERIC_MAX_DISPLAY_SCALE);
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power_var_int(base, (int) expval64, result, rscale);
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/* Okay, use power_var_int */
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power_var_int(base, (int) expval64, exp->dscale, result);
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return;
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}
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}
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@ -10475,19 +10470,76 @@ power_var(const NumericVar *base, const NumericVar *exp, NumericVar *result)
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* power_var_int() -
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*
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* Raise base to the power of exp, where exp is an integer.
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*
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* Note: this routine chooses dscale of the result.
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*/
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static void
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power_var_int(const NumericVar *base, int exp, NumericVar *result, int rscale)
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power_var_int(const NumericVar *base, int exp, int exp_dscale,
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NumericVar *result)
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{
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double f;
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int p;
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int i;
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int rscale;
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int sig_digits;
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unsigned int mask;
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bool neg;
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NumericVar base_prod;
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int local_rscale;
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/*
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* Choose the result scale. For this we need an estimate of the decimal
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* weight of the result, which we obtain by approximating using double
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* precision arithmetic.
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*
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* We also perform crude overflow/underflow tests here so that we can exit
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* early if the result is sure to overflow/underflow, and to guard against
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* integer overflow when choosing the result scale.
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*/
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if (base->ndigits != 0)
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{
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/*----------
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* Choose f (double) and p (int) such that base ~= f * 10^p.
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* Then log10(result) = log10(base^exp) ~= exp * (log10(f) + p).
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*----------
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*/
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f = base->digits[0];
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p = base->weight * DEC_DIGITS;
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for (i = 1; i < base->ndigits && i * DEC_DIGITS < 16; i++)
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{
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f = f * NBASE + base->digits[i];
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p -= DEC_DIGITS;
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}
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f = exp * (log10(f) + p); /* approximate decimal result weight */
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}
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else
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f = 0; /* result is 0 or 1 (weight 0), or error */
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/* overflow/underflow tests with fuzz factors */
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if (f > (SHRT_MAX + 1) * DEC_DIGITS)
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ereport(ERROR,
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(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
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errmsg("value overflows numeric format")));
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if (f + 1 < -NUMERIC_MAX_DISPLAY_SCALE)
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{
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zero_var(result);
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result->dscale = NUMERIC_MAX_DISPLAY_SCALE;
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return;
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}
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/*
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* Choose the result scale in the same way as power_var(), so it has at
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* least NUMERIC_MIN_SIG_DIGITS significant digits and is not less than
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* either input's display scale.
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*/
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rscale = NUMERIC_MIN_SIG_DIGITS - (int) f;
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rscale = Max(rscale, base->dscale);
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rscale = Max(rscale, exp_dscale);
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rscale = Max(rscale, NUMERIC_MIN_DISPLAY_SCALE);
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rscale = Min(rscale, NUMERIC_MAX_DISPLAY_SCALE);
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/* Handle some common special cases, as well as corner cases */
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switch (exp)
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{
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@ -10532,43 +10584,15 @@ power_var_int(const NumericVar *base, int exp, NumericVar *result, int rscale)
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* The general case repeatedly multiplies base according to the bit
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* pattern of exp.
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*
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* First we need to estimate the weight of the result so that we know how
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* many significant digits are needed.
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* The local rscale used for each multiplication is varied to keep a fixed
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* number of significant digits, sufficient to give the required result
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* scale.
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*/
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f = base->digits[0];
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p = base->weight * DEC_DIGITS;
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for (i = 1; i < base->ndigits && i * DEC_DIGITS < 16; i++)
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{
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f = f * NBASE + base->digits[i];
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p -= DEC_DIGITS;
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}
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/*----------
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* We have base ~= f * 10^p
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* so log10(result) = log10(base^exp) ~= exp * (log10(f) + p)
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*----------
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*/
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f = exp * (log10(f) + p);
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/*
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* Apply crude overflow/underflow tests so we can exit early if the result
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* certainly will overflow/underflow.
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*/
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if (f > 3 * SHRT_MAX * DEC_DIGITS)
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ereport(ERROR,
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(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
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errmsg("value overflows numeric format")));
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if (f + 1 < -rscale || f + 1 < -NUMERIC_MAX_DISPLAY_SCALE)
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{
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zero_var(result);
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result->dscale = rscale;
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return;
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}
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/*
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* Approximate number of significant digits in the result. Note that the
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* underflow test above means that this is necessarily >= 0.
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* underflow test above, together with the choice of rscale, ensures that
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* this approximation is necessarily > 0.
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*/
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sig_digits = 1 + rscale + (int) f;
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@ -952,44 +952,44 @@ WITH v(x) AS
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SELECT x1, x2,
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power(x1, x2)
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FROM v AS v1(x1), v AS v2(x2) WHERE x1 != 0 OR x2 >= 0;
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x1 | x2 | power
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----------+----------+---------------------
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0 | 0 | 1.0000000000000000
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0 | 1 | 0.0000000000000000
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0 | 2 | 0.0000000000000000
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0 | 4.2 | 0.0000000000000000
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0 | Infinity | 0
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0 | NaN | NaN
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1 | 0 | 1.0000000000000000
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1 | 1 | 1.0000000000000000
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1 | 2 | 1.0000000000000000
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1 | 4.2 | 1.0000000000000000
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1 | Infinity | 1
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1 | NaN | 1
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2 | 0 | 1.0000000000000000
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2 | 1 | 2.0000000000000000
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2 | 2 | 4.0000000000000000
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2 | 4.2 | 18.379173679952560
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2 | Infinity | Infinity
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2 | NaN | NaN
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4.2 | 0 | 1.0000000000000000
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4.2 | 1 | 4.2000000000000000
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4.2 | 2 | 17.6400000000000000
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4.2 | 4.2 | 414.61691860129675
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4.2 | Infinity | Infinity
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4.2 | NaN | NaN
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Infinity | 0 | 1
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Infinity | 1 | Infinity
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Infinity | 2 | Infinity
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Infinity | 4.2 | Infinity
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Infinity | Infinity | Infinity
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Infinity | NaN | NaN
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NaN | 0 | 1
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NaN | 1 | NaN
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NaN | 2 | NaN
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NaN | 4.2 | NaN
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NaN | Infinity | NaN
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NaN | NaN | NaN
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x1 | x2 | power
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----------+----------+--------------------
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0 | 0 | 1.0000000000000000
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0 | 1 | 0.0000000000000000
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0 | 2 | 0.0000000000000000
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0 | 4.2 | 0.0000000000000000
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0 | Infinity | 0
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0 | NaN | NaN
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1 | 0 | 1.0000000000000000
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1 | 1 | 1.0000000000000000
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1 | 2 | 1.0000000000000000
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1 | 4.2 | 1.0000000000000000
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1 | Infinity | 1
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1 | NaN | 1
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2 | 0 | 1.0000000000000000
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2 | 1 | 2.0000000000000000
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2 | 2 | 4.0000000000000000
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2 | 4.2 | 18.379173679952560
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2 | Infinity | Infinity
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2 | NaN | NaN
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4.2 | 0 | 1.0000000000000000
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4.2 | 1 | 4.2000000000000000
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4.2 | 2 | 17.640000000000000
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4.2 | 4.2 | 414.61691860129675
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4.2 | Infinity | Infinity
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4.2 | NaN | NaN
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Infinity | 0 | 1
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Infinity | 1 | Infinity
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Infinity | 2 | Infinity
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Infinity | 4.2 | Infinity
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Infinity | Infinity | Infinity
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Infinity | NaN | NaN
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NaN | 0 | 1
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NaN | 1 | NaN
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NaN | 2 | NaN
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NaN | 4.2 | NaN
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NaN | Infinity | NaN
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NaN | NaN | NaN
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(36 rows)
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SELECT power('0'::numeric, '-1');
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@ -2431,15 +2431,15 @@ select sqrt(8015491789940783531003294973900307::numeric);
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-- Test code path for raising to integer powers
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--
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select 10.0 ^ -2147483648 as rounds_to_zero;
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rounds_to_zero
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--------------------
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0.0000000000000000
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rounds_to_zero
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--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
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0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
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(1 row)
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select 10.0 ^ -2147483647 as rounds_to_zero;
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rounds_to_zero
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--------------------
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0.0000000000000000
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rounds_to_zero
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--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
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0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
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(1 row)
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select 10.0 ^ 2147483647 as overflows;
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@ -2447,28 +2447,28 @@ ERROR: value overflows numeric format
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select 117743296169.0 ^ 1000000000 as overflows;
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ERROR: value overflows numeric format
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-- cases that used to return inaccurate results
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select 3.789 ^ 21;
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select 3.789 ^ 21.0000000000000000;
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?column?
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--------------------------------
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1409343026052.8716016316022141
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(1 row)
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select 3.789 ^ 35;
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select 3.789 ^ 35.0000000000000000;
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?column?
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----------------------------------------
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177158169650516670809.3820586142670135
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(1 row)
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select 1.2 ^ 345;
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?column?
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-----------------------------------------------
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2077446682327378559843444695.5827049735727869
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?column?
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--------------------------------
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2077446682327378559843444695.6
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(1 row)
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select 0.12 ^ (-20);
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?column?
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--------------------------------------
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2608405330458882702.5529619561355838
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?column?
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------------------------
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2608405330458882702.55
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(1 row)
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select 1.000000000123 ^ (-2147483648);
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@ -2491,15 +2491,15 @@ select round(((1 - 1.500012345678e-1000) ^ 1.45e1003) * 1e1000);
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-- cases that used to error out
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select 0.12 ^ (-25);
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?column?
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-------------------------------------------
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104825960103961013959336.4983657883169110
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?column?
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-----------------------------
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104825960103961013959336.50
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(1 row)
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select 0.5678 ^ (-85);
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?column?
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----------------------------------------
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782333637740774446257.7719390061997396
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?column?
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----------------------------
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782333637740774446257.7719
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(1 row)
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select coalesce(nullif(0.9999999999 ^ 70000000000000, 0), 0) as underflows;
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@ -2539,6 +2539,54 @@ select (-1.0) ^ 1000000000000001;
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-1.0000000000000000
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(1 row)
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-- integer powers of 10
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select n, 10.0 ^ n as "10^n", (10.0 ^ n) * (10.0 ^ (-n)) = 1 as ok
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from generate_series(-20, 20) n;
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n | 10^n | ok
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-----+----------------------------------------+----
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-20 | 0.000000000000000000010000000000000000 | t
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-19 | 0.00000000000000000010000000000000000 | t
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-18 | 0.0000000000000000010000000000000000 | t
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-17 | 0.000000000000000010000000000000000 | t
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-16 | 0.00000000000000010000000000000000 | t
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-15 | 0.0000000000000010000000000000000 | t
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-14 | 0.000000000000010000000000000000 | t
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-13 | 0.00000000000010000000000000000 | t
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-12 | 0.0000000000010000000000000000 | t
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-11 | 0.000000000010000000000000000 | t
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-10 | 0.00000000010000000000000000 | t
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-9 | 0.0000000010000000000000000 | t
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-8 | 0.000000010000000000000000 | t
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-7 | 0.00000010000000000000000 | t
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-6 | 0.0000010000000000000000 | t
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-5 | 0.000010000000000000000 | t
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-4 | 0.00010000000000000000 | t
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-3 | 0.0010000000000000000 | t
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-2 | 0.010000000000000000 | t
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-1 | 0.10000000000000000 | t
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0 | 1.0000000000000000 | t
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1 | 10.000000000000000 | t
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2 | 100.00000000000000 | t
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3 | 1000.0000000000000 | t
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4 | 10000.000000000000 | t
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5 | 100000.00000000000 | t
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6 | 1000000.0000000000 | t
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7 | 10000000.000000000 | t
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8 | 100000000.00000000 | t
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9 | 1000000000.0000000 | t
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10 | 10000000000.000000 | t
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11 | 100000000000.00000 | t
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12 | 1000000000000.0000 | t
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13 | 10000000000000.000 | t
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14 | 100000000000000.00 | t
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15 | 1000000000000000.0 | t
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16 | 10000000000000000.0 | t
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17 | 100000000000000000.0 | t
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18 | 1000000000000000000.0 | t
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19 | 10000000000000000000.0 | t
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20 | 100000000000000000000.0 | t
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(41 rows)
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--
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-- Tests for raising to non-integer powers
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--
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@ -2630,9 +2678,9 @@ select 12.3 ^ (-45.6);
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-- big test
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select 1.234 ^ 5678;
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?column?
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----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
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307239295662090741644584872593956173493568238595074141254349565406661439636598896798876823220904084953233015553994854875890890858118656468658643918169805277399402542281777901029346337707622181574346585989613344285010764501017625366742865066948856161360224801370482171458030533346309750557140549621313515752078638620714732831815297168231790779296290266207315344008883935010274044001522606235576584215999260117523114297033944018699691024106823438431754073086813382242140602291215149759520833200152654884259619588924545324.5973362312547382
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?column?
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---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
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307239295662090741644584872593956173493568238595074141254349565406661439636598896798876823220904084953233015553994854875890890858118656468658643918169805277399402542281777901029346337707622181574346585989613344285010764501017625366742865066948856161360224801370482171458030533346309750557140549621313515752078638620714732831815297168231790779296290266207315344008883935010274044001522606235576584215999260117523114297033944018699691024106823438431754073086813382242140602291215149759520833200152654884259619588924545324.597
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(1 row)
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--
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|
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@ -686,91 +686,91 @@ SELECT t1.id1, t1.result, t2.expected
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-- echo "($b, $p, $r),"
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-- done
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WITH t(b, p, bc_result) AS (VALUES
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(0.084738, -20, 2744326694304960114888.7859130502035257),
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(0.084738, -19, 232548755422013710215.4459407000481464),
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(0.084738, -18, 19705716436950597776.2364581230406798),
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(0.084738, -17, 1669822999434319754.3627249884302211),
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(0.084738, -16, 141497461326065387.3451885900696001),
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(0.084738, -15, 11990211877848128.7928565907453178),
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(0.084738, -14, 1016026574105094.7376490817865767),
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(0.084738, -13, 86096059836517.5178789078924309),
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(0.084738, -12, 7295607918426.8214300228969888),
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(0.084738, -11, 618215223791.6519943372802450),
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(0.084738, -10, 52386321633.6570066961524534),
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(0.084738, -9, 4439112122.5928274334185666),
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(0.084738, -8, 376161483.0442710110530225),
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(0.084738, -7, 31875171.7502054369346110),
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(0.084738, -6, 2701038.3037689083149651),
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(0.084738, -5, 228880.5837847697527935),
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(0.084738, -4, 19394.8829087538193122),
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||||
(0.084738, -3, 1643.4835879219811409),
|
||||
(0.084738, -2, 139.2655122733328379),
|
||||
(0.084738, -1, 11.8010809790176780),
|
||||
(0.084738, -20, 2744326694304960114888.785913),
|
||||
(0.084738, -19, 232548755422013710215.445941),
|
||||
(0.084738, -18, 19705716436950597776.236458),
|
||||
(0.084738, -17, 1669822999434319754.362725),
|
||||
(0.084738, -16, 141497461326065387.345189),
|
||||
(0.084738, -15, 11990211877848128.792857),
|
||||
(0.084738, -14, 1016026574105094.737649),
|
||||
(0.084738, -13, 86096059836517.517879),
|
||||
(0.084738, -12, 7295607918426.821430),
|
||||
(0.084738, -11, 618215223791.651994),
|
||||
(0.084738, -10, 52386321633.657007),
|
||||
(0.084738, -9, 4439112122.5928274),
|
||||
(0.084738, -8, 376161483.04427101),
|
||||
(0.084738, -7, 31875171.750205437),
|
||||
(0.084738, -6, 2701038.3037689083),
|
||||
(0.084738, -5, 228880.58378476975),
|
||||
(0.084738, -4, 19394.882908753819),
|
||||
(0.084738, -3, 1643.4835879219811),
|
||||
(0.084738, -2, 139.26551227333284),
|
||||
(0.084738, -1, 11.801080979017678),
|
||||
(0.084738, 0, 1),
|
||||
(0.084738, 1, .084738),
|
||||
(0.084738, 2, .007180528644),
|
||||
(0.084738, 3, .0006084636362353),
|
||||
(0.084738, 4, .0000515599916073),
|
||||
(0.084738, 5, .0000043690905688),
|
||||
(0.084738, 6, .0000003702279966),
|
||||
(0.084738, 7, .0000000313723800),
|
||||
(0.084738, 8, .0000000026584327),
|
||||
(0.084738, 9, .0000000002252703),
|
||||
(0.084738, 10, .0000000000190890),
|
||||
(0.084738, 11, .0000000000016176),
|
||||
(0.084738, 12, .0000000000001371),
|
||||
(0.084738, 13, .0000000000000116),
|
||||
(0.084738, 14, .0000000000000010),
|
||||
(0.084738, 15, .0000000000000001),
|
||||
(0.084738, 16, .0000000000000000),
|
||||
(0.084738, 17, .0000000000000000),
|
||||
(0.084738, 18, .0000000000000000),
|
||||
(0.084738, 19, .0000000000000000),
|
||||
(0.084738, 20, .0000000000000000))
|
||||
(0.084738, 3, .000608463636235272),
|
||||
(0.084738, 4, .00005155999160730448),
|
||||
(0.084738, 5, .000004369090568819767),
|
||||
(0.084738, 6, .0000003702279966206494),
|
||||
(0.084738, 7, .00000003137237997764059),
|
||||
(0.084738, 8, .000000002658432734545308),
|
||||
(0.084738, 9, .0000000002252702730599003),
|
||||
(0.084738, 10, .00000000001908895239854983),
|
||||
(0.084738, 11, .000000000001617559648348316),
|
||||
(0.084738, 12, .0000000000001370687694817396),
|
||||
(0.084738, 13, .00000000000001161493338834365),
|
||||
(0.084738, 14, .0000000000000009842262254614642),
|
||||
(0.084738, 15, .00000000000000008340136189315355),
|
||||
(0.084738, 16, .000000000000000007067264604102046),
|
||||
(0.084738, 17, .0000000000000000005988658680223991),
|
||||
(0.084738, 18, .00000000000000000005074669592448206),
|
||||
(0.084738, 19, .000000000000000000004300173519248761),
|
||||
(0.084738, 20, .0000000000000000000003643881036741015))
|
||||
SELECT b, p, bc_result, b^p AS power, b^p - bc_result AS diff FROM t;
|
||||
b | p | bc_result | power | diff
|
||||
----------+-----+-----------------------------------------+-----------------------------------------+--------------------
|
||||
0.084738 | -20 | 2744326694304960114888.7859130502035257 | 2744326694304960114888.7859130502035257 | 0.0000000000000000
|
||||
0.084738 | -19 | 232548755422013710215.4459407000481464 | 232548755422013710215.4459407000481464 | 0.0000000000000000
|
||||
0.084738 | -18 | 19705716436950597776.2364581230406798 | 19705716436950597776.2364581230406798 | 0.0000000000000000
|
||||
0.084738 | -17 | 1669822999434319754.3627249884302211 | 1669822999434319754.3627249884302211 | 0.0000000000000000
|
||||
0.084738 | -16 | 141497461326065387.3451885900696001 | 141497461326065387.3451885900696001 | 0.0000000000000000
|
||||
0.084738 | -15 | 11990211877848128.7928565907453178 | 11990211877848128.7928565907453178 | 0.0000000000000000
|
||||
0.084738 | -14 | 1016026574105094.7376490817865767 | 1016026574105094.7376490817865767 | 0.0000000000000000
|
||||
0.084738 | -13 | 86096059836517.5178789078924309 | 86096059836517.5178789078924309 | 0.0000000000000000
|
||||
0.084738 | -12 | 7295607918426.8214300228969888 | 7295607918426.8214300228969888 | 0.0000000000000000
|
||||
0.084738 | -11 | 618215223791.6519943372802450 | 618215223791.6519943372802450 | 0.0000000000000000
|
||||
0.084738 | -10 | 52386321633.6570066961524534 | 52386321633.6570066961524534 | 0.0000000000000000
|
||||
0.084738 | -9 | 4439112122.5928274334185666 | 4439112122.5928274334185666 | 0.0000000000000000
|
||||
0.084738 | -8 | 376161483.0442710110530225 | 376161483.0442710110530225 | 0.0000000000000000
|
||||
0.084738 | -7 | 31875171.7502054369346110 | 31875171.7502054369346110 | 0.0000000000000000
|
||||
0.084738 | -6 | 2701038.3037689083149651 | 2701038.3037689083149651 | 0.0000000000000000
|
||||
0.084738 | -5 | 228880.5837847697527935 | 228880.5837847697527935 | 0.0000000000000000
|
||||
0.084738 | -4 | 19394.8829087538193122 | 19394.8829087538193122 | 0.0000000000000000
|
||||
0.084738 | -3 | 1643.4835879219811409 | 1643.4835879219811409 | 0.0000000000000000
|
||||
0.084738 | -2 | 139.2655122733328379 | 139.2655122733328379 | 0.0000000000000000
|
||||
0.084738 | -1 | 11.8010809790176780 | 11.8010809790176780 | 0.0000000000000000
|
||||
0.084738 | 0 | 1 | 1.0000000000000000 | 0.0000000000000000
|
||||
0.084738 | 1 | 0.084738 | 0.0847380000000000 | 0.0000000000000000
|
||||
0.084738 | 2 | 0.007180528644 | 0.0071805286440000 | 0.0000000000000000
|
||||
0.084738 | 3 | 0.0006084636362353 | 0.0006084636362353 | 0.0000000000000000
|
||||
0.084738 | 4 | 0.0000515599916073 | 0.0000515599916073 | 0.0000000000000000
|
||||
0.084738 | 5 | 0.0000043690905688 | 0.0000043690905688 | 0.0000000000000000
|
||||
0.084738 | 6 | 0.0000003702279966 | 0.0000003702279966 | 0.0000000000000000
|
||||
0.084738 | 7 | 0.0000000313723800 | 0.0000000313723800 | 0.0000000000000000
|
||||
0.084738 | 8 | 0.0000000026584327 | 0.0000000026584327 | 0.0000000000000000
|
||||
0.084738 | 9 | 0.0000000002252703 | 0.0000000002252703 | 0.0000000000000000
|
||||
0.084738 | 10 | 0.0000000000190890 | 0.0000000000190890 | 0.0000000000000000
|
||||
0.084738 | 11 | 0.0000000000016176 | 0.0000000000016176 | 0.0000000000000000
|
||||
0.084738 | 12 | 0.0000000000001371 | 0.0000000000001371 | 0.0000000000000000
|
||||
0.084738 | 13 | 0.0000000000000116 | 0.0000000000000116 | 0.0000000000000000
|
||||
0.084738 | 14 | 0.0000000000000010 | 0.0000000000000010 | 0.0000000000000000
|
||||
0.084738 | 15 | 0.0000000000000001 | 0.0000000000000001 | 0.0000000000000000
|
||||
0.084738 | 16 | 0.0000000000000000 | 0.0000000000000000 | 0.0000000000000000
|
||||
0.084738 | 17 | 0.0000000000000000 | 0.0000000000000000 | 0.0000000000000000
|
||||
0.084738 | 18 | 0.0000000000000000 | 0.0000000000000000 | 0.0000000000000000
|
||||
0.084738 | 19 | 0.0000000000000000 | 0.0000000000000000 | 0.0000000000000000
|
||||
0.084738 | 20 | 0.0000000000000000 | 0.0000000000000000 | 0.0000000000000000
|
||||
b | p | bc_result | power | diff
|
||||
----------+-----+-----------------------------------------+-----------------------------------------+-----------------------------------------
|
||||
0.084738 | -20 | 2744326694304960114888.785913 | 2744326694304960114888.785913 | 0.000000
|
||||
0.084738 | -19 | 232548755422013710215.445941 | 232548755422013710215.445941 | 0.000000
|
||||
0.084738 | -18 | 19705716436950597776.236458 | 19705716436950597776.236458 | 0.000000
|
||||
0.084738 | -17 | 1669822999434319754.362725 | 1669822999434319754.362725 | 0.000000
|
||||
0.084738 | -16 | 141497461326065387.345189 | 141497461326065387.345189 | 0.000000
|
||||
0.084738 | -15 | 11990211877848128.792857 | 11990211877848128.792857 | 0.000000
|
||||
0.084738 | -14 | 1016026574105094.737649 | 1016026574105094.737649 | 0.000000
|
||||
0.084738 | -13 | 86096059836517.517879 | 86096059836517.517879 | 0.000000
|
||||
0.084738 | -12 | 7295607918426.821430 | 7295607918426.821430 | 0.000000
|
||||
0.084738 | -11 | 618215223791.651994 | 618215223791.651994 | 0.000000
|
||||
0.084738 | -10 | 52386321633.657007 | 52386321633.657007 | 0.000000
|
||||
0.084738 | -9 | 4439112122.5928274 | 4439112122.5928274 | 0.0000000
|
||||
0.084738 | -8 | 376161483.04427101 | 376161483.04427101 | 0.00000000
|
||||
0.084738 | -7 | 31875171.750205437 | 31875171.750205437 | 0.000000000
|
||||
0.084738 | -6 | 2701038.3037689083 | 2701038.3037689083 | 0.0000000000
|
||||
0.084738 | -5 | 228880.58378476975 | 228880.58378476975 | 0.00000000000
|
||||
0.084738 | -4 | 19394.882908753819 | 19394.882908753819 | 0.000000000000
|
||||
0.084738 | -3 | 1643.4835879219811 | 1643.4835879219811 | 0.0000000000000
|
||||
0.084738 | -2 | 139.26551227333284 | 139.26551227333284 | 0.00000000000000
|
||||
0.084738 | -1 | 11.801080979017678 | 11.801080979017678 | 0.000000000000000
|
||||
0.084738 | 0 | 1 | 1.0000000000000000 | 0.0000000000000000
|
||||
0.084738 | 1 | 0.084738 | 0.08473800000000000 | 0.00000000000000000
|
||||
0.084738 | 2 | 0.007180528644 | 0.007180528644000000 | 0.000000000000000000
|
||||
0.084738 | 3 | 0.000608463636235272 | 0.0006084636362352720 | 0.0000000000000000000
|
||||
0.084738 | 4 | 0.00005155999160730448 | 0.00005155999160730448 | 0.00000000000000000000
|
||||
0.084738 | 5 | 0.000004369090568819767 | 0.000004369090568819767 | 0.000000000000000000000
|
||||
0.084738 | 6 | 0.0000003702279966206494 | 0.0000003702279966206494 | 0.0000000000000000000000
|
||||
0.084738 | 7 | 0.00000003137237997764059 | 0.00000003137237997764059 | 0.00000000000000000000000
|
||||
0.084738 | 8 | 0.000000002658432734545308 | 0.000000002658432734545308 | 0.000000000000000000000000
|
||||
0.084738 | 9 | 0.0000000002252702730599003 | 0.0000000002252702730599003 | 0.0000000000000000000000000
|
||||
0.084738 | 10 | 0.00000000001908895239854983 | 0.00000000001908895239854983 | 0.00000000000000000000000000
|
||||
0.084738 | 11 | 0.000000000001617559648348316 | 0.000000000001617559648348316 | 0.000000000000000000000000000
|
||||
0.084738 | 12 | 0.0000000000001370687694817396 | 0.0000000000001370687694817396 | 0.0000000000000000000000000000
|
||||
0.084738 | 13 | 0.00000000000001161493338834365 | 0.00000000000001161493338834365 | 0.00000000000000000000000000000
|
||||
0.084738 | 14 | 0.0000000000000009842262254614642 | 0.0000000000000009842262254614642 | 0.0000000000000000000000000000000
|
||||
0.084738 | 15 | 0.00000000000000008340136189315355 | 0.00000000000000008340136189315355 | 0.00000000000000000000000000000000
|
||||
0.084738 | 16 | 0.000000000000000007067264604102046 | 0.000000000000000007067264604102046 | 0.000000000000000000000000000000000
|
||||
0.084738 | 17 | 0.0000000000000000005988658680223991 | 0.0000000000000000005988658680223991 | 0.0000000000000000000000000000000000
|
||||
0.084738 | 18 | 0.00000000000000000005074669592448206 | 0.00000000000000000005074669592448206 | 0.00000000000000000000000000000000000
|
||||
0.084738 | 19 | 0.000000000000000000004300173519248761 | 0.000000000000000000004300173519248761 | 0.000000000000000000000000000000000000
|
||||
0.084738 | 20 | 0.0000000000000000000003643881036741015 | 0.0000000000000000000003643881036741015 | 0.0000000000000000000000000000000000000
|
||||
(41 rows)
|
||||
|
||||
-- base greater than 1
|
||||
|
|
@ -785,91 +785,91 @@ SELECT b, p, bc_result, b^p AS power, b^p - bc_result AS diff FROM t;
|
|||
-- echo "($b, $p, $r),"
|
||||
-- done
|
||||
WITH t(b, p, bc_result) AS (VALUES
|
||||
(37.821637, -20, .0000000000000000),
|
||||
(37.821637, -19, .0000000000000000),
|
||||
(37.821637, -18, .0000000000000000),
|
||||
(37.821637, -17, .0000000000000000),
|
||||
(37.821637, -16, .0000000000000000),
|
||||
(37.821637, -15, .0000000000000000),
|
||||
(37.821637, -14, .0000000000000000),
|
||||
(37.821637, -13, .0000000000000000),
|
||||
(37.821637, -12, .0000000000000000),
|
||||
(37.821637, -11, .0000000000000000),
|
||||
(37.821637, -10, .0000000000000002),
|
||||
(37.821637, -9, .0000000000000063),
|
||||
(37.821637, -8, .0000000000002388),
|
||||
(37.821637, -7, .0000000000090327),
|
||||
(37.821637, -6, .0000000003416316),
|
||||
(37.821637, -5, .0000000129210673),
|
||||
(37.821637, -4, .0000004886959182),
|
||||
(37.821637, -3, .0000184832796213),
|
||||
(37.821637, -2, .0006990678924066),
|
||||
(37.821637, -1, .0264398920649574),
|
||||
(37.821637, -20, .00000000000000000000000000000002787363175065101),
|
||||
(37.821637, -19, .000000000000000000000000000001054226381944797),
|
||||
(37.821637, -18, .00000000000000000000000000003987256753373947),
|
||||
(37.821637, -17, .000000000000000000000000001508045775519079),
|
||||
(37.821637, -16, .00000000000000000000000005703675990106610),
|
||||
(37.821637, -15, .000000000000000000000002157223628634278),
|
||||
(37.821637, -14, .00000000000000000000008158972901002847),
|
||||
(37.821637, -13, .000000000000000000003085857113545666),
|
||||
(37.821637, -12, .0000000000000000001167121675823920),
|
||||
(37.821637, -11, .000000000000000004414245235784397),
|
||||
(37.821637, -10, .0000000000000001669539809368169),
|
||||
(37.821637, -9, .000000000000006314472862697207),
|
||||
(37.821637, -8, .0000000000002388237004592846),
|
||||
(37.821637, -7, .000000000009032703305767796),
|
||||
(37.821637, -6, .0000000003416316255594496),
|
||||
(37.821637, -5, .00000001292106732962942),
|
||||
(37.821637, -4, .0000004886959181938034),
|
||||
(37.821637, -3, .00001848327962130773),
|
||||
(37.821637, -2, .0006990678924065984),
|
||||
(37.821637, -1, .02643989206495742),
|
||||
(37.821637, 0, 1),
|
||||
(37.821637, 1, 37.821637),
|
||||
(37.821637, 2, 1430.476225359769),
|
||||
(37.821637, 3, 54102.9525326873775219),
|
||||
(37.821637, 4, 2046262.2313195326271135),
|
||||
(37.821637, 5, 77392987.3197773940323425),
|
||||
(37.821637, 6, 2927129472.7542235178972258),
|
||||
(37.821637, 7, 110708828370.5116321107718772),
|
||||
(37.821637, 8, 4187189119324.7924539711577286),
|
||||
(37.821637, 9, 158366346921451.9852944363360812),
|
||||
(37.821637, 10, 5989674486279224.5007355092228730),
|
||||
(37.821637, 11, 226539294168214309.7083246628376531),
|
||||
(37.821637, 12, 8568086950266418559.9938312759931069),
|
||||
(37.821637, 13, 324059074417413536066.1494087598581043),
|
||||
(37.821637, 14, 12256444679171401239980.3109258799733927),
|
||||
(37.821637, 15, 463558801566202198479885.2069857662592280),
|
||||
(37.821637, 16, 17532552720991931019508170.1002855156233684),
|
||||
(37.821637, 17, 663109844696719094948877928.0672523682648687),
|
||||
(37.821637, 18, 25079899837245684700124994552.6717306599041850),
|
||||
(37.821637, 19, 948562867640665366544581398598.1275771806665398),
|
||||
(37.821637, 20, 35876200451584291931921101974730.6901038166532866))
|
||||
(37.821637, 3, 54102.952532687378),
|
||||
(37.821637, 4, 2046262.2313195326),
|
||||
(37.821637, 5, 77392987.319777394),
|
||||
(37.821637, 6, 2927129472.7542235),
|
||||
(37.821637, 7, 110708828370.511632),
|
||||
(37.821637, 8, 4187189119324.792454),
|
||||
(37.821637, 9, 158366346921451.985294),
|
||||
(37.821637, 10, 5989674486279224.500736),
|
||||
(37.821637, 11, 226539294168214309.708325),
|
||||
(37.821637, 12, 8568086950266418559.993831),
|
||||
(37.821637, 13, 324059074417413536066.149409),
|
||||
(37.821637, 14, 12256444679171401239980.310926),
|
||||
(37.821637, 15, 463558801566202198479885.206986),
|
||||
(37.821637, 16, 17532552720991931019508170.100286),
|
||||
(37.821637, 17, 663109844696719094948877928.067252),
|
||||
(37.821637, 18, 25079899837245684700124994552.671731),
|
||||
(37.821637, 19, 948562867640665366544581398598.127577),
|
||||
(37.821637, 20, 35876200451584291931921101974730.690104))
|
||||
SELECT b, p, bc_result, b^p AS power, b^p - bc_result AS diff FROM t;
|
||||
b | p | bc_result | power | diff
|
||||
-----------+-----+---------------------------------------------------+---------------------------------------------------+--------------------
|
||||
37.821637 | -20 | 0.0000000000000000 | 0.0000000000000000 | 0.0000000000000000
|
||||
37.821637 | -19 | 0.0000000000000000 | 0.0000000000000000 | 0.0000000000000000
|
||||
37.821637 | -18 | 0.0000000000000000 | 0.0000000000000000 | 0.0000000000000000
|
||||
37.821637 | -17 | 0.0000000000000000 | 0.0000000000000000 | 0.0000000000000000
|
||||
37.821637 | -16 | 0.0000000000000000 | 0.0000000000000000 | 0.0000000000000000
|
||||
37.821637 | -15 | 0.0000000000000000 | 0.0000000000000000 | 0.0000000000000000
|
||||
37.821637 | -14 | 0.0000000000000000 | 0.0000000000000000 | 0.0000000000000000
|
||||
37.821637 | -13 | 0.0000000000000000 | 0.0000000000000000 | 0.0000000000000000
|
||||
37.821637 | -12 | 0.0000000000000000 | 0.0000000000000000 | 0.0000000000000000
|
||||
37.821637 | -11 | 0.0000000000000000 | 0.0000000000000000 | 0.0000000000000000
|
||||
37.821637 | -10 | 0.0000000000000002 | 0.0000000000000002 | 0.0000000000000000
|
||||
37.821637 | -9 | 0.0000000000000063 | 0.0000000000000063 | 0.0000000000000000
|
||||
37.821637 | -8 | 0.0000000000002388 | 0.0000000000002388 | 0.0000000000000000
|
||||
37.821637 | -7 | 0.0000000000090327 | 0.0000000000090327 | 0.0000000000000000
|
||||
37.821637 | -6 | 0.0000000003416316 | 0.0000000003416316 | 0.0000000000000000
|
||||
37.821637 | -5 | 0.0000000129210673 | 0.0000000129210673 | 0.0000000000000000
|
||||
37.821637 | -4 | 0.0000004886959182 | 0.0000004886959182 | 0.0000000000000000
|
||||
37.821637 | -3 | 0.0000184832796213 | 0.0000184832796213 | 0.0000000000000000
|
||||
37.821637 | -2 | 0.0006990678924066 | 0.0006990678924066 | 0.0000000000000000
|
||||
37.821637 | -1 | 0.0264398920649574 | 0.0264398920649574 | 0.0000000000000000
|
||||
37.821637 | 0 | 1 | 1.0000000000000000 | 0.0000000000000000
|
||||
37.821637 | 1 | 37.821637 | 37.8216370000000000 | 0.0000000000000000
|
||||
37.821637 | 2 | 1430.476225359769 | 1430.4762253597690000 | 0.0000000000000000
|
||||
37.821637 | 3 | 54102.9525326873775219 | 54102.9525326873775219 | 0.0000000000000000
|
||||
37.821637 | 4 | 2046262.2313195326271135 | 2046262.2313195326271135 | 0.0000000000000000
|
||||
37.821637 | 5 | 77392987.3197773940323425 | 77392987.3197773940323425 | 0.0000000000000000
|
||||
37.821637 | 6 | 2927129472.7542235178972258 | 2927129472.7542235178972258 | 0.0000000000000000
|
||||
37.821637 | 7 | 110708828370.5116321107718772 | 110708828370.5116321107718772 | 0.0000000000000000
|
||||
37.821637 | 8 | 4187189119324.7924539711577286 | 4187189119324.7924539711577286 | 0.0000000000000000
|
||||
37.821637 | 9 | 158366346921451.9852944363360812 | 158366346921451.9852944363360812 | 0.0000000000000000
|
||||
37.821637 | 10 | 5989674486279224.5007355092228730 | 5989674486279224.5007355092228730 | 0.0000000000000000
|
||||
37.821637 | 11 | 226539294168214309.7083246628376531 | 226539294168214309.7083246628376531 | 0.0000000000000000
|
||||
37.821637 | 12 | 8568086950266418559.9938312759931069 | 8568086950266418559.9938312759931069 | 0.0000000000000000
|
||||
37.821637 | 13 | 324059074417413536066.1494087598581043 | 324059074417413536066.1494087598581043 | 0.0000000000000000
|
||||
37.821637 | 14 | 12256444679171401239980.3109258799733927 | 12256444679171401239980.3109258799733927 | 0.0000000000000000
|
||||
37.821637 | 15 | 463558801566202198479885.2069857662592280 | 463558801566202198479885.2069857662592280 | 0.0000000000000000
|
||||
37.821637 | 16 | 17532552720991931019508170.1002855156233684 | 17532552720991931019508170.1002855156233684 | 0.0000000000000000
|
||||
37.821637 | 17 | 663109844696719094948877928.0672523682648687 | 663109844696719094948877928.0672523682648687 | 0.0000000000000000
|
||||
37.821637 | 18 | 25079899837245684700124994552.6717306599041850 | 25079899837245684700124994552.6717306599041850 | 0.0000000000000000
|
||||
37.821637 | 19 | 948562867640665366544581398598.1275771806665398 | 948562867640665366544581398598.1275771806665398 | 0.0000000000000000
|
||||
37.821637 | 20 | 35876200451584291931921101974730.6901038166532866 | 35876200451584291931921101974730.6901038166532866 | 0.0000000000000000
|
||||
b | p | bc_result | power | diff
|
||||
-----------+-----+---------------------------------------------------+---------------------------------------------------+---------------------------------------------------
|
||||
37.821637 | -20 | 0.00000000000000000000000000000002787363175065101 | 0.00000000000000000000000000000002787363175065101 | 0.00000000000000000000000000000000000000000000000
|
||||
37.821637 | -19 | 0.000000000000000000000000000001054226381944797 | 0.000000000000000000000000000001054226381944797 | 0.000000000000000000000000000000000000000000000
|
||||
37.821637 | -18 | 0.00000000000000000000000000003987256753373947 | 0.00000000000000000000000000003987256753373947 | 0.00000000000000000000000000000000000000000000
|
||||
37.821637 | -17 | 0.000000000000000000000000001508045775519079 | 0.000000000000000000000000001508045775519079 | 0.000000000000000000000000000000000000000000
|
||||
37.821637 | -16 | 0.00000000000000000000000005703675990106610 | 0.00000000000000000000000005703675990106610 | 0.00000000000000000000000000000000000000000
|
||||
37.821637 | -15 | 0.000000000000000000000002157223628634278 | 0.000000000000000000000002157223628634278 | 0.000000000000000000000000000000000000000
|
||||
37.821637 | -14 | 0.00000000000000000000008158972901002847 | 0.00000000000000000000008158972901002847 | 0.00000000000000000000000000000000000000
|
||||
37.821637 | -13 | 0.000000000000000000003085857113545666 | 0.000000000000000000003085857113545666 | 0.000000000000000000000000000000000000
|
||||
37.821637 | -12 | 0.0000000000000000001167121675823920 | 0.0000000000000000001167121675823920 | 0.0000000000000000000000000000000000
|
||||
37.821637 | -11 | 0.000000000000000004414245235784397 | 0.000000000000000004414245235784397 | 0.000000000000000000000000000000000
|
||||
37.821637 | -10 | 0.0000000000000001669539809368169 | 0.0000000000000001669539809368169 | 0.0000000000000000000000000000000
|
||||
37.821637 | -9 | 0.000000000000006314472862697207 | 0.000000000000006314472862697207 | 0.000000000000000000000000000000
|
||||
37.821637 | -8 | 0.0000000000002388237004592846 | 0.0000000000002388237004592846 | 0.0000000000000000000000000000
|
||||
37.821637 | -7 | 0.000000000009032703305767796 | 0.000000000009032703305767796 | 0.000000000000000000000000000
|
||||
37.821637 | -6 | 0.0000000003416316255594496 | 0.0000000003416316255594496 | 0.0000000000000000000000000
|
||||
37.821637 | -5 | 0.00000001292106732962942 | 0.00000001292106732962942 | 0.00000000000000000000000
|
||||
37.821637 | -4 | 0.0000004886959181938034 | 0.0000004886959181938034 | 0.0000000000000000000000
|
||||
37.821637 | -3 | 0.00001848327962130773 | 0.00001848327962130773 | 0.00000000000000000000
|
||||
37.821637 | -2 | 0.0006990678924065984 | 0.0006990678924065984 | 0.0000000000000000000
|
||||
37.821637 | -1 | 0.02643989206495742 | 0.02643989206495742 | 0.00000000000000000
|
||||
37.821637 | 0 | 1 | 1.0000000000000000 | 0.0000000000000000
|
||||
37.821637 | 1 | 37.821637 | 37.821637000000000 | 0.000000000000000
|
||||
37.821637 | 2 | 1430.476225359769 | 1430.4762253597690 | 0.0000000000000
|
||||
37.821637 | 3 | 54102.952532687378 | 54102.952532687378 | 0.000000000000
|
||||
37.821637 | 4 | 2046262.2313195326 | 2046262.2313195326 | 0.0000000000
|
||||
37.821637 | 5 | 77392987.319777394 | 77392987.319777394 | 0.000000000
|
||||
37.821637 | 6 | 2927129472.7542235 | 2927129472.7542235 | 0.0000000
|
||||
37.821637 | 7 | 110708828370.511632 | 110708828370.511632 | 0.000000
|
||||
37.821637 | 8 | 4187189119324.792454 | 4187189119324.792454 | 0.000000
|
||||
37.821637 | 9 | 158366346921451.985294 | 158366346921451.985294 | 0.000000
|
||||
37.821637 | 10 | 5989674486279224.500736 | 5989674486279224.500736 | 0.000000
|
||||
37.821637 | 11 | 226539294168214309.708325 | 226539294168214309.708325 | 0.000000
|
||||
37.821637 | 12 | 8568086950266418559.993831 | 8568086950266418559.993831 | 0.000000
|
||||
37.821637 | 13 | 324059074417413536066.149409 | 324059074417413536066.149409 | 0.000000
|
||||
37.821637 | 14 | 12256444679171401239980.310926 | 12256444679171401239980.310926 | 0.000000
|
||||
37.821637 | 15 | 463558801566202198479885.206986 | 463558801566202198479885.206986 | 0.000000
|
||||
37.821637 | 16 | 17532552720991931019508170.100286 | 17532552720991931019508170.100286 | 0.000000
|
||||
37.821637 | 17 | 663109844696719094948877928.067252 | 663109844696719094948877928.067252 | 0.000000
|
||||
37.821637 | 18 | 25079899837245684700124994552.671731 | 25079899837245684700124994552.671731 | 0.000000
|
||||
37.821637 | 19 | 948562867640665366544581398598.127577 | 948562867640665366544581398598.127577 | 0.000000
|
||||
37.821637 | 20 | 35876200451584291931921101974730.690104 | 35876200451584291931921101974730.690104 | 0.000000
|
||||
(41 rows)
|
||||
|
||||
--
|
||||
|
|
|
|||
|
|
@ -1142,8 +1142,8 @@ select 10.0 ^ 2147483647 as overflows;
|
|||
select 117743296169.0 ^ 1000000000 as overflows;
|
||||
|
||||
-- cases that used to return inaccurate results
|
||||
select 3.789 ^ 21;
|
||||
select 3.789 ^ 35;
|
||||
select 3.789 ^ 21.0000000000000000;
|
||||
select 3.789 ^ 35.0000000000000000;
|
||||
select 1.2 ^ 345;
|
||||
select 0.12 ^ (-20);
|
||||
select 1.000000000123 ^ (-2147483648);
|
||||
|
|
@ -1162,6 +1162,10 @@ select (-1.0) ^ 2147483648;
|
|||
select (-1.0) ^ 1000000000000000;
|
||||
select (-1.0) ^ 1000000000000001;
|
||||
|
||||
-- integer powers of 10
|
||||
select n, 10.0 ^ n as "10^n", (10.0 ^ n) * (10.0 ^ (-n)) = 1 as ok
|
||||
from generate_series(-20, 20) n;
|
||||
|
||||
--
|
||||
-- Tests for raising to non-integer powers
|
||||
--
|
||||
|
|
|
|||
|
|
@ -664,47 +664,47 @@ SELECT t1.id1, t1.result, t2.expected
|
|||
-- done
|
||||
|
||||
WITH t(b, p, bc_result) AS (VALUES
|
||||
(0.084738, -20, 2744326694304960114888.7859130502035257),
|
||||
(0.084738, -19, 232548755422013710215.4459407000481464),
|
||||
(0.084738, -18, 19705716436950597776.2364581230406798),
|
||||
(0.084738, -17, 1669822999434319754.3627249884302211),
|
||||
(0.084738, -16, 141497461326065387.3451885900696001),
|
||||
(0.084738, -15, 11990211877848128.7928565907453178),
|
||||
(0.084738, -14, 1016026574105094.7376490817865767),
|
||||
(0.084738, -13, 86096059836517.5178789078924309),
|
||||
(0.084738, -12, 7295607918426.8214300228969888),
|
||||
(0.084738, -11, 618215223791.6519943372802450),
|
||||
(0.084738, -10, 52386321633.6570066961524534),
|
||||
(0.084738, -9, 4439112122.5928274334185666),
|
||||
(0.084738, -8, 376161483.0442710110530225),
|
||||
(0.084738, -7, 31875171.7502054369346110),
|
||||
(0.084738, -6, 2701038.3037689083149651),
|
||||
(0.084738, -5, 228880.5837847697527935),
|
||||
(0.084738, -4, 19394.8829087538193122),
|
||||
(0.084738, -3, 1643.4835879219811409),
|
||||
(0.084738, -2, 139.2655122733328379),
|
||||
(0.084738, -1, 11.8010809790176780),
|
||||
(0.084738, -20, 2744326694304960114888.785913),
|
||||
(0.084738, -19, 232548755422013710215.445941),
|
||||
(0.084738, -18, 19705716436950597776.236458),
|
||||
(0.084738, -17, 1669822999434319754.362725),
|
||||
(0.084738, -16, 141497461326065387.345189),
|
||||
(0.084738, -15, 11990211877848128.792857),
|
||||
(0.084738, -14, 1016026574105094.737649),
|
||||
(0.084738, -13, 86096059836517.517879),
|
||||
(0.084738, -12, 7295607918426.821430),
|
||||
(0.084738, -11, 618215223791.651994),
|
||||
(0.084738, -10, 52386321633.657007),
|
||||
(0.084738, -9, 4439112122.5928274),
|
||||
(0.084738, -8, 376161483.04427101),
|
||||
(0.084738, -7, 31875171.750205437),
|
||||
(0.084738, -6, 2701038.3037689083),
|
||||
(0.084738, -5, 228880.58378476975),
|
||||
(0.084738, -4, 19394.882908753819),
|
||||
(0.084738, -3, 1643.4835879219811),
|
||||
(0.084738, -2, 139.26551227333284),
|
||||
(0.084738, -1, 11.801080979017678),
|
||||
(0.084738, 0, 1),
|
||||
(0.084738, 1, .084738),
|
||||
(0.084738, 2, .007180528644),
|
||||
(0.084738, 3, .0006084636362353),
|
||||
(0.084738, 4, .0000515599916073),
|
||||
(0.084738, 5, .0000043690905688),
|
||||
(0.084738, 6, .0000003702279966),
|
||||
(0.084738, 7, .0000000313723800),
|
||||
(0.084738, 8, .0000000026584327),
|
||||
(0.084738, 9, .0000000002252703),
|
||||
(0.084738, 10, .0000000000190890),
|
||||
(0.084738, 11, .0000000000016176),
|
||||
(0.084738, 12, .0000000000001371),
|
||||
(0.084738, 13, .0000000000000116),
|
||||
(0.084738, 14, .0000000000000010),
|
||||
(0.084738, 15, .0000000000000001),
|
||||
(0.084738, 16, .0000000000000000),
|
||||
(0.084738, 17, .0000000000000000),
|
||||
(0.084738, 18, .0000000000000000),
|
||||
(0.084738, 19, .0000000000000000),
|
||||
(0.084738, 20, .0000000000000000))
|
||||
(0.084738, 3, .000608463636235272),
|
||||
(0.084738, 4, .00005155999160730448),
|
||||
(0.084738, 5, .000004369090568819767),
|
||||
(0.084738, 6, .0000003702279966206494),
|
||||
(0.084738, 7, .00000003137237997764059),
|
||||
(0.084738, 8, .000000002658432734545308),
|
||||
(0.084738, 9, .0000000002252702730599003),
|
||||
(0.084738, 10, .00000000001908895239854983),
|
||||
(0.084738, 11, .000000000001617559648348316),
|
||||
(0.084738, 12, .0000000000001370687694817396),
|
||||
(0.084738, 13, .00000000000001161493338834365),
|
||||
(0.084738, 14, .0000000000000009842262254614642),
|
||||
(0.084738, 15, .00000000000000008340136189315355),
|
||||
(0.084738, 16, .000000000000000007067264604102046),
|
||||
(0.084738, 17, .0000000000000000005988658680223991),
|
||||
(0.084738, 18, .00000000000000000005074669592448206),
|
||||
(0.084738, 19, .000000000000000000004300173519248761),
|
||||
(0.084738, 20, .0000000000000000000003643881036741015))
|
||||
SELECT b, p, bc_result, b^p AS power, b^p - bc_result AS diff FROM t;
|
||||
|
||||
-- base greater than 1
|
||||
|
|
@ -720,47 +720,47 @@ SELECT b, p, bc_result, b^p AS power, b^p - bc_result AS diff FROM t;
|
|||
-- done
|
||||
|
||||
WITH t(b, p, bc_result) AS (VALUES
|
||||
(37.821637, -20, .0000000000000000),
|
||||
(37.821637, -19, .0000000000000000),
|
||||
(37.821637, -18, .0000000000000000),
|
||||
(37.821637, -17, .0000000000000000),
|
||||
(37.821637, -16, .0000000000000000),
|
||||
(37.821637, -15, .0000000000000000),
|
||||
(37.821637, -14, .0000000000000000),
|
||||
(37.821637, -13, .0000000000000000),
|
||||
(37.821637, -12, .0000000000000000),
|
||||
(37.821637, -11, .0000000000000000),
|
||||
(37.821637, -10, .0000000000000002),
|
||||
(37.821637, -9, .0000000000000063),
|
||||
(37.821637, -8, .0000000000002388),
|
||||
(37.821637, -7, .0000000000090327),
|
||||
(37.821637, -6, .0000000003416316),
|
||||
(37.821637, -5, .0000000129210673),
|
||||
(37.821637, -4, .0000004886959182),
|
||||
(37.821637, -3, .0000184832796213),
|
||||
(37.821637, -2, .0006990678924066),
|
||||
(37.821637, -1, .0264398920649574),
|
||||
(37.821637, -20, .00000000000000000000000000000002787363175065101),
|
||||
(37.821637, -19, .000000000000000000000000000001054226381944797),
|
||||
(37.821637, -18, .00000000000000000000000000003987256753373947),
|
||||
(37.821637, -17, .000000000000000000000000001508045775519079),
|
||||
(37.821637, -16, .00000000000000000000000005703675990106610),
|
||||
(37.821637, -15, .000000000000000000000002157223628634278),
|
||||
(37.821637, -14, .00000000000000000000008158972901002847),
|
||||
(37.821637, -13, .000000000000000000003085857113545666),
|
||||
(37.821637, -12, .0000000000000000001167121675823920),
|
||||
(37.821637, -11, .000000000000000004414245235784397),
|
||||
(37.821637, -10, .0000000000000001669539809368169),
|
||||
(37.821637, -9, .000000000000006314472862697207),
|
||||
(37.821637, -8, .0000000000002388237004592846),
|
||||
(37.821637, -7, .000000000009032703305767796),
|
||||
(37.821637, -6, .0000000003416316255594496),
|
||||
(37.821637, -5, .00000001292106732962942),
|
||||
(37.821637, -4, .0000004886959181938034),
|
||||
(37.821637, -3, .00001848327962130773),
|
||||
(37.821637, -2, .0006990678924065984),
|
||||
(37.821637, -1, .02643989206495742),
|
||||
(37.821637, 0, 1),
|
||||
(37.821637, 1, 37.821637),
|
||||
(37.821637, 2, 1430.476225359769),
|
||||
(37.821637, 3, 54102.9525326873775219),
|
||||
(37.821637, 4, 2046262.2313195326271135),
|
||||
(37.821637, 5, 77392987.3197773940323425),
|
||||
(37.821637, 6, 2927129472.7542235178972258),
|
||||
(37.821637, 7, 110708828370.5116321107718772),
|
||||
(37.821637, 8, 4187189119324.7924539711577286),
|
||||
(37.821637, 9, 158366346921451.9852944363360812),
|
||||
(37.821637, 10, 5989674486279224.5007355092228730),
|
||||
(37.821637, 11, 226539294168214309.7083246628376531),
|
||||
(37.821637, 12, 8568086950266418559.9938312759931069),
|
||||
(37.821637, 13, 324059074417413536066.1494087598581043),
|
||||
(37.821637, 14, 12256444679171401239980.3109258799733927),
|
||||
(37.821637, 15, 463558801566202198479885.2069857662592280),
|
||||
(37.821637, 16, 17532552720991931019508170.1002855156233684),
|
||||
(37.821637, 17, 663109844696719094948877928.0672523682648687),
|
||||
(37.821637, 18, 25079899837245684700124994552.6717306599041850),
|
||||
(37.821637, 19, 948562867640665366544581398598.1275771806665398),
|
||||
(37.821637, 20, 35876200451584291931921101974730.6901038166532866))
|
||||
(37.821637, 3, 54102.952532687378),
|
||||
(37.821637, 4, 2046262.2313195326),
|
||||
(37.821637, 5, 77392987.319777394),
|
||||
(37.821637, 6, 2927129472.7542235),
|
||||
(37.821637, 7, 110708828370.511632),
|
||||
(37.821637, 8, 4187189119324.792454),
|
||||
(37.821637, 9, 158366346921451.985294),
|
||||
(37.821637, 10, 5989674486279224.500736),
|
||||
(37.821637, 11, 226539294168214309.708325),
|
||||
(37.821637, 12, 8568086950266418559.993831),
|
||||
(37.821637, 13, 324059074417413536066.149409),
|
||||
(37.821637, 14, 12256444679171401239980.310926),
|
||||
(37.821637, 15, 463558801566202198479885.206986),
|
||||
(37.821637, 16, 17532552720991931019508170.100286),
|
||||
(37.821637, 17, 663109844696719094948877928.067252),
|
||||
(37.821637, 18, 25079899837245684700124994552.671731),
|
||||
(37.821637, 19, 948562867640665366544581398598.127577),
|
||||
(37.821637, 20, 35876200451584291931921101974730.690104))
|
||||
SELECT b, p, bc_result, b^p AS power, b^p - bc_result AS diff FROM t;
|
||||
|
||||
--
|
||||
|
|
|
|||
Loading…
Reference in New Issue