>>>>> "Andrew" == Andrew Gierth <and...@tao11.riddles.org.uk> writes:
Andrew> This code in particular was very heavily into using mixed
Andrew> declarations and code throughout. Removing those was moderately
Andrew> painful.
Andrew> And it turns out I missed one, sigh.
Andrew> Updated patch.
And again to fix the windows build - why does Mkvcbuild.pm have its own
private copy of the file list for src/common?
--
Andrew (irc:RhodiumToad)
diff --git a/src/backend/utils/adt/float.c b/src/backend/utils/adt/float.c
index cf9327f885..24d41c2e89 100644
--- a/src/backend/utils/adt/float.c
+++ b/src/backend/utils/adt/float.c
@@ -21,6 +21,7 @@
#include "catalog/pg_type.h"
#include "common/int.h"
+#include "common/ryu.h"
#include "libpq/pqformat.h"
#include "utils/array.h"
#include "utils/float.h"
@@ -29,7 +30,7 @@
/* Configurable GUC parameter */
-int extra_float_digits = 0; /* Added to DBL_DIG or FLT_DIG */
+int extra_float_digits = 1; /* Added to DBL_DIG or FLT_DIG */
/* Cached constants for degree-based trig functions */
static bool degree_consts_set = false;
@@ -246,6 +247,12 @@ float4out(PG_FUNCTION_ARGS)
char *ascii = (char *) palloc(32);
int ndig = FLT_DIG + extra_float_digits;
+ if (extra_float_digits > 0)
+ {
+ ryu_f2s_buffered(num, ascii);
+ PG_RETURN_CSTRING(ascii);
+ }
+
(void) pg_strfromd(ascii, 32, ndig, num);
PG_RETURN_CSTRING(ascii);
}
@@ -462,6 +469,12 @@ float8out_internal(double num)
char *ascii = (char *) palloc(32);
int ndig = DBL_DIG + extra_float_digits;
+ if (extra_float_digits > 0)
+ {
+ ryu_d2s_buffered(num, ascii);
+ return ascii;
+ }
+
(void) pg_strfromd(ascii, 32, ndig, num);
return ascii;
}
diff --git a/src/backend/utils/misc/guc.c b/src/backend/utils/misc/guc.c
index 6fe1939881..6e223335bc 100644
--- a/src/backend/utils/misc/guc.c
+++ b/src/backend/utils/misc/guc.c
@@ -2631,11 +2631,12 @@ static struct config_int ConfigureNamesInt[] =
{"extra_float_digits", PGC_USERSET, CLIENT_CONN_LOCALE,
gettext_noop("Sets the number of digits displayed for floating-point values."),
gettext_noop("This affects real, double precision, and geometric data types. "
- "The parameter value is added to the standard number of digits "
- "(FLT_DIG or DBL_DIG as appropriate).")
+ "A zero or negative parameter value is added to the standard "
+ "number of digits (FLT_DIG or DBL_DIG as appropriate). "
+ "Any value greater than zero selects round-trip-safe output.")
},
&extra_float_digits,
- 0, -15, 3,
+ 1, -15, 3,
NULL, NULL, NULL
},
diff --git a/src/common/Makefile b/src/common/Makefile
index ec8139f014..02622f8c48 100644
--- a/src/common/Makefile
+++ b/src/common/Makefile
@@ -44,8 +44,10 @@ override CPPFLAGS += -DVAL_LIBS="\"$(LIBS)\""
override CPPFLAGS := -DFRONTEND $(CPPFLAGS)
LIBS += $(PTHREAD_LIBS)
-OBJS_COMMON = base64.o config_info.o controldata_utils.o exec.o file_perm.o \
- ip.o keywords.o link-canary.o md5.o pg_lzcompress.o \
+# If you add objects here, see also src/tools/msvc/Mkvcbuild.pm
+
+OBJS_COMMON = base64.o config_info.o controldata_utils.o d2s.o exec.o f2s.o \
+ file_perm.o ip.o keywords.o link-canary.o md5.o pg_lzcompress.o \
pgfnames.o psprintf.o relpath.o \
rmtree.o saslprep.o scram-common.o string.o unicode_norm.o \
username.o wait_error.o
diff --git a/src/common/d2s.c b/src/common/d2s.c
new file mode 100644
index 0000000000..5155dceeea
--- /dev/null
+++ b/src/common/d2s.c
@@ -0,0 +1,961 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output for double precision.
+ *
+ * Portions Copyright (c) 2018, 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/ryu.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 (;;)
+ {
+ uint64 q;
+ uint32 r;
+
+ Assert(value != 0);
+
+ q = div5(value);
+ 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 & ((1ull << 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_UINT128)
+
+/* 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;
+ const 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_UINT128) &&
+ * !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 = (1ull << DOUBLE_MANTISSA_BITS) | ieeeMantissa;
+ }
+
+ {
+ const bool even = (m2 & 1) == 0;
+ const bool acceptBounds = even;
+
+ /* 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_t 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);
+ uint32 vmMod10;
+ uint64 vrDiv10;
+ uint32 vrMod10;
+
+ if (vpDiv10 <= vmDiv10)
+ break;
+
+ vmMod10 = (uint32) (vm - 10 * vmDiv10);
+ vrDiv10 = div10(vr);
+ vrMod10 = (uint32) (vr - 10 * vrDiv10);
+
+ vmIsTrailingZeros &= vmMod10 == 0;
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8_t) vrMod10;
+ vr = vrDiv10;
+ vp = vpDiv10;
+ vm = vmDiv10;
+ ++removed;
+ }
+
+ if (vmIsTrailingZeros)
+ {
+ for (;;)
+ {
+ const uint64 vmDiv10 = div10(vm);
+ const uint32 vmMod10 = (uint32) (vm - 10 * vmDiv10);
+ uint64 vpDiv10;
+ uint64 vrDiv10;
+ uint32 vrMod10;
+
+ if (vmMod10 != 0)
+ break;
+
+ vpDiv10 = div10(vp);
+ vrDiv10 = div10(vr);
+ vrMod10 = (uint32) (vr - 10 * vrDiv10);
+
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8_t) 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);
+ uint64 vrDiv10;
+ uint32 vrMod10;
+
+ if (vpDiv10 <= vmDiv10)
+ break;
+
+ vrDiv10 = div10(vr);
+ 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 else, which might mean
+ * adding zeros:
+ *
+ * exp | format
+ * 1+ | ddddddddd000000
+ * 0 | ddddddddd
+ * -1 .. -len+1 | dddddddd.d to d.ddddddddd
+ * -len ... | 0.ddddddddd to 0.0000dddddd
+ */
+ uint32 i = 0;
+ int32 nexp = exp + olength;
+
+ if (nexp <= 0)
+ {
+ /* 0.0000ddddd */
+ index = 2 - nexp;
+ memset(result, '0', index);
+ result[1] = '.';
+ }
+ else if (exp < 0)
+ {
+ /*
+ * dddd.dddd; leave space at the start and move the '.' in after
+ */
+ index = 1;
+ }
+
+ /*
+ * 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)
+ {
+ memmove(result, result+1, nexp);
+ result[nexp] = '.';
+ index = olength + 1;
+ }
+ else if (exp >= 0)
+ {
+ if (exp > 0)
+ memset(result + olength, '0', exp);
+ index = olength + exp;
+ }
+ else
+ {
+ index = olength + (2 - nexp);
+ }
+
+ return index;
+}
+
+static inline int
+to_chars(const floating_decimal_64 v, const bool sign, char *const result)
+{
+ /* Step 5: Print the decimal representation. */
+ int index = 0;
+
+ uint64 output = v.mantissa;
+ const uint32 olength = decimalLength(output);
+ int32 exp = v.exponent + olength - 1;
+ uint32 i = 0;
+
+ if (sign)
+ {
+ result[index++] = '-';
+ }
+
+ if (exp >= -4 && exp < 15)
+ return to_chars_df(v, olength, result+index) + sign;
+
+ /*----
+ * 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;
+ *----
+ */
+
+ /*
+ * 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 - 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);
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+
+ output2 /= 10000;
+ 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;
+}
+
+int
+ryu_d2s_buffered_n(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 & ((1ull << 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, ieeeMantissa);
+ }
+
+ {
+ const floating_decimal_64 v = d2d(ieeeMantissa, ieeeExponent);
+
+ return to_chars(v, ieeeSign, result);
+ }
+}
+
+void
+ryu_d2s_buffered(double f, char *result)
+{
+ const int index = ryu_d2s_buffered_n(f, result);
+
+ /* Terminate the string. */
+ result[index] = '\0';
+}
+
+char *
+ryu_d2s(double f)
+{
+ char *const result = (char *) malloc(25);
+
+ ryu_d2s_buffered(f, result);
+ return result;
+}
diff --git a/src/common/d2s_full_table.h b/src/common/d2s_full_table.h
new file mode 100644
index 0000000000..f23f94b51c
--- /dev/null
+++ b/src/common/d2s_full_table.h
@@ -0,0 +1,357 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output for double precision.
+ *
+ * Portions Copyright (c) 2018, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/d2s_full_table.h
+ *
+ * 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.
+ *
+ *---------------------------------------------------------------------------
+ */
+
+#ifndef RYU_D2S_FULL_TABLE_H
+#define RYU_D2S_FULL_TABLE_H
+
+/*
+ * These tables are generated by PrintDoubleLookupTable from the upstream
+ * sources at github.com/ulfjack/ryu, and then modified by adding UINT64CONST.
+ */
+static const uint64 DOUBLE_POW5_INV_SPLIT[292][2] = {
+ {UINT64CONST(1), UINT64CONST(288230376151711744)}, {UINT64CONST(3689348814741910324), UINT64CONST(230584300921369395)},
+ {UINT64CONST(2951479051793528259), UINT64CONST(184467440737095516)}, {UINT64CONST(17118578500402463900), UINT64CONST(147573952589676412)},
+ {UINT64CONST(12632330341676300947), UINT64CONST(236118324143482260)}, {UINT64CONST(10105864273341040758), UINT64CONST(188894659314785808)},
+ {UINT64CONST(15463389048156653253), UINT64CONST(151115727451828646)}, {UINT64CONST(17362724847566824558), UINT64CONST(241785163922925834)},
+ {UINT64CONST(17579528692795369969), UINT64CONST(193428131138340667)}, {UINT64CONST(6684925324752475329), UINT64CONST(154742504910672534)},
+ {UINT64CONST(18074578149087781173), UINT64CONST(247588007857076054)}, {UINT64CONST(18149011334012135262), UINT64CONST(198070406285660843)},
+ {UINT64CONST(3451162622983977240), UINT64CONST(158456325028528675)}, {UINT64CONST(5521860196774363583), UINT64CONST(253530120045645880)},
+ {UINT64CONST(4417488157419490867), UINT64CONST(202824096036516704)}, {UINT64CONST(7223339340677503017), UINT64CONST(162259276829213363)},
+ {UINT64CONST(7867994130342094503), UINT64CONST(259614842926741381)}, {UINT64CONST(2605046489531765280), UINT64CONST(207691874341393105)},
+ {UINT64CONST(2084037191625412224), UINT64CONST(166153499473114484)}, {UINT64CONST(10713157136084480204), UINT64CONST(265845599156983174)},
+ {UINT64CONST(12259874523609494487), UINT64CONST(212676479325586539)}, {UINT64CONST(13497248433629505913), UINT64CONST(170141183460469231)},
+ {UINT64CONST(14216899864323388813), UINT64CONST(272225893536750770)}, {UINT64CONST(11373519891458711051), UINT64CONST(217780714829400616)},
+ {UINT64CONST(5409467098425058518), UINT64CONST(174224571863520493)}, {UINT64CONST(4965798542738183305), UINT64CONST(278759314981632789)},
+ {UINT64CONST(7661987648932456967), UINT64CONST(223007451985306231)}, {UINT64CONST(2440241304404055250), UINT64CONST(178405961588244985)},
+ {UINT64CONST(3904386087046488400), UINT64CONST(285449538541191976)}, {UINT64CONST(17880904128604832013), UINT64CONST(228359630832953580)},
+ {UINT64CONST(14304723302883865611), UINT64CONST(182687704666362864)}, {UINT64CONST(15133127457049002812), UINT64CONST(146150163733090291)},
+ {UINT64CONST(16834306301794583852), UINT64CONST(233840261972944466)}, {UINT64CONST(9778096226693756759), UINT64CONST(187072209578355573)},
+ {UINT64CONST(15201174610838826053), UINT64CONST(149657767662684458)}, {UINT64CONST(2185786488890659746), UINT64CONST(239452428260295134)},
+ {UINT64CONST(5437978005854438120), UINT64CONST(191561942608236107)}, {UINT64CONST(15418428848909281466), UINT64CONST(153249554086588885)},
+ {UINT64CONST(6222742084545298729), UINT64CONST(245199286538542217)}, {UINT64CONST(16046240111861969953), UINT64CONST(196159429230833773)},
+ {UINT64CONST(1768945645263844993), UINT64CONST(156927543384667019)}, {UINT64CONST(10209010661905972635), UINT64CONST(251084069415467230)},
+ {UINT64CONST(8167208529524778108), UINT64CONST(200867255532373784)}, {UINT64CONST(10223115638361732810), UINT64CONST(160693804425899027)},
+ {UINT64CONST(1599589762411131202), UINT64CONST(257110087081438444)}, {UINT64CONST(4969020624670815285), UINT64CONST(205688069665150755)},
+ {UINT64CONST(3975216499736652228), UINT64CONST(164550455732120604)}, {UINT64CONST(13739044029062464211), UINT64CONST(263280729171392966)},
+ {UINT64CONST(7301886408508061046), UINT64CONST(210624583337114373)}, {UINT64CONST(13220206756290269483), UINT64CONST(168499666669691498)},
+ {UINT64CONST(17462981995322520850), UINT64CONST(269599466671506397)}, {UINT64CONST(6591687966774196033), UINT64CONST(215679573337205118)},
+ {UINT64CONST(12652048002903177473), UINT64CONST(172543658669764094)}, {UINT64CONST(9175230360419352987), UINT64CONST(276069853871622551)},
+ {UINT64CONST(3650835473593572067), UINT64CONST(220855883097298041)}, {UINT64CONST(17678063637842498946), UINT64CONST(176684706477838432)},
+ {UINT64CONST(13527506561580357021), UINT64CONST(282695530364541492)}, {UINT64CONST(3443307619780464970), UINT64CONST(226156424291633194)},
+ {UINT64CONST(6443994910566282300), UINT64CONST(180925139433306555)}, {UINT64CONST(5155195928453025840), UINT64CONST(144740111546645244)},
+ {UINT64CONST(15627011115008661990), UINT64CONST(231584178474632390)}, {UINT64CONST(12501608892006929592), UINT64CONST(185267342779705912)},
+ {UINT64CONST(2622589484121723027), UINT64CONST(148213874223764730)}, {UINT64CONST(4196143174594756843), UINT64CONST(237142198758023568)},
+ {UINT64CONST(10735612169159626121), UINT64CONST(189713759006418854)}, {UINT64CONST(12277838550069611220), UINT64CONST(151771007205135083)},
+ {UINT64CONST(15955192865369467629), UINT64CONST(242833611528216133)}, {UINT64CONST(1696107848069843133), UINT64CONST(194266889222572907)},
+ {UINT64CONST(12424932722681605476), UINT64CONST(155413511378058325)}, {UINT64CONST(1433148282581017146), UINT64CONST(248661618204893321)},
+ {UINT64CONST(15903913885032455010), UINT64CONST(198929294563914656)}, {UINT64CONST(9033782293284053685), UINT64CONST(159143435651131725)},
+ {UINT64CONST(14454051669254485895), UINT64CONST(254629497041810760)}, {UINT64CONST(11563241335403588716), UINT64CONST(203703597633448608)},
+ {UINT64CONST(16629290697806691620), UINT64CONST(162962878106758886)}, {UINT64CONST(781423413297334329), UINT64CONST(260740604970814219)},
+ {UINT64CONST(4314487545379777786), UINT64CONST(208592483976651375)}, {UINT64CONST(3451590036303822229), UINT64CONST(166873987181321100)},
+ {UINT64CONST(5522544058086115566), UINT64CONST(266998379490113760)}, {UINT64CONST(4418035246468892453), UINT64CONST(213598703592091008)},
+ {UINT64CONST(10913125826658934609), UINT64CONST(170878962873672806)}, {UINT64CONST(10082303693170474728), UINT64CONST(273406340597876490)},
+ {UINT64CONST(8065842954536379782), UINT64CONST(218725072478301192)}, {UINT64CONST(17520720807854834795), UINT64CONST(174980057982640953)},
+ {UINT64CONST(5897060404116273733), UINT64CONST(279968092772225526)}, {UINT64CONST(1028299508551108663), UINT64CONST(223974474217780421)},
+ {UINT64CONST(15580034865808528224), UINT64CONST(179179579374224336)}, {UINT64CONST(17549358155809824511), UINT64CONST(286687326998758938)},
+ {UINT64CONST(2971440080422128639), UINT64CONST(229349861599007151)}, {UINT64CONST(17134547323305344204), UINT64CONST(183479889279205720)},
+ {UINT64CONST(13707637858644275364), UINT64CONST(146783911423364576)}, {UINT64CONST(14553522944347019935), UINT64CONST(234854258277383322)},
+ {UINT64CONST(4264120725993795302), UINT64CONST(187883406621906658)}, {UINT64CONST(10789994210278856888), UINT64CONST(150306725297525326)},
+ {UINT64CONST(9885293106962350374), UINT64CONST(240490760476040522)}, {UINT64CONST(529536856086059653), UINT64CONST(192392608380832418)},
+ {UINT64CONST(7802327114352668369), UINT64CONST(153914086704665934)}, {UINT64CONST(1415676938738538420), UINT64CONST(246262538727465495)},
+ {UINT64CONST(1132541550990830736), UINT64CONST(197010030981972396)}, {UINT64CONST(15663428499760305882), UINT64CONST(157608024785577916)},
+ {UINT64CONST(17682787970132668764), UINT64CONST(252172839656924666)}, {UINT64CONST(10456881561364224688), UINT64CONST(201738271725539733)},
+ {UINT64CONST(15744202878575200397), UINT64CONST(161390617380431786)}, {UINT64CONST(17812026976236499989), UINT64CONST(258224987808690858)},
+ {UINT64CONST(3181575136763469022), UINT64CONST(206579990246952687)}, {UINT64CONST(13613306553636506187), UINT64CONST(165263992197562149)},
+ {UINT64CONST(10713244041592678929), UINT64CONST(264422387516099439)}, {UINT64CONST(12259944048016053467), UINT64CONST(211537910012879551)},
+ {UINT64CONST(6118606423670932450), UINT64CONST(169230328010303641)}, {UINT64CONST(2411072648389671274), UINT64CONST(270768524816485826)},
+ {UINT64CONST(16686253377679378312), UINT64CONST(216614819853188660)}, {UINT64CONST(13349002702143502650), UINT64CONST(173291855882550928)},
+ {UINT64CONST(17669055508687693916), UINT64CONST(277266969412081485)}, {UINT64CONST(14135244406950155133), UINT64CONST(221813575529665188)},
+ {UINT64CONST(240149081334393137), UINT64CONST(177450860423732151)}, {UINT64CONST(11452284974360759988), UINT64CONST(283921376677971441)},
+ {UINT64CONST(5472479164746697667), UINT64CONST(227137101342377153)}, {UINT64CONST(11756680961281178780), UINT64CONST(181709681073901722)},
+ {UINT64CONST(2026647139541122378), UINT64CONST(145367744859121378)}, {UINT64CONST(18000030682233437097), UINT64CONST(232588391774594204)},
+ {UINT64CONST(18089373360528660001), UINT64CONST(186070713419675363)}, {UINT64CONST(3403452244197197031), UINT64CONST(148856570735740291)},
+ {UINT64CONST(16513570034941246220), UINT64CONST(238170513177184465)}, {UINT64CONST(13210856027952996976), UINT64CONST(190536410541747572)},
+ {UINT64CONST(3189987192878576934), UINT64CONST(152429128433398058)}, {UINT64CONST(1414630693863812771), UINT64CONST(243886605493436893)},
+ {UINT64CONST(8510402184574870864), UINT64CONST(195109284394749514)}, {UINT64CONST(10497670562401807014), UINT64CONST(156087427515799611)},
+ {UINT64CONST(9417575270359070576), UINT64CONST(249739884025279378)}, {UINT64CONST(14912757845771077107), UINT64CONST(199791907220223502)},
+ {UINT64CONST(4551508647133041040), UINT64CONST(159833525776178802)}, {UINT64CONST(10971762650154775986), UINT64CONST(255733641241886083)},
+ {UINT64CONST(16156107749607641435), UINT64CONST(204586912993508866)}, {UINT64CONST(9235537384944202825), UINT64CONST(163669530394807093)},
+ {UINT64CONST(11087511001168814197), UINT64CONST(261871248631691349)}, {UINT64CONST(12559357615676961681), UINT64CONST(209496998905353079)},
+ {UINT64CONST(13736834907283479668), UINT64CONST(167597599124282463)}, {UINT64CONST(18289587036911657145), UINT64CONST(268156158598851941)},
+ {UINT64CONST(10942320814787415393), UINT64CONST(214524926879081553)}, {UINT64CONST(16132554281313752961), UINT64CONST(171619941503265242)},
+ {UINT64CONST(11054691591134363444), UINT64CONST(274591906405224388)}, {UINT64CONST(16222450902391311402), UINT64CONST(219673525124179510)},
+ {UINT64CONST(12977960721913049122), UINT64CONST(175738820099343608)}, {UINT64CONST(17075388340318968271), UINT64CONST(281182112158949773)},
+ {UINT64CONST(2592264228029443648), UINT64CONST(224945689727159819)}, {UINT64CONST(5763160197165465241), UINT64CONST(179956551781727855)},
+ {UINT64CONST(9221056315464744386), UINT64CONST(287930482850764568)}, {UINT64CONST(14755542681855616155), UINT64CONST(230344386280611654)},
+ {UINT64CONST(15493782960226403247), UINT64CONST(184275509024489323)}, {UINT64CONST(1326979923955391628), UINT64CONST(147420407219591459)},
+ {UINT64CONST(9501865507812447252), UINT64CONST(235872651551346334)}, {UINT64CONST(11290841220991868125), UINT64CONST(188698121241077067)},
+ {UINT64CONST(1653975347309673853), UINT64CONST(150958496992861654)}, {UINT64CONST(10025058185179298811), UINT64CONST(241533595188578646)},
+ {UINT64CONST(4330697733401528726), UINT64CONST(193226876150862917)}, {UINT64CONST(14532604630946953951), UINT64CONST(154581500920690333)},
+ {UINT64CONST(1116074521063664381), UINT64CONST(247330401473104534)}, {UINT64CONST(4582208431592841828), UINT64CONST(197864321178483627)},
+ {UINT64CONST(14733813189500004432), UINT64CONST(158291456942786901)}, {UINT64CONST(16195403473716186445), UINT64CONST(253266331108459042)},
+ {UINT64CONST(5577625149489128510), UINT64CONST(202613064886767234)}, {UINT64CONST(8151448934333213131), UINT64CONST(162090451909413787)},
+ {UINT64CONST(16731667109675051333), UINT64CONST(259344723055062059)}, {UINT64CONST(17074682502481951390), UINT64CONST(207475778444049647)},
+ {UINT64CONST(6281048372501740465), UINT64CONST(165980622755239718)}, {UINT64CONST(6360328581260874421), UINT64CONST(265568996408383549)},
+ {UINT64CONST(8777611679750609860), UINT64CONST(212455197126706839)}, {UINT64CONST(10711438158542398211), UINT64CONST(169964157701365471)},
+ {UINT64CONST(9759603424184016492), UINT64CONST(271942652322184754)}, {UINT64CONST(11497031554089123517), UINT64CONST(217554121857747803)},
+ {UINT64CONST(16576322872755119460), UINT64CONST(174043297486198242)}, {UINT64CONST(11764721337440549842), UINT64CONST(278469275977917188)},
+ {UINT64CONST(16790474699436260520), UINT64CONST(222775420782333750)}, {UINT64CONST(13432379759549008416), UINT64CONST(178220336625867000)},
+ {UINT64CONST(3045063541568861850), UINT64CONST(285152538601387201)}, {UINT64CONST(17193446092222730773), UINT64CONST(228122030881109760)},
+ {UINT64CONST(13754756873778184618), UINT64CONST(182497624704887808)}, {UINT64CONST(18382503128506368341), UINT64CONST(145998099763910246)},
+ {UINT64CONST(3586563302416817083), UINT64CONST(233596959622256395)}, {UINT64CONST(2869250641933453667), UINT64CONST(186877567697805116)},
+ {UINT64CONST(17052795772514404226), UINT64CONST(149502054158244092)}, {UINT64CONST(12527077977055405469), UINT64CONST(239203286653190548)},
+ {UINT64CONST(17400360011128145022), UINT64CONST(191362629322552438)}, {UINT64CONST(2852241564676785048), UINT64CONST(153090103458041951)},
+ {UINT64CONST(15631632947708587046), UINT64CONST(244944165532867121)}, {UINT64CONST(8815957543424959314), UINT64CONST(195955332426293697)},
+ {UINT64CONST(18120812478965698421), UINT64CONST(156764265941034957)}, {UINT64CONST(14235904707377476180), UINT64CONST(250822825505655932)},
+ {UINT64CONST(4010026136418160298), UINT64CONST(200658260404524746)}, {UINT64CONST(17965416168102169531), UINT64CONST(160526608323619796)},
+ {UINT64CONST(2919224165770098987), UINT64CONST(256842573317791675)}, {UINT64CONST(2335379332616079190), UINT64CONST(205474058654233340)},
+ {UINT64CONST(1868303466092863352), UINT64CONST(164379246923386672)}, {UINT64CONST(6678634360490491686), UINT64CONST(263006795077418675)},
+ {UINT64CONST(5342907488392393349), UINT64CONST(210405436061934940)}, {UINT64CONST(4274325990713914679), UINT64CONST(168324348849547952)},
+ {UINT64CONST(10528270399884173809), UINT64CONST(269318958159276723)}, {UINT64CONST(15801313949391159694), UINT64CONST(215455166527421378)},
+ {UINT64CONST(1573004715287196786), UINT64CONST(172364133221937103)}, {UINT64CONST(17274202803427156150), UINT64CONST(275782613155099364)},
+ {UINT64CONST(17508711057483635243), UINT64CONST(220626090524079491)}, {UINT64CONST(10317620031244997871), UINT64CONST(176500872419263593)},
+ {UINT64CONST(12818843235250086271), UINT64CONST(282401395870821749)}, {UINT64CONST(13944423402941979340), UINT64CONST(225921116696657399)},
+ {UINT64CONST(14844887537095493795), UINT64CONST(180736893357325919)}, {UINT64CONST(15565258844418305359), UINT64CONST(144589514685860735)},
+ {UINT64CONST(6457670077359736959), UINT64CONST(231343223497377177)}, {UINT64CONST(16234182506113520537), UINT64CONST(185074578797901741)},
+ {UINT64CONST(9297997190148906106), UINT64CONST(148059663038321393)}, {UINT64CONST(11187446689496339446), UINT64CONST(236895460861314229)},
+ {UINT64CONST(12639306166338981880), UINT64CONST(189516368689051383)}, {UINT64CONST(17490142562555006151), UINT64CONST(151613094951241106)},
+ {UINT64CONST(2158786396894637579), UINT64CONST(242580951921985771)}, {UINT64CONST(16484424376483351356), UINT64CONST(194064761537588616)},
+ {UINT64CONST(9498190686444770762), UINT64CONST(155251809230070893)}, {UINT64CONST(11507756283569722895), UINT64CONST(248402894768113429)},
+ {UINT64CONST(12895553841597688639), UINT64CONST(198722315814490743)}, {UINT64CONST(17695140702761971558), UINT64CONST(158977852651592594)},
+ {UINT64CONST(17244178680193423523), UINT64CONST(254364564242548151)}, {UINT64CONST(10105994129412828495), UINT64CONST(203491651394038521)},
+ {UINT64CONST(4395446488788352473), UINT64CONST(162793321115230817)}, {UINT64CONST(10722063196803274280), UINT64CONST(260469313784369307)},
+ {UINT64CONST(1198952927958798777), UINT64CONST(208375451027495446)}, {UINT64CONST(15716557601334680315), UINT64CONST(166700360821996356)},
+ {UINT64CONST(17767794532651667857), UINT64CONST(266720577315194170)}, {UINT64CONST(14214235626121334286), UINT64CONST(213376461852155336)},
+ {UINT64CONST(7682039686155157106), UINT64CONST(170701169481724269)}, {UINT64CONST(1223217053622520399), UINT64CONST(273121871170758831)},
+ {UINT64CONST(15735968901865657612), UINT64CONST(218497496936607064)}, {UINT64CONST(16278123936234436413), UINT64CONST(174797997549285651)},
+ {UINT64CONST(219556594781725998), UINT64CONST(279676796078857043)}, {UINT64CONST(7554342905309201445), UINT64CONST(223741436863085634)},
+ {UINT64CONST(9732823138989271479), UINT64CONST(178993149490468507)}, {UINT64CONST(815121763415193074), UINT64CONST(286389039184749612)},
+ {UINT64CONST(11720143854957885429), UINT64CONST(229111231347799689)}, {UINT64CONST(13065463898708218666), UINT64CONST(183288985078239751)},
+ {UINT64CONST(6763022304224664610), UINT64CONST(146631188062591801)}, {UINT64CONST(3442138057275642729), UINT64CONST(234609900900146882)},
+ {UINT64CONST(13821756890046245153), UINT64CONST(187687920720117505)}, {UINT64CONST(11057405512036996122), UINT64CONST(150150336576094004)},
+ {UINT64CONST(6623802375033462826), UINT64CONST(240240538521750407)}, {UINT64CONST(16367088344252501231), UINT64CONST(192192430817400325)},
+ {UINT64CONST(13093670675402000985), UINT64CONST(153753944653920260)}, {UINT64CONST(2503129006933649959), UINT64CONST(246006311446272417)},
+ {UINT64CONST(13070549649772650937), UINT64CONST(196805049157017933)}, {UINT64CONST(17835137349301941396), UINT64CONST(157444039325614346)},
+ {UINT64CONST(2710778055689733971), UINT64CONST(251910462920982955)}, {UINT64CONST(2168622444551787177), UINT64CONST(201528370336786364)},
+ {UINT64CONST(5424246770383340065), UINT64CONST(161222696269429091)}, {UINT64CONST(1300097203129523457), UINT64CONST(257956314031086546)},
+ {UINT64CONST(15797473021471260058), UINT64CONST(206365051224869236)}, {UINT64CONST(8948629602435097724), UINT64CONST(165092040979895389)},
+ {UINT64CONST(3249760919670425388), UINT64CONST(264147265567832623)}, {UINT64CONST(9978506365220160957), UINT64CONST(211317812454266098)},
+ {UINT64CONST(15361502721659949412), UINT64CONST(169054249963412878)}, {UINT64CONST(2442311466204457120), UINT64CONST(270486799941460606)},
+ {UINT64CONST(16711244431931206989), UINT64CONST(216389439953168484)}, {UINT64CONST(17058344360286875914), UINT64CONST(173111551962534787)},
+ {UINT64CONST(12535955717491360170), UINT64CONST(276978483140055660)}, {UINT64CONST(10028764573993088136), UINT64CONST(221582786512044528)},
+ {UINT64CONST(15401709288678291155), UINT64CONST(177266229209635622)}, {UINT64CONST(9885339602917624555), UINT64CONST(283625966735416996)},
+ {UINT64CONST(4218922867592189321), UINT64CONST(226900773388333597)}, {UINT64CONST(14443184738299482427), UINT64CONST(181520618710666877)},
+ {UINT64CONST(4175850161155765295), UINT64CONST(145216494968533502)}, {UINT64CONST(10370709072591134795), UINT64CONST(232346391949653603)},
+ {UINT64CONST(15675264887556728482), UINT64CONST(185877113559722882)}, {UINT64CONST(5161514280561562140), UINT64CONST(148701690847778306)},
+ {UINT64CONST(879725219414678777), UINT64CONST(237922705356445290)}, {UINT64CONST(703780175531743021), UINT64CONST(190338164285156232)},
+ {UINT64CONST(11631070584651125387), UINT64CONST(152270531428124985)}, {UINT64CONST(162968861732249003), UINT64CONST(243632850284999977)},
+ {UINT64CONST(11198421533611530172), UINT64CONST(194906280227999981)}, {UINT64CONST(5269388412147313814), UINT64CONST(155925024182399985)},
+ {UINT64CONST(8431021459435702103), UINT64CONST(249480038691839976)}, {UINT64CONST(3055468352806651359), UINT64CONST(199584030953471981)},
+ {UINT64CONST(17201769941212962380), UINT64CONST(159667224762777584)}, {UINT64CONST(16454785461715008838), UINT64CONST(255467559620444135)},
+ {UINT64CONST(13163828369372007071), UINT64CONST(204374047696355308)}, {UINT64CONST(17909760324981426303), UINT64CONST(163499238157084246)},
+ {UINT64CONST(2830174816776909822), UINT64CONST(261598781051334795)}, {UINT64CONST(2264139853421527858), UINT64CONST(209279024841067836)},
+ {UINT64CONST(16568707141704863579), UINT64CONST(167423219872854268)}, {UINT64CONST(4373838538276319787), UINT64CONST(267877151796566830)},
+ {UINT64CONST(3499070830621055830), UINT64CONST(214301721437253464)}, {UINT64CONST(6488605479238754987), UINT64CONST(171441377149802771)},
+ {UINT64CONST(3003071137298187333), UINT64CONST(274306203439684434)}, {UINT64CONST(6091805724580460189), UINT64CONST(219444962751747547)},
+ {UINT64CONST(15941491023890099121), UINT64CONST(175555970201398037)}, {UINT64CONST(10748990379256517301), UINT64CONST(280889552322236860)},
+ {UINT64CONST(8599192303405213841), UINT64CONST(224711641857789488)}, {UINT64CONST(14258051472207991719), UINT64CONST(179769313486231590)}
+};
+
+static const uint64 DOUBLE_POW5_SPLIT[326][2] = {
+ {UINT64CONST(0), UINT64CONST(72057594037927936)}, {UINT64CONST(0), UINT64CONST(90071992547409920)},
+ {UINT64CONST(0), UINT64CONST(112589990684262400)}, {UINT64CONST(0), UINT64CONST(140737488355328000)},
+ {UINT64CONST(0), UINT64CONST(87960930222080000)}, {UINT64CONST(0), UINT64CONST(109951162777600000)},
+ {UINT64CONST(0), UINT64CONST(137438953472000000)}, {UINT64CONST(0), UINT64CONST(85899345920000000)},
+ {UINT64CONST(0), UINT64CONST(107374182400000000)}, {UINT64CONST(0), UINT64CONST(134217728000000000)},
+ {UINT64CONST(0), UINT64CONST(83886080000000000)}, {UINT64CONST(0), UINT64CONST(104857600000000000)},
+ {UINT64CONST(0), UINT64CONST(131072000000000000)}, {UINT64CONST(0), UINT64CONST(81920000000000000)},
+ {UINT64CONST(0), UINT64CONST(102400000000000000)}, {UINT64CONST(0), UINT64CONST(128000000000000000)},
+ {UINT64CONST(0), UINT64CONST(80000000000000000)}, {UINT64CONST(0), UINT64CONST(100000000000000000)},
+ {UINT64CONST(0), UINT64CONST(125000000000000000)}, {UINT64CONST(0), UINT64CONST(78125000000000000)},
+ {UINT64CONST(0), UINT64CONST(97656250000000000)}, {UINT64CONST(0), UINT64CONST(122070312500000000)},
+ {UINT64CONST(0), UINT64CONST(76293945312500000)}, {UINT64CONST(0), UINT64CONST(95367431640625000)},
+ {UINT64CONST(0), UINT64CONST(119209289550781250)}, {UINT64CONST(4611686018427387904), UINT64CONST(74505805969238281)},
+ {UINT64CONST(10376293541461622784), UINT64CONST(93132257461547851)}, {UINT64CONST(8358680908399640576), UINT64CONST(116415321826934814)},
+ {UINT64CONST(612489549322387456), UINT64CONST(72759576141834259)}, {UINT64CONST(14600669991935148032), UINT64CONST(90949470177292823)},
+ {UINT64CONST(13639151471491547136), UINT64CONST(113686837721616029)}, {UINT64CONST(3213881284082270208), UINT64CONST(142108547152020037)},
+ {UINT64CONST(4314518811765112832), UINT64CONST(88817841970012523)}, {UINT64CONST(781462496279003136), UINT64CONST(111022302462515654)},
+ {UINT64CONST(10200200157203529728), UINT64CONST(138777878078144567)}, {UINT64CONST(13292654125893287936), UINT64CONST(86736173798840354)},
+ {UINT64CONST(7392445620511834112), UINT64CONST(108420217248550443)}, {UINT64CONST(4628871007212404736), UINT64CONST(135525271560688054)},
+ {UINT64CONST(16728102434789916672), UINT64CONST(84703294725430033)}, {UINT64CONST(7075069988205232128), UINT64CONST(105879118406787542)},
+ {UINT64CONST(18067209522111315968), UINT64CONST(132348898008484427)}, {UINT64CONST(8986162942105878528), UINT64CONST(82718061255302767)},
+ {UINT64CONST(6621017659204960256), UINT64CONST(103397576569128459)}, {UINT64CONST(3664586055578812416), UINT64CONST(129246970711410574)},
+ {UINT64CONST(16125424340018921472), UINT64CONST(80779356694631608)}, {UINT64CONST(1710036351314100224), UINT64CONST(100974195868289511)},
+ {UINT64CONST(15972603494424788992), UINT64CONST(126217744835361888)}, {UINT64CONST(9982877184015493120), UINT64CONST(78886090522101180)},
+ {UINT64CONST(12478596480019366400), UINT64CONST(98607613152626475)}, {UINT64CONST(10986559581596820096), UINT64CONST(123259516440783094)},
+ {UINT64CONST(2254913720070624656), UINT64CONST(77037197775489434)}, {UINT64CONST(12042014186943056628), UINT64CONST(96296497219361792)},
+ {UINT64CONST(15052517733678820785), UINT64CONST(120370621524202240)}, {UINT64CONST(9407823583549262990), UINT64CONST(75231638452626400)},
+ {UINT64CONST(11759779479436578738), UINT64CONST(94039548065783000)}, {UINT64CONST(14699724349295723422), UINT64CONST(117549435082228750)},
+ {UINT64CONST(4575641699882439235), UINT64CONST(73468396926392969)}, {UINT64CONST(10331238143280436948), UINT64CONST(91835496157991211)},
+ {UINT64CONST(8302361660673158281), UINT64CONST(114794370197489014)}, {UINT64CONST(1154580038986672043), UINT64CONST(143492962746861268)},
+ {UINT64CONST(9944984561221445835), UINT64CONST(89683101716788292)}, {UINT64CONST(12431230701526807293), UINT64CONST(112103877145985365)},
+ {UINT64CONST(1703980321626345405), UINT64CONST(140129846432481707)}, {UINT64CONST(17205888765512323542), UINT64CONST(87581154020301066)},
+ {UINT64CONST(12283988920035628619), UINT64CONST(109476442525376333)}, {UINT64CONST(1519928094762372062), UINT64CONST(136845553156720417)},
+ {UINT64CONST(12479170105294952299), UINT64CONST(85528470722950260)}, {UINT64CONST(15598962631618690374), UINT64CONST(106910588403687825)},
+ {UINT64CONST(5663645234241199255), UINT64CONST(133638235504609782)}, {UINT64CONST(17374836326682913246), UINT64CONST(83523897190381113)},
+ {UINT64CONST(7883487353071477846), UINT64CONST(104404871487976392)}, {UINT64CONST(9854359191339347308), UINT64CONST(130506089359970490)},
+ {UINT64CONST(10770660513014479971), UINT64CONST(81566305849981556)}, {UINT64CONST(13463325641268099964), UINT64CONST(101957882312476945)},
+ {UINT64CONST(2994098996302961243), UINT64CONST(127447352890596182)}, {UINT64CONST(15706369927971514489), UINT64CONST(79654595556622613)},
+ {UINT64CONST(5797904354682229399), UINT64CONST(99568244445778267)}, {UINT64CONST(2635694424925398845), UINT64CONST(124460305557222834)},
+ {UINT64CONST(6258995034005762182), UINT64CONST(77787690973264271)}, {UINT64CONST(3212057774079814824), UINT64CONST(97234613716580339)},
+ {UINT64CONST(17850130272881932242), UINT64CONST(121543267145725423)}, {UINT64CONST(18073860448192289507), UINT64CONST(75964541966078389)},
+ {UINT64CONST(8757267504958198172), UINT64CONST(94955677457597987)}, {UINT64CONST(6334898362770359811), UINT64CONST(118694596821997484)},
+ {UINT64CONST(13182683513586250689), UINT64CONST(74184123013748427)}, {UINT64CONST(11866668373555425458), UINT64CONST(92730153767185534)},
+ {UINT64CONST(5609963430089506015), UINT64CONST(115912692208981918)}, {UINT64CONST(17341285199088104971), UINT64CONST(72445432630613698)},
+ {UINT64CONST(12453234462005355406), UINT64CONST(90556790788267123)}, {UINT64CONST(10954857059079306353), UINT64CONST(113195988485333904)},
+ {UINT64CONST(13693571323849132942), UINT64CONST(141494985606667380)}, {UINT64CONST(17781854114260483896), UINT64CONST(88434366004167112)},
+ {UINT64CONST(3780573569116053255), UINT64CONST(110542957505208891)}, {UINT64CONST(114030942967678664), UINT64CONST(138178696881511114)},
+ {UINT64CONST(4682955357782187069), UINT64CONST(86361685550944446)}, {UINT64CONST(15077066234082509644), UINT64CONST(107952106938680557)},
+ {UINT64CONST(5011274737320973344), UINT64CONST(134940133673350697)}, {UINT64CONST(14661261756894078100), UINT64CONST(84337583545844185)},
+ {UINT64CONST(4491519140835433913), UINT64CONST(105421979432305232)}, {UINT64CONST(5614398926044292391), UINT64CONST(131777474290381540)},
+ {UINT64CONST(12732371365632458552), UINT64CONST(82360921431488462)}, {UINT64CONST(6692092170185797382), UINT64CONST(102951151789360578)},
+ {UINT64CONST(17588487249587022536), UINT64CONST(128688939736700722)}, {UINT64CONST(15604490549419276989), UINT64CONST(80430587335437951)},
+ {UINT64CONST(14893927168346708332), UINT64CONST(100538234169297439)}, {UINT64CONST(14005722942005997511), UINT64CONST(125672792711621799)},
+ {UINT64CONST(15671105866394830300), UINT64CONST(78545495444763624)}, {UINT64CONST(1142138259283986260), UINT64CONST(98181869305954531)},
+ {UINT64CONST(15262730879387146537), UINT64CONST(122727336632443163)}, {UINT64CONST(7233363790403272633), UINT64CONST(76704585395276977)},
+ {UINT64CONST(13653390756431478696), UINT64CONST(95880731744096221)}, {UINT64CONST(3231680390257184658), UINT64CONST(119850914680120277)},
+ {UINT64CONST(4325643253124434363), UINT64CONST(74906821675075173)}, {UINT64CONST(10018740084832930858), UINT64CONST(93633527093843966)},
+ {UINT64CONST(3300053069186387764), UINT64CONST(117041908867304958)}, {UINT64CONST(15897591223523656064), UINT64CONST(73151193042065598)},
+ {UINT64CONST(10648616992549794273), UINT64CONST(91438991302581998)}, {UINT64CONST(4087399203832467033), UINT64CONST(114298739128227498)},
+ {UINT64CONST(14332621041645359599), UINT64CONST(142873423910284372)}, {UINT64CONST(18181260187883125557), UINT64CONST(89295889943927732)},
+ {UINT64CONST(4279831161144355331), UINT64CONST(111619862429909666)}, {UINT64CONST(14573160988285219972), UINT64CONST(139524828037387082)},
+ {UINT64CONST(13719911636105650386), UINT64CONST(87203017523366926)}, {UINT64CONST(7926517508277287175), UINT64CONST(109003771904208658)},
+ {UINT64CONST(684774848491833161), UINT64CONST(136254714880260823)}, {UINT64CONST(7345513307948477581), UINT64CONST(85159196800163014)},
+ {UINT64CONST(18405263671790372785), UINT64CONST(106448996000203767)}, {UINT64CONST(18394893571310578077), UINT64CONST(133061245000254709)},
+ {UINT64CONST(13802651491282805250), UINT64CONST(83163278125159193)}, {UINT64CONST(3418256308821342851), UINT64CONST(103954097656448992)},
+ {UINT64CONST(4272820386026678563), UINT64CONST(129942622070561240)}, {UINT64CONST(2670512741266674102), UINT64CONST(81214138794100775)},
+ {UINT64CONST(17173198981865506339), UINT64CONST(101517673492625968)}, {UINT64CONST(3019754653622331308), UINT64CONST(126897091865782461)},
+ {UINT64CONST(4193189667727651020), UINT64CONST(79310682416114038)}, {UINT64CONST(14464859121514339583), UINT64CONST(99138353020142547)},
+ {UINT64CONST(13469387883465536574), UINT64CONST(123922941275178184)}, {UINT64CONST(8418367427165960359), UINT64CONST(77451838296986365)},
+ {UINT64CONST(15134645302384838353), UINT64CONST(96814797871232956)}, {UINT64CONST(471562554271496325), UINT64CONST(121018497339041196)},
+ {UINT64CONST(9518098633274461011), UINT64CONST(75636560836900747)}, {UINT64CONST(7285937273165688360), UINT64CONST(94545701046125934)},
+ {UINT64CONST(18330793628311886258), UINT64CONST(118182126307657417)}, {UINT64CONST(4539216990053847055), UINT64CONST(73863828942285886)},
+ {UINT64CONST(14897393274422084627), UINT64CONST(92329786177857357)}, {UINT64CONST(4786683537745442072), UINT64CONST(115412232722321697)},
+ {UINT64CONST(14520892257159371055), UINT64CONST(72132645451451060)}, {UINT64CONST(18151115321449213818), UINT64CONST(90165806814313825)},
+ {UINT64CONST(8853836096529353561), UINT64CONST(112707258517892282)}, {UINT64CONST(1843923083806916143), UINT64CONST(140884073147365353)},
+ {UINT64CONST(12681666973447792349), UINT64CONST(88052545717103345)}, {UINT64CONST(2017025661527576725), UINT64CONST(110065682146379182)},
+ {UINT64CONST(11744654113764246714), UINT64CONST(137582102682973977)}, {UINT64CONST(422879793461572340), UINT64CONST(85988814176858736)},
+ {UINT64CONST(528599741826965425), UINT64CONST(107486017721073420)}, {UINT64CONST(660749677283706782), UINT64CONST(134357522151341775)},
+ {UINT64CONST(7330497575943398595), UINT64CONST(83973451344588609)}, {UINT64CONST(13774807988356636147), UINT64CONST(104966814180735761)},
+ {UINT64CONST(3383451930163631472), UINT64CONST(131208517725919702)}, {UINT64CONST(15949715511634433382), UINT64CONST(82005323578699813)},
+ {UINT64CONST(6102086334260878016), UINT64CONST(102506654473374767)}, {UINT64CONST(3015921899398709616), UINT64CONST(128133318091718459)},
+ {UINT64CONST(18025852251620051174), UINT64CONST(80083323807324036)}, {UINT64CONST(4085571240815512351), UINT64CONST(100104154759155046)},
+ {UINT64CONST(14330336087874166247), UINT64CONST(125130193448943807)}, {UINT64CONST(15873989082562435760), UINT64CONST(78206370905589879)},
+ {UINT64CONST(15230800334775656796), UINT64CONST(97757963631987349)}, {UINT64CONST(5203442363187407284), UINT64CONST(122197454539984187)},
+ {UINT64CONST(946308467778435600), UINT64CONST(76373409087490117)}, {UINT64CONST(5794571603150432404), UINT64CONST(95466761359362646)},
+ {UINT64CONST(16466586540792816313), UINT64CONST(119333451699203307)}, {UINT64CONST(7985773578781816244), UINT64CONST(74583407312002067)},
+ {UINT64CONST(5370530955049882401), UINT64CONST(93229259140002584)}, {UINT64CONST(6713163693812353001), UINT64CONST(116536573925003230)},
+ {UINT64CONST(18030785363914884337), UINT64CONST(72835358703127018)}, {UINT64CONST(13315109668038829614), UINT64CONST(91044198378908773)},
+ {UINT64CONST(2808829029766373305), UINT64CONST(113805247973635967)}, {UINT64CONST(17346094342490130344), UINT64CONST(142256559967044958)},
+ {UINT64CONST(6229622945628943561), UINT64CONST(88910349979403099)}, {UINT64CONST(3175342663608791547), UINT64CONST(111137937474253874)},
+ {UINT64CONST(13192550366365765242), UINT64CONST(138922421842817342)}, {UINT64CONST(3633657960551215372), UINT64CONST(86826513651760839)},
+ {UINT64CONST(18377130505971182927), UINT64CONST(108533142064701048)}, {UINT64CONST(4524669058754427043), UINT64CONST(135666427580876311)},
+ {UINT64CONST(9745447189362598758), UINT64CONST(84791517238047694)}, {UINT64CONST(2958436949848472639), UINT64CONST(105989396547559618)},
+ {UINT64CONST(12921418224165366607), UINT64CONST(132486745684449522)}, {UINT64CONST(12687572408530742033), UINT64CONST(82804216052780951)},
+ {UINT64CONST(11247779492236039638), UINT64CONST(103505270065976189)}, {UINT64CONST(224666310012885835), UINT64CONST(129381587582470237)},
+ {UINT64CONST(2446259452971747599), UINT64CONST(80863492239043898)}, {UINT64CONST(12281196353069460307), UINT64CONST(101079365298804872)},
+ {UINT64CONST(15351495441336825384), UINT64CONST(126349206623506090)}, {UINT64CONST(14206370669262903769), UINT64CONST(78968254139691306)},
+ {UINT64CONST(8534591299723853903), UINT64CONST(98710317674614133)}, {UINT64CONST(15279925143082205283), UINT64CONST(123387897093267666)},
+ {UINT64CONST(14161639232853766206), UINT64CONST(77117435683292291)}, {UINT64CONST(13090363022639819853), UINT64CONST(96396794604115364)},
+ {UINT64CONST(16362953778299774816), UINT64CONST(120495993255144205)}, {UINT64CONST(12532689120651053212), UINT64CONST(75309995784465128)},
+ {UINT64CONST(15665861400813816515), UINT64CONST(94137494730581410)}, {UINT64CONST(10358954714162494836), UINT64CONST(117671868413226763)},
+ {UINT64CONST(4168503687137865320), UINT64CONST(73544917758266727)}, {UINT64CONST(598943590494943747), UINT64CONST(91931147197833409)},
+ {UINT64CONST(5360365506546067587), UINT64CONST(114913933997291761)}, {UINT64CONST(11312142901609972388), UINT64CONST(143642417496614701)},
+ {UINT64CONST(9375932322719926695), UINT64CONST(89776510935384188)}, {UINT64CONST(11719915403399908368), UINT64CONST(112220638669230235)},
+ {UINT64CONST(10038208235822497557), UINT64CONST(140275798336537794)}, {UINT64CONST(10885566165816448877), UINT64CONST(87672373960336121)},
+ {UINT64CONST(18218643725697949000), UINT64CONST(109590467450420151)}, {UINT64CONST(18161618638695048346), UINT64CONST(136988084313025189)},
+ {UINT64CONST(13656854658398099168), UINT64CONST(85617552695640743)}, {UINT64CONST(12459382304570236056), UINT64CONST(107021940869550929)},
+ {UINT64CONST(1739169825430631358), UINT64CONST(133777426086938662)}, {UINT64CONST(14922039196176308311), UINT64CONST(83610891304336663)},
+ {UINT64CONST(14040862976792997485), UINT64CONST(104513614130420829)}, {UINT64CONST(3716020665709083144), UINT64CONST(130642017663026037)},
+ {UINT64CONST(4628355925281870917), UINT64CONST(81651261039391273)}, {UINT64CONST(10397130925029726550), UINT64CONST(102064076299239091)},
+ {UINT64CONST(8384727637859770284), UINT64CONST(127580095374048864)}, {UINT64CONST(5240454773662356427), UINT64CONST(79737559608780540)},
+ {UINT64CONST(6550568467077945534), UINT64CONST(99671949510975675)}, {UINT64CONST(3576524565420044014), UINT64CONST(124589936888719594)},
+ {UINT64CONST(6847013871814915412), UINT64CONST(77868710555449746)}, {UINT64CONST(17782139376623420074), UINT64CONST(97335888194312182)},
+ {UINT64CONST(13004302183924499284), UINT64CONST(121669860242890228)}, {UINT64CONST(17351060901807587860), UINT64CONST(76043662651806392)},
+ {UINT64CONST(3242082053549933210), UINT64CONST(95054578314757991)}, {UINT64CONST(17887660622219580224), UINT64CONST(118818222893447488)},
+ {UINT64CONST(11179787888887237640), UINT64CONST(74261389308404680)}, {UINT64CONST(13974734861109047050), UINT64CONST(92826736635505850)},
+ {UINT64CONST(8245046539531533005), UINT64CONST(116033420794382313)}, {UINT64CONST(16682369133275677888), UINT64CONST(72520887996488945)},
+ {UINT64CONST(7017903361312433648), UINT64CONST(90651109995611182)}, {UINT64CONST(17995751238495317868), UINT64CONST(113313887494513977)},
+ {UINT64CONST(8659630992836983623), UINT64CONST(141642359368142472)}, {UINT64CONST(5412269370523114764), UINT64CONST(88526474605089045)},
+ {UINT64CONST(11377022731581281359), UINT64CONST(110658093256361306)}, {UINT64CONST(4997906377621825891), UINT64CONST(138322616570451633)},
+ {UINT64CONST(14652906532082110942), UINT64CONST(86451635356532270)}, {UINT64CONST(9092761128247862869), UINT64CONST(108064544195665338)},
+ {UINT64CONST(2142579373455052779), UINT64CONST(135080680244581673)}, {UINT64CONST(12868327154477877747), UINT64CONST(84425425152863545)},
+ {UINT64CONST(2250350887815183471), UINT64CONST(105531781441079432)}, {UINT64CONST(2812938609768979339), UINT64CONST(131914726801349290)},
+ {UINT64CONST(6369772649532999991), UINT64CONST(82446704250843306)}, {UINT64CONST(17185587848771025797), UINT64CONST(103058380313554132)},
+ {UINT64CONST(3035240737254230630), UINT64CONST(128822975391942666)}, {UINT64CONST(6508711479211282048), UINT64CONST(80514359619964166)},
+ {UINT64CONST(17359261385868878368), UINT64CONST(100642949524955207)}, {UINT64CONST(17087390713908710056), UINT64CONST(125803686906194009)},
+ {UINT64CONST(3762090168551861929), UINT64CONST(78627304316371256)}, {UINT64CONST(4702612710689827411), UINT64CONST(98284130395464070)},
+ {UINT64CONST(15101637925217060072), UINT64CONST(122855162994330087)}, {UINT64CONST(16356052730901744401), UINT64CONST(76784476871456304)},
+ {UINT64CONST(1998321839917628885), UINT64CONST(95980596089320381)}, {UINT64CONST(7109588318324424010), UINT64CONST(119975745111650476)},
+ {UINT64CONST(13666864735807540814), UINT64CONST(74984840694781547)}, {UINT64CONST(12471894901332038114), UINT64CONST(93731050868476934)},
+ {UINT64CONST(6366496589810271835), UINT64CONST(117163813585596168)}, {UINT64CONST(3979060368631419896), UINT64CONST(73227383490997605)},
+ {UINT64CONST(9585511479216662775), UINT64CONST(91534229363747006)}, {UINT64CONST(2758517312166052660), UINT64CONST(114417786704683758)},
+ {UINT64CONST(12671518677062341634), UINT64CONST(143022233380854697)}, {UINT64CONST(1002170145522881665), UINT64CONST(89388895863034186)},
+ {UINT64CONST(10476084718758377889), UINT64CONST(111736119828792732)}, {UINT64CONST(13095105898447972362), UINT64CONST(139670149785990915)},
+ {UINT64CONST(5878598177316288774), UINT64CONST(87293843616244322)}, {UINT64CONST(16571619758500136775), UINT64CONST(109117304520305402)},
+ {UINT64CONST(11491152661270395161), UINT64CONST(136396630650381753)}, {UINT64CONST(264441385652915120), UINT64CONST(85247894156488596)},
+ {UINT64CONST(330551732066143900), UINT64CONST(106559867695610745)}, {UINT64CONST(5024875683510067779), UINT64CONST(133199834619513431)},
+ {UINT64CONST(10058076329834874218), UINT64CONST(83249896637195894)}, {UINT64CONST(3349223375438816964), UINT64CONST(104062370796494868)},
+ {UINT64CONST(4186529219298521205), UINT64CONST(130077963495618585)}, {UINT64CONST(14145795808130045513), UINT64CONST(81298727184761615)},
+ {UINT64CONST(13070558741735168987), UINT64CONST(101623408980952019)}, {UINT64CONST(11726512408741573330), UINT64CONST(127029261226190024)},
+ {UINT64CONST(7329070255463483331), UINT64CONST(79393288266368765)}, {UINT64CONST(13773023837756742068), UINT64CONST(99241610332960956)},
+ {UINT64CONST(17216279797195927585), UINT64CONST(124052012916201195)}, {UINT64CONST(8454331864033760789), UINT64CONST(77532508072625747)},
+ {UINT64CONST(5956228811614813082), UINT64CONST(96915635090782184)}, {UINT64CONST(7445286014518516353), UINT64CONST(121144543863477730)},
+ {UINT64CONST(9264989777501460624), UINT64CONST(75715339914673581)}, {UINT64CONST(16192923240304213684), UINT64CONST(94644174893341976)},
+ {UINT64CONST(1794409976670715490), UINT64CONST(118305218616677471)}, {UINT64CONST(8039035263060279037), UINT64CONST(73940761635423419)},
+ {UINT64CONST(5437108060397960892), UINT64CONST(92425952044279274)}, {UINT64CONST(16019757112352226923), UINT64CONST(115532440055349092)},
+ {UINT64CONST(788976158365366019), UINT64CONST(72207775034593183)}, {UINT64CONST(14821278253238871236), UINT64CONST(90259718793241478)},
+ {UINT64CONST(9303225779693813237), UINT64CONST(112824648491551848)}, {UINT64CONST(11629032224617266546), UINT64CONST(141030810614439810)},
+ {UINT64CONST(11879831158813179495), UINT64CONST(88144256634024881)}, {UINT64CONST(1014730893234310657), UINT64CONST(110180320792531102)},
+ {UINT64CONST(10491785653397664129), UINT64CONST(137725400990663877)}, {UINT64CONST(8863209042587234033), UINT64CONST(86078375619164923)},
+ {UINT64CONST(6467325284806654637), UINT64CONST(107597969523956154)}, {UINT64CONST(17307528642863094104), UINT64CONST(134497461904945192)},
+ {UINT64CONST(10817205401789433815), UINT64CONST(84060913690590745)}, {UINT64CONST(18133192770664180173), UINT64CONST(105076142113238431)},
+ {UINT64CONST(18054804944902837312), UINT64CONST(131345177641548039)}, {UINT64CONST(18201782118205355176), UINT64CONST(82090736025967524)},
+ {UINT64CONST(4305483574047142354), UINT64CONST(102613420032459406)}, {UINT64CONST(14605226504413703751), UINT64CONST(128266775040574257)},
+ {UINT64CONST(2210737537617482988), UINT64CONST(80166734400358911)}, {UINT64CONST(16598479977304017447), UINT64CONST(100208418000448638)},
+ {UINT64CONST(11524727934775246001), UINT64CONST(125260522500560798)}, {UINT64CONST(2591268940807140847), UINT64CONST(78287826562850499)},
+ {UINT64CONST(17074144231291089770), UINT64CONST(97859783203563123)}, {UINT64CONST(16730994270686474309), UINT64CONST(122324729004453904)},
+ {UINT64CONST(10456871419179046443), UINT64CONST(76452955627783690)}, {UINT64CONST(3847717237119032246), UINT64CONST(95566194534729613)},
+ {UINT64CONST(9421332564826178211), UINT64CONST(119457743168412016)}, {UINT64CONST(5888332853016361382), UINT64CONST(74661089480257510)},
+ {UINT64CONST(16583788103125227536), UINT64CONST(93326361850321887)}, {UINT64CONST(16118049110479146516), UINT64CONST(116657952312902359)},
+ {UINT64CONST(16991309721690548428), UINT64CONST(72911220195563974)}, {UINT64CONST(12015765115258409727), UINT64CONST(91139025244454968)},
+ {UINT64CONST(15019706394073012159), UINT64CONST(113923781555568710)}, {UINT64CONST(9551260955736489391), UINT64CONST(142404726944460888)},
+ {UINT64CONST(5969538097335305869), UINT64CONST(89002954340288055)}, {UINT64CONST(2850236603241744433), UINT64CONST(111253692925360069)}
+};
+
+#endif /* RYU_D2S_FULL_TABLE_H */
diff --git a/src/common/d2s_intrinsics.h b/src/common/d2s_intrinsics.h
new file mode 100644
index 0000000000..db70395f82
--- /dev/null
+++ b/src/common/d2s_intrinsics.h
@@ -0,0 +1,202 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output for double precision.
+ *
+ * Portions Copyright (c) 2018, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/d2s_intrinsics.h
+ *
+ * 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.
+ *
+ *---------------------------------------------------------------------------
+ */
+#ifndef RYU_D2S_INTRINSICS_H
+#define RYU_D2S_INTRINSICS_H
+
+#if defined(HAS_64_BIT_INTRINSICS)
+
+#include <intrin.h>
+
+static inline uint64
+umul128(const uint64 a, const uint64 b, uint64 *const productHi)
+{
+ return _umul128(a, b, productHi);
+}
+
+static inline uint64
+shiftright128(const uint64 lo, const uint64 hi, const uint32 dist)
+{
+ /*
+ * For the __shiftright128 intrinsic, the shift value is always modulo 64.
+ * In the current implementation of the double-precision version of Ryu,
+ * the shift value is always < 64. (In the case RYU_OPTIMIZE_SIZE == 0,
+ * the shift value is in the range [49, 58]. Otherwise in the range [2,
+ * 59].) Check this here in case a future change requires larger shift
+ * values. In this case this function needs to be adjusted.
+ */
+ Assert(dist < 64);
+ return __shiftright128(lo, hi, (unsigned char) dist);
+}
+
+#else /* defined(HAS_64_BIT_INTRINSICS) */
+
+static inline uint64
+umul128(const uint64 a, const uint64 b, uint64 *const productHi)
+{
+ /*
+ * The casts here help MSVC to avoid calls to the __allmul library
+ * function.
+ */
+ const uint32 aLo = (uint32) a;
+ const uint32 aHi = (uint32) (a >> 32);
+ const uint32 bLo = (uint32) b;
+ const uint32 bHi = (uint32) (b >> 32);
+
+ const uint64 b00 = (uint64) aLo * bLo;
+ const uint64 b01 = (uint64) aLo * bHi;
+ const uint64 b10 = (uint64) aHi * bLo;
+ const uint64 b11 = (uint64) aHi * bHi;
+
+ const uint32 b00Lo = (uint32) b00;
+ const uint32 b00Hi = (uint32) (b00 >> 32);
+
+ const uint64 mid1 = b10 + b00Hi;
+ const uint32 mid1Lo = (uint32) (mid1);
+ const uint32 mid1Hi = (uint32) (mid1 >> 32);
+
+ const uint64 mid2 = b01 + mid1Lo;
+ const uint32 mid2Lo = (uint32) (mid2);
+ const uint32 mid2Hi = (uint32) (mid2 >> 32);
+
+ const uint64 pHi = b11 + mid1Hi + mid2Hi;
+ const uint64 pLo = ((uint64) mid2Lo << 32) + b00Lo;
+
+ *productHi = pHi;
+ return pLo;
+}
+
+static inline uint64
+shiftright128(const uint64 lo, const uint64 hi, const uint32 dist)
+{
+ /* We don't need to handle the case dist >= 64 here (see above). */
+ Assert(dist < 64);
+#if defined(RYU_OPTIMIZE_SIZE) || !defined(RYU_32_BIT_PLATFORM)
+ Assert(dist > 0);
+ return (hi << (64 - dist)) | (lo >> dist);
+#else
+ /* Avoid a 64-bit shift by taking advantage of the range of shift values. */
+ Assert(dist >= 32);
+ return (hi << (64 - dist)) | ((uint32) (lo >> 32) >> (dist - 32));
+#endif
+}
+
+#endif /* // defined(HAS_64_BIT_INTRINSICS) */
+
+#ifdef RYU_32_BIT_PLATFORM
+
+/* Returns the high 64 bits of the 128-bit product of a and b. */
+static inline uint64
+umulh(const uint64 a, const uint64 b)
+{
+ /*
+ * Reuse the umul128 implementation. Optimizers will likely eliminate the
+ * instructions used to compute the low part of the product.
+ */
+ uint64 hi;
+
+ umul128(a, b, &hi);
+ return hi;
+}
+
+/*----
+ * On 32-bit platforms, compilers typically generate calls to library
+ * functions for 64-bit divisions, even if the divisor is a constant.
+ *
+ * E.g.:
+ * https://bugs.llvm.org/show_bug.cgi?id=37932
+ * https://gcc.gnu.org/bugzilla/show_bug.cgi?id=17958
+ * https://gcc.gnu.org/bugzilla/show_bug.cgi?id=37443
+ *
+ * The functions here perform division-by-constant using multiplications
+ * in the same way as 64-bit compilers would do.
+ *
+ * NB:
+ * The multipliers and shift values are the ones generated by clang x64
+ * for expressions like x/5, x/10, etc.
+ *----
+ */
+
+static inline uint64
+div5(const uint64 x)
+{
+ return umulh(x, 0xCCCCCCCCCCCCCCCDu) >> 2;
+}
+
+static inline uint64
+div10(const uint64 x)
+{
+ return umulh(x, 0xCCCCCCCCCCCCCCCDu) >> 3;
+}
+
+static inline uint64
+div100(const uint64 x)
+{
+ return umulh(x >> 2, 0x28F5C28F5C28F5C3u) >> 2;
+}
+
+static inline uint64
+div1e8(const uint64 x)
+{
+ return umulh(x, 0xABCC77118461CEFDu) >> 26;
+}
+
+#else /* RYU_32_BIT_PLATFORM */
+
+static inline uint64
+div5(const uint64 x)
+{
+ return x / 5;
+}
+
+static inline uint64
+div10(const uint64 x)
+{
+ return x / 10;
+}
+
+static inline uint64
+div100(const uint64 x)
+{
+ return x / 100;
+}
+
+static inline uint64
+div1e8(const uint64 x)
+{
+ return x / 100000000;
+}
+
+#endif /* RYU_32_BIT_PLATFORM */
+
+#endif /* RYU_D2S_INTRINSICS_H */
diff --git a/src/common/digit_table.h b/src/common/digit_table.h
new file mode 100644
index 0000000000..483aa17142
--- /dev/null
+++ b/src/common/digit_table.h
@@ -0,0 +1,21 @@
+#ifndef RYU_DIGIT_TABLE_H
+#define RYU_DIGIT_TABLE_H
+
+/*
+ * A table of all two-digit numbers. This is used to speed up decimal digit
+ * generation by copying pairs of digits into the final output.
+ */
+static const char DIGIT_TABLE[200] = {
+ '0', '0', '0', '1', '0', '2', '0', '3', '0', '4', '0', '5', '0', '6', '0', '7', '0', '8', '0', '9',
+ '1', '0', '1', '1', '1', '2', '1', '3', '1', '4', '1', '5', '1', '6', '1', '7', '1', '8', '1', '9',
+ '2', '0', '2', '1', '2', '2', '2', '3', '2', '4', '2', '5', '2', '6', '2', '7', '2', '8', '2', '9',
+ '3', '0', '3', '1', '3', '2', '3', '3', '3', '4', '3', '5', '3', '6', '3', '7', '3', '8', '3', '9',
+ '4', '0', '4', '1', '4', '2', '4', '3', '4', '4', '4', '5', '4', '6', '4', '7', '4', '8', '4', '9',
+ '5', '0', '5', '1', '5', '2', '5', '3', '5', '4', '5', '5', '5', '6', '5', '7', '5', '8', '5', '9',
+ '6', '0', '6', '1', '6', '2', '6', '3', '6', '4', '6', '5', '6', '6', '6', '7', '6', '8', '6', '9',
+ '7', '0', '7', '1', '7', '2', '7', '3', '7', '4', '7', '5', '7', '6', '7', '7', '7', '8', '7', '9',
+ '8', '0', '8', '1', '8', '2', '8', '3', '8', '4', '8', '5', '8', '6', '8', '7', '8', '8', '8', '9',
+ '9', '0', '9', '1', '9', '2', '9', '3', '9', '4', '9', '5', '9', '6', '9', '7', '9', '8', '9', '9'
+};
+
+#endif /* RYU_DIGIT_TABLE_H */
diff --git a/src/common/f2s.c b/src/common/f2s.c
new file mode 100644
index 0000000000..cb42fa4a3f
--- /dev/null
+++ b/src/common/f2s.c
@@ -0,0 +1,667 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output for single precision.
+ *
+ * Portions Copyright (c) 2018, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/f2s.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.
+ *
+ *---------------------------------------------------------------------------
+ */
+
+#ifndef FRONTEND
+#include "postgres.h"
+#else
+#include "postgres_fe.h"
+#endif
+
+#include "common/ryu.h"
+
+#include "ryu_common.h"
+#include "digit_table.h"
+
+#define FLOAT_MANTISSA_BITS 23
+#define FLOAT_EXPONENT_BITS 8
+#define FLOAT_BIAS 127
+
+/* This table is generated by PrintFloatLookupTable. */
+#define FLOAT_POW5_INV_BITCOUNT 59
+static const uint64 FLOAT_POW5_INV_SPLIT[31] = {
+ UINT64CONST(576460752303423489), UINT64CONST(461168601842738791), UINT64CONST(368934881474191033), UINT64CONST(295147905179352826),
+ UINT64CONST(472236648286964522), UINT64CONST(377789318629571618), UINT64CONST(302231454903657294), UINT64CONST(483570327845851670),
+ UINT64CONST(386856262276681336), UINT64CONST(309485009821345069), UINT64CONST(495176015714152110), UINT64CONST(396140812571321688),
+ UINT64CONST(316912650057057351), UINT64CONST(507060240091291761), UINT64CONST(405648192073033409), UINT64CONST(324518553658426727),
+ UINT64CONST(519229685853482763), UINT64CONST(415383748682786211), UINT64CONST(332306998946228969), UINT64CONST(531691198313966350),
+ UINT64CONST(425352958651173080), UINT64CONST(340282366920938464), UINT64CONST(544451787073501542), UINT64CONST(435561429658801234),
+ UINT64CONST(348449143727040987), UINT64CONST(557518629963265579), UINT64CONST(446014903970612463), UINT64CONST(356811923176489971),
+ UINT64CONST(570899077082383953), UINT64CONST(456719261665907162), UINT64CONST(365375409332725730)
+};
+#define FLOAT_POW5_BITCOUNT 61
+static const uint64 FLOAT_POW5_SPLIT[47] = {
+ UINT64CONST(1152921504606846976), UINT64CONST(1441151880758558720), UINT64CONST(1801439850948198400), UINT64CONST(2251799813685248000),
+ UINT64CONST(1407374883553280000), UINT64CONST(1759218604441600000), UINT64CONST(2199023255552000000), UINT64CONST(1374389534720000000),
+ UINT64CONST(1717986918400000000), UINT64CONST(2147483648000000000), UINT64CONST(1342177280000000000), UINT64CONST(1677721600000000000),
+ UINT64CONST(2097152000000000000), UINT64CONST(1310720000000000000), UINT64CONST(1638400000000000000), UINT64CONST(2048000000000000000),
+ UINT64CONST(1280000000000000000), UINT64CONST(1600000000000000000), UINT64CONST(2000000000000000000), UINT64CONST(1250000000000000000),
+ UINT64CONST(1562500000000000000), UINT64CONST(1953125000000000000), UINT64CONST(1220703125000000000), UINT64CONST(1525878906250000000),
+ UINT64CONST(1907348632812500000), UINT64CONST(1192092895507812500), UINT64CONST(1490116119384765625), UINT64CONST(1862645149230957031),
+ UINT64CONST(1164153218269348144), UINT64CONST(1455191522836685180), UINT64CONST(1818989403545856475), UINT64CONST(2273736754432320594),
+ UINT64CONST(1421085471520200371), UINT64CONST(1776356839400250464), UINT64CONST(2220446049250313080), UINT64CONST(1387778780781445675),
+ UINT64CONST(1734723475976807094), UINT64CONST(2168404344971008868), UINT64CONST(1355252715606880542), UINT64CONST(1694065894508600678),
+ UINT64CONST(2117582368135750847), UINT64CONST(1323488980084844279), UINT64CONST(1654361225106055349), UINT64CONST(2067951531382569187),
+ UINT64CONST(1292469707114105741), UINT64CONST(1615587133892632177), UINT64CONST(2019483917365790221)
+};
+
+static inline uint32
+pow5Factor(uint32 value)
+{
+ uint32 count = 0;
+
+ for (;;)
+ {
+ uint32 q;
+ uint32 r;
+
+ Assert(value != 0);
+ q = value / 5;
+ r = value % 5;
+
+ if (r != 0)
+ break;
+
+ value = q;
+ ++count;
+ }
+ return count;
+}
+
+/* Returns true if value is divisible by 5^p. */
+static inline bool
+multipleOfPowerOf5(const uint32 value, const uint32 p)
+{
+ return pow5Factor(value) >= p;
+}
+
+/* Returns true if value is divisible by 2^p. */
+static inline bool
+multipleOfPowerOf2(const uint32 value, const uint32 p)
+{
+ /* return __builtin_ctz(value) >= p; */
+ return (value & ((1u << p) - 1)) == 0;
+}
+
+/*
+ * It seems to be slightly faster to avoid uint128_t here, although the
+ * generated code for uint128_t looks slightly nicer.
+ */
+static inline uint32
+mulShift(const uint32 m, const uint64 factor, const int32 shift)
+{
+ /*
+ * The casts here help MSVC to avoid calls to the __allmul library
+ * function.
+ */
+ const uint32 factorLo = (uint32) (factor);
+ const uint32 factorHi = (uint32) (factor >> 32);
+ const uint64 bits0 = (uint64) m * factorLo;
+ const uint64 bits1 = (uint64) m * factorHi;
+
+ Assert(shift > 32);
+
+#ifdef RYU_32_BIT_PLATFORM
+ {
+ /*
+ * On 32-bit platforms we can avoid a 64-bit shift-right since we only
+ * need the upper 32 bits of the result and the shift value is > 32.
+ */
+ const uint32 bits0Hi = (uint32) (bits0 >> 32);
+ uint32 bits1Lo = (uint32) (bits1);
+ uint32 bits1Hi = (uint32) (bits1 >> 32);
+ int32 s;
+
+ bits1Lo += bits0Hi;
+ bits1Hi += (bits1Lo < bits0Hi);
+
+ s = shift - 32;
+ return (bits1Hi << (32 - s)) | (bits1Lo >> s);
+ }
+#else /* RYU_32_BIT_PLATFORM */
+ {
+ const uint64 sum = (bits0 >> 32) + bits1;
+ const uint64 shiftedSum = sum >> (shift - 32);
+
+ Assert(shiftedSum <= UINT32_MAX);
+ return (uint32) shiftedSum;
+ }
+#endif /* RYU_32_BIT_PLATFORM */
+}
+
+static inline uint32
+mulPow5InvDivPow2(const uint32 m, const uint32 q, const int32 j)
+{
+ return mulShift(m, FLOAT_POW5_INV_SPLIT[q], j);
+}
+
+static inline uint32
+mulPow5divPow2(const uint32 m, const uint32 i, const int32 j)
+{
+ return mulShift(m, FLOAT_POW5_SPLIT[i], j);
+}
+
+static inline uint32
+decimalLength(const uint32 v)
+{
+ /* Function precondition: v is not a 10-digit number. */
+ /* (9 digits are sufficient for round-tripping.) */
+ Assert(v < 1000000000);
+ if (v >= 100000000)
+ {
+ return 9;
+ }
+ if (v >= 10000000)
+ {
+ return 8;
+ }
+ if (v >= 1000000)
+ {
+ return 7;
+ }
+ if (v >= 100000)
+ {
+ return 6;
+ }
+ if (v >= 10000)
+ {
+ return 5;
+ }
+ if (v >= 1000)
+ {
+ return 4;
+ }
+ if (v >= 100)
+ {
+ return 3;
+ }
+ if (v >= 10)
+ {
+ return 2;
+ }
+ return 1;
+}
+
+/* A floating decimal representing m * 10^e. */
+typedef struct floating_decimal_32
+{
+ uint32 mantissa;
+ int32 exponent;
+} floating_decimal_32;
+
+static inline floating_decimal_32
+f2d(const uint32 ieeeMantissa, const uint32 ieeeExponent)
+{
+ int32 e2;
+ uint32 m2;
+
+ if (ieeeExponent == 0)
+ {
+ /* We subtract 2 so that the bounds computation has 2 additional bits. */
+ e2 = 1 - FLOAT_BIAS - FLOAT_MANTISSA_BITS - 2;
+ m2 = ieeeMantissa;
+ }
+ else
+ {
+ e2 = ieeeExponent - FLOAT_BIAS - FLOAT_MANTISSA_BITS - 2;
+ m2 = (1u << FLOAT_MANTISSA_BITS) | ieeeMantissa;
+ }
+
+ {
+ const bool even = (m2 & 1) == 0;
+ const bool acceptBounds = even;
+
+ /* Step 2: Determine the interval of legal decimal representations. */
+ const uint32 mv = 4 * m2;
+ const uint32 mp = 4 * m2 + 2;
+
+ /* Implicit bool -> int conversion. True is 1, false is 0. */
+ const uint32 mmShift = ieeeMantissa != 0 || ieeeExponent <= 1;
+ const uint32 mm = 4 * m2 - 1 - mmShift;
+
+ /* Step 3: Convert to a decimal power base using 64-bit arithmetic. */
+ uint32 vr,
+ vp,
+ vm;
+ int32 e10;
+ bool vmIsTrailingZeros = false;
+ bool vrIsTrailingZeros = false;
+ uint8_t lastRemovedDigit = 0;
+
+ if (e2 >= 0)
+ {
+ const uint32 q = log10Pow2(e2);
+ const int32 k = FLOAT_POW5_INV_BITCOUNT + pow5bits(q) - 1;
+ const int32 i = -e2 + q + k;
+
+ e10 = q;
+ vr = mulPow5InvDivPow2(mv, q, i);
+ vp = mulPow5InvDivPow2(mp, q, i);
+ vm = mulPow5InvDivPow2(mm, q, i);
+
+ if (q != 0 && (vp - 1) / 10 <= vm / 10)
+ {
+ /*
+ * We need to know one removed digit even if we are not going
+ * to loop below. We could use q = X - 1 above, except that
+ * would require 33 bits for the result, and we've found that
+ * 32-bit arithmetic is faster even on 64-bit machines.
+ */
+ const int32 l = FLOAT_POW5_INV_BITCOUNT + pow5bits(q - 1) - 1;
+
+ lastRemovedDigit = (uint8_t) (mulPow5InvDivPow2(mv, q - 1, -e2 + q - 1 + l) % 10);
+ }
+ if (q <= 9)
+ {
+ /*
+ * The largest power of 5 that fits in 24 bits is 5^10, but q
+ * <= 9 seems to be safe as well.
+ *
+ * Only one of mp, mv, and mm can be a multiple of 5, if any.
+ */
+ if (mv % 5 == 0)
+ {
+ vrIsTrailingZeros = multipleOfPowerOf5(mv, q);
+ }
+ else if (acceptBounds)
+ {
+ vmIsTrailingZeros = multipleOfPowerOf5(mm, q);
+ }
+ else
+ {
+ vp -= multipleOfPowerOf5(mp, q);
+ }
+ }
+ }
+ else
+ {
+ const uint32 q = log10Pow5(-e2);
+ const int32 i = -e2 - q;
+ const int32 k = pow5bits(i) - FLOAT_POW5_BITCOUNT;
+ int32 j = q - k;
+
+ e10 = q + e2;
+
+ vr = mulPow5divPow2(mv, i, j);
+ vp = mulPow5divPow2(mp, i, j);
+ vm = mulPow5divPow2(mm, i, j);
+
+ if (q != 0 && (vp - 1) / 10 <= vm / 10)
+ {
+ j = q - 1 - (pow5bits(i + 1) - FLOAT_POW5_BITCOUNT);
+ lastRemovedDigit = (uint8_t) (mulPow5divPow2(mv, i + 1, j) % 10);
+ }
+ 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 < 31)
+ {
+ /* TODO(ulfjack):Use a tighter bound here. */
+ vrIsTrailingZeros = multipleOfPowerOf2(mv, q - 1);
+ }
+ }
+
+ /*
+ * Step 4: Find the shortest decimal representation in the interval of
+ * legal representations.
+ */
+ {
+ uint32 removed = 0;
+ uint32 output;
+
+ if (vmIsTrailingZeros || vrIsTrailingZeros)
+ {
+ /* General case, which happens rarely (~4.0%). */
+ while (vp / 10 > vm / 10)
+ {
+ vmIsTrailingZeros &= vm - (vm / 10) * 10 == 0;
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8_t) (vr % 10);
+ vr /= 10;
+ vp /= 10;
+ vm /= 10;
+ ++removed;
+ }
+ if (vmIsTrailingZeros)
+ {
+ while (vm % 10 == 0)
+ {
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8_t) (vr % 10);
+ vr /= 10;
+ vp /= 10;
+ vm /= 10;
+ ++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 (~96.0%). Percentages below
+ * are relative to this.
+ *
+ * Loop iterations below (approximately): 0: 13.6%, 1: 70.7%,
+ * 2: 14.1%, 3: 1.39%, 4: 0.14%, 5+: 0.01%
+ */
+ while (vp / 10 > vm / 10)
+ {
+ lastRemovedDigit = (uint8_t) (vr % 10);
+ vr /= 10;
+ vp /= 10;
+ vm /= 10;
+ ++removed;
+ }
+
+ /*
+ * We need to take vr + 1 if vr is outside bounds or we need
+ * to round up.
+ */
+ output = vr + (vr == vm || lastRemovedDigit >= 5);
+ }
+
+ {
+ const int32 exp = e10 + removed;
+
+ floating_decimal_32 fd;
+
+ fd.exponent = exp;
+ fd.mantissa = output;
+ return fd;
+ }
+ }
+ }
+}
+
+static inline int
+to_chars_f(const floating_decimal_32 v, const uint32 olength, char *const result)
+{
+ /* Step 5: Print the decimal representation. */
+ int index = 0;
+
+ uint32 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 else, which might mean
+ * adding zeros:
+ *
+ * exp | format
+ * 1+ | ddddddddd000000
+ * 0 | ddddddddd
+ * -1 .. -len+1 | dddddddd.d to d.ddddddddd
+ * -len ... | 0.ddddddddd to 0.0000dddddd
+ */
+ uint32 i = 0;
+ int32 nexp = exp + olength;
+
+ if (nexp <= 0)
+ {
+ /* 0.0000ddddd */
+ index = 2 - nexp;
+ memset(result, '0', index);
+ result[1] = '.';
+ }
+ else if (exp < 0)
+ {
+ /*
+ * dddd.dddd; leave space at the start and move the '.' in after
+ */
+ index = 1;
+ }
+
+ while (output >= 10000)
+ {
+ const uint32 c = output - 10000 * (output / 10000);
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+
+ output /= 10000;
+
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 4, DIGIT_TABLE + c1, 2);
+ i += 4;
+ }
+ if (output >= 100)
+ {
+ const uint32 c = (output % 100) << 1;
+
+ output /= 100;
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
+ i += 2;
+ }
+ if (output >= 10)
+ {
+ const uint32 c = output << 1;
+ memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
+ }
+ else
+ {
+ result[index] = (char) ('0' + output);
+ }
+
+ if (index == 1)
+ {
+ memmove(result, result+1, nexp);
+ result[nexp] = '.';
+ index = olength + 1;
+ }
+ else if (exp >= 0)
+ {
+ if (exp > 0)
+ memset(result + olength, '0', exp);
+ index = olength + exp;
+ }
+ else
+ {
+ index = olength + (2 - nexp);
+ }
+
+ return index;
+}
+
+static inline int
+to_chars(const floating_decimal_32 v, const bool sign, char *const result)
+{
+ /* Step 5: Print the decimal representation. */
+ int index = 0;
+
+ uint32 output = v.mantissa;
+ const uint32 olength = decimalLength(output);
+ int32 exp = v.exponent + olength - 1;
+ uint32 i = 0;
+
+ if (sign)
+ result[index++] = '-';
+
+ if (exp >= -4 && exp < 6)
+ return to_chars_f(v, olength, result+index) + sign;
+
+ /*----
+ * 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;
+ */
+
+ while (output >= 10000)
+ {
+ const uint32 c = output - 10000 * (output / 10000);
+ const uint32 c0 = (c % 100) << 1;
+ const uint32 c1 = (c / 100) << 1;
+
+ output /= 10000;
+
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
+ i += 4;
+ }
+ if (output >= 100)
+ {
+ const uint32 c = (output % 100) << 1;
+
+ output /= 100;
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c, 2);
+ i += 2;
+ }
+ if (output >= 10)
+ {
+ const uint32 c = output << 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' + output);
+ }
+
+ /* 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++] = '+';
+
+ memcpy(result + index, DIGIT_TABLE + 2 * exp, 2);
+ index += 2;
+ }
+
+ return index;
+}
+
+int
+ryu_f2s_buffered_n(float f, char *result)
+{
+ /*
+ * Step 1: Decode the floating-point number, and unify normalized and
+ * subnormal cases.
+ */
+ const uint32 bits = float_to_bits(f);
+
+ /* Decode bits into sign, mantissa, and exponent. */
+ const bool ieeeSign = ((bits >> (FLOAT_MANTISSA_BITS + FLOAT_EXPONENT_BITS)) & 1) != 0;
+ const uint32 ieeeMantissa = bits & ((1u << FLOAT_MANTISSA_BITS) - 1);
+ const uint32 ieeeExponent = (bits >> FLOAT_MANTISSA_BITS) & ((1u << FLOAT_EXPONENT_BITS) - 1);
+
+ /* Case distinction; exit early for the easy cases. */
+ if (ieeeExponent == ((1u << FLOAT_EXPONENT_BITS) - 1u) || (ieeeExponent == 0 && ieeeMantissa == 0))
+ {
+ return copy_special_str(result, ieeeSign, ieeeExponent, ieeeMantissa);
+ }
+
+ {
+ const floating_decimal_32 v = f2d(ieeeMantissa, ieeeExponent);
+
+ return to_chars(v, ieeeSign, result);
+ }
+}
+
+void
+ryu_f2s_buffered(float f, char *result)
+{
+ const int index = ryu_f2s_buffered_n(f, result);
+
+ /* Terminate the string. */
+ result[index] = '\0';
+}
+
+char *
+ryu_f2s(float f)
+{
+ char *const result = (char *) malloc(16);
+
+ ryu_f2s_buffered(f, result);
+ return result;
+}
diff --git a/src/common/ryu_common.h b/src/common/ryu_common.h
new file mode 100644
index 0000000000..4de7ccd8af
--- /dev/null
+++ b/src/common/ryu_common.h
@@ -0,0 +1,122 @@
+/*---------------------------------------------------------------------------
+ *
+ * Common routines for Ryu floating-point output.
+ *
+ * Portions Copyright (c) 2018, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/common/ryu_common.h
+ *
+ * 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.
+ *
+ *---------------------------------------------------------------------------
+ */
+#ifndef RYU_COMMON_H
+#define RYU_COMMON_H
+
+#if SIZEOF_SIZE_T < 8
+#define RYU_32_BIT_PLATFORM
+#endif
+
+/* Returns e == 0 ? 1 : ceil(log_2(5^e)). */
+static inline uint32
+pow5bits(const int32 e)
+{
+ /*
+ * This approximation works up to the point that the multiplication
+ * overflows at e = 3529.
+ *
+ * If the multiplication were done in 64 bits, it would fail at 5^4004
+ * which is just greater than 2^9297.
+ */
+ Assert(e >= 0);
+ Assert(e <= 3528);
+ return ((((uint32) e) * 1217359) >> 19) + 1;
+}
+
+/* Returns floor(log_10(2^e)). */
+static inline int32
+log10Pow2(const int32 e)
+{
+ /*
+ * The first value this approximation fails for is 2^1651 which is just
+ * greater than 10^297.
+ */
+ Assert(e >= 0);
+ Assert(e <= 1650);
+ return (int32) ((((uint32) e) * 78913) >> 18);
+}
+
+/* Returns floor(log_10(5^e)). */
+static inline int32
+log10Pow5(const int32 e)
+{
+ /*
+ * The first value this approximation fails for is 5^2621 which is just
+ * greater than 10^1832.
+ */
+ Assert(e >= 0);
+ Assert(e <= 2620);
+ return (int32) ((((uint32) e) * 732923) >> 20);
+}
+
+static inline int
+copy_special_str(char *const result, const bool sign, const bool exponent, const bool mantissa)
+{
+ if (mantissa)
+ {
+ memcpy(result, "NaN", 3);
+ return 3;
+ }
+ if (sign)
+ {
+ result[0] = '-';
+ }
+ if (exponent)
+ {
+ memcpy(result + sign, "Infinity", 8);
+ return sign + 8;
+ }
+ result[sign] = '0';
+ return sign + 1;
+}
+
+static inline uint32
+float_to_bits(const float f)
+{
+ uint32 bits = 0;
+
+ memcpy(&bits, &f, sizeof(float));
+ return bits;
+}
+
+static inline uint64
+double_to_bits(const double d)
+{
+ uint64 bits = 0;
+
+ memcpy(&bits, &d, sizeof(double));
+ return bits;
+}
+
+#endif /* RYU_COMMON_H */
diff --git a/src/include/common/ryu.h b/src/include/common/ryu.h
new file mode 100644
index 0000000000..bd8e823c01
--- /dev/null
+++ b/src/include/common/ryu.h
@@ -0,0 +1,45 @@
+/*---------------------------------------------------------------------------
+ *
+ * Ryu floating-point output.
+ *
+ * Portions Copyright (c) 2018, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/include/common/ryu.h
+ *
+ * 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.
+ *
+ *---------------------------------------------------------------------------
+ */
+#ifndef RYU_H
+#define RYU_H
+
+int ryu_d2s_buffered_n(double f, char *result);
+void ryu_d2s_buffered(double f, char *result);
+char *ryu_d2s(double f);
+
+int ryu_f2s_buffered_n(float f, char *result);
+void ryu_f2s_buffered(float f, char *result);
+char *ryu_f2s(float f);
+
+#endif /* RYU_H */
diff --git a/src/tools/msvc/Mkvcbuild.pm b/src/tools/msvc/Mkvcbuild.pm
index 2921d193a1..70cafcce8e 100644
--- a/src/tools/msvc/Mkvcbuild.pm
+++ b/src/tools/msvc/Mkvcbuild.pm
@@ -117,7 +117,7 @@ sub mkvcbuild
}
our @pgcommonallfiles = qw(
- base64.c config_info.c controldata_utils.c exec.c file_perm.c ip.c
+ base64.c config_info.c controldata_utils.c d2s.c exec.c f2s.c file_perm.c ip.c
keywords.c link-canary.c md5.c
pg_lzcompress.c pgfnames.c psprintf.c relpath.c rmtree.c
saslprep.c scram-common.c string.c unicode_norm.c username.c
