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Re-implement division for numeric values using the traditional "schoolbook"
algorithm. This is a good deal slower than our old roundoff-error-prone code for long inputs, so we keep the old code for use in the transcendental functions, where everything is approximate anyway. Also create a user-accessible function div(numeric, numeric) to provide access to the exact result of trunc(x/y) --- since the regular numeric / operator will round off its result, simply computing that expression in SQL doesn't reliably give the desired answer. This fixes bug #3387 and various related corner cases, and improves the usefulness of PG for high-precision integer arithmetic.
This commit is contained in:
Tom Lane
parent
b6f0ad4b0e
commit
a0fad9762a
@ -1,4 +1,4 @@
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<!-- $PostgreSQL: pgsql/doc/src/sgml/func.sgml,v 1.426 2008/04/04 16:57:21 momjian Exp $ -->
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<!-- $PostgreSQL: pgsql/doc/src/sgml/func.sgml,v 1.427 2008/04/04 18:45:36 tgl Exp $ -->
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<chapter id="functions">
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<title>Functions and Operators</title>
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@ -617,6 +617,9 @@
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<indexterm>
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<primary>degrees</primary>
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</indexterm>
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<indexterm>
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<primary>div</primary>
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</indexterm>
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<indexterm>
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<primary>exp</primary>
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</indexterm>
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@ -717,6 +720,15 @@
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<entry><literal>28.6478897565412</literal></entry>
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</row>
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<row>
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<entry><literal><function>div</function>(<parameter>y</parameter> <type>numeric</>,
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<parameter>x</parameter> <type>numeric</>)</literal></entry>
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<entry><type>numeric</></entry>
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<entry>integer quotient of <parameter>y</parameter>/<parameter>x</parameter></entry>
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<entry><literal>div(9,4)</literal></entry>
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<entry><literal>2</literal></entry>
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</row>
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<row>
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<entry><literal><function>exp</function>(<type>dp</type> or <type>numeric</type>)</literal></entry>
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<entry>(same as input)</entry>
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@ -14,7 +14,7 @@
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* Copyright (c) 1998-2008, PostgreSQL Global Development Group
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*
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* IDENTIFICATION
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* $PostgreSQL: pgsql/src/backend/utils/adt/numeric.c,v 1.108 2008/01/01 19:45:52 momjian Exp $
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* $PostgreSQL: pgsql/src/backend/utils/adt/numeric.c,v 1.109 2008/04/04 18:45:36 tgl Exp $
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*
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*-------------------------------------------------------------------------
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*/
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@ -53,7 +53,7 @@
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* NBASE that's less than sqrt(INT_MAX), in practice we are only interested
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* in NBASE a power of ten, so that I/O conversions and decimal rounding
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* are easy. Also, it's actually more efficient if NBASE is rather less than
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* sqrt(INT_MAX), so that there is "headroom" for mul_var and div_var to
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* sqrt(INT_MAX), so that there is "headroom" for mul_var and div_var_fast to
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* postpone processing carries.
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* ----------
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*/
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@ -90,6 +90,10 @@ typedef int16 NumericDigit;
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/* ----------
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* NumericVar is the format we use for arithmetic. The digit-array part
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* is the same as the NumericData storage format, but the header is more
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* complex.
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*
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* The value represented by a NumericVar is determined by the sign, weight,
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* ndigits, and digits[] array.
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* Note: the first digit of a NumericVar's value is assumed to be multiplied
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@ -100,7 +104,7 @@ typedef int16 NumericDigit;
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* NumericVar. digits points at the first digit in actual use (the one
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* with the specified weight). We normally leave an unused digit or two
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* (preset to zeroes) between buf and digits, so that there is room to store
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* a carry out of the top digit without special pushups. We just need to
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* a carry out of the top digit without reallocating space. We just need to
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* decrement digits (and increment weight) to make room for the carry digit.
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* (There is no such extra space in a numeric value stored in the database,
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* only in a NumericVar in memory.)
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@ -265,6 +269,8 @@ static void mul_var(NumericVar *var1, NumericVar *var2, NumericVar *result,
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int rscale);
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static void div_var(NumericVar *var1, NumericVar *var2, NumericVar *result,
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int rscale, bool round);
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static void div_var_fast(NumericVar *var1, NumericVar *var2, NumericVar *result,
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int rscale, bool round);
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static int select_div_scale(NumericVar *var1, NumericVar *var2);
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static void mod_var(NumericVar *var1, NumericVar *var2, NumericVar *result);
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static void ceil_var(NumericVar *var, NumericVar *result);
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@ -1419,6 +1425,52 @@ numeric_div(PG_FUNCTION_ARGS)
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}
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/*
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* numeric_div_trunc() -
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*
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* Divide one numeric into another, truncating the result to an integer
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*/
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Datum
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numeric_div_trunc(PG_FUNCTION_ARGS)
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{
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Numeric num1 = PG_GETARG_NUMERIC(0);
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Numeric num2 = PG_GETARG_NUMERIC(1);
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NumericVar arg1;
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NumericVar arg2;
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NumericVar result;
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Numeric res;
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/*
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* Handle NaN
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*/
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if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2))
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PG_RETURN_NUMERIC(make_result(&const_nan));
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/*
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* Unpack the arguments
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*/
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init_var(&arg1);
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init_var(&arg2);
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init_var(&result);
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set_var_from_num(num1, &arg1);
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set_var_from_num(num2, &arg2);
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/*
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* Do the divide and return the result
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*/
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div_var(&arg1, &arg2, &result, 0, false);
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res = make_result(&result);
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free_var(&arg1);
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free_var(&arg2);
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free_var(&result);
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PG_RETURN_NUMERIC(res);
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}
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/*
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* numeric_mod() -
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*
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@ -4036,12 +4088,291 @@ mul_var(NumericVar *var1, NumericVar *var2, NumericVar *result,
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/*
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* div_var() -
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*
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* Division on variable level. Quotient of var1 / var2 is stored
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* in result. Result is rounded to no more than rscale fractional digits.
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* Division on variable level. Quotient of var1 / var2 is stored in result.
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* The quotient is figured to exactly rscale fractional digits.
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* If round is true, it is rounded at the rscale'th digit; if false, it
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* is truncated (towards zero) at that digit.
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*/
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static void
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div_var(NumericVar *var1, NumericVar *var2, NumericVar *result,
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int rscale, bool round)
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{
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int div_ndigits;
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int res_ndigits;
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int res_sign;
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int res_weight;
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int carry;
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int borrow;
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int divisor1;
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int divisor2;
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NumericDigit *dividend;
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NumericDigit *divisor;
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NumericDigit *res_digits;
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int i;
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int j;
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/* copy these values into local vars for speed in inner loop */
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int var1ndigits = var1->ndigits;
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int var2ndigits = var2->ndigits;
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/*
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* First of all division by zero check; we must not be handed an
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* unnormalized divisor.
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*/
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if (var2ndigits == 0 || var2->digits[0] == 0)
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ereport(ERROR,
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(errcode(ERRCODE_DIVISION_BY_ZERO),
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errmsg("division by zero")));
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/*
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* Now result zero check
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*/
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if (var1ndigits == 0)
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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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* Determine the result sign, weight and number of digits to calculate.
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* The weight figured here is correct if the emitted quotient has no
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* leading zero digits; otherwise strip_var() will fix things up.
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*/
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if (var1->sign == var2->sign)
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res_sign = NUMERIC_POS;
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else
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res_sign = NUMERIC_NEG;
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res_weight = var1->weight - var2->weight;
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/* The number of accurate result digits we need to produce: */
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res_ndigits = res_weight + 1 + (rscale + DEC_DIGITS - 1) / DEC_DIGITS;
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/* ... but always at least 1 */
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res_ndigits = Max(res_ndigits, 1);
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/* If rounding needed, figure one more digit to ensure correct result */
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if (round)
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res_ndigits++;
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/*
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* The working dividend normally requires res_ndigits + var2ndigits
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* digits, but make it at least var1ndigits so we can load all of var1
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* into it. (There will be an additional digit dividend[0] in the
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* dividend space, but for consistency with Knuth's notation we don't
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* count that in div_ndigits.)
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*/
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div_ndigits = res_ndigits + var2ndigits;
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div_ndigits = Max(div_ndigits, var1ndigits);
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/*
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* We need a workspace with room for the working dividend (div_ndigits+1
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* digits) plus room for the possibly-normalized divisor (var2ndigits
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* digits). It is convenient also to have a zero at divisor[0] with
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* the actual divisor data in divisor[1 .. var2ndigits]. Transferring the
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* digits into the workspace also allows us to realloc the result (which
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* might be the same as either input var) before we begin the main loop.
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* Note that we use palloc0 to ensure that divisor[0], dividend[0], and
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* any additional dividend positions beyond var1ndigits, start out 0.
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*/
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dividend = (NumericDigit *)
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palloc0((div_ndigits + var2ndigits + 2) * sizeof(NumericDigit));
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divisor = dividend + (div_ndigits + 1);
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memcpy(dividend + 1, var1->digits, var1ndigits * sizeof(NumericDigit));
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memcpy(divisor + 1, var2->digits, var2ndigits * sizeof(NumericDigit));
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/*
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* Now we can realloc the result to hold the generated quotient digits.
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*/
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alloc_var(result, res_ndigits);
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res_digits = result->digits;
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if (var2ndigits == 1)
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{
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/*
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* If there's only a single divisor digit, we can use a fast path
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* (cf. Knuth section 4.3.1 exercise 16).
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*/
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divisor1 = divisor[1];
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carry = 0;
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for (i = 0; i < res_ndigits; i++)
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{
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carry = carry * NBASE + dividend[i + 1];
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res_digits[i] = carry / divisor1;
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carry = carry % divisor1;
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}
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}
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else
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{
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/*
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* The full multiple-place algorithm is taken from Knuth volume 2,
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* Algorithm 4.3.1D.
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*
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* We need the first divisor digit to be >= NBASE/2. If it isn't,
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* make it so by scaling up both the divisor and dividend by the
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* factor "d". (The reason for allocating dividend[0] above is to
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* leave room for possible carry here.)
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*/
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if (divisor[1] < HALF_NBASE)
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{
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int d = NBASE / (divisor[1] + 1);
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carry = 0;
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for (i = var2ndigits; i > 0; i--)
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{
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carry += divisor[i] * d;
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divisor[i] = carry % NBASE;
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carry = carry / NBASE;
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}
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Assert(carry == 0);
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carry = 0;
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/* at this point only var1ndigits of dividend can be nonzero */
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for (i = var1ndigits; i >= 0; i--)
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{
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carry += dividend[i] * d;
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dividend[i] = carry % NBASE;
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carry = carry / NBASE;
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}
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Assert(carry == 0);
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Assert(divisor[1] >= HALF_NBASE);
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}
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/* First 2 divisor digits are used repeatedly in main loop */
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divisor1 = divisor[1];
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divisor2 = divisor[2];
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/*
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* Begin the main loop. Each iteration of this loop produces the
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* j'th quotient digit by dividing dividend[j .. j + var2ndigits]
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* by the divisor; this is essentially the same as the common manual
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* procedure for long division.
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*/
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for (j = 0; j < res_ndigits; j++)
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{
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/* Estimate quotient digit from the first two dividend digits */
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int next2digits = dividend[j] * NBASE + dividend[j+1];
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int qhat;
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/*
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* If next2digits are 0, then quotient digit must be 0 and there's
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* no need to adjust the working dividend. It's worth testing
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* here to fall out ASAP when processing trailing zeroes in
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* a dividend.
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*/
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if (next2digits == 0)
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{
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res_digits[j] = 0;
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continue;
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}
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if (dividend[j] == divisor1)
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qhat = NBASE - 1;
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else
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qhat = next2digits / divisor1;
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/*
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* Adjust quotient digit if it's too large. Knuth proves that
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* after this step, the quotient digit will be either correct
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* or just one too large. (Note: it's OK to use dividend[j+2]
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* here because we know the divisor length is at least 2.)
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*/
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while (divisor2 * qhat >
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(next2digits - qhat * divisor1) * NBASE + dividend[j+2])
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qhat--;
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/* As above, need do nothing more when quotient digit is 0 */
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if (qhat > 0)
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{
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/*
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* Multiply the divisor by qhat, and subtract that from the
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* working dividend. "carry" tracks the multiplication,
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* "borrow" the subtraction (could we fold these together?)
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*/
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carry = 0;
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borrow = 0;
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for (i = var2ndigits; i >= 0; i--)
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{
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carry += divisor[i] * qhat;
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borrow -= carry % NBASE;
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carry = carry / NBASE;
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borrow += dividend[j + i];
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if (borrow < 0)
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{
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dividend[j + i] = borrow + NBASE;
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borrow = -1;
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}
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else
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{
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dividend[j + i] = borrow;
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borrow = 0;
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}
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}
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Assert(carry == 0);
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/*
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* If we got a borrow out of the top dividend digit, then
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* indeed qhat was one too large. Fix it, and add back the
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* divisor to correct the working dividend. (Knuth proves
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* that this will occur only about 3/NBASE of the time; hence,
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* it's a good idea to test this code with small NBASE to be
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* sure this section gets exercised.)
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*/
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if (borrow)
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{
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qhat--;
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carry = 0;
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for (i = var2ndigits; i >= 0; i--)
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{
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carry += dividend[j + i] + divisor[i];
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if (carry >= NBASE)
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{
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dividend[j + i] = carry - NBASE;
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carry = 1;
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}
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else
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{
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dividend[j + i] = carry;
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carry = 0;
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}
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}
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/* A carry should occur here to cancel the borrow above */
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Assert(carry == 1);
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}
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}
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/* And we're done with this quotient digit */
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res_digits[j] = qhat;
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}
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}
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pfree(dividend);
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/*
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* Finally, round or truncate the result to the requested precision.
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*/
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result->weight = res_weight;
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result->sign = res_sign;
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/* Round or truncate to target rscale (and set result->dscale) */
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if (round)
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round_var(result, rscale);
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else
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trunc_var(result, rscale);
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/* Strip leading and trailing zeroes */
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strip_var(result);
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}
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/*
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* div_var_fast() -
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*
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* This has the same API as div_var, but is implemented using the division
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* algorithm from the "FM" library, rather than Knuth's schoolbook-division
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* approach. This is significantly faster but can produce inaccurate
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* results, because it sometimes has to propagate rounding to the left,
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* and so we can never be entirely sure that we know the requested digits
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* exactly. We compute DIV_GUARD_DIGITS extra digits, but there is
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* no certainty that that's enough. We use this only in the transcendental
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* function calculation routines, where everything is approximate anyway.
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*/
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static void
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div_var_fast(NumericVar *var1, NumericVar *var2, NumericVar *result,
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int rscale, bool round)
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{
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int div_ndigits;
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int res_sign;
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@ -4367,30 +4698,21 @@ static void
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mod_var(NumericVar *var1, NumericVar *var2, NumericVar *result)
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{
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NumericVar tmp;
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int rscale;
|
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init_var(&tmp);
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/* ---------
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* We do this using the equation
|
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* mod(x,y) = x - trunc(x/y)*y
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* We set rscale the same way numeric_div and numeric_mul do
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* to get the right answer from the equation. The final result,
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* however, need not be displayed to more precision than the inputs.
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||||
* div_var can be persuaded to give us trunc(x/y) directly.
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* ----------
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*/
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rscale = select_div_scale(var1, var2);
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div_var(var1, var2, &tmp, 0, false);
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div_var(var1, var2, &tmp, rscale, false);
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trunc_var(&tmp, 0);
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mul_var(var2, &tmp, &tmp, var2->dscale + tmp.dscale);
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mul_var(var2, &tmp, &tmp, var2->dscale);
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sub_var(var1, &tmp, result);
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|
||||
round_var(result, Max(var1->dscale, var2->dscale));
|
||||
|
||||
free_var(&tmp);
|
||||
}
|
||||
|
||||
@ -4497,7 +4819,7 @@ sqrt_var(NumericVar *arg, NumericVar *result, int rscale)
|
||||
|
||||
for (;;)
|
||||
{
|
||||
div_var(&tmp_arg, result, &tmp_val, local_rscale, true);
|
||||
div_var_fast(&tmp_arg, result, &tmp_val, local_rscale, true);
|
||||
|
||||
add_var(result, &tmp_val, result);
|
||||
mul_var(result, &const_zero_point_five, result, local_rscale);
|
||||
@ -4587,7 +4909,7 @@ exp_var(NumericVar *arg, NumericVar *result, int rscale)
|
||||
|
||||
/* Compensate for input sign, and round to requested rscale */
|
||||
if (xneg)
|
||||
div_var(&const_one, result, result, rscale, true);
|
||||
div_var_fast(&const_one, result, result, rscale, true);
|
||||
else
|
||||
round_var(result, rscale);
|
||||
|
||||
@ -4652,7 +4974,7 @@ exp_var_internal(NumericVar *arg, NumericVar *result, int rscale)
|
||||
add_var(&ni, &const_one, &ni);
|
||||
mul_var(&xpow, &x, &xpow, local_rscale);
|
||||
mul_var(&ifac, &ni, &ifac, 0);
|
||||
div_var(&xpow, &ifac, &elem, local_rscale, true);
|
||||
div_var_fast(&xpow, &ifac, &elem, local_rscale, true);
|
||||
|
||||
if (elem.ndigits == 0)
|
||||
break;
|
||||
@ -4736,7 +5058,7 @@ ln_var(NumericVar *arg, NumericVar *result, int rscale)
|
||||
*/
|
||||
sub_var(&x, &const_one, result);
|
||||
add_var(&x, &const_one, &elem);
|
||||
div_var(result, &elem, result, local_rscale, true);
|
||||
div_var_fast(result, &elem, result, local_rscale, true);
|
||||
set_var_from_var(result, &xx);
|
||||
mul_var(result, result, &x, local_rscale);
|
||||
|
||||
@ -4746,7 +5068,7 @@ ln_var(NumericVar *arg, NumericVar *result, int rscale)
|
||||
{
|
||||
add_var(&ni, &const_two, &ni);
|
||||
mul_var(&xx, &x, &xx, local_rscale);
|
||||
div_var(&xx, &ni, &elem, local_rscale, true);
|
||||
div_var_fast(&xx, &ni, &elem, local_rscale, true);
|
||||
|
||||
if (elem.ndigits == 0)
|
||||
break;
|
||||
@ -4816,7 +5138,7 @@ log_var(NumericVar *base, NumericVar *num, NumericVar *result)
|
||||
/* Select scale for division result */
|
||||
rscale = select_div_scale(&ln_num, &ln_base);
|
||||
|
||||
div_var(&ln_num, &ln_base, result, rscale, true);
|
||||
div_var_fast(&ln_num, &ln_base, result, rscale, true);
|
||||
|
||||
free_var(&ln_num);
|
||||
free_var(&ln_base);
|
||||
@ -4990,7 +5312,7 @@ power_var_int(NumericVar *base, int exp, NumericVar *result, int rscale)
|
||||
|
||||
/* Compensate for input sign, and round to requested rscale */
|
||||
if (neg)
|
||||
div_var(&const_one, result, result, rscale, true);
|
||||
div_var_fast(&const_one, result, result, rscale, true);
|
||||
else
|
||||
round_var(result, rscale);
|
||||
}
|
||||
@ -5361,8 +5683,8 @@ round_var(NumericVar *var, int rscale)
|
||||
/*
|
||||
* trunc_var
|
||||
*
|
||||
* Truncate the value of a variable at rscale decimal digits after the
|
||||
* decimal point. NOTE: we allow rscale < 0 here, implying
|
||||
* Truncate (towards zero) the value of a variable at rscale decimal digits
|
||||
* after the decimal point. NOTE: we allow rscale < 0 here, implying
|
||||
* truncation before the decimal point.
|
||||
*/
|
||||
static void
|
||||
|
||||
@ -37,7 +37,7 @@
|
||||
* Portions Copyright (c) 1996-2008, PostgreSQL Global Development Group
|
||||
* Portions Copyright (c) 1994, Regents of the University of California
|
||||
*
|
||||
* $PostgreSQL: pgsql/src/include/catalog/catversion.h,v 1.444 2008/03/23 00:24:19 tgl Exp $
|
||||
* $PostgreSQL: pgsql/src/include/catalog/catversion.h,v 1.445 2008/04/04 18:45:36 tgl Exp $
|
||||
*
|
||||
*-------------------------------------------------------------------------
|
||||
*/
|
||||
@ -53,6 +53,6 @@
|
||||
*/
|
||||
|
||||
/* yyyymmddN */
|
||||
#define CATALOG_VERSION_NO 200803222
|
||||
#define CATALOG_VERSION_NO 200804041
|
||||
|
||||
#endif
|
||||
|
||||
@ -7,7 +7,7 @@
|
||||
* Portions Copyright (c) 1996-2008, PostgreSQL Global Development Group
|
||||
* Portions Copyright (c) 1994, Regents of the University of California
|
||||
*
|
||||
* $PostgreSQL: pgsql/src/include/catalog/pg_proc.h,v 1.486 2008/04/04 16:57:21 momjian Exp $
|
||||
* $PostgreSQL: pgsql/src/include/catalog/pg_proc.h,v 1.487 2008/04/04 18:45:36 tgl Exp $
|
||||
*
|
||||
* NOTES
|
||||
* The script catalog/genbki.sh reads this file and generates .bki
|
||||
@ -1115,7 +1115,7 @@ DESCR("does not match LIKE expression");
|
||||
DATA(insert OID = 860 ( bpchar PGNSP PGUID 12 1 0 f f t f i 1 1042 "18" _null_ _null_ _null_ char_bpchar - _null_ _null_ ));
|
||||
DESCR("convert char to char()");
|
||||
|
||||
DATA(insert OID = 861 ( current_database PGNSP PGUID 12 1 0 f f t f i 0 19 "" _null_ _null_ _null_ current_database - _null_ _null_ ));
|
||||
DATA(insert OID = 861 ( current_database PGNSP PGUID 12 1 0 f f t f s 0 19 "" _null_ _null_ _null_ current_database - _null_ _null_ ));
|
||||
DESCR("returns the current database");
|
||||
DATA(insert OID = 817 ( current_query PGNSP PGUID 12 1 0 f f f f v 0 25 "" _null_ _null_ _null_ current_query - _null_ _null_ ));
|
||||
DESCR("returns the currently executing query");
|
||||
@ -2573,6 +2573,10 @@ DATA(insert OID = 1745 ( float4 PGNSP PGUID 12 1 0 f f t f i 1 700 "1700" _n
|
||||
DESCR("(internal)");
|
||||
DATA(insert OID = 1746 ( float8 PGNSP PGUID 12 1 0 f f t f i 1 701 "1700" _null_ _null_ _null_ numeric_float8 - _null_ _null_ ));
|
||||
DESCR("(internal)");
|
||||
DATA(insert OID = 1973 ( div PGNSP PGUID 12 1 0 f f t f i 2 1700 "1700 1700" _null_ _null_ _null_ numeric_div_trunc - _null_ _null_ ));
|
||||
DESCR("trunc(x/y)");
|
||||
DATA(insert OID = 1980 ( numeric_div_trunc PGNSP PGUID 12 1 0 f f t f i 2 1700 "1700 1700" _null_ _null_ _null_ numeric_div_trunc - _null_ _null_ ));
|
||||
DESCR("trunc(x/y)");
|
||||
DATA(insert OID = 2170 ( width_bucket PGNSP PGUID 12 1 0 f f t f i 4 23 "1700 1700 1700 23" _null_ _null_ _null_ width_bucket_numeric - _null_ _null_ ));
|
||||
DESCR("bucket number of operand in equidepth histogram");
|
||||
|
||||
|
||||
@ -7,7 +7,7 @@
|
||||
* Portions Copyright (c) 1996-2008, PostgreSQL Global Development Group
|
||||
* Portions Copyright (c) 1994, Regents of the University of California
|
||||
*
|
||||
* $PostgreSQL: pgsql/src/include/utils/builtins.h,v 1.311 2008/04/04 16:57:21 momjian Exp $
|
||||
* $PostgreSQL: pgsql/src/include/utils/builtins.h,v 1.312 2008/04/04 18:45:36 tgl Exp $
|
||||
*
|
||||
*-------------------------------------------------------------------------
|
||||
*/
|
||||
@ -845,6 +845,7 @@ extern Datum numeric_add(PG_FUNCTION_ARGS);
|
||||
extern Datum numeric_sub(PG_FUNCTION_ARGS);
|
||||
extern Datum numeric_mul(PG_FUNCTION_ARGS);
|
||||
extern Datum numeric_div(PG_FUNCTION_ARGS);
|
||||
extern Datum numeric_div_trunc(PG_FUNCTION_ARGS);
|
||||
extern Datum numeric_mod(PG_FUNCTION_ARGS);
|
||||
extern Datum numeric_inc(PG_FUNCTION_ARGS);
|
||||
extern Datum numeric_smaller(PG_FUNCTION_ARGS);
|
||||
|
||||
@ -1260,3 +1260,84 @@ SELECT * FROM num_input_test;
|
||||
-555.50
|
||||
(5 rows)
|
||||
|
||||
--
|
||||
-- Test some corner cases for division
|
||||
--
|
||||
select 999999999999999999999::numeric/1000000000000000000000;
|
||||
?column?
|
||||
------------------------
|
||||
1.00000000000000000000
|
||||
(1 row)
|
||||
|
||||
select div(999999999999999999999::numeric,1000000000000000000000);
|
||||
div
|
||||
-----
|
||||
0
|
||||
(1 row)
|
||||
|
||||
select mod(999999999999999999999::numeric,1000000000000000000000);
|
||||
mod
|
||||
-----------------------
|
||||
999999999999999999999
|
||||
(1 row)
|
||||
|
||||
select div(-9999999999999999999999::numeric,1000000000000000000000);
|
||||
div
|
||||
-----
|
||||
-9
|
||||
(1 row)
|
||||
|
||||
select mod(-9999999999999999999999::numeric,1000000000000000000000);
|
||||
mod
|
||||
------------------------
|
||||
-999999999999999999999
|
||||
(1 row)
|
||||
|
||||
select div(-9999999999999999999999::numeric,1000000000000000000000)*1000000000000000000000 + mod(-9999999999999999999999::numeric,1000000000000000000000);
|
||||
?column?
|
||||
-------------------------
|
||||
-9999999999999999999999
|
||||
(1 row)
|
||||
|
||||
select mod (70.0,70) ;
|
||||
mod
|
||||
-----
|
||||
0.0
|
||||
(1 row)
|
||||
|
||||
select div (70.0,70) ;
|
||||
div
|
||||
-----
|
||||
1
|
||||
(1 row)
|
||||
|
||||
select 70.0 / 70 ;
|
||||
?column?
|
||||
------------------------
|
||||
1.00000000000000000000
|
||||
(1 row)
|
||||
|
||||
select 12345678901234567890 % 123;
|
||||
?column?
|
||||
----------
|
||||
78
|
||||
(1 row)
|
||||
|
||||
select 12345678901234567890 / 123;
|
||||
?column?
|
||||
--------------------
|
||||
100371373180768845
|
||||
(1 row)
|
||||
|
||||
select div(12345678901234567890, 123);
|
||||
div
|
||||
--------------------
|
||||
100371373180768844
|
||||
(1 row)
|
||||
|
||||
select div(12345678901234567890, 123) * 123 + 12345678901234567890 % 123;
|
||||
?column?
|
||||
----------------------
|
||||
12345678901234567890
|
||||
(1 row)
|
||||
|
||||
|
||||
@ -805,3 +805,21 @@ INSERT INTO num_input_test(n1) VALUES ('');
|
||||
INSERT INTO num_input_test(n1) VALUES (' N aN ');
|
||||
|
||||
SELECT * FROM num_input_test;
|
||||
|
||||
--
|
||||
-- Test some corner cases for division
|
||||
--
|
||||
|
||||
select 999999999999999999999::numeric/1000000000000000000000;
|
||||
select div(999999999999999999999::numeric,1000000000000000000000);
|
||||
select mod(999999999999999999999::numeric,1000000000000000000000);
|
||||
select div(-9999999999999999999999::numeric,1000000000000000000000);
|
||||
select mod(-9999999999999999999999::numeric,1000000000000000000000);
|
||||
select div(-9999999999999999999999::numeric,1000000000000000000000)*1000000000000000000000 + mod(-9999999999999999999999::numeric,1000000000000000000000);
|
||||
select mod (70.0,70) ;
|
||||
select div (70.0,70) ;
|
||||
select 70.0 / 70 ;
|
||||
select 12345678901234567890 % 123;
|
||||
select 12345678901234567890 / 123;
|
||||
select div(12345678901234567890, 123);
|
||||
select div(12345678901234567890, 123) * 123 + 12345678901234567890 % 123;
|
||||
|
||||
Loading…
Reference in New Issue
Block a user