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postgresql/src/common/f2s.c

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/*---------------------------------------------------------------------------
*
* Ryu floating-point output for single precision.
*
* Portions Copyright (c) 2018-2019, 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/shortest_dec.h"
#include "digit_table.h"
#include "ryu_common.h"
#define FLOAT_MANTISSA_BITS 23
#define FLOAT_EXPONENT_BITS 8
#define FLOAT_BIAS 127
/*
* This table is generated (by the upstream) by PrintFloatLookupTable,
* and modified (by us) to add UINT64CONST.
*/
#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 (;;)
{
Assert(value != 0);
const uint32 q = value / 5;
const uint32 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);
bits1Lo += bits0Hi;
bits1Hi += (bits1Lo < bits0Hi);
const int32 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 <= PG_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;
}
#if STRICTLY_SHORTEST
const bool even = (m2 & 1) == 0;
const bool acceptBounds = even;
#else
const bool acceptBounds = false;
#endif
/* Step 2: Determine the interval of legal decimal representations. */
const 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 lastRemovedDigit = 0;
if (e2 >= 0)
{
const uint32 q = log10Pow2(e2);
e10 = q;
const int32 k = FLOAT_POW5_INV_BITCOUNT + pow5bits(q) - 1;
const int32 i = -e2 + q + k;
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) (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);
e10 = q + e2;
const int32 i = -e2 - q;
const int32 k = pow5bits(i) - FLOAT_POW5_BITCOUNT;
int32 j = q - k;
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) (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) (vr % 10);
vr /= 10;
vp /= 10;
vm /= 10;
++removed;
}
if (vmIsTrailingZeros)
{
while (vm % 10 == 0)
{
vrIsTrailingZeros &= lastRemovedDigit == 0;
lastRemovedDigit = (uint8) (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) (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 depending on the output length
* and exponent, which might mean adding zeros:
*
* exp | format
* 1+ | ddddddddd000000
* 0 | ddddddddd
* -1 .. -len+1 | dddddddd.d to d.ddddddddd
* -len ... | 0.ddddddddd to 0.000dddddd
*/
uint32 i = 0;
int32 nexp = exp + olength;
if (nexp <= 0)
{
/* -nexp is number of 0s to add after '.' */
Assert(nexp >= -3);
/* 0.000ddddd */
index = 2 - nexp;
/* copy 8 bytes rather than 5 to let compiler optimize */
memcpy(result, "0.000000", 8);
}
else if (exp < 0)
{
/*
* dddd.dddd; leave space at the start and move the '.' in after
*/
index = 1;
}
else
{
/*
* We can save some code later by pre-filling with zeros. We know that
* there can be no more than 6 output digits in this form, otherwise
* we would not choose fixed-point output. memset 8 rather than 6
* bytes to let the compiler optimize it.
*/
Assert(exp < 6 && exp + olength <= 6);
memset(result, '0', 8);
}
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)
{
/*
* nexp is 1..6 here, representing the number of digits before the
* point. A value of 7+ is not possible because we switch to
* scientific notation when the display exponent reaches 6.
*/
Assert(nexp < 7);
/* gcc only seems to want to optimize memmove for small 2^n */
if (nexp & 4)
{
memmove(result + index - 1, result + index, 4);
index += 4;
}
if (nexp & 2)
{
memmove(result + index - 1, result + index, 2);
index += 2;
}
if (nexp & 1)
{
result[index - 1] = result[index];
}
result[nexp] = '.';
index = olength + 1;
}
else if (exp >= 0)
{
/* we supplied the trailing zeros earlier, now just set the length. */
index = olength + exp;
}
else
{
index = olength + (2 - nexp);
}
return index;
}
static inline int
to_chars(const floating_decimal_32 v, const bool sign, char *const result)
{
/* Step 5: Print the decimal representation. */
int index = 0;
uint32 output = v.mantissa;
uint32 olength = decimalLength(output);
int32 exp = v.exponent + olength - 1;
if (sign)
result[index++] = '-';
/*
* The thresholds for fixed-point output are chosen to match printf
* defaults. Beware that both the code of to_chars_f and the value of
* FLOAT_SHORTEST_DECIMAL_LEN are sensitive to these thresholds.
*/
if (exp >= -4 && exp < 6)
return to_chars_f(v, olength, result + index) + sign;
/*
* If v.exponent is exactly 0, we might have reached here via the small
* integer fast path, in which case v.mantissa might contain trailing
* (decimal) zeros. For scientific notation we need to move these zeros
* into the exponent. (For fixed point this doesn't matter, which is why
* we do this here rather than above.)
*
* Since we already calculated the display exponent (exp) above based on
* the old decimal length, that value does not change here. Instead, we
* just reduce the display length for each digit removed.
*
* If we didn't get here via the fast path, the raw exponent will not
* usually be 0, and there will be no trailing zeros, so we pay no more
* than one div10/multiply extra cost. We claw back half of that by
* checking for divisibility by 2 before dividing by 10.
*/
if (v.exponent == 0)
{
while ((output & 1) == 0)
{
const uint32 q = output / 10;
const uint32 r = output - 10 * q;
if (r != 0)
break;
output = q;
--olength;
}
}
/*----
* Print the decimal digits.
* The following code is equivalent to:
*
* for (uint32 i = 0; i < olength - 1; ++i) {
* const uint32 c = output % 10; output /= 10;
* result[index + olength - i] = (char) ('0' + c);
* }
* result[index] = '0' + output % 10;
*/
uint32 i = 0;
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;
}
static inline bool
f2d_small_int(const uint32 ieeeMantissa,
const uint32 ieeeExponent,
floating_decimal_32 *v)
{
const int32 e2 = (int32) ieeeExponent - FLOAT_BIAS - FLOAT_MANTISSA_BITS;
/*
* Avoid using multiple "return false;" here since it tends to provoke the
* compiler into inlining multiple copies of f2d, which is undesirable.
*/
if (e2 >= -FLOAT_MANTISSA_BITS && e2 <= 0)
{
/*----
* Since 2^23 <= m2 < 2^24 and 0 <= -e2 <= 23:
* 1 <= f = m2 / 2^-e2 < 2^24.
*
* Test if the lower -e2 bits of the significand are 0, i.e. whether
* the fraction is 0. We can use ieeeMantissa here, since the implied
* 1 bit can never be tested by this; the implied 1 can only be part
* of a fraction if e2 < -FLOAT_MANTISSA_BITS which we already
* checked. (e.g. 0.5 gives ieeeMantissa == 0 and e2 == -24)
*/
const uint32 mask = (1U << -e2) - 1;
const uint32 fraction = ieeeMantissa & mask;
if (fraction == 0)
{
/*----
* f is an integer in the range [1, 2^24).
* Note: mantissa might contain trailing (decimal) 0's.
* Note: since 2^24 < 10^9, there is no need to adjust
* decimalLength().
*/
const uint32 m2 = (1U << FLOAT_MANTISSA_BITS) | ieeeMantissa;
v->mantissa = m2 >> -e2;
v->exponent = 0;
return true;
}
}
return false;
}
/*
* Store the shortest decimal representation of the given float as an
* UNTERMINATED string in the caller's supplied buffer (which must be at least
* FLOAT_SHORTEST_DECIMAL_LEN-1 bytes long).
*
* Returns the number of bytes stored.
*/
int
float_to_shortest_decimal_bufn(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 != 0), (ieeeMantissa != 0));
}
floating_decimal_32 v;
const bool isSmallInt = f2d_small_int(ieeeMantissa, ieeeExponent, &v);
if (!isSmallInt)
{
v = f2d(ieeeMantissa, ieeeExponent);
}
return to_chars(v, ieeeSign, result);
}
/*
* Store the shortest decimal representation of the given float as a
* null-terminated string in the caller's supplied buffer (which must be at
* least FLOAT_SHORTEST_DECIMAL_LEN bytes long).
*
* Returns the string length.
*/
int
float_to_shortest_decimal_buf(float f, char *result)
{
const int index = float_to_shortest_decimal_bufn(f, result);
/* Terminate the string. */
Assert(index < FLOAT_SHORTEST_DECIMAL_LEN);
result[index] = '\0';
return index;
}
/*
* Return the shortest decimal representation as a null-terminated palloc'd
* string (outside the backend, uses malloc() instead).
*
* Caller is responsible for freeing the result.
*/
char *
float_to_shortest_decimal(float f)
{
char *const result = (char *) palloc(FLOAT_SHORTEST_DECIMAL_LEN);
float_to_shortest_decimal_buf(f, result);
return result;
}
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