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Diffstat (limited to 'src/common/d2s.c')
| -rw-r--r-- | src/common/d2s.c | 1076 |
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diff --git a/src/common/d2s.c b/src/common/d2s.c new file mode 100644 index 0000000..8b0b7ce --- /dev/null +++ b/src/common/d2s.c @@ -0,0 +1,1076 @@ +/*--------------------------------------------------------------------------- + * + * Ryu floating-point output for double precision. + * + * Portions Copyright (c) 2018-2020, PostgreSQL Global Development Group + * + * IDENTIFICATION + * src/common/d2s.c + * + * This is a modification of code taken from github.com/ulfjack/ryu under the + * terms of the Boost license (not the Apache license). The original copyright + * notice follows: + * + * Copyright 2018 Ulf Adams + * + * The contents of this file may be used under the terms of the Apache + * License, Version 2.0. + * + * (See accompanying file LICENSE-Apache or copy at + * http://www.apache.org/licenses/LICENSE-2.0) + * + * Alternatively, the contents of this file may be used under the terms of the + * Boost Software License, Version 1.0. + * + * (See accompanying file LICENSE-Boost or copy at + * https://www.boost.org/LICENSE_1_0.txt) + * + * Unless required by applicable law or agreed to in writing, this software is + * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY + * KIND, either express or implied. + * + *--------------------------------------------------------------------------- + */ + +/* + * Runtime compiler options: + * + * -DRYU_ONLY_64_BIT_OPS Avoid using uint128 or 64-bit intrinsics. Slower, + * depending on your compiler. + */ + +#ifndef FRONTEND +#include "postgres.h" +#else +#include "postgres_fe.h" +#endif + +#include "common/shortest_dec.h" + +/* + * For consistency, we use 128-bit types if and only if the rest of PG also + * does, even though we could use them here without worrying about the + * alignment concerns that apply elsewhere. + */ +#if !defined(HAVE_INT128) && defined(_MSC_VER) \ + && !defined(RYU_ONLY_64_BIT_OPS) && defined(_M_X64) +#define HAS_64_BIT_INTRINSICS +#endif + +#include "ryu_common.h" +#include "digit_table.h" +#include "d2s_full_table.h" +#include "d2s_intrinsics.h" + +#define DOUBLE_MANTISSA_BITS 52 +#define DOUBLE_EXPONENT_BITS 11 +#define DOUBLE_BIAS 1023 + +#define DOUBLE_POW5_INV_BITCOUNT 122 +#define DOUBLE_POW5_BITCOUNT 121 + + +static inline uint32 +pow5Factor(uint64 value) +{ + uint32 count = 0; + + for (;;) + { + Assert(value != 0); + const uint64 q = div5(value); + const uint32 r = (uint32) (value - 5 * q); + + if (r != 0) + break; + + value = q; + ++count; + } + return count; +} + +/* Returns true if value is divisible by 5^p. */ +static inline bool +multipleOfPowerOf5(const uint64 value, const uint32 p) +{ + /* + * I tried a case distinction on p, but there was no performance + * difference. + */ + return pow5Factor(value) >= p; +} + +/* Returns true if value is divisible by 2^p. */ +static inline bool +multipleOfPowerOf2(const uint64 value, const uint32 p) +{ + /* return __builtin_ctzll(value) >= p; */ + return (value & ((UINT64CONST(1) << p) - 1)) == 0; +} + +/* + * We need a 64x128-bit multiplication and a subsequent 128-bit shift. + * + * Multiplication: + * + * The 64-bit factor is variable and passed in, the 128-bit factor comes + * from a lookup table. We know that the 64-bit factor only has 55 + * significant bits (i.e., the 9 topmost bits are zeros). The 128-bit + * factor only has 124 significant bits (i.e., the 4 topmost bits are + * zeros). + * + * Shift: + * + * In principle, the multiplication result requires 55 + 124 = 179 bits to + * represent. However, we then shift this value to the right by j, which is + * at least j >= 115, so the result is guaranteed to fit into 179 - 115 = + * 64 bits. This means that we only need the topmost 64 significant bits of + * the 64x128-bit multiplication. + * + * There are several ways to do this: + * + * 1. Best case: the compiler exposes a 128-bit type. + * We perform two 64x64-bit multiplications, add the higher 64 bits of the + * lower result to the higher result, and shift by j - 64 bits. + * + * We explicitly cast from 64-bit to 128-bit, so the compiler can tell + * that these are only 64-bit inputs, and can map these to the best + * possible sequence of assembly instructions. x86-64 machines happen to + * have matching assembly instructions for 64x64-bit multiplications and + * 128-bit shifts. + * + * 2. Second best case: the compiler exposes intrinsics for the x86-64 + * assembly instructions mentioned in 1. + * + * 3. We only have 64x64 bit instructions that return the lower 64 bits of + * the result, i.e., we have to use plain C. + * + * Our inputs are less than the full width, so we have three options: + * a. Ignore this fact and just implement the intrinsics manually. + * b. Split both into 31-bit pieces, which guarantees no internal + * overflow, but requires extra work upfront (unless we change the + * lookup table). + * c. Split only the first factor into 31-bit pieces, which also + * guarantees no internal overflow, but requires extra work since the + * intermediate results are not perfectly aligned. + */ +#if defined(HAVE_INT128) + +/* Best case: use 128-bit type. */ +static inline uint64 +mulShift(const uint64 m, const uint64 *const mul, const int32 j) +{ + const uint128 b0 = ((uint128) m) * mul[0]; + const uint128 b2 = ((uint128) m) * mul[1]; + + return (uint64) (((b0 >> 64) + b2) >> (j - 64)); +} + +static inline uint64 +mulShiftAll(const uint64 m, const uint64 *const mul, const int32 j, + uint64 *const vp, uint64 *const vm, const uint32 mmShift) +{ + *vp = mulShift(4 * m + 2, mul, j); + *vm = mulShift(4 * m - 1 - mmShift, mul, j); + return mulShift(4 * m, mul, j); +} + +#elif defined(HAS_64_BIT_INTRINSICS) + +static inline uint64 +mulShift(const uint64 m, const uint64 *const mul, const int32 j) +{ + /* m is maximum 55 bits */ + uint64 high1; + + /* 128 */ + const uint64 low1 = umul128(m, mul[1], &high1); + + /* 64 */ + uint64 high0; + uint64 sum; + + /* 64 */ + umul128(m, mul[0], &high0); + /* 0 */ + sum = high0 + low1; + + if (sum < high0) + { + ++high1; + /* overflow into high1 */ + } + return shiftright128(sum, high1, j - 64); +} + +static inline uint64 +mulShiftAll(const uint64 m, const uint64 *const mul, const int32 j, + uint64 *const vp, uint64 *const vm, const uint32 mmShift) +{ + *vp = mulShift(4 * m + 2, mul, j); + *vm = mulShift(4 * m - 1 - mmShift, mul, j); + return mulShift(4 * m, mul, j); +} + +#else /* // !defined(HAVE_INT128) && + * !defined(HAS_64_BIT_INTRINSICS) */ + +static inline uint64 +mulShiftAll(uint64 m, const uint64 *const mul, const int32 j, + uint64 *const vp, uint64 *const vm, const uint32 mmShift) +{ + m <<= 1; /* m is maximum 55 bits */ + + uint64 tmp; + const uint64 lo = umul128(m, mul[0], &tmp); + uint64 hi; + const uint64 mid = tmp + umul128(m, mul[1], &hi); + + hi += mid < tmp; /* overflow into hi */ + + const uint64 lo2 = lo + mul[0]; + const uint64 mid2 = mid + mul[1] + (lo2 < lo); + const uint64 hi2 = hi + (mid2 < mid); + + *vp = shiftright128(mid2, hi2, j - 64 - 1); + + if (mmShift == 1) + { + const uint64 lo3 = lo - mul[0]; + const uint64 mid3 = mid - mul[1] - (lo3 > lo); + const uint64 hi3 = hi - (mid3 > mid); + + *vm = shiftright128(mid3, hi3, j - 64 - 1); + } + else + { + const uint64 lo3 = lo + lo; + const uint64 mid3 = mid + mid + (lo3 < lo); + const uint64 hi3 = hi + hi + (mid3 < mid); + const uint64 lo4 = lo3 - mul[0]; + const uint64 mid4 = mid3 - mul[1] - (lo4 > lo3); + const uint64 hi4 = hi3 - (mid4 > mid3); + + *vm = shiftright128(mid4, hi4, j - 64); + } + + return shiftright128(mid, hi, j - 64 - 1); +} + +#endif /* // HAS_64_BIT_INTRINSICS */ + +static inline uint32 +decimalLength(const uint64 v) +{ + /* This is slightly faster than a loop. */ + /* The average output length is 16.38 digits, so we check high-to-low. */ + /* Function precondition: v is not an 18, 19, or 20-digit number. */ + /* (17 digits are sufficient for round-tripping.) */ + Assert(v < 100000000000000000L); + if (v >= 10000000000000000L) + { + return 17; + } + if (v >= 1000000000000000L) + { + return 16; + } + if (v >= 100000000000000L) + { + return 15; + } + if (v >= 10000000000000L) + { + return 14; + } + if (v >= 1000000000000L) + { + return 13; + } + if (v >= 100000000000L) + { + return 12; + } + if (v >= 10000000000L) + { + return 11; + } + if (v >= 1000000000L) + { + return 10; + } + if (v >= 100000000L) + { + return 9; + } + if (v >= 10000000L) + { + return 8; + } + if (v >= 1000000L) + { + return 7; + } + if (v >= 100000L) + { + return 6; + } + if (v >= 10000L) + { + return 5; + } + if (v >= 1000L) + { + return 4; + } + if (v >= 100L) + { + return 3; + } + if (v >= 10L) + { + return 2; + } + return 1; +} + +/* A floating decimal representing m * 10^e. */ +typedef struct floating_decimal_64 +{ + uint64 mantissa; + int32 exponent; +} floating_decimal_64; + +static inline floating_decimal_64 +d2d(const uint64 ieeeMantissa, const uint32 ieeeExponent) +{ + int32 e2; + uint64 m2; + + if (ieeeExponent == 0) + { + /* We subtract 2 so that the bounds computation has 2 additional bits. */ + e2 = 1 - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2; + m2 = ieeeMantissa; + } + else + { + e2 = ieeeExponent - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2; + m2 = (UINT64CONST(1) << DOUBLE_MANTISSA_BITS) | ieeeMantissa; + } + +#if STRICTLY_SHORTEST + const bool even = (m2 & 1) == 0; + const bool acceptBounds = even; +#else + const bool acceptBounds = false; +#endif + + /* Step 2: Determine the interval of legal decimal representations. */ + const uint64 mv = 4 * m2; + + /* Implicit bool -> int conversion. True is 1, false is 0. */ + const uint32 mmShift = ieeeMantissa != 0 || ieeeExponent <= 1; + + /* We would compute mp and mm like this: */ + /* uint64 mp = 4 * m2 + 2; */ + /* uint64 mm = mv - 1 - mmShift; */ + + /* Step 3: Convert to a decimal power base using 128-bit arithmetic. */ + uint64 vr, + vp, + vm; + int32 e10; + bool vmIsTrailingZeros = false; + bool vrIsTrailingZeros = false; + + if (e2 >= 0) + { + /* + * I tried special-casing q == 0, but there was no effect on + * performance. + * + * This expr is slightly faster than max(0, log10Pow2(e2) - 1). + */ + const uint32 q = log10Pow2(e2) - (e2 > 3); + const int32 k = DOUBLE_POW5_INV_BITCOUNT + pow5bits(q) - 1; + const int32 i = -e2 + q + k; + + e10 = q; + + vr = mulShiftAll(m2, DOUBLE_POW5_INV_SPLIT[q], i, &vp, &vm, mmShift); + + if (q <= 21) + { + /* + * This should use q <= 22, but I think 21 is also safe. Smaller + * values may still be safe, but it's more difficult to reason + * about them. + * + * Only one of mp, mv, and mm can be a multiple of 5, if any. + */ + const uint32 mvMod5 = (uint32) (mv - 5 * div5(mv)); + + if (mvMod5 == 0) + { + vrIsTrailingZeros = multipleOfPowerOf5(mv, q); + } + else if (acceptBounds) + { + /*---- + * Same as min(e2 + (~mm & 1), pow5Factor(mm)) >= q + * <=> e2 + (~mm & 1) >= q && pow5Factor(mm) >= q + * <=> true && pow5Factor(mm) >= q, since e2 >= q. + *---- + */ + vmIsTrailingZeros = multipleOfPowerOf5(mv - 1 - mmShift, q); + } + else + { + /* Same as min(e2 + 1, pow5Factor(mp)) >= q. */ + vp -= multipleOfPowerOf5(mv + 2, q); + } + } + } + else + { + /* + * This expression is slightly faster than max(0, log10Pow5(-e2) - 1). + */ + const uint32 q = log10Pow5(-e2) - (-e2 > 1); + const int32 i = -e2 - q; + const int32 k = pow5bits(i) - DOUBLE_POW5_BITCOUNT; + const int32 j = q - k; + + e10 = q + e2; + + vr = mulShiftAll(m2, DOUBLE_POW5_SPLIT[i], j, &vp, &vm, mmShift); + + if (q <= 1) + { + /* + * {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q + * trailing 0 bits. + */ + /* mv = 4 * m2, so it always has at least two trailing 0 bits. */ + vrIsTrailingZeros = true; + if (acceptBounds) + { + /* + * mm = mv - 1 - mmShift, so it has 1 trailing 0 bit iff + * mmShift == 1. + */ + vmIsTrailingZeros = mmShift == 1; + } + else + { + /* + * mp = mv + 2, so it always has at least one trailing 0 bit. + */ + --vp; + } + } + else if (q < 63) + { + /* TODO(ulfjack):Use a tighter bound here. */ + /* + * We need to compute min(ntz(mv), pow5Factor(mv) - e2) >= q - 1 + */ + /* <=> ntz(mv) >= q - 1 && pow5Factor(mv) - e2 >= q - 1 */ + /* <=> ntz(mv) >= q - 1 (e2 is negative and -e2 >= q) */ + /* <=> (mv & ((1 << (q - 1)) - 1)) == 0 */ + + /* + * We also need to make sure that the left shift does not + * overflow. + */ + vrIsTrailingZeros = multipleOfPowerOf2(mv, q - 1); + } + } + + /* + * Step 4: Find the shortest decimal representation in the interval of + * legal representations. + */ + uint32 removed = 0; + uint8 lastRemovedDigit = 0; + uint64 output; + + /* On average, we remove ~2 digits. */ + if (vmIsTrailingZeros || vrIsTrailingZeros) + { + /* General case, which happens rarely (~0.7%). */ + for (;;) + { + const uint64 vpDiv10 = div10(vp); + const uint64 vmDiv10 = div10(vm); + + if (vpDiv10 <= vmDiv10) + break; + + const uint32 vmMod10 = (uint32) (vm - 10 * vmDiv10); + const uint64 vrDiv10 = div10(vr); + const uint32 vrMod10 = (uint32) (vr - 10 * vrDiv10); + + vmIsTrailingZeros &= vmMod10 == 0; + vrIsTrailingZeros &= lastRemovedDigit == 0; + lastRemovedDigit = (uint8) vrMod10; + vr = vrDiv10; + vp = vpDiv10; + vm = vmDiv10; + ++removed; + } + + if (vmIsTrailingZeros) + { + for (;;) + { + const uint64 vmDiv10 = div10(vm); + const uint32 vmMod10 = (uint32) (vm - 10 * vmDiv10); + + if (vmMod10 != 0) + break; + + const uint64 vpDiv10 = div10(vp); + const uint64 vrDiv10 = div10(vr); + const uint32 vrMod10 = (uint32) (vr - 10 * vrDiv10); + + vrIsTrailingZeros &= lastRemovedDigit == 0; + lastRemovedDigit = (uint8) vrMod10; + vr = vrDiv10; + vp = vpDiv10; + vm = vmDiv10; + ++removed; + } + } + + if (vrIsTrailingZeros && lastRemovedDigit == 5 && vr % 2 == 0) + { + /* Round even if the exact number is .....50..0. */ + lastRemovedDigit = 4; + } + + /* + * We need to take vr + 1 if vr is outside bounds or we need to round + * up. + */ + output = vr + ((vr == vm && (!acceptBounds || !vmIsTrailingZeros)) || lastRemovedDigit >= 5); + } + else + { + /* + * Specialized for the common case (~99.3%). Percentages below are + * relative to this. + */ + bool roundUp = false; + const uint64 vpDiv100 = div100(vp); + const uint64 vmDiv100 = div100(vm); + + if (vpDiv100 > vmDiv100) + { + /* Optimization:remove two digits at a time(~86.2 %). */ + const uint64 vrDiv100 = div100(vr); + const uint32 vrMod100 = (uint32) (vr - 100 * vrDiv100); + + roundUp = vrMod100 >= 50; + vr = vrDiv100; + vp = vpDiv100; + vm = vmDiv100; + removed += 2; + } + + /*---- + * Loop iterations below (approximately), without optimization + * above: + * + * 0: 0.03%, 1: 13.8%, 2: 70.6%, 3: 14.0%, 4: 1.40%, 5: 0.14%, + * 6+: 0.02% + * + * Loop iterations below (approximately), with optimization + * above: + * + * 0: 70.6%, 1: 27.8%, 2: 1.40%, 3: 0.14%, 4+: 0.02% + *---- + */ + for (;;) + { + const uint64 vpDiv10 = div10(vp); + const uint64 vmDiv10 = div10(vm); + + if (vpDiv10 <= vmDiv10) + break; + + const uint64 vrDiv10 = div10(vr); + const uint32 vrMod10 = (uint32) (vr - 10 * vrDiv10); + + roundUp = vrMod10 >= 5; + vr = vrDiv10; + vp = vpDiv10; + vm = vmDiv10; + ++removed; + } + + /* + * We need to take vr + 1 if vr is outside bounds or we need to round + * up. + */ + output = vr + (vr == vm || roundUp); + } + + const int32 exp = e10 + removed; + + floating_decimal_64 fd; + + fd.exponent = exp; + fd.mantissa = output; + return fd; +} + +static inline int +to_chars_df(const floating_decimal_64 v, const uint32 olength, char *const result) +{ + /* Step 5: Print the decimal representation. */ + int index = 0; + + uint64 output = v.mantissa; + int32 exp = v.exponent; + + /*---- + * On entry, mantissa * 10^exp is the result to be output. + * Caller has already done the - sign if needed. + * + * We want to insert the point somewhere depending on the output length + * and exponent, which might mean adding zeros: + * + * exp | format + * 1+ | ddddddddd000000 + * 0 | ddddddddd + * -1 .. -len+1 | dddddddd.d to d.ddddddddd + * -len ... | 0.ddddddddd to 0.000dddddd + */ + uint32 i = 0; + int32 nexp = exp + olength; + + if (nexp <= 0) + { + /* -nexp is number of 0s to add after '.' */ + Assert(nexp >= -3); + /* 0.000ddddd */ + index = 2 - nexp; + /* won't need more than this many 0s */ + memcpy(result, "0.000000", 8); + } + else if (exp < 0) + { + /* + * dddd.dddd; leave space at the start and move the '.' in after + */ + index = 1; + } + else + { + /* + * We can save some code later by pre-filling with zeros. We know that + * there can be no more than 16 output digits in this form, otherwise + * we would not choose fixed-point output. + */ + Assert(exp < 16 && exp + olength <= 16); + memset(result, '0', 16); + } + + /* + * We prefer 32-bit operations, even on 64-bit platforms. We have at most + * 17 digits, and uint32 can store 9 digits. If output doesn't fit into + * uint32, we cut off 8 digits, so the rest will fit into uint32. + */ + if ((output >> 32) != 0) + { + /* Expensive 64-bit division. */ + const uint64 q = div1e8(output); + uint32 output2 = (uint32) (output - 100000000 * q); + const uint32 c = output2 % 10000; + + output = q; + output2 /= 10000; + + const uint32 d = output2 % 10000; + const uint32 c0 = (c % 100) << 1; + const uint32 c1 = (c / 100) << 1; + const uint32 d0 = (d % 100) << 1; + const uint32 d1 = (d / 100) << 1; + + memcpy(result + index + olength - i - 2, DIGIT_TABLE + c0, 2); + memcpy(result + index + olength - i - 4, DIGIT_TABLE + c1, 2); + memcpy(result + index + olength - i - 6, DIGIT_TABLE + d0, 2); + memcpy(result + index + olength - i - 8, DIGIT_TABLE + d1, 2); + i += 8; + } + + uint32 output2 = (uint32) output; + + while (output2 >= 10000) + { + const uint32 c = output2 - 10000 * (output2 / 10000); + const uint32 c0 = (c % 100) << 1; + const uint32 c1 = (c / 100) << 1; + + output2 /= 10000; + memcpy(result + index + olength - i - 2, DIGIT_TABLE + c0, 2); + memcpy(result + index + olength - i - 4, DIGIT_TABLE + c1, 2); + i += 4; + } + if (output2 >= 100) + { + const uint32 c = (output2 % 100) << 1; + + output2 /= 100; + memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2); + i += 2; + } + if (output2 >= 10) + { + const uint32 c = output2 << 1; + + memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2); + } + else + { + result[index] = (char) ('0' + output2); + } + + if (index == 1) + { + /* + * nexp is 1..15 here, representing the number of digits before the + * point. A value of 16 is not possible because we switch to + * scientific notation when the display exponent reaches 15. + */ + Assert(nexp < 16); + /* gcc only seems to want to optimize memmove for small 2^n */ + if (nexp & 8) + { + memmove(result + index - 1, result + index, 8); + index += 8; + } + if (nexp & 4) + { + memmove(result + index - 1, result + index, 4); + index += 4; + } + if (nexp & 2) + { + memmove(result + index - 1, result + index, 2); + index += 2; + } + if (nexp & 1) + { + result[index - 1] = result[index]; + } + result[nexp] = '.'; + index = olength + 1; + } + else if (exp >= 0) + { + /* we supplied the trailing zeros earlier, now just set the length. */ + index = olength + exp; + } + else + { + index = olength + (2 - nexp); + } + + return index; +} + +static inline int +to_chars(floating_decimal_64 v, const bool sign, char *const result) +{ + /* Step 5: Print the decimal representation. */ + int index = 0; + + uint64 output = v.mantissa; + uint32 olength = decimalLength(output); + int32 exp = v.exponent + olength - 1; + + if (sign) + { + result[index++] = '-'; + } + + /* + * The thresholds for fixed-point output are chosen to match printf + * defaults. Beware that both the code of to_chars_df and the value of + * DOUBLE_SHORTEST_DECIMAL_LEN are sensitive to these thresholds. + */ + if (exp >= -4 && exp < 15) + return to_chars_df(v, olength, result + index) + sign; + + /* + * If v.exponent is exactly 0, we might have reached here via the small + * integer fast path, in which case v.mantissa might contain trailing + * (decimal) zeros. For scientific notation we need to move these zeros + * into the exponent. (For fixed point this doesn't matter, which is why + * we do this here rather than above.) + * + * Since we already calculated the display exponent (exp) above based on + * the old decimal length, that value does not change here. Instead, we + * just reduce the display length for each digit removed. + * + * If we didn't get here via the fast path, the raw exponent will not + * usually be 0, and there will be no trailing zeros, so we pay no more + * than one div10/multiply extra cost. We claw back half of that by + * checking for divisibility by 2 before dividing by 10. + */ + if (v.exponent == 0) + { + while ((output & 1) == 0) + { + const uint64 q = div10(output); + const uint32 r = (uint32) (output - 10 * q); + + if (r != 0) + break; + output = q; + --olength; + } + } + + /*---- + * Print the decimal digits. + * + * The following code is equivalent to: + * + * for (uint32 i = 0; i < olength - 1; ++i) { + * const uint32 c = output % 10; output /= 10; + * result[index + olength - i] = (char) ('0' + c); + * } + * result[index] = '0' + output % 10; + *---- + */ + + uint32 i = 0; + + /* + * We prefer 32-bit operations, even on 64-bit platforms. We have at most + * 17 digits, and uint32 can store 9 digits. If output doesn't fit into + * uint32, we cut off 8 digits, so the rest will fit into uint32. + */ + if ((output >> 32) != 0) + { + /* Expensive 64-bit division. */ + const uint64 q = div1e8(output); + uint32 output2 = (uint32) (output - 100000000 * q); + + output = q; + + const uint32 c = output2 % 10000; + + output2 /= 10000; + + const uint32 d = output2 % 10000; + const uint32 c0 = (c % 100) << 1; + const uint32 c1 = (c / 100) << 1; + const uint32 d0 = (d % 100) << 1; + const uint32 d1 = (d / 100) << 1; + + memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2); + memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2); + memcpy(result + index + olength - i - 5, DIGIT_TABLE + d0, 2); + memcpy(result + index + olength - i - 7, DIGIT_TABLE + d1, 2); + i += 8; + } + + uint32 output2 = (uint32) output; + + while (output2 >= 10000) + { + const uint32 c = output2 - 10000 * (output2 / 10000); + + output2 /= 10000; + + const uint32 c0 = (c % 100) << 1; + const uint32 c1 = (c / 100) << 1; + + memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2); + memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2); + i += 4; + } + if (output2 >= 100) + { + const uint32 c = (output2 % 100) << 1; + + output2 /= 100; + memcpy(result + index + olength - i - 1, DIGIT_TABLE + c, 2); + i += 2; + } + if (output2 >= 10) + { + const uint32 c = output2 << 1; + + /* + * We can't use memcpy here: the decimal dot goes between these two + * digits. + */ + result[index + olength - i] = DIGIT_TABLE[c + 1]; + result[index] = DIGIT_TABLE[c]; + } + else + { + result[index] = (char) ('0' + output2); + } + + /* Print decimal point if needed. */ + if (olength > 1) + { + result[index + 1] = '.'; + index += olength + 1; + } + else + { + ++index; + } + + /* Print the exponent. */ + result[index++] = 'e'; + if (exp < 0) + { + result[index++] = '-'; + exp = -exp; + } + else + result[index++] = '+'; + + if (exp >= 100) + { + const int32 c = exp % 10; + + memcpy(result + index, DIGIT_TABLE + 2 * (exp / 10), 2); + result[index + 2] = (char) ('0' + c); + index += 3; + } + else + { + memcpy(result + index, DIGIT_TABLE + 2 * exp, 2); + index += 2; + } + + return index; +} + +static inline bool +d2d_small_int(const uint64 ieeeMantissa, + const uint32 ieeeExponent, + floating_decimal_64 *v) +{ + const int32 e2 = (int32) ieeeExponent - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS; + + /* + * Avoid using multiple "return false;" here since it tends to provoke the + * compiler into inlining multiple copies of d2d, which is undesirable. + */ + + if (e2 >= -DOUBLE_MANTISSA_BITS && e2 <= 0) + { + /*---- + * Since 2^52 <= m2 < 2^53 and 0 <= -e2 <= 52: + * 1 <= f = m2 / 2^-e2 < 2^53. + * + * Test if the lower -e2 bits of the significand are 0, i.e. whether + * the fraction is 0. We can use ieeeMantissa here, since the implied + * 1 bit can never be tested by this; the implied 1 can only be part + * of a fraction if e2 < -DOUBLE_MANTISSA_BITS which we already + * checked. (e.g. 0.5 gives ieeeMantissa == 0 and e2 == -53) + */ + const uint64 mask = (UINT64CONST(1) << -e2) - 1; + const uint64 fraction = ieeeMantissa & mask; + + if (fraction == 0) + { + /*---- + * f is an integer in the range [1, 2^53). + * Note: mantissa might contain trailing (decimal) 0's. + * Note: since 2^53 < 10^16, there is no need to adjust + * decimalLength(). + */ + const uint64 m2 = (UINT64CONST(1) << DOUBLE_MANTISSA_BITS) | ieeeMantissa; + + v->mantissa = m2 >> -e2; + v->exponent = 0; + return true; + } + } + + return false; +} + +/* + * Store the shortest decimal representation of the given double as an + * UNTERMINATED string in the caller's supplied buffer (which must be at least + * DOUBLE_SHORTEST_DECIMAL_LEN-1 bytes long). + * + * Returns the number of bytes stored. + */ +int +double_to_shortest_decimal_bufn(double f, char *result) +{ + /* + * Step 1: Decode the floating-point number, and unify normalized and + * subnormal cases. + */ + const uint64 bits = double_to_bits(f); + + /* Decode bits into sign, mantissa, and exponent. */ + const bool ieeeSign = ((bits >> (DOUBLE_MANTISSA_BITS + DOUBLE_EXPONENT_BITS)) & 1) != 0; + const uint64 ieeeMantissa = bits & ((UINT64CONST(1) << DOUBLE_MANTISSA_BITS) - 1); + const uint32 ieeeExponent = (uint32) ((bits >> DOUBLE_MANTISSA_BITS) & ((1u << DOUBLE_EXPONENT_BITS) - 1)); + + /* Case distinction; exit early for the easy cases. */ + if (ieeeExponent == ((1u << DOUBLE_EXPONENT_BITS) - 1u) || (ieeeExponent == 0 && ieeeMantissa == 0)) + { + return copy_special_str(result, ieeeSign, (ieeeExponent != 0), (ieeeMantissa != 0)); + } + + floating_decimal_64 v; + const bool isSmallInt = d2d_small_int(ieeeMantissa, ieeeExponent, &v); + + if (!isSmallInt) + { + v = d2d(ieeeMantissa, ieeeExponent); + } + + return to_chars(v, ieeeSign, result); +} + +/* + * Store the shortest decimal representation of the given double as a + * null-terminated string in the caller's supplied buffer (which must be at + * least DOUBLE_SHORTEST_DECIMAL_LEN bytes long). + * + * Returns the string length. + */ +int +double_to_shortest_decimal_buf(double f, char *result) +{ + const int index = double_to_shortest_decimal_bufn(f, result); + + /* Terminate the string. */ + Assert(index < DOUBLE_SHORTEST_DECIMAL_LEN); + result[index] = '\0'; + return index; +} + +/* + * Return the shortest decimal representation as a null-terminated palloc'd + * string (outside the backend, uses malloc() instead). + * + * Caller is responsible for freeing the result. + */ +char * +double_to_shortest_decimal(double f) +{ + char *const result = (char *) palloc(DOUBLE_SHORTEST_DECIMAL_LEN); + + double_to_shortest_decimal_buf(f, result); + return result; +} |