/*--------------------------------------------------------------------------- * * Ryu floating-point output for single precision. * * Portions Copyright (c) 2018-2020, 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; }