/*------------------------------------------------------------------------- * * numeric.c * An exact numeric data type for the Postgres database system * * Original coding 1998, Jan Wieck. Heavily revised 2003, Tom Lane. * * Many of the algorithmic ideas are borrowed from David M. Smith's "FM" * multiple-precision math library, most recently published as Algorithm * 786: Multiple-Precision Complex Arithmetic and Functions, ACM * Transactions on Mathematical Software, Vol. 24, No. 4, December 1998, * pages 359-367. * * Copyright (c) 1998-2020, PostgreSQL Global Development Group * * IDENTIFICATION * src/backend/utils/adt/numeric.c * *------------------------------------------------------------------------- */ #include "postgres.h" #include #include #include #include #include "catalog/pg_type.h" #include "common/hashfn.h" #include "common/int.h" #include "funcapi.h" #include "lib/hyperloglog.h" #include "libpq/pqformat.h" #include "miscadmin.h" #include "nodes/nodeFuncs.h" #include "nodes/supportnodes.h" #include "utils/array.h" #include "utils/builtins.h" #include "utils/float.h" #include "utils/guc.h" #include "utils/int8.h" #include "utils/numeric.h" #include "utils/sortsupport.h" /* ---------- * Uncomment the following to enable compilation of dump_numeric() * and dump_var() and to get a dump of any result produced by make_result(). * ---------- #define NUMERIC_DEBUG */ /* ---------- * Local data types * * Numeric values are represented in a base-NBASE floating point format. * Each "digit" ranges from 0 to NBASE-1. The type NumericDigit is signed * and wide enough to store a digit. We assume that NBASE*NBASE can fit in * an int. Although the purely calculational routines could handle any even * NBASE that's less than sqrt(INT_MAX), in practice we are only interested * in NBASE a power of ten, so that I/O conversions and decimal rounding * are easy. Also, it's actually more efficient if NBASE is rather less than * sqrt(INT_MAX), so that there is "headroom" for mul_var and div_var_fast to * postpone processing carries. * * Values of NBASE other than 10000 are considered of historical interest only * and are no longer supported in any sense; no mechanism exists for the client * to discover the base, so every client supporting binary mode expects the * base-10000 format. If you plan to change this, also note the numeric * abbreviation code, which assumes NBASE=10000. * ---------- */ #if 0 #define NBASE 10 #define HALF_NBASE 5 #define DEC_DIGITS 1 /* decimal digits per NBASE digit */ #define MUL_GUARD_DIGITS 4 /* these are measured in NBASE digits */ #define DIV_GUARD_DIGITS 8 typedef signed char NumericDigit; #endif #if 0 #define NBASE 100 #define HALF_NBASE 50 #define DEC_DIGITS 2 /* decimal digits per NBASE digit */ #define MUL_GUARD_DIGITS 3 /* these are measured in NBASE digits */ #define DIV_GUARD_DIGITS 6 typedef signed char NumericDigit; #endif #if 1 #define NBASE 10000 #define HALF_NBASE 5000 #define DEC_DIGITS 4 /* decimal digits per NBASE digit */ #define MUL_GUARD_DIGITS 2 /* these are measured in NBASE digits */ #define DIV_GUARD_DIGITS 4 typedef int16 NumericDigit; #endif /* * The Numeric type as stored on disk. * * If the high bits of the first word of a NumericChoice (n_header, or * n_short.n_header, or n_long.n_sign_dscale) are NUMERIC_SHORT, then the * numeric follows the NumericShort format; if they are NUMERIC_POS or * NUMERIC_NEG, it follows the NumericLong format. If they are NUMERIC_NAN, * it is a NaN. We currently always store a NaN using just two bytes (i.e. * only n_header), but previous releases used only the NumericLong format, * so we might find 4-byte NaNs on disk if a database has been migrated using * pg_upgrade. In either case, when the high bits indicate a NaN, the * remaining bits are never examined. Currently, we always initialize these * to zero, but it might be possible to use them for some other purpose in * the future. * * In the NumericShort format, the remaining 14 bits of the header word * (n_short.n_header) are allocated as follows: 1 for sign (positive or * negative), 6 for dynamic scale, and 7 for weight. In practice, most * commonly-encountered values can be represented this way. * * In the NumericLong format, the remaining 14 bits of the header word * (n_long.n_sign_dscale) represent the display scale; and the weight is * stored separately in n_weight. * * NOTE: by convention, values in the packed form have been stripped of * all leading and trailing zero digits (where a "digit" is of base NBASE). * In particular, if the value is zero, there will be no digits at all! * The weight is arbitrary in that case, but we normally set it to zero. */ struct NumericShort { uint16 n_header; /* Sign + display scale + weight */ NumericDigit n_data[FLEXIBLE_ARRAY_MEMBER]; /* Digits */ }; struct NumericLong { uint16 n_sign_dscale; /* Sign + display scale */ int16 n_weight; /* Weight of 1st digit */ NumericDigit n_data[FLEXIBLE_ARRAY_MEMBER]; /* Digits */ }; union NumericChoice { uint16 n_header; /* Header word */ struct NumericLong n_long; /* Long form (4-byte header) */ struct NumericShort n_short; /* Short form (2-byte header) */ }; struct NumericData { int32 vl_len_; /* varlena header (do not touch directly!) */ union NumericChoice choice; /* choice of format */ }; /* * Interpretation of high bits. */ #define NUMERIC_SIGN_MASK 0xC000 #define NUMERIC_POS 0x0000 #define NUMERIC_NEG 0x4000 #define NUMERIC_SHORT 0x8000 #define NUMERIC_NAN 0xC000 #define NUMERIC_FLAGBITS(n) ((n)->choice.n_header & NUMERIC_SIGN_MASK) #define NUMERIC_IS_NAN(n) (NUMERIC_FLAGBITS(n) == NUMERIC_NAN) #define NUMERIC_IS_SHORT(n) (NUMERIC_FLAGBITS(n) == NUMERIC_SHORT) #define NUMERIC_HDRSZ (VARHDRSZ + sizeof(uint16) + sizeof(int16)) #define NUMERIC_HDRSZ_SHORT (VARHDRSZ + sizeof(uint16)) /* * If the flag bits are NUMERIC_SHORT or NUMERIC_NAN, we want the short header; * otherwise, we want the long one. Instead of testing against each value, we * can just look at the high bit, for a slight efficiency gain. */ #define NUMERIC_HEADER_IS_SHORT(n) (((n)->choice.n_header & 0x8000) != 0) #define NUMERIC_HEADER_SIZE(n) \ (VARHDRSZ + sizeof(uint16) + \ (NUMERIC_HEADER_IS_SHORT(n) ? 0 : sizeof(int16))) /* * Short format definitions. */ #define NUMERIC_SHORT_SIGN_MASK 0x2000 #define NUMERIC_SHORT_DSCALE_MASK 0x1F80 #define NUMERIC_SHORT_DSCALE_SHIFT 7 #define NUMERIC_SHORT_DSCALE_MAX \ (NUMERIC_SHORT_DSCALE_MASK >> NUMERIC_SHORT_DSCALE_SHIFT) #define NUMERIC_SHORT_WEIGHT_SIGN_MASK 0x0040 #define NUMERIC_SHORT_WEIGHT_MASK 0x003F #define NUMERIC_SHORT_WEIGHT_MAX NUMERIC_SHORT_WEIGHT_MASK #define NUMERIC_SHORT_WEIGHT_MIN (-(NUMERIC_SHORT_WEIGHT_MASK+1)) /* * Extract sign, display scale, weight. */ #define NUMERIC_DSCALE_MASK 0x3FFF #define NUMERIC_DSCALE_MAX NUMERIC_DSCALE_MASK #define NUMERIC_SIGN(n) \ (NUMERIC_IS_SHORT(n) ? \ (((n)->choice.n_short.n_header & NUMERIC_SHORT_SIGN_MASK) ? \ NUMERIC_NEG : NUMERIC_POS) : NUMERIC_FLAGBITS(n)) #define NUMERIC_DSCALE(n) (NUMERIC_HEADER_IS_SHORT((n)) ? \ ((n)->choice.n_short.n_header & NUMERIC_SHORT_DSCALE_MASK) \ >> NUMERIC_SHORT_DSCALE_SHIFT \ : ((n)->choice.n_long.n_sign_dscale & NUMERIC_DSCALE_MASK)) #define NUMERIC_WEIGHT(n) (NUMERIC_HEADER_IS_SHORT((n)) ? \ (((n)->choice.n_short.n_header & NUMERIC_SHORT_WEIGHT_SIGN_MASK ? \ ~NUMERIC_SHORT_WEIGHT_MASK : 0) \ | ((n)->choice.n_short.n_header & NUMERIC_SHORT_WEIGHT_MASK)) \ : ((n)->choice.n_long.n_weight)) /* ---------- * NumericVar is the format we use for arithmetic. The digit-array part * is the same as the NumericData storage format, but the header is more * complex. * * The value represented by a NumericVar is determined by the sign, weight, * ndigits, and digits[] array. * * Note: the first digit of a NumericVar's value is assumed to be multiplied * by NBASE ** weight. Another way to say it is that there are weight+1 * digits before the decimal point. It is possible to have weight < 0. * * buf points at the physical start of the palloc'd digit buffer for the * NumericVar. digits points at the first digit in actual use (the one * with the specified weight). We normally leave an unused digit or two * (preset to zeroes) between buf and digits, so that there is room to store * a carry out of the top digit without reallocating space. We just need to * decrement digits (and increment weight) to make room for the carry digit. * (There is no such extra space in a numeric value stored in the database, * only in a NumericVar in memory.) * * If buf is NULL then the digit buffer isn't actually palloc'd and should * not be freed --- see the constants below for an example. * * dscale, or display scale, is the nominal precision expressed as number * of digits after the decimal point (it must always be >= 0 at present). * dscale may be more than the number of physically stored fractional digits, * implying that we have suppressed storage of significant trailing zeroes. * It should never be less than the number of stored digits, since that would * imply hiding digits that are present. NOTE that dscale is always expressed * in *decimal* digits, and so it may correspond to a fractional number of * base-NBASE digits --- divide by DEC_DIGITS to convert to NBASE digits. * * rscale, or result scale, is the target precision for a computation. * Like dscale it is expressed as number of *decimal* digits after the decimal * point, and is always >= 0 at present. * Note that rscale is not stored in variables --- it's figured on-the-fly * from the dscales of the inputs. * * While we consistently use "weight" to refer to the base-NBASE weight of * a numeric value, it is convenient in some scale-related calculations to * make use of the base-10 weight (ie, the approximate log10 of the value). * To avoid confusion, such a decimal-units weight is called a "dweight". * * NB: All the variable-level functions are written in a style that makes it * possible to give one and the same variable as argument and destination. * This is feasible because the digit buffer is separate from the variable. * ---------- */ typedef struct NumericVar { int ndigits; /* # of digits in digits[] - can be 0! */ int weight; /* weight of first digit */ int sign; /* NUMERIC_POS, NUMERIC_NEG, or NUMERIC_NAN */ int dscale; /* display scale */ NumericDigit *buf; /* start of palloc'd space for digits[] */ NumericDigit *digits; /* base-NBASE digits */ } NumericVar; /* ---------- * Data for generate_series * ---------- */ typedef struct { NumericVar current; NumericVar stop; NumericVar step; } generate_series_numeric_fctx; /* ---------- * Sort support. * ---------- */ typedef struct { void *buf; /* buffer for short varlenas */ int64 input_count; /* number of non-null values seen */ bool estimating; /* true if estimating cardinality */ hyperLogLogState abbr_card; /* cardinality estimator */ } NumericSortSupport; /* ---------- * Fast sum accumulator. * * NumericSumAccum is used to implement SUM(), and other standard aggregates * that track the sum of input values. It uses 32-bit integers to store the * digits, instead of the normal 16-bit integers (with NBASE=10000). This * way, we can safely accumulate up to NBASE - 1 values without propagating * carry, before risking overflow of any of the digits. 'num_uncarried' * tracks how many values have been accumulated without propagating carry. * * Positive and negative values are accumulated separately, in 'pos_digits' * and 'neg_digits'. This is simpler and faster than deciding whether to add * or subtract from the current value, for each new value (see sub_var() for * the logic we avoid by doing this). Both buffers are of same size, and * have the same weight and scale. In accum_sum_final(), the positive and * negative sums are added together to produce the final result. * * When a new value has a larger ndigits or weight than the accumulator * currently does, the accumulator is enlarged to accommodate the new value. * We normally have one zero digit reserved for carry propagation, and that * is indicated by the 'have_carry_space' flag. When accum_sum_carry() uses * up the reserved digit, it clears the 'have_carry_space' flag. The next * call to accum_sum_add() will enlarge the buffer, to make room for the * extra digit, and set the flag again. * * To initialize a new accumulator, simply reset all fields to zeros. * * The accumulator does not handle NaNs. * ---------- */ typedef struct NumericSumAccum { int ndigits; int weight; int dscale; int num_uncarried; bool have_carry_space; int32 *pos_digits; int32 *neg_digits; } NumericSumAccum; /* * We define our own macros for packing and unpacking abbreviated-key * representations for numeric values in order to avoid depending on * USE_FLOAT8_BYVAL. The type of abbreviation we use is based only on * the size of a datum, not the argument-passing convention for float8. */ #define NUMERIC_ABBREV_BITS (SIZEOF_DATUM * BITS_PER_BYTE) #if SIZEOF_DATUM == 8 #define NumericAbbrevGetDatum(X) ((Datum) (X)) #define DatumGetNumericAbbrev(X) ((int64) (X)) #define NUMERIC_ABBREV_NAN NumericAbbrevGetDatum(PG_INT64_MIN) #else #define NumericAbbrevGetDatum(X) ((Datum) (X)) #define DatumGetNumericAbbrev(X) ((int32) (X)) #define NUMERIC_ABBREV_NAN NumericAbbrevGetDatum(PG_INT32_MIN) #endif /* ---------- * Some preinitialized constants * ---------- */ static const NumericDigit const_zero_data[1] = {0}; static const NumericVar const_zero = {0, 0, NUMERIC_POS, 0, NULL, (NumericDigit *) const_zero_data}; static const NumericDigit const_one_data[1] = {1}; static const NumericVar const_one = {1, 0, NUMERIC_POS, 0, NULL, (NumericDigit *) const_one_data}; static const NumericDigit const_two_data[1] = {2}; static const NumericVar const_two = {1, 0, NUMERIC_POS, 0, NULL, (NumericDigit *) const_two_data}; #if DEC_DIGITS == 4 static const NumericDigit const_zero_point_nine_data[1] = {9000}; #elif DEC_DIGITS == 2 static const NumericDigit const_zero_point_nine_data[1] = {90}; #elif DEC_DIGITS == 1 static const NumericDigit const_zero_point_nine_data[1] = {9}; #endif static const NumericVar const_zero_point_nine = {1, -1, NUMERIC_POS, 1, NULL, (NumericDigit *) const_zero_point_nine_data}; #if DEC_DIGITS == 4 static const NumericDigit const_one_point_one_data[2] = {1, 1000}; #elif DEC_DIGITS == 2 static const NumericDigit const_one_point_one_data[2] = {1, 10}; #elif DEC_DIGITS == 1 static const NumericDigit const_one_point_one_data[2] = {1, 1}; #endif static const NumericVar const_one_point_one = {2, 0, NUMERIC_POS, 1, NULL, (NumericDigit *) const_one_point_one_data}; static const NumericVar const_nan = {0, 0, NUMERIC_NAN, 0, NULL, NULL}; #if DEC_DIGITS == 4 static const int round_powers[4] = {0, 1000, 100, 10}; #endif /* ---------- * Local functions * ---------- */ #ifdef NUMERIC_DEBUG static void dump_numeric(const char *str, Numeric num); static void dump_var(const char *str, NumericVar *var); #else #define dump_numeric(s,n) #define dump_var(s,v) #endif #define digitbuf_alloc(ndigits) \ ((NumericDigit *) palloc((ndigits) * sizeof(NumericDigit))) #define digitbuf_free(buf) \ do { \ if ((buf) != NULL) \ pfree(buf); \ } while (0) #define init_var(v) MemSetAligned(v, 0, sizeof(NumericVar)) #define NUMERIC_DIGITS(num) (NUMERIC_HEADER_IS_SHORT(num) ? \ (num)->choice.n_short.n_data : (num)->choice.n_long.n_data) #define NUMERIC_NDIGITS(num) \ ((VARSIZE(num) - NUMERIC_HEADER_SIZE(num)) / sizeof(NumericDigit)) #define NUMERIC_CAN_BE_SHORT(scale,weight) \ ((scale) <= NUMERIC_SHORT_DSCALE_MAX && \ (weight) <= NUMERIC_SHORT_WEIGHT_MAX && \ (weight) >= NUMERIC_SHORT_WEIGHT_MIN) static void alloc_var(NumericVar *var, int ndigits); static void free_var(NumericVar *var); static void zero_var(NumericVar *var); static const char *set_var_from_str(const char *str, const char *cp, NumericVar *dest); static void set_var_from_num(Numeric value, NumericVar *dest); static void init_var_from_num(Numeric num, NumericVar *dest); static void set_var_from_var(const NumericVar *value, NumericVar *dest); static char *get_str_from_var(const NumericVar *var); static char *get_str_from_var_sci(const NumericVar *var, int rscale); static Numeric make_result(const NumericVar *var); static Numeric make_result_opt_error(const NumericVar *var, bool *error); static void apply_typmod(NumericVar *var, int32 typmod); static bool numericvar_to_int32(const NumericVar *var, int32 *result); static bool numericvar_to_int64(const NumericVar *var, int64 *result); static void int64_to_numericvar(int64 val, NumericVar *var); #ifdef HAVE_INT128 static bool numericvar_to_int128(const NumericVar *var, int128 *result); static void int128_to_numericvar(int128 val, NumericVar *var); #endif static double numeric_to_double_no_overflow(Numeric num); static double numericvar_to_double_no_overflow(const NumericVar *var); static Datum numeric_abbrev_convert(Datum original_datum, SortSupport ssup); static bool numeric_abbrev_abort(int memtupcount, SortSupport ssup); static int numeric_fast_cmp(Datum x, Datum y, SortSupport ssup); static int numeric_cmp_abbrev(Datum x, Datum y, SortSupport ssup); static Datum numeric_abbrev_convert_var(const NumericVar *var, NumericSortSupport *nss); static int cmp_numerics(Numeric num1, Numeric num2); static int cmp_var(const NumericVar *var1, const NumericVar *var2); static int cmp_var_common(const NumericDigit *var1digits, int var1ndigits, int var1weight, int var1sign, const NumericDigit *var2digits, int var2ndigits, int var2weight, int var2sign); static void add_var(const NumericVar *var1, const NumericVar *var2, NumericVar *result); static void sub_var(const NumericVar *var1, const NumericVar *var2, NumericVar *result); static void mul_var(const NumericVar *var1, const NumericVar *var2, NumericVar *result, int rscale); static void div_var(const NumericVar *var1, const NumericVar *var2, NumericVar *result, int rscale, bool round); static void div_var_fast(const NumericVar *var1, const NumericVar *var2, NumericVar *result, int rscale, bool round); static int select_div_scale(const NumericVar *var1, const NumericVar *var2); static void mod_var(const NumericVar *var1, const NumericVar *var2, NumericVar *result); static void div_mod_var(const NumericVar *var1, const NumericVar *var2, NumericVar *quot, NumericVar *rem); static void ceil_var(const NumericVar *var, NumericVar *result); static void floor_var(const NumericVar *var, NumericVar *result); static void gcd_var(const NumericVar *var1, const NumericVar *var2, NumericVar *result); static void sqrt_var(const NumericVar *arg, NumericVar *result, int rscale); static void exp_var(const NumericVar *arg, NumericVar *result, int rscale); static int estimate_ln_dweight(const NumericVar *var); static void ln_var(const NumericVar *arg, NumericVar *result, int rscale); static void log_var(const NumericVar *base, const NumericVar *num, NumericVar *result); static void power_var(const NumericVar *base, const NumericVar *exp, NumericVar *result); static void power_var_int(const NumericVar *base, int exp, NumericVar *result, int rscale); static void power_ten_int(int exp, NumericVar *result); static int cmp_abs(const NumericVar *var1, const NumericVar *var2); static int cmp_abs_common(const NumericDigit *var1digits, int var1ndigits, int var1weight, const NumericDigit *var2digits, int var2ndigits, int var2weight); static void add_abs(const NumericVar *var1, const NumericVar *var2, NumericVar *result); static void sub_abs(const NumericVar *var1, const NumericVar *var2, NumericVar *result); static void round_var(NumericVar *var, int rscale); static void trunc_var(NumericVar *var, int rscale); static void strip_var(NumericVar *var); static void compute_bucket(Numeric operand, Numeric bound1, Numeric bound2, const NumericVar *count_var, NumericVar *result_var); static void accum_sum_add(NumericSumAccum *accum, const NumericVar *var1); static void accum_sum_rescale(NumericSumAccum *accum, const NumericVar *val); static void accum_sum_carry(NumericSumAccum *accum); static void accum_sum_reset(NumericSumAccum *accum); static void accum_sum_final(NumericSumAccum *accum, NumericVar *result); static void accum_sum_copy(NumericSumAccum *dst, NumericSumAccum *src); static void accum_sum_combine(NumericSumAccum *accum, NumericSumAccum *accum2); /* ---------------------------------------------------------------------- * * Input-, output- and rounding-functions * * ---------------------------------------------------------------------- */ /* * numeric_in() - * * Input function for numeric data type */ Datum numeric_in(PG_FUNCTION_ARGS) { char *str = PG_GETARG_CSTRING(0); #ifdef NOT_USED Oid typelem = PG_GETARG_OID(1); #endif int32 typmod = PG_GETARG_INT32(2); Numeric res; const char *cp; /* Skip leading spaces */ cp = str; while (*cp) { if (!isspace((unsigned char) *cp)) break; cp++; } /* * Check for NaN */ if (pg_strncasecmp(cp, "NaN", 3) == 0) { res = make_result(&const_nan); /* Should be nothing left but spaces */ cp += 3; while (*cp) { if (!isspace((unsigned char) *cp)) ereport(ERROR, (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION), errmsg("invalid input syntax for type %s: \"%s\"", "numeric", str))); cp++; } } else { /* * Use set_var_from_str() to parse a normal numeric value */ NumericVar value; init_var(&value); cp = set_var_from_str(str, cp, &value); /* * We duplicate a few lines of code here because we would like to * throw any trailing-junk syntax error before any semantic error * resulting from apply_typmod. We can't easily fold the two cases * together because we mustn't apply apply_typmod to a NaN. */ while (*cp) { if (!isspace((unsigned char) *cp)) ereport(ERROR, (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION), errmsg("invalid input syntax for type %s: \"%s\"", "numeric", str))); cp++; } apply_typmod(&value, typmod); res = make_result(&value); free_var(&value); } PG_RETURN_NUMERIC(res); } /* * numeric_out() - * * Output function for numeric data type */ Datum numeric_out(PG_FUNCTION_ARGS) { Numeric num = PG_GETARG_NUMERIC(0); NumericVar x; char *str; /* * Handle NaN */ if (NUMERIC_IS_NAN(num)) PG_RETURN_CSTRING(pstrdup("NaN")); /* * Get the number in the variable format. */ init_var_from_num(num, &x); str = get_str_from_var(&x); PG_RETURN_CSTRING(str); } /* * numeric_is_nan() - * * Is Numeric value a NaN? */ bool numeric_is_nan(Numeric num) { return NUMERIC_IS_NAN(num); } /* * numeric_maximum_size() - * * Maximum size of a numeric with given typmod, or -1 if unlimited/unknown. */ int32 numeric_maximum_size(int32 typmod) { int precision; int numeric_digits; if (typmod < (int32) (VARHDRSZ)) return -1; /* precision (ie, max # of digits) is in upper bits of typmod */ precision = ((typmod - VARHDRSZ) >> 16) & 0xffff; /* * This formula computes the maximum number of NumericDigits we could need * in order to store the specified number of decimal digits. Because the * weight is stored as a number of NumericDigits rather than a number of * decimal digits, it's possible that the first NumericDigit will contain * only a single decimal digit. Thus, the first two decimal digits can * require two NumericDigits to store, but it isn't until we reach * DEC_DIGITS + 2 decimal digits that we potentially need a third * NumericDigit. */ numeric_digits = (precision + 2 * (DEC_DIGITS - 1)) / DEC_DIGITS; /* * In most cases, the size of a numeric will be smaller than the value * computed below, because the varlena header will typically get toasted * down to a single byte before being stored on disk, and it may also be * possible to use a short numeric header. But our job here is to compute * the worst case. */ return NUMERIC_HDRSZ + (numeric_digits * sizeof(NumericDigit)); } /* * numeric_out_sci() - * * Output function for numeric data type in scientific notation. */ char * numeric_out_sci(Numeric num, int scale) { NumericVar x; char *str; /* * Handle NaN */ if (NUMERIC_IS_NAN(num)) return pstrdup("NaN"); init_var_from_num(num, &x); str = get_str_from_var_sci(&x, scale); return str; } /* * numeric_normalize() - * * Output function for numeric data type, suppressing insignificant trailing * zeroes and then any trailing decimal point. The intent of this is to * produce strings that are equal if and only if the input numeric values * compare equal. */ char * numeric_normalize(Numeric num) { NumericVar x; char *str; int last; /* * Handle NaN */ if (NUMERIC_IS_NAN(num)) return pstrdup("NaN"); init_var_from_num(num, &x); str = get_str_from_var(&x); /* If there's no decimal point, there's certainly nothing to remove. */ if (strchr(str, '.') != NULL) { /* * Back up over trailing fractional zeroes. Since there is a decimal * point, this loop will terminate safely. */ last = strlen(str) - 1; while (str[last] == '0') last--; /* We want to get rid of the decimal point too, if it's now last. */ if (str[last] == '.') last--; /* Delete whatever we backed up over. */ str[last + 1] = '\0'; } return str; } /* * numeric_recv - converts external binary format to numeric * * External format is a sequence of int16's: * ndigits, weight, sign, dscale, NumericDigits. */ Datum numeric_recv(PG_FUNCTION_ARGS) { StringInfo buf = (StringInfo) PG_GETARG_POINTER(0); #ifdef NOT_USED Oid typelem = PG_GETARG_OID(1); #endif int32 typmod = PG_GETARG_INT32(2); NumericVar value; Numeric res; int len, i; init_var(&value); len = (uint16) pq_getmsgint(buf, sizeof(uint16)); alloc_var(&value, len); value.weight = (int16) pq_getmsgint(buf, sizeof(int16)); /* we allow any int16 for weight --- OK? */ value.sign = (uint16) pq_getmsgint(buf, sizeof(uint16)); if (!(value.sign == NUMERIC_POS || value.sign == NUMERIC_NEG || value.sign == NUMERIC_NAN)) ereport(ERROR, (errcode(ERRCODE_INVALID_BINARY_REPRESENTATION), errmsg("invalid sign in external \"numeric\" value"))); value.dscale = (uint16) pq_getmsgint(buf, sizeof(uint16)); if ((value.dscale & NUMERIC_DSCALE_MASK) != value.dscale) ereport(ERROR, (errcode(ERRCODE_INVALID_BINARY_REPRESENTATION), errmsg("invalid scale in external \"numeric\" value"))); for (i = 0; i < len; i++) { NumericDigit d = pq_getmsgint(buf, sizeof(NumericDigit)); if (d < 0 || d >= NBASE) ereport(ERROR, (errcode(ERRCODE_INVALID_BINARY_REPRESENTATION), errmsg("invalid digit in external \"numeric\" value"))); value.digits[i] = d; } /* * If the given dscale would hide any digits, truncate those digits away. * We could alternatively throw an error, but that would take a bunch of * extra code (about as much as trunc_var involves), and it might cause * client compatibility issues. */ trunc_var(&value, value.dscale); apply_typmod(&value, typmod); res = make_result(&value); free_var(&value); PG_RETURN_NUMERIC(res); } /* * numeric_send - converts numeric to binary format */ Datum numeric_send(PG_FUNCTION_ARGS) { Numeric num = PG_GETARG_NUMERIC(0); NumericVar x; StringInfoData buf; int i; init_var_from_num(num, &x); pq_begintypsend(&buf); pq_sendint16(&buf, x.ndigits); pq_sendint16(&buf, x.weight); pq_sendint16(&buf, x.sign); pq_sendint16(&buf, x.dscale); for (i = 0; i < x.ndigits; i++) pq_sendint16(&buf, x.digits[i]); PG_RETURN_BYTEA_P(pq_endtypsend(&buf)); } /* * numeric_support() * * Planner support function for the numeric() length coercion function. * * Flatten calls that solely represent increases in allowable precision. * Scale changes mutate every datum, so they are unoptimizable. Some values, * e.g. 1E-1001, can only fit into an unconstrained numeric, so a change from * an unconstrained numeric to any constrained numeric is also unoptimizable. */ Datum numeric_support(PG_FUNCTION_ARGS) { Node *rawreq = (Node *) PG_GETARG_POINTER(0); Node *ret = NULL; if (IsA(rawreq, SupportRequestSimplify)) { SupportRequestSimplify *req = (SupportRequestSimplify *) rawreq; FuncExpr *expr = req->fcall; Node *typmod; Assert(list_length(expr->args) >= 2); typmod = (Node *) lsecond(expr->args); if (IsA(typmod, Const) && !((Const *) typmod)->constisnull) { Node *source = (Node *) linitial(expr->args); int32 old_typmod = exprTypmod(source); int32 new_typmod = DatumGetInt32(((Const *) typmod)->constvalue); int32 old_scale = (old_typmod - VARHDRSZ) & 0xffff; int32 new_scale = (new_typmod - VARHDRSZ) & 0xffff; int32 old_precision = (old_typmod - VARHDRSZ) >> 16 & 0xffff; int32 new_precision = (new_typmod - VARHDRSZ) >> 16 & 0xffff; /* * If new_typmod < VARHDRSZ, the destination is unconstrained; * that's always OK. If old_typmod >= VARHDRSZ, the source is * constrained, and we're OK if the scale is unchanged and the * precision is not decreasing. See further notes in function * header comment. */ if (new_typmod < (int32) VARHDRSZ || (old_typmod >= (int32) VARHDRSZ && new_scale == old_scale && new_precision >= old_precision)) ret = relabel_to_typmod(source, new_typmod); } } PG_RETURN_POINTER(ret); } /* * numeric() - * * This is a special function called by the Postgres database system * before a value is stored in a tuple's attribute. The precision and * scale of the attribute have to be applied on the value. */ Datum numeric (PG_FUNCTION_ARGS) { Numeric num = PG_GETARG_NUMERIC(0); int32 typmod = PG_GETARG_INT32(1); Numeric new; int32 tmp_typmod; int precision; int scale; int ddigits; int maxdigits; NumericVar var; /* * Handle NaN */ if (NUMERIC_IS_NAN(num)) PG_RETURN_NUMERIC(make_result(&const_nan)); /* * If the value isn't a valid type modifier, simply return a copy of the * input value */ if (typmod < (int32) (VARHDRSZ)) { new = (Numeric) palloc(VARSIZE(num)); memcpy(new, num, VARSIZE(num)); PG_RETURN_NUMERIC(new); } /* * Get the precision and scale out of the typmod value */ tmp_typmod = typmod - VARHDRSZ; precision = (tmp_typmod >> 16) & 0xffff; scale = tmp_typmod & 0xffff; maxdigits = precision - scale; /* * If the number is certainly in bounds and due to the target scale no * rounding could be necessary, just make a copy of the input and modify * its scale fields, unless the larger scale forces us to abandon the * short representation. (Note we assume the existing dscale is * honest...) */ ddigits = (NUMERIC_WEIGHT(num) + 1) * DEC_DIGITS; if (ddigits <= maxdigits && scale >= NUMERIC_DSCALE(num) && (NUMERIC_CAN_BE_SHORT(scale, NUMERIC_WEIGHT(num)) || !NUMERIC_IS_SHORT(num))) { new = (Numeric) palloc(VARSIZE(num)); memcpy(new, num, VARSIZE(num)); if (NUMERIC_IS_SHORT(num)) new->choice.n_short.n_header = (num->choice.n_short.n_header & ~NUMERIC_SHORT_DSCALE_MASK) | (scale << NUMERIC_SHORT_DSCALE_SHIFT); else new->choice.n_long.n_sign_dscale = NUMERIC_SIGN(new) | ((uint16) scale & NUMERIC_DSCALE_MASK); PG_RETURN_NUMERIC(new); } /* * We really need to fiddle with things - unpack the number into a * variable and let apply_typmod() do it. */ init_var(&var); set_var_from_num(num, &var); apply_typmod(&var, typmod); new = make_result(&var); free_var(&var); PG_RETURN_NUMERIC(new); } Datum numerictypmodin(PG_FUNCTION_ARGS) { ArrayType *ta = PG_GETARG_ARRAYTYPE_P(0); int32 *tl; int n; int32 typmod; tl = ArrayGetIntegerTypmods(ta, &n); if (n == 2) { if (tl[0] < 1 || tl[0] > NUMERIC_MAX_PRECISION) ereport(ERROR, (errcode(ERRCODE_INVALID_PARAMETER_VALUE), errmsg("NUMERIC precision %d must be between 1 and %d", tl[0], NUMERIC_MAX_PRECISION))); if (tl[1] < 0 || tl[1] > tl[0]) ereport(ERROR, (errcode(ERRCODE_INVALID_PARAMETER_VALUE), errmsg("NUMERIC scale %d must be between 0 and precision %d", tl[1], tl[0]))); typmod = ((tl[0] << 16) | tl[1]) + VARHDRSZ; } else if (n == 1) { if (tl[0] < 1 || tl[0] > NUMERIC_MAX_PRECISION) ereport(ERROR, (errcode(ERRCODE_INVALID_PARAMETER_VALUE), errmsg("NUMERIC precision %d must be between 1 and %d", tl[0], NUMERIC_MAX_PRECISION))); /* scale defaults to zero */ typmod = (tl[0] << 16) + VARHDRSZ; } else { ereport(ERROR, (errcode(ERRCODE_INVALID_PARAMETER_VALUE), errmsg("invalid NUMERIC type modifier"))); typmod = 0; /* keep compiler quiet */ } PG_RETURN_INT32(typmod); } Datum numerictypmodout(PG_FUNCTION_ARGS) { int32 typmod = PG_GETARG_INT32(0); char *res = (char *) palloc(64); if (typmod >= 0) snprintf(res, 64, "(%d,%d)", ((typmod - VARHDRSZ) >> 16) & 0xffff, (typmod - VARHDRSZ) & 0xffff); else *res = '\0'; PG_RETURN_CSTRING(res); } /* ---------------------------------------------------------------------- * * Sign manipulation, rounding and the like * * ---------------------------------------------------------------------- */ Datum numeric_abs(PG_FUNCTION_ARGS) { Numeric num = PG_GETARG_NUMERIC(0); Numeric res; /* * Handle NaN */ if (NUMERIC_IS_NAN(num)) PG_RETURN_NUMERIC(make_result(&const_nan)); /* * Do it the easy way directly on the packed format */ res = (Numeric) palloc(VARSIZE(num)); memcpy(res, num, VARSIZE(num)); if (NUMERIC_IS_SHORT(num)) res->choice.n_short.n_header = num->choice.n_short.n_header & ~NUMERIC_SHORT_SIGN_MASK; else res->choice.n_long.n_sign_dscale = NUMERIC_POS | NUMERIC_DSCALE(num); PG_RETURN_NUMERIC(res); } Datum numeric_uminus(PG_FUNCTION_ARGS) { Numeric num = PG_GETARG_NUMERIC(0); Numeric res; /* * Handle NaN */ if (NUMERIC_IS_NAN(num)) PG_RETURN_NUMERIC(make_result(&const_nan)); /* * Do it the easy way directly on the packed format */ res = (Numeric) palloc(VARSIZE(num)); memcpy(res, num, VARSIZE(num)); /* * The packed format is known to be totally zero digit trimmed always. So * we can identify a ZERO by the fact that there are no digits at all. Do * nothing to a zero. */ if (NUMERIC_NDIGITS(num) != 0) { /* Else, flip the sign */ if (NUMERIC_IS_SHORT(num)) res->choice.n_short.n_header = num->choice.n_short.n_header ^ NUMERIC_SHORT_SIGN_MASK; else if (NUMERIC_SIGN(num) == NUMERIC_POS) res->choice.n_long.n_sign_dscale = NUMERIC_NEG | NUMERIC_DSCALE(num); else res->choice.n_long.n_sign_dscale = NUMERIC_POS | NUMERIC_DSCALE(num); } PG_RETURN_NUMERIC(res); } Datum numeric_uplus(PG_FUNCTION_ARGS) { Numeric num = PG_GETARG_NUMERIC(0); Numeric res; res = (Numeric) palloc(VARSIZE(num)); memcpy(res, num, VARSIZE(num)); PG_RETURN_NUMERIC(res); } /* * numeric_sign() - * * returns -1 if the argument is less than 0, 0 if the argument is equal * to 0, and 1 if the argument is greater than zero. */ Datum numeric_sign(PG_FUNCTION_ARGS) { Numeric num = PG_GETARG_NUMERIC(0); Numeric res; NumericVar result; /* * Handle NaN */ if (NUMERIC_IS_NAN(num)) PG_RETURN_NUMERIC(make_result(&const_nan)); init_var(&result); /* * The packed format is known to be totally zero digit trimmed always. So * we can identify a ZERO by the fact that there are no digits at all. */ if (NUMERIC_NDIGITS(num) == 0) set_var_from_var(&const_zero, &result); else { /* * And if there are some, we return a copy of ONE with the sign of our * argument */ set_var_from_var(&const_one, &result); result.sign = NUMERIC_SIGN(num); } res = make_result(&result); free_var(&result); PG_RETURN_NUMERIC(res); } /* * numeric_round() - * * Round a value to have 'scale' digits after the decimal point. * We allow negative 'scale', implying rounding before the decimal * point --- Oracle interprets rounding that way. */ Datum numeric_round(PG_FUNCTION_ARGS) { Numeric num = PG_GETARG_NUMERIC(0); int32 scale = PG_GETARG_INT32(1); Numeric res; NumericVar arg; /* * Handle NaN */ if (NUMERIC_IS_NAN(num)) PG_RETURN_NUMERIC(make_result(&const_nan)); /* * Limit the scale value to avoid possible overflow in calculations */ scale = Max(scale, -NUMERIC_MAX_RESULT_SCALE); scale = Min(scale, NUMERIC_MAX_RESULT_SCALE); /* * Unpack the argument and round it at the proper digit position */ init_var(&arg); set_var_from_num(num, &arg); round_var(&arg, scale); /* We don't allow negative output dscale */ if (scale < 0) arg.dscale = 0; /* * Return the rounded result */ res = make_result(&arg); free_var(&arg); PG_RETURN_NUMERIC(res); } /* * numeric_trunc() - * * Truncate a value to have 'scale' digits after the decimal point. * We allow negative 'scale', implying a truncation before the decimal * point --- Oracle interprets truncation that way. */ Datum numeric_trunc(PG_FUNCTION_ARGS) { Numeric num = PG_GETARG_NUMERIC(0); int32 scale = PG_GETARG_INT32(1); Numeric res; NumericVar arg; /* * Handle NaN */ if (NUMERIC_IS_NAN(num)) PG_RETURN_NUMERIC(make_result(&const_nan)); /* * Limit the scale value to avoid possible overflow in calculations */ scale = Max(scale, -NUMERIC_MAX_RESULT_SCALE); scale = Min(scale, NUMERIC_MAX_RESULT_SCALE); /* * Unpack the argument and truncate it at the proper digit position */ init_var(&arg); set_var_from_num(num, &arg); trunc_var(&arg, scale); /* We don't allow negative output dscale */ if (scale < 0) arg.dscale = 0; /* * Return the truncated result */ res = make_result(&arg); free_var(&arg); PG_RETURN_NUMERIC(res); } /* * numeric_ceil() - * * Return the smallest integer greater than or equal to the argument */ Datum numeric_ceil(PG_FUNCTION_ARGS) { Numeric num = PG_GETARG_NUMERIC(0); Numeric res; NumericVar result; if (NUMERIC_IS_NAN(num)) PG_RETURN_NUMERIC(make_result(&const_nan)); init_var_from_num(num, &result); ceil_var(&result, &result); res = make_result(&result); free_var(&result); PG_RETURN_NUMERIC(res); } /* * numeric_floor() - * * Return the largest integer equal to or less than the argument */ Datum numeric_floor(PG_FUNCTION_ARGS) { Numeric num = PG_GETARG_NUMERIC(0); Numeric res; NumericVar result; if (NUMERIC_IS_NAN(num)) PG_RETURN_NUMERIC(make_result(&const_nan)); init_var_from_num(num, &result); floor_var(&result, &result); res = make_result(&result); free_var(&result); PG_RETURN_NUMERIC(res); } /* * generate_series_numeric() - * * Generate series of numeric. */ Datum generate_series_numeric(PG_FUNCTION_ARGS) { return generate_series_step_numeric(fcinfo); } Datum generate_series_step_numeric(PG_FUNCTION_ARGS) { generate_series_numeric_fctx *fctx; FuncCallContext *funcctx; MemoryContext oldcontext; if (SRF_IS_FIRSTCALL()) { Numeric start_num = PG_GETARG_NUMERIC(0); Numeric stop_num = PG_GETARG_NUMERIC(1); NumericVar steploc = const_one; /* handle NaN in start and stop values */ if (NUMERIC_IS_NAN(start_num)) ereport(ERROR, (errcode(ERRCODE_INVALID_PARAMETER_VALUE), errmsg("start value cannot be NaN"))); if (NUMERIC_IS_NAN(stop_num)) ereport(ERROR, (errcode(ERRCODE_INVALID_PARAMETER_VALUE), errmsg("stop value cannot be NaN"))); /* see if we were given an explicit step size */ if (PG_NARGS() == 3) { Numeric step_num = PG_GETARG_NUMERIC(2); if (NUMERIC_IS_NAN(step_num)) ereport(ERROR, (errcode(ERRCODE_INVALID_PARAMETER_VALUE), errmsg("step size cannot be NaN"))); init_var_from_num(step_num, &steploc); if (cmp_var(&steploc, &const_zero) == 0) ereport(ERROR, (errcode(ERRCODE_INVALID_PARAMETER_VALUE), errmsg("step size cannot equal zero"))); } /* create a function context for cross-call persistence */ funcctx = SRF_FIRSTCALL_INIT(); /* * Switch to memory context appropriate for multiple function calls. */ oldcontext = MemoryContextSwitchTo(funcctx->multi_call_memory_ctx); /* allocate memory for user context */ fctx = (generate_series_numeric_fctx *) palloc(sizeof(generate_series_numeric_fctx)); /* * Use fctx to keep state from call to call. Seed current with the * original start value. We must copy the start_num and stop_num * values rather than pointing to them, since we may have detoasted * them in the per-call context. */ init_var(&fctx->current); init_var(&fctx->stop); init_var(&fctx->step); set_var_from_num(start_num, &fctx->current); set_var_from_num(stop_num, &fctx->stop); set_var_from_var(&steploc, &fctx->step); funcctx->user_fctx = fctx; MemoryContextSwitchTo(oldcontext); } /* stuff done on every call of the function */ funcctx = SRF_PERCALL_SETUP(); /* * Get the saved state and use current state as the result of this * iteration. */ fctx = funcctx->user_fctx; if ((fctx->step.sign == NUMERIC_POS && cmp_var(&fctx->current, &fctx->stop) <= 0) || (fctx->step.sign == NUMERIC_NEG && cmp_var(&fctx->current, &fctx->stop) >= 0)) { Numeric result = make_result(&fctx->current); /* switch to memory context appropriate for iteration calculation */ oldcontext = MemoryContextSwitchTo(funcctx->multi_call_memory_ctx); /* increment current in preparation for next iteration */ add_var(&fctx->current, &fctx->step, &fctx->current); MemoryContextSwitchTo(oldcontext); /* do when there is more left to send */ SRF_RETURN_NEXT(funcctx, NumericGetDatum(result)); } else /* do when there is no more left */ SRF_RETURN_DONE(funcctx); } /* * Implements the numeric version of the width_bucket() function * defined by SQL2003. See also width_bucket_float8(). * * 'bound1' and 'bound2' are the lower and upper bounds of the * histogram's range, respectively. 'count' is the number of buckets * in the histogram. width_bucket() returns an integer indicating the * bucket number that 'operand' belongs to in an equiwidth histogram * with the specified characteristics. An operand smaller than the * lower bound is assigned to bucket 0. An operand greater than the * upper bound is assigned to an additional bucket (with number * count+1). We don't allow "NaN" for any of the numeric arguments. */ Datum width_bucket_numeric(PG_FUNCTION_ARGS) { Numeric operand = PG_GETARG_NUMERIC(0); Numeric bound1 = PG_GETARG_NUMERIC(1); Numeric bound2 = PG_GETARG_NUMERIC(2); int32 count = PG_GETARG_INT32(3); NumericVar count_var; NumericVar result_var; int32 result; if (count <= 0) ereport(ERROR, (errcode(ERRCODE_INVALID_ARGUMENT_FOR_WIDTH_BUCKET_FUNCTION), errmsg("count must be greater than zero"))); if (NUMERIC_IS_NAN(operand) || NUMERIC_IS_NAN(bound1) || NUMERIC_IS_NAN(bound2)) ereport(ERROR, (errcode(ERRCODE_INVALID_ARGUMENT_FOR_WIDTH_BUCKET_FUNCTION), errmsg("operand, lower bound, and upper bound cannot be NaN"))); init_var(&result_var); init_var(&count_var); /* Convert 'count' to a numeric, for ease of use later */ int64_to_numericvar((int64) count, &count_var); switch (cmp_numerics(bound1, bound2)) { case 0: ereport(ERROR, (errcode(ERRCODE_INVALID_ARGUMENT_FOR_WIDTH_BUCKET_FUNCTION), errmsg("lower bound cannot equal upper bound"))); break; /* bound1 < bound2 */ case -1: if (cmp_numerics(operand, bound1) < 0) set_var_from_var(&const_zero, &result_var); else if (cmp_numerics(operand, bound2) >= 0) add_var(&count_var, &const_one, &result_var); else compute_bucket(operand, bound1, bound2, &count_var, &result_var); break; /* bound1 > bound2 */ case 1: if (cmp_numerics(operand, bound1) > 0) set_var_from_var(&const_zero, &result_var); else if (cmp_numerics(operand, bound2) <= 0) add_var(&count_var, &const_one, &result_var); else compute_bucket(operand, bound1, bound2, &count_var, &result_var); break; } /* if result exceeds the range of a legal int4, we ereport here */ if (!numericvar_to_int32(&result_var, &result)) ereport(ERROR, (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE), errmsg("integer out of range"))); free_var(&count_var); free_var(&result_var); PG_RETURN_INT32(result); } /* * If 'operand' is not outside the bucket range, determine the correct * bucket for it to go. The calculations performed by this function * are derived directly from the SQL2003 spec. */ static void compute_bucket(Numeric operand, Numeric bound1, Numeric bound2, const NumericVar *count_var, NumericVar *result_var) { NumericVar bound1_var; NumericVar bound2_var; NumericVar operand_var; init_var_from_num(bound1, &bound1_var); init_var_from_num(bound2, &bound2_var); init_var_from_num(operand, &operand_var); if (cmp_var(&bound1_var, &bound2_var) < 0) { sub_var(&operand_var, &bound1_var, &operand_var); sub_var(&bound2_var, &bound1_var, &bound2_var); div_var(&operand_var, &bound2_var, result_var, select_div_scale(&operand_var, &bound2_var), true); } else { sub_var(&bound1_var, &operand_var, &operand_var); sub_var(&bound1_var, &bound2_var, &bound1_var); div_var(&operand_var, &bound1_var, result_var, select_div_scale(&operand_var, &bound1_var), true); } mul_var(result_var, count_var, result_var, result_var->dscale + count_var->dscale); add_var(result_var, &const_one, result_var); floor_var(result_var, result_var); free_var(&bound1_var); free_var(&bound2_var); free_var(&operand_var); } /* ---------------------------------------------------------------------- * * Comparison functions * * Note: btree indexes need these routines not to leak memory; therefore, * be careful to free working copies of toasted datums. Most places don't * need to be so careful. * * Sort support: * * We implement the sortsupport strategy routine in order to get the benefit of * abbreviation. The ordinary numeric comparison can be quite slow as a result * of palloc/pfree cycles (due to detoasting packed values for alignment); * while this could be worked on itself, the abbreviation strategy gives more * speedup in many common cases. * * Two different representations are used for the abbreviated form, one in * int32 and one in int64, whichever fits into a by-value Datum. In both cases * the representation is negated relative to the original value, because we use * the largest negative value for NaN, which sorts higher than other values. We * convert the absolute value of the numeric to a 31-bit or 63-bit positive * value, and then negate it if the original number was positive. * * We abort the abbreviation process if the abbreviation cardinality is below * 0.01% of the row count (1 per 10k non-null rows). The actual break-even * point is somewhat below that, perhaps 1 per 30k (at 1 per 100k there's a * very small penalty), but we don't want to build up too many abbreviated * values before first testing for abort, so we take the slightly pessimistic * number. We make no attempt to estimate the cardinality of the real values, * since it plays no part in the cost model here (if the abbreviation is equal, * the cost of comparing equal and unequal underlying values is comparable). * We discontinue even checking for abort (saving us the hashing overhead) if * the estimated cardinality gets to 100k; that would be enough to support many * billions of rows while doing no worse than breaking even. * * ---------------------------------------------------------------------- */ /* * Sort support strategy routine. */ Datum numeric_sortsupport(PG_FUNCTION_ARGS) { SortSupport ssup = (SortSupport) PG_GETARG_POINTER(0); ssup->comparator = numeric_fast_cmp; if (ssup->abbreviate) { NumericSortSupport *nss; MemoryContext oldcontext = MemoryContextSwitchTo(ssup->ssup_cxt); nss = palloc(sizeof(NumericSortSupport)); /* * palloc a buffer for handling unaligned packed values in addition to * the support struct */ nss->buf = palloc(VARATT_SHORT_MAX + VARHDRSZ + 1); nss->input_count = 0; nss->estimating = true; initHyperLogLog(&nss->abbr_card, 10); ssup->ssup_extra = nss; ssup->abbrev_full_comparator = ssup->comparator; ssup->comparator = numeric_cmp_abbrev; ssup->abbrev_converter = numeric_abbrev_convert; ssup->abbrev_abort = numeric_abbrev_abort; MemoryContextSwitchTo(oldcontext); } PG_RETURN_VOID(); } /* * Abbreviate a numeric datum, handling NaNs and detoasting * (must not leak memory!) */ static Datum numeric_abbrev_convert(Datum original_datum, SortSupport ssup) { NumericSortSupport *nss = ssup->ssup_extra; void *original_varatt = PG_DETOAST_DATUM_PACKED(original_datum); Numeric value; Datum result; nss->input_count += 1; /* * This is to handle packed datums without needing a palloc/pfree cycle; * we keep and reuse a buffer large enough to handle any short datum. */ if (VARATT_IS_SHORT(original_varatt)) { void *buf = nss->buf; Size sz = VARSIZE_SHORT(original_varatt) - VARHDRSZ_SHORT; Assert(sz <= VARATT_SHORT_MAX - VARHDRSZ_SHORT); SET_VARSIZE(buf, VARHDRSZ + sz); memcpy(VARDATA(buf), VARDATA_SHORT(original_varatt), sz); value = (Numeric) buf; } else value = (Numeric) original_varatt; if (NUMERIC_IS_NAN(value)) { result = NUMERIC_ABBREV_NAN; } else { NumericVar var; init_var_from_num(value, &var); result = numeric_abbrev_convert_var(&var, nss); } /* should happen only for external/compressed toasts */ if ((Pointer) original_varatt != DatumGetPointer(original_datum)) pfree(original_varatt); return result; } /* * Consider whether to abort abbreviation. * * We pay no attention to the cardinality of the non-abbreviated data. There is * no reason to do so: unlike text, we have no fast check for equal values, so * we pay the full overhead whenever the abbreviations are equal regardless of * whether the underlying values are also equal. */ static bool numeric_abbrev_abort(int memtupcount, SortSupport ssup) { NumericSortSupport *nss = ssup->ssup_extra; double abbr_card; if (memtupcount < 10000 || nss->input_count < 10000 || !nss->estimating) return false; abbr_card = estimateHyperLogLog(&nss->abbr_card); /* * If we have >100k distinct values, then even if we were sorting many * billion rows we'd likely still break even, and the penalty of undoing * that many rows of abbrevs would probably not be worth it. Stop even * counting at that point. */ if (abbr_card > 100000.0) { #ifdef TRACE_SORT if (trace_sort) elog(LOG, "numeric_abbrev: estimation ends at cardinality %f" " after " INT64_FORMAT " values (%d rows)", abbr_card, nss->input_count, memtupcount); #endif nss->estimating = false; return false; } /* * Target minimum cardinality is 1 per ~10k of non-null inputs. (The * break even point is somewhere between one per 100k rows, where * abbreviation has a very slight penalty, and 1 per 10k where it wins by * a measurable percentage.) We use the relatively pessimistic 10k * threshold, and add a 0.5 row fudge factor, because it allows us to * abort earlier on genuinely pathological data where we've had exactly * one abbreviated value in the first 10k (non-null) rows. */ if (abbr_card < nss->input_count / 10000.0 + 0.5) { #ifdef TRACE_SORT if (trace_sort) elog(LOG, "numeric_abbrev: aborting abbreviation at cardinality %f" " below threshold %f after " INT64_FORMAT " values (%d rows)", abbr_card, nss->input_count / 10000.0 + 0.5, nss->input_count, memtupcount); #endif return true; } #ifdef TRACE_SORT if (trace_sort) elog(LOG, "numeric_abbrev: cardinality %f" " after " INT64_FORMAT " values (%d rows)", abbr_card, nss->input_count, memtupcount); #endif return false; } /* * Non-fmgr interface to the comparison routine to allow sortsupport to elide * the fmgr call. The saving here is small given how slow numeric comparisons * are, but it is a required part of the sort support API when abbreviations * are performed. * * Two palloc/pfree cycles could be saved here by using persistent buffers for * aligning short-varlena inputs, but this has not so far been considered to * be worth the effort. */ static int numeric_fast_cmp(Datum x, Datum y, SortSupport ssup) { Numeric nx = DatumGetNumeric(x); Numeric ny = DatumGetNumeric(y); int result; result = cmp_numerics(nx, ny); if ((Pointer) nx != DatumGetPointer(x)) pfree(nx); if ((Pointer) ny != DatumGetPointer(y)) pfree(ny); return result; } /* * Compare abbreviations of values. (Abbreviations may be equal where the true * values differ, but if the abbreviations differ, they must reflect the * ordering of the true values.) */ static int numeric_cmp_abbrev(Datum x, Datum y, SortSupport ssup) { /* * NOTE WELL: this is intentionally backwards, because the abbreviation is * negated relative to the original value, to handle NaN. */ if (DatumGetNumericAbbrev(x) < DatumGetNumericAbbrev(y)) return 1; if (DatumGetNumericAbbrev(x) > DatumGetNumericAbbrev(y)) return -1; return 0; } /* * Abbreviate a NumericVar according to the available bit size. * * The 31-bit value is constructed as: * * 0 + 7bits digit weight + 24 bits digit value * * where the digit weight is in single decimal digits, not digit words, and * stored in excess-44 representation[1]. The 24-bit digit value is the 7 most * significant decimal digits of the value converted to binary. Values whose * weights would fall outside the representable range are rounded off to zero * (which is also used to represent actual zeros) or to 0x7FFFFFFF (which * otherwise cannot occur). Abbreviation therefore fails to gain any advantage * where values are outside the range 10^-44 to 10^83, which is not considered * to be a serious limitation, or when values are of the same magnitude and * equal in the first 7 decimal digits, which is considered to be an * unavoidable limitation given the available bits. (Stealing three more bits * to compare another digit would narrow the range of representable weights by * a factor of 8, which starts to look like a real limiting factor.) * * (The value 44 for the excess is essentially arbitrary) * * The 63-bit value is constructed as: * * 0 + 7bits weight + 4 x 14-bit packed digit words * * The weight in this case is again stored in excess-44, but this time it is * the original weight in digit words (i.e. powers of 10000). The first four * digit words of the value (if present; trailing zeros are assumed as needed) * are packed into 14 bits each to form the rest of the value. Again, * out-of-range values are rounded off to 0 or 0x7FFFFFFFFFFFFFFF. The * representable range in this case is 10^-176 to 10^332, which is considered * to be good enough for all practical purposes, and comparison of 4 words * means that at least 13 decimal digits are compared, which is considered to * be a reasonable compromise between effectiveness and efficiency in computing * the abbreviation. * * (The value 44 for the excess is even more arbitrary here, it was chosen just * to match the value used in the 31-bit case) * * [1] - Excess-k representation means that the value is offset by adding 'k' * and then treated as unsigned, so the smallest representable value is stored * with all bits zero. This allows simple comparisons to work on the composite * value. */ #if NUMERIC_ABBREV_BITS == 64 static Datum numeric_abbrev_convert_var(const NumericVar *var, NumericSortSupport *nss) { int ndigits = var->ndigits; int weight = var->weight; int64 result; if (ndigits == 0 || weight < -44) { result = 0; } else if (weight > 83) { result = PG_INT64_MAX; } else { result = ((int64) (weight + 44) << 56); switch (ndigits) { default: result |= ((int64) var->digits[3]); /* FALLTHROUGH */ case 3: result |= ((int64) var->digits[2]) << 14; /* FALLTHROUGH */ case 2: result |= ((int64) var->digits[1]) << 28; /* FALLTHROUGH */ case 1: result |= ((int64) var->digits[0]) << 42; break; } } /* the abbrev is negated relative to the original */ if (var->sign == NUMERIC_POS) result = -result; if (nss->estimating) { uint32 tmp = ((uint32) result ^ (uint32) ((uint64) result >> 32)); addHyperLogLog(&nss->abbr_card, DatumGetUInt32(hash_uint32(tmp))); } return NumericAbbrevGetDatum(result); } #endif /* NUMERIC_ABBREV_BITS == 64 */ #if NUMERIC_ABBREV_BITS == 32 static Datum numeric_abbrev_convert_var(const NumericVar *var, NumericSortSupport *nss) { int ndigits = var->ndigits; int weight = var->weight; int32 result; if (ndigits == 0 || weight < -11) { result = 0; } else if (weight > 20) { result = PG_INT32_MAX; } else { NumericDigit nxt1 = (ndigits > 1) ? var->digits[1] : 0; weight = (weight + 11) * 4; result = var->digits[0]; /* * "result" now has 1 to 4 nonzero decimal digits. We pack in more * digits to make 7 in total (largest we can fit in 24 bits) */ if (result > 999) { /* already have 4 digits, add 3 more */ result = (result * 1000) + (nxt1 / 10); weight += 3; } else if (result > 99) { /* already have 3 digits, add 4 more */ result = (result * 10000) + nxt1; weight += 2; } else if (result > 9) { NumericDigit nxt2 = (ndigits > 2) ? var->digits[2] : 0; /* already have 2 digits, add 5 more */ result = (result * 100000) + (nxt1 * 10) + (nxt2 / 1000); weight += 1; } else { NumericDigit nxt2 = (ndigits > 2) ? var->digits[2] : 0; /* already have 1 digit, add 6 more */ result = (result * 1000000) + (nxt1 * 100) + (nxt2 / 100); } result = result | (weight << 24); } /* the abbrev is negated relative to the original */ if (var->sign == NUMERIC_POS) result = -result; if (nss->estimating) { uint32 tmp = (uint32) result; addHyperLogLog(&nss->abbr_card, DatumGetUInt32(hash_uint32(tmp))); } return NumericAbbrevGetDatum(result); } #endif /* NUMERIC_ABBREV_BITS == 32 */ /* * Ordinary (non-sortsupport) comparisons follow. */ Datum numeric_cmp(PG_FUNCTION_ARGS) { Numeric num1 = PG_GETARG_NUMERIC(0); Numeric num2 = PG_GETARG_NUMERIC(1); int result; result = cmp_numerics(num1, num2); PG_FREE_IF_COPY(num1, 0); PG_FREE_IF_COPY(num2, 1); PG_RETURN_INT32(result); } Datum numeric_eq(PG_FUNCTION_ARGS) { Numeric num1 = PG_GETARG_NUMERIC(0); Numeric num2 = PG_GETARG_NUMERIC(1); bool result; result = cmp_numerics(num1, num2) == 0; PG_FREE_IF_COPY(num1, 0); PG_FREE_IF_COPY(num2, 1); PG_RETURN_BOOL(result); } Datum numeric_ne(PG_FUNCTION_ARGS) { Numeric num1 = PG_GETARG_NUMERIC(0); Numeric num2 = PG_GETARG_NUMERIC(1); bool result; result = cmp_numerics(num1, num2) != 0; PG_FREE_IF_COPY(num1, 0); PG_FREE_IF_COPY(num2, 1); PG_RETURN_BOOL(result); } Datum numeric_gt(PG_FUNCTION_ARGS) { Numeric num1 = PG_GETARG_NUMERIC(0); Numeric num2 = PG_GETARG_NUMERIC(1); bool result; result = cmp_numerics(num1, num2) > 0; PG_FREE_IF_COPY(num1, 0); PG_FREE_IF_COPY(num2, 1); PG_RETURN_BOOL(result); } Datum numeric_ge(PG_FUNCTION_ARGS) { Numeric num1 = PG_GETARG_NUMERIC(0); Numeric num2 = PG_GETARG_NUMERIC(1); bool result; result = cmp_numerics(num1, num2) >= 0; PG_FREE_IF_COPY(num1, 0); PG_FREE_IF_COPY(num2, 1); PG_RETURN_BOOL(result); } Datum numeric_lt(PG_FUNCTION_ARGS) { Numeric num1 = PG_GETARG_NUMERIC(0); Numeric num2 = PG_GETARG_NUMERIC(1); bool result; result = cmp_numerics(num1, num2) < 0; PG_FREE_IF_COPY(num1, 0); PG_FREE_IF_COPY(num2, 1); PG_RETURN_BOOL(result); } Datum numeric_le(PG_FUNCTION_ARGS) { Numeric num1 = PG_GETARG_NUMERIC(0); Numeric num2 = PG_GETARG_NUMERIC(1); bool result; result = cmp_numerics(num1, num2) <= 0; PG_FREE_IF_COPY(num1, 0); PG_FREE_IF_COPY(num2, 1); PG_RETURN_BOOL(result); } static int cmp_numerics(Numeric num1, Numeric num2) { int result; /* * We consider all NANs to be equal and larger than any non-NAN. This is * somewhat arbitrary; the important thing is to have a consistent sort * order. */ if (NUMERIC_IS_NAN(num1)) { if (NUMERIC_IS_NAN(num2)) result = 0; /* NAN = NAN */ else result = 1; /* NAN > non-NAN */ } else if (NUMERIC_IS_NAN(num2)) { result = -1; /* non-NAN < NAN */ } else { result = cmp_var_common(NUMERIC_DIGITS(num1), NUMERIC_NDIGITS(num1), NUMERIC_WEIGHT(num1), NUMERIC_SIGN(num1), NUMERIC_DIGITS(num2), NUMERIC_NDIGITS(num2), NUMERIC_WEIGHT(num2), NUMERIC_SIGN(num2)); } return result; } /* * in_range support function for numeric. */ Datum in_range_numeric_numeric(PG_FUNCTION_ARGS) { Numeric val = PG_GETARG_NUMERIC(0); Numeric base = PG_GETARG_NUMERIC(1); Numeric offset = PG_GETARG_NUMERIC(2); bool sub = PG_GETARG_BOOL(3); bool less = PG_GETARG_BOOL(4); bool result; /* * Reject negative or NaN offset. Negative is per spec, and NaN is * because appropriate semantics for that seem non-obvious. */ if (NUMERIC_IS_NAN(offset) || NUMERIC_SIGN(offset) == NUMERIC_NEG) ereport(ERROR, (errcode(ERRCODE_INVALID_PRECEDING_OR_FOLLOWING_SIZE), errmsg("invalid preceding or following size in window function"))); /* * Deal with cases where val and/or base is NaN, following the rule that * NaN sorts after non-NaN (cf cmp_numerics). The offset cannot affect * the conclusion. */ if (NUMERIC_IS_NAN(val)) { if (NUMERIC_IS_NAN(base)) result = true; /* NAN = NAN */ else result = !less; /* NAN > non-NAN */ } else if (NUMERIC_IS_NAN(base)) { result = less; /* non-NAN < NAN */ } else { /* * Otherwise go ahead and compute base +/- offset. While it's * possible for this to overflow the numeric format, it's unlikely * enough that we don't take measures to prevent it. */ NumericVar valv; NumericVar basev; NumericVar offsetv; NumericVar sum; init_var_from_num(val, &valv); init_var_from_num(base, &basev); init_var_from_num(offset, &offsetv); init_var(&sum); if (sub) sub_var(&basev, &offsetv, &sum); else add_var(&basev, &offsetv, &sum); if (less) result = (cmp_var(&valv, &sum) <= 0); else result = (cmp_var(&valv, &sum) >= 0); free_var(&sum); } PG_FREE_IF_COPY(val, 0); PG_FREE_IF_COPY(base, 1); PG_FREE_IF_COPY(offset, 2); PG_RETURN_BOOL(result); } Datum hash_numeric(PG_FUNCTION_ARGS) { Numeric key = PG_GETARG_NUMERIC(0); Datum digit_hash; Datum result; int weight; int start_offset; int end_offset; int i; int hash_len; NumericDigit *digits; /* If it's NaN, don't try to hash the rest of the fields */ if (NUMERIC_IS_NAN(key)) PG_RETURN_UINT32(0); weight = NUMERIC_WEIGHT(key); start_offset = 0; end_offset = 0; /* * Omit any leading or trailing zeros from the input to the hash. The * numeric implementation *should* guarantee that leading and trailing * zeros are suppressed, but we're paranoid. Note that we measure the * starting and ending offsets in units of NumericDigits, not bytes. */ digits = NUMERIC_DIGITS(key); for (i = 0; i < NUMERIC_NDIGITS(key); i++) { if (digits[i] != (NumericDigit) 0) break; start_offset++; /* * The weight is effectively the # of digits before the decimal point, * so decrement it for each leading zero we skip. */ weight--; } /* * If there are no non-zero digits, then the value of the number is zero, * regardless of any other fields. */ if (NUMERIC_NDIGITS(key) == start_offset) PG_RETURN_UINT32(-1); for (i = NUMERIC_NDIGITS(key) - 1; i >= 0; i--) { if (digits[i] != (NumericDigit) 0) break; end_offset++; } /* If we get here, there should be at least one non-zero digit */ Assert(start_offset + end_offset < NUMERIC_NDIGITS(key)); /* * Note that we don't hash on the Numeric's scale, since two numerics can * compare equal but have different scales. We also don't hash on the * sign, although we could: since a sign difference implies inequality, * this shouldn't affect correctness. */ hash_len = NUMERIC_NDIGITS(key) - start_offset - end_offset; digit_hash = hash_any((unsigned char *) (NUMERIC_DIGITS(key) + start_offset), hash_len * sizeof(NumericDigit)); /* Mix in the weight, via XOR */ result = digit_hash ^ weight; PG_RETURN_DATUM(result); } /* * Returns 64-bit value by hashing a value to a 64-bit value, with a seed. * Otherwise, similar to hash_numeric. */ Datum hash_numeric_extended(PG_FUNCTION_ARGS) { Numeric key = PG_GETARG_NUMERIC(0); uint64 seed = PG_GETARG_INT64(1); Datum digit_hash; Datum result; int weight; int start_offset; int end_offset; int i; int hash_len; NumericDigit *digits; if (NUMERIC_IS_NAN(key)) PG_RETURN_UINT64(seed); weight = NUMERIC_WEIGHT(key); start_offset = 0; end_offset = 0; digits = NUMERIC_DIGITS(key); for (i = 0; i < NUMERIC_NDIGITS(key); i++) { if (digits[i] != (NumericDigit) 0) break; start_offset++; weight--; } if (NUMERIC_NDIGITS(key) == start_offset) PG_RETURN_UINT64(seed - 1); for (i = NUMERIC_NDIGITS(key) - 1; i >= 0; i--) { if (digits[i] != (NumericDigit) 0) break; end_offset++; } Assert(start_offset + end_offset < NUMERIC_NDIGITS(key)); hash_len = NUMERIC_NDIGITS(key) - start_offset - end_offset; digit_hash = hash_any_extended((unsigned char *) (NUMERIC_DIGITS(key) + start_offset), hash_len * sizeof(NumericDigit), seed); result = UInt64GetDatum(DatumGetUInt64(digit_hash) ^ weight); PG_RETURN_DATUM(result); } /* ---------------------------------------------------------------------- * * Basic arithmetic functions * * ---------------------------------------------------------------------- */ /* * numeric_add() - * * Add two numerics */ Datum numeric_add(PG_FUNCTION_ARGS) { Numeric num1 = PG_GETARG_NUMERIC(0); Numeric num2 = PG_GETARG_NUMERIC(1); Numeric res; res = numeric_add_opt_error(num1, num2, NULL); PG_RETURN_NUMERIC(res); } /* * numeric_add_opt_error() - * * Internal version of numeric_add(). If "*have_error" flag is provided, * on error it's set to true, NULL returned. This is helpful when caller * need to handle errors by itself. */ Numeric numeric_add_opt_error(Numeric num1, Numeric num2, bool *have_error) { NumericVar arg1; NumericVar arg2; NumericVar result; Numeric res; /* * Handle NaN */ if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2)) return make_result(&const_nan); /* * Unpack the values, let add_var() compute the result and return it. */ init_var_from_num(num1, &arg1); init_var_from_num(num2, &arg2); init_var(&result); add_var(&arg1, &arg2, &result); res = make_result_opt_error(&result, have_error); free_var(&result); return res; } /* * numeric_sub() - * * Subtract one numeric from another */ Datum numeric_sub(PG_FUNCTION_ARGS) { Numeric num1 = PG_GETARG_NUMERIC(0); Numeric num2 = PG_GETARG_NUMERIC(1); Numeric res; res = numeric_sub_opt_error(num1, num2, NULL); PG_RETURN_NUMERIC(res); } /* * numeric_sub_opt_error() - * * Internal version of numeric_sub(). If "*have_error" flag is provided, * on error it's set to true, NULL returned. This is helpful when caller * need to handle errors by itself. */ Numeric numeric_sub_opt_error(Numeric num1, Numeric num2, bool *have_error) { NumericVar arg1; NumericVar arg2; NumericVar result; Numeric res; /* * Handle NaN */ if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2)) return make_result(&const_nan); /* * Unpack the values, let sub_var() compute the result and return it. */ init_var_from_num(num1, &arg1); init_var_from_num(num2, &arg2); init_var(&result); sub_var(&arg1, &arg2, &result); res = make_result_opt_error(&result, have_error); free_var(&result); return res; } /* * numeric_mul() - * * Calculate the product of two numerics */ Datum numeric_mul(PG_FUNCTION_ARGS) { Numeric num1 = PG_GETARG_NUMERIC(0); Numeric num2 = PG_GETARG_NUMERIC(1); Numeric res; res = numeric_mul_opt_error(num1, num2, NULL); PG_RETURN_NUMERIC(res); } /* * numeric_mul_opt_error() - * * Internal version of numeric_mul(). If "*have_error" flag is provided, * on error it's set to true, NULL returned. This is helpful when caller * need to handle errors by itself. */ Numeric numeric_mul_opt_error(Numeric num1, Numeric num2, bool *have_error) { NumericVar arg1; NumericVar arg2; NumericVar result; Numeric res; /* * Handle NaN */ if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2)) return make_result(&const_nan); /* * Unpack the values, let mul_var() compute the result and return it. * Unlike add_var() and sub_var(), mul_var() will round its result. In the * case of numeric_mul(), which is invoked for the * operator on numerics, * we request exact representation for the product (rscale = sum(dscale of * arg1, dscale of arg2)). If the exact result has more digits after the * decimal point than can be stored in a numeric, we round it. Rounding * after computing the exact result ensures that the final result is * correctly rounded (rounding in mul_var() using a truncated product * would not guarantee this). */ init_var_from_num(num1, &arg1); init_var_from_num(num2, &arg2); init_var(&result); mul_var(&arg1, &arg2, &result, arg1.dscale + arg2.dscale); if (result.dscale > NUMERIC_DSCALE_MAX) round_var(&result, NUMERIC_DSCALE_MAX); res = make_result_opt_error(&result, have_error); free_var(&result); return res; } /* * numeric_div() - * * Divide one numeric into another */ Datum numeric_div(PG_FUNCTION_ARGS) { Numeric num1 = PG_GETARG_NUMERIC(0); Numeric num2 = PG_GETARG_NUMERIC(1); Numeric res; res = numeric_div_opt_error(num1, num2, NULL); PG_RETURN_NUMERIC(res); } /* * numeric_div_opt_error() - * * Internal version of numeric_div(). If "*have_error" flag is provided, * on error it's set to true, NULL returned. This is helpful when caller * need to handle errors by itself. */ Numeric numeric_div_opt_error(Numeric num1, Numeric num2, bool *have_error) { NumericVar arg1; NumericVar arg2; NumericVar result; Numeric res; int rscale; if (have_error) *have_error = false; /* * Handle NaN */ if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2)) return make_result(&const_nan); /* * Unpack the arguments */ init_var_from_num(num1, &arg1); init_var_from_num(num2, &arg2); init_var(&result); /* * Select scale for division result */ rscale = select_div_scale(&arg1, &arg2); /* * If "have_error" is provided, check for division by zero here */ if (have_error && (arg2.ndigits == 0 || arg2.digits[0] == 0)) { *have_error = true; return NULL; } /* * Do the divide and return the result */ div_var(&arg1, &arg2, &result, rscale, true); res = make_result_opt_error(&result, have_error); free_var(&result); return res; } /* * numeric_div_trunc() - * * Divide one numeric into another, truncating the result to an integer */ Datum numeric_div_trunc(PG_FUNCTION_ARGS) { Numeric num1 = PG_GETARG_NUMERIC(0); Numeric num2 = PG_GETARG_NUMERIC(1); NumericVar arg1; NumericVar arg2; NumericVar result; Numeric res; /* * Handle NaN */ if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2)) PG_RETURN_NUMERIC(make_result(&const_nan)); /* * Unpack the arguments */ init_var_from_num(num1, &arg1); init_var_from_num(num2, &arg2); init_var(&result); /* * Do the divide and return the result */ div_var(&arg1, &arg2, &result, 0, false); res = make_result(&result); free_var(&result); PG_RETURN_NUMERIC(res); } /* * numeric_mod() - * * Calculate the modulo of two numerics */ Datum numeric_mod(PG_FUNCTION_ARGS) { Numeric num1 = PG_GETARG_NUMERIC(0); Numeric num2 = PG_GETARG_NUMERIC(1); Numeric res; res = numeric_mod_opt_error(num1, num2, NULL); PG_RETURN_NUMERIC(res); } /* * numeric_mod_opt_error() - * * Internal version of numeric_mod(). If "*have_error" flag is provided, * on error it's set to true, NULL returned. This is helpful when caller * need to handle errors by itself. */ Numeric numeric_mod_opt_error(Numeric num1, Numeric num2, bool *have_error) { Numeric res; NumericVar arg1; NumericVar arg2; NumericVar result; if (have_error) *have_error = false; if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2)) return make_result(&const_nan); init_var_from_num(num1, &arg1); init_var_from_num(num2, &arg2); init_var(&result); /* * If "have_error" is provided, check for division by zero here */ if (have_error && (arg2.ndigits == 0 || arg2.digits[0] == 0)) { *have_error = true; return NULL; } mod_var(&arg1, &arg2, &result); res = make_result_opt_error(&result, NULL); free_var(&result); return res; } /* * numeric_inc() - * * Increment a number by one */ Datum numeric_inc(PG_FUNCTION_ARGS) { Numeric num = PG_GETARG_NUMERIC(0); NumericVar arg; Numeric res; /* * Handle NaN */ if (NUMERIC_IS_NAN(num)) PG_RETURN_NUMERIC(make_result(&const_nan)); /* * Compute the result and return it */ init_var_from_num(num, &arg); add_var(&arg, &const_one, &arg); res = make_result(&arg); free_var(&arg); PG_RETURN_NUMERIC(res); } /* * numeric_smaller() - * * Return the smaller of two numbers */ Datum numeric_smaller(PG_FUNCTION_ARGS) { Numeric num1 = PG_GETARG_NUMERIC(0); Numeric num2 = PG_GETARG_NUMERIC(1); /* * Use cmp_numerics so that this will agree with the comparison operators, * particularly as regards comparisons involving NaN. */ if (cmp_numerics(num1, num2) < 0) PG_RETURN_NUMERIC(num1); else PG_RETURN_NUMERIC(num2); } /* * numeric_larger() - * * Return the larger of two numbers */ Datum numeric_larger(PG_FUNCTION_ARGS) { Numeric num1 = PG_GETARG_NUMERIC(0); Numeric num2 = PG_GETARG_NUMERIC(1); /* * Use cmp_numerics so that this will agree with the comparison operators, * particularly as regards comparisons involving NaN. */ if (cmp_numerics(num1, num2) > 0) PG_RETURN_NUMERIC(num1); else PG_RETURN_NUMERIC(num2); } /* ---------------------------------------------------------------------- * * Advanced math functions * * ---------------------------------------------------------------------- */ /* * numeric_gcd() - * * Calculate the greatest common divisor of two numerics */ Datum numeric_gcd(PG_FUNCTION_ARGS) { Numeric num1 = PG_GETARG_NUMERIC(0); Numeric num2 = PG_GETARG_NUMERIC(1); NumericVar arg1; NumericVar arg2; NumericVar result; Numeric res; /* * Handle NaN */ if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2)) PG_RETURN_NUMERIC(make_result(&const_nan)); /* * Unpack the arguments */ init_var_from_num(num1, &arg1); init_var_from_num(num2, &arg2); init_var(&result); /* * Find the GCD and return the result */ gcd_var(&arg1, &arg2, &result); res = make_result(&result); free_var(&result); PG_RETURN_NUMERIC(res); } /* * numeric_lcm() - * * Calculate the least common multiple of two numerics */ Datum numeric_lcm(PG_FUNCTION_ARGS) { Numeric num1 = PG_GETARG_NUMERIC(0); Numeric num2 = PG_GETARG_NUMERIC(1); NumericVar arg1; NumericVar arg2; NumericVar result; Numeric res; /* * Handle NaN */ if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2)) PG_RETURN_NUMERIC(make_result(&const_nan)); /* * Unpack the arguments */ init_var_from_num(num1, &arg1); init_var_from_num(num2, &arg2); init_var(&result); /* * Compute the result using lcm(x, y) = abs(x / gcd(x, y) * y), returning * zero if either input is zero. * * Note that the division is guaranteed to be exact, returning an integer * result, so the LCM is an integral multiple of both x and y. A display * scale of Min(x.dscale, y.dscale) would be sufficient to represent it, * but as with other numeric functions, we choose to return a result whose * display scale is no smaller than either input. */ if (arg1.ndigits == 0 || arg2.ndigits == 0) set_var_from_var(&const_zero, &result); else { gcd_var(&arg1, &arg2, &result); div_var(&arg1, &result, &result, 0, false); mul_var(&arg2, &result, &result, arg2.dscale); result.sign = NUMERIC_POS; } result.dscale = Max(arg1.dscale, arg2.dscale); res = make_result(&result); free_var(&result); PG_RETURN_NUMERIC(res); } /* * numeric_fac() * * Compute factorial */ Datum numeric_fac(PG_FUNCTION_ARGS) { int64 num = PG_GETARG_INT64(0); Numeric res; NumericVar fact; NumericVar result; if (num <= 1) { res = make_result(&const_one); PG_RETURN_NUMERIC(res); } /* Fail immediately if the result would overflow */ if (num > 32177) ereport(ERROR, (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE), errmsg("value overflows numeric format"))); init_var(&fact); init_var(&result); int64_to_numericvar(num, &result); for (num = num - 1; num > 1; num--) { /* this loop can take awhile, so allow it to be interrupted */ CHECK_FOR_INTERRUPTS(); int64_to_numericvar(num, &fact); mul_var(&result, &fact, &result, 0); } res = make_result(&result); free_var(&fact); free_var(&result); PG_RETURN_NUMERIC(res); } /* * numeric_sqrt() - * * Compute the square root of a numeric. */ Datum numeric_sqrt(PG_FUNCTION_ARGS) { Numeric num = PG_GETARG_NUMERIC(0); Numeric res; NumericVar arg; NumericVar result; int sweight; int rscale; /* * Handle NaN */ if (NUMERIC_IS_NAN(num)) PG_RETURN_NUMERIC(make_result(&const_nan)); /* * Unpack the argument and determine the result scale. We choose a scale * to give at least NUMERIC_MIN_SIG_DIGITS significant digits; but in any * case not less than the input's dscale. */ init_var_from_num(num, &arg); init_var(&result); /* Assume the input was normalized, so arg.weight is accurate */ sweight = (arg.weight + 1) * DEC_DIGITS / 2 - 1; rscale = NUMERIC_MIN_SIG_DIGITS - sweight; rscale = Max(rscale, arg.dscale); rscale = Max(rscale, NUMERIC_MIN_DISPLAY_SCALE); rscale = Min(rscale, NUMERIC_MAX_DISPLAY_SCALE); /* * Let sqrt_var() do the calculation and return the result. */ sqrt_var(&arg, &result, rscale); res = make_result(&result); free_var(&result); PG_RETURN_NUMERIC(res); } /* * numeric_exp() - * * Raise e to the power of x */ Datum numeric_exp(PG_FUNCTION_ARGS) { Numeric num = PG_GETARG_NUMERIC(0); Numeric res; NumericVar arg; NumericVar result; int rscale; double val; /* * Handle NaN */ if (NUMERIC_IS_NAN(num)) PG_RETURN_NUMERIC(make_result(&const_nan)); /* * Unpack the argument and determine the result scale. We choose a scale * to give at least NUMERIC_MIN_SIG_DIGITS significant digits; but in any * case not less than the input's dscale. */ init_var_from_num(num, &arg); init_var(&result); /* convert input to float8, ignoring overflow */ val = numericvar_to_double_no_overflow(&arg); /* * log10(result) = num * log10(e), so this is approximately the decimal * weight of the result: */ val *= 0.434294481903252; /* limit to something that won't cause integer overflow */ val = Max(val, -NUMERIC_MAX_RESULT_SCALE); val = Min(val, NUMERIC_MAX_RESULT_SCALE); rscale = NUMERIC_MIN_SIG_DIGITS - (int) val; rscale = Max(rscale, arg.dscale); rscale = Max(rscale, NUMERIC_MIN_DISPLAY_SCALE); rscale = Min(rscale, NUMERIC_MAX_DISPLAY_SCALE); /* * Let exp_var() do the calculation and return the result. */ exp_var(&arg, &result, rscale); res = make_result(&result); free_var(&result); PG_RETURN_NUMERIC(res); } /* * numeric_ln() - * * Compute the natural logarithm of x */ Datum numeric_ln(PG_FUNCTION_ARGS) { Numeric num = PG_GETARG_NUMERIC(0); Numeric res; NumericVar arg; NumericVar result; int ln_dweight; int rscale; /* * Handle NaN */ if (NUMERIC_IS_NAN(num)) PG_RETURN_NUMERIC(make_result(&const_nan)); init_var_from_num(num, &arg); init_var(&result); /* Estimated dweight of logarithm */ ln_dweight = estimate_ln_dweight(&arg); rscale = NUMERIC_MIN_SIG_DIGITS - ln_dweight; rscale = Max(rscale, arg.dscale); rscale = Max(rscale, NUMERIC_MIN_DISPLAY_SCALE); rscale = Min(rscale, NUMERIC_MAX_DISPLAY_SCALE); ln_var(&arg, &result, rscale); res = make_result(&result); free_var(&result); PG_RETURN_NUMERIC(res); } /* * numeric_log() - * * Compute the logarithm of x in a given base */ Datum numeric_log(PG_FUNCTION_ARGS) { Numeric num1 = PG_GETARG_NUMERIC(0); Numeric num2 = PG_GETARG_NUMERIC(1); Numeric res; NumericVar arg1; NumericVar arg2; NumericVar result; /* * Handle NaN */ if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2)) PG_RETURN_NUMERIC(make_result(&const_nan)); /* * Initialize things */ init_var_from_num(num1, &arg1); init_var_from_num(num2, &arg2); init_var(&result); /* * Call log_var() to compute and return the result; note it handles scale * selection itself. */ log_var(&arg1, &arg2, &result); res = make_result(&result); free_var(&result); PG_RETURN_NUMERIC(res); } /* * numeric_power() - * * Raise b to the power of x */ Datum numeric_power(PG_FUNCTION_ARGS) { Numeric num1 = PG_GETARG_NUMERIC(0); Numeric num2 = PG_GETARG_NUMERIC(1); Numeric res; NumericVar arg1; NumericVar arg2; NumericVar arg2_trunc; NumericVar result; /* * Handle NaN cases. We follow the POSIX spec for pow(3), which says that * NaN ^ 0 = 1, and 1 ^ NaN = 1, while all other cases with NaN inputs * yield NaN (with no error). */ if (NUMERIC_IS_NAN(num1)) { if (!NUMERIC_IS_NAN(num2)) { init_var_from_num(num2, &arg2); if (cmp_var(&arg2, &const_zero) == 0) PG_RETURN_NUMERIC(make_result(&const_one)); } PG_RETURN_NUMERIC(make_result(&const_nan)); } if (NUMERIC_IS_NAN(num2)) { init_var_from_num(num1, &arg1); if (cmp_var(&arg1, &const_one) == 0) PG_RETURN_NUMERIC(make_result(&const_one)); PG_RETURN_NUMERIC(make_result(&const_nan)); } /* * Initialize things */ init_var(&arg2_trunc); init_var(&result); init_var_from_num(num1, &arg1); init_var_from_num(num2, &arg2); set_var_from_var(&arg2, &arg2_trunc); trunc_var(&arg2_trunc, 0); /* * The SQL spec requires that we emit a particular SQLSTATE error code for * certain error conditions. Specifically, we don't return a * divide-by-zero error code for 0 ^ -1. Raising a negative number to a * non-integer power must produce the same error code, but that case is * handled in power_var(). */ if (cmp_var(&arg1, &const_zero) == 0 && cmp_var(&arg2, &const_zero) < 0) ereport(ERROR, (errcode(ERRCODE_INVALID_ARGUMENT_FOR_POWER_FUNCTION), errmsg("zero raised to a negative power is undefined"))); /* * Call power_var() to compute and return the result; note it handles * scale selection itself. */ power_var(&arg1, &arg2, &result); res = make_result(&result); free_var(&result); free_var(&arg2_trunc); PG_RETURN_NUMERIC(res); } /* * numeric_scale() - * * Returns the scale, i.e. the count of decimal digits in the fractional part */ Datum numeric_scale(PG_FUNCTION_ARGS) { Numeric num = PG_GETARG_NUMERIC(0); if (NUMERIC_IS_NAN(num)) PG_RETURN_NULL(); PG_RETURN_INT32(NUMERIC_DSCALE(num)); } /* * Calculate minimum scale for value. */ static int get_min_scale(NumericVar *var) { int min_scale; int last_digit_pos; /* * Ordinarily, the input value will be "stripped" so that the last * NumericDigit is nonzero. But we don't want to get into an infinite * loop if it isn't, so explicitly find the last nonzero digit. */ last_digit_pos = var->ndigits - 1; while (last_digit_pos >= 0 && var->digits[last_digit_pos] == 0) last_digit_pos--; if (last_digit_pos >= 0) { /* compute min_scale assuming that last ndigit has no zeroes */ min_scale = (last_digit_pos - var->weight) * DEC_DIGITS; /* * We could get a negative result if there are no digits after the * decimal point. In this case the min_scale must be zero. */ if (min_scale > 0) { /* * Reduce min_scale if trailing digit(s) in last NumericDigit are * zero. */ NumericDigit last_digit = var->digits[last_digit_pos]; while (last_digit % 10 == 0) { min_scale--; last_digit /= 10; } } else min_scale = 0; } else min_scale = 0; /* result if input is zero */ return min_scale; } /* * Returns minimum scale required to represent supplied value without loss. */ Datum numeric_min_scale(PG_FUNCTION_ARGS) { Numeric num = PG_GETARG_NUMERIC(0); NumericVar arg; int min_scale; if (NUMERIC_IS_NAN(num)) PG_RETURN_NULL(); init_var_from_num(num, &arg); min_scale = get_min_scale(&arg); free_var(&arg); PG_RETURN_INT32(min_scale); } /* * Reduce scale of numeric value to represent supplied value without loss. */ Datum numeric_trim_scale(PG_FUNCTION_ARGS) { Numeric num = PG_GETARG_NUMERIC(0); Numeric res; NumericVar result; if (NUMERIC_IS_NAN(num)) PG_RETURN_NUMERIC(make_result(&const_nan)); init_var_from_num(num, &result); result.dscale = get_min_scale(&result); res = make_result(&result); free_var(&result); PG_RETURN_NUMERIC(res); } /* ---------------------------------------------------------------------- * * Type conversion functions * * ---------------------------------------------------------------------- */ Datum int4_numeric(PG_FUNCTION_ARGS) { int32 val = PG_GETARG_INT32(0); Numeric res; NumericVar result; init_var(&result); int64_to_numericvar((int64) val, &result); res = make_result(&result); free_var(&result); PG_RETURN_NUMERIC(res); } int32 numeric_int4_opt_error(Numeric num, bool *have_error) { NumericVar x; int32 result; if (have_error) *have_error = false; /* XXX would it be better to return NULL? */ if (NUMERIC_IS_NAN(num)) { if (have_error) { *have_error = true; return 0; } else { ereport(ERROR, (errcode(ERRCODE_FEATURE_NOT_SUPPORTED), errmsg("cannot convert NaN to integer"))); } } /* Convert to variable format, then convert to int4 */ init_var_from_num(num, &x); if (!numericvar_to_int32(&x, &result)) { if (have_error) { *have_error = true; return 0; } else { ereport(ERROR, (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE), errmsg("integer out of range"))); } } return result; } Datum numeric_int4(PG_FUNCTION_ARGS) { Numeric num = PG_GETARG_NUMERIC(0); PG_RETURN_INT32(numeric_int4_opt_error(num, NULL)); } /* * Given a NumericVar, convert it to an int32. If the NumericVar * exceeds the range of an int32, false is returned, otherwise true is returned. * The input NumericVar is *not* free'd. */ static bool numericvar_to_int32(const NumericVar *var, int32 *result) { int64 val; if (!numericvar_to_int64(var, &val)) return false; if (unlikely(val < PG_INT32_MIN) || unlikely(val > PG_INT32_MAX)) return false; /* Down-convert to int4 */ *result = (int32) val; return true; } Datum int8_numeric(PG_FUNCTION_ARGS) { int64 val = PG_GETARG_INT64(0); Numeric res; NumericVar result; init_var(&result); int64_to_numericvar(val, &result); res = make_result(&result); free_var(&result); PG_RETURN_NUMERIC(res); } Datum numeric_int8(PG_FUNCTION_ARGS) { Numeric num = PG_GETARG_NUMERIC(0); NumericVar x; int64 result; /* XXX would it be better to return NULL? */ if (NUMERIC_IS_NAN(num)) ereport(ERROR, (errcode(ERRCODE_FEATURE_NOT_SUPPORTED), errmsg("cannot convert NaN to bigint"))); /* Convert to variable format and thence to int8 */ init_var_from_num(num, &x); if (!numericvar_to_int64(&x, &result)) ereport(ERROR, (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE), errmsg("bigint out of range"))); PG_RETURN_INT64(result); } Datum int2_numeric(PG_FUNCTION_ARGS) { int16 val = PG_GETARG_INT16(0); Numeric res; NumericVar result; init_var(&result); int64_to_numericvar((int64) val, &result); res = make_result(&result); free_var(&result); PG_RETURN_NUMERIC(res); } Datum numeric_int2(PG_FUNCTION_ARGS) { Numeric num = PG_GETARG_NUMERIC(0); NumericVar x; int64 val; int16 result; /* XXX would it be better to return NULL? */ if (NUMERIC_IS_NAN(num)) ereport(ERROR, (errcode(ERRCODE_FEATURE_NOT_SUPPORTED), errmsg("cannot convert NaN to smallint"))); /* Convert to variable format and thence to int8 */ init_var_from_num(num, &x); if (!numericvar_to_int64(&x, &val)) ereport(ERROR, (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE), errmsg("smallint out of range"))); if (unlikely(val < PG_INT16_MIN) || unlikely(val > PG_INT16_MAX)) ereport(ERROR, (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE), errmsg("smallint out of range"))); /* Down-convert to int2 */ result = (int16) val; PG_RETURN_INT16(result); } Datum float8_numeric(PG_FUNCTION_ARGS) { float8 val = PG_GETARG_FLOAT8(0); Numeric res; NumericVar result; char buf[DBL_DIG + 100]; if (isnan(val)) PG_RETURN_NUMERIC(make_result(&const_nan)); if (isinf(val)) ereport(ERROR, (errcode(ERRCODE_FEATURE_NOT_SUPPORTED), errmsg("cannot convert infinity to numeric"))); snprintf(buf, sizeof(buf), "%.*g", DBL_DIG, val); init_var(&result); /* Assume we need not worry about leading/trailing spaces */ (void) set_var_from_str(buf, buf, &result); res = make_result(&result); free_var(&result); PG_RETURN_NUMERIC(res); } Datum numeric_float8(PG_FUNCTION_ARGS) { Numeric num = PG_GETARG_NUMERIC(0); char *tmp; Datum result; if (NUMERIC_IS_NAN(num)) PG_RETURN_FLOAT8(get_float8_nan()); tmp = DatumGetCString(DirectFunctionCall1(numeric_out, NumericGetDatum(num))); result = DirectFunctionCall1(float8in, CStringGetDatum(tmp)); pfree(tmp); PG_RETURN_DATUM(result); } /* * Convert numeric to float8; if out of range, return +/- HUGE_VAL * * (internal helper function, not directly callable from SQL) */ Datum numeric_float8_no_overflow(PG_FUNCTION_ARGS) { Numeric num = PG_GETARG_NUMERIC(0); double val; if (NUMERIC_IS_NAN(num)) PG_RETURN_FLOAT8(get_float8_nan()); val = numeric_to_double_no_overflow(num); PG_RETURN_FLOAT8(val); } Datum float4_numeric(PG_FUNCTION_ARGS) { float4 val = PG_GETARG_FLOAT4(0); Numeric res; NumericVar result; char buf[FLT_DIG + 100]; if (isnan(val)) PG_RETURN_NUMERIC(make_result(&const_nan)); if (isinf(val)) ereport(ERROR, (errcode(ERRCODE_FEATURE_NOT_SUPPORTED), errmsg("cannot convert infinity to numeric"))); snprintf(buf, sizeof(buf), "%.*g", FLT_DIG, val); init_var(&result); /* Assume we need not worry about leading/trailing spaces */ (void) set_var_from_str(buf, buf, &result); res = make_result(&result); free_var(&result); PG_RETURN_NUMERIC(res); } Datum numeric_float4(PG_FUNCTION_ARGS) { Numeric num = PG_GETARG_NUMERIC(0); char *tmp; Datum result; if (NUMERIC_IS_NAN(num)) PG_RETURN_FLOAT4(get_float4_nan()); tmp = DatumGetCString(DirectFunctionCall1(numeric_out, NumericGetDatum(num))); result = DirectFunctionCall1(float4in, CStringGetDatum(tmp)); pfree(tmp); PG_RETURN_DATUM(result); } /* ---------------------------------------------------------------------- * * Aggregate functions * * The transition datatype for all these aggregates is declared as INTERNAL. * Actually, it's a pointer to a NumericAggState allocated in the aggregate * context. The digit buffers for the NumericVars will be there too. * * On platforms which support 128-bit integers some aggregates instead use a * 128-bit integer based transition datatype to speed up calculations. * * ---------------------------------------------------------------------- */ typedef struct NumericAggState { bool calcSumX2; /* if true, calculate sumX2 */ MemoryContext agg_context; /* context we're calculating in */ int64 N; /* count of processed numbers */ NumericSumAccum sumX; /* sum of processed numbers */ NumericSumAccum sumX2; /* sum of squares of processed numbers */ int maxScale; /* maximum scale seen so far */ int64 maxScaleCount; /* number of values seen with maximum scale */ int64 NaNcount; /* count of NaN values (not included in N!) */ } NumericAggState; /* * Prepare state data for a numeric aggregate function that needs to compute * sum, count and optionally sum of squares of the input. */ static NumericAggState * makeNumericAggState(FunctionCallInfo fcinfo, bool calcSumX2) { NumericAggState *state; MemoryContext agg_context; MemoryContext old_context; if (!AggCheckCallContext(fcinfo, &agg_context)) elog(ERROR, "aggregate function called in non-aggregate context"); old_context = MemoryContextSwitchTo(agg_context); state = (NumericAggState *) palloc0(sizeof(NumericAggState)); state->calcSumX2 = calcSumX2; state->agg_context = agg_context; MemoryContextSwitchTo(old_context); return state; } /* * Like makeNumericAggState(), but allocate the state in the current memory * context. */ static NumericAggState * makeNumericAggStateCurrentContext(bool calcSumX2) { NumericAggState *state; state = (NumericAggState *) palloc0(sizeof(NumericAggState)); state->calcSumX2 = calcSumX2; state->agg_context = CurrentMemoryContext; return state; } /* * Accumulate a new input value for numeric aggregate functions. */ static void do_numeric_accum(NumericAggState *state, Numeric newval) { NumericVar X; NumericVar X2; MemoryContext old_context; /* Count NaN inputs separately from all else */ if (NUMERIC_IS_NAN(newval)) { state->NaNcount++; return; } /* load processed number in short-lived context */ init_var_from_num(newval, &X); /* * Track the highest input dscale that we've seen, to support inverse * transitions (see do_numeric_discard). */ if (X.dscale > state->maxScale) { state->maxScale = X.dscale; state->maxScaleCount = 1; } else if (X.dscale == state->maxScale) state->maxScaleCount++; /* if we need X^2, calculate that in short-lived context */ if (state->calcSumX2) { init_var(&X2); mul_var(&X, &X, &X2, X.dscale * 2); } /* The rest of this needs to work in the aggregate context */ old_context = MemoryContextSwitchTo(state->agg_context); state->N++; /* Accumulate sums */ accum_sum_add(&(state->sumX), &X); if (state->calcSumX2) accum_sum_add(&(state->sumX2), &X2); MemoryContextSwitchTo(old_context); } /* * Attempt to remove an input value from the aggregated state. * * If the value cannot be removed then the function will return false; the * possible reasons for failing are described below. * * If we aggregate the values 1.01 and 2 then the result will be 3.01. * If we are then asked to un-aggregate the 1.01 then we must fail as we * won't be able to tell what the new aggregated value's dscale should be. * We don't want to return 2.00 (dscale = 2), since the sum's dscale would * have been zero if we'd really aggregated only 2. * * Note: alternatively, we could count the number of inputs with each possible * dscale (up to some sane limit). Not yet clear if it's worth the trouble. */ static bool do_numeric_discard(NumericAggState *state, Numeric newval) { NumericVar X; NumericVar X2; MemoryContext old_context; /* Count NaN inputs separately from all else */ if (NUMERIC_IS_NAN(newval)) { state->NaNcount--; return true; } /* load processed number in short-lived context */ init_var_from_num(newval, &X); /* * state->sumX's dscale is the maximum dscale of any of the inputs. * Removing the last input with that dscale would require us to recompute * the maximum dscale of the *remaining* inputs, which we cannot do unless * no more non-NaN inputs remain at all. So we report a failure instead, * and force the aggregation to be redone from scratch. */ if (X.dscale == state->maxScale) { if (state->maxScaleCount > 1 || state->maxScale == 0) { /* * Some remaining inputs have same dscale, or dscale hasn't gotten * above zero anyway */ state->maxScaleCount--; } else if (state->N == 1) { /* No remaining non-NaN inputs at all, so reset maxScale */ state->maxScale = 0; state->maxScaleCount = 0; } else { /* Correct new maxScale is uncertain, must fail */ return false; } } /* if we need X^2, calculate that in short-lived context */ if (state->calcSumX2) { init_var(&X2); mul_var(&X, &X, &X2, X.dscale * 2); } /* The rest of this needs to work in the aggregate context */ old_context = MemoryContextSwitchTo(state->agg_context); if (state->N-- > 1) { /* Negate X, to subtract it from the sum */ X.sign = (X.sign == NUMERIC_POS ? NUMERIC_NEG : NUMERIC_POS); accum_sum_add(&(state->sumX), &X); if (state->calcSumX2) { /* Negate X^2. X^2 is always positive */ X2.sign = NUMERIC_NEG; accum_sum_add(&(state->sumX2), &X2); } } else { /* Zero the sums */ Assert(state->N == 0); accum_sum_reset(&state->sumX); if (state->calcSumX2) accum_sum_reset(&state->sumX2); } MemoryContextSwitchTo(old_context); return true; } /* * Generic transition function for numeric aggregates that require sumX2. */ Datum numeric_accum(PG_FUNCTION_ARGS) { NumericAggState *state; state = PG_ARGISNULL(0) ? NULL : (NumericAggState *) PG_GETARG_POINTER(0); /* Create the state data on the first call */ if (state == NULL) state = makeNumericAggState(fcinfo, true); if (!PG_ARGISNULL(1)) do_numeric_accum(state, PG_GETARG_NUMERIC(1)); PG_RETURN_POINTER(state); } /* * Generic combine function for numeric aggregates which require sumX2 */ Datum numeric_combine(PG_FUNCTION_ARGS) { NumericAggState *state1; NumericAggState *state2; MemoryContext agg_context; MemoryContext old_context; if (!AggCheckCallContext(fcinfo, &agg_context)) elog(ERROR, "aggregate function called in non-aggregate context"); state1 = PG_ARGISNULL(0) ? NULL : (NumericAggState *) PG_GETARG_POINTER(0); state2 = PG_ARGISNULL(1) ? NULL : (NumericAggState *) PG_GETARG_POINTER(1); if (state2 == NULL) PG_RETURN_POINTER(state1); /* manually copy all fields from state2 to state1 */ if (state1 == NULL) { old_context = MemoryContextSwitchTo(agg_context); state1 = makeNumericAggStateCurrentContext(true); state1->N = state2->N; state1->NaNcount = state2->NaNcount; state1->maxScale = state2->maxScale; state1->maxScaleCount = state2->maxScaleCount; accum_sum_copy(&state1->sumX, &state2->sumX); accum_sum_copy(&state1->sumX2, &state2->sumX2); MemoryContextSwitchTo(old_context); PG_RETURN_POINTER(state1); } state1->N += state2->N; state1->NaNcount += state2->NaNcount; if (state2->N > 0) { /* * These are currently only needed for moving aggregates, but let's do * the right thing anyway... */ if (state2->maxScale > state1->maxScale) { state1->maxScale = state2->maxScale; state1->maxScaleCount = state2->maxScaleCount; } else if (state2->maxScale == state1->maxScale) state1->maxScaleCount += state2->maxScaleCount; /* The rest of this needs to work in the aggregate context */ old_context = MemoryContextSwitchTo(agg_context); /* Accumulate sums */ accum_sum_combine(&state1->sumX, &state2->sumX); accum_sum_combine(&state1->sumX2, &state2->sumX2); MemoryContextSwitchTo(old_context); } PG_RETURN_POINTER(state1); } /* * Generic transition function for numeric aggregates that don't require sumX2. */ Datum numeric_avg_accum(PG_FUNCTION_ARGS) { NumericAggState *state; state = PG_ARGISNULL(0) ? NULL : (NumericAggState *) PG_GETARG_POINTER(0); /* Create the state data on the first call */ if (state == NULL) state = makeNumericAggState(fcinfo, false); if (!PG_ARGISNULL(1)) do_numeric_accum(state, PG_GETARG_NUMERIC(1)); PG_RETURN_POINTER(state); } /* * Combine function for numeric aggregates which don't require sumX2 */ Datum numeric_avg_combine(PG_FUNCTION_ARGS) { NumericAggState *state1; NumericAggState *state2; MemoryContext agg_context; MemoryContext old_context; if (!AggCheckCallContext(fcinfo, &agg_context)) elog(ERROR, "aggregate function called in non-aggregate context"); state1 = PG_ARGISNULL(0) ? NULL : (NumericAggState *) PG_GETARG_POINTER(0); state2 = PG_ARGISNULL(1) ? NULL : (NumericAggState *) PG_GETARG_POINTER(1); if (state2 == NULL) PG_RETURN_POINTER(state1); /* manually copy all fields from state2 to state1 */ if (state1 == NULL) { old_context = MemoryContextSwitchTo(agg_context); state1 = makeNumericAggStateCurrentContext(false); state1->N = state2->N; state1->NaNcount = state2->NaNcount; state1->maxScale = state2->maxScale; state1->maxScaleCount = state2->maxScaleCount; accum_sum_copy(&state1->sumX, &state2->sumX); MemoryContextSwitchTo(old_context); PG_RETURN_POINTER(state1); } state1->N += state2->N; state1->NaNcount += state2->NaNcount; if (state2->N > 0) { /* * These are currently only needed for moving aggregates, but let's do * the right thing anyway... */ if (state2->maxScale > state1->maxScale) { state1->maxScale = state2->maxScale; state1->maxScaleCount = state2->maxScaleCount; } else if (state2->maxScale == state1->maxScale) state1->maxScaleCount += state2->maxScaleCount; /* The rest of this needs to work in the aggregate context */ old_context = MemoryContextSwitchTo(agg_context); /* Accumulate sums */ accum_sum_combine(&state1->sumX, &state2->sumX); MemoryContextSwitchTo(old_context); } PG_RETURN_POINTER(state1); } /* * numeric_avg_serialize * Serialize NumericAggState for numeric aggregates that don't require * sumX2. */ Datum numeric_avg_serialize(PG_FUNCTION_ARGS) { NumericAggState *state; StringInfoData buf; Datum temp; bytea *sumX; bytea *result; NumericVar tmp_var; /* Ensure we disallow calling when not in aggregate context */ if (!AggCheckCallContext(fcinfo, NULL)) elog(ERROR, "aggregate function called in non-aggregate context"); state = (NumericAggState *) PG_GETARG_POINTER(0); /* * This is a little wasteful since make_result converts the NumericVar * into a Numeric and numeric_send converts it back again. Is it worth * splitting the tasks in numeric_send into separate functions to stop * this? Doing so would also remove the fmgr call overhead. */ init_var(&tmp_var); accum_sum_final(&state->sumX, &tmp_var); temp = DirectFunctionCall1(numeric_send, NumericGetDatum(make_result(&tmp_var))); sumX = DatumGetByteaPP(temp); free_var(&tmp_var); pq_begintypsend(&buf); /* N */ pq_sendint64(&buf, state->N); /* sumX */ pq_sendbytes(&buf, VARDATA_ANY(sumX), VARSIZE_ANY_EXHDR(sumX)); /* maxScale */ pq_sendint32(&buf, state->maxScale); /* maxScaleCount */ pq_sendint64(&buf, state->maxScaleCount); /* NaNcount */ pq_sendint64(&buf, state->NaNcount); result = pq_endtypsend(&buf); PG_RETURN_BYTEA_P(result); } /* * numeric_avg_deserialize * Deserialize bytea into NumericAggState for numeric aggregates that * don't require sumX2. */ Datum numeric_avg_deserialize(PG_FUNCTION_ARGS) { bytea *sstate; NumericAggState *result; Datum temp; NumericVar tmp_var; StringInfoData buf; if (!AggCheckCallContext(fcinfo, NULL)) elog(ERROR, "aggregate function called in non-aggregate context"); sstate = PG_GETARG_BYTEA_PP(0); /* * Copy the bytea into a StringInfo so that we can "receive" it using the * standard recv-function infrastructure. */ initStringInfo(&buf); appendBinaryStringInfo(&buf, VARDATA_ANY(sstate), VARSIZE_ANY_EXHDR(sstate)); result = makeNumericAggStateCurrentContext(false); /* N */ result->N = pq_getmsgint64(&buf); /* sumX */ temp = DirectFunctionCall3(numeric_recv, PointerGetDatum(&buf), ObjectIdGetDatum(InvalidOid), Int32GetDatum(-1)); init_var_from_num(DatumGetNumeric(temp), &tmp_var); accum_sum_add(&(result->sumX), &tmp_var); /* maxScale */ result->maxScale = pq_getmsgint(&buf, 4); /* maxScaleCount */ result->maxScaleCount = pq_getmsgint64(&buf); /* NaNcount */ result->NaNcount = pq_getmsgint64(&buf); pq_getmsgend(&buf); pfree(buf.data); PG_RETURN_POINTER(result); } /* * numeric_serialize * Serialization function for NumericAggState for numeric aggregates that * require sumX2. */ Datum numeric_serialize(PG_FUNCTION_ARGS) { NumericAggState *state; StringInfoData buf; Datum temp; bytea *sumX; NumericVar tmp_var; bytea *sumX2; bytea *result; /* Ensure we disallow calling when not in aggregate context */ if (!AggCheckCallContext(fcinfo, NULL)) elog(ERROR, "aggregate function called in non-aggregate context"); state = (NumericAggState *) PG_GETARG_POINTER(0); /* * This is a little wasteful since make_result converts the NumericVar * into a Numeric and numeric_send converts it back again. Is it worth * splitting the tasks in numeric_send into separate functions to stop * this? Doing so would also remove the fmgr call overhead. */ init_var(&tmp_var); accum_sum_final(&state->sumX, &tmp_var); temp = DirectFunctionCall1(numeric_send, NumericGetDatum(make_result(&tmp_var))); sumX = DatumGetByteaPP(temp); accum_sum_final(&state->sumX2, &tmp_var); temp = DirectFunctionCall1(numeric_send, NumericGetDatum(make_result(&tmp_var))); sumX2 = DatumGetByteaPP(temp); free_var(&tmp_var); pq_begintypsend(&buf); /* N */ pq_sendint64(&buf, state->N); /* sumX */ pq_sendbytes(&buf, VARDATA_ANY(sumX), VARSIZE_ANY_EXHDR(sumX)); /* sumX2 */ pq_sendbytes(&buf, VARDATA_ANY(sumX2), VARSIZE_ANY_EXHDR(sumX2)); /* maxScale */ pq_sendint32(&buf, state->maxScale); /* maxScaleCount */ pq_sendint64(&buf, state->maxScaleCount); /* NaNcount */ pq_sendint64(&buf, state->NaNcount); result = pq_endtypsend(&buf); PG_RETURN_BYTEA_P(result); } /* * numeric_deserialize * Deserialization function for NumericAggState for numeric aggregates that * require sumX2. */ Datum numeric_deserialize(PG_FUNCTION_ARGS) { bytea *sstate; NumericAggState *result; Datum temp; NumericVar sumX_var; NumericVar sumX2_var; StringInfoData buf; if (!AggCheckCallContext(fcinfo, NULL)) elog(ERROR, "aggregate function called in non-aggregate context"); sstate = PG_GETARG_BYTEA_PP(0); /* * Copy the bytea into a StringInfo so that we can "receive" it using the * standard recv-function infrastructure. */ initStringInfo(&buf); appendBinaryStringInfo(&buf, VARDATA_ANY(sstate), VARSIZE_ANY_EXHDR(sstate)); result = makeNumericAggStateCurrentContext(false); /* N */ result->N = pq_getmsgint64(&buf); /* sumX */ temp = DirectFunctionCall3(numeric_recv, PointerGetDatum(&buf), ObjectIdGetDatum(InvalidOid), Int32GetDatum(-1)); init_var_from_num(DatumGetNumeric(temp), &sumX_var); accum_sum_add(&(result->sumX), &sumX_var); /* sumX2 */ temp = DirectFunctionCall3(numeric_recv, PointerGetDatum(&buf), ObjectIdGetDatum(InvalidOid), Int32GetDatum(-1)); init_var_from_num(DatumGetNumeric(temp), &sumX2_var); accum_sum_add(&(result->sumX2), &sumX2_var); /* maxScale */ result->maxScale = pq_getmsgint(&buf, 4); /* maxScaleCount */ result->maxScaleCount = pq_getmsgint64(&buf); /* NaNcount */ result->NaNcount = pq_getmsgint64(&buf); pq_getmsgend(&buf); pfree(buf.data); PG_RETURN_POINTER(result); } /* * Generic inverse transition function for numeric aggregates * (with or without requirement for X^2). */ Datum numeric_accum_inv(PG_FUNCTION_ARGS) { NumericAggState *state; state = PG_ARGISNULL(0) ? NULL : (NumericAggState *) PG_GETARG_POINTER(0); /* Should not get here with no state */ if (state == NULL) elog(ERROR, "numeric_accum_inv called with NULL state"); if (!PG_ARGISNULL(1)) { /* If we fail to perform the inverse transition, return NULL */ if (!do_numeric_discard(state, PG_GETARG_NUMERIC(1))) PG_RETURN_NULL(); } PG_RETURN_POINTER(state); } /* * Integer data types in general use Numeric accumulators to share code * and avoid risk of overflow. * * However for performance reasons optimized special-purpose accumulator * routines are used when possible. * * On platforms with 128-bit integer support, the 128-bit routines will be * used when sum(X) or sum(X*X) fit into 128-bit. * * For 16 and 32 bit inputs, the N and sum(X) fit into 64-bit so the 64-bit * accumulators will be used for SUM and AVG of these data types. */ #ifdef HAVE_INT128 typedef struct Int128AggState { bool calcSumX2; /* if true, calculate sumX2 */ int64 N; /* count of processed numbers */ int128 sumX; /* sum of processed numbers */ int128 sumX2; /* sum of squares of processed numbers */ } Int128AggState; /* * Prepare state data for a 128-bit aggregate function that needs to compute * sum, count and optionally sum of squares of the input. */ static Int128AggState * makeInt128AggState(FunctionCallInfo fcinfo, bool calcSumX2) { Int128AggState *state; MemoryContext agg_context; MemoryContext old_context; if (!AggCheckCallContext(fcinfo, &agg_context)) elog(ERROR, "aggregate function called in non-aggregate context"); old_context = MemoryContextSwitchTo(agg_context); state = (Int128AggState *) palloc0(sizeof(Int128AggState)); state->calcSumX2 = calcSumX2; MemoryContextSwitchTo(old_context); return state; } /* * Like makeInt128AggState(), but allocate the state in the current memory * context. */ static Int128AggState * makeInt128AggStateCurrentContext(bool calcSumX2) { Int128AggState *state; state = (Int128AggState *) palloc0(sizeof(Int128AggState)); state->calcSumX2 = calcSumX2; return state; } /* * Accumulate a new input value for 128-bit aggregate functions. */ static void do_int128_accum(Int128AggState *state, int128 newval) { if (state->calcSumX2) state->sumX2 += newval * newval; state->sumX += newval; state->N++; } /* * Remove an input value from the aggregated state. */ static void do_int128_discard(Int128AggState *state, int128 newval) { if (state->calcSumX2) state->sumX2 -= newval * newval; state->sumX -= newval; state->N--; } typedef Int128AggState PolyNumAggState; #define makePolyNumAggState makeInt128AggState #define makePolyNumAggStateCurrentContext makeInt128AggStateCurrentContext #else typedef NumericAggState PolyNumAggState; #define makePolyNumAggState makeNumericAggState #define makePolyNumAggStateCurrentContext makeNumericAggStateCurrentContext #endif Datum int2_accum(PG_FUNCTION_ARGS) { PolyNumAggState *state; state = PG_ARGISNULL(0) ? NULL : (PolyNumAggState *) PG_GETARG_POINTER(0); /* Create the state data on the first call */ if (state == NULL) state = makePolyNumAggState(fcinfo, true); if (!PG_ARGISNULL(1)) { #ifdef HAVE_INT128 do_int128_accum(state, (int128) PG_GETARG_INT16(1)); #else Numeric newval; newval = DatumGetNumeric(DirectFunctionCall1(int2_numeric, PG_GETARG_DATUM(1))); do_numeric_accum(state, newval); #endif } PG_RETURN_POINTER(state); } Datum int4_accum(PG_FUNCTION_ARGS) { PolyNumAggState *state; state = PG_ARGISNULL(0) ? NULL : (PolyNumAggState *) PG_GETARG_POINTER(0); /* Create the state data on the first call */ if (state == NULL) state = makePolyNumAggState(fcinfo, true); if (!PG_ARGISNULL(1)) { #ifdef HAVE_INT128 do_int128_accum(state, (int128) PG_GETARG_INT32(1)); #else Numeric newval; newval = DatumGetNumeric(DirectFunctionCall1(int4_numeric, PG_GETARG_DATUM(1))); do_numeric_accum(state, newval); #endif } PG_RETURN_POINTER(state); } Datum int8_accum(PG_FUNCTION_ARGS) { NumericAggState *state; state = PG_ARGISNULL(0) ? NULL : (NumericAggState *) PG_GETARG_POINTER(0); /* Create the state data on the first call */ if (state == NULL) state = makeNumericAggState(fcinfo, true); if (!PG_ARGISNULL(1)) { Numeric newval; newval = DatumGetNumeric(DirectFunctionCall1(int8_numeric, PG_GETARG_DATUM(1))); do_numeric_accum(state, newval); } PG_RETURN_POINTER(state); } /* * Combine function for numeric aggregates which require sumX2 */ Datum numeric_poly_combine(PG_FUNCTION_ARGS) { PolyNumAggState *state1; PolyNumAggState *state2; MemoryContext agg_context; MemoryContext old_context; if (!AggCheckCallContext(fcinfo, &agg_context)) elog(ERROR, "aggregate function called in non-aggregate context"); state1 = PG_ARGISNULL(0) ? NULL : (PolyNumAggState *) PG_GETARG_POINTER(0); state2 = PG_ARGISNULL(1) ? NULL : (PolyNumAggState *) PG_GETARG_POINTER(1); if (state2 == NULL) PG_RETURN_POINTER(state1); /* manually copy all fields from state2 to state1 */ if (state1 == NULL) { old_context = MemoryContextSwitchTo(agg_context); state1 = makePolyNumAggState(fcinfo, true); state1->N = state2->N; #ifdef HAVE_INT128 state1->sumX = state2->sumX; state1->sumX2 = state2->sumX2; #else accum_sum_copy(&state1->sumX, &state2->sumX); accum_sum_copy(&state1->sumX2, &state2->sumX2); #endif MemoryContextSwitchTo(old_context); PG_RETURN_POINTER(state1); } if (state2->N > 0) { state1->N += state2->N; #ifdef HAVE_INT128 state1->sumX += state2->sumX; state1->sumX2 += state2->sumX2; #else /* The rest of this needs to work in the aggregate context */ old_context = MemoryContextSwitchTo(agg_context); /* Accumulate sums */ accum_sum_combine(&state1->sumX, &state2->sumX); accum_sum_combine(&state1->sumX2, &state2->sumX2); MemoryContextSwitchTo(old_context); #endif } PG_RETURN_POINTER(state1); } /* * numeric_poly_serialize * Serialize PolyNumAggState into bytea for aggregate functions which * require sumX2. */ Datum numeric_poly_serialize(PG_FUNCTION_ARGS) { PolyNumAggState *state; StringInfoData buf; bytea *sumX; bytea *sumX2; bytea *result; /* Ensure we disallow calling when not in aggregate context */ if (!AggCheckCallContext(fcinfo, NULL)) elog(ERROR, "aggregate function called in non-aggregate context"); state = (PolyNumAggState *) PG_GETARG_POINTER(0); /* * If the platform supports int128 then sumX and sumX2 will be a 128 bit * integer type. Here we'll convert that into a numeric type so that the * combine state is in the same format for both int128 enabled machines * and machines which don't support that type. The logic here is that one * day we might like to send these over to another server for further * processing and we want a standard format to work with. */ { Datum temp; NumericVar num; init_var(&num); #ifdef HAVE_INT128 int128_to_numericvar(state->sumX, &num); #else accum_sum_final(&state->sumX, &num); #endif temp = DirectFunctionCall1(numeric_send, NumericGetDatum(make_result(&num))); sumX = DatumGetByteaPP(temp); #ifdef HAVE_INT128 int128_to_numericvar(state->sumX2, &num); #else accum_sum_final(&state->sumX2, &num); #endif temp = DirectFunctionCall1(numeric_send, NumericGetDatum(make_result(&num))); sumX2 = DatumGetByteaPP(temp); free_var(&num); } pq_begintypsend(&buf); /* N */ pq_sendint64(&buf, state->N); /* sumX */ pq_sendbytes(&buf, VARDATA_ANY(sumX), VARSIZE_ANY_EXHDR(sumX)); /* sumX2 */ pq_sendbytes(&buf, VARDATA_ANY(sumX2), VARSIZE_ANY_EXHDR(sumX2)); result = pq_endtypsend(&buf); PG_RETURN_BYTEA_P(result); } /* * numeric_poly_deserialize * Deserialize PolyNumAggState from bytea for aggregate functions which * require sumX2. */ Datum numeric_poly_deserialize(PG_FUNCTION_ARGS) { bytea *sstate; PolyNumAggState *result; Datum sumX; NumericVar sumX_var; Datum sumX2; NumericVar sumX2_var; StringInfoData buf; if (!AggCheckCallContext(fcinfo, NULL)) elog(ERROR, "aggregate function called in non-aggregate context"); sstate = PG_GETARG_BYTEA_PP(0); /* * Copy the bytea into a StringInfo so that we can "receive" it using the * standard recv-function infrastructure. */ initStringInfo(&buf); appendBinaryStringInfo(&buf, VARDATA_ANY(sstate), VARSIZE_ANY_EXHDR(sstate)); result = makePolyNumAggStateCurrentContext(false); /* N */ result->N = pq_getmsgint64(&buf); /* sumX */ sumX = DirectFunctionCall3(numeric_recv, PointerGetDatum(&buf), ObjectIdGetDatum(InvalidOid), Int32GetDatum(-1)); /* sumX2 */ sumX2 = DirectFunctionCall3(numeric_recv, PointerGetDatum(&buf), ObjectIdGetDatum(InvalidOid), Int32GetDatum(-1)); init_var_from_num(DatumGetNumeric(sumX), &sumX_var); #ifdef HAVE_INT128 numericvar_to_int128(&sumX_var, &result->sumX); #else accum_sum_add(&result->sumX, &sumX_var); #endif init_var_from_num(DatumGetNumeric(sumX2), &sumX2_var); #ifdef HAVE_INT128 numericvar_to_int128(&sumX2_var, &result->sumX2); #else accum_sum_add(&result->sumX2, &sumX2_var); #endif pq_getmsgend(&buf); pfree(buf.data); PG_RETURN_POINTER(result); } /* * Transition function for int8 input when we don't need sumX2. */ Datum int8_avg_accum(PG_FUNCTION_ARGS) { PolyNumAggState *state; state = PG_ARGISNULL(0) ? NULL : (PolyNumAggState *) PG_GETARG_POINTER(0); /* Create the state data on the first call */ if (state == NULL) state = makePolyNumAggState(fcinfo, false); if (!PG_ARGISNULL(1)) { #ifdef HAVE_INT128 do_int128_accum(state, (int128) PG_GETARG_INT64(1)); #else Numeric newval; newval = DatumGetNumeric(DirectFunctionCall1(int8_numeric, PG_GETARG_DATUM(1))); do_numeric_accum(state, newval); #endif } PG_RETURN_POINTER(state); } /* * Combine function for PolyNumAggState for aggregates which don't require * sumX2 */ Datum int8_avg_combine(PG_FUNCTION_ARGS) { PolyNumAggState *state1; PolyNumAggState *state2; MemoryContext agg_context; MemoryContext old_context; if (!AggCheckCallContext(fcinfo, &agg_context)) elog(ERROR, "aggregate function called in non-aggregate context"); state1 = PG_ARGISNULL(0) ? NULL : (PolyNumAggState *) PG_GETARG_POINTER(0); state2 = PG_ARGISNULL(1) ? NULL : (PolyNumAggState *) PG_GETARG_POINTER(1); if (state2 == NULL) PG_RETURN_POINTER(state1); /* manually copy all fields from state2 to state1 */ if (state1 == NULL) { old_context = MemoryContextSwitchTo(agg_context); state1 = makePolyNumAggState(fcinfo, false); state1->N = state2->N; #ifdef HAVE_INT128 state1->sumX = state2->sumX; #else accum_sum_copy(&state1->sumX, &state2->sumX); #endif MemoryContextSwitchTo(old_context); PG_RETURN_POINTER(state1); } if (state2->N > 0) { state1->N += state2->N; #ifdef HAVE_INT128 state1->sumX += state2->sumX; #else /* The rest of this needs to work in the aggregate context */ old_context = MemoryContextSwitchTo(agg_context); /* Accumulate sums */ accum_sum_combine(&state1->sumX, &state2->sumX); MemoryContextSwitchTo(old_context); #endif } PG_RETURN_POINTER(state1); } /* * int8_avg_serialize * Serialize PolyNumAggState into bytea using the standard * recv-function infrastructure. */ Datum int8_avg_serialize(PG_FUNCTION_ARGS) { PolyNumAggState *state; StringInfoData buf; bytea *sumX; bytea *result; /* Ensure we disallow calling when not in aggregate context */ if (!AggCheckCallContext(fcinfo, NULL)) elog(ERROR, "aggregate function called in non-aggregate context"); state = (PolyNumAggState *) PG_GETARG_POINTER(0); /* * If the platform supports int128 then sumX will be a 128 integer type. * Here we'll convert that into a numeric type so that the combine state * is in the same format for both int128 enabled machines and machines * which don't support that type. The logic here is that one day we might * like to send these over to another server for further processing and we * want a standard format to work with. */ { Datum temp; NumericVar num; init_var(&num); #ifdef HAVE_INT128 int128_to_numericvar(state->sumX, &num); #else accum_sum_final(&state->sumX, &num); #endif temp = DirectFunctionCall1(numeric_send, NumericGetDatum(make_result(&num))); sumX = DatumGetByteaPP(temp); free_var(&num); } pq_begintypsend(&buf); /* N */ pq_sendint64(&buf, state->N); /* sumX */ pq_sendbytes(&buf, VARDATA_ANY(sumX), VARSIZE_ANY_EXHDR(sumX)); result = pq_endtypsend(&buf); PG_RETURN_BYTEA_P(result); } /* * int8_avg_deserialize * Deserialize bytea back into PolyNumAggState. */ Datum int8_avg_deserialize(PG_FUNCTION_ARGS) { bytea *sstate; PolyNumAggState *result; StringInfoData buf; Datum temp; NumericVar num; if (!AggCheckCallContext(fcinfo, NULL)) elog(ERROR, "aggregate function called in non-aggregate context"); sstate = PG_GETARG_BYTEA_PP(0); /* * Copy the bytea into a StringInfo so that we can "receive" it using the * standard recv-function infrastructure. */ initStringInfo(&buf); appendBinaryStringInfo(&buf, VARDATA_ANY(sstate), VARSIZE_ANY_EXHDR(sstate)); result = makePolyNumAggStateCurrentContext(false); /* N */ result->N = pq_getmsgint64(&buf); /* sumX */ temp = DirectFunctionCall3(numeric_recv, PointerGetDatum(&buf), ObjectIdGetDatum(InvalidOid), Int32GetDatum(-1)); init_var_from_num(DatumGetNumeric(temp), &num); #ifdef HAVE_INT128 numericvar_to_int128(&num, &result->sumX); #else accum_sum_add(&result->sumX, &num); #endif pq_getmsgend(&buf); pfree(buf.data); PG_RETURN_POINTER(result); } /* * Inverse transition functions to go with the above. */ Datum int2_accum_inv(PG_FUNCTION_ARGS) { PolyNumAggState *state; state = PG_ARGISNULL(0) ? NULL : (PolyNumAggState *) PG_GETARG_POINTER(0); /* Should not get here with no state */ if (state == NULL) elog(ERROR, "int2_accum_inv called with NULL state"); if (!PG_ARGISNULL(1)) { #ifdef HAVE_INT128 do_int128_discard(state, (int128) PG_GETARG_INT16(1)); #else Numeric newval; newval = DatumGetNumeric(DirectFunctionCall1(int2_numeric, PG_GETARG_DATUM(1))); /* Should never fail, all inputs have dscale 0 */ if (!do_numeric_discard(state, newval)) elog(ERROR, "do_numeric_discard failed unexpectedly"); #endif } PG_RETURN_POINTER(state); } Datum int4_accum_inv(PG_FUNCTION_ARGS) { PolyNumAggState *state; state = PG_ARGISNULL(0) ? NULL : (PolyNumAggState *) PG_GETARG_POINTER(0); /* Should not get here with no state */ if (state == NULL) elog(ERROR, "int4_accum_inv called with NULL state"); if (!PG_ARGISNULL(1)) { #ifdef HAVE_INT128 do_int128_discard(state, (int128) PG_GETARG_INT32(1)); #else Numeric newval; newval = DatumGetNumeric(DirectFunctionCall1(int4_numeric, PG_GETARG_DATUM(1))); /* Should never fail, all inputs have dscale 0 */ if (!do_numeric_discard(state, newval)) elog(ERROR, "do_numeric_discard failed unexpectedly"); #endif } PG_RETURN_POINTER(state); } Datum int8_accum_inv(PG_FUNCTION_ARGS) { NumericAggState *state; state = PG_ARGISNULL(0) ? NULL : (NumericAggState *) PG_GETARG_POINTER(0); /* Should not get here with no state */ if (state == NULL) elog(ERROR, "int8_accum_inv called with NULL state"); if (!PG_ARGISNULL(1)) { Numeric newval; newval = DatumGetNumeric(DirectFunctionCall1(int8_numeric, PG_GETARG_DATUM(1))); /* Should never fail, all inputs have dscale 0 */ if (!do_numeric_discard(state, newval)) elog(ERROR, "do_numeric_discard failed unexpectedly"); } PG_RETURN_POINTER(state); } Datum int8_avg_accum_inv(PG_FUNCTION_ARGS) { PolyNumAggState *state; state = PG_ARGISNULL(0) ? NULL : (PolyNumAggState *) PG_GETARG_POINTER(0); /* Should not get here with no state */ if (state == NULL) elog(ERROR, "int8_avg_accum_inv called with NULL state"); if (!PG_ARGISNULL(1)) { #ifdef HAVE_INT128 do_int128_discard(state, (int128) PG_GETARG_INT64(1)); #else Numeric newval; newval = DatumGetNumeric(DirectFunctionCall1(int8_numeric, PG_GETARG_DATUM(1))); /* Should never fail, all inputs have dscale 0 */ if (!do_numeric_discard(state, newval)) elog(ERROR, "do_numeric_discard failed unexpectedly"); #endif } PG_RETURN_POINTER(state); } Datum numeric_poly_sum(PG_FUNCTION_ARGS) { #ifdef HAVE_INT128 PolyNumAggState *state; Numeric res; NumericVar result; state = PG_ARGISNULL(0) ? NULL : (PolyNumAggState *) PG_GETARG_POINTER(0); /* If there were no non-null inputs, return NULL */ if (state == NULL || state->N == 0) PG_RETURN_NULL(); init_var(&result); int128_to_numericvar(state->sumX, &result); res = make_result(&result); free_var(&result); PG_RETURN_NUMERIC(res); #else return numeric_sum(fcinfo); #endif } Datum numeric_poly_avg(PG_FUNCTION_ARGS) { #ifdef HAVE_INT128 PolyNumAggState *state; NumericVar result; Datum countd, sumd; state = PG_ARGISNULL(0) ? NULL : (PolyNumAggState *) PG_GETARG_POINTER(0); /* If there were no non-null inputs, return NULL */ if (state == NULL || state->N == 0) PG_RETURN_NULL(); init_var(&result); int128_to_numericvar(state->sumX, &result); countd = DirectFunctionCall1(int8_numeric, Int64GetDatumFast(state->N)); sumd = NumericGetDatum(make_result(&result)); free_var(&result); PG_RETURN_DATUM(DirectFunctionCall2(numeric_div, sumd, countd)); #else return numeric_avg(fcinfo); #endif } Datum numeric_avg(PG_FUNCTION_ARGS) { NumericAggState *state; Datum N_datum; Datum sumX_datum; NumericVar sumX_var; state = PG_ARGISNULL(0) ? NULL : (NumericAggState *) PG_GETARG_POINTER(0); /* If there were no non-null inputs, return NULL */ if (state == NULL || (state->N + state->NaNcount) == 0) PG_RETURN_NULL(); if (state->NaNcount > 0) /* there was at least one NaN input */ PG_RETURN_NUMERIC(make_result(&const_nan)); N_datum = DirectFunctionCall1(int8_numeric, Int64GetDatum(state->N)); init_var(&sumX_var); accum_sum_final(&state->sumX, &sumX_var); sumX_datum = NumericGetDatum(make_result(&sumX_var)); free_var(&sumX_var); PG_RETURN_DATUM(DirectFunctionCall2(numeric_div, sumX_datum, N_datum)); } Datum numeric_sum(PG_FUNCTION_ARGS) { NumericAggState *state; NumericVar sumX_var; Numeric result; state = PG_ARGISNULL(0) ? NULL : (NumericAggState *) PG_GETARG_POINTER(0); /* If there were no non-null inputs, return NULL */ if (state == NULL || (state->N + state->NaNcount) == 0) PG_RETURN_NULL(); if (state->NaNcount > 0) /* there was at least one NaN input */ PG_RETURN_NUMERIC(make_result(&const_nan)); init_var(&sumX_var); accum_sum_final(&state->sumX, &sumX_var); result = make_result(&sumX_var); free_var(&sumX_var); PG_RETURN_NUMERIC(result); } /* * Workhorse routine for the standard deviance and variance * aggregates. 'state' is aggregate's transition state. * 'variance' specifies whether we should calculate the * variance or the standard deviation. 'sample' indicates whether the * caller is interested in the sample or the population * variance/stddev. * * If appropriate variance statistic is undefined for the input, * *is_null is set to true and NULL is returned. */ static Numeric numeric_stddev_internal(NumericAggState *state, bool variance, bool sample, bool *is_null) { Numeric res; NumericVar vN, vsumX, vsumX2, vNminus1; const NumericVar *comp; int rscale; /* Deal with empty input and NaN-input cases */ if (state == NULL || (state->N + state->NaNcount) == 0) { *is_null = true; return NULL; } *is_null = false; if (state->NaNcount > 0) return make_result(&const_nan); init_var(&vN); init_var(&vsumX); init_var(&vsumX2); int64_to_numericvar(state->N, &vN); accum_sum_final(&(state->sumX), &vsumX); accum_sum_final(&(state->sumX2), &vsumX2); /* * Sample stddev and variance are undefined when N <= 1; population stddev * is undefined when N == 0. Return NULL in either case. */ if (sample) comp = &const_one; else comp = &const_zero; if (cmp_var(&vN, comp) <= 0) { *is_null = true; return NULL; } init_var(&vNminus1); sub_var(&vN, &const_one, &vNminus1); /* compute rscale for mul_var calls */ rscale = vsumX.dscale * 2; mul_var(&vsumX, &vsumX, &vsumX, rscale); /* vsumX = sumX * sumX */ mul_var(&vN, &vsumX2, &vsumX2, rscale); /* vsumX2 = N * sumX2 */ sub_var(&vsumX2, &vsumX, &vsumX2); /* N * sumX2 - sumX * sumX */ if (cmp_var(&vsumX2, &const_zero) <= 0) { /* Watch out for roundoff error producing a negative numerator */ res = make_result(&const_zero); } else { if (sample) mul_var(&vN, &vNminus1, &vNminus1, 0); /* N * (N - 1) */ else mul_var(&vN, &vN, &vNminus1, 0); /* N * N */ rscale = select_div_scale(&vsumX2, &vNminus1); div_var(&vsumX2, &vNminus1, &vsumX, rscale, true); /* variance */ if (!variance) sqrt_var(&vsumX, &vsumX, rscale); /* stddev */ res = make_result(&vsumX); } free_var(&vNminus1); free_var(&vsumX); free_var(&vsumX2); return res; } Datum numeric_var_samp(PG_FUNCTION_ARGS) { NumericAggState *state; Numeric res; bool is_null; state = PG_ARGISNULL(0) ? NULL : (NumericAggState *) PG_GETARG_POINTER(0); res = numeric_stddev_internal(state, true, true, &is_null); if (is_null) PG_RETURN_NULL(); else PG_RETURN_NUMERIC(res); } Datum numeric_stddev_samp(PG_FUNCTION_ARGS) { NumericAggState *state; Numeric res; bool is_null; state = PG_ARGISNULL(0) ? NULL : (NumericAggState *) PG_GETARG_POINTER(0); res = numeric_stddev_internal(state, false, true, &is_null); if (is_null) PG_RETURN_NULL(); else PG_RETURN_NUMERIC(res); } Datum numeric_var_pop(PG_FUNCTION_ARGS) { NumericAggState *state; Numeric res; bool is_null; state = PG_ARGISNULL(0) ? NULL : (NumericAggState *) PG_GETARG_POINTER(0); res = numeric_stddev_internal(state, true, false, &is_null); if (is_null) PG_RETURN_NULL(); else PG_RETURN_NUMERIC(res); } Datum numeric_stddev_pop(PG_FUNCTION_ARGS) { NumericAggState *state; Numeric res; bool is_null; state = PG_ARGISNULL(0) ? NULL : (NumericAggState *) PG_GETARG_POINTER(0); res = numeric_stddev_internal(state, false, false, &is_null); if (is_null) PG_RETURN_NULL(); else PG_RETURN_NUMERIC(res); } #ifdef HAVE_INT128 static Numeric numeric_poly_stddev_internal(Int128AggState *state, bool variance, bool sample, bool *is_null) { NumericAggState numstate; Numeric res; /* Initialize an empty agg state */ memset(&numstate, 0, sizeof(NumericAggState)); if (state) { NumericVar tmp_var; numstate.N = state->N; init_var(&tmp_var); int128_to_numericvar(state->sumX, &tmp_var); accum_sum_add(&numstate.sumX, &tmp_var); int128_to_numericvar(state->sumX2, &tmp_var); accum_sum_add(&numstate.sumX2, &tmp_var); free_var(&tmp_var); } res = numeric_stddev_internal(&numstate, variance, sample, is_null); if (numstate.sumX.ndigits > 0) { pfree(numstate.sumX.pos_digits); pfree(numstate.sumX.neg_digits); } if (numstate.sumX2.ndigits > 0) { pfree(numstate.sumX2.pos_digits); pfree(numstate.sumX2.neg_digits); } return res; } #endif Datum numeric_poly_var_samp(PG_FUNCTION_ARGS) { #ifdef HAVE_INT128 PolyNumAggState *state; Numeric res; bool is_null; state = PG_ARGISNULL(0) ? NULL : (PolyNumAggState *) PG_GETARG_POINTER(0); res = numeric_poly_stddev_internal(state, true, true, &is_null); if (is_null) PG_RETURN_NULL(); else PG_RETURN_NUMERIC(res); #else return numeric_var_samp(fcinfo); #endif } Datum numeric_poly_stddev_samp(PG_FUNCTION_ARGS) { #ifdef HAVE_INT128 PolyNumAggState *state; Numeric res; bool is_null; state = PG_ARGISNULL(0) ? NULL : (PolyNumAggState *) PG_GETARG_POINTER(0); res = numeric_poly_stddev_internal(state, false, true, &is_null); if (is_null) PG_RETURN_NULL(); else PG_RETURN_NUMERIC(res); #else return numeric_stddev_samp(fcinfo); #endif } Datum numeric_poly_var_pop(PG_FUNCTION_ARGS) { #ifdef HAVE_INT128 PolyNumAggState *state; Numeric res; bool is_null; state = PG_ARGISNULL(0) ? NULL : (PolyNumAggState *) PG_GETARG_POINTER(0); res = numeric_poly_stddev_internal(state, true, false, &is_null); if (is_null) PG_RETURN_NULL(); else PG_RETURN_NUMERIC(res); #else return numeric_var_pop(fcinfo); #endif } Datum numeric_poly_stddev_pop(PG_FUNCTION_ARGS) { #ifdef HAVE_INT128 PolyNumAggState *state; Numeric res; bool is_null; state = PG_ARGISNULL(0) ? NULL : (PolyNumAggState *) PG_GETARG_POINTER(0); res = numeric_poly_stddev_internal(state, false, false, &is_null); if (is_null) PG_RETURN_NULL(); else PG_RETURN_NUMERIC(res); #else return numeric_stddev_pop(fcinfo); #endif } /* * SUM transition functions for integer datatypes. * * To avoid overflow, we use accumulators wider than the input datatype. * A Numeric accumulator is needed for int8 input; for int4 and int2 * inputs, we use int8 accumulators which should be sufficient for practical * purposes. (The latter two therefore don't really belong in this file, * but we keep them here anyway.) * * Because SQL defines the SUM() of no values to be NULL, not zero, * the initial condition of the transition data value needs to be NULL. This * means we can't rely on ExecAgg to automatically insert the first non-null * data value into the transition data: it doesn't know how to do the type * conversion. The upshot is that these routines have to be marked non-strict * and handle substitution of the first non-null input themselves. * * Note: these functions are used only in plain aggregation mode. * In moving-aggregate mode, we use intX_avg_accum and intX_avg_accum_inv. */ Datum int2_sum(PG_FUNCTION_ARGS) { int64 newval; if (PG_ARGISNULL(0)) { /* No non-null input seen so far... */ if (PG_ARGISNULL(1)) PG_RETURN_NULL(); /* still no non-null */ /* This is the first non-null input. */ newval = (int64) PG_GETARG_INT16(1); PG_RETURN_INT64(newval); } /* * If we're invoked as an aggregate, we can cheat and modify our first * parameter in-place to avoid palloc overhead. If not, we need to return * the new value of the transition variable. (If int8 is pass-by-value, * then of course this is useless as well as incorrect, so just ifdef it * out.) */ #ifndef USE_FLOAT8_BYVAL /* controls int8 too */ if (AggCheckCallContext(fcinfo, NULL)) { int64 *oldsum = (int64 *) PG_GETARG_POINTER(0); /* Leave the running sum unchanged in the new input is null */ if (!PG_ARGISNULL(1)) *oldsum = *oldsum + (int64) PG_GETARG_INT16(1); PG_RETURN_POINTER(oldsum); } else #endif { int64 oldsum = PG_GETARG_INT64(0); /* Leave sum unchanged if new input is null. */ if (PG_ARGISNULL(1)) PG_RETURN_INT64(oldsum); /* OK to do the addition. */ newval = oldsum + (int64) PG_GETARG_INT16(1); PG_RETURN_INT64(newval); } } Datum int4_sum(PG_FUNCTION_ARGS) { int64 newval; if (PG_ARGISNULL(0)) { /* No non-null input seen so far... */ if (PG_ARGISNULL(1)) PG_RETURN_NULL(); /* still no non-null */ /* This is the first non-null input. */ newval = (int64) PG_GETARG_INT32(1); PG_RETURN_INT64(newval); } /* * If we're invoked as an aggregate, we can cheat and modify our first * parameter in-place to avoid palloc overhead. If not, we need to return * the new value of the transition variable. (If int8 is pass-by-value, * then of course this is useless as well as incorrect, so just ifdef it * out.) */ #ifndef USE_FLOAT8_BYVAL /* controls int8 too */ if (AggCheckCallContext(fcinfo, NULL)) { int64 *oldsum = (int64 *) PG_GETARG_POINTER(0); /* Leave the running sum unchanged in the new input is null */ if (!PG_ARGISNULL(1)) *oldsum = *oldsum + (int64) PG_GETARG_INT32(1); PG_RETURN_POINTER(oldsum); } else #endif { int64 oldsum = PG_GETARG_INT64(0); /* Leave sum unchanged if new input is null. */ if (PG_ARGISNULL(1)) PG_RETURN_INT64(oldsum); /* OK to do the addition. */ newval = oldsum + (int64) PG_GETARG_INT32(1); PG_RETURN_INT64(newval); } } /* * Note: this function is obsolete, it's no longer used for SUM(int8). */ Datum int8_sum(PG_FUNCTION_ARGS) { Numeric oldsum; Datum newval; if (PG_ARGISNULL(0)) { /* No non-null input seen so far... */ if (PG_ARGISNULL(1)) PG_RETURN_NULL(); /* still no non-null */ /* This is the first non-null input. */ newval = DirectFunctionCall1(int8_numeric, PG_GETARG_DATUM(1)); PG_RETURN_DATUM(newval); } /* * Note that we cannot special-case the aggregate case here, as we do for * int2_sum and int4_sum: numeric is of variable size, so we cannot modify * our first parameter in-place. */ oldsum = PG_GETARG_NUMERIC(0); /* Leave sum unchanged if new input is null. */ if (PG_ARGISNULL(1)) PG_RETURN_NUMERIC(oldsum); /* OK to do the addition. */ newval = DirectFunctionCall1(int8_numeric, PG_GETARG_DATUM(1)); PG_RETURN_DATUM(DirectFunctionCall2(numeric_add, NumericGetDatum(oldsum), newval)); } /* * Routines for avg(int2) and avg(int4). The transition datatype * is a two-element int8 array, holding count and sum. * * These functions are also used for sum(int2) and sum(int4) when * operating in moving-aggregate mode, since for correct inverse transitions * we need to count the inputs. */ typedef struct Int8TransTypeData { int64 count; int64 sum; } Int8TransTypeData; Datum int2_avg_accum(PG_FUNCTION_ARGS) { ArrayType *transarray; int16 newval = PG_GETARG_INT16(1); Int8TransTypeData *transdata; /* * If we're invoked as an aggregate, we can cheat and modify our first * parameter in-place to reduce palloc overhead. Otherwise we need to make * a copy of it before scribbling on it. */ if (AggCheckCallContext(fcinfo, NULL)) transarray = PG_GETARG_ARRAYTYPE_P(0); else transarray = PG_GETARG_ARRAYTYPE_P_COPY(0); if (ARR_HASNULL(transarray) || ARR_SIZE(transarray) != ARR_OVERHEAD_NONULLS(1) + sizeof(Int8TransTypeData)) elog(ERROR, "expected 2-element int8 array"); transdata = (Int8TransTypeData *) ARR_DATA_PTR(transarray); transdata->count++; transdata->sum += newval; PG_RETURN_ARRAYTYPE_P(transarray); } Datum int4_avg_accum(PG_FUNCTION_ARGS) { ArrayType *transarray; int32 newval = PG_GETARG_INT32(1); Int8TransTypeData *transdata; /* * If we're invoked as an aggregate, we can cheat and modify our first * parameter in-place to reduce palloc overhead. Otherwise we need to make * a copy of it before scribbling on it. */ if (AggCheckCallContext(fcinfo, NULL)) transarray = PG_GETARG_ARRAYTYPE_P(0); else transarray = PG_GETARG_ARRAYTYPE_P_COPY(0); if (ARR_HASNULL(transarray) || ARR_SIZE(transarray) != ARR_OVERHEAD_NONULLS(1) + sizeof(Int8TransTypeData)) elog(ERROR, "expected 2-element int8 array"); transdata = (Int8TransTypeData *) ARR_DATA_PTR(transarray); transdata->count++; transdata->sum += newval; PG_RETURN_ARRAYTYPE_P(transarray); } Datum int4_avg_combine(PG_FUNCTION_ARGS) { ArrayType *transarray1; ArrayType *transarray2; Int8TransTypeData *state1; Int8TransTypeData *state2; if (!AggCheckCallContext(fcinfo, NULL)) elog(ERROR, "aggregate function called in non-aggregate context"); transarray1 = PG_GETARG_ARRAYTYPE_P(0); transarray2 = PG_GETARG_ARRAYTYPE_P(1); if (ARR_HASNULL(transarray1) || ARR_SIZE(transarray1) != ARR_OVERHEAD_NONULLS(1) + sizeof(Int8TransTypeData)) elog(ERROR, "expected 2-element int8 array"); if (ARR_HASNULL(transarray2) || ARR_SIZE(transarray2) != ARR_OVERHEAD_NONULLS(1) + sizeof(Int8TransTypeData)) elog(ERROR, "expected 2-element int8 array"); state1 = (Int8TransTypeData *) ARR_DATA_PTR(transarray1); state2 = (Int8TransTypeData *) ARR_DATA_PTR(transarray2); state1->count += state2->count; state1->sum += state2->sum; PG_RETURN_ARRAYTYPE_P(transarray1); } Datum int2_avg_accum_inv(PG_FUNCTION_ARGS) { ArrayType *transarray; int16 newval = PG_GETARG_INT16(1); Int8TransTypeData *transdata; /* * If we're invoked as an aggregate, we can cheat and modify our first * parameter in-place to reduce palloc overhead. Otherwise we need to make * a copy of it before scribbling on it. */ if (AggCheckCallContext(fcinfo, NULL)) transarray = PG_GETARG_ARRAYTYPE_P(0); else transarray = PG_GETARG_ARRAYTYPE_P_COPY(0); if (ARR_HASNULL(transarray) || ARR_SIZE(transarray) != ARR_OVERHEAD_NONULLS(1) + sizeof(Int8TransTypeData)) elog(ERROR, "expected 2-element int8 array"); transdata = (Int8TransTypeData *) ARR_DATA_PTR(transarray); transdata->count--; transdata->sum -= newval; PG_RETURN_ARRAYTYPE_P(transarray); } Datum int4_avg_accum_inv(PG_FUNCTION_ARGS) { ArrayType *transarray; int32 newval = PG_GETARG_INT32(1); Int8TransTypeData *transdata; /* * If we're invoked as an aggregate, we can cheat and modify our first * parameter in-place to reduce palloc overhead. Otherwise we need to make * a copy of it before scribbling on it. */ if (AggCheckCallContext(fcinfo, NULL)) transarray = PG_GETARG_ARRAYTYPE_P(0); else transarray = PG_GETARG_ARRAYTYPE_P_COPY(0); if (ARR_HASNULL(transarray) || ARR_SIZE(transarray) != ARR_OVERHEAD_NONULLS(1) + sizeof(Int8TransTypeData)) elog(ERROR, "expected 2-element int8 array"); transdata = (Int8TransTypeData *) ARR_DATA_PTR(transarray); transdata->count--; transdata->sum -= newval; PG_RETURN_ARRAYTYPE_P(transarray); } Datum int8_avg(PG_FUNCTION_ARGS) { ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0); Int8TransTypeData *transdata; Datum countd, sumd; if (ARR_HASNULL(transarray) || ARR_SIZE(transarray) != ARR_OVERHEAD_NONULLS(1) + sizeof(Int8TransTypeData)) elog(ERROR, "expected 2-element int8 array"); transdata = (Int8TransTypeData *) ARR_DATA_PTR(transarray); /* SQL defines AVG of no values to be NULL */ if (transdata->count == 0) PG_RETURN_NULL(); countd = DirectFunctionCall1(int8_numeric, Int64GetDatumFast(transdata->count)); sumd = DirectFunctionCall1(int8_numeric, Int64GetDatumFast(transdata->sum)); PG_RETURN_DATUM(DirectFunctionCall2(numeric_div, sumd, countd)); } /* * SUM(int2) and SUM(int4) both return int8, so we can use this * final function for both. */ Datum int2int4_sum(PG_FUNCTION_ARGS) { ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0); Int8TransTypeData *transdata; if (ARR_HASNULL(transarray) || ARR_SIZE(transarray) != ARR_OVERHEAD_NONULLS(1) + sizeof(Int8TransTypeData)) elog(ERROR, "expected 2-element int8 array"); transdata = (Int8TransTypeData *) ARR_DATA_PTR(transarray); /* SQL defines SUM of no values to be NULL */ if (transdata->count == 0) PG_RETURN_NULL(); PG_RETURN_DATUM(Int64GetDatumFast(transdata->sum)); } /* ---------------------------------------------------------------------- * * Debug support * * ---------------------------------------------------------------------- */ #ifdef NUMERIC_DEBUG /* * dump_numeric() - Dump a value in the db storage format for debugging */ static void dump_numeric(const char *str, Numeric num) { NumericDigit *digits = NUMERIC_DIGITS(num); int ndigits; int i; ndigits = NUMERIC_NDIGITS(num); printf("%s: NUMERIC w=%d d=%d ", str, NUMERIC_WEIGHT(num), NUMERIC_DSCALE(num)); switch (NUMERIC_SIGN(num)) { case NUMERIC_POS: printf("POS"); break; case NUMERIC_NEG: printf("NEG"); break; case NUMERIC_NAN: printf("NaN"); break; default: printf("SIGN=0x%x", NUMERIC_SIGN(num)); break; } for (i = 0; i < ndigits; i++) printf(" %0*d", DEC_DIGITS, digits[i]); printf("\n"); } /* * dump_var() - Dump a value in the variable format for debugging */ static void dump_var(const char *str, NumericVar *var) { int i; printf("%s: VAR w=%d d=%d ", str, var->weight, var->dscale); switch (var->sign) { case NUMERIC_POS: printf("POS"); break; case NUMERIC_NEG: printf("NEG"); break; case NUMERIC_NAN: printf("NaN"); break; default: printf("SIGN=0x%x", var->sign); break; } for (i = 0; i < var->ndigits; i++) printf(" %0*d", DEC_DIGITS, var->digits[i]); printf("\n"); } #endif /* NUMERIC_DEBUG */ /* ---------------------------------------------------------------------- * * Local functions follow * * In general, these do not support NaNs --- callers must eliminate * the possibility of NaN first. (make_result() is an exception.) * * ---------------------------------------------------------------------- */ /* * alloc_var() - * * Allocate a digit buffer of ndigits digits (plus a spare digit for rounding) */ static void alloc_var(NumericVar *var, int ndigits) { digitbuf_free(var->buf); var->buf = digitbuf_alloc(ndigits + 1); var->buf[0] = 0; /* spare digit for rounding */ var->digits = var->buf + 1; var->ndigits = ndigits; } /* * free_var() - * * Return the digit buffer of a variable to the free pool */ static void free_var(NumericVar *var) { digitbuf_free(var->buf); var->buf = NULL; var->digits = NULL; var->sign = NUMERIC_NAN; } /* * zero_var() - * * Set a variable to ZERO. * Note: its dscale is not touched. */ static void zero_var(NumericVar *var) { digitbuf_free(var->buf); var->buf = NULL; var->digits = NULL; var->ndigits = 0; var->weight = 0; /* by convention; doesn't really matter */ var->sign = NUMERIC_POS; /* anything but NAN... */ } /* * set_var_from_str() * * Parse a string and put the number into a variable * * This function does not handle leading or trailing spaces, and it doesn't * accept "NaN" either. It returns the end+1 position so that caller can * check for trailing spaces/garbage if deemed necessary. * * cp is the place to actually start parsing; str is what to use in error * reports. (Typically cp would be the same except advanced over spaces.) */ static const char * set_var_from_str(const char *str, const char *cp, NumericVar *dest) { bool have_dp = false; int i; unsigned char *decdigits; int sign = NUMERIC_POS; int dweight = -1; int ddigits; int dscale = 0; int weight; int ndigits; int offset; NumericDigit *digits; /* * We first parse the string to extract decimal digits and determine the * correct decimal weight. Then convert to NBASE representation. */ switch (*cp) { case '+': sign = NUMERIC_POS; cp++; break; case '-': sign = NUMERIC_NEG; cp++; break; } if (*cp == '.') { have_dp = true; cp++; } if (!isdigit((unsigned char) *cp)) ereport(ERROR, (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION), errmsg("invalid input syntax for type %s: \"%s\"", "numeric", str))); decdigits = (unsigned char *) palloc(strlen(cp) + DEC_DIGITS * 2); /* leading padding for digit alignment later */ memset(decdigits, 0, DEC_DIGITS); i = DEC_DIGITS; while (*cp) { if (isdigit((unsigned char) *cp)) { decdigits[i++] = *cp++ - '0'; if (!have_dp) dweight++; else dscale++; } else if (*cp == '.') { if (have_dp) ereport(ERROR, (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION), errmsg("invalid input syntax for type %s: \"%s\"", "numeric", str))); have_dp = true; cp++; } else break; } ddigits = i - DEC_DIGITS; /* trailing padding for digit alignment later */ memset(decdigits + i, 0, DEC_DIGITS - 1); /* Handle exponent, if any */ if (*cp == 'e' || *cp == 'E') { long exponent; char *endptr; cp++; exponent = strtol(cp, &endptr, 10); if (endptr == cp) ereport(ERROR, (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION), errmsg("invalid input syntax for type %s: \"%s\"", "numeric", str))); cp = endptr; /* * At this point, dweight and dscale can't be more than about * INT_MAX/2 due to the MaxAllocSize limit on string length, so * constraining the exponent similarly should be enough to prevent * integer overflow in this function. If the value is too large to * fit in storage format, make_result() will complain about it later; * for consistency use the same ereport errcode/text as make_result(). */ if (exponent >= INT_MAX / 2 || exponent <= -(INT_MAX / 2)) ereport(ERROR, (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE), errmsg("value overflows numeric format"))); dweight += (int) exponent; dscale -= (int) exponent; if (dscale < 0) dscale = 0; } /* * Okay, convert pure-decimal representation to base NBASE. First we need * to determine the converted weight and ndigits. offset is the number of * decimal zeroes to insert before the first given digit to have a * correctly aligned first NBASE digit. */ if (dweight >= 0) weight = (dweight + 1 + DEC_DIGITS - 1) / DEC_DIGITS - 1; else weight = -((-dweight - 1) / DEC_DIGITS + 1); offset = (weight + 1) * DEC_DIGITS - (dweight + 1); ndigits = (ddigits + offset + DEC_DIGITS - 1) / DEC_DIGITS; alloc_var(dest, ndigits); dest->sign = sign; dest->weight = weight; dest->dscale = dscale; i = DEC_DIGITS - offset; digits = dest->digits; while (ndigits-- > 0) { #if DEC_DIGITS == 4 *digits++ = ((decdigits[i] * 10 + decdigits[i + 1]) * 10 + decdigits[i + 2]) * 10 + decdigits[i + 3]; #elif DEC_DIGITS == 2 *digits++ = decdigits[i] * 10 + decdigits[i + 1]; #elif DEC_DIGITS == 1 *digits++ = decdigits[i]; #else #error unsupported NBASE #endif i += DEC_DIGITS; } pfree(decdigits); /* Strip any leading/trailing zeroes, and normalize weight if zero */ strip_var(dest); /* Return end+1 position for caller */ return cp; } /* * set_var_from_num() - * * Convert the packed db format into a variable */ static void set_var_from_num(Numeric num, NumericVar *dest) { int ndigits; ndigits = NUMERIC_NDIGITS(num); alloc_var(dest, ndigits); dest->weight = NUMERIC_WEIGHT(num); dest->sign = NUMERIC_SIGN(num); dest->dscale = NUMERIC_DSCALE(num); memcpy(dest->digits, NUMERIC_DIGITS(num), ndigits * sizeof(NumericDigit)); } /* * init_var_from_num() - * * Initialize a variable from packed db format. The digits array is not * copied, which saves some cycles when the resulting var is not modified. * Also, there's no need to call free_var(), as long as you don't assign any * other value to it (with set_var_* functions, or by using the var as the * destination of a function like add_var()) * * CAUTION: Do not modify the digits buffer of a var initialized with this * function, e.g by calling round_var() or trunc_var(), as the changes will * propagate to the original Numeric! It's OK to use it as the destination * argument of one of the calculational functions, though. */ static void init_var_from_num(Numeric num, NumericVar *dest) { dest->ndigits = NUMERIC_NDIGITS(num); dest->weight = NUMERIC_WEIGHT(num); dest->sign = NUMERIC_SIGN(num); dest->dscale = NUMERIC_DSCALE(num); dest->digits = NUMERIC_DIGITS(num); dest->buf = NULL; /* digits array is not palloc'd */ } /* * set_var_from_var() - * * Copy one variable into another */ static void set_var_from_var(const NumericVar *value, NumericVar *dest) { NumericDigit *newbuf; newbuf = digitbuf_alloc(value->ndigits + 1); newbuf[0] = 0; /* spare digit for rounding */ if (value->ndigits > 0) /* else value->digits might be null */ memcpy(newbuf + 1, value->digits, value->ndigits * sizeof(NumericDigit)); digitbuf_free(dest->buf); memmove(dest, value, sizeof(NumericVar)); dest->buf = newbuf; dest->digits = newbuf + 1; } /* * get_str_from_var() - * * Convert a var to text representation (guts of numeric_out). * The var is displayed to the number of digits indicated by its dscale. * Returns a palloc'd string. */ static char * get_str_from_var(const NumericVar *var) { int dscale; char *str; char *cp; char *endcp; int i; int d; NumericDigit dig; #if DEC_DIGITS > 1 NumericDigit d1; #endif dscale = var->dscale; /* * Allocate space for the result. * * i is set to the # of decimal digits before decimal point. dscale is the * # of decimal digits we will print after decimal point. We may generate * as many as DEC_DIGITS-1 excess digits at the end, and in addition we * need room for sign, decimal point, null terminator. */ i = (var->weight + 1) * DEC_DIGITS; if (i <= 0) i = 1; str = palloc(i + dscale + DEC_DIGITS + 2); cp = str; /* * Output a dash for negative values */ if (var->sign == NUMERIC_NEG) *cp++ = '-'; /* * Output all digits before the decimal point */ if (var->weight < 0) { d = var->weight + 1; *cp++ = '0'; } else { for (d = 0; d <= var->weight; d++) { dig = (d < var->ndigits) ? var->digits[d] : 0; /* In the first digit, suppress extra leading decimal zeroes */ #if DEC_DIGITS == 4 { bool putit = (d > 0); d1 = dig / 1000; dig -= d1 * 1000; putit |= (d1 > 0); if (putit) *cp++ = d1 + '0'; d1 = dig / 100; dig -= d1 * 100; putit |= (d1 > 0); if (putit) *cp++ = d1 + '0'; d1 = dig / 10; dig -= d1 * 10; putit |= (d1 > 0); if (putit) *cp++ = d1 + '0'; *cp++ = dig + '0'; } #elif DEC_DIGITS == 2 d1 = dig / 10; dig -= d1 * 10; if (d1 > 0 || d > 0) *cp++ = d1 + '0'; *cp++ = dig + '0'; #elif DEC_DIGITS == 1 *cp++ = dig + '0'; #else #error unsupported NBASE #endif } } /* * If requested, output a decimal point and all the digits that follow it. * We initially put out a multiple of DEC_DIGITS digits, then truncate if * needed. */ if (dscale > 0) { *cp++ = '.'; endcp = cp + dscale; for (i = 0; i < dscale; d++, i += DEC_DIGITS) { dig = (d >= 0 && d < var->ndigits) ? var->digits[d] : 0; #if DEC_DIGITS == 4 d1 = dig / 1000; dig -= d1 * 1000; *cp++ = d1 + '0'; d1 = dig / 100; dig -= d1 * 100; *cp++ = d1 + '0'; d1 = dig / 10; dig -= d1 * 10; *cp++ = d1 + '0'; *cp++ = dig + '0'; #elif DEC_DIGITS == 2 d1 = dig / 10; dig -= d1 * 10; *cp++ = d1 + '0'; *cp++ = dig + '0'; #elif DEC_DIGITS == 1 *cp++ = dig + '0'; #else #error unsupported NBASE #endif } cp = endcp; } /* * terminate the string and return it */ *cp = '\0'; return str; } /* * get_str_from_var_sci() - * * Convert a var to a normalised scientific notation text representation. * This function does the heavy lifting for numeric_out_sci(). * * This notation has the general form a * 10^b, where a is known as the * "significand" and b is known as the "exponent". * * Because we can't do superscript in ASCII (and because we want to copy * printf's behaviour) we display the exponent using E notation, with a * minimum of two exponent digits. * * For example, the value 1234 could be output as 1.2e+03. * * We assume that the exponent can fit into an int32. * * rscale is the number of decimal digits desired after the decimal point in * the output, negative values will be treated as meaning zero. * * Returns a palloc'd string. */ static char * get_str_from_var_sci(const NumericVar *var, int rscale) { int32 exponent; NumericVar tmp_var; size_t len; char *str; char *sig_out; if (rscale < 0) rscale = 0; /* * Determine the exponent of this number in normalised form. * * This is the exponent required to represent the number with only one * significant digit before the decimal place. */ if (var->ndigits > 0) { exponent = (var->weight + 1) * DEC_DIGITS; /* * Compensate for leading decimal zeroes in the first numeric digit by * decrementing the exponent. */ exponent -= DEC_DIGITS - (int) log10(var->digits[0]); } else { /* * If var has no digits, then it must be zero. * * Zero doesn't technically have a meaningful exponent in normalised * notation, but we just display the exponent as zero for consistency * of output. */ exponent = 0; } /* * Divide var by 10^exponent to get the significand, rounding to rscale * decimal digits in the process. */ init_var(&tmp_var); power_ten_int(exponent, &tmp_var); div_var(var, &tmp_var, &tmp_var, rscale, true); sig_out = get_str_from_var(&tmp_var); free_var(&tmp_var); /* * Allocate space for the result. * * In addition to the significand, we need room for the exponent * decoration ("e"), the sign of the exponent, up to 10 digits for the * exponent itself, and of course the null terminator. */ len = strlen(sig_out) + 13; str = palloc(len); snprintf(str, len, "%se%+03d", sig_out, exponent); pfree(sig_out); return str; } /* * make_result_opt_error() - * * Create the packed db numeric format in palloc()'d memory from * a variable. If "*have_error" flag is provided, on error it's set to * true, NULL returned. This is helpful when caller need to handle errors * by itself. */ static Numeric make_result_opt_error(const NumericVar *var, bool *have_error) { Numeric result; NumericDigit *digits = var->digits; int weight = var->weight; int sign = var->sign; int n; Size len; if (have_error) *have_error = false; if (sign == NUMERIC_NAN) { result = (Numeric) palloc(NUMERIC_HDRSZ_SHORT); SET_VARSIZE(result, NUMERIC_HDRSZ_SHORT); result->choice.n_header = NUMERIC_NAN; /* the header word is all we need */ dump_numeric("make_result()", result); return result; } n = var->ndigits; /* truncate leading zeroes */ while (n > 0 && *digits == 0) { digits++; weight--; n--; } /* truncate trailing zeroes */ while (n > 0 && digits[n - 1] == 0) n--; /* If zero result, force to weight=0 and positive sign */ if (n == 0) { weight = 0; sign = NUMERIC_POS; } /* Build the result */ if (NUMERIC_CAN_BE_SHORT(var->dscale, weight)) { len = NUMERIC_HDRSZ_SHORT + n * sizeof(NumericDigit); result = (Numeric) palloc(len); SET_VARSIZE(result, len); result->choice.n_short.n_header = (sign == NUMERIC_NEG ? (NUMERIC_SHORT | NUMERIC_SHORT_SIGN_MASK) : NUMERIC_SHORT) | (var->dscale << NUMERIC_SHORT_DSCALE_SHIFT) | (weight < 0 ? NUMERIC_SHORT_WEIGHT_SIGN_MASK : 0) | (weight & NUMERIC_SHORT_WEIGHT_MASK); } else { len = NUMERIC_HDRSZ + n * sizeof(NumericDigit); result = (Numeric) palloc(len); SET_VARSIZE(result, len); result->choice.n_long.n_sign_dscale = sign | (var->dscale & NUMERIC_DSCALE_MASK); result->choice.n_long.n_weight = weight; } Assert(NUMERIC_NDIGITS(result) == n); if (n > 0) memcpy(NUMERIC_DIGITS(result), digits, n * sizeof(NumericDigit)); /* Check for overflow of int16 fields */ if (NUMERIC_WEIGHT(result) != weight || NUMERIC_DSCALE(result) != var->dscale) { if (have_error) { *have_error = true; return NULL; } else { ereport(ERROR, (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE), errmsg("value overflows numeric format"))); } } dump_numeric("make_result()", result); return result; } /* * make_result() - * * An interface to make_result_opt_error() without "have_error" argument. */ static Numeric make_result(const NumericVar *var) { return make_result_opt_error(var, NULL); } /* * apply_typmod() - * * Do bounds checking and rounding according to the attributes * typmod field. */ static void apply_typmod(NumericVar *var, int32 typmod) { int precision; int scale; int maxdigits; int ddigits; int i; /* Do nothing if we have a default typmod (-1) */ if (typmod < (int32) (VARHDRSZ)) return; typmod -= VARHDRSZ; precision = (typmod >> 16) & 0xffff; scale = typmod & 0xffff; maxdigits = precision - scale; /* Round to target scale (and set var->dscale) */ round_var(var, scale); /* * Check for overflow - note we can't do this before rounding, because * rounding could raise the weight. Also note that the var's weight could * be inflated by leading zeroes, which will be stripped before storage * but perhaps might not have been yet. In any case, we must recognize a * true zero, whose weight doesn't mean anything. */ ddigits = (var->weight + 1) * DEC_DIGITS; if (ddigits > maxdigits) { /* Determine true weight; and check for all-zero result */ for (i = 0; i < var->ndigits; i++) { NumericDigit dig = var->digits[i]; if (dig) { /* Adjust for any high-order decimal zero digits */ #if DEC_DIGITS == 4 if (dig < 10) ddigits -= 3; else if (dig < 100) ddigits -= 2; else if (dig < 1000) ddigits -= 1; #elif DEC_DIGITS == 2 if (dig < 10) ddigits -= 1; #elif DEC_DIGITS == 1 /* no adjustment */ #else #error unsupported NBASE #endif if (ddigits > maxdigits) ereport(ERROR, (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE), errmsg("numeric field overflow"), errdetail("A field with precision %d, scale %d must round to an absolute value less than %s%d.", precision, scale, /* Display 10^0 as 1 */ maxdigits ? "10^" : "", maxdigits ? maxdigits : 1 ))); break; } ddigits -= DEC_DIGITS; } } } /* * Convert numeric to int8, rounding if needed. * * If overflow, return false (no error is raised). Return true if okay. */ static bool numericvar_to_int64(const NumericVar *var, int64 *result) { NumericDigit *digits; int ndigits; int weight; int i; int64 val; bool neg; NumericVar rounded; /* Round to nearest integer */ init_var(&rounded); set_var_from_var(var, &rounded); round_var(&rounded, 0); /* Check for zero input */ strip_var(&rounded); ndigits = rounded.ndigits; if (ndigits == 0) { *result = 0; free_var(&rounded); return true; } /* * For input like 10000000000, we must treat stripped digits as real. So * the loop assumes there are weight+1 digits before the decimal point. */ weight = rounded.weight; Assert(weight >= 0 && ndigits <= weight + 1); /* * Construct the result. To avoid issues with converting a value * corresponding to INT64_MIN (which can't be represented as a positive 64 * bit two's complement integer), accumulate value as a negative number. */ digits = rounded.digits; neg = (rounded.sign == NUMERIC_NEG); val = -digits[0]; for (i = 1; i <= weight; i++) { if (unlikely(pg_mul_s64_overflow(val, NBASE, &val))) { free_var(&rounded); return false; } if (i < ndigits) { if (unlikely(pg_sub_s64_overflow(val, digits[i], &val))) { free_var(&rounded); return false; } } } free_var(&rounded); if (!neg) { if (unlikely(val == PG_INT64_MIN)) return false; val = -val; } *result = val; return true; } /* * Convert int8 value to numeric. */ static void int64_to_numericvar(int64 val, NumericVar *var) { uint64 uval, newuval; NumericDigit *ptr; int ndigits; /* int64 can require at most 19 decimal digits; add one for safety */ alloc_var(var, 20 / DEC_DIGITS); if (val < 0) { var->sign = NUMERIC_NEG; uval = -val; } else { var->sign = NUMERIC_POS; uval = val; } var->dscale = 0; if (val == 0) { var->ndigits = 0; var->weight = 0; return; } ptr = var->digits + var->ndigits; ndigits = 0; do { ptr--; ndigits++; newuval = uval / NBASE; *ptr = uval - newuval * NBASE; uval = newuval; } while (uval); var->digits = ptr; var->ndigits = ndigits; var->weight = ndigits - 1; } #ifdef HAVE_INT128 /* * Convert numeric to int128, rounding if needed. * * If overflow, return false (no error is raised). Return true if okay. */ static bool numericvar_to_int128(const NumericVar *var, int128 *result) { NumericDigit *digits; int ndigits; int weight; int i; int128 val, oldval; bool neg; NumericVar rounded; /* Round to nearest integer */ init_var(&rounded); set_var_from_var(var, &rounded); round_var(&rounded, 0); /* Check for zero input */ strip_var(&rounded); ndigits = rounded.ndigits; if (ndigits == 0) { *result = 0; free_var(&rounded); return true; } /* * For input like 10000000000, we must treat stripped digits as real. So * the loop assumes there are weight+1 digits before the decimal point. */ weight = rounded.weight; Assert(weight >= 0 && ndigits <= weight + 1); /* Construct the result */ digits = rounded.digits; neg = (rounded.sign == NUMERIC_NEG); val = digits[0]; for (i = 1; i <= weight; i++) { oldval = val; val *= NBASE; if (i < ndigits) val += digits[i]; /* * The overflow check is a bit tricky because we want to accept * INT128_MIN, which will overflow the positive accumulator. We can * detect this case easily though because INT128_MIN is the only * nonzero value for which -val == val (on a two's complement machine, * anyway). */ if ((val / NBASE) != oldval) /* possible overflow? */ { if (!neg || (-val) != val || val == 0 || oldval < 0) { free_var(&rounded); return false; } } } free_var(&rounded); *result = neg ? -val : val; return true; } /* * Convert 128 bit integer to numeric. */ static void int128_to_numericvar(int128 val, NumericVar *var) { uint128 uval, newuval; NumericDigit *ptr; int ndigits; /* int128 can require at most 39 decimal digits; add one for safety */ alloc_var(var, 40 / DEC_DIGITS); if (val < 0) { var->sign = NUMERIC_NEG; uval = -val; } else { var->sign = NUMERIC_POS; uval = val; } var->dscale = 0; if (val == 0) { var->ndigits = 0; var->weight = 0; return; } ptr = var->digits + var->ndigits; ndigits = 0; do { ptr--; ndigits++; newuval = uval / NBASE; *ptr = uval - newuval * NBASE; uval = newuval; } while (uval); var->digits = ptr; var->ndigits = ndigits; var->weight = ndigits - 1; } #endif /* * Convert numeric to float8; if out of range, return +/- HUGE_VAL */ static double numeric_to_double_no_overflow(Numeric num) { char *tmp; double val; char *endptr; tmp = DatumGetCString(DirectFunctionCall1(numeric_out, NumericGetDatum(num))); /* unlike float8in, we ignore ERANGE from strtod */ val = strtod(tmp, &endptr); if (*endptr != '\0') { /* shouldn't happen ... */ ereport(ERROR, (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION), errmsg("invalid input syntax for type %s: \"%s\"", "double precision", tmp))); } pfree(tmp); return val; } /* As above, but work from a NumericVar */ static double numericvar_to_double_no_overflow(const NumericVar *var) { char *tmp; double val; char *endptr; tmp = get_str_from_var(var); /* unlike float8in, we ignore ERANGE from strtod */ val = strtod(tmp, &endptr); if (*endptr != '\0') { /* shouldn't happen ... */ ereport(ERROR, (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION), errmsg("invalid input syntax for type %s: \"%s\"", "double precision", tmp))); } pfree(tmp); return val; } /* * cmp_var() - * * Compare two values on variable level. We assume zeroes have been * truncated to no digits. */ static int cmp_var(const NumericVar *var1, const NumericVar *var2) { return cmp_var_common(var1->digits, var1->ndigits, var1->weight, var1->sign, var2->digits, var2->ndigits, var2->weight, var2->sign); } /* * cmp_var_common() - * * Main routine of cmp_var(). This function can be used by both * NumericVar and Numeric. */ static int cmp_var_common(const NumericDigit *var1digits, int var1ndigits, int var1weight, int var1sign, const NumericDigit *var2digits, int var2ndigits, int var2weight, int var2sign) { if (var1ndigits == 0) { if (var2ndigits == 0) return 0; if (var2sign == NUMERIC_NEG) return 1; return -1; } if (var2ndigits == 0) { if (var1sign == NUMERIC_POS) return 1; return -1; } if (var1sign == NUMERIC_POS) { if (var2sign == NUMERIC_NEG) return 1; return cmp_abs_common(var1digits, var1ndigits, var1weight, var2digits, var2ndigits, var2weight); } if (var2sign == NUMERIC_POS) return -1; return cmp_abs_common(var2digits, var2ndigits, var2weight, var1digits, var1ndigits, var1weight); } /* * add_var() - * * Full version of add functionality on variable level (handling signs). * result might point to one of the operands too without danger. */ static void add_var(const NumericVar *var1, const NumericVar *var2, NumericVar *result) { /* * Decide on the signs of the two variables what to do */ if (var1->sign == NUMERIC_POS) { if (var2->sign == NUMERIC_POS) { /* * Both are positive result = +(ABS(var1) + ABS(var2)) */ add_abs(var1, var2, result); result->sign = NUMERIC_POS; } else { /* * var1 is positive, var2 is negative Must compare absolute values */ switch (cmp_abs(var1, var2)) { case 0: /* ---------- * ABS(var1) == ABS(var2) * result = ZERO * ---------- */ zero_var(result); result->dscale = Max(var1->dscale, var2->dscale); break; case 1: /* ---------- * ABS(var1) > ABS(var2) * result = +(ABS(var1) - ABS(var2)) * ---------- */ sub_abs(var1, var2, result); result->sign = NUMERIC_POS; break; case -1: /* ---------- * ABS(var1) < ABS(var2) * result = -(ABS(var2) - ABS(var1)) * ---------- */ sub_abs(var2, var1, result); result->sign = NUMERIC_NEG; break; } } } else { if (var2->sign == NUMERIC_POS) { /* ---------- * var1 is negative, var2 is positive * Must compare absolute values * ---------- */ switch (cmp_abs(var1, var2)) { case 0: /* ---------- * ABS(var1) == ABS(var2) * result = ZERO * ---------- */ zero_var(result); result->dscale = Max(var1->dscale, var2->dscale); break; case 1: /* ---------- * ABS(var1) > ABS(var2) * result = -(ABS(var1) - ABS(var2)) * ---------- */ sub_abs(var1, var2, result); result->sign = NUMERIC_NEG; break; case -1: /* ---------- * ABS(var1) < ABS(var2) * result = +(ABS(var2) - ABS(var1)) * ---------- */ sub_abs(var2, var1, result); result->sign = NUMERIC_POS; break; } } else { /* ---------- * Both are negative * result = -(ABS(var1) + ABS(var2)) * ---------- */ add_abs(var1, var2, result); result->sign = NUMERIC_NEG; } } } /* * sub_var() - * * Full version of sub functionality on variable level (handling signs). * result might point to one of the operands too without danger. */ static void sub_var(const NumericVar *var1, const NumericVar *var2, NumericVar *result) { /* * Decide on the signs of the two variables what to do */ if (var1->sign == NUMERIC_POS) { if (var2->sign == NUMERIC_NEG) { /* ---------- * var1 is positive, var2 is negative * result = +(ABS(var1) + ABS(var2)) * ---------- */ add_abs(var1, var2, result); result->sign = NUMERIC_POS; } else { /* ---------- * Both are positive * Must compare absolute values * ---------- */ switch (cmp_abs(var1, var2)) { case 0: /* ---------- * ABS(var1) == ABS(var2) * result = ZERO * ---------- */ zero_var(result); result->dscale = Max(var1->dscale, var2->dscale); break; case 1: /* ---------- * ABS(var1) > ABS(var2) * result = +(ABS(var1) - ABS(var2)) * ---------- */ sub_abs(var1, var2, result); result->sign = NUMERIC_POS; break; case -1: /* ---------- * ABS(var1) < ABS(var2) * result = -(ABS(var2) - ABS(var1)) * ---------- */ sub_abs(var2, var1, result); result->sign = NUMERIC_NEG; break; } } } else { if (var2->sign == NUMERIC_NEG) { /* ---------- * Both are negative * Must compare absolute values * ---------- */ switch (cmp_abs(var1, var2)) { case 0: /* ---------- * ABS(var1) == ABS(var2) * result = ZERO * ---------- */ zero_var(result); result->dscale = Max(var1->dscale, var2->dscale); break; case 1: /* ---------- * ABS(var1) > ABS(var2) * result = -(ABS(var1) - ABS(var2)) * ---------- */ sub_abs(var1, var2, result); result->sign = NUMERIC_NEG; break; case -1: /* ---------- * ABS(var1) < ABS(var2) * result = +(ABS(var2) - ABS(var1)) * ---------- */ sub_abs(var2, var1, result); result->sign = NUMERIC_POS; break; } } else { /* ---------- * var1 is negative, var2 is positive * result = -(ABS(var1) + ABS(var2)) * ---------- */ add_abs(var1, var2, result); result->sign = NUMERIC_NEG; } } } /* * mul_var() - * * Multiplication on variable level. Product of var1 * var2 is stored * in result. Result is rounded to no more than rscale fractional digits. */ static void mul_var(const NumericVar *var1, const NumericVar *var2, NumericVar *result, int rscale) { int res_ndigits; int res_sign; int res_weight; int maxdigits; int *dig; int carry; int maxdig; int newdig; int var1ndigits; int var2ndigits; NumericDigit *var1digits; NumericDigit *var2digits; NumericDigit *res_digits; int i, i1, i2; /* * Arrange for var1 to be the shorter of the two numbers. This improves * performance because the inner multiplication loop is much simpler than * the outer loop, so it's better to have a smaller number of iterations * of the outer loop. This also reduces the number of times that the * accumulator array needs to be normalized. */ if (var1->ndigits > var2->ndigits) { const NumericVar *tmp = var1; var1 = var2; var2 = tmp; } /* copy these values into local vars for speed in inner loop */ var1ndigits = var1->ndigits; var2ndigits = var2->ndigits; var1digits = var1->digits; var2digits = var2->digits; if (var1ndigits == 0 || var2ndigits == 0) { /* one or both inputs is zero; so is result */ zero_var(result); result->dscale = rscale; return; } /* Determine result sign and (maximum possible) weight */ if (var1->sign == var2->sign) res_sign = NUMERIC_POS; else res_sign = NUMERIC_NEG; res_weight = var1->weight + var2->weight + 2; /* * Determine the number of result digits to compute. If the exact result * would have more than rscale fractional digits, truncate the computation * with MUL_GUARD_DIGITS guard digits, i.e., ignore input digits that * would only contribute to the right of that. (This will give the exact * rounded-to-rscale answer unless carries out of the ignored positions * would have propagated through more than MUL_GUARD_DIGITS digits.) * * Note: an exact computation could not produce more than var1ndigits + * var2ndigits digits, but we allocate one extra output digit in case * rscale-driven rounding produces a carry out of the highest exact digit. */ res_ndigits = var1ndigits + var2ndigits + 1; maxdigits = res_weight + 1 + (rscale + DEC_DIGITS - 1) / DEC_DIGITS + MUL_GUARD_DIGITS; res_ndigits = Min(res_ndigits, maxdigits); if (res_ndigits < 3) { /* All input digits will be ignored; so result is zero */ zero_var(result); result->dscale = rscale; return; } /* * We do the arithmetic in an array "dig[]" of signed int's. Since * INT_MAX is noticeably larger than NBASE*NBASE, this gives us headroom * to avoid normalizing carries immediately. * * maxdig tracks the maximum possible value of any dig[] entry; when this * threatens to exceed INT_MAX, we take the time to propagate carries. * Furthermore, we need to ensure that overflow doesn't occur during the * carry propagation passes either. The carry values could be as much as * INT_MAX/NBASE, so really we must normalize when digits threaten to * exceed INT_MAX - INT_MAX/NBASE. * * To avoid overflow in maxdig itself, it actually represents the max * possible value divided by NBASE-1, ie, at the top of the loop it is * known that no dig[] entry exceeds maxdig * (NBASE-1). */ dig = (int *) palloc0(res_ndigits * sizeof(int)); maxdig = 0; /* * The least significant digits of var1 should be ignored if they don't * contribute directly to the first res_ndigits digits of the result that * we are computing. * * Digit i1 of var1 and digit i2 of var2 are multiplied and added to digit * i1+i2+2 of the accumulator array, so we need only consider digits of * var1 for which i1 <= res_ndigits - 3. */ for (i1 = Min(var1ndigits - 1, res_ndigits - 3); i1 >= 0; i1--) { int var1digit = var1digits[i1]; if (var1digit == 0) continue; /* Time to normalize? */ maxdig += var1digit; if (maxdig > (INT_MAX - INT_MAX / NBASE) / (NBASE - 1)) { /* Yes, do it */ carry = 0; for (i = res_ndigits - 1; i >= 0; i--) { newdig = dig[i] + carry; if (newdig >= NBASE) { carry = newdig / NBASE; newdig -= carry * NBASE; } else carry = 0; dig[i] = newdig; } Assert(carry == 0); /* Reset maxdig to indicate new worst-case */ maxdig = 1 + var1digit; } /* * Add the appropriate multiple of var2 into the accumulator. * * As above, digits of var2 can be ignored if they don't contribute, * so we only include digits for which i1+i2+2 <= res_ndigits - 1. */ for (i2 = Min(var2ndigits - 1, res_ndigits - i1 - 3), i = i1 + i2 + 2; i2 >= 0; i2--) dig[i--] += var1digit * var2digits[i2]; } /* * Now we do a final carry propagation pass to normalize the result, which * we combine with storing the result digits into the output. Note that * this is still done at full precision w/guard digits. */ alloc_var(result, res_ndigits); res_digits = result->digits; carry = 0; for (i = res_ndigits - 1; i >= 0; i--) { newdig = dig[i] + carry; if (newdig >= NBASE) { carry = newdig / NBASE; newdig -= carry * NBASE; } else carry = 0; res_digits[i] = newdig; } Assert(carry == 0); pfree(dig); /* * Finally, round the result to the requested precision. */ result->weight = res_weight; result->sign = res_sign; /* Round to target rscale (and set result->dscale) */ round_var(result, rscale); /* Strip leading and trailing zeroes */ strip_var(result); } /* * div_var() - * * Division on variable level. Quotient of var1 / var2 is stored in result. * The quotient is figured to exactly rscale fractional digits. * If round is true, it is rounded at the rscale'th digit; if false, it * is truncated (towards zero) at that digit. */ static void div_var(const NumericVar *var1, const NumericVar *var2, NumericVar *result, int rscale, bool round) { int div_ndigits; int res_ndigits; int res_sign; int res_weight; int carry; int borrow; int divisor1; int divisor2; NumericDigit *dividend; NumericDigit *divisor; NumericDigit *res_digits; int i; int j; /* copy these values into local vars for speed in inner loop */ int var1ndigits = var1->ndigits; int var2ndigits = var2->ndigits; /* * First of all division by zero check; we must not be handed an * unnormalized divisor. */ if (var2ndigits == 0 || var2->digits[0] == 0) ereport(ERROR, (errcode(ERRCODE_DIVISION_BY_ZERO), errmsg("division by zero"))); /* * Now result zero check */ if (var1ndigits == 0) { zero_var(result); result->dscale = rscale; return; } /* * Determine the result sign, weight and number of digits to calculate. * The weight figured here is correct if the emitted quotient has no * leading zero digits; otherwise strip_var() will fix things up. */ if (var1->sign == var2->sign) res_sign = NUMERIC_POS; else res_sign = NUMERIC_NEG; res_weight = var1->weight - var2->weight; /* The number of accurate result digits we need to produce: */ res_ndigits = res_weight + 1 + (rscale + DEC_DIGITS - 1) / DEC_DIGITS; /* ... but always at least 1 */ res_ndigits = Max(res_ndigits, 1); /* If rounding needed, figure one more digit to ensure correct result */ if (round) res_ndigits++; /* * The working dividend normally requires res_ndigits + var2ndigits * digits, but make it at least var1ndigits so we can load all of var1 * into it. (There will be an additional digit dividend[0] in the * dividend space, but for consistency with Knuth's notation we don't * count that in div_ndigits.) */ div_ndigits = res_ndigits + var2ndigits; div_ndigits = Max(div_ndigits, var1ndigits); /* * We need a workspace with room for the working dividend (div_ndigits+1 * digits) plus room for the possibly-normalized divisor (var2ndigits * digits). It is convenient also to have a zero at divisor[0] with the * actual divisor data in divisor[1 .. var2ndigits]. Transferring the * digits into the workspace also allows us to realloc the result (which * might be the same as either input var) before we begin the main loop. * Note that we use palloc0 to ensure that divisor[0], dividend[0], and * any additional dividend positions beyond var1ndigits, start out 0. */ dividend = (NumericDigit *) palloc0((div_ndigits + var2ndigits + 2) * sizeof(NumericDigit)); divisor = dividend + (div_ndigits + 1); memcpy(dividend + 1, var1->digits, var1ndigits * sizeof(NumericDigit)); memcpy(divisor + 1, var2->digits, var2ndigits * sizeof(NumericDigit)); /* * Now we can realloc the result to hold the generated quotient digits. */ alloc_var(result, res_ndigits); res_digits = result->digits; if (var2ndigits == 1) { /* * If there's only a single divisor digit, we can use a fast path (cf. * Knuth section 4.3.1 exercise 16). */ divisor1 = divisor[1]; carry = 0; for (i = 0; i < res_ndigits; i++) { carry = carry * NBASE + dividend[i + 1]; res_digits[i] = carry / divisor1; carry = carry % divisor1; } } else { /* * The full multiple-place algorithm is taken from Knuth volume 2, * Algorithm 4.3.1D. * * We need the first divisor digit to be >= NBASE/2. If it isn't, * make it so by scaling up both the divisor and dividend by the * factor "d". (The reason for allocating dividend[0] above is to * leave room for possible carry here.) */ if (divisor[1] < HALF_NBASE) { int d = NBASE / (divisor[1] + 1); carry = 0; for (i = var2ndigits; i > 0; i--) { carry += divisor[i] * d; divisor[i] = carry % NBASE; carry = carry / NBASE; } Assert(carry == 0); carry = 0; /* at this point only var1ndigits of dividend can be nonzero */ for (i = var1ndigits; i >= 0; i--) { carry += dividend[i] * d; dividend[i] = carry % NBASE; carry = carry / NBASE; } Assert(carry == 0); Assert(divisor[1] >= HALF_NBASE); } /* First 2 divisor digits are used repeatedly in main loop */ divisor1 = divisor[1]; divisor2 = divisor[2]; /* * Begin the main loop. Each iteration of this loop produces the j'th * quotient digit by dividing dividend[j .. j + var2ndigits] by the * divisor; this is essentially the same as the common manual * procedure for long division. */ for (j = 0; j < res_ndigits; j++) { /* Estimate quotient digit from the first two dividend digits */ int next2digits = dividend[j] * NBASE + dividend[j + 1]; int qhat; /* * If next2digits are 0, then quotient digit must be 0 and there's * no need to adjust the working dividend. It's worth testing * here to fall out ASAP when processing trailing zeroes in a * dividend. */ if (next2digits == 0) { res_digits[j] = 0; continue; } if (dividend[j] == divisor1) qhat = NBASE - 1; else qhat = next2digits / divisor1; /* * Adjust quotient digit if it's too large. Knuth proves that * after this step, the quotient digit will be either correct or * just one too large. (Note: it's OK to use dividend[j+2] here * because we know the divisor length is at least 2.) */ while (divisor2 * qhat > (next2digits - qhat * divisor1) * NBASE + dividend[j + 2]) qhat--; /* As above, need do nothing more when quotient digit is 0 */ if (qhat > 0) { /* * Multiply the divisor by qhat, and subtract that from the * working dividend. "carry" tracks the multiplication, * "borrow" the subtraction (could we fold these together?) */ carry = 0; borrow = 0; for (i = var2ndigits; i >= 0; i--) { carry += divisor[i] * qhat; borrow -= carry % NBASE; carry = carry / NBASE; borrow += dividend[j + i]; if (borrow < 0) { dividend[j + i] = borrow + NBASE; borrow = -1; } else { dividend[j + i] = borrow; borrow = 0; } } Assert(carry == 0); /* * If we got a borrow out of the top dividend digit, then * indeed qhat was one too large. Fix it, and add back the * divisor to correct the working dividend. (Knuth proves * that this will occur only about 3/NBASE of the time; hence, * it's a good idea to test this code with small NBASE to be * sure this section gets exercised.) */ if (borrow) { qhat--; carry = 0; for (i = var2ndigits; i >= 0; i--) { carry += dividend[j + i] + divisor[i]; if (carry >= NBASE) { dividend[j + i] = carry - NBASE; carry = 1; } else { dividend[j + i] = carry; carry = 0; } } /* A carry should occur here to cancel the borrow above */ Assert(carry == 1); } } /* And we're done with this quotient digit */ res_digits[j] = qhat; } } pfree(dividend); /* * Finally, round or truncate the result to the requested precision. */ result->weight = res_weight; result->sign = res_sign; /* Round or truncate to target rscale (and set result->dscale) */ if (round) round_var(result, rscale); else trunc_var(result, rscale); /* Strip leading and trailing zeroes */ strip_var(result); } /* * div_var_fast() - * * This has the same API as div_var, but is implemented using the division * algorithm from the "FM" library, rather than Knuth's schoolbook-division * approach. This is significantly faster but can produce inaccurate * results, because it sometimes has to propagate rounding to the left, * and so we can never be entirely sure that we know the requested digits * exactly. We compute DIV_GUARD_DIGITS extra digits, but there is * no certainty that that's enough. We use this only in the transcendental * function calculation routines, where everything is approximate anyway. * * Although we provide a "round" argument for consistency with div_var, * it is unwise to use this function with round=false. In truncation mode * it is possible to get a result with no significant digits, for example * with rscale=0 we might compute 0.99999... and truncate that to 0 when * the correct answer is 1. */ static void div_var_fast(const NumericVar *var1, const NumericVar *var2, NumericVar *result, int rscale, bool round) { int div_ndigits; int load_ndigits; int res_sign; int res_weight; int *div; int qdigit; int carry; int maxdiv; int newdig; NumericDigit *res_digits; double fdividend, fdivisor, fdivisorinverse, fquotient; int qi; int i; /* copy these values into local vars for speed in inner loop */ int var1ndigits = var1->ndigits; int var2ndigits = var2->ndigits; NumericDigit *var1digits = var1->digits; NumericDigit *var2digits = var2->digits; /* * First of all division by zero check; we must not be handed an * unnormalized divisor. */ if (var2ndigits == 0 || var2digits[0] == 0) ereport(ERROR, (errcode(ERRCODE_DIVISION_BY_ZERO), errmsg("division by zero"))); /* * Now result zero check */ if (var1ndigits == 0) { zero_var(result); result->dscale = rscale; return; } /* * Determine the result sign, weight and number of digits to calculate */ if (var1->sign == var2->sign) res_sign = NUMERIC_POS; else res_sign = NUMERIC_NEG; res_weight = var1->weight - var2->weight + 1; /* The number of accurate result digits we need to produce: */ div_ndigits = res_weight + 1 + (rscale + DEC_DIGITS - 1) / DEC_DIGITS; /* Add guard digits for roundoff error */ div_ndigits += DIV_GUARD_DIGITS; if (div_ndigits < DIV_GUARD_DIGITS) div_ndigits = DIV_GUARD_DIGITS; /* * We do the arithmetic in an array "div[]" of signed int's. Since * INT_MAX is noticeably larger than NBASE*NBASE, this gives us headroom * to avoid normalizing carries immediately. * * We start with div[] containing one zero digit followed by the * dividend's digits (plus appended zeroes to reach the desired precision * including guard digits). Each step of the main loop computes an * (approximate) quotient digit and stores it into div[], removing one * position of dividend space. A final pass of carry propagation takes * care of any mistaken quotient digits. * * Note that div[] doesn't necessarily contain all of the digits from the * dividend --- the desired precision plus guard digits might be less than * the dividend's precision. This happens, for example, in the square * root algorithm, where we typically divide a 2N-digit number by an * N-digit number, and only require a result with N digits of precision. */ div = (int *) palloc0((div_ndigits + 1) * sizeof(int)); load_ndigits = Min(div_ndigits, var1ndigits); for (i = 0; i < load_ndigits; i++) div[i + 1] = var1digits[i]; /* * We estimate each quotient digit using floating-point arithmetic, taking * the first four digits of the (current) dividend and divisor. This must * be float to avoid overflow. The quotient digits will generally be off * by no more than one from the exact answer. */ fdivisor = (double) var2digits[0]; for (i = 1; i < 4; i++) { fdivisor *= NBASE; if (i < var2ndigits) fdivisor += (double) var2digits[i]; } fdivisorinverse = 1.0 / fdivisor; /* * maxdiv tracks the maximum possible absolute value of any div[] entry; * when this threatens to exceed INT_MAX, we take the time to propagate * carries. Furthermore, we need to ensure that overflow doesn't occur * during the carry propagation passes either. The carry values may have * an absolute value as high as INT_MAX/NBASE + 1, so really we must * normalize when digits threaten to exceed INT_MAX - INT_MAX/NBASE - 1. * * To avoid overflow in maxdiv itself, it represents the max absolute * value divided by NBASE-1, ie, at the top of the loop it is known that * no div[] entry has an absolute value exceeding maxdiv * (NBASE-1). * * Actually, though, that holds good only for div[] entries after div[qi]; * the adjustment done at the bottom of the loop may cause div[qi + 1] to * exceed the maxdiv limit, so that div[qi] in the next iteration is * beyond the limit. This does not cause problems, as explained below. */ maxdiv = 1; /* * Outer loop computes next quotient digit, which will go into div[qi] */ for (qi = 0; qi < div_ndigits; qi++) { /* Approximate the current dividend value */ fdividend = (double) div[qi]; for (i = 1; i < 4; i++) { fdividend *= NBASE; if (qi + i <= div_ndigits) fdividend += (double) div[qi + i]; } /* Compute the (approximate) quotient digit */ fquotient = fdividend * fdivisorinverse; qdigit = (fquotient >= 0.0) ? ((int) fquotient) : (((int) fquotient) - 1); /* truncate towards -infinity */ if (qdigit != 0) { /* Do we need to normalize now? */ maxdiv += Abs(qdigit); if (maxdiv > (INT_MAX - INT_MAX / NBASE - 1) / (NBASE - 1)) { /* * Yes, do it. Note that if var2ndigits is much smaller than * div_ndigits, we can save a significant amount of effort * here by noting that we only need to normalise those div[] * entries touched where prior iterations subtracted multiples * of the divisor. */ carry = 0; for (i = Min(qi + var2ndigits - 2, div_ndigits); i > qi; i--) { newdig = div[i] + carry; if (newdig < 0) { carry = -((-newdig - 1) / NBASE) - 1; newdig -= carry * NBASE; } else if (newdig >= NBASE) { carry = newdig / NBASE; newdig -= carry * NBASE; } else carry = 0; div[i] = newdig; } newdig = div[qi] + carry; div[qi] = newdig; /* * All the div[] digits except possibly div[qi] are now in the * range 0..NBASE-1. We do not need to consider div[qi] in * the maxdiv value anymore, so we can reset maxdiv to 1. */ maxdiv = 1; /* * Recompute the quotient digit since new info may have * propagated into the top four dividend digits */ fdividend = (double) div[qi]; for (i = 1; i < 4; i++) { fdividend *= NBASE; if (qi + i <= div_ndigits) fdividend += (double) div[qi + i]; } /* Compute the (approximate) quotient digit */ fquotient = fdividend * fdivisorinverse; qdigit = (fquotient >= 0.0) ? ((int) fquotient) : (((int) fquotient) - 1); /* truncate towards -infinity */ maxdiv += Abs(qdigit); } /* * Subtract off the appropriate multiple of the divisor. * * The digits beyond div[qi] cannot overflow, because we know they * will fall within the maxdiv limit. As for div[qi] itself, note * that qdigit is approximately trunc(div[qi] / vardigits[0]), * which would make the new value simply div[qi] mod vardigits[0]. * The lower-order terms in qdigit can change this result by not * more than about twice INT_MAX/NBASE, so overflow is impossible. */ if (qdigit != 0) { int istop = Min(var2ndigits, div_ndigits - qi + 1); for (i = 0; i < istop; i++) div[qi + i] -= qdigit * var2digits[i]; } } /* * The dividend digit we are about to replace might still be nonzero. * Fold it into the next digit position. * * There is no risk of overflow here, although proving that requires * some care. Much as with the argument for div[qi] not overflowing, * if we consider the first two terms in the numerator and denominator * of qdigit, we can see that the final value of div[qi + 1] will be * approximately a remainder mod (vardigits[0]*NBASE + vardigits[1]). * Accounting for the lower-order terms is a bit complicated but ends * up adding not much more than INT_MAX/NBASE to the possible range. * Thus, div[qi + 1] cannot overflow here, and in its role as div[qi] * in the next loop iteration, it can't be large enough to cause * overflow in the carry propagation step (if any), either. * * But having said that: div[qi] can be more than INT_MAX/NBASE, as * noted above, which means that the product div[qi] * NBASE *can* * overflow. When that happens, adding it to div[qi + 1] will always * cause a canceling overflow so that the end result is correct. We * could avoid the intermediate overflow by doing the multiplication * and addition in int64 arithmetic, but so far there appears no need. */ div[qi + 1] += div[qi] * NBASE; div[qi] = qdigit; } /* * Approximate and store the last quotient digit (div[div_ndigits]) */ fdividend = (double) div[qi]; for (i = 1; i < 4; i++) fdividend *= NBASE; fquotient = fdividend * fdivisorinverse; qdigit = (fquotient >= 0.0) ? ((int) fquotient) : (((int) fquotient) - 1); /* truncate towards -infinity */ div[qi] = qdigit; /* * Because the quotient digits might be off by one, some of them might be * -1 or NBASE at this point. The represented value is correct in a * mathematical sense, but it doesn't look right. We do a final carry * propagation pass to normalize the digits, which we combine with storing * the result digits into the output. Note that this is still done at * full precision w/guard digits. */ alloc_var(result, div_ndigits + 1); res_digits = result->digits; carry = 0; for (i = div_ndigits; i >= 0; i--) { newdig = div[i] + carry; if (newdig < 0) { carry = -((-newdig - 1) / NBASE) - 1; newdig -= carry * NBASE; } else if (newdig >= NBASE) { carry = newdig / NBASE; newdig -= carry * NBASE; } else carry = 0; res_digits[i] = newdig; } Assert(carry == 0); pfree(div); /* * Finally, round the result to the requested precision. */ result->weight = res_weight; result->sign = res_sign; /* Round to target rscale (and set result->dscale) */ if (round) round_var(result, rscale); else trunc_var(result, rscale); /* Strip leading and trailing zeroes */ strip_var(result); } /* * Default scale selection for division * * Returns the appropriate result scale for the division result. */ static int select_div_scale(const NumericVar *var1, const NumericVar *var2) { int weight1, weight2, qweight, i; NumericDigit firstdigit1, firstdigit2; int rscale; /* * The result scale of a division isn't specified in any SQL standard. For * PostgreSQL we select a result scale that will give at least * NUMERIC_MIN_SIG_DIGITS significant digits, so that numeric gives a * result no less accurate than float8; but use a scale not less than * either input's display scale. */ /* Get the actual (normalized) weight and first digit of each input */ weight1 = 0; /* values to use if var1 is zero */ firstdigit1 = 0; for (i = 0; i < var1->ndigits; i++) { firstdigit1 = var1->digits[i]; if (firstdigit1 != 0) { weight1 = var1->weight - i; break; } } weight2 = 0; /* values to use if var2 is zero */ firstdigit2 = 0; for (i = 0; i < var2->ndigits; i++) { firstdigit2 = var2->digits[i]; if (firstdigit2 != 0) { weight2 = var2->weight - i; break; } } /* * Estimate weight of quotient. If the two first digits are equal, we * can't be sure, but assume that var1 is less than var2. */ qweight = weight1 - weight2; if (firstdigit1 <= firstdigit2) qweight--; /* Select result scale */ rscale = NUMERIC_MIN_SIG_DIGITS - qweight * DEC_DIGITS; rscale = Max(rscale, var1->dscale); rscale = Max(rscale, var2->dscale); rscale = Max(rscale, NUMERIC_MIN_DISPLAY_SCALE); rscale = Min(rscale, NUMERIC_MAX_DISPLAY_SCALE); return rscale; } /* * mod_var() - * * Calculate the modulo of two numerics at variable level */ static void mod_var(const NumericVar *var1, const NumericVar *var2, NumericVar *result) { NumericVar tmp; init_var(&tmp); /* --------- * We do this using the equation * mod(x,y) = x - trunc(x/y)*y * div_var can be persuaded to give us trunc(x/y) directly. * ---------- */ div_var(var1, var2, &tmp, 0, false); mul_var(var2, &tmp, &tmp, var2->dscale); sub_var(var1, &tmp, result); free_var(&tmp); } /* * div_mod_var() - * * Calculate the truncated integer quotient and numeric remainder of two * numeric variables. The remainder is precise to var2's dscale. */ static void div_mod_var(const NumericVar *var1, const NumericVar *var2, NumericVar *quot, NumericVar *rem) { NumericVar q; NumericVar r; init_var(&q); init_var(&r); /* * Use div_var_fast() to get an initial estimate for the integer quotient. * This might be inaccurate (per the warning in div_var_fast's comments), * but we can correct it below. */ div_var_fast(var1, var2, &q, 0, false); /* Compute initial estimate of remainder using the quotient estimate. */ mul_var(var2, &q, &r, var2->dscale); sub_var(var1, &r, &r); /* * Adjust the results if necessary --- the remainder should have the same * sign as var1, and its absolute value should be less than the absolute * value of var2. */ while (r.ndigits != 0 && r.sign != var1->sign) { /* The absolute value of the quotient is too large */ if (var1->sign == var2->sign) { sub_var(&q, &const_one, &q); add_var(&r, var2, &r); } else { add_var(&q, &const_one, &q); sub_var(&r, var2, &r); } } while (cmp_abs(&r, var2) >= 0) { /* The absolute value of the quotient is too small */ if (var1->sign == var2->sign) { add_var(&q, &const_one, &q); sub_var(&r, var2, &r); } else { sub_var(&q, &const_one, &q); add_var(&r, var2, &r); } } set_var_from_var(&q, quot); set_var_from_var(&r, rem); free_var(&q); free_var(&r); } /* * ceil_var() - * * Return the smallest integer greater than or equal to the argument * on variable level */ static void ceil_var(const NumericVar *var, NumericVar *result) { NumericVar tmp; init_var(&tmp); set_var_from_var(var, &tmp); trunc_var(&tmp, 0); if (var->sign == NUMERIC_POS && cmp_var(var, &tmp) != 0) add_var(&tmp, &const_one, &tmp); set_var_from_var(&tmp, result); free_var(&tmp); } /* * floor_var() - * * Return the largest integer equal to or less than the argument * on variable level */ static void floor_var(const NumericVar *var, NumericVar *result) { NumericVar tmp; init_var(&tmp); set_var_from_var(var, &tmp); trunc_var(&tmp, 0); if (var->sign == NUMERIC_NEG && cmp_var(var, &tmp) != 0) sub_var(&tmp, &const_one, &tmp); set_var_from_var(&tmp, result); free_var(&tmp); } /* * gcd_var() - * * Calculate the greatest common divisor of two numerics at variable level */ static void gcd_var(const NumericVar *var1, const NumericVar *var2, NumericVar *result) { int res_dscale; int cmp; NumericVar tmp_arg; NumericVar mod; res_dscale = Max(var1->dscale, var2->dscale); /* * Arrange for var1 to be the number with the greater absolute value. * * This would happen automatically in the loop below, but avoids an * expensive modulo operation. */ cmp = cmp_abs(var1, var2); if (cmp < 0) { const NumericVar *tmp = var1; var1 = var2; var2 = tmp; } /* * Also avoid the taking the modulo if the inputs have the same absolute * value, or if the smaller input is zero. */ if (cmp == 0 || var2->ndigits == 0) { set_var_from_var(var1, result); result->sign = NUMERIC_POS; result->dscale = res_dscale; return; } init_var(&tmp_arg); init_var(&mod); /* Use the Euclidean algorithm to find the GCD */ set_var_from_var(var1, &tmp_arg); set_var_from_var(var2, result); for (;;) { /* this loop can take a while, so allow it to be interrupted */ CHECK_FOR_INTERRUPTS(); mod_var(&tmp_arg, result, &mod); if (mod.ndigits == 0) break; set_var_from_var(result, &tmp_arg); set_var_from_var(&mod, result); } result->sign = NUMERIC_POS; result->dscale = res_dscale; free_var(&tmp_arg); free_var(&mod); } /* * sqrt_var() - * * Compute the square root of x using the Karatsuba Square Root algorithm. * NOTE: we allow rscale < 0 here, implying rounding before the decimal * point. */ static void sqrt_var(const NumericVar *arg, NumericVar *result, int rscale) { int stat; int res_weight; int res_ndigits; int src_ndigits; int step; int ndigits[32]; int blen; int64 arg_int64; int src_idx; int64 s_int64; int64 r_int64; NumericVar s_var; NumericVar r_var; NumericVar a0_var; NumericVar a1_var; NumericVar q_var; NumericVar u_var; stat = cmp_var(arg, &const_zero); if (stat == 0) { zero_var(result); result->dscale = rscale; return; } /* * SQL2003 defines sqrt() in terms of power, so we need to emit the right * SQLSTATE error code if the operand is negative. */ if (stat < 0) ereport(ERROR, (errcode(ERRCODE_INVALID_ARGUMENT_FOR_POWER_FUNCTION), errmsg("cannot take square root of a negative number"))); init_var(&s_var); init_var(&r_var); init_var(&a0_var); init_var(&a1_var); init_var(&q_var); init_var(&u_var); /* * The result weight is half the input weight, rounded towards minus * infinity --- res_weight = floor(arg->weight / 2). */ if (arg->weight >= 0) res_weight = arg->weight / 2; else res_weight = -((-arg->weight - 1) / 2 + 1); /* * Number of NBASE digits to compute. To ensure correct rounding, compute * at least 1 extra decimal digit. We explicitly allow rscale to be * negative here, but must always compute at least 1 NBASE digit. Thus * res_ndigits = res_weight + 1 + ceil((rscale + 1) / DEC_DIGITS) or 1. */ if (rscale + 1 >= 0) res_ndigits = res_weight + 1 + (rscale + DEC_DIGITS) / DEC_DIGITS; else res_ndigits = res_weight + 1 - (-rscale - 1) / DEC_DIGITS; res_ndigits = Max(res_ndigits, 1); /* * Number of source NBASE digits logically required to produce a result * with this precision --- every digit before the decimal point, plus 2 * for each result digit after the decimal point (or minus 2 for each * result digit we round before the decimal point). */ src_ndigits = arg->weight + 1 + (res_ndigits - res_weight - 1) * 2; src_ndigits = Max(src_ndigits, 1); /* ---------- * From this point on, we treat the input and the result as integers and * compute the integer square root and remainder using the Karatsuba * Square Root algorithm, which may be written recursively as follows: * * SqrtRem(n = a3*b^3 + a2*b^2 + a1*b + a0): * [ for some base b, and coefficients a0,a1,a2,a3 chosen so that * 0 <= a0,a1,a2 < b and a3 >= b/4 ] * Let (s,r) = SqrtRem(a3*b + a2) * Let (q,u) = DivRem(r*b + a1, 2*s) * Let s = s*b + q * Let r = u*b + a0 - q^2 * If r < 0 Then * Let r = r + s * Let s = s - 1 * Let r = r + s * Return (s,r) * * See "Karatsuba Square Root", Paul Zimmermann, INRIA Research Report * RR-3805, November 1999. At the time of writing this was available * on the net at . * * The way to read the assumption "n = a3*b^3 + a2*b^2 + a1*b + a0" is * "choose a base b such that n requires at least four base-b digits to * express; then those digits are a3,a2,a1,a0, with a3 possibly larger * than b". For optimal performance, b should have approximately a * quarter the number of digits in the input, so that the outer square * root computes roughly twice as many digits as the inner one. For * simplicity, we choose b = NBASE^blen, an integer power of NBASE. * * We implement the algorithm iteratively rather than recursively, to * allow the working variables to be reused. With this approach, each * digit of the input is read precisely once --- src_idx tracks the number * of input digits used so far. * * The array ndigits[] holds the number of NBASE digits of the input that * will have been used at the end of each iteration, which roughly doubles * each time. Note that the array elements are stored in reverse order, * so if the final iteration requires src_ndigits = 37 input digits, the * array will contain [37,19,11,7,5,3], and we would start by computing * the square root of the 3 most significant NBASE digits. * * In each iteration, we choose blen to be the largest integer for which * the input number has a3 >= b/4, when written in the form above. In * general, this means blen = src_ndigits / 4 (truncated), but if * src_ndigits is a multiple of 4, that might lead to the coefficient a3 * being less than b/4 (if the first input digit is less than NBASE/4), in * which case we choose blen = src_ndigits / 4 - 1. The number of digits * in the inner square root is then src_ndigits - 2*blen. So, for * example, if we have src_ndigits = 26 initially, the array ndigits[] * will be either [26,14,8,4] or [26,14,8,6,4], depending on the size of * the first input digit. * * Additionally, we can put an upper bound on the number of steps required * as follows --- suppose that the number of source digits is an n-bit * number in the range [2^(n-1), 2^n-1], then blen will be in the range * [2^(n-3)-1, 2^(n-2)-1] and the number of digits in the inner square * root will be in the range [2^(n-2), 2^(n-1)+1]. In the next step, blen * will be in the range [2^(n-4)-1, 2^(n-3)] and the number of digits in * the next inner square root will be in the range [2^(n-3), 2^(n-2)+1]. * This pattern repeats, and in the worst case the array ndigits[] will * contain [2^n-1, 2^(n-1)+1, 2^(n-2)+1, ... 9, 5, 3], and the computation * will require n steps. Therefore, since all digit array sizes are * signed 32-bit integers, the number of steps required is guaranteed to * be less than 32. * ---------- */ step = 0; while ((ndigits[step] = src_ndigits) > 4) { /* Choose b so that a3 >= b/4, as described above */ blen = src_ndigits / 4; if (blen * 4 == src_ndigits && arg->digits[0] < NBASE / 4) blen--; /* Number of digits in the next step (inner square root) */ src_ndigits -= 2 * blen; step++; } /* * First iteration (innermost square root and remainder): * * Here src_ndigits <= 4, and the input fits in an int64. Its square root * has at most 9 decimal digits, so estimate it using double precision * arithmetic, which will in fact almost certainly return the correct * result with no further correction required. */ arg_int64 = arg->digits[0]; for (src_idx = 1; src_idx < src_ndigits; src_idx++) { arg_int64 *= NBASE; if (src_idx < arg->ndigits) arg_int64 += arg->digits[src_idx]; } s_int64 = (int64) sqrt((double) arg_int64); r_int64 = arg_int64 - s_int64 * s_int64; /* * Use Newton's method to correct the result, if necessary. * * This uses integer division with truncation to compute the truncated * integer square root by iterating using the formula x -> (x + n/x) / 2. * This is known to converge to isqrt(n), unless n+1 is a perfect square. * If n+1 is a perfect square, the sequence will oscillate between the two * values isqrt(n) and isqrt(n)+1, so we can be assured of convergence by * checking the remainder. */ while (r_int64 < 0 || r_int64 > 2 * s_int64) { s_int64 = (s_int64 + arg_int64 / s_int64) / 2; r_int64 = arg_int64 - s_int64 * s_int64; } /* * Iterations with src_ndigits <= 8: * * The next 1 or 2 iterations compute larger (outer) square roots with * src_ndigits <= 8, so the result still fits in an int64 (even though the * input no longer does) and we can continue to compute using int64 * variables to avoid more expensive numeric computations. * * It is fairly easy to see that there is no risk of the intermediate * values below overflowing 64-bit integers. In the worst case, the * previous iteration will have computed a 3-digit square root (of a * 6-digit input less than NBASE^6 / 4), so at the start of this * iteration, s will be less than NBASE^3 / 2 = 10^12 / 2, and r will be * less than 10^12. In this case, blen will be 1, so numer will be less * than 10^17, and denom will be less than 10^12 (and hence u will also be * less than 10^12). Finally, since q^2 = u*b + a0 - r, we can also be * sure that q^2 < 10^17. Therefore all these quantities fit comfortably * in 64-bit integers. */ step--; while (step >= 0 && (src_ndigits = ndigits[step]) <= 8) { int b; int a0; int a1; int i; int64 numer; int64 denom; int64 q; int64 u; blen = (src_ndigits - src_idx) / 2; /* Extract a1 and a0, and compute b */ a0 = 0; a1 = 0; b = 1; for (i = 0; i < blen; i++, src_idx++) { b *= NBASE; a1 *= NBASE; if (src_idx < arg->ndigits) a1 += arg->digits[src_idx]; } for (i = 0; i < blen; i++, src_idx++) { a0 *= NBASE; if (src_idx < arg->ndigits) a0 += arg->digits[src_idx]; } /* Compute (q,u) = DivRem(r*b + a1, 2*s) */ numer = r_int64 * b + a1; denom = 2 * s_int64; q = numer / denom; u = numer - q * denom; /* Compute s = s*b + q and r = u*b + a0 - q^2 */ s_int64 = s_int64 * b + q; r_int64 = u * b + a0 - q * q; if (r_int64 < 0) { /* s is too large by 1; set r += s, s--, r += s */ r_int64 += s_int64; s_int64--; r_int64 += s_int64; } Assert(src_idx == src_ndigits); /* All input digits consumed */ step--; } /* * On platforms with 128-bit integer support, we can further delay the * need to use numeric variables. */ #ifdef HAVE_INT128 if (step >= 0) { int128 s_int128; int128 r_int128; s_int128 = s_int64; r_int128 = r_int64; /* * Iterations with src_ndigits <= 16: * * The result fits in an int128 (even though the input doesn't) so we * use int128 variables to avoid more expensive numeric computations. */ while (step >= 0 && (src_ndigits = ndigits[step]) <= 16) { int64 b; int64 a0; int64 a1; int64 i; int128 numer; int128 denom; int128 q; int128 u; blen = (src_ndigits - src_idx) / 2; /* Extract a1 and a0, and compute b */ a0 = 0; a1 = 0; b = 1; for (i = 0; i < blen; i++, src_idx++) { b *= NBASE; a1 *= NBASE; if (src_idx < arg->ndigits) a1 += arg->digits[src_idx]; } for (i = 0; i < blen; i++, src_idx++) { a0 *= NBASE; if (src_idx < arg->ndigits) a0 += arg->digits[src_idx]; } /* Compute (q,u) = DivRem(r*b + a1, 2*s) */ numer = r_int128 * b + a1; denom = 2 * s_int128; q = numer / denom; u = numer - q * denom; /* Compute s = s*b + q and r = u*b + a0 - q^2 */ s_int128 = s_int128 * b + q; r_int128 = u * b + a0 - q * q; if (r_int128 < 0) { /* s is too large by 1; set r += s, s--, r += s */ r_int128 += s_int128; s_int128--; r_int128 += s_int128; } Assert(src_idx == src_ndigits); /* All input digits consumed */ step--; } /* * All remaining iterations require numeric variables. Convert the * integer values to NumericVar and continue. Note that in the final * iteration we don't need the remainder, so we can save a few cycles * there by not fully computing it. */ int128_to_numericvar(s_int128, &s_var); if (step >= 0) int128_to_numericvar(r_int128, &r_var); } else { int64_to_numericvar(s_int64, &s_var); /* step < 0, so we certainly don't need r */ } #else /* !HAVE_INT128 */ int64_to_numericvar(s_int64, &s_var); if (step >= 0) int64_to_numericvar(r_int64, &r_var); #endif /* HAVE_INT128 */ /* * The remaining iterations with src_ndigits > 8 (or 16, if have int128) * use numeric variables. */ while (step >= 0) { int tmp_len; src_ndigits = ndigits[step]; blen = (src_ndigits - src_idx) / 2; /* Extract a1 and a0 */ if (src_idx < arg->ndigits) { tmp_len = Min(blen, arg->ndigits - src_idx); alloc_var(&a1_var, tmp_len); memcpy(a1_var.digits, arg->digits + src_idx, tmp_len * sizeof(NumericDigit)); a1_var.weight = blen - 1; a1_var.sign = NUMERIC_POS; a1_var.dscale = 0; strip_var(&a1_var); } else { zero_var(&a1_var); a1_var.dscale = 0; } src_idx += blen; if (src_idx < arg->ndigits) { tmp_len = Min(blen, arg->ndigits - src_idx); alloc_var(&a0_var, tmp_len); memcpy(a0_var.digits, arg->digits + src_idx, tmp_len * sizeof(NumericDigit)); a0_var.weight = blen - 1; a0_var.sign = NUMERIC_POS; a0_var.dscale = 0; strip_var(&a0_var); } else { zero_var(&a0_var); a0_var.dscale = 0; } src_idx += blen; /* Compute (q,u) = DivRem(r*b + a1, 2*s) */ set_var_from_var(&r_var, &q_var); q_var.weight += blen; add_var(&q_var, &a1_var, &q_var); add_var(&s_var, &s_var, &u_var); div_mod_var(&q_var, &u_var, &q_var, &u_var); /* Compute s = s*b + q */ s_var.weight += blen; add_var(&s_var, &q_var, &s_var); /* * Compute r = u*b + a0 - q^2. * * In the final iteration, we don't actually need r; we just need to * know whether it is negative, so that we know whether to adjust s. * So instead of the final subtraction we can just compare. */ u_var.weight += blen; add_var(&u_var, &a0_var, &u_var); mul_var(&q_var, &q_var, &q_var, 0); if (step > 0) { /* Need r for later iterations */ sub_var(&u_var, &q_var, &r_var); if (r_var.sign == NUMERIC_NEG) { /* s is too large by 1; set r += s, s--, r += s */ add_var(&r_var, &s_var, &r_var); sub_var(&s_var, &const_one, &s_var); add_var(&r_var, &s_var, &r_var); } } else { /* Don't need r anymore, except to test if s is too large by 1 */ if (cmp_var(&u_var, &q_var) < 0) sub_var(&s_var, &const_one, &s_var); } Assert(src_idx == src_ndigits); /* All input digits consumed */ step--; } /* * Construct the final result, rounding it to the requested precision. */ set_var_from_var(&s_var, result); result->weight = res_weight; result->sign = NUMERIC_POS; /* Round to target rscale (and set result->dscale) */ round_var(result, rscale); /* Strip leading and trailing zeroes */ strip_var(result); free_var(&s_var); free_var(&r_var); free_var(&a0_var); free_var(&a1_var); free_var(&q_var); free_var(&u_var); } /* * exp_var() - * * Raise e to the power of x, computed to rscale fractional digits */ static void exp_var(const NumericVar *arg, NumericVar *result, int rscale) { NumericVar x; NumericVar elem; NumericVar ni; double val; int dweight; int ndiv2; int sig_digits; int local_rscale; init_var(&x); init_var(&elem); init_var(&ni); set_var_from_var(arg, &x); /* * Estimate the dweight of the result using floating point arithmetic, so * that we can choose an appropriate local rscale for the calculation. */ val = numericvar_to_double_no_overflow(&x); /* Guard against overflow/underflow */ /* If you change this limit, see also power_var()'s limit */ if (Abs(val) >= NUMERIC_MAX_RESULT_SCALE * 3) { if (val > 0) ereport(ERROR, (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE), errmsg("value overflows numeric format"))); zero_var(result); result->dscale = rscale; return; } /* decimal weight = log10(e^x) = x * log10(e) */ dweight = (int) (val * 0.434294481903252); /* * Reduce x to the range -0.01 <= x <= 0.01 (approximately) by dividing by * 2^n, to improve the convergence rate of the Taylor series. */ if (Abs(val) > 0.01) { NumericVar tmp; init_var(&tmp); set_var_from_var(&const_two, &tmp); ndiv2 = 1; val /= 2; while (Abs(val) > 0.01) { ndiv2++; val /= 2; add_var(&tmp, &tmp, &tmp); } local_rscale = x.dscale + ndiv2; div_var_fast(&x, &tmp, &x, local_rscale, true); free_var(&tmp); } else ndiv2 = 0; /* * Set the scale for the Taylor series expansion. The final result has * (dweight + rscale + 1) significant digits. In addition, we have to * raise the Taylor series result to the power 2^ndiv2, which introduces * an error of up to around log10(2^ndiv2) digits, so work with this many * extra digits of precision (plus a few more for good measure). */ sig_digits = 1 + dweight + rscale + (int) (ndiv2 * 0.301029995663981); sig_digits = Max(sig_digits, 0) + 8; local_rscale = sig_digits - 1; /* * Use the Taylor series * * exp(x) = 1 + x + x^2/2! + x^3/3! + ... * * Given the limited range of x, this should converge reasonably quickly. * We run the series until the terms fall below the local_rscale limit. */ add_var(&const_one, &x, result); mul_var(&x, &x, &elem, local_rscale); set_var_from_var(&const_two, &ni); div_var_fast(&elem, &ni, &elem, local_rscale, true); while (elem.ndigits != 0) { add_var(result, &elem, result); mul_var(&elem, &x, &elem, local_rscale); add_var(&ni, &const_one, &ni); div_var_fast(&elem, &ni, &elem, local_rscale, true); } /* * Compensate for the argument range reduction. Since the weight of the * result doubles with each multiplication, we can reduce the local rscale * as we proceed. */ while (ndiv2-- > 0) { local_rscale = sig_digits - result->weight * 2 * DEC_DIGITS; local_rscale = Max(local_rscale, NUMERIC_MIN_DISPLAY_SCALE); mul_var(result, result, result, local_rscale); } /* Round to requested rscale */ round_var(result, rscale); free_var(&x); free_var(&elem); free_var(&ni); } /* * Estimate the dweight of the most significant decimal digit of the natural * logarithm of a number. * * Essentially, we're approximating log10(abs(ln(var))). This is used to * determine the appropriate rscale when computing natural logarithms. */ static int estimate_ln_dweight(const NumericVar *var) { int ln_dweight; if (cmp_var(var, &const_zero_point_nine) >= 0 && cmp_var(var, &const_one_point_one) <= 0) { /* * 0.9 <= var <= 1.1 * * ln(var) has a negative weight (possibly very large). To get a * reasonably accurate result, estimate it using ln(1+x) ~= x. */ NumericVar x; init_var(&x); sub_var(var, &const_one, &x); if (x.ndigits > 0) { /* Use weight of most significant decimal digit of x */ ln_dweight = x.weight * DEC_DIGITS + (int) log10(x.digits[0]); } else { /* x = 0. Since ln(1) = 0 exactly, we don't need extra digits */ ln_dweight = 0; } free_var(&x); } else { /* * Estimate the logarithm using the first couple of digits from the * input number. This will give an accurate result whenever the input * is not too close to 1. */ if (var->ndigits > 0) { int digits; int dweight; double ln_var; digits = var->digits[0]; dweight = var->weight * DEC_DIGITS; if (var->ndigits > 1) { digits = digits * NBASE + var->digits[1]; dweight -= DEC_DIGITS; } /*---------- * We have var ~= digits * 10^dweight * so ln(var) ~= ln(digits) + dweight * ln(10) *---------- */ ln_var = log((double) digits) + dweight * 2.302585092994046; ln_dweight = (int) log10(Abs(ln_var)); } else { /* Caller should fail on ln(0), but for the moment return zero */ ln_dweight = 0; } } return ln_dweight; } /* * ln_var() - * * Compute the natural log of x */ static void ln_var(const NumericVar *arg, NumericVar *result, int rscale) { NumericVar x; NumericVar xx; NumericVar ni; NumericVar elem; NumericVar fact; int nsqrt; int local_rscale; int cmp; cmp = cmp_var(arg, &const_zero); if (cmp == 0) ereport(ERROR, (errcode(ERRCODE_INVALID_ARGUMENT_FOR_LOG), errmsg("cannot take logarithm of zero"))); else if (cmp < 0) ereport(ERROR, (errcode(ERRCODE_INVALID_ARGUMENT_FOR_LOG), errmsg("cannot take logarithm of a negative number"))); init_var(&x); init_var(&xx); init_var(&ni); init_var(&elem); init_var(&fact); set_var_from_var(arg, &x); set_var_from_var(&const_two, &fact); /* * Reduce input into range 0.9 < x < 1.1 with repeated sqrt() operations. * * The final logarithm will have up to around rscale+6 significant digits. * Each sqrt() will roughly halve the weight of x, so adjust the local * rscale as we work so that we keep this many significant digits at each * step (plus a few more for good measure). * * Note that we allow local_rscale < 0 during this input reduction * process, which implies rounding before the decimal point. sqrt_var() * explicitly supports this, and it significantly reduces the work * required to reduce very large inputs to the required range. Once the * input reduction is complete, x.weight will be 0 and its display scale * will be non-negative again. */ nsqrt = 0; while (cmp_var(&x, &const_zero_point_nine) <= 0) { local_rscale = rscale - x.weight * DEC_DIGITS / 2 + 8; sqrt_var(&x, &x, local_rscale); mul_var(&fact, &const_two, &fact, 0); nsqrt++; } while (cmp_var(&x, &const_one_point_one) >= 0) { local_rscale = rscale - x.weight * DEC_DIGITS / 2 + 8; sqrt_var(&x, &x, local_rscale); mul_var(&fact, &const_two, &fact, 0); nsqrt++; } /* * We use the Taylor series for 0.5 * ln((1+z)/(1-z)), * * z + z^3/3 + z^5/5 + ... * * where z = (x-1)/(x+1) is in the range (approximately) -0.053 .. 0.048 * due to the above range-reduction of x. * * The convergence of this is not as fast as one would like, but is * tolerable given that z is small. * * The Taylor series result will be multiplied by 2^(nsqrt+1), which has a * decimal weight of (nsqrt+1) * log10(2), so work with this many extra * digits of precision (plus a few more for good measure). */ local_rscale = rscale + (int) ((nsqrt + 1) * 0.301029995663981) + 8; sub_var(&x, &const_one, result); add_var(&x, &const_one, &elem); div_var_fast(result, &elem, result, local_rscale, true); set_var_from_var(result, &xx); mul_var(result, result, &x, local_rscale); set_var_from_var(&const_one, &ni); for (;;) { add_var(&ni, &const_two, &ni); mul_var(&xx, &x, &xx, local_rscale); div_var_fast(&xx, &ni, &elem, local_rscale, true); if (elem.ndigits == 0) break; add_var(result, &elem, result); if (elem.weight < (result->weight - local_rscale * 2 / DEC_DIGITS)) break; } /* Compensate for argument range reduction, round to requested rscale */ mul_var(result, &fact, result, rscale); free_var(&x); free_var(&xx); free_var(&ni); free_var(&elem); free_var(&fact); } /* * log_var() - * * Compute the logarithm of num in a given base. * * Note: this routine chooses dscale of the result. */ static void log_var(const NumericVar *base, const NumericVar *num, NumericVar *result) { NumericVar ln_base; NumericVar ln_num; int ln_base_dweight; int ln_num_dweight; int result_dweight; int rscale; int ln_base_rscale; int ln_num_rscale; init_var(&ln_base); init_var(&ln_num); /* Estimated dweights of ln(base), ln(num) and the final result */ ln_base_dweight = estimate_ln_dweight(base); ln_num_dweight = estimate_ln_dweight(num); result_dweight = ln_num_dweight - ln_base_dweight; /* * Select the scale of the result so that it will have at least * NUMERIC_MIN_SIG_DIGITS significant digits and is not less than either * input's display scale. */ rscale = NUMERIC_MIN_SIG_DIGITS - result_dweight; rscale = Max(rscale, base->dscale); rscale = Max(rscale, num->dscale); rscale = Max(rscale, NUMERIC_MIN_DISPLAY_SCALE); rscale = Min(rscale, NUMERIC_MAX_DISPLAY_SCALE); /* * Set the scales for ln(base) and ln(num) so that they each have more * significant digits than the final result. */ ln_base_rscale = rscale + result_dweight - ln_base_dweight + 8; ln_base_rscale = Max(ln_base_rscale, NUMERIC_MIN_DISPLAY_SCALE); ln_num_rscale = rscale + result_dweight - ln_num_dweight + 8; ln_num_rscale = Max(ln_num_rscale, NUMERIC_MIN_DISPLAY_SCALE); /* Form natural logarithms */ ln_var(base, &ln_base, ln_base_rscale); ln_var(num, &ln_num, ln_num_rscale); /* Divide and round to the required scale */ div_var_fast(&ln_num, &ln_base, result, rscale, true); free_var(&ln_num); free_var(&ln_base); } /* * power_var() - * * Raise base to the power of exp * * Note: this routine chooses dscale of the result. */ static void power_var(const NumericVar *base, const NumericVar *exp, NumericVar *result) { int res_sign; NumericVar abs_base; NumericVar ln_base; NumericVar ln_num; int ln_dweight; int rscale; int sig_digits; int local_rscale; double val; /* If exp can be represented as an integer, use power_var_int */ if (exp->ndigits == 0 || exp->ndigits <= exp->weight + 1) { /* exact integer, but does it fit in int? */ int64 expval64; if (numericvar_to_int64(exp, &expval64)) { if (expval64 >= PG_INT32_MIN && expval64 <= PG_INT32_MAX) { /* Okay, select rscale */ rscale = NUMERIC_MIN_SIG_DIGITS; rscale = Max(rscale, base->dscale); rscale = Max(rscale, NUMERIC_MIN_DISPLAY_SCALE); rscale = Min(rscale, NUMERIC_MAX_DISPLAY_SCALE); power_var_int(base, (int) expval64, result, rscale); return; } } } /* * This avoids log(0) for cases of 0 raised to a non-integer. 0 ^ 0 is * handled by power_var_int(). */ if (cmp_var(base, &const_zero) == 0) { set_var_from_var(&const_zero, result); result->dscale = NUMERIC_MIN_SIG_DIGITS; /* no need to round */ return; } init_var(&abs_base); init_var(&ln_base); init_var(&ln_num); /* * If base is negative, insist that exp be an integer. The result is then * positive if exp is even and negative if exp is odd. */ if (base->sign == NUMERIC_NEG) { /* * Check that exp is an integer. This error code is defined by the * SQL standard, and matches other errors in numeric_power(). */ if (exp->ndigits > 0 && exp->ndigits > exp->weight + 1) ereport(ERROR, (errcode(ERRCODE_INVALID_ARGUMENT_FOR_POWER_FUNCTION), errmsg("a negative number raised to a non-integer power yields a complex result"))); /* Test if exp is odd or even */ if (exp->ndigits > 0 && exp->ndigits == exp->weight + 1 && (exp->digits[exp->ndigits - 1] & 1)) res_sign = NUMERIC_NEG; else res_sign = NUMERIC_POS; /* Then work with abs(base) below */ set_var_from_var(base, &abs_base); abs_base.sign = NUMERIC_POS; base = &abs_base; } else res_sign = NUMERIC_POS; /*---------- * Decide on the scale for the ln() calculation. For this we need an * estimate of the weight of the result, which we obtain by doing an * initial low-precision calculation of exp * ln(base). * * We want result = e ^ (exp * ln(base)) * so result dweight = log10(result) = exp * ln(base) * log10(e) * * We also perform a crude overflow test here so that we can exit early if * the full-precision result is sure to overflow, and to guard against * integer overflow when determining the scale for the real calculation. * exp_var() supports inputs up to NUMERIC_MAX_RESULT_SCALE * 3, so the * result will overflow if exp * ln(base) >= NUMERIC_MAX_RESULT_SCALE * 3. * Since the values here are only approximations, we apply a small fuzz * factor to this overflow test and let exp_var() determine the exact * overflow threshold so that it is consistent for all inputs. *---------- */ ln_dweight = estimate_ln_dweight(base); local_rscale = 8 - ln_dweight; local_rscale = Max(local_rscale, NUMERIC_MIN_DISPLAY_SCALE); local_rscale = Min(local_rscale, NUMERIC_MAX_DISPLAY_SCALE); ln_var(base, &ln_base, local_rscale); mul_var(&ln_base, exp, &ln_num, local_rscale); val = numericvar_to_double_no_overflow(&ln_num); /* initial overflow/underflow test with fuzz factor */ if (Abs(val) > NUMERIC_MAX_RESULT_SCALE * 3.01) { if (val > 0) ereport(ERROR, (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE), errmsg("value overflows numeric format"))); zero_var(result); result->dscale = NUMERIC_MAX_DISPLAY_SCALE; return; } val *= 0.434294481903252; /* approximate decimal result weight */ /* choose the result scale */ rscale = NUMERIC_MIN_SIG_DIGITS - (int) val; rscale = Max(rscale, base->dscale); rscale = Max(rscale, exp->dscale); rscale = Max(rscale, NUMERIC_MIN_DISPLAY_SCALE); rscale = Min(rscale, NUMERIC_MAX_DISPLAY_SCALE); /* significant digits required in the result */ sig_digits = rscale + (int) val; sig_digits = Max(sig_digits, 0); /* set the scale for the real exp * ln(base) calculation */ local_rscale = sig_digits - ln_dweight + 8; local_rscale = Max(local_rscale, NUMERIC_MIN_DISPLAY_SCALE); /* and do the real calculation */ ln_var(base, &ln_base, local_rscale); mul_var(&ln_base, exp, &ln_num, local_rscale); exp_var(&ln_num, result, rscale); if (res_sign == NUMERIC_NEG && result->ndigits > 0) result->sign = NUMERIC_NEG; free_var(&ln_num); free_var(&ln_base); free_var(&abs_base); } /* * power_var_int() - * * Raise base to the power of exp, where exp is an integer. */ static void power_var_int(const NumericVar *base, int exp, NumericVar *result, int rscale) { double f; int p; int i; int sig_digits; unsigned int mask; bool neg; NumericVar base_prod; int local_rscale; /* Handle some common special cases, as well as corner cases */ switch (exp) { case 0: /* * While 0 ^ 0 can be either 1 or indeterminate (error), we treat * it as 1 because most programming languages do this. SQL:2003 * also requires a return value of 1. * https://en.wikipedia.org/wiki/Exponentiation#Zero_to_the_zero_power */ set_var_from_var(&const_one, result); result->dscale = rscale; /* no need to round */ return; case 1: set_var_from_var(base, result); round_var(result, rscale); return; case -1: div_var(&const_one, base, result, rscale, true); return; case 2: mul_var(base, base, result, rscale); return; default: break; } /* Handle the special case where the base is zero */ if (base->ndigits == 0) { if (exp < 0) ereport(ERROR, (errcode(ERRCODE_DIVISION_BY_ZERO), errmsg("division by zero"))); zero_var(result); result->dscale = rscale; return; } /* * The general case repeatedly multiplies base according to the bit * pattern of exp. * * First we need to estimate the weight of the result so that we know how * many significant digits are needed. */ f = base->digits[0]; p = base->weight * DEC_DIGITS; for (i = 1; i < base->ndigits && i * DEC_DIGITS < 16; i++) { f = f * NBASE + base->digits[i]; p -= DEC_DIGITS; } /*---------- * We have base ~= f * 10^p * so log10(result) = log10(base^exp) ~= exp * (log10(f) + p) *---------- */ f = exp * (log10(f) + p); /* * Apply crude overflow/underflow tests so we can exit early if the result * certainly will overflow/underflow. */ if (f > 3 * SHRT_MAX * DEC_DIGITS) ereport(ERROR, (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE), errmsg("value overflows numeric format"))); if (f + 1 < -rscale || f + 1 < -NUMERIC_MAX_DISPLAY_SCALE) { zero_var(result); result->dscale = rscale; return; } /* * Approximate number of significant digits in the result. Note that the * underflow test above means that this is necessarily >= 0. */ sig_digits = 1 + rscale + (int) f; /* * The multiplications to produce the result may introduce an error of up * to around log10(abs(exp)) digits, so work with this many extra digits * of precision (plus a few more for good measure). */ sig_digits += (int) log(fabs((double) exp)) + 8; /* * Now we can proceed with the multiplications. */ neg = (exp < 0); mask = Abs(exp); init_var(&base_prod); set_var_from_var(base, &base_prod); if (mask & 1) set_var_from_var(base, result); else set_var_from_var(&const_one, result); while ((mask >>= 1) > 0) { /* * Do the multiplications using rscales large enough to hold the * results to the required number of significant digits, but don't * waste time by exceeding the scales of the numbers themselves. */ local_rscale = sig_digits - 2 * base_prod.weight * DEC_DIGITS; local_rscale = Min(local_rscale, 2 * base_prod.dscale); local_rscale = Max(local_rscale, NUMERIC_MIN_DISPLAY_SCALE); mul_var(&base_prod, &base_prod, &base_prod, local_rscale); if (mask & 1) { local_rscale = sig_digits - (base_prod.weight + result->weight) * DEC_DIGITS; local_rscale = Min(local_rscale, base_prod.dscale + result->dscale); local_rscale = Max(local_rscale, NUMERIC_MIN_DISPLAY_SCALE); mul_var(&base_prod, result, result, local_rscale); } /* * When abs(base) > 1, the number of digits to the left of the decimal * point in base_prod doubles at each iteration, so if exp is large we * could easily spend large amounts of time and memory space doing the * multiplications. But once the weight exceeds what will fit in * int16, the final result is guaranteed to overflow (or underflow, if * exp < 0), so we can give up before wasting too many cycles. */ if (base_prod.weight > SHRT_MAX || result->weight > SHRT_MAX) { /* overflow, unless neg, in which case result should be 0 */ if (!neg) ereport(ERROR, (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE), errmsg("value overflows numeric format"))); zero_var(result); neg = false; break; } } free_var(&base_prod); /* Compensate for input sign, and round to requested rscale */ if (neg) div_var_fast(&const_one, result, result, rscale, true); else round_var(result, rscale); } /* * power_ten_int() - * * Raise ten to the power of exp, where exp is an integer. Note that unlike * power_var_int(), this does no overflow/underflow checking or rounding. */ static void power_ten_int(int exp, NumericVar *result) { /* Construct the result directly, starting from 10^0 = 1 */ set_var_from_var(&const_one, result); /* Scale needed to represent the result exactly */ result->dscale = exp < 0 ? -exp : 0; /* Base-NBASE weight of result and remaining exponent */ if (exp >= 0) result->weight = exp / DEC_DIGITS; else result->weight = (exp + 1) / DEC_DIGITS - 1; exp -= result->weight * DEC_DIGITS; /* Final adjustment of the result's single NBASE digit */ while (exp-- > 0) result->digits[0] *= 10; } /* ---------------------------------------------------------------------- * * Following are the lowest level functions that operate unsigned * on the variable level * * ---------------------------------------------------------------------- */ /* ---------- * cmp_abs() - * * Compare the absolute values of var1 and var2 * Returns: -1 for ABS(var1) < ABS(var2) * 0 for ABS(var1) == ABS(var2) * 1 for ABS(var1) > ABS(var2) * ---------- */ static int cmp_abs(const NumericVar *var1, const NumericVar *var2) { return cmp_abs_common(var1->digits, var1->ndigits, var1->weight, var2->digits, var2->ndigits, var2->weight); } /* ---------- * cmp_abs_common() - * * Main routine of cmp_abs(). This function can be used by both * NumericVar and Numeric. * ---------- */ static int cmp_abs_common(const NumericDigit *var1digits, int var1ndigits, int var1weight, const NumericDigit *var2digits, int var2ndigits, int var2weight) { int i1 = 0; int i2 = 0; /* Check any digits before the first common digit */ while (var1weight > var2weight && i1 < var1ndigits) { if (var1digits[i1++] != 0) return 1; var1weight--; } while (var2weight > var1weight && i2 < var2ndigits) { if (var2digits[i2++] != 0) return -1; var2weight--; } /* At this point, either w1 == w2 or we've run out of digits */ if (var1weight == var2weight) { while (i1 < var1ndigits && i2 < var2ndigits) { int stat = var1digits[i1++] - var2digits[i2++]; if (stat) { if (stat > 0) return 1; return -1; } } } /* * At this point, we've run out of digits on one side or the other; so any * remaining nonzero digits imply that side is larger */ while (i1 < var1ndigits) { if (var1digits[i1++] != 0) return 1; } while (i2 < var2ndigits) { if (var2digits[i2++] != 0) return -1; } return 0; } /* * add_abs() - * * Add the absolute values of two variables into result. * result might point to one of the operands without danger. */ static void add_abs(const NumericVar *var1, const NumericVar *var2, NumericVar *result) { NumericDigit *res_buf; NumericDigit *res_digits; int res_ndigits; int res_weight; int res_rscale, rscale1, rscale2; int res_dscale; int i, i1, i2; int carry = 0; /* copy these values into local vars for speed in inner loop */ int var1ndigits = var1->ndigits; int var2ndigits = var2->ndigits; NumericDigit *var1digits = var1->digits; NumericDigit *var2digits = var2->digits; res_weight = Max(var1->weight, var2->weight) + 1; res_dscale = Max(var1->dscale, var2->dscale); /* Note: here we are figuring rscale in base-NBASE digits */ rscale1 = var1->ndigits - var1->weight - 1; rscale2 = var2->ndigits - var2->weight - 1; res_rscale = Max(rscale1, rscale2); res_ndigits = res_rscale + res_weight + 1; if (res_ndigits <= 0) res_ndigits = 1; res_buf = digitbuf_alloc(res_ndigits + 1); res_buf[0] = 0; /* spare digit for later rounding */ res_digits = res_buf + 1; i1 = res_rscale + var1->weight + 1; i2 = res_rscale + var2->weight + 1; for (i = res_ndigits - 1; i >= 0; i--) { i1--; i2--; if (i1 >= 0 && i1 < var1ndigits) carry += var1digits[i1]; if (i2 >= 0 && i2 < var2ndigits) carry += var2digits[i2]; if (carry >= NBASE) { res_digits[i] = carry - NBASE; carry = 1; } else { res_digits[i] = carry; carry = 0; } } Assert(carry == 0); /* else we failed to allow for carry out */ digitbuf_free(result->buf); result->ndigits = res_ndigits; result->buf = res_buf; result->digits = res_digits; result->weight = res_weight; result->dscale = res_dscale; /* Remove leading/trailing zeroes */ strip_var(result); } /* * sub_abs() * * Subtract the absolute value of var2 from the absolute value of var1 * and store in result. result might point to one of the operands * without danger. * * ABS(var1) MUST BE GREATER OR EQUAL ABS(var2) !!! */ static void sub_abs(const NumericVar *var1, const NumericVar *var2, NumericVar *result) { NumericDigit *res_buf; NumericDigit *res_digits; int res_ndigits; int res_weight; int res_rscale, rscale1, rscale2; int res_dscale; int i, i1, i2; int borrow = 0; /* copy these values into local vars for speed in inner loop */ int var1ndigits = var1->ndigits; int var2ndigits = var2->ndigits; NumericDigit *var1digits = var1->digits; NumericDigit *var2digits = var2->digits; res_weight = var1->weight; res_dscale = Max(var1->dscale, var2->dscale); /* Note: here we are figuring rscale in base-NBASE digits */ rscale1 = var1->ndigits - var1->weight - 1; rscale2 = var2->ndigits - var2->weight - 1; res_rscale = Max(rscale1, rscale2); res_ndigits = res_rscale + res_weight + 1; if (res_ndigits <= 0) res_ndigits = 1; res_buf = digitbuf_alloc(res_ndigits + 1); res_buf[0] = 0; /* spare digit for later rounding */ res_digits = res_buf + 1; i1 = res_rscale + var1->weight + 1; i2 = res_rscale + var2->weight + 1; for (i = res_ndigits - 1; i >= 0; i--) { i1--; i2--; if (i1 >= 0 && i1 < var1ndigits) borrow += var1digits[i1]; if (i2 >= 0 && i2 < var2ndigits) borrow -= var2digits[i2]; if (borrow < 0) { res_digits[i] = borrow + NBASE; borrow = -1; } else { res_digits[i] = borrow; borrow = 0; } } Assert(borrow == 0); /* else caller gave us var1 < var2 */ digitbuf_free(result->buf); result->ndigits = res_ndigits; result->buf = res_buf; result->digits = res_digits; result->weight = res_weight; result->dscale = res_dscale; /* Remove leading/trailing zeroes */ strip_var(result); } /* * round_var * * Round the value of a variable to no more than rscale decimal digits * after the decimal point. NOTE: we allow rscale < 0 here, implying * rounding before the decimal point. */ static void round_var(NumericVar *var, int rscale) { NumericDigit *digits = var->digits; int di; int ndigits; int carry; var->dscale = rscale; /* decimal digits wanted */ di = (var->weight + 1) * DEC_DIGITS + rscale; /* * If di = 0, the value loses all digits, but could round up to 1 if its * first extra digit is >= 5. If di < 0 the result must be 0. */ if (di < 0) { var->ndigits = 0; var->weight = 0; var->sign = NUMERIC_POS; } else { /* NBASE digits wanted */ ndigits = (di + DEC_DIGITS - 1) / DEC_DIGITS; /* 0, or number of decimal digits to keep in last NBASE digit */ di %= DEC_DIGITS; if (ndigits < var->ndigits || (ndigits == var->ndigits && di > 0)) { var->ndigits = ndigits; #if DEC_DIGITS == 1 /* di must be zero */ carry = (digits[ndigits] >= HALF_NBASE) ? 1 : 0; #else if (di == 0) carry = (digits[ndigits] >= HALF_NBASE) ? 1 : 0; else { /* Must round within last NBASE digit */ int extra, pow10; #if DEC_DIGITS == 4 pow10 = round_powers[di]; #elif DEC_DIGITS == 2 pow10 = 10; #else #error unsupported NBASE #endif extra = digits[--ndigits] % pow10; digits[ndigits] -= extra; carry = 0; if (extra >= pow10 / 2) { pow10 += digits[ndigits]; if (pow10 >= NBASE) { pow10 -= NBASE; carry = 1; } digits[ndigits] = pow10; } } #endif /* Propagate carry if needed */ while (carry) { carry += digits[--ndigits]; if (carry >= NBASE) { digits[ndigits] = carry - NBASE; carry = 1; } else { digits[ndigits] = carry; carry = 0; } } if (ndigits < 0) { Assert(ndigits == -1); /* better not have added > 1 digit */ Assert(var->digits > var->buf); var->digits--; var->ndigits++; var->weight++; } } } } /* * trunc_var * * 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 trunc_var(NumericVar *var, int rscale) { int di; int ndigits; var->dscale = rscale; /* decimal digits wanted */ di = (var->weight + 1) * DEC_DIGITS + rscale; /* * If di <= 0, the value loses all digits. */ if (di <= 0) { var->ndigits = 0; var->weight = 0; var->sign = NUMERIC_POS; } else { /* NBASE digits wanted */ ndigits = (di + DEC_DIGITS - 1) / DEC_DIGITS; if (ndigits <= var->ndigits) { var->ndigits = ndigits; #if DEC_DIGITS == 1 /* no within-digit stuff to worry about */ #else /* 0, or number of decimal digits to keep in last NBASE digit */ di %= DEC_DIGITS; if (di > 0) { /* Must truncate within last NBASE digit */ NumericDigit *digits = var->digits; int extra, pow10; #if DEC_DIGITS == 4 pow10 = round_powers[di]; #elif DEC_DIGITS == 2 pow10 = 10; #else #error unsupported NBASE #endif extra = digits[--ndigits] % pow10; digits[ndigits] -= extra; } #endif } } } /* * strip_var * * Strip any leading and trailing zeroes from a numeric variable */ static void strip_var(NumericVar *var) { NumericDigit *digits = var->digits; int ndigits = var->ndigits; /* Strip leading zeroes */ while (ndigits > 0 && *digits == 0) { digits++; var->weight--; ndigits--; } /* Strip trailing zeroes */ while (ndigits > 0 && digits[ndigits - 1] == 0) ndigits--; /* If it's zero, normalize the sign and weight */ if (ndigits == 0) { var->sign = NUMERIC_POS; var->weight = 0; } var->digits = digits; var->ndigits = ndigits; } /* ---------------------------------------------------------------------- * * Fast sum accumulator functions * * ---------------------------------------------------------------------- */ /* * Reset the accumulator's value to zero. The buffers to hold the digits * are not free'd. */ static void accum_sum_reset(NumericSumAccum *accum) { int i; accum->dscale = 0; for (i = 0; i < accum->ndigits; i++) { accum->pos_digits[i] = 0; accum->neg_digits[i] = 0; } } /* * Accumulate a new value. */ static void accum_sum_add(NumericSumAccum *accum, const NumericVar *val) { int32 *accum_digits; int i, val_i; int val_ndigits; NumericDigit *val_digits; /* * If we have accumulated too many values since the last carry * propagation, do it now, to avoid overflowing. (We could allow more * than NBASE - 1, if we reserved two extra digits, rather than one, for * carry propagation. But even with NBASE - 1, this needs to be done so * seldom, that the performance difference is negligible.) */ if (accum->num_uncarried == NBASE - 1) accum_sum_carry(accum); /* * Adjust the weight or scale of the old value, so that it can accommodate * the new value. */ accum_sum_rescale(accum, val); /* */ if (val->sign == NUMERIC_POS) accum_digits = accum->pos_digits; else accum_digits = accum->neg_digits; /* copy these values into local vars for speed in loop */ val_ndigits = val->ndigits; val_digits = val->digits; i = accum->weight - val->weight; for (val_i = 0; val_i < val_ndigits; val_i++) { accum_digits[i] += (int32) val_digits[val_i]; i++; } accum->num_uncarried++; } /* * Propagate carries. */ static void accum_sum_carry(NumericSumAccum *accum) { int i; int ndigits; int32 *dig; int32 carry; int32 newdig = 0; /* * If no new values have been added since last carry propagation, nothing * to do. */ if (accum->num_uncarried == 0) return; /* * We maintain that the weight of the accumulator is always one larger * than needed to hold the current value, before carrying, to make sure * there is enough space for the possible extra digit when carry is * propagated. We cannot expand the buffer here, unless we require * callers of accum_sum_final() to switch to the right memory context. */ Assert(accum->pos_digits[0] == 0 && accum->neg_digits[0] == 0); ndigits = accum->ndigits; /* Propagate carry in the positive sum */ dig = accum->pos_digits; carry = 0; for (i = ndigits - 1; i >= 0; i--) { newdig = dig[i] + carry; if (newdig >= NBASE) { carry = newdig / NBASE; newdig -= carry * NBASE; } else carry = 0; dig[i] = newdig; } /* Did we use up the digit reserved for carry propagation? */ if (newdig > 0) accum->have_carry_space = false; /* And the same for the negative sum */ dig = accum->neg_digits; carry = 0; for (i = ndigits - 1; i >= 0; i--) { newdig = dig[i] + carry; if (newdig >= NBASE) { carry = newdig / NBASE; newdig -= carry * NBASE; } else carry = 0; dig[i] = newdig; } if (newdig > 0) accum->have_carry_space = false; accum->num_uncarried = 0; } /* * Re-scale accumulator to accommodate new value. * * If the new value has more digits than the current digit buffers in the * accumulator, enlarge the buffers. */ static void accum_sum_rescale(NumericSumAccum *accum, const NumericVar *val) { int old_weight = accum->weight; int old_ndigits = accum->ndigits; int accum_ndigits; int accum_weight; int accum_rscale; int val_rscale; accum_weight = old_weight; accum_ndigits = old_ndigits; /* * Does the new value have a larger weight? If so, enlarge the buffers, * and shift the existing value to the new weight, by adding leading * zeros. * * We enforce that the accumulator always has a weight one larger than * needed for the inputs, so that we have space for an extra digit at the * final carry-propagation phase, if necessary. */ if (val->weight >= accum_weight) { accum_weight = val->weight + 1; accum_ndigits = accum_ndigits + (accum_weight - old_weight); } /* * Even though the new value is small, we might've used up the space * reserved for the carry digit in the last call to accum_sum_carry(). If * so, enlarge to make room for another one. */ else if (!accum->have_carry_space) { accum_weight++; accum_ndigits++; } /* Is the new value wider on the right side? */ accum_rscale = accum_ndigits - accum_weight - 1; val_rscale = val->ndigits - val->weight - 1; if (val_rscale > accum_rscale) accum_ndigits = accum_ndigits + (val_rscale - accum_rscale); if (accum_ndigits != old_ndigits || accum_weight != old_weight) { int32 *new_pos_digits; int32 *new_neg_digits; int weightdiff; weightdiff = accum_weight - old_weight; new_pos_digits = palloc0(accum_ndigits * sizeof(int32)); new_neg_digits = palloc0(accum_ndigits * sizeof(int32)); if (accum->pos_digits) { memcpy(&new_pos_digits[weightdiff], accum->pos_digits, old_ndigits * sizeof(int32)); pfree(accum->pos_digits); memcpy(&new_neg_digits[weightdiff], accum->neg_digits, old_ndigits * sizeof(int32)); pfree(accum->neg_digits); } accum->pos_digits = new_pos_digits; accum->neg_digits = new_neg_digits; accum->weight = accum_weight; accum->ndigits = accum_ndigits; Assert(accum->pos_digits[0] == 0 && accum->neg_digits[0] == 0); accum->have_carry_space = true; } if (val->dscale > accum->dscale) accum->dscale = val->dscale; } /* * Return the current value of the accumulator. This perform final carry * propagation, and adds together the positive and negative sums. * * Unlike all the other routines, the caller is not required to switch to * the memory context that holds the accumulator. */ static void accum_sum_final(NumericSumAccum *accum, NumericVar *result) { int i; NumericVar pos_var; NumericVar neg_var; if (accum->ndigits == 0) { set_var_from_var(&const_zero, result); return; } /* Perform final carry */ accum_sum_carry(accum); /* Create NumericVars representing the positive and negative sums */ init_var(&pos_var); init_var(&neg_var); pos_var.ndigits = neg_var.ndigits = accum->ndigits; pos_var.weight = neg_var.weight = accum->weight; pos_var.dscale = neg_var.dscale = accum->dscale; pos_var.sign = NUMERIC_POS; neg_var.sign = NUMERIC_NEG; pos_var.buf = pos_var.digits = digitbuf_alloc(accum->ndigits); neg_var.buf = neg_var.digits = digitbuf_alloc(accum->ndigits); for (i = 0; i < accum->ndigits; i++) { Assert(accum->pos_digits[i] < NBASE); pos_var.digits[i] = (int16) accum->pos_digits[i]; Assert(accum->neg_digits[i] < NBASE); neg_var.digits[i] = (int16) accum->neg_digits[i]; } /* And add them together */ add_var(&pos_var, &neg_var, result); /* Remove leading/trailing zeroes */ strip_var(result); } /* * Copy an accumulator's state. * * 'dst' is assumed to be uninitialized beforehand. No attempt is made at * freeing old values. */ static void accum_sum_copy(NumericSumAccum *dst, NumericSumAccum *src) { dst->pos_digits = palloc(src->ndigits * sizeof(int32)); dst->neg_digits = palloc(src->ndigits * sizeof(int32)); memcpy(dst->pos_digits, src->pos_digits, src->ndigits * sizeof(int32)); memcpy(dst->neg_digits, src->neg_digits, src->ndigits * sizeof(int32)); dst->num_uncarried = src->num_uncarried; dst->ndigits = src->ndigits; dst->weight = src->weight; dst->dscale = src->dscale; } /* * Add the current value of 'accum2' into 'accum'. */ static void accum_sum_combine(NumericSumAccum *accum, NumericSumAccum *accum2) { NumericVar tmp_var; init_var(&tmp_var); accum_sum_final(accum2, &tmp_var); accum_sum_add(accum, &tmp_var); free_var(&tmp_var); }