mirror of
https://git.postgresql.org/git/postgresql.git
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be76af171c
This is still using the 2.0 version of pg_bsd_indent. I thought it would be good to commit this separately, so as to document the differences between 2.0 and 2.1 behavior. Discussion: https://postgr.es/m/16296.1558103386@sss.pgh.pa.us
1077 lines
26 KiB
C
1077 lines
26 KiB
C
/*---------------------------------------------------------------------------
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*
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* Ryu floating-point output for double precision.
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*
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* Portions Copyright (c) 2018-2019, PostgreSQL Global Development Group
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*
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* IDENTIFICATION
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* src/common/d2s.c
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*
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* This is a modification of code taken from github.com/ulfjack/ryu under the
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* terms of the Boost license (not the Apache license). The original copyright
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* notice follows:
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*
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* Copyright 2018 Ulf Adams
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*
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* The contents of this file may be used under the terms of the Apache
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* License, Version 2.0.
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*
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* (See accompanying file LICENSE-Apache or copy at
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* http://www.apache.org/licenses/LICENSE-2.0)
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*
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* Alternatively, the contents of this file may be used under the terms of the
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* Boost Software License, Version 1.0.
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*
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* (See accompanying file LICENSE-Boost or copy at
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* https://www.boost.org/LICENSE_1_0.txt)
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*
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* Unless required by applicable law or agreed to in writing, this software is
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* distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
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* KIND, either express or implied.
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*
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*---------------------------------------------------------------------------
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*/
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/*
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* Runtime compiler options:
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*
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* -DRYU_ONLY_64_BIT_OPS Avoid using uint128 or 64-bit intrinsics. Slower,
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* depending on your compiler.
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*/
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#ifndef FRONTEND
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#include "postgres.h"
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#else
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#include "postgres_fe.h"
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#endif
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#include "common/shortest_dec.h"
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/*
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* For consistency, we use 128-bit types if and only if the rest of PG also
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* does, even though we could use them here without worrying about the
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* alignment concerns that apply elsewhere.
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*/
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#if !defined(HAVE_INT128) && defined(_MSC_VER) \
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&& !defined(RYU_ONLY_64_BIT_OPS) && defined(_M_X64)
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#define HAS_64_BIT_INTRINSICS
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#endif
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#include "ryu_common.h"
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#include "digit_table.h"
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#include "d2s_full_table.h"
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#include "d2s_intrinsics.h"
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#define DOUBLE_MANTISSA_BITS 52
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#define DOUBLE_EXPONENT_BITS 11
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#define DOUBLE_BIAS 1023
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#define DOUBLE_POW5_INV_BITCOUNT 122
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#define DOUBLE_POW5_BITCOUNT 121
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static inline uint32
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pow5Factor(uint64 value)
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{
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uint32 count = 0;
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for (;;)
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{
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Assert(value != 0);
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const uint64 q = div5(value);
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const uint32 r = (uint32) (value - 5 * q);
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if (r != 0)
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break;
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value = q;
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++count;
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}
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return count;
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}
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/* Returns true if value is divisible by 5^p. */
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static inline bool
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multipleOfPowerOf5(const uint64 value, const uint32 p)
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{
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/*
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* I tried a case distinction on p, but there was no performance
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* difference.
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*/
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return pow5Factor(value) >= p;
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}
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/* Returns true if value is divisible by 2^p. */
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static inline bool
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multipleOfPowerOf2(const uint64 value, const uint32 p)
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{
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/* return __builtin_ctzll(value) >= p; */
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return (value & ((UINT64CONST(1) << p) - 1)) == 0;
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}
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/*
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* We need a 64x128-bit multiplication and a subsequent 128-bit shift.
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*
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* Multiplication:
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*
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* The 64-bit factor is variable and passed in, the 128-bit factor comes
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* from a lookup table. We know that the 64-bit factor only has 55
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* significant bits (i.e., the 9 topmost bits are zeros). The 128-bit
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* factor only has 124 significant bits (i.e., the 4 topmost bits are
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* zeros).
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*
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* Shift:
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*
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* In principle, the multiplication result requires 55 + 124 = 179 bits to
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* represent. However, we then shift this value to the right by j, which is
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* at least j >= 115, so the result is guaranteed to fit into 179 - 115 =
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* 64 bits. This means that we only need the topmost 64 significant bits of
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* the 64x128-bit multiplication.
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*
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* There are several ways to do this:
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*
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* 1. Best case: the compiler exposes a 128-bit type.
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* We perform two 64x64-bit multiplications, add the higher 64 bits of the
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* lower result to the higher result, and shift by j - 64 bits.
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*
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* We explicitly cast from 64-bit to 128-bit, so the compiler can tell
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* that these are only 64-bit inputs, and can map these to the best
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* possible sequence of assembly instructions. x86-64 machines happen to
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* have matching assembly instructions for 64x64-bit multiplications and
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* 128-bit shifts.
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*
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* 2. Second best case: the compiler exposes intrinsics for the x86-64
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* assembly instructions mentioned in 1.
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*
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* 3. We only have 64x64 bit instructions that return the lower 64 bits of
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* the result, i.e., we have to use plain C.
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*
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* Our inputs are less than the full width, so we have three options:
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* a. Ignore this fact and just implement the intrinsics manually.
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* b. Split both into 31-bit pieces, which guarantees no internal
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* overflow, but requires extra work upfront (unless we change the
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* lookup table).
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* c. Split only the first factor into 31-bit pieces, which also
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* guarantees no internal overflow, but requires extra work since the
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* intermediate results are not perfectly aligned.
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*/
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#if defined(HAVE_INT128)
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/* Best case: use 128-bit type. */
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static inline uint64
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mulShift(const uint64 m, const uint64 *const mul, const int32 j)
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{
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const uint128 b0 = ((uint128) m) * mul[0];
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const uint128 b2 = ((uint128) m) * mul[1];
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return (uint64) (((b0 >> 64) + b2) >> (j - 64));
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}
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static inline uint64
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mulShiftAll(const uint64 m, const uint64 *const mul, const int32 j,
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uint64 *const vp, uint64 *const vm, const uint32 mmShift)
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{
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*vp = mulShift(4 * m + 2, mul, j);
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*vm = mulShift(4 * m - 1 - mmShift, mul, j);
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return mulShift(4 * m, mul, j);
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}
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#elif defined(HAS_64_BIT_INTRINSICS)
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static inline uint64
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mulShift(const uint64 m, const uint64 *const mul, const int32 j)
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{
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/* m is maximum 55 bits */
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uint64 high1;
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/* 128 */
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const uint64 low1 = umul128(m, mul[1], &high1);
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/* 64 */
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uint64 high0;
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uint64 sum;
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/* 64 */
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umul128(m, mul[0], &high0);
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/* 0 */
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sum = high0 + low1;
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if (sum < high0)
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{
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++high1;
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/* overflow into high1 */
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}
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return shiftright128(sum, high1, j - 64);
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}
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static inline uint64
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mulShiftAll(const uint64 m, const uint64 *const mul, const int32 j,
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uint64 *const vp, uint64 *const vm, const uint32 mmShift)
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{
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*vp = mulShift(4 * m + 2, mul, j);
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*vm = mulShift(4 * m - 1 - mmShift, mul, j);
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return mulShift(4 * m, mul, j);
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}
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#else /* // !defined(HAVE_INT128) &&
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* !defined(HAS_64_BIT_INTRINSICS) */
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static inline uint64
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mulShiftAll(uint64 m, const uint64 *const mul, const int32 j,
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uint64 *const vp, uint64 *const vm, const uint32 mmShift)
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{
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m <<= 1; /* m is maximum 55 bits */
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uint64 tmp;
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const uint64 lo = umul128(m, mul[0], &tmp);
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uint64 hi;
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const uint64 mid = tmp + umul128(m, mul[1], &hi);
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hi += mid < tmp; /* overflow into hi */
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const uint64 lo2 = lo + mul[0];
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const uint64 mid2 = mid + mul[1] + (lo2 < lo);
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const uint64 hi2 = hi + (mid2 < mid);
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*vp = shiftright128(mid2, hi2, j - 64 - 1);
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if (mmShift == 1)
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{
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const uint64 lo3 = lo - mul[0];
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const uint64 mid3 = mid - mul[1] - (lo3 > lo);
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const uint64 hi3 = hi - (mid3 > mid);
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*vm = shiftright128(mid3, hi3, j - 64 - 1);
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}
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else
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{
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const uint64 lo3 = lo + lo;
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const uint64 mid3 = mid + mid + (lo3 < lo);
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const uint64 hi3 = hi + hi + (mid3 < mid);
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const uint64 lo4 = lo3 - mul[0];
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const uint64 mid4 = mid3 - mul[1] - (lo4 > lo3);
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const uint64 hi4 = hi3 - (mid4 > mid3);
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*vm = shiftright128(mid4, hi4, j - 64);
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}
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return shiftright128(mid, hi, j - 64 - 1);
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}
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#endif /* // HAS_64_BIT_INTRINSICS */
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static inline uint32
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decimalLength(const uint64 v)
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{
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/* This is slightly faster than a loop. */
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/* The average output length is 16.38 digits, so we check high-to-low. */
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/* Function precondition: v is not an 18, 19, or 20-digit number. */
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/* (17 digits are sufficient for round-tripping.) */
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Assert(v < 100000000000000000L);
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if (v >= 10000000000000000L)
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{
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return 17;
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}
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if (v >= 1000000000000000L)
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{
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return 16;
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}
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if (v >= 100000000000000L)
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{
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return 15;
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}
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if (v >= 10000000000000L)
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{
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return 14;
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}
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if (v >= 1000000000000L)
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{
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return 13;
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}
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if (v >= 100000000000L)
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{
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return 12;
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}
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if (v >= 10000000000L)
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{
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return 11;
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}
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if (v >= 1000000000L)
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{
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return 10;
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}
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if (v >= 100000000L)
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{
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return 9;
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}
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if (v >= 10000000L)
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{
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return 8;
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}
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if (v >= 1000000L)
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{
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return 7;
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}
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if (v >= 100000L)
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{
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return 6;
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}
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if (v >= 10000L)
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{
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return 5;
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}
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if (v >= 1000L)
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{
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return 4;
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}
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if (v >= 100L)
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{
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return 3;
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}
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if (v >= 10L)
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{
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return 2;
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}
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return 1;
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}
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/* A floating decimal representing m * 10^e. */
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typedef struct floating_decimal_64
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{
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uint64 mantissa;
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int32 exponent;
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} floating_decimal_64;
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static inline floating_decimal_64
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d2d(const uint64 ieeeMantissa, const uint32 ieeeExponent)
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{
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int32 e2;
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uint64 m2;
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if (ieeeExponent == 0)
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{
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/* We subtract 2 so that the bounds computation has 2 additional bits. */
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e2 = 1 - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2;
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m2 = ieeeMantissa;
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}
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else
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{
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e2 = ieeeExponent - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2;
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m2 = (UINT64CONST(1) << DOUBLE_MANTISSA_BITS) | ieeeMantissa;
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}
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#if STRICTLY_SHORTEST
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const bool even = (m2 & 1) == 0;
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const bool acceptBounds = even;
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#else
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const bool acceptBounds = false;
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#endif
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/* Step 2: Determine the interval of legal decimal representations. */
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const uint64 mv = 4 * m2;
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/* Implicit bool -> int conversion. True is 1, false is 0. */
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const uint32 mmShift = ieeeMantissa != 0 || ieeeExponent <= 1;
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/* We would compute mp and mm like this: */
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/* uint64 mp = 4 * m2 + 2; */
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/* uint64 mm = mv - 1 - mmShift; */
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/* Step 3: Convert to a decimal power base using 128-bit arithmetic. */
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uint64 vr,
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vp,
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vm;
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int32 e10;
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bool vmIsTrailingZeros = false;
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bool vrIsTrailingZeros = false;
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if (e2 >= 0)
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{
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/*
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* I tried special-casing q == 0, but there was no effect on
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* performance.
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*
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* This expr is slightly faster than max(0, log10Pow2(e2) - 1).
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*/
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const uint32 q = log10Pow2(e2) - (e2 > 3);
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const int32 k = DOUBLE_POW5_INV_BITCOUNT + pow5bits(q) - 1;
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const int32 i = -e2 + q + k;
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e10 = q;
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vr = mulShiftAll(m2, DOUBLE_POW5_INV_SPLIT[q], i, &vp, &vm, mmShift);
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if (q <= 21)
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{
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/*
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* This should use q <= 22, but I think 21 is also safe. Smaller
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* values may still be safe, but it's more difficult to reason
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* about them.
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*
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* Only one of mp, mv, and mm can be a multiple of 5, if any.
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*/
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const uint32 mvMod5 = (uint32) (mv - 5 * div5(mv));
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if (mvMod5 == 0)
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{
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vrIsTrailingZeros = multipleOfPowerOf5(mv, q);
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}
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else if (acceptBounds)
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{
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/*----
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* Same as min(e2 + (~mm & 1), pow5Factor(mm)) >= q
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* <=> e2 + (~mm & 1) >= q && pow5Factor(mm) >= q
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* <=> true && pow5Factor(mm) >= q, since e2 >= q.
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*----
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*/
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vmIsTrailingZeros = multipleOfPowerOf5(mv - 1 - mmShift, q);
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}
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else
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{
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/* Same as min(e2 + 1, pow5Factor(mp)) >= q. */
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vp -= multipleOfPowerOf5(mv + 2, q);
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}
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}
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}
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else
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{
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/*
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* This expression is slightly faster than max(0, log10Pow5(-e2) - 1).
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*/
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const uint32 q = log10Pow5(-e2) - (-e2 > 1);
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const int32 i = -e2 - q;
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const int32 k = pow5bits(i) - DOUBLE_POW5_BITCOUNT;
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const int32 j = q - k;
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e10 = q + e2;
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vr = mulShiftAll(m2, DOUBLE_POW5_SPLIT[i], j, &vp, &vm, mmShift);
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if (q <= 1)
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{
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/*
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* {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q
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* trailing 0 bits.
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*/
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/* mv = 4 * m2, so it always has at least two trailing 0 bits. */
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vrIsTrailingZeros = true;
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if (acceptBounds)
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{
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/*
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* mm = mv - 1 - mmShift, so it has 1 trailing 0 bit iff
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* mmShift == 1.
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*/
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vmIsTrailingZeros = mmShift == 1;
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}
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else
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{
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/*
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* mp = mv + 2, so it always has at least one trailing 0 bit.
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*/
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--vp;
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}
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}
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else if (q < 63)
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{
|
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/* TODO(ulfjack):Use a tighter bound here. */
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/*
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* We need to compute min(ntz(mv), pow5Factor(mv) - e2) >= q - 1
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*/
|
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/* <=> ntz(mv) >= q - 1 && pow5Factor(mv) - e2 >= q - 1 */
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/* <=> ntz(mv) >= q - 1 (e2 is negative and -e2 >= q) */
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/* <=> (mv & ((1 << (q - 1)) - 1)) == 0 */
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|
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/*
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* We also need to make sure that the left shift does not
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* overflow.
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*/
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vrIsTrailingZeros = multipleOfPowerOf2(mv, q - 1);
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}
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}
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|
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/*
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|
* Step 4: Find the shortest decimal representation in the interval of
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* legal representations.
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|
*/
|
|
uint32 removed = 0;
|
|
uint8 lastRemovedDigit = 0;
|
|
uint64 output;
|
|
|
|
/* On average, we remove ~2 digits. */
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if (vmIsTrailingZeros || vrIsTrailingZeros)
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{
|
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/* General case, which happens rarely (~0.7%). */
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|
for (;;)
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|
{
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const uint64 vpDiv10 = div10(vp);
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const uint64 vmDiv10 = div10(vm);
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|
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if (vpDiv10 <= vmDiv10)
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break;
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const uint32 vmMod10 = (uint32) (vm - 10 * vmDiv10);
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const uint64 vrDiv10 = div10(vr);
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const uint32 vrMod10 = (uint32) (vr - 10 * vrDiv10);
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vmIsTrailingZeros &= vmMod10 == 0;
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vrIsTrailingZeros &= lastRemovedDigit == 0;
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lastRemovedDigit = (uint8) vrMod10;
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|
vr = vrDiv10;
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vp = vpDiv10;
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vm = vmDiv10;
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++removed;
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}
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|
|
if (vmIsTrailingZeros)
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|
{
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for (;;)
|
|
{
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|
const uint64 vmDiv10 = div10(vm);
|
|
const uint32 vmMod10 = (uint32) (vm - 10 * vmDiv10);
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|
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if (vmMod10 != 0)
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|
break;
|
|
|
|
const uint64 vpDiv10 = div10(vp);
|
|
const uint64 vrDiv10 = div10(vr);
|
|
const uint32 vrMod10 = (uint32) (vr - 10 * vrDiv10);
|
|
|
|
vrIsTrailingZeros &= lastRemovedDigit == 0;
|
|
lastRemovedDigit = (uint8) vrMod10;
|
|
vr = vrDiv10;
|
|
vp = vpDiv10;
|
|
vm = vmDiv10;
|
|
++removed;
|
|
}
|
|
}
|
|
|
|
if (vrIsTrailingZeros && lastRemovedDigit == 5 && vr % 2 == 0)
|
|
{
|
|
/* Round even if the exact number is .....50..0. */
|
|
lastRemovedDigit = 4;
|
|
}
|
|
|
|
/*
|
|
* We need to take vr + 1 if vr is outside bounds or we need to round
|
|
* up.
|
|
*/
|
|
output = vr + ((vr == vm && (!acceptBounds || !vmIsTrailingZeros)) || lastRemovedDigit >= 5);
|
|
}
|
|
else
|
|
{
|
|
/*
|
|
* Specialized for the common case (~99.3%). Percentages below are
|
|
* relative to this.
|
|
*/
|
|
bool roundUp = false;
|
|
const uint64 vpDiv100 = div100(vp);
|
|
const uint64 vmDiv100 = div100(vm);
|
|
|
|
if (vpDiv100 > vmDiv100)
|
|
{
|
|
/* Optimization:remove two digits at a time(~86.2 %). */
|
|
const uint64 vrDiv100 = div100(vr);
|
|
const uint32 vrMod100 = (uint32) (vr - 100 * vrDiv100);
|
|
|
|
roundUp = vrMod100 >= 50;
|
|
vr = vrDiv100;
|
|
vp = vpDiv100;
|
|
vm = vmDiv100;
|
|
removed += 2;
|
|
}
|
|
|
|
/*----
|
|
* Loop iterations below (approximately), without optimization
|
|
* above:
|
|
*
|
|
* 0: 0.03%, 1: 13.8%, 2: 70.6%, 3: 14.0%, 4: 1.40%, 5: 0.14%,
|
|
* 6+: 0.02%
|
|
*
|
|
* Loop iterations below (approximately), with optimization
|
|
* above:
|
|
*
|
|
* 0: 70.6%, 1: 27.8%, 2: 1.40%, 3: 0.14%, 4+: 0.02%
|
|
*----
|
|
*/
|
|
for (;;)
|
|
{
|
|
const uint64 vpDiv10 = div10(vp);
|
|
const uint64 vmDiv10 = div10(vm);
|
|
|
|
if (vpDiv10 <= vmDiv10)
|
|
break;
|
|
|
|
const uint64 vrDiv10 = div10(vr);
|
|
const uint32 vrMod10 = (uint32) (vr - 10 * vrDiv10);
|
|
|
|
roundUp = vrMod10 >= 5;
|
|
vr = vrDiv10;
|
|
vp = vpDiv10;
|
|
vm = vmDiv10;
|
|
++removed;
|
|
}
|
|
|
|
/*
|
|
* We need to take vr + 1 if vr is outside bounds or we need to round
|
|
* up.
|
|
*/
|
|
output = vr + (vr == vm || roundUp);
|
|
}
|
|
|
|
const int32 exp = e10 + removed;
|
|
|
|
floating_decimal_64 fd;
|
|
|
|
fd.exponent = exp;
|
|
fd.mantissa = output;
|
|
return fd;
|
|
}
|
|
|
|
static inline int
|
|
to_chars_df(const floating_decimal_64 v, const uint32 olength, char *const result)
|
|
{
|
|
/* Step 5: Print the decimal representation. */
|
|
int index = 0;
|
|
|
|
uint64 output = v.mantissa;
|
|
int32 exp = v.exponent;
|
|
|
|
/*----
|
|
* On entry, mantissa * 10^exp is the result to be output.
|
|
* Caller has already done the - sign if needed.
|
|
*
|
|
* We want to insert the point somewhere depending on the output length
|
|
* and exponent, which might mean adding zeros:
|
|
*
|
|
* exp | format
|
|
* 1+ | ddddddddd000000
|
|
* 0 | ddddddddd
|
|
* -1 .. -len+1 | dddddddd.d to d.ddddddddd
|
|
* -len ... | 0.ddddddddd to 0.000dddddd
|
|
*/
|
|
uint32 i = 0;
|
|
int32 nexp = exp + olength;
|
|
|
|
if (nexp <= 0)
|
|
{
|
|
/* -nexp is number of 0s to add after '.' */
|
|
Assert(nexp >= -3);
|
|
/* 0.000ddddd */
|
|
index = 2 - nexp;
|
|
/* won't need more than this many 0s */
|
|
memcpy(result, "0.000000", 8);
|
|
}
|
|
else if (exp < 0)
|
|
{
|
|
/*
|
|
* dddd.dddd; leave space at the start and move the '.' in after
|
|
*/
|
|
index = 1;
|
|
}
|
|
else
|
|
{
|
|
/*
|
|
* We can save some code later by pre-filling with zeros. We know that
|
|
* there can be no more than 16 output digits in this form, otherwise
|
|
* we would not choose fixed-point output.
|
|
*/
|
|
Assert(exp < 16 && exp + olength <= 16);
|
|
memset(result, '0', 16);
|
|
}
|
|
|
|
/*
|
|
* We prefer 32-bit operations, even on 64-bit platforms. We have at most
|
|
* 17 digits, and uint32 can store 9 digits. If output doesn't fit into
|
|
* uint32, we cut off 8 digits, so the rest will fit into uint32.
|
|
*/
|
|
if ((output >> 32) != 0)
|
|
{
|
|
/* Expensive 64-bit division. */
|
|
const uint64 q = div1e8(output);
|
|
uint32 output2 = (uint32) (output - 100000000 * q);
|
|
const uint32 c = output2 % 10000;
|
|
|
|
output = q;
|
|
output2 /= 10000;
|
|
|
|
const uint32 d = output2 % 10000;
|
|
const uint32 c0 = (c % 100) << 1;
|
|
const uint32 c1 = (c / 100) << 1;
|
|
const uint32 d0 = (d % 100) << 1;
|
|
const uint32 d1 = (d / 100) << 1;
|
|
|
|
memcpy(result + index + olength - i - 2, DIGIT_TABLE + c0, 2);
|
|
memcpy(result + index + olength - i - 4, DIGIT_TABLE + c1, 2);
|
|
memcpy(result + index + olength - i - 6, DIGIT_TABLE + d0, 2);
|
|
memcpy(result + index + olength - i - 8, DIGIT_TABLE + d1, 2);
|
|
i += 8;
|
|
}
|
|
|
|
uint32 output2 = (uint32) output;
|
|
|
|
while (output2 >= 10000)
|
|
{
|
|
const uint32 c = output2 - 10000 * (output2 / 10000);
|
|
const uint32 c0 = (c % 100) << 1;
|
|
const uint32 c1 = (c / 100) << 1;
|
|
|
|
output2 /= 10000;
|
|
memcpy(result + index + olength - i - 2, DIGIT_TABLE + c0, 2);
|
|
memcpy(result + index + olength - i - 4, DIGIT_TABLE + c1, 2);
|
|
i += 4;
|
|
}
|
|
if (output2 >= 100)
|
|
{
|
|
const uint32 c = (output2 % 100) << 1;
|
|
|
|
output2 /= 100;
|
|
memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
|
|
i += 2;
|
|
}
|
|
if (output2 >= 10)
|
|
{
|
|
const uint32 c = output2 << 1;
|
|
|
|
memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
|
|
}
|
|
else
|
|
{
|
|
result[index] = (char) ('0' + output2);
|
|
}
|
|
|
|
if (index == 1)
|
|
{
|
|
/*
|
|
* nexp is 1..15 here, representing the number of digits before the
|
|
* point. A value of 16 is not possible because we switch to
|
|
* scientific notation when the display exponent reaches 15.
|
|
*/
|
|
Assert(nexp < 16);
|
|
/* gcc only seems to want to optimize memmove for small 2^n */
|
|
if (nexp & 8)
|
|
{
|
|
memmove(result + index - 1, result + index, 8);
|
|
index += 8;
|
|
}
|
|
if (nexp & 4)
|
|
{
|
|
memmove(result + index - 1, result + index, 4);
|
|
index += 4;
|
|
}
|
|
if (nexp & 2)
|
|
{
|
|
memmove(result + index - 1, result + index, 2);
|
|
index += 2;
|
|
}
|
|
if (nexp & 1)
|
|
{
|
|
result[index - 1] = result[index];
|
|
}
|
|
result[nexp] = '.';
|
|
index = olength + 1;
|
|
}
|
|
else if (exp >= 0)
|
|
{
|
|
/* we supplied the trailing zeros earlier, now just set the length. */
|
|
index = olength + exp;
|
|
}
|
|
else
|
|
{
|
|
index = olength + (2 - nexp);
|
|
}
|
|
|
|
return index;
|
|
}
|
|
|
|
static inline int
|
|
to_chars(floating_decimal_64 v, const bool sign, char *const result)
|
|
{
|
|
/* Step 5: Print the decimal representation. */
|
|
int index = 0;
|
|
|
|
uint64 output = v.mantissa;
|
|
uint32 olength = decimalLength(output);
|
|
int32 exp = v.exponent + olength - 1;
|
|
|
|
if (sign)
|
|
{
|
|
result[index++] = '-';
|
|
}
|
|
|
|
/*
|
|
* The thresholds for fixed-point output are chosen to match printf
|
|
* defaults. Beware that both the code of to_chars_df and the value of
|
|
* DOUBLE_SHORTEST_DECIMAL_LEN are sensitive to these thresholds.
|
|
*/
|
|
if (exp >= -4 && exp < 15)
|
|
return to_chars_df(v, olength, result + index) + sign;
|
|
|
|
/*
|
|
* If v.exponent is exactly 0, we might have reached here via the small
|
|
* integer fast path, in which case v.mantissa might contain trailing
|
|
* (decimal) zeros. For scientific notation we need to move these zeros
|
|
* into the exponent. (For fixed point this doesn't matter, which is why
|
|
* we do this here rather than above.)
|
|
*
|
|
* Since we already calculated the display exponent (exp) above based on
|
|
* the old decimal length, that value does not change here. Instead, we
|
|
* just reduce the display length for each digit removed.
|
|
*
|
|
* If we didn't get here via the fast path, the raw exponent will not
|
|
* usually be 0, and there will be no trailing zeros, so we pay no more
|
|
* than one div10/multiply extra cost. We claw back half of that by
|
|
* checking for divisibility by 2 before dividing by 10.
|
|
*/
|
|
if (v.exponent == 0)
|
|
{
|
|
while ((output & 1) == 0)
|
|
{
|
|
const uint64 q = div10(output);
|
|
const uint32 r = (uint32) (output - 10 * q);
|
|
|
|
if (r != 0)
|
|
break;
|
|
output = q;
|
|
--olength;
|
|
}
|
|
}
|
|
|
|
/*----
|
|
* Print the decimal digits.
|
|
*
|
|
* The following code is equivalent to:
|
|
*
|
|
* for (uint32 i = 0; i < olength - 1; ++i) {
|
|
* const uint32 c = output % 10; output /= 10;
|
|
* result[index + olength - i] = (char) ('0' + c);
|
|
* }
|
|
* result[index] = '0' + output % 10;
|
|
*----
|
|
*/
|
|
|
|
uint32 i = 0;
|
|
|
|
/*
|
|
* We prefer 32-bit operations, even on 64-bit platforms. We have at most
|
|
* 17 digits, and uint32 can store 9 digits. If output doesn't fit into
|
|
* uint32, we cut off 8 digits, so the rest will fit into uint32.
|
|
*/
|
|
if ((output >> 32) != 0)
|
|
{
|
|
/* Expensive 64-bit division. */
|
|
const uint64 q = div1e8(output);
|
|
uint32 output2 = (uint32) (output - 100000000 * q);
|
|
|
|
output = q;
|
|
|
|
const uint32 c = output2 % 10000;
|
|
|
|
output2 /= 10000;
|
|
|
|
const uint32 d = output2 % 10000;
|
|
const uint32 c0 = (c % 100) << 1;
|
|
const uint32 c1 = (c / 100) << 1;
|
|
const uint32 d0 = (d % 100) << 1;
|
|
const uint32 d1 = (d / 100) << 1;
|
|
|
|
memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
|
|
memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
|
|
memcpy(result + index + olength - i - 5, DIGIT_TABLE + d0, 2);
|
|
memcpy(result + index + olength - i - 7, DIGIT_TABLE + d1, 2);
|
|
i += 8;
|
|
}
|
|
|
|
uint32 output2 = (uint32) output;
|
|
|
|
while (output2 >= 10000)
|
|
{
|
|
const uint32 c = output2 - 10000 * (output2 / 10000);
|
|
|
|
output2 /= 10000;
|
|
|
|
const uint32 c0 = (c % 100) << 1;
|
|
const uint32 c1 = (c / 100) << 1;
|
|
|
|
memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
|
|
memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
|
|
i += 4;
|
|
}
|
|
if (output2 >= 100)
|
|
{
|
|
const uint32 c = (output2 % 100) << 1;
|
|
|
|
output2 /= 100;
|
|
memcpy(result + index + olength - i - 1, DIGIT_TABLE + c, 2);
|
|
i += 2;
|
|
}
|
|
if (output2 >= 10)
|
|
{
|
|
const uint32 c = output2 << 1;
|
|
|
|
/*
|
|
* We can't use memcpy here: the decimal dot goes between these two
|
|
* digits.
|
|
*/
|
|
result[index + olength - i] = DIGIT_TABLE[c + 1];
|
|
result[index] = DIGIT_TABLE[c];
|
|
}
|
|
else
|
|
{
|
|
result[index] = (char) ('0' + output2);
|
|
}
|
|
|
|
/* Print decimal point if needed. */
|
|
if (olength > 1)
|
|
{
|
|
result[index + 1] = '.';
|
|
index += olength + 1;
|
|
}
|
|
else
|
|
{
|
|
++index;
|
|
}
|
|
|
|
/* Print the exponent. */
|
|
result[index++] = 'e';
|
|
if (exp < 0)
|
|
{
|
|
result[index++] = '-';
|
|
exp = -exp;
|
|
}
|
|
else
|
|
result[index++] = '+';
|
|
|
|
if (exp >= 100)
|
|
{
|
|
const int32 c = exp % 10;
|
|
|
|
memcpy(result + index, DIGIT_TABLE + 2 * (exp / 10), 2);
|
|
result[index + 2] = (char) ('0' + c);
|
|
index += 3;
|
|
}
|
|
else
|
|
{
|
|
memcpy(result + index, DIGIT_TABLE + 2 * exp, 2);
|
|
index += 2;
|
|
}
|
|
|
|
return index;
|
|
}
|
|
|
|
static inline bool
|
|
d2d_small_int(const uint64 ieeeMantissa,
|
|
const uint32 ieeeExponent,
|
|
floating_decimal_64 *v)
|
|
{
|
|
const int32 e2 = (int32) ieeeExponent - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS;
|
|
|
|
/*
|
|
* Avoid using multiple "return false;" here since it tends to provoke the
|
|
* compiler into inlining multiple copies of d2d, which is undesirable.
|
|
*/
|
|
|
|
if (e2 >= -DOUBLE_MANTISSA_BITS && e2 <= 0)
|
|
{
|
|
/*----
|
|
* Since 2^52 <= m2 < 2^53 and 0 <= -e2 <= 52:
|
|
* 1 <= f = m2 / 2^-e2 < 2^53.
|
|
*
|
|
* Test if the lower -e2 bits of the significand are 0, i.e. whether
|
|
* the fraction is 0. We can use ieeeMantissa here, since the implied
|
|
* 1 bit can never be tested by this; the implied 1 can only be part
|
|
* of a fraction if e2 < -DOUBLE_MANTISSA_BITS which we already
|
|
* checked. (e.g. 0.5 gives ieeeMantissa == 0 and e2 == -53)
|
|
*/
|
|
const uint64 mask = (UINT64CONST(1) << -e2) - 1;
|
|
const uint64 fraction = ieeeMantissa & mask;
|
|
|
|
if (fraction == 0)
|
|
{
|
|
/*----
|
|
* f is an integer in the range [1, 2^53).
|
|
* Note: mantissa might contain trailing (decimal) 0's.
|
|
* Note: since 2^53 < 10^16, there is no need to adjust
|
|
* decimalLength().
|
|
*/
|
|
const uint64 m2 = (UINT64CONST(1) << DOUBLE_MANTISSA_BITS) | ieeeMantissa;
|
|
|
|
v->mantissa = m2 >> -e2;
|
|
v->exponent = 0;
|
|
return true;
|
|
}
|
|
}
|
|
|
|
return false;
|
|
}
|
|
|
|
/*
|
|
* Store the shortest decimal representation of the given double as an
|
|
* UNTERMINATED string in the caller's supplied buffer (which must be at least
|
|
* DOUBLE_SHORTEST_DECIMAL_LEN-1 bytes long).
|
|
*
|
|
* Returns the number of bytes stored.
|
|
*/
|
|
int
|
|
double_to_shortest_decimal_bufn(double f, char *result)
|
|
{
|
|
/*
|
|
* Step 1: Decode the floating-point number, and unify normalized and
|
|
* subnormal cases.
|
|
*/
|
|
const uint64 bits = double_to_bits(f);
|
|
|
|
/* Decode bits into sign, mantissa, and exponent. */
|
|
const bool ieeeSign = ((bits >> (DOUBLE_MANTISSA_BITS + DOUBLE_EXPONENT_BITS)) & 1) != 0;
|
|
const uint64 ieeeMantissa = bits & ((UINT64CONST(1) << DOUBLE_MANTISSA_BITS) - 1);
|
|
const uint32 ieeeExponent = (uint32) ((bits >> DOUBLE_MANTISSA_BITS) & ((1u << DOUBLE_EXPONENT_BITS) - 1));
|
|
|
|
/* Case distinction; exit early for the easy cases. */
|
|
if (ieeeExponent == ((1u << DOUBLE_EXPONENT_BITS) - 1u) || (ieeeExponent == 0 && ieeeMantissa == 0))
|
|
{
|
|
return copy_special_str(result, ieeeSign, (ieeeExponent != 0), (ieeeMantissa != 0));
|
|
}
|
|
|
|
floating_decimal_64 v;
|
|
const bool isSmallInt = d2d_small_int(ieeeMantissa, ieeeExponent, &v);
|
|
|
|
if (!isSmallInt)
|
|
{
|
|
v = d2d(ieeeMantissa, ieeeExponent);
|
|
}
|
|
|
|
return to_chars(v, ieeeSign, result);
|
|
}
|
|
|
|
/*
|
|
* Store the shortest decimal representation of the given double as a
|
|
* null-terminated string in the caller's supplied buffer (which must be at
|
|
* least DOUBLE_SHORTEST_DECIMAL_LEN bytes long).
|
|
*
|
|
* Returns the string length.
|
|
*/
|
|
int
|
|
double_to_shortest_decimal_buf(double f, char *result)
|
|
{
|
|
const int index = double_to_shortest_decimal_bufn(f, result);
|
|
|
|
/* Terminate the string. */
|
|
Assert(index < DOUBLE_SHORTEST_DECIMAL_LEN);
|
|
result[index] = '\0';
|
|
return index;
|
|
}
|
|
|
|
/*
|
|
* Return the shortest decimal representation as a null-terminated palloc'd
|
|
* string (outside the backend, uses malloc() instead).
|
|
*
|
|
* Caller is responsible for freeing the result.
|
|
*/
|
|
char *
|
|
double_to_shortest_decimal(double f)
|
|
{
|
|
char *const result = (char *) palloc(DOUBLE_SHORTEST_DECIMAL_LEN);
|
|
|
|
double_to_shortest_decimal_buf(f, result);
|
|
return result;
|
|
}
|