// 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_DEBUG Generate verbose debugging output to stdout. // // -DRYU_ONLY_64_BIT_OPS Avoid using uint128_t or 64-bit intrinsics. Slower, // depending on your compiler. // // CHANGE_FOR_ERLANG: "ryu/ryu.h" -> "ryu.h" #include "ryu.h" // END CHANGE_FOR_ERLANG #include #include #include #include #include #ifdef RYU_DEBUG #include #include #endif // CHANGE_FOR_ERLANG: "ryu/*.h" -> "*.h" #include "common.h" #include "digit_table.h" #include "d2s_intrinsics.h" // END CHANGE_FOR_ERLANG // CHANGE_FOR_ERLANG we got rid of the small_table. Also namespace as above #include "d2s_full_table.h" // END CHANGE_FOR_ERLANG #define DOUBLE_MANTISSA_BITS 52 #define DOUBLE_EXPONENT_BITS 11 #define DOUBLE_BIAS 1023 static inline uint32_t decimalLength17(const uint64_t 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_t mantissa; // Decimal exponent's range is -324 to 308 // inclusive, and can fit in a short if needed. int32_t exponent; } floating_decimal_64; static inline floating_decimal_64 d2d(const uint64_t ieeeMantissa, const uint32_t ieeeExponent) { int32_t e2; uint64_t 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 = (int32_t) ieeeExponent - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2; m2 = (1ull << DOUBLE_MANTISSA_BITS) | ieeeMantissa; } const bool even = (m2 & 1) == 0; const bool acceptBounds = even; #ifdef RYU_DEBUG printf("-> %" PRIu64 " * 2^%d\n", m2, e2 + 2); #endif // Step 2: Determine the interval of valid decimal representations. const uint64_t mv = 4 * m2; // Implicit bool -> int conversion. True is 1, false is 0. const uint32_t mmShift = ieeeMantissa != 0 || ieeeExponent <= 1; // We would compute mp and mm like this: // uint64_t mp = 4 * m2 + 2; // uint64_t mm = mv - 1 - mmShift; // Step 3: Convert to a decimal power base using 128-bit arithmetic. uint64_t vr, vp, vm; int32_t e10; bool vmIsTrailingZeros = false; bool vrIsTrailingZeros = false; if (e2 >= 0) { // I tried special-casing q == 0, but there was no effect on performance. // This expression is slightly faster than max(0, log10Pow2(e2) - 1). const uint32_t q = log10Pow2(e2) - (e2 > 3); e10 = (int32_t) q; const int32_t k = DOUBLE_POW5_INV_BITCOUNT + pow5bits((int32_t) q) - 1; const int32_t i = -e2 + (int32_t) q + k; vr = mulShiftAll64(m2, DOUBLE_POW5_INV_SPLIT[q], i, &vp, &vm, mmShift); #ifdef RYU_DEBUG printf("%" PRIu64 " * 2^%d / 10^%u\n", mv, e2, q); printf("V+=%" PRIu64 "\nV =%" PRIu64 "\nV-=%" PRIu64 "\n", vp, vr, vm); #endif 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_t mvMod5 = ((uint32_t) mv) - 5 * ((uint32_t) 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_t q = log10Pow5(-e2) - (-e2 > 1); e10 = (int32_t) q + e2; const int32_t i = -e2 - (int32_t) q; const int32_t k = pow5bits(i) - DOUBLE_POW5_BITCOUNT; const int32_t j = (int32_t) q - k; vr = mulShiftAll64(m2, DOUBLE_POW5_SPLIT[i], j, &vp, &vm, mmShift); #ifdef RYU_DEBUG printf("%" PRIu64 " * 5^%d / 10^%u\n", mv, -e2, q); printf("%u %d %d %d\n", q, i, k, j); printf("V+=%" PRIu64 "\nV =%" PRIu64 "\nV-=%" PRIu64 "\n", vp, vr, vm); #endif 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 want to know if the full product has at least q trailing zeros. // We need to compute min(p2(mv), p5(mv) - e2) >= q // <=> p2(mv) >= q && p5(mv) - e2 >= q // <=> p2(mv) >= q (because -e2 >= q) vrIsTrailingZeros = multipleOfPowerOf2(mv, q); #ifdef RYU_DEBUG printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false"); #endif } } #ifdef RYU_DEBUG printf("e10=%d\n", e10); printf("V+=%" PRIu64 "\nV =%" PRIu64 "\nV-=%" PRIu64 "\n", vp, vr, vm); printf("vm is trailing zeros=%s\n", vmIsTrailingZeros ? "true" : "false"); printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false"); #endif // Step 4: Find the shortest decimal representation in the interval of valid representations. int32_t removed = 0; uint8_t lastRemovedDigit = 0; uint64_t output; // On average, we remove ~2 digits. if (vmIsTrailingZeros || vrIsTrailingZeros) { // General case, which happens rarely (~0.7%). for (;;) { const uint64_t vpDiv10 = div10(vp); const uint64_t vmDiv10 = div10(vm); if (vpDiv10 <= vmDiv10) { break; } const uint32_t vmMod10 = ((uint32_t) vm) - 10 * ((uint32_t) vmDiv10); const uint64_t vrDiv10 = div10(vr); const uint32_t vrMod10 = ((uint32_t) vr) - 10 * ((uint32_t) vrDiv10); vmIsTrailingZeros &= vmMod10 == 0; vrIsTrailingZeros &= lastRemovedDigit == 0; lastRemovedDigit = (uint8_t) vrMod10; vr = vrDiv10; vp = vpDiv10; vm = vmDiv10; ++removed; } #ifdef RYU_DEBUG printf("V+=%" PRIu64 "\nV =%" PRIu64 "\nV-=%" PRIu64 "\n", vp, vr, vm); printf("d-10=%s\n", vmIsTrailingZeros ? "true" : "false"); #endif if (vmIsTrailingZeros) { for (;;) { const uint64_t vmDiv10 = div10(vm); const uint32_t vmMod10 = ((uint32_t) vm) - 10 * ((uint32_t) vmDiv10); if (vmMod10 != 0) { break; } const uint64_t vpDiv10 = div10(vp); const uint64_t vrDiv10 = div10(vr); const uint32_t vrMod10 = ((uint32_t) vr) - 10 * ((uint32_t) vrDiv10); vrIsTrailingZeros &= lastRemovedDigit == 0; lastRemovedDigit = (uint8_t) vrMod10; vr = vrDiv10; vp = vpDiv10; vm = vmDiv10; ++removed; } } #ifdef RYU_DEBUG printf("%" PRIu64 " %d\n", vr, lastRemovedDigit); printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false"); #endif 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_t vpDiv100 = div100(vp); const uint64_t vmDiv100 = div100(vm); if (vpDiv100 > vmDiv100) { // Optimization: remove two digits at a time (~86.2%). const uint64_t vrDiv100 = div100(vr); const uint32_t vrMod100 = ((uint32_t) vr) - 100 * ((uint32_t) 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_t vpDiv10 = div10(vp); const uint64_t vmDiv10 = div10(vm); if (vpDiv10 <= vmDiv10) { break; } const uint64_t vrDiv10 = div10(vr); const uint32_t vrMod10 = ((uint32_t) vr) - 10 * ((uint32_t) vrDiv10); roundUp = vrMod10 >= 5; vr = vrDiv10; vp = vpDiv10; vm = vmDiv10; ++removed; } #ifdef RYU_DEBUG printf("%" PRIu64 " roundUp=%s\n", vr, roundUp ? "true" : "false"); printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false"); #endif // We need to take vr + 1 if vr is outside bounds or we need to round up. output = vr + (vr == vm || roundUp); } const int32_t exp = e10 + removed; #ifdef RYU_DEBUG printf("V+=%" PRIu64 "\nV =%" PRIu64 "\nV-=%" PRIu64 "\n", vp, vr, vm); printf("O=%" PRIu64 "\n", output); printf("EXP=%d\n", exp); #endif floating_decimal_64 fd; fd.exponent = exp; fd.mantissa = output; return fd; } //CHANGE_FOR_ERLANG: This format is new, it is here to handle the different format switch used in the STL code enum chars_format { FMT_SCIENTIFIC, FMT_FIXED, FMT_GENERAL }; // This is inspired from the MS STL Charconv, under Apache with LLVM exception licence // see https://github.com/microsoft/STL/blob/main/LICENSE.txt // The inspiration is at https://github.com/microsoft/STL/blob/e745bad3b1d05b5b19ec652d68abb37865ffa454/stl/inc/xcharconv_ryu.h#L1926 // CHANGE_FOR_ERLANG all the types and typecast have been adapted to C types from Cpp. // I have also kept the Ryu original function head as it allows to not impact the rest of the code // __v and __mantissa and __exponent have lost their double underscore over the whole function // all the test on the lenght of the buffer have been dropped too. This could need change, but // we always pass a 256 bytes buffer when we only need 26 bytes maximum. static inline int to_chars(const floating_decimal_64 v, const bool sign, char* const result) { // Step 5: Print the decimal representation. uint64_t __output = v.mantissa; int32_t _Ryu_exponent = v.exponent; const uint32_t __olength = decimalLength17(__output); int32_t _Scientific_exponent = _Ryu_exponent + ((int32_t) __olength) - 1; // CHANGE_FOR_ERLANG: we use our chars_format instead of the STL one enum chars_format _Fmt; int32_t _Lower; int32_t _Upper; if (__olength == 1) { // CHANGE_FOR_ERLANG the format and examples have been adapted to the erlang format // as the original would have not shown a change in format // (erlang always add ".0" to scientific format) and omit the + in the exponent // Value | Fixed | Scientific // 1e-4 | "0.0001" | "1.0e-4" // 1e2 | "100.0" | "1.0e2" // CHANGE_FOR_ERLANG the values for a switch, as seen in the example above, for erlang // are different than for STL format. _Lower = -4; _Upper = 2; } else if (_Scientific_exponent >= 10) { // CHANGE_FOR_ERLANG This case does not exist for the STL and is due to the // negative sign in the exponent. // Value | Fixed | Scientific // 123456789e1 | "1234567890.0" | "1.23456789e9" // 123456789e2 | "12345678900.0" | "1.23456789e10" _Lower = - (int32_t) (__olength + 2); _Upper = 2; } else { // CHANGE_FOR_ERLANG the format and examples have been adapted to the erlang format // as the original would have not shown a change in format // (erlang always add ".0" to scientific format) and omit the + in the exponent // Value | Fixed | Scientific // 1234e-6 | "0.001234" | "1.234e-4" // 1234e1 | "12340.0" | "1.234e4" // CHANGE_FOR_ERLANG the values for a switch, as seen in the example above, for erlang // are different than for STL format. _Lower = - (int32_t) (__olength + 2); _Upper = 1; } if (_Lower <= _Ryu_exponent && _Ryu_exponent <= _Upper) { // CHANGE_FOR_ERLANG this is added to handle the -2**53, 2**53 range special case // These are edge cases not captured above, all the other are naturally handled // by _Lower nad _Upper if ((__output >= (1ull << 53) && _Ryu_exponent == 0) || (__output > ((1ull << 52) / 5) && _Ryu_exponent == 1) || (__output > ((1ull << 51) / 25) && _Ryu_exponent == 2)) { _Fmt = FMT_SCIENTIFIC; } else { _Fmt = FMT_FIXED; } } else { // CHANGE_FOR_ERLANG we do not need to handle the %g case here. _Fmt = FMT_SCIENTIFIC; } // CHANGE_FOR_ERLANG we handle the sign here as it is handled outside of this in the STL case // and we need it to compute the start of the buffer for the characters after if (sign) { result[0] = '-'; } // CHANGE_FOR_ERLANG we compute the start of the usable buffer. It is done here // in order to be fixed for both branches of formatting. char* const __result = result + sign; if (_Fmt == FMT_FIXED) { // CHANGE_FOR_ERLANG this whole table has been adapted to erlang examples to help // debug and evolve the edge cases // Example: __output == 1729, __olength == 4 // _Ryu_exponent | Printed | _Whole_digits | _Total_fixed_length | Notes // --------------|----------|---------------|----------------------|--------------------------------------- // 1 | 17290.0 | 5 | _Whole_digits + 2 | Unified length cases. // 0 | 1729.0 | 4 | | // --------------|----------|---------------|----------------------|--------------------------------------- // -1 | 172.9 | 3 | __olength + 1 | This case can't happen for // -2 | 17.29 | 2 | | __olength == 1, but no additional // -3 | 1.729 | 1 | | code is needed to avoid it. // --------------|----------|---------------|----------------------|--------------------------------------- // -4 | 0.1729 | 0 | 2 - _Ryu_exponent | If the decimal point appears, we need // -5 | 0.01729 | -1 | | to put the "0" in front // -6 | 0.001729 | -2 | | const int32_t _Whole_digits = (int32_t) (__olength) + _Ryu_exponent; uint32_t _Total_fixed_length; if (_Ryu_exponent >= 0) { // CHANGE_FOR_ERLANG the examples and values have been adapted to erlang format one // CHANGE_FOR_ERLANG we also dropped the whole adjustement, as it is only of value // for %f which we do not handle // cases "17290.0" and "1729.0" _Total_fixed_length = (uint32_t) (_Whole_digits) + 2; } else if (_Whole_digits > 0) { // case "17.29" _Total_fixed_length = __olength + 1; } else { // case "0.001729" _Total_fixed_length = (uint32_t) (2 - _Ryu_exponent); } char* _Mid; if (_Ryu_exponent >= 0) { // case "172900.0" // CHANGE_FOR_ERLANG we do not need the can_use_ryu, as we are not doing %f // but always shortest round_trip. The whole complexity here is dropped // Print the decimal digits, left-aligned within [result, result + _Total_fixed_length). _Mid = __result + __olength; } else { // cases "1729.0", "17.29", and "0.001729" // Print the decimal digits, right-aligned within [result, result + _Total_fixed_length). _Mid = __result + _Total_fixed_length; } // We prefer 32-bit operations, even on 64-bit platforms. // We have at most 17 digits, and uint32_t can store 9 digits. // If __output doesn't fit into uint32_t, we cut off 8 digits, // so the rest will fit into uint32_t. // CHANGE_FOR_ERLANG we consider in this whole thing that memcopy use the same // char has defined in the DIGIT_TABLE // CHANGE_FOR_ERLANG __DIGIT_TABLE became DIGIT_TABLE if ((__output >> 32) != 0) { // Expensive 64-bit division. const uint64_t __q = div1e8(__output); uint32_t __output2 = (uint32_t) (__output - 100000000 * __q); __output = __q; const uint32_t __c = __output2 % 10000; __output2 /= 10000; const uint32_t __d = __output2 % 10000; const uint32_t __c0 = (__c % 100) << 1; const uint32_t __c1 = (__c / 100) << 1; const uint32_t __d0 = (__d % 100) << 1; const uint32_t __d1 = (__d / 100) << 1; memcpy(_Mid -= 2, DIGIT_TABLE + __c0, 2); memcpy(_Mid -= 2, DIGIT_TABLE + __c1, 2); memcpy(_Mid -= 2, DIGIT_TABLE + __d0, 2); memcpy(_Mid -= 2, DIGIT_TABLE + __d1, 2); } uint32_t __output2 = (uint32_t) __output; while (__output2 >= 10000) { #ifdef __clang__ // TRANSITION, LLVM-38217 const uint32_t __c = __output2 - 10000 * (__output2 / 10000); #else const uint32_t __c = __output2 % 10000; #endif __output2 /= 10000; const uint32_t __c0 = (__c % 100) << 1; const uint32_t __c1 = (__c / 100) << 1; memcpy(_Mid -= 2, DIGIT_TABLE + __c0, 2); memcpy(_Mid -= 2, DIGIT_TABLE + __c1, 2); } if (__output2 >= 100) { const uint32_t __c = (__output2 % 100) << 1; __output2 /= 100; memcpy(_Mid -= 2, DIGIT_TABLE + __c, 2); } if (__output2 >= 10) { const uint32_t __c = __output2 << 1; memcpy(_Mid -= 2, DIGIT_TABLE + __c, 2); } else { *--_Mid = (char) ('0' + __output2); } if (_Ryu_exponent > 0) { // case "172900.0" // Performance note: it might be more efficient to do this immediately after setting _Mid. // CHANGE_FOR_ERLANG we have different case here, so we have to add the ".0" here // we use memset as we do not have access to fill_n memset(__result + __olength, '0', (size_t) _Ryu_exponent); __result[__olength + (size_t) _Ryu_exponent] = '.'; __result[__olength + (size_t) _Ryu_exponent + 1] = '0'; } else if (_Ryu_exponent == 0) { // case "1729.0" // CHANGE_FOR_ERLANG we have different case here, so we have to add the ".0" here __result[__olength] = '.'; __result[__olength + 1] = '0'; } else if (_Whole_digits > 0) { // case "17.29" // Performance note: moving digits might not be optimal. memmove(__result, __result + 1, (size_t) _Whole_digits); __result[_Whole_digits] = '.'; } else { // case "0.001729" // CHANGE_FOR_ERLANG we use the memset here as we do not have access to fill_n // Performance note: a larger memset() followed by overwriting '.' might be more efficient. __result[0] = '0'; __result[1] = '.'; memset(__result + 2, '0', (size_t) (-_Whole_digits)); } // CHANGE_FOR_ERLANG we do not need the errc and we are only interested in // returning the length, as it is what Ryu and erlang expect. We do add the // sign as we did it here instead of adding it by default as in the STL return _Total_fixed_length + sign; } uint32_t _Scientific_exponent_length; // CHANGE_FOR_ERLANG we have to do a little bit more complex logic here because we do not always // print the exponent sign, only if it is negative if (_Scientific_exponent <= -100) { // "e-100" _Scientific_exponent_length = 5; } else if (_Scientific_exponent <= -10 || _Scientific_exponent >= 100) { // "e-10" or "e100" _Scientific_exponent_length = 4; } else if ((_Scientific_exponent > -10 && _Scientific_exponent < 0) || _Scientific_exponent >= 10) { // "e-9" or "e10" _Scientific_exponent_length = 3; } else { // "e1" _Scientific_exponent_length = 2; } // CHANGE_FOR_ERLANG we do not need the ternary as we did all the logic above const uint32_t _Total_scientific_length = __olength + 1 +(__olength == 1) // digits + decimal point + possible 0 after decimal point + _Scientific_exponent_length; // + scientific exponent // Print the decimal digits. uint32_t __i = 0; // We prefer 32-bit operations, even on 64-bit platforms. // We have at most 17 digits, and uint32_t can store 9 digits. // If __output doesn't fit into uint32_t, we cut off 8 digits, // so the rest will fit into uint32_t. // CHANGE_FOR_ERLANG we consider in this whole thing that memcopy use the same // char has defined in the DIGIT_TABLE // CHANGE_FOR_ERLANG __DIGIT_TABLE became DIGIT_TABLE if ((__output >> 32) != 0) { // Expensive 64-bit division. const uint64_t __q = div1e8(__output); uint32_t __output2 = (uint32_t) (__output) - 100000000 * (uint32_t) (__q); __output = __q; const uint32_t __c = __output2 % 10000; __output2 /= 10000; const uint32_t __d = __output2 % 10000; const uint32_t __c0 = (__c % 100) << 1; const uint32_t __c1 = (__c / 100) << 1; const uint32_t __d0 = (__d % 100) << 1; const uint32_t __d1 = (__d / 100) << 1; memcpy(__result + __olength - __i - 1, DIGIT_TABLE + __c0, 2); memcpy(__result + __olength - __i - 3, DIGIT_TABLE + __c1, 2); memcpy(__result + __olength - __i - 5, DIGIT_TABLE + __d0, 2); memcpy(__result + __olength - __i - 7, DIGIT_TABLE + __d1, 2); __i += 8; } uint32_t __output2 = (uint32_t) (__output); while (__output2 >= 10000) { #ifdef __clang__ // TRANSITION, LLVM-38217 const uint32_t __c = __output2 - 10000 * (__output2 / 10000); #else const uint32_t __c = __output2 % 10000; #endif __output2 /= 10000; const uint32_t __c0 = (__c % 100) << 1; const uint32_t __c1 = (__c / 100) << 1; memcpy(__result + __olength - __i - 1, DIGIT_TABLE + __c0, 2); memcpy(__result + __olength - __i - 3, DIGIT_TABLE + __c1, 2); __i += 4; } if (__output2 >= 100) { const uint32_t __c = (__output2 % 100) << 1; __output2 /= 100; memcpy(__result + __olength - __i - 1, DIGIT_TABLE + __c, 2); __i += 2; } if (__output2 >= 10) { const uint32_t __c = __output2 << 1; // We can't use memcpy here: the decimal dot goes between these two digits. __result[2] = DIGIT_TABLE[__c + 1]; __result[0] = DIGIT_TABLE[__c]; } else { __result[0] = (char) ('0' + __output2); } // Print decimal point if needed. uint32_t __index; if (__olength > 1) { __result[1] = '.'; __index = __olength + 1; } else { // In erlang we _have_ to print the ".0" in the case this is an integer __result[1] = '.'; __result[2] = '0'; __index = __olength + 2; } // Print the exponent. __result[__index++] = 'e'; if (_Scientific_exponent < 0) { __result[__index++] = '-'; _Scientific_exponent = -_Scientific_exponent; } // CHANGE_FOR_ERLANG no else, as we do not print the positive sign on the exponent if (_Scientific_exponent >= 100) { const int32_t __c = _Scientific_exponent % 10; memcpy(__result + __index, DIGIT_TABLE + 2 * (_Scientific_exponent / 10), 2); __result[__index + 2] = (char) ('0' + __c); __index += 3; } else if (_Scientific_exponent >= 10) { // CHANGE_FOR_ERLANG we have to do this only if the exponent is larger than 10 memcpy(__result + __index, DIGIT_TABLE + 2 * _Scientific_exponent, 2); __index += 2; } else { // CHANGE_FOR_ERLANG we can have an exponent under 10, which is not handled by the table // so we handle it here __result[__index++] = (char) ('0' + _Scientific_exponent); } // CHANGE_FOR_ERLANG we do not need the errc and we are only interested in // returning the length, as it is what Ryu and erlang expect. We do add the // sign as we did it here instead of adding it by default as in the STL return _Total_scientific_length + sign; } // end of STL code, back to ryu static inline bool d2d_small_int(const uint64_t ieeeMantissa, const uint32_t ieeeExponent, floating_decimal_64* const v) { const uint64_t m2 = (1ull << DOUBLE_MANTISSA_BITS) | ieeeMantissa; const int32_t e2 = (int32_t) ieeeExponent - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS; if (e2 > 0) { // f = m2 * 2^e2 >= 2^53 is an integer. // Ignore this case for now. return false; } if (e2 < -52) { // f < 1. return false; } // 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. const uint64_t mask = (1ull << -e2) - 1; const uint64_t fraction = m2 & mask; if (fraction != 0) { return false; } // 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 decimalLength17(). v->mantissa = m2 >> -e2; v->exponent = 0; return true; } int d2s_buffered_n(double f, char* result) { // Step 1: Decode the floating-point number, and unify normalized and subnormal cases. const uint64_t bits = double_to_bits(f); #ifdef RYU_DEBUG printf("IN="); for (int32_t bit = 63; bit >= 0; --bit) { printf("%d", (int) ((bits >> bit) & 1)); } printf("\n"); #endif // Decode bits into sign, mantissa, and exponent. const bool ieeeSign = ((bits >> (DOUBLE_MANTISSA_BITS + DOUBLE_EXPONENT_BITS)) & 1) != 0; const uint64_t ieeeMantissa = bits & ((1ull << DOUBLE_MANTISSA_BITS) - 1); const uint32_t ieeeExponent = (uint32_t) ((bits >> DOUBLE_MANTISSA_BITS) & ((1u << DOUBLE_EXPONENT_BITS) - 1)); // Case distinction; exit early for the easy cases. if (ieeeExponent == ((1u << DOUBLE_EXPONENT_BITS) - 1u) || (ieeeExponent == 0 && ieeeMantissa == 0)) { return copy_special_str(result, ieeeSign, ieeeExponent, ieeeMantissa); } floating_decimal_64 v; const bool isSmallInt = d2d_small_int(ieeeMantissa, ieeeExponent, &v); if (isSmallInt) { // For small integers in the range [1, 2^53), v.mantissa might contain trailing (decimal) zeros. // For scientific notation we need to move these zeros into the exponent. // (This is not needed for fixed-point notation, so it might be beneficial to trim // trailing zeros in to_chars only if needed - once fixed-point notation output is implemented.) for (;;) { const uint64_t q = div10(v.mantissa); const uint32_t r = ((uint32_t) v.mantissa) - 10 * ((uint32_t) q); if (r != 0) { break; } v.mantissa = q; ++v.exponent; } } else { v = d2d(ieeeMantissa, ieeeExponent); } return to_chars(v, ieeeSign, result); } void d2s_buffered(double f, char* result) { const int index = d2s_buffered_n(f, result); // Terminate the string. result[index] = '\0'; } char* d2s(double f) { char* const result = (char*) malloc(25); d2s_buffered(f, result); return result; }