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+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output for double precision.
+ *
+ * Portions Copyright (c) 2018-2020, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/d2s.c
+ *
+ * This is a modification of code taken from github.com/ulfjack/ryu under the
+ * terms of the Boost license (not the Apache license). The original copyright
+ * notice follows:
+ *
+ * Copyright 2018 Ulf Adams
+ *
+ * The contents of this file may be used under the terms of the Apache
+ * License, Version 2.0.
+ *
+ * (See accompanying file LICENSE-Apache or copy at
+ * http://www.apache.org/licenses/LICENSE-2.0)
+ *
+ * Alternatively, the contents of this file may be used under the terms of the
+ * Boost Software License, Version 1.0.
+ *
+ * (See accompanying file LICENSE-Boost or copy at
+ * https://www.boost.org/LICENSE_1_0.txt)
+ *
+ * Unless required by applicable law or agreed to in writing, this software is
+ * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.
+ *
+ *---------------------------------------------------------------------------
+ */
+
+/*
+ * Runtime compiler options:
+ *
+ * -DRYU_ONLY_64_BIT_OPS Avoid using uint128 or 64-bit intrinsics. Slower,
+ * depending on your compiler.
+ */
+
+#ifndef FRONTEND
+#include "postgres.h"
+#else
+#include "postgres_fe.h"
+#endif
+
+#include "common/shortest_dec.h"
+
+/*
+ * For consistency, we use 128-bit types if and only if the rest of PG also
+ * does, even though we could use them here without worrying about the
+ * alignment concerns that apply elsewhere.
+ */
+#if !defined(HAVE_INT128) && defined(_MSC_VER) \
+ && !defined(RYU_ONLY_64_BIT_OPS) && defined(_M_X64)
+#define HAS_64_BIT_INTRINSICS
+#endif
+
+#include "ryu_common.h"
+#include "digit_table.h"
+#include "d2s_full_table.h"
+#include "d2s_intrinsics.h"
+
+#define DOUBLE_MANTISSA_BITS 52
+#define DOUBLE_EXPONENT_BITS 11
+#define DOUBLE_BIAS 1023
+
+#define DOUBLE_POW5_INV_BITCOUNT 122
+#define DOUBLE_POW5_BITCOUNT 121
+
+
+static inline uint32
+pow5Factor(uint64 value)
+{
+ uint32 count = 0;
+
+ for (;;)
+ {
+ Assert(value != 0);
+ const uint64 q = div5(value);
+ const uint32 r = (uint32) (value - 5 * q);
+
+ if (r != 0)
+ break;
+
+ value = q;
+ ++count;
+ }
+ return count;
+}
+
+/* Returns true if value is divisible by 5^p. */
+static inline bool
+multipleOfPowerOf5(const uint64 value, const uint32 p)
+{
+ /*
+ * I tried a case distinction on p, but there was no performance
+ * difference.
+ */
+ return pow5Factor(value) >= p;
+}
+
+/* Returns true if value is divisible by 2^p. */
+static inline bool
+multipleOfPowerOf2(const uint64 value, const uint32 p)
+{
+ /* return __builtin_ctzll(value) >= p; */
+ return (value & ((UINT64CONST(1) << p) - 1)) == 0;
+}
+
+/*
+ * We need a 64x128-bit multiplication and a subsequent 128-bit shift.
+ *
+ * Multiplication:
+ *
+ * The 64-bit factor is variable and passed in, the 128-bit factor comes
+ * from a lookup table. We know that the 64-bit factor only has 55
+ * significant bits (i.e., the 9 topmost bits are zeros). The 128-bit
+ * factor only has 124 significant bits (i.e., the 4 topmost bits are
+ * zeros).
+ *
+ * Shift:
+ *
+ * In principle, the multiplication result requires 55 + 124 = 179 bits to
+ * represent. However, we then shift this value to the right by j, which is
+ * at least j >= 115, so the result is guaranteed to fit into 179 - 115 =
+ * 64 bits. This means that we only need the topmost 64 significant bits of
+ * the 64x128-bit multiplication.
+ *
+ * There are several ways to do this:
+ *
+ * 1. Best case: the compiler exposes a 128-bit type.
+ * We perform two 64x64-bit multiplications, add the higher 64 bits of the
+ * lower result to the higher result, and shift by j - 64 bits.
+ *
+ * We explicitly cast from 64-bit to 128-bit, so the compiler can tell
+ * that these are only 64-bit inputs, and can map these to the best
+ * possible sequence of assembly instructions. x86-64 machines happen to
+ * have matching assembly instructions for 64x64-bit multiplications and
+ * 128-bit shifts.
+ *
+ * 2. Second best case: the compiler exposes intrinsics for the x86-64
+ * assembly instructions mentioned in 1.
+ *
+ * 3. We only have 64x64 bit instructions that return the lower 64 bits of
+ * the result, i.e., we have to use plain C.
+ *
+ * Our inputs are less than the full width, so we have three options:
+ * a. Ignore this fact and just implement the intrinsics manually.
+ * b. Split both into 31-bit pieces, which guarantees no internal
+ * overflow, but requires extra work upfront (unless we change the
+ * lookup table).
+ * c. Split only the first factor into 31-bit pieces, which also
+ * guarantees no internal overflow, but requires extra work since the
+ * intermediate results are not perfectly aligned.
+ */
+#if defined(HAVE_INT128)
+
+/* Best case: use 128-bit type. */
+static inline uint64
+mulShift(const uint64 m, const uint64 *const mul, const int32 j)
+{
+ const uint128 b0 = ((uint128) m) * mul[0];
+ const uint128 b2 = ((uint128) m) * mul[1];
+
+ return (uint64) (((b0 >> 64) + b2) >> (j - 64));
+}
+
+static inline uint64
+mulShiftAll(const uint64 m, const uint64 *const mul, const int32 j,
+ uint64 *const vp, uint64 *const vm, const uint32 mmShift)
+{
+ *vp = mulShift(4 * m + 2, mul, j);
+ *vm = mulShift(4 * m - 1 - mmShift, mul, j);
+ return mulShift(4 * m, mul, j);
+}
+
+#elif defined(HAS_64_BIT_INTRINSICS)
+
+static inline uint64
+mulShift(const uint64 m, const uint64 *const mul, const int32 j)
+{
+ /* m is maximum 55 bits */
+ uint64 high1;
+
+ /* 128 */
+ const uint64 low1 = umul128(m, mul[1], &high1);
+
+ /* 64 */
+ uint64 high0;
+ uint64 sum;
+
+ /* 64 */
+ umul128(m, mul[0], &high0);
+ /* 0 */
+ sum = high0 + low1;
+
+ if (sum < high0)
+ {
+ ++high1;
+ /* overflow into high1 */
+ }
+ return shiftright128(sum, high1, j - 64);
+}
+
+static inline uint64
+mulShiftAll(const uint64 m, const uint64 *const mul, const int32 j,
+ uint64 *const vp, uint64 *const vm, const uint32 mmShift)
+{
+ *vp = mulShift(4 * m + 2, mul, j);
+ *vm = mulShift(4 * m - 1 - mmShift, mul, j);
+ return mulShift(4 * m, mul, j);
+}
+
+#else /* // !defined(HAVE_INT128) &&
+ * !defined(HAS_64_BIT_INTRINSICS) */
+
+static inline uint64
+mulShiftAll(uint64 m, const uint64 *const mul, const int32 j,
+ uint64 *const vp, uint64 *const vm, const uint32 mmShift)
+{
+ m <<= 1; /* m is maximum 55 bits */
+
+ uint64 tmp;
+ const uint64 lo = umul128(m, mul[0], &tmp);
+ uint64 hi;
+ const uint64 mid = tmp + umul128(m, mul[1], &hi);
+
+ hi += mid < tmp; /* overflow into hi */
+
+ const uint64 lo2 = lo + mul[0];
+ const uint64 mid2 = mid + mul[1] + (lo2 < lo);
+ const uint64 hi2 = hi + (mid2 < mid);
+
+ *vp = shiftright128(mid2, hi2, j - 64 - 1);
+
+ if (mmShift == 1)
+ {
+ const uint64 lo3 = lo - mul[0];
+ const uint64 mid3 = mid - mul[1] - (lo3 > lo);
+ const uint64 hi3 = hi - (mid3 > mid);
+
+ *vm = shiftright128(mid3, hi3, j - 64 - 1);
+ }
+ else
+ {
+ const uint64 lo3 = lo + lo;
+ const uint64 mid3 = mid + mid + (lo3 < lo);
+ const uint64 hi3 = hi + hi + (mid3 < mid);
+ const uint64 lo4 = lo3 - mul[0];
+ const uint64 mid4 = mid3 - mul[1] - (lo4 > lo3);
+ const uint64 hi4 = hi3 - (mid4 > mid3);
+
+ *vm = shiftright128(mid4, hi4, j - 64);
+ }
+
+ return shiftright128(mid, hi, j - 64 - 1);
+}
+
+#endif /* // HAS_64_BIT_INTRINSICS */
+
+static inline uint32
+decimalLength(const uint64 v)
+{
+ /* This is slightly faster than a loop. */
+ /* The average output length is 16.38 digits, so we check high-to-low. */
+ /* Function precondition: v is not an 18, 19, or 20-digit number. */
+ /* (17 digits are sufficient for round-tripping.) */
+ Assert(v < 100000000000000000L);
+ if (v >= 10000000000000000L)
+ {
+ return 17;
+ }
+ if (v >= 1000000000000000L)
+ {
+ return 16;
+ }
+ if (v >= 100000000000000L)
+ {
+ return 15;
+ }
+ if (v >= 10000000000000L)
+ {
+ return 14;
+ }
+ if (v >= 1000000000000L)
+ {
+ return 13;
+ }
+ if (v >= 100000000000L)
+ {
+ return 12;
+ }
+ if (v >= 10000000000L)
+ {
+ return 11;
+ }
+ if (v >= 1000000000L)
+ {
+ return 10;
+ }
+ if (v >= 100000000L)
+ {
+ return 9;
+ }
+ if (v >= 10000000L)
+ {
+ return 8;
+ }
+ if (v >= 1000000L)
+ {
+ return 7;
+ }
+ if (v >= 100000L)
+ {
+ return 6;
+ }
+ if (v >= 10000L)
+ {
+ return 5;
+ }
+ if (v >= 1000L)
+ {
+ return 4;
+ }
+ if (v >= 100L)
+ {
+ return 3;
+ }
+ if (v >= 10L)
+ {
+ return 2;
+ }
+ return 1;
+}
+
+/* A floating decimal representing m * 10^e. */
+typedef struct floating_decimal_64
+{
+ uint64 mantissa;
+ int32 exponent;
+} floating_decimal_64;
+
+static inline floating_decimal_64
+d2d(const uint64 ieeeMantissa, const uint32 ieeeExponent)
+{
+ int32 e2;
+ uint64 m2;
+
+ if (ieeeExponent == 0)
+ {
+ /* We subtract 2 so that the bounds computation has 2 additional bits. */
+ e2 = 1 - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2;
+ m2 = ieeeMantissa;
+ }
+ else
+ {
+ e2 = ieeeExponent - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2;
+ m2 = (UINT64CONST(1) << DOUBLE_MANTISSA_BITS) | ieeeMantissa;
+ }
+
+#if STRICTLY_SHORTEST
+ const bool even = (m2 & 1) == 0;
+ const bool acceptBounds = even;
+#else
+ const bool acceptBounds = false;
+#endif
+
+ /* Step 2: Determine the interval of legal decimal representations. */
+ const uint64 mv = 4 * m2;
+
+ /* Implicit bool -> int conversion. True is 1, false is 0. */
+ const uint32 mmShift = ieeeMantissa != 0 || ieeeExponent <= 1;
+
+ /* We would compute mp and mm like this: */
+ /* uint64 mp = 4 * m2 + 2; */
+ /* uint64 mm = mv - 1 - mmShift; */
+
+ /* Step 3: Convert to a decimal power base using 128-bit arithmetic. */
+ uint64 vr,
+ vp,
+ vm;
+ int32 e10;
+ bool vmIsTrailingZeros = false;
+ bool vrIsTrailingZeros = false;
+
+ if (e2 >= 0)
+ {
+ /*
+ * I tried special-casing q == 0, but there was no effect on
+ * performance.
+ *
+ * This expr is slightly faster than max(0, log10Pow2(e2) - 1).
+ */
+ const uint32 q = log10Pow2(e2) - (e2 > 3);
+ const int32 k = DOUBLE_POW5_INV_BITCOUNT + pow5bits(q) - 1;
+ const int32 i = -e2 + q + k;
+
+ e10 = q;
+
+ vr = mulShiftAll(m2, DOUBLE_POW5_INV_SPLIT[q], i, &vp, &vm, mmShift);
+
+ if (q <= 21)
+ {
+ /*
+ * This should use q <= 22, but I think 21 is also safe. Smaller
+ * values may still be safe, but it's more difficult to reason
+ * about them.
+ *
+ * Only one of mp, mv, and mm can be a multiple of 5, if any.
+ */
+ const uint32 mvMod5 = (uint32) (mv - 5 * div5(mv));
+
+ if (mvMod5 == 0)
+ {
+ vrIsTrailingZeros = multipleOfPowerOf5(mv, q);
+ }
+ else if (acceptBounds)
+ {
+ /*----
+ * Same as min(e2 + (~mm & 1), pow5Factor(mm)) >= q
+ * <=> e2 + (~mm & 1) >= q && pow5Factor(mm) >= q
+ * <=> true && pow5Factor(mm) >= q, since e2 >= q.
+ *----
+ */
+ vmIsTrailingZeros = multipleOfPowerOf5(mv - 1 - mmShift, q);
+ }
+ else
+ {
+ /* Same as min(e2 + 1, pow5Factor(mp)) >= q. */
+ vp -= multipleOfPowerOf5(mv + 2, q);
+ }
+ }
+ }
+ else
+ {
+ /*
+ * This expression is slightly faster than max(0, log10Pow5(-e2) - 1).
+ */
+ const uint32 q = log10Pow5(-e2) - (-e2 > 1);
+ const int32 i = -e2 - q;
+ const int32 k = pow5bits(i) - DOUBLE_POW5_BITCOUNT;
+ const int32 j = q - k;
+
+ e10 = q + e2;
+
+ vr = mulShiftAll(m2, DOUBLE_POW5_SPLIT[i], j, &vp, &vm, mmShift);
+
+ if (q <= 1)
+ {
+ /*
+ * {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q
+ * trailing 0 bits.
+ */
+ /* mv = 4 * m2, so it always has at least two trailing 0 bits. */
+ vrIsTrailingZeros = true;
+ if (acceptBounds)
+ {
+ /*
+ * mm = mv - 1 - mmShift, so it has 1 trailing 0 bit iff
+ * mmShift == 1.
+ */
+ vmIsTrailingZeros = mmShift == 1;
+ }
+ else
+ {
+ /*
+ * mp = mv + 2, so it always has at least one trailing 0 bit.
+ */
+ --vp;
+ }
+ }
+ else if (q < 63)
+ {
+ /* TODO(ulfjack):Use a tighter bound here. */
+ /*
+ * We need to compute min(ntz(mv), pow5Factor(mv) - e2) >= q - 1
+ */
+ /* <=> ntz(mv) >= q - 1 && pow5Factor(mv) - e2 >= q - 1 */
+ /* <=> ntz(mv) >= q - 1 (e2 is negative and -e2 >= q) */
+ /* <=> (mv & ((1 << (q - 1)) - 1)) == 0 */
+
+ /*
+ * We also need to make sure that the left shift does not
+ * overflow.
+ */
+ vrIsTrailingZeros = multipleOfPowerOf2(mv, q - 1);
+ }
+ }
+
+ /*
+ * Step 4: Find the shortest decimal representation in the interval of
+ * legal representations.
+ */
+ uint32 removed = 0;
+ uint8 lastRemovedDigit = 0;
+ uint64 output;
+
+ /* On average, we remove ~2 digits. */
+ if (vmIsTrailingZeros || vrIsTrailingZeros)
+ {
+ /* General case, which happens rarely (~0.7%). */
+ for (;;)
+ {
+ const uint64 vpDiv10 = div10(vp);
+ const uint64 vmDiv10 = div10(vm);
+
+ if (vpDiv10 <= vmDiv10)
+ break;
+
+ const uint32 vmMod10 = (uint32) (vm - 10 * vmDiv10);
+ const uint64 vrDiv10 = div10(vr);
+ const uint32 vrMod10 = (uint32) (vr - 10 * vrDiv10);
+
+ vmIsTrailingZeros &= vmMod10 == 0;
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8) vrMod10;
+ vr = vrDiv10;
+ vp = vpDiv10;
+ vm = vmDiv10;
+ ++removed;
+ }
+
+ if (vmIsTrailingZeros)
+ {
+ for (;;)
+ {
+ const uint64 vmDiv10 = div10(vm);
+ const uint32 vmMod10 = (uint32) (vm - 10 * vmDiv10);
+
+ if (vmMod10 != 0)
+ break;
+
+ const uint64 vpDiv10 = div10(vp);
+ const uint64 vrDiv10 = div10(vr);
+ const uint32 vrMod10 = (uint32) (vr - 10 * vrDiv10);
+
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8) vrMod10;
+ vr = vrDiv10;
+ vp = vpDiv10;
+ vm = vmDiv10;
+ ++removed;
+ }
+ }
+
+ if (vrIsTrailingZeros && lastRemovedDigit == 5 && vr % 2 == 0)
+ {
+ /* Round even if the exact number is .....50..0. */
+ lastRemovedDigit = 4;
+ }
+
+ /*
+ * We need to take vr + 1 if vr is outside bounds or we need to round
+ * up.
+ */
+ output = vr + ((vr == vm && (!acceptBounds || !vmIsTrailingZeros)) || lastRemovedDigit >= 5);
+ }
+ else
+ {
+ /*
+ * Specialized for the common case (~99.3%). Percentages below are
+ * relative to this.
+ */
+ bool roundUp = false;
+ const uint64 vpDiv100 = div100(vp);
+ const uint64 vmDiv100 = div100(vm);
+
+ if (vpDiv100 > vmDiv100)
+ {
+ /* Optimization:remove two digits at a time(~86.2 %). */
+ const uint64 vrDiv100 = div100(vr);
+ const uint32 vrMod100 = (uint32) (vr - 100 * vrDiv100);
+
+ roundUp = vrMod100 >= 50;
+ vr = vrDiv100;
+ vp = vpDiv100;
+ vm = vmDiv100;
+ removed += 2;
+ }
+
+ /*----
+ * Loop iterations below (approximately), without optimization
+ * above:
+ *
+ * 0: 0.03%, 1: 13.8%, 2: 70.6%, 3: 14.0%, 4: 1.40%, 5: 0.14%,
+ * 6+: 0.02%
+ *
+ * Loop iterations below (approximately), with optimization
+ * above:
+ *
+ * 0: 70.6%, 1: 27.8%, 2: 1.40%, 3: 0.14%, 4+: 0.02%
+ *----
+ */
+ for (;;)
+ {
+ const uint64 vpDiv10 = div10(vp);
+ const uint64 vmDiv10 = div10(vm);
+
+ if (vpDiv10 <= vmDiv10)
+ break;
+
+ const uint64 vrDiv10 = div10(vr);
+ const uint32 vrMod10 = (uint32) (vr - 10 * vrDiv10);
+
+ roundUp = vrMod10 >= 5;
+ vr = vrDiv10;
+ vp = vpDiv10;
+ vm = vmDiv10;
+ ++removed;
+ }
+
+ /*
+ * We need to take vr + 1 if vr is outside bounds or we need to round
+ * up.
+ */
+ output = vr + (vr == vm || roundUp);
+ }
+
+ const int32 exp = e10 + removed;
+
+ floating_decimal_64 fd;
+
+ fd.exponent = exp;
+ fd.mantissa = output;
+ return fd;
+}
+
+static inline int
+to_chars_df(const floating_decimal_64 v, const uint32 olength, char *const result)
+{
+ /* Step 5: Print the decimal representation. */
+ int index = 0;
+
+ uint64 output = v.mantissa;
+ int32 exp = v.exponent;
+
+ /*----
+ * On entry, mantissa * 10^exp is the result to be output.
+ * Caller has already done the - sign if needed.
+ *
+ * We want to insert the point somewhere depending on the output length
+ * and exponent, which might mean adding zeros:
+ *
+ * exp | format
+ * 1+ | ddddddddd000000
+ * 0 | ddddddddd
+ * -1 .. -len+1 | dddddddd.d to d.ddddddddd
+ * -len ... | 0.ddddddddd to 0.000dddddd
+ */
+ uint32 i = 0;
+ int32 nexp = exp + olength;
+
+ if (nexp <= 0)
+ {
+ /* -nexp is number of 0s to add after '.' */
+ Assert(nexp >= -3);
+ /* 0.000ddddd */
+ index = 2 - nexp;
+ /* won't need more than this many 0s */
+ memcpy(result, "0.000000", 8);
+ }
+ else if (exp < 0)
+ {
+ /*
+ * dddd.dddd; leave space at the start and move the '.' in after
+ */
+ index = 1;
+ }
+ else
+ {
+ /*
+ * We can save some code later by pre-filling with zeros. We know that
+ * there can be no more than 16 output digits in this form, otherwise
+ * we would not choose fixed-point output.
+ */
+ Assert(exp < 16 && exp + olength <= 16);
+ memset(result, '0', 16);
+ }
+
+ /*
+ * We prefer 32-bit operations, even on 64-bit platforms. We have at most
+ * 17 digits, and uint32 can store 9 digits. If output doesn't fit into
+ * uint32, we cut off 8 digits, so the rest will fit into uint32.
+ */
+ if ((output >> 32) != 0)
+ {
+ /* Expensive 64-bit division. */
+ const uint64 q = div1e8(output);
+ uint32 output2 = (uint32) (output - 100000000 * q);
+ const uint32 c = output2 % 10000;
+
+ output = q;
+ output2 /= 10000;
+
+ const uint32 d = output2 % 10000;
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+ const uint32 d0 = (d % 100) << 1;
+ const uint32 d1 = (d / 100) << 1;
+
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 4, DIGIT_TABLE + c1, 2);
+ memcpy(result + index + olength - i - 6, DIGIT_TABLE + d0, 2);
+ memcpy(result + index + olength - i - 8, DIGIT_TABLE + d1, 2);
+ i += 8;
+ }
+
+ uint32 output2 = (uint32) output;
+
+ while (output2 >= 10000)
+ {
+ const uint32 c = output2 - 10000 * (output2 / 10000);
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+
+ output2 /= 10000;
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 4, DIGIT_TABLE + c1, 2);
+ i += 4;
+ }
+ if (output2 >= 100)
+ {
+ const uint32 c = (output2 % 100) << 1;
+
+ output2 /= 100;
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
+ i += 2;
+ }
+ if (output2 >= 10)
+ {
+ const uint32 c = output2 << 1;
+
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
+ }
+ else
+ {
+ result[index] = (char) ('0' + output2);
+ }
+
+ if (index == 1)
+ {
+ /*
+ * nexp is 1..15 here, representing the number of digits before the
+ * point. A value of 16 is not possible because we switch to
+ * scientific notation when the display exponent reaches 15.
+ */
+ Assert(nexp < 16);
+ /* gcc only seems to want to optimize memmove for small 2^n */
+ if (nexp & 8)
+ {
+ memmove(result + index - 1, result + index, 8);
+ index += 8;
+ }
+ if (nexp & 4)
+ {
+ memmove(result + index - 1, result + index, 4);
+ index += 4;
+ }
+ if (nexp & 2)
+ {
+ memmove(result + index - 1, result + index, 2);
+ index += 2;
+ }
+ if (nexp & 1)
+ {
+ result[index - 1] = result[index];
+ }
+ result[nexp] = '.';
+ index = olength + 1;
+ }
+ else if (exp >= 0)
+ {
+ /* we supplied the trailing zeros earlier, now just set the length. */
+ index = olength + exp;
+ }
+ else
+ {
+ index = olength + (2 - nexp);
+ }
+
+ return index;
+}
+
+static inline int
+to_chars(floating_decimal_64 v, const bool sign, char *const result)
+{
+ /* Step 5: Print the decimal representation. */
+ int index = 0;
+
+ uint64 output = v.mantissa;
+ uint32 olength = decimalLength(output);
+ int32 exp = v.exponent + olength - 1;
+
+ if (sign)
+ {
+ result[index++] = '-';
+ }
+
+ /*
+ * The thresholds for fixed-point output are chosen to match printf
+ * defaults. Beware that both the code of to_chars_df and the value of
+ * DOUBLE_SHORTEST_DECIMAL_LEN are sensitive to these thresholds.
+ */
+ if (exp >= -4 && exp < 15)
+ return to_chars_df(v, olength, result + index) + sign;
+
+ /*
+ * If v.exponent is exactly 0, we might have reached here via the small
+ * integer fast path, in which case v.mantissa might contain trailing
+ * (decimal) zeros. For scientific notation we need to move these zeros
+ * into the exponent. (For fixed point this doesn't matter, which is why
+ * we do this here rather than above.)
+ *
+ * Since we already calculated the display exponent (exp) above based on
+ * the old decimal length, that value does not change here. Instead, we
+ * just reduce the display length for each digit removed.
+ *
+ * If we didn't get here via the fast path, the raw exponent will not
+ * usually be 0, and there will be no trailing zeros, so we pay no more
+ * than one div10/multiply extra cost. We claw back half of that by
+ * checking for divisibility by 2 before dividing by 10.
+ */
+ if (v.exponent == 0)
+ {
+ while ((output & 1) == 0)
+ {
+ const uint64 q = div10(output);
+ const uint32 r = (uint32) (output - 10 * q);
+
+ if (r != 0)
+ break;
+ output = q;
+ --olength;
+ }
+ }
+
+ /*----
+ * Print the decimal digits.
+ *
+ * The following code is equivalent to:
+ *
+ * for (uint32 i = 0; i < olength - 1; ++i) {
+ * const uint32 c = output % 10; output /= 10;
+ * result[index + olength - i] = (char) ('0' + c);
+ * }
+ * result[index] = '0' + output % 10;
+ *----
+ */
+
+ uint32 i = 0;
+
+ /*
+ * We prefer 32-bit operations, even on 64-bit platforms. We have at most
+ * 17 digits, and uint32 can store 9 digits. If output doesn't fit into
+ * uint32, we cut off 8 digits, so the rest will fit into uint32.
+ */
+ if ((output >> 32) != 0)
+ {
+ /* Expensive 64-bit division. */
+ const uint64 q = div1e8(output);
+ uint32 output2 = (uint32) (output - 100000000 * q);
+
+ output = q;
+
+ const uint32 c = output2 % 10000;
+
+ output2 /= 10000;
+
+ const uint32 d = output2 % 10000;
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+ const uint32 d0 = (d % 100) << 1;
+ const uint32 d1 = (d / 100) << 1;
+
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
+ memcpy(result + index + olength - i - 5, DIGIT_TABLE + d0, 2);
+ memcpy(result + index + olength - i - 7, DIGIT_TABLE + d1, 2);
+ i += 8;
+ }
+
+ uint32 output2 = (uint32) output;
+
+ while (output2 >= 10000)
+ {
+ const uint32 c = output2 - 10000 * (output2 / 10000);
+
+ output2 /= 10000;
+
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
+ i += 4;
+ }
+ if (output2 >= 100)
+ {
+ const uint32 c = (output2 % 100) << 1;
+
+ output2 /= 100;
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c, 2);
+ i += 2;
+ }
+ if (output2 >= 10)
+ {
+ const uint32 c = output2 << 1;
+
+ /*
+ * We can't use memcpy here: the decimal dot goes between these two
+ * digits.
+ */
+ result[index + olength - i] = DIGIT_TABLE[c + 1];
+ result[index] = DIGIT_TABLE[c];
+ }
+ else
+ {
+ result[index] = (char) ('0' + output2);
+ }
+
+ /* Print decimal point if needed. */
+ if (olength > 1)
+ {
+ result[index + 1] = '.';
+ index += olength + 1;
+ }
+ else
+ {
+ ++index;
+ }
+
+ /* Print the exponent. */
+ result[index++] = 'e';
+ if (exp < 0)
+ {
+ result[index++] = '-';
+ exp = -exp;
+ }
+ else
+ result[index++] = '+';
+
+ if (exp >= 100)
+ {
+ const int32 c = exp % 10;
+
+ memcpy(result + index, DIGIT_TABLE + 2 * (exp / 10), 2);
+ result[index + 2] = (char) ('0' + c);
+ index += 3;
+ }
+ else
+ {
+ memcpy(result + index, DIGIT_TABLE + 2 * exp, 2);
+ index += 2;
+ }
+
+ return index;
+}
+
+static inline bool
+d2d_small_int(const uint64 ieeeMantissa,
+ const uint32 ieeeExponent,
+ floating_decimal_64 *v)
+{
+ const int32 e2 = (int32) ieeeExponent - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS;
+
+ /*
+ * Avoid using multiple "return false;" here since it tends to provoke the
+ * compiler into inlining multiple copies of d2d, which is undesirable.
+ */
+
+ if (e2 >= -DOUBLE_MANTISSA_BITS && e2 <= 0)
+ {
+ /*----
+ * Since 2^52 <= m2 < 2^53 and 0 <= -e2 <= 52:
+ * 1 <= f = m2 / 2^-e2 < 2^53.
+ *
+ * Test if the lower -e2 bits of the significand are 0, i.e. whether
+ * the fraction is 0. We can use ieeeMantissa here, since the implied
+ * 1 bit can never be tested by this; the implied 1 can only be part
+ * of a fraction if e2 < -DOUBLE_MANTISSA_BITS which we already
+ * checked. (e.g. 0.5 gives ieeeMantissa == 0 and e2 == -53)
+ */
+ const uint64 mask = (UINT64CONST(1) << -e2) - 1;
+ const uint64 fraction = ieeeMantissa & mask;
+
+ if (fraction == 0)
+ {
+ /*----
+ * f is an integer in the range [1, 2^53).
+ * Note: mantissa might contain trailing (decimal) 0's.
+ * Note: since 2^53 < 10^16, there is no need to adjust
+ * decimalLength().
+ */
+ const uint64 m2 = (UINT64CONST(1) << DOUBLE_MANTISSA_BITS) | ieeeMantissa;
+
+ v->mantissa = m2 >> -e2;
+ v->exponent = 0;
+ return true;
+ }
+ }
+
+ return false;
+}
+
+/*
+ * Store the shortest decimal representation of the given double as an
+ * UNTERMINATED string in the caller's supplied buffer (which must be at least
+ * DOUBLE_SHORTEST_DECIMAL_LEN-1 bytes long).
+ *
+ * Returns the number of bytes stored.
+ */
+int
+double_to_shortest_decimal_bufn(double f, char *result)
+{
+ /*
+ * Step 1: Decode the floating-point number, and unify normalized and
+ * subnormal cases.
+ */
+ const uint64 bits = double_to_bits(f);
+
+ /* Decode bits into sign, mantissa, and exponent. */
+ const bool ieeeSign = ((bits >> (DOUBLE_MANTISSA_BITS + DOUBLE_EXPONENT_BITS)) & 1) != 0;
+ const uint64 ieeeMantissa = bits & ((UINT64CONST(1) << DOUBLE_MANTISSA_BITS) - 1);
+ const uint32 ieeeExponent = (uint32) ((bits >> DOUBLE_MANTISSA_BITS) & ((1u << DOUBLE_EXPONENT_BITS) - 1));
+
+ /* Case distinction; exit early for the easy cases. */
+ if (ieeeExponent == ((1u << DOUBLE_EXPONENT_BITS) - 1u) || (ieeeExponent == 0 && ieeeMantissa == 0))
+ {
+ return copy_special_str(result, ieeeSign, (ieeeExponent != 0), (ieeeMantissa != 0));
+ }
+
+ floating_decimal_64 v;
+ const bool isSmallInt = d2d_small_int(ieeeMantissa, ieeeExponent, &v);
+
+ if (!isSmallInt)
+ {
+ v = d2d(ieeeMantissa, ieeeExponent);
+ }
+
+ return to_chars(v, ieeeSign, result);
+}
+
+/*
+ * Store the shortest decimal representation of the given double as a
+ * null-terminated string in the caller's supplied buffer (which must be at
+ * least DOUBLE_SHORTEST_DECIMAL_LEN bytes long).
+ *
+ * Returns the string length.
+ */
+int
+double_to_shortest_decimal_buf(double f, char *result)
+{
+ const int index = double_to_shortest_decimal_bufn(f, result);
+
+ /* Terminate the string. */
+ Assert(index < DOUBLE_SHORTEST_DECIMAL_LEN);
+ result[index] = '\0';
+ return index;
+}
+
+/*
+ * Return the shortest decimal representation as a null-terminated palloc'd
+ * string (outside the backend, uses malloc() instead).
+ *
+ * Caller is responsible for freeing the result.
+ */
+char *
+double_to_shortest_decimal(double f)
+{
+ char *const result = (char *) palloc(DOUBLE_SHORTEST_DECIMAL_LEN);
+
+ double_to_shortest_decimal_buf(f, result);
+ return result;
+}