forked from openGauss-Ecosystem/openGauss-server
!2307 提升numeric除法性能
Merge pull request !2307 from cc_db_dev/improve_div
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@ -236,6 +236,7 @@ static void sub_var(NumericVar* var1, NumericVar* var2, NumericVar* result);
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static void mul_var(NumericVar* var1, NumericVar* var2, NumericVar* result, int rscale);
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static void div_var(NumericVar* var1, NumericVar* var2, NumericVar* result, int rscale, bool round);
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static void div_var_fast(NumericVar* var1, NumericVar* var2, NumericVar* result, int rscale, bool round);
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static void div_var_int(const NumericVar *var, int ival, int ival_weight, NumericVar *result, 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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@ -5454,11 +5455,36 @@ static void div_var(NumericVar* var1, NumericVar* var2, NumericVar* result, int
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*/
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if (var2ndigits == 0 || var2->digits[0] == 0)
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ereport(ERROR, (errcode(ERRCODE_DIVISION_BY_ZERO), errmsg("division by zero")));
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/*
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* If the divisor has just one or two digits, delegate to div_var_int(),
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* which uses fast short division.
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*/
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if (var2ndigits <= 2)
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{
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int idivisor;
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int idivisor_weight;
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idivisor = var2->digits[0];
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idivisor_weight = var2->weight;
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if (var2ndigits == 2)
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{
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idivisor = idivisor * NBASE + var2->digits[1];
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idivisor_weight--;
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}
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if (var2->sign == NUMERIC_NEG)
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idivisor = -idivisor;
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div_var_int(var1, idivisor, idivisor_weight, result, rscale, round);
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return;
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}
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/*
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* Now result zero check
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* Otherwise, perform full long division.
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*/
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if (var1ndigits == 0) {
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/* Result zero check */
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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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@ -5515,141 +5541,130 @@ static void div_var(NumericVar* var1, NumericVar* var2, NumericVar* result, int
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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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* If there's only a single divisor digit, we can use a fast path (cf.
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* Knuth section 4.3.1 exercise 16).
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*/
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divisor1 = divisor[1];
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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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int d = NBASE / (divisor[1] + 1);
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carry = 0;
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for (i = 0; i < res_ndigits; i++) {
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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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for (i = var2ndigits; i > 0; i--) {
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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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} else {
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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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int d = NBASE / (divisor[1] + 1);
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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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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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carry = 0;
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for (i = var2ndigits; i > 0; i--) {
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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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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 j'th
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* quotient digit by dividing dividend[j .. j + var2ndigits] by the
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* 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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/* 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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* Begin the main loop. Each iteration of this loop produces the j'th
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* quotient digit by dividing dividend[j .. j + var2ndigits] by the
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* divisor; this is essentially the same as the common manual
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* procedure for long division.
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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 a
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* dividend.
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*/
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for (j = 0; j < res_ndigits; j++) {
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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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if (next2digits == 0) {
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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 or
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* just one too large. (Note: it's OK to use dividend[j+2] here
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* because we know the divisor length is at least 2.)
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*/
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while (divisor2 * qhat > (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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NumericDigit *dividend_j = ÷nd[j];
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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 a
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* dividend.
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*/
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if (next2digits == 0) {
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res_digits[j] = 0;
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continue;
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* Multiply the divisor by qhat, and subtract that from the
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* working dividend. The multiplication and subtraction are
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* folded together here, noting that qhat <= NBASE (since it might
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* be one too large), and so the intermediate result "tmp_result"
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* is in the range [-NBASE^2, NBASE - 1], and "borrow" is in the
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* range [0, NBASE].
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*/
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borrow = 0;
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for (i = var2ndigits; i >= 0; i--)
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{
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int tmp_result;
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tmp_result = dividend_j[i] - borrow - divisor[i] * qhat;
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borrow = (NBASE - 1 - tmp_result) / NBASE;
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dividend_j[i] = tmp_result + borrow * NBASE;
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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 or
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* just one too large. (Note: it's OK to use dividend[j+2] here
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* because we know the divisor length is at least 2.)
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* If we got a borrow out of the top dividend digit, then indeed
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* qhat was one too large. Fix it, and add back the divisor to
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* correct the working dividend. (Knuth proves that this will
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* occur only about 3/NBASE of the time; hence, it's a good idea
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* to test this code with small NBASE to be sure this section gets
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* exercised.)
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*/
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while (divisor2 * qhat > (next2digits - qhat * divisor1) * NBASE + dividend[j + 2])
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if (borrow)
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{
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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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* 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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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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dividend[j + i] = borrow + NBASE;
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borrow = -1;
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} else {
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dividend[j + i] = borrow;
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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 += 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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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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qhat--;
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carry = 0;
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for (i = var2ndigits; i >= 0; i--) {
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carry += dividend[j + i] + divisor[i];
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if (carry >= NBASE) {
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dividend[j + i] = carry - NBASE;
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carry = 1;
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} else {
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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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/* 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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/* And we're done with this quotient digit */
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res_digits[j] = qhat;
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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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pfree_ext(dividend);
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@ -5910,6 +5925,116 @@ static void div_var_fast(NumericVar* var1, NumericVar* var2, NumericVar* result,
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strip_var(result);
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}
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/*
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* div_var_int() -
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*
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* Divide a numeric variable by a 32-bit integer with the specified weight.
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* The quotient var / (ival * NBASE^ival_weight) is stored in result.
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*/
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static void
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div_var_int(const NumericVar *var, int ival, int ival_weight,
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NumericVar *result, int rscale, bool round)
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{
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NumericDigit *var_digits = var->digits;
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int var_ndigits = var->ndigits;
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int res_sign;
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int res_weight;
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int res_ndigits;
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NumericDigit *res_buf;
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NumericDigit *res_digits;
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uint32 divisor;
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int i;
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/* Guard against division by zero */
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if (ival == 0)
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ereport(ERROR, (errcode(ERRCODE_DIVISION_BY_ZERO), errmsg("division by zero")));
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/* Result zero check */
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if (var_ndigits == 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 (var->sign == NUMERIC_POS)
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res_sign = ival > 0 ? NUMERIC_POS : NUMERIC_NEG;
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else
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res_sign = ival > 0 ? NUMERIC_NEG : NUMERIC_POS;
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res_weight = var->weight - ival_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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res_buf = digitbuf_alloc(res_ndigits + 1);
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res_buf[0] = 0; /* spare digit for later rounding */
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res_digits = res_buf + 1;
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/*
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* Now compute the quotient digits. This is the short division algorithm
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* described in Knuth volume 2, section 4.3.1 exercise 16, except that we
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* allow the divisor to exceed the internal base.
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*
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* In this algorithm, the carry from one digit to the next is at most
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* divisor - 1. Therefore, while processing the next digit, carry may
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* become as large as divisor * NBASE - 1, and so it requires a 64-bit
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* integer if this exceeds UINT_MAX.
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*/
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divisor = Abs(ival);
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if (divisor <= UINT_MAX / NBASE)
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{
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/* carry cannot overflow 32 bits */
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uint32 carry = 0;
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for (i = 0; i < res_ndigits; i++)
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{
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carry = carry * NBASE + (i < var_ndigits ? var_digits[i] : 0);
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res_digits[i] = (NumericDigit) (carry / divisor);
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carry = carry % divisor;
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}
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}
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else
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{
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/* carry may exceed 32 bits */
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uint64 carry = 0;
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for (i = 0; i < res_ndigits; i++)
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{
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carry = carry * NBASE + (i < var_ndigits ? var_digits[i] : 0);
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res_digits[i] = (NumericDigit) (carry / divisor);
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carry = carry % divisor;
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}
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}
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/* Store the quotient in result */
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digitbuf_free(result->buf);
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result->ndigits = res_ndigits;
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result->buf = res_buf;
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result->digits = res_digits;
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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/trailing zeroes */
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strip_var(result);
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}
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/*
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* Default scale selection for division
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*
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