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May 26, 2021 03:03
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| ## Copyright 2020 Junekey Jeon | |
| ## Copyright 2020 Alexander Bolz | |
| ## | |
| ## Distributed under the Boost Software License, Version 1.0. | |
| ## (See accompanying file LICENSE_1_0.txt or copy at https://www.boost.org/LICENSE_1_0.txt) | |
| ## char* output_end = Dtoa(buffer, value); | |
| ## | |
| ## Converts the given double-precision number into decimal form and stores the result in the given | |
| ## buffer. | |
| ## | |
| ## The buffer must be large enough, i.e. >= DtoaMinBufferLength. | |
| ## The output format is similar to printf("%g"). | |
| ## The output is _not_ null-terminted. | |
| ## | |
| ## The output is optimal, i.e. the output string | |
| ## 1. rounds back to the input number when read in (using round-to-nearest-even) | |
| ## 2. is as short as possible, | |
| ## 3. is as close to the input number as possible. | |
| ## | |
| ## Note: | |
| ## This function may temporarily write up to DtoaMinBufferLength characters into the buffer. | |
| var DtoaMinBufferLength*: cint = 64 | |
| proc Dtoa*(buffer: cstring; value: cdouble): cstring | |
| ## namespace dragonbox | |
| ## -------------------------------------------------------------------------------------------------- | |
| ## This file contains an implementation of Junekey Jeon's Dragonbox algorithm. | |
| ## | |
| ## It is a simplified version of the reference implementation found here: | |
| ## https://github.com/jk-jeon/dragonbox | |
| ## | |
| ## The reference implementation also works with single-precision floating-point numbers and | |
| ## has options to configure the rounding mode. | |
| ## -------------------------------------------------------------------------------------------------- | |
| when defined(_MSC_VER): | |
| discard | |
| when not defined(DRAGONBOX_ASSERT): | |
| template DRAGONBOX_ASSERT*(X: untyped): untyped = | |
| assert(X) | |
| ## ================================================================================================== | |
| ## | |
| ## ================================================================================================== | |
| proc ReinterpretBits*[Dest; Source](source: Source): Dest {.inline.} = | |
| static_assert(sizeof((Dest)) == sizeof((Source)), "size mismatch") | |
| var dest: Dest | |
| memcpy(addr(dest), addr(source), sizeof((Source))) | |
| return dest | |
| type | |
| Double* {.bycopy.} = object | |
| bits*: bits_type ## = p (includes the hidden bit) | |
| ## static constexpr int32_t MaxExponent = std::numeric_limits<value_type>::max_exponent - 1 - (SignificandSize - 1); | |
| ## static constexpr int32_t MinExponent = std::numeric_limits<value_type>::min_exponent - 1 - (SignificandSize - 1); | |
| ## = 2^(p-1) | |
| ## = 2^(p-1) - 1 | |
| ## !!!Ignored construct: static_assert ( std :: numeric_limits < double > :: is_iec559 && std :: numeric_limits < double > :: digits == 53 && std :: numeric_limits < double > :: max_exponent == 1024 , IEEE-754 double-precision implementation required ) ; | |
| ## Error: token expected: ) but got: ::!!! | |
| type | |
| value_type* = cdouble | |
| bits_type* = uint64_t | |
| const | |
| SignificandSize*: int32_t = digits | |
| const | |
| ExponentBias*: int32_t = max_exponent - 1 + (SignificandSize - 1) | |
| const | |
| MaxIeeeExponent*: bits_type = bits_type(2 * max_exponent - 1) | |
| const | |
| HiddenBit*: bits_type = bits_type(1) shl (SignificandSize - 1) | |
| const | |
| SignificandMask*: bits_type = HiddenBit - 1 | |
| const | |
| ExponentMask*: bits_type = MaxIeeeExponent shl (SignificandSize - 1) | |
| const | |
| SignMask*: bits_type = not (not bits_type(0) shr 1) | |
| proc constructDouble*(bits_: bits_type): Double {.constructor.} = | |
| discard | |
| proc constructDouble*(value: value_type): Double {.constructor.} = | |
| discard | |
| proc PhysicalSignificand*(this: Double): bits_type {.noSideEffect.} = | |
| return bits and SignificandMask | |
| proc PhysicalExponent*(this: Double): bits_type {.noSideEffect.} = | |
| return (bits and ExponentMask) shr (SignificandSize - 1) | |
| proc IsFinite*(this: Double): bool {.noSideEffect.} = | |
| return (bits and ExponentMask) != ExponentMask | |
| proc IsInf*(this: Double): bool {.noSideEffect.} = | |
| return (bits and ExponentMask) == ExponentMask and | |
| (bits and SignificandMask) == 0 | |
| proc IsNaN*(this: Double): bool {.noSideEffect.} = | |
| return (bits and ExponentMask) == ExponentMask and | |
| (bits and SignificandMask) != 0 | |
| proc IsZero*(this: Double): bool {.noSideEffect.} = | |
| return (bits and not SignMask) == 0 | |
| proc SignBit*(this: Double): bool {.noSideEffect.} = | |
| return (bits and SignMask) != 0 | |
| ## namespace | |
| ## ================================================================================================== | |
| ## | |
| ## ================================================================================================== | |
| ## Returns floor(x / 2^n). | |
| ## | |
| ## Technically, right-shift of negative integers is implementation defined... | |
| ## Should easily be optimized into SAR (or equivalent) instruction. | |
| proc FloorDivPow2*(x: int32_t; n: int32_t): int32_t {.inline.} = | |
| when 0: | |
| return if x < 0: not (not x shr n) else: (x shr n) | |
| else: | |
| return x shr n | |
| proc FloorLog2Pow10*(e: int32_t): int32_t {.inline.} = | |
| DRAGONBOX_ASSERT(e >= -1233) | |
| DRAGONBOX_ASSERT(e <= 1233) | |
| return FloorDivPow2(e * 1741647, 19) | |
| proc FloorLog10Pow2*(e: int32_t): int32_t {.inline.} = | |
| DRAGONBOX_ASSERT(e >= -1500) | |
| DRAGONBOX_ASSERT(e <= 1500) | |
| return FloorDivPow2(e * 1262611, 22) | |
| proc FloorLog10ThreeQuartersPow2*(e: int32_t): int32_t {.inline.} = | |
| DRAGONBOX_ASSERT(e >= -1500) | |
| DRAGONBOX_ASSERT(e <= 1500) | |
| return FloorDivPow2(e * 1262611 - 524031, 22) | |
| ## ================================================================================================== | |
| ## | |
| ## ================================================================================================== | |
| type | |
| uint64x2* {.bycopy.} = object | |
| hi*: uint64_t | |
| lo*: uint64_t | |
| proc ComputePow10*(k: int32_t): uint64x2 {.inline.} = | |
| var kMin: int32_t = -292 | |
| var kMax: int32_t = 326 | |
| var Pow10: array[kMax - kMin + 1, uint64x2] = [[0xFF77B1FCBEBCDC4F'i64, | |
| 0x25E8E89C13BB0F7B'i64], [0x9FAACF3DF73609B1'i64, 0x77B191618C54E9AD'i64], [ | |
| 0xC795830D75038C1D'i64, 0xD59DF5B9EF6A2418'i64], [0xF97AE3D0D2446F25'i64, | |
| 0x4B0573286B44AD1E'i64], [0x9BECCE62836AC577'i64, 0x4EE367F9430AEC33'i64], [ | |
| 0xC2E801FB244576D5'i64, 0x229C41F793CDA740'i64], [0xF3A20279ED56D48A'i64, | |
| 0x6B43527578C11110'i64], [0x9845418C345644D6'i64, 0x830A13896B78AAAA'i64], [ | |
| 0xBE5691EF416BD60C'i64, 0x23CC986BC656D554'i64], [0xEDEC366B11C6CB8F'i64, | |
| 0x2CBFBE86B7EC8AA9'i64], [0x94B3A202EB1C3F39'i64, 0x7BF7D71432F3D6AA'i64], [ | |
| 0xB9E08A83A5E34F07'i64, 0xDAF5CCD93FB0CC54'i64], [0xE858AD248F5C22C9'i64, | |
| 0xD1B3400F8F9CFF69'i64], [0x91376C36D99995BE'i64, 0x23100809B9C21FA2'i64], [ | |
| 0xB58547448FFFFB2D'i64, 0xABD40A0C2832A78B'i64], [0xE2E69915B3FFF9F9'i64, | |
| 0x16C90C8F323F516D'i64], [0x8DD01FAD907FFC3B'i64, 0xAE3DA7D97F6792E4'i64], [ | |
| 0xB1442798F49FFB4A'i64, 0x99CD11CFDF41779D'i64], [0xDD95317F31C7FA1D'i64, | |
| 0x40405643D711D584'i64], [0x8A7D3EEF7F1CFC52'i64, 0x482835EA666B2573'i64], [ | |
| 0xAD1C8EAB5EE43B66'i64, 0xDA3243650005EED0'i64], [0xD863B256369D4A40'i64, | |
| 0x90BED43E40076A83'i64], [0x873E4F75E2224E68'i64, 0x5A7744A6E804A292'i64], [ | |
| 0xA90DE3535AAAE202'i64, 0x711515D0A205CB37'i64], [0xD3515C2831559A83'i64, | |
| 0x0D5A5B44CA873E04'i64], [0x8412D9991ED58091'i64, 0xE858790AFE9486C3'i64], [ | |
| 0xA5178FFF668AE0B6'i64, 0x626E974DBE39A873'i64], [0xCE5D73FF402D98E3'i64, | |
| 0xFB0A3D212DC81290'i64], [0x80FA687F881C7F8E'i64, 0x7CE66634BC9D0B9A'i64], [ | |
| 0xA139029F6A239F72'i64, 0x1C1FFFC1EBC44E81'i64], [0xC987434744AC874E'i64, | |
| 0xA327FFB266B56221'i64], [0xFBE9141915D7A922'i64, 0x4BF1FF9F0062BAA9'i64], [ | |
| 0x9D71AC8FADA6C9B5'i64, 0x6F773FC3603DB4AA'i64], [0xC4CE17B399107C22'i64, | |
| 0xCB550FB4384D21D4'i64], [0xF6019DA07F549B2B'i64, 0x7E2A53A146606A49'i64], [ | |
| 0x99C102844F94E0FB'i64, 0x2EDA7444CBFC426E'i64], [0xC0314325637A1939'i64, | |
| 0xFA911155FEFB5309'i64], [0xF03D93EEBC589F88'i64, 0x793555AB7EBA27CB'i64], [ | |
| 0x96267C7535B763B5'i64, 0x4BC1558B2F3458DF'i64], [0xBBB01B9283253CA2'i64, | |
| 0x9EB1AAEDFB016F17'i64], [0xEA9C227723EE8BCB'i64, 0x465E15A979C1CADD'i64], [ | |
| 0x92A1958A7675175F'i64, 0x0BFACD89EC191ECA'i64], [0xB749FAED14125D36'i64, | |
| 0xCEF980EC671F667C'i64], [0xE51C79A85916F484'i64, 0x82B7E12780E7401B'i64], [ | |
| 0x8F31CC0937AE58D2'i64, 0xD1B2ECB8B0908811'i64], [0xB2FE3F0B8599EF07'i64, | |
| 0x861FA7E6DCB4AA16'i64], [0xDFBDCECE67006AC9'i64, 0x67A791E093E1D49B'i64], [ | |
| 0x8BD6A141006042BD'i64, 0xE0C8BB2C5C6D24E1'i64], [0xAECC49914078536D'i64, | |
| 0x58FAE9F773886E19'i64], [0xDA7F5BF590966848'i64, 0xAF39A475506A899F'i64], [ | |
| 0x888F99797A5E012D'i64, 0x6D8406C952429604'i64], [0xAAB37FD7D8F58178'i64, | |
| 0xC8E5087BA6D33B84'i64], [0xD5605FCDCF32E1D6'i64, 0xFB1E4A9A90880A65'i64], [ | |
| 0x855C3BE0A17FCD26'i64, 0x5CF2EEA09A550680'i64], [0xA6B34AD8C9DFC06F'i64, | |
| 0xF42FAA48C0EA481F'i64], [0xD0601D8EFC57B08B'i64, 0xF13B94DAF124DA27'i64], [ | |
| 0x823C12795DB6CE57'i64, 0x76C53D08D6B70859'i64], [0xA2CB1717B52481ED'i64, | |
| 0x54768C4B0C64CA6F'i64], [0xCB7DDCDDA26DA268'i64, 0xA9942F5DCF7DFD0A'i64], [ | |
| 0xFE5D54150B090B02'i64, 0xD3F93B35435D7C4D'i64], [0x9EFA548D26E5A6E1'i64, | |
| 0xC47BC5014A1A6DB0'i64], [0xC6B8E9B0709F109A'i64, 0x359AB6419CA1091C'i64], [ | |
| 0xF867241C8CC6D4C0'i64, 0xC30163D203C94B63'i64], [0x9B407691D7FC44F8'i64, | |
| 0x79E0DE63425DCF1E'i64], [0xC21094364DFB5636'i64, 0x985915FC12F542E5'i64], [ | |
| 0xF294B943E17A2BC4'i64, 0x3E6F5B7B17B2939E'i64], [0x979CF3CA6CEC5B5A'i64, | |
| 0xA705992CEECF9C43'i64], [0xBD8430BD08277231'i64, 0x50C6FF782A838354'i64], [ | |
| 0xECE53CEC4A314EBD'i64, 0xA4F8BF5635246429'i64], [0x940F4613AE5ED136'i64, | |
| 0x871B7795E136BE9A'i64], [0xB913179899F68584'i64, 0x28E2557B59846E40'i64], [ | |
| 0xE757DD7EC07426E5'i64, 0x331AEADA2FE589D0'i64], [0x9096EA6F3848984F'i64, | |
| 0x3FF0D2C85DEF7622'i64], [0xB4BCA50B065ABE63'i64, 0x0FED077A756B53AA'i64], [ | |
| 0xE1EBCE4DC7F16DFB'i64, 0xD3E8495912C62895'i64], [0x8D3360F09CF6E4BD'i64, | |
| 0x64712DD7ABBBD95D'i64], [0xB080392CC4349DEC'i64, 0xBD8D794D96AACFB4'i64], [ | |
| 0xDCA04777F541C567'i64, 0xECF0D7A0FC5583A1'i64], [0x89E42CAAF9491B60'i64, | |
| 0xF41686C49DB57245'i64], [0xAC5D37D5B79B6239'i64, 0x311C2875C522CED6'i64], [ | |
| 0xD77485CB25823AC7'i64, 0x7D633293366B828C'i64], [0x86A8D39EF77164BC'i64, | |
| 0xAE5DFF9C02033198'i64], [0xA8530886B54DBDEB'i64, 0xD9F57F830283FDFD'i64], [ | |
| 0xD267CAA862A12D66'i64, 0xD072DF63C324FD7C'i64], [0x8380DEA93DA4BC60'i64, | |
| 0x4247CB9E59F71E6E'i64], [0xA46116538D0DEB78'i64, 0x52D9BE85F074E609'i64], [ | |
| 0xCD795BE870516656'i64, 0x67902E276C921F8C'i64], [0x806BD9714632DFF6'i64, | |
| 0x00BA1CD8A3DB53B7'i64], [0xA086CFCD97BF97F3'i64, 0x80E8A40ECCD228A5'i64], [ | |
| 0xC8A883C0FDAF7DF0'i64, 0x6122CD128006B2CE'i64], [0xFAD2A4B13D1B5D6C'i64, | |
| 0x796B805720085F82'i64], [0x9CC3A6EEC6311A63'i64, 0xCBE3303674053BB1'i64], [ | |
| 0xC3F490AA77BD60FC'i64, 0xBEDBFC4411068A9D'i64], [0xF4F1B4D515ACB93B'i64, | |
| 0xEE92FB5515482D45'i64], [0x991711052D8BF3C5'i64, 0x751BDD152D4D1C4B'i64], [ | |
| 0xBF5CD54678EEF0B6'i64, 0xD262D45A78A0635E'i64], [0xEF340A98172AACE4'i64, | |
| 0x86FB897116C87C35'i64], [0x9580869F0E7AAC0E'i64, 0xD45D35E6AE3D4DA1'i64], [ | |
| 0xBAE0A846D2195712'i64, 0x8974836059CCA10A'i64], [0xE998D258869FACD7'i64, | |
| 0x2BD1A438703FC94C'i64], [0x91FF83775423CC06'i64, 0x7B6306A34627DDD0'i64], [ | |
| 0xB67F6455292CBF08'i64, 0x1A3BC84C17B1D543'i64], [0xE41F3D6A7377EECA'i64, | |
| 0x20CABA5F1D9E4A94'i64], [0x8E938662882AF53E'i64, 0x547EB47B7282EE9D'i64], [ | |
| 0xB23867FB2A35B28D'i64, 0xE99E619A4F23AA44'i64], [0xDEC681F9F4C31F31'i64, | |
| 0x6405FA00E2EC94D5'i64], [0x8B3C113C38F9F37E'i64, 0xDE83BC408DD3DD05'i64], [ | |
| 0xAE0B158B4738705E'i64, 0x9624AB50B148D446'i64], [0xD98DDAEE19068C76'i64, | |
| 0x3BADD624DD9B0958'i64], [0x87F8A8D4CFA417C9'i64, 0xE54CA5D70A80E5D7'i64], [ | |
| 0xA9F6D30A038D1DBC'i64, 0x5E9FCF4CCD211F4D'i64], [0xD47487CC8470652B'i64, | |
| 0x7647C32000696720'i64], [0x84C8D4DFD2C63F3B'i64, 0x29ECD9F40041E074'i64], [ | |
| 0xA5FB0A17C777CF09'i64, 0xF468107100525891'i64], [0xCF79CC9DB955C2CC'i64, | |
| 0x7182148D4066EEB5'i64], [0x81AC1FE293D599BF'i64, 0xC6F14CD848405531'i64], [ | |
| 0xA21727DB38CB002F'i64, 0xB8ADA00E5A506A7D'i64], [0xCA9CF1D206FDC03B'i64, | |
| 0xA6D90811F0E4851D'i64], [0xFD442E4688BD304A'i64, 0x908F4A166D1DA664'i64], [ | |
| 0x9E4A9CEC15763E2E'i64, 0x9A598E4E043287FF'i64], [0xC5DD44271AD3CDBA'i64, | |
| 0x40EFF1E1853F29FE'i64], [0xF7549530E188C128'i64, 0xD12BEE59E68EF47D'i64], [ | |
| 0x9A94DD3E8CF578B9'i64, 0x82BB74F8301958CF'i64], [0xC13A148E3032D6E7'i64, | |
| 0xE36A52363C1FAF02'i64], [0xF18899B1BC3F8CA1'i64, 0xDC44E6C3CB279AC2'i64], [ | |
| 0x96F5600F15A7B7E5'i64, 0x29AB103A5EF8C0BA'i64], [0xBCB2B812DB11A5DE'i64, | |
| 0x7415D448F6B6F0E8'i64], [0xEBDF661791D60F56'i64, 0x111B495B3464AD22'i64], [ | |
| 0x936B9FCEBB25C995'i64, 0xCAB10DD900BEEC35'i64], [0xB84687C269EF3BFB'i64, | |
| 0x3D5D514F40EEA743'i64], [0xE65829B3046B0AFA'i64, 0x0CB4A5A3112A5113'i64], [ | |
| 0x8FF71A0FE2C2E6DC'i64, 0x47F0E785EABA72AC'i64], [0xB3F4E093DB73A093'i64, | |
| 0x59ED216765690F57'i64], [0xE0F218B8D25088B8'i64, 0x306869C13EC3532D'i64], [ | |
| 0x8C974F7383725573'i64, 0x1E414218C73A13FC'i64], [0xAFBD2350644EEACF'i64, | |
| 0xE5D1929EF90898FB'i64], [0xDBAC6C247D62A583'i64, 0xDF45F746B74ABF3A'i64], [ | |
| 0x894BC396CE5DA772'i64, 0x6B8BBA8C328EB784'i64], [0xAB9EB47C81F5114F'i64, | |
| 0x066EA92F3F326565'i64], [0xD686619BA27255A2'i64, 0xC80A537B0EFEFEBE'i64], [ | |
| 0x8613FD0145877585'i64, 0xBD06742CE95F5F37'i64], [0xA798FC4196E952E7'i64, | |
| 0x2C48113823B73705'i64], [0xD17F3B51FCA3A7A0'i64, 0xF75A15862CA504C6'i64], [ | |
| 0x82EF85133DE648C4'i64, 0x9A984D73DBE722FC'i64], [0xA3AB66580D5FDAF5'i64, | |
| 0xC13E60D0D2E0EBBB'i64], [0xCC963FEE10B7D1B3'i64, 0x318DF905079926A9'i64], [ | |
| 0xFFBBCFE994E5C61F'i64, 0xFDF17746497F7053'i64], [0x9FD561F1FD0F9BD3'i64, | |
| 0xFEB6EA8BEDEFA634'i64], [0xC7CABA6E7C5382C8'i64, 0xFE64A52EE96B8FC1'i64], [ | |
| 0xF9BD690A1B68637B'i64, 0x3DFDCE7AA3C673B1'i64], [0x9C1661A651213E2D'i64, | |
| 0x06BEA10CA65C084F'i64], [0xC31BFA0FE5698DB8'i64, 0x486E494FCFF30A63'i64], [ | |
| 0xF3E2F893DEC3F126'i64, 0x5A89DBA3C3EFCCFB'i64], [0x986DDB5C6B3A76B7'i64, | |
| 0xF89629465A75E01D'i64], [0xBE89523386091465'i64, 0xF6BBB397F1135824'i64], [ | |
| 0xEE2BA6C0678B597F'i64, 0x746AA07DED582E2D'i64], [0x94DB483840B717EF'i64, | |
| 0xA8C2A44EB4571CDD'i64], [0xBA121A4650E4DDEB'i64, 0x92F34D62616CE414'i64], [ | |
| 0xE896A0D7E51E1566'i64, 0x77B020BAF9C81D18'i64], [0x915E2486EF32CD60'i64, | |
| 0x0ACE1474DC1D122F'i64], [0xB5B5ADA8AAFF80B8'i64, 0x0D819992132456BB'i64], [ | |
| 0xE3231912D5BF60E6'i64, 0x10E1FFF697ED6C6A'i64], [0x8DF5EFABC5979C8F'i64, | |
| 0xCA8D3FFA1EF463C2'i64], [0xB1736B96B6FD83B3'i64, 0xBD308FF8A6B17CB3'i64], [ | |
| 0xDDD0467C64BCE4A0'i64, 0xAC7CB3F6D05DDBDF'i64], [0x8AA22C0DBEF60EE4'i64, | |
| 0x6BCDF07A423AA96C'i64], [0xAD4AB7112EB3929D'i64, 0x86C16C98D2C953C7'i64], [ | |
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| 0x81F14FAE158C5F6E'i64, 0x4FCB7E8F3F60C07E'i64], [0xA26DA3999AEF7749'i64, | |
| 0xE3BE5E330F38F09D'i64], [0xCB090C8001AB551C'i64, 0x5CADF5BFD3072CC5'i64], [ | |
| 0xFDCB4FA002162A63'i64, 0x73D9732FC7C8F7F6'i64], [0x9E9F11C4014DDA7E'i64, | |
| 0x2867E7FDDCDD9AFA'i64], [0xC646D63501A1511D'i64, 0xB281E1FD541501B8'i64], [ | |
| 0xF7D88BC24209A565'i64, 0x1F225A7CA91A4226'i64], [0x9AE757596946075F'i64, | |
| 0x3375788DE9B06958'i64], [0xC1A12D2FC3978937'i64, 0x0052D6B1641C83AE'i64], [ | |
| 0xF209787BB47D6B84'i64, 0xC0678C5DBD23A49A'i64], [0x9745EB4D50CE6332'i64, | |
| 0xF840B7BA963646E0'i64], [0xBD176620A501FBFF'i64, 0xB650E5A93BC3D898'i64], [ | |
| 0xEC5D3FA8CE427AFF'i64, 0xA3E51F138AB4CEBE'i64], [0x93BA47C980E98CDF'i64, | |
| 0xC66F336C36B10137'i64], [0xB8A8D9BBE123F017'i64, 0xB80B0047445D4184'i64], [ | |
| 0xE6D3102AD96CEC1D'i64, 0xA60DC059157491E5'i64], [0x9043EA1AC7E41392'i64, | |
| 0x87C89837AD68DB2F'i64], [0xB454E4A179DD1877'i64, 0x29BABE4598C311FB'i64], [ | |
| 0xE16A1DC9D8545E94'i64, 0xF4296DD6FEF3D67A'i64], [0x8CE2529E2734BB1D'i64, | |
| 0x1899E4A65F58660C'i64], [0xB01AE745B101E9E4'i64, 0x5EC05DCFF72E7F8F'i64], [ | |
| 0xDC21A1171D42645D'i64, 0x76707543F4FA1F73'i64], [0x899504AE72497EBA'i64, | |
| 0x6A06494A791C53A8'i64], [0xABFA45DA0EDBDE69'i64, 0x0487DB9D17636892'i64], [ | |
| 0xD6F8D7509292D603'i64, 0x45A9D2845D3C42B6'i64], [0x865B86925B9BC5C2'i64, | |
| 0x0B8A2392BA45A9B2'i64], [0xA7F26836F282B732'i64, 0x8E6CAC7768D7141E'i64], [ | |
| 0xD1EF0244AF2364FF'i64, 0x3207D795430CD926'i64], [0x8335616AED761F1F'i64, | |
| 0x7F44E6BD49E807B8'i64], [0xA402B9C5A8D3A6E7'i64, 0x5F16206C9C6209A6'i64], [ | |
| 0xCD036837130890A1'i64, 0x36DBA887C37A8C0F'i64], [0x802221226BE55A64'i64, | |
| 0xC2494954DA2C9789'i64], [0xA02AA96B06DEB0FD'i64, 0xF2DB9BAA10B7BD6C'i64], [ | |
| 0xC83553C5C8965D3D'i64, 0x6F92829494E5ACC7'i64], [0xFA42A8B73ABBF48C'i64, | |
| 0xCB772339BA1F17F9'i64], [0x9C69A97284B578D7'i64, 0xFF2A760414536EFB'i64], [ | |
| 0xC38413CF25E2D70D'i64, 0xFEF5138519684ABA'i64], [0xF46518C2EF5B8CD1'i64, | |
| 0x7EB258665FC25D69'i64], [0x98BF2F79D5993802'i64, 0xEF2F773FFBD97A61'i64], [ | |
| 0xBEEEFB584AFF8603'i64, 0xAAFB550FFACFD8FA'i64], [0xEEAABA2E5DBF6784'i64, | |
| 0x95BA2A53F983CF38'i64], [0x952AB45CFA97A0B2'i64, 0xDD945A747BF26183'i64], [ | |
| 0xBA756174393D88DF'i64, 0x94F971119AEEF9E4'i64], [0xE912B9D1478CEB17'i64, | |
| 0x7A37CD5601AAB85D'i64], [0x91ABB422CCB812EE'i64, 0xAC62E055C10AB33A'i64], [ | |
| 0xB616A12B7FE617AA'i64, 0x577B986B314D6009'i64], [0xE39C49765FDF9D94'i64, | |
| 0xED5A7E85FDA0B80B'i64], [0x8E41ADE9FBEBC27D'i64, 0x14588F13BE847307'i64], [ | |
| 0xB1D219647AE6B31C'i64, 0x596EB2D8AE258FC8'i64], [0xDE469FBD99A05FE3'i64, | |
| 0x6FCA5F8ED9AEF3BB'i64], [0x8AEC23D680043BEE'i64, 0x25DE7BB9480D5854'i64], [ | |
| 0xADA72CCC20054AE9'i64, 0xAF561AA79A10AE6A'i64], [0xD910F7FF28069DA4'i64, | |
| 0x1B2BA1518094DA04'i64], [0x87AA9AFF79042286'i64, 0x90FB44D2F05D0842'i64], [ | |
| 0xA99541BF57452B28'i64, 0x353A1607AC744A53'i64], [0xD3FA922F2D1675F2'i64, | |
| 0x42889B8997915CE8'i64], [0x847C9B5D7C2E09B7'i64, 0x69956135FEBADA11'i64], [ | |
| 0xA59BC234DB398C25'i64, 0x43FAB9837E699095'i64], [0xCF02B2C21207EF2E'i64, | |
| 0x94F967E45E03F4BB'i64], [0x8161AFB94B44F57D'i64, 0x1D1BE0EEBAC278F5'i64], [ | |
| 0xA1BA1BA79E1632DC'i64, 0x6462D92A69731732'i64], [0xCA28A291859BBF93'i64, | |
| 0x7D7B8F7503CFDCFE'i64], [0xFCB2CB35E702AF78'i64, 0x5CDA735244C3D43E'i64], [ | |
| 0x9DEFBF01B061ADAB'i64, 0x3A0888136AFA64A7'i64], [0xC56BAEC21C7A1916'i64, | |
| 0x088AAA1845B8FDD0'i64], [0xF6C69A72A3989F5B'i64, 0x8AAD549E57273D45'i64], [ | |
| 0x9A3C2087A63F6399'i64, 0x36AC54E2F678864B'i64], [0xC0CB28A98FCF3C7F'i64, | |
| 0x84576A1BB416A7DD'i64], [0xF0FDF2D3F3C30B9F'i64, 0x656D44A2A11C51D5'i64], [ | |
| 0x969EB7C47859E743'i64, 0x9F644AE5A4B1B325'i64], [0xBC4665B596706114'i64, | |
| 0x873D5D9F0DDE1FEE'i64], [0xEB57FF22FC0C7959'i64, 0xA90CB506D155A7EA'i64], [ | |
| 0x9316FF75DD87CBD8'i64, 0x09A7F12442D588F2'i64], [0xB7DCBF5354E9BECE'i64, | |
| 0x0C11ED6D538AEB2F'i64], [0xE5D3EF282A242E81'i64, 0x8F1668C8A86DA5FA'i64], [ | |
| 0x8FA475791A569D10'i64, 0xF96E017D694487BC'i64], [0xB38D92D760EC4455'i64, | |
| 0x37C981DCC395A9AC'i64], [0xE070F78D3927556A'i64, 0x85BBE253F47B1417'i64], [ | |
| 0x8C469AB843B89562'i64, 0x93956D7478CCEC8E'i64], [0xAF58416654A6BABB'i64, | |
| 0x387AC8D1970027B2'i64], [0xDB2E51BFE9D0696A'i64, 0x06997B05FCC0319E'i64], [ | |
| 0x88FCF317F22241E2'i64, 0x441FECE3BDF81F03'i64], [0xAB3C2FDDEEAAD25A'i64, | |
| 0xD527E81CAD7626C3'i64], [0xD60B3BD56A5586F1'i64, 0x8A71E223D8D3B074'i64], [ | |
| 0x85C7056562757456'i64, 0xF6872D5667844E49'i64], [0xA738C6BEBB12D16C'i64, | |
| 0xB428F8AC016561DB'i64], [0xD106F86E69D785C7'i64, 0xE13336D701BEBA52'i64], [ | |
| 0x82A45B450226B39C'i64, 0xECC0024661173473'i64], [0xA34D721642B06084'i64, | |
| 0x27F002D7F95D0190'i64], [0xCC20CE9BD35C78A5'i64, 0x31EC038DF7B441F4'i64], [ | |
| 0xFF290242C83396CE'i64, 0x7E67047175A15271'i64], [0x9F79A169BD203E41'i64, | |
| 0x0F0062C6E984D386'i64], [0xC75809C42C684DD1'i64, 0x52C07B78A3E60868'i64], [ | |
| 0xF92E0C3537826145'i64, 0xA7709A56CCDF8A82'i64], [0x9BBCC7A142B17CCB'i64, | |
| 0x88A66076400BB691'i64], [0xC2ABF989935DDBFE'i64, 0x6ACFF893D00EA435'i64], [ | |
| 0xF356F7EBF83552FE'i64, 0x0583F6B8C4124D43'i64], [0x98165AF37B2153DE'i64, | |
| 0xC3727A337A8B704A'i64], [0xBE1BF1B059E9A8D6'i64, 0x744F18C0592E4C5C'i64], [ | |
| 0xEDA2EE1C7064130C'i64, 0x1162DEF06F79DF73'i64], [0x9485D4D1C63E8BE7'i64, | |
| 0x8ADDCB5645AC2BA8'i64], [0xB9A74A0637CE2EE1'i64, 0x6D953E2BD7173692'i64], [ | |
| 0xE8111C87C5C1BA99'i64, 0xC8FA8DB6CCDD0437'i64], [0x910AB1D4DB9914A0'i64, | |
| 0x1D9C9892400A22A2'i64], [0xB54D5E4A127F59C8'i64, 0x2503BEB6D00CAB4B'i64], [ | |
| 0xE2A0B5DC971F303A'i64, 0x2E44AE64840FD61D'i64], [0x8DA471A9DE737E24'i64, | |
| 0x5CEAECFED289E5D2'i64], [0xB10D8E1456105DAD'i64, 0x7425A83E872C5F47'i64], [ | |
| 0xDD50F1996B947518'i64, 0xD12F124E28F77719'i64], [0x8A5296FFE33CC92F'i64, | |
| 0x82BD6B70D99AAA6F'i64], [0xACE73CBFDC0BFB7B'i64, 0x636CC64D1001550B'i64], [ | |
| 0xD8210BEFD30EFA5A'i64, 0x3C47F7E05401AA4E'i64], [0x8714A775E3E95C78'i64, | |
| 0x65ACFAEC34810A71'i64], [0xA8D9D1535CE3B396'i64, 0x7F1839A741A14D0D'i64], [ | |
| 0xD31045A8341CA07C'i64, 0x1EDE48111209A050'i64], [0x83EA2B892091E44D'i64, | |
| 0x934AED0AAB460432'i64], [0xA4E4B66B68B65D60'i64, 0xF81DA84D5617853F'i64], [ | |
| 0xCE1DE40642E3F4B9'i64, 0x36251260AB9D668E'i64], [0x80D2AE83E9CE78F3'i64, | |
| 0xC1D72B7C6B426019'i64], [0xA1075A24E4421730'i64, 0xB24CF65B8612F81F'i64], [ | |
| 0xC94930AE1D529CFC'i64, 0xDEE033F26797B627'i64], [0xFB9B7CD9A4A7443C'i64, | |
| 0x169840EF017DA3B1'i64], [0x9D412E0806E88AA5'i64, 0x8E1F289560EE864E'i64], [ | |
| 0xC491798A08A2AD4E'i64, 0xF1A6F2BAB92A27E2'i64], [0xF5B5D7EC8ACB58A2'i64, | |
| 0xAE10AF696774B1DB'i64], [0x9991A6F3D6BF1765'i64, 0xACCA6DA1E0A8EF29'i64], [ | |
| 0xBFF610B0CC6EDD3F'i64, 0x17FD090A58D32AF3'i64], [0xEFF394DCFF8A948E'i64, | |
| 0xDDFC4B4CEF07F5B0'i64], [0x95F83D0A1FB69CD9'i64, 0x4ABDAF101564F98E'i64], [ | |
| 0xBB764C4CA7A4440F'i64, 0x9D6D1AD41ABE37F1'i64], [0xEA53DF5FD18D5513'i64, | |
| 0x84C86189216DC5ED'i64], [0x92746B9BE2F8552C'i64, 0x32FD3CF5B4E49BB4'i64], [ | |
| 0xB7118682DBB66A77'i64, 0x3FBC8C33221DC2A1'i64], [0xE4D5E82392A40515'i64, | |
| 0x0FABAF3FEAA5334A'i64], [0x8F05B1163BA6832D'i64, 0x29CB4D87F2A7400E'i64], [ | |
| 0xB2C71D5BCA9023F8'i64, 0x743E20E9EF511012'i64], [0xDF78E4B2BD342CF6'i64, | |
| 0x914DA9246B255416'i64], [0x8BAB8EEFB6409C1A'i64, 0x1AD089B6C2F7548E'i64], [ | |
| 0xAE9672ABA3D0C320'i64, 0xA184AC2473B529B1'i64], [0xDA3C0F568CC4F3E8'i64, | |
| 0xC9E5D72D90A2741E'i64], [0x8865899617FB1871'i64, 0x7E2FA67C7A658892'i64], [ | |
| 0xAA7EEBFB9DF9DE8D'i64, 0xDDBB901B98FEEAB7'i64], [0xD51EA6FA85785631'i64, | |
| 0x552A74227F3EA565'i64], [0x8533285C936B35DE'i64, 0xD53A88958F87275F'i64], [ | |
| 0xA67FF273B8460356'i64, 0x8A892ABAF368F137'i64], [0xD01FEF10A657842C'i64, | |
| 0x2D2B7569B0432D85'i64], [0x8213F56A67F6B29B'i64, 0x9C3B29620E29FC73'i64], [ | |
| 0xA298F2C501F45F42'i64, 0x8349F3BA91B47B8F'i64], [0xCB3F2F7642717713'i64, | |
| 0x241C70A936219A73'i64], [0xFE0EFB53D30DD4D7'i64, 0xED238CD383AA0110'i64], [ | |
| 0x9EC95D1463E8A506'i64, 0xF4363804324A40AA'i64], [0xC67BB4597CE2CE48'i64, | |
| 0xB143C6053EDCD0D5'i64], [0xF81AA16FDC1B81DA'i64, 0xDD94B7868E94050A'i64], [ | |
| 0x9B10A4E5E9913128'i64, 0xCA7CF2B4191C8326'i64], [0xC1D4CE1F63F57D72'i64, | |
| 0xFD1C2F611F63A3F0'i64], [0xF24A01A73CF2DCCF'i64, 0xBC633B39673C8CEC'i64], [ | |
| 0x976E41088617CA01'i64, 0xD5BE0503E085D813'i64], [0xBD49D14AA79DBC82'i64, | |
| 0x4B2D8644D8A74E18'i64], [0xEC9C459D51852BA2'i64, 0xDDF8E7D60ED1219E'i64], [ | |
| 0x93E1AB8252F33B45'i64, 0xCABB90E5C942B503'i64], [0xB8DA1662E7B00A17'i64, | |
| 0x3D6A751F3B936243'i64], [0xE7109BFBA19C0C9D'i64, 0x0CC512670A783AD4'i64], [ | |
| 0x906A617D450187E2'i64, 0x27FB2B80668B24C5'i64], [0xB484F9DC9641E9DA'i64, | |
| 0xB1F9F660802DEDF6'i64], [0xE1A63853BBD26451'i64, 0x5E7873F8A0396973'i64], [ | |
| 0x8D07E33455637EB2'i64, 0xDB0B487B6423E1E8'i64], [0xB049DC016ABC5E5F'i64, | |
| 0x91CE1A9A3D2CDA62'i64], [0xDC5C5301C56B75F7'i64, 0x7641A140CC7810FB'i64], [ | |
| 0x89B9B3E11B6329BA'i64, 0xA9E904C87FCB0A9D'i64], [0xAC2820D9623BF429'i64, | |
| 0x546345FA9FBDCD44'i64], [0xD732290FBACAF133'i64, 0xA97C177947AD4095'i64], [ | |
| 0x867F59A9D4BED6C0'i64, 0x49ED8EABCCCC485D'i64], [0xA81F301449EE8C70'i64, | |
| 0x5C68F256BFFF5A74'i64], [0xD226FC195C6A2F8C'i64, 0x73832EEC6FFF3111'i64], [ | |
| 0x83585D8FD9C25DB7'i64, 0xC831FD53C5FF7EAB'i64], [0xA42E74F3D032F525'i64, | |
| 0xBA3E7CA8B77F5E55'i64], [0xCD3A1230C43FB26F'i64, 0x28CE1BD2E55F35EB'i64], [ | |
| 0x80444B5E7AA7CF85'i64, 0x7980D163CF5B81B3'i64], [0xA0555E361951C366'i64, | |
| 0xD7E105BCC332621F'i64], [0xC86AB5C39FA63440'i64, 0x8DD9472BF3FEFAA7'i64], [ | |
| 0xFA856334878FC150'i64, 0xB14F98F6F0FEB951'i64], [0x9C935E00D4B9D8D2'i64, | |
| 0x6ED1BF9A569F33D3'i64], [0xC3B8358109E84F07'i64, 0x0A862F80EC4700C8'i64], [ | |
| 0xF4A642E14C6262C8'i64, 0xCD27BB612758C0FA'i64], [0x98E7E9CCCFBD7DBD'i64, | |
| 0x8038D51CB897789C'i64], [0xBF21E44003ACDD2C'i64, 0xE0470A63E6BD56C3'i64], [ | |
| 0xEEEA5D5004981478'i64, 0x1858CCFCE06CAC74'i64], [0x95527A5202DF0CCB'i64, | |
| 0x0F37801E0C43EBC8'i64], [0xBAA718E68396CFFD'i64, 0xD30560258F54E6BA'i64], [ | |
| 0xE950DF20247C83FD'i64, 0x47C6B82EF32A2069'i64], [0x91D28B7416CDD27E'i64, | |
| 0x4CDC331D57FA5441'i64], [0xB6472E511C81471D'i64, 0xE0133FE4ADF8E952'i64], [ | |
| 0xE3D8F9E563A198E5'i64, 0x58180FDDD97723A6'i64], [0x8E679C2F5E44FF8F'i64, | |
| 0x570F09EAA7EA7648'i64], [0xB201833B35D63F73'i64, 0x2CD2CC6551E513DA'i64], [ | |
| 0xDE81E40A034BCF4F'i64, 0xF8077F7EA65E58D1'i64], [0x8B112E86420F6191'i64, | |
| 0xFB04AFAF27FAF782'i64], [0xADD57A27D29339F6'i64, 0x79C5DB9AF1F9B563'i64], [ | |
| 0xD94AD8B1C7380874'i64, 0x18375281AE7822BC'i64], [0x87CEC76F1C830548'i64, | |
| 0x8F2293910D0B15B5'i64], [0xA9C2794AE3A3C69A'i64, 0xB2EB3875504DDB22'i64], [ | |
| 0xD433179D9C8CB841'i64, 0x5FA60692A46151EB'i64], [0x849FEEC281D7F328'i64, | |
| 0xDBC7C41BA6BCD333'i64], [0xA5C7EA73224DEFF3'i64, 0x12B9B522906C0800'i64], [ | |
| 0xCF39E50FEAE16BEF'i64, 0xD768226B34870A00'i64], [0x81842F29F2CCE375'i64, | |
| 0xE6A1158300D46640'i64], [0xA1E53AF46F801C53'i64, 0x60495AE3C1097FD0'i64], [ | |
| 0xCA5E89B18B602368'i64, 0x385BB19CB14BDFC4'i64], [0xFCF62C1DEE382C42'i64, | |
| 0x46729E03DD9ED7B5'i64], [0x9E19DB92B4E31BA9'i64, 0x6C07A2C26A8346D1'i64], [ | |
| 0xC5A05277621BE293'i64, 0xC7098B7305241885'i64], [0xF70867153AA2DB38'i64, | |
| 0xB8CBEE4FC66D1EA7'i64]] | |
| DRAGONBOX_ASSERT(k >= kMin) | |
| DRAGONBOX_ASSERT(k <= kMax) | |
| return Pow10[static_cast[uint32_t](k - kMin)] | |
| ## Returns whether value is divisible by 2^e2 | |
| proc MultipleOfPow2*(value: uint64_t; e2: int32_t): bool {.inline.} = | |
| DRAGONBOX_ASSERT(e2 >= 0) | |
| return e2 < 64 and (value and ((uint64_t(1) shl e2) - 1)) == 0 | |
| ## Returns whether value is divisible by 5^e5 | |
| proc MultipleOfPow5*(value: uint64_t; e5: int32_t): bool {.inline.} = | |
| type | |
| MulCmp {.bycopy.} = object | |
| mul: uint64_t | |
| cmp: uint64_t | |
| var Mod5: UncheckedArray[MulCmp] = [[0x0000000000000001'i64, 0xFFFFFFFFFFFFFFFF'i64], [ | |
| 0xCCCCCCCCCCCCCCCD'i64, 0x3333333333333333'i64], [0x8F5C28F5C28F5C29'i64, | |
| 0x0A3D70A3D70A3D70'i64], [0x1CAC083126E978D5'i64, 0x020C49BA5E353F7C'i64], [ | |
| 0xD288CE703AFB7E91'i64, 0x0068DB8BAC710CB2'i64], [0x5D4E8FB00BCBE61D'i64, | |
| 0x0014F8B588E368F0'i64], [0x790FB65668C26139'i64, 0x000431BDE82D7B63'i64], [ | |
| 0xE5032477AE8D46A5'i64, 0x0000D6BF94D5E57A'i64], [0xC767074B22E90E21'i64, | |
| 0x00002AF31DC46118'i64], [0x8E47CE423A2E9C6D'i64, 0x0000089705F4136B'i64], [ | |
| 0x4FA7F60D3ED61F49'i64, 0x000001B7CDFD9D7B'i64], [0x0FEE64690C913975'i64, | |
| 0x00000057F5FF85E5'i64], [0x3662E0E1CF503EB1'i64, 0x000000119799812D'i64], [ | |
| 0xA47A2CF9F6433FBD'i64, 0x0000000384B84D09'i64], [0x54186F653140A659'i64, | |
| 0x00000000B424DC35'i64], [0x7738164770402145'i64, 0x0000000024075F3D'i64], [ | |
| 0xE4A4D1417CD9A041'i64, 0x000000000734ACA5'i64], [0xC75429D9E5C5200D'i64, | |
| 0x000000000170EF54'i64], [0xC1773B91FAC10669'i64, 0x000000000049C977'i64], [ | |
| 0x26B172506559CE15'i64, 0x00000000000EC1E4'i64], [0xD489E3A9ADDEC2D1'i64, | |
| 0x000000000002F394'i64], [0x90E860BB892C8D5D'i64, 0x000000000000971D'i64], [ | |
| 0x502E79BF1B6F4F79'i64, 0x0000000000001E39'i64], [0xDCD618596BE30FE5'i64, | |
| 0x000000000000060B'i64], [0x2C2AD1AB7BFA3661'i64, 0x0000000000000135'i64]] | |
| DRAGONBOX_ASSERT(e5 >= 0) | |
| DRAGONBOX_ASSERT(e5 <= 24) | |
| var m5: MulCmp = Mod5[static_cast[cuint](e5)] | |
| return value * m5.mul <= m5.cmp | |
| type | |
| FloatingDecimal64* {.bycopy.} = object | |
| significand*: uint64_t | |
| exponent*: int32_t | |
| proc ToDecimal64_asymmetric_interval*(e2: int32_t): FloatingDecimal64 {.inline.} = | |
| ## NB: | |
| ## accept_lower_endpoint = true | |
| ## accept_upper_endpoint = true | |
| var P: int32_t = SignificandSize | |
| ## Compute k and beta | |
| var minus_k: int32_t = FloorLog10ThreeQuartersPow2(e2) | |
| var beta_minus_1: int32_t = e2 + FloorLog2Pow10(-minus_k) | |
| ## Compute xi and zi | |
| var pow10: uint64x2 = ComputePow10(-minus_k) | |
| var lower_endpoint: uint64_t = (pow10.hi - (pow10.hi shr (P + 1))) shr | |
| (64 - P - beta_minus_1) | |
| var upper_endpoint: uint64_t = (pow10.hi + (pow10.hi shr (P + 0))) shr | |
| (64 - P - beta_minus_1) | |
| ## If we don't accept the left endpoint (but we do!) or | |
| ## if the left endpoint is not an integer, increase it | |
| var lower_endpoint_is_integer: bool = (2 <= e2 and e2 <= 3) | |
| var xi: uint64_t = lower_endpoint + not lower_endpoint_is_integer | |
| var zi: uint64_t = upper_endpoint | |
| ## Try bigger divisor | |
| var q: uint64_t = zi div 10 | |
| if q * 10 >= xi: | |
| return (q, minus_k + 1) | |
| q = ((pow10.hi shr (64 - (P + 1) - beta_minus_1)) + 1) div 2 | |
| ## When tie occurs, choose one of them according to the rule | |
| if e2 == -77: | |
| dec(q, (q mod 2 != 0)) | |
| ## Round to even. | |
| else: | |
| inc(q, (q < xi)) | |
| return (q, minus_k) | |
| proc ComputeDelta*(pow10: uint64x2; beta_minus_1: int32_t): uint32_t {.inline.} = | |
| DRAGONBOX_ASSERT(beta_minus_1 >= 0) | |
| DRAGONBOX_ASSERT(beta_minus_1 <= 63) | |
| return static_cast[uint32_t](pow10.hi shr (64 - 1 - beta_minus_1)) | |
| when defined(__SIZEOF_INT128__): | |
| proc Mul128*(x: uint64_t; y: uint64_t): uint64x2 {.inline.} = | |
| ## 1 mulx | |
| ## !!!Ignored construct: __extension__ using uint128_t = unsigned __int128 ; | |
| ## Error: token expected: ; but got: [identifier]!!! | |
| var p: uint128_t = uint128_t(x) * y | |
| var hi: uint64_t = static_cast[uint64_t](p shr 64) | |
| var lo: uint64_t = static_cast[uint64_t](p) | |
| return (hi, lo) | |
| elif defined(_MSC_VER) and defined(_M_X64): | |
| proc Mul128*(x: uint64_t; y: uint64_t): uint64x2 {.inline.} = | |
| var hi: uint64_t = 0 | |
| var lo: uint64_t = _umul128(x, y, addr(hi)) | |
| return (hi, lo) | |
| else: | |
| proc Lo32*(x: uint64_t): uint32_t {.inline.} = | |
| return static_cast[uint32_t](x) | |
| proc Hi32*(x: uint64_t): uint32_t {.inline.} = | |
| return static_cast[uint32_t](x shr 32) | |
| proc Mul128*(a: uint64_t; b: uint64_t): uint64x2 {.inline.} = | |
| var b00: uint64_t = uint64_t(Lo32(a)) * Lo32(b) | |
| var b01: uint64_t = uint64_t(Lo32(a)) * Hi32(b) | |
| var b10: uint64_t = uint64_t(Hi32(a)) * Lo32(b) | |
| var b11: uint64_t = uint64_t(Hi32(a)) * Hi32(b) | |
| var mid1: uint64_t = b10 + Hi32(b00) | |
| var mid2: uint64_t = b01 + Lo32(mid1) | |
| var hi: uint64_t = b11 + Hi32(mid1) + Hi32(mid2) | |
| var lo: uint64_t = Lo32(b00) or uint64_t(Lo32(mid2)) shl 32 | |
| return (hi, lo) | |
| ## Returns (x * y) / 2^128 | |
| proc MulShift*(x: uint64_t; y: uint64x2): uint64_t {.inline.} = | |
| ## 2 mulx | |
| var p1: uint64x2 = Mul128(x, y.hi) | |
| var p0: uint64x2 = Mul128(x, y.lo) | |
| inc(p1.lo, p0.hi) | |
| inc(p1.hi, p1.lo < p0.hi) | |
| return p1.hi | |
| proc MulParity*(two_f: uint64_t; pow10: uint64x2; beta_minus_1: int32_t): bool {.inline.} = | |
| ## 1 mulx, 1 mul | |
| DRAGONBOX_ASSERT(beta_minus_1 >= 1) | |
| DRAGONBOX_ASSERT(beta_minus_1 <= 63) | |
| var p01: uint64_t = two_f * pow10.hi | |
| var p10: uint64_t = Mul128(two_f, pow10.lo).hi | |
| var mid: uint64_t = p01 + p10 | |
| return (mid and (uint64_t(1) shl (64 - beta_minus_1))) != 0 | |
| proc IsIntegralEndpoint*(two_f: uint64_t; e2: int32_t; minus_k: int32_t): bool {.inline.} = | |
| if e2 < -2: | |
| return false | |
| if e2 <= 9: | |
| return true | |
| if e2 <= 86: | |
| return MultipleOfPow5(two_f, minus_k) | |
| return false | |
| proc IsIntegralMidpoint*(two_f: uint64_t; e2: int32_t; minus_k: int32_t): bool {.inline.} = | |
| if e2 < -4: | |
| return MultipleOfPow2(two_f, minus_k - e2 + 1) | |
| if e2 <= 9: | |
| return true | |
| if e2 <= 86: | |
| return MultipleOfPow5(two_f, minus_k) | |
| return false | |
| proc ToDecimal64*(ieee_significand: uint64_t; ieee_exponent: uint64_t): FloatingDecimal64 {. | |
| inline.} = | |
| var Kappa: int32_t = 2 | |
| var BigDivisor: uint32_t = 1000 | |
| ## 10^(kappa + 1) | |
| var SmallDivisor: uint32_t = 100 | |
| ## 10^(kappa) | |
| ## | |
| ## Step 1: | |
| ## integer promotion & Schubfach multiplier calculation. | |
| ## | |
| var m2: uint64_t | |
| var e2: int32_t | |
| if ieee_exponent != 0: | |
| m2 = HiddenBit or ieee_significand | |
| e2 = static_cast[int32_t](ieee_exponent) - ExponentBias | |
| if 0 <= -e2 and -e2 < SignificandSize and MultipleOfPow2(m2, -e2): | |
| ## Small integer. | |
| return (m2 shr -e2, 0) | |
| if ieee_significand == 0 and ieee_exponent > 1: | |
| ## Shorter interval case; proceed like Schubfach. | |
| return ToDecimal64_asymmetric_interval(e2) | |
| else: | |
| ## Subnormal case; interval is always regular. | |
| m2 = ieee_significand | |
| e2 = 1 - ExponentBias | |
| var is_even: bool = (m2 mod 2 == 0) | |
| var accept_lower: bool = is_even | |
| var accept_upper: bool = is_even | |
| ## Compute k and beta. | |
| var minus_k: int32_t = FloorLog10Pow2(e2) - Kappa | |
| var beta_minus_1: int32_t = e2 + FloorLog2Pow10(-minus_k) | |
| DRAGONBOX_ASSERT(beta_minus_1 >= 6) | |
| DRAGONBOX_ASSERT(beta_minus_1 <= 9) | |
| var pow10: uint64x2 = ComputePow10(-minus_k) | |
| ## Compute delta | |
| ## 10^kappa <= delta < 10^(kappa + 1) | |
| ## 100 <= delta < 1000 | |
| var delta: uint32_t = ComputeDelta(pow10, beta_minus_1) | |
| DRAGONBOX_ASSERT(delta >= SmallDivisor) | |
| DRAGONBOX_ASSERT(delta < BigDivisor) | |
| var two_fl: uint64_t = 2 * m2 - 1 | |
| var two_fc: uint64_t = 2 * m2 | |
| var two_fr: uint64_t = 2 * m2 + 1 | |
| ## (54 bits) | |
| ## Compute zi | |
| ## (54 + 9 = 63 bits) | |
| var zi: uint64_t = MulShift(two_fr shl beta_minus_1, pow10) | |
| ## 2 mulx | |
| ## | |
| ## Step 2: | |
| ## Try larger divisor. | |
| ## | |
| var q: uint64_t = zi div BigDivisor | |
| ## uint64_t q = Mul128(zi, 0x83126E978D4FDF3Cu).hi >> 9; // 1 mulx | |
| var r: uint32_t = static_cast[uint32_t](zi) - | |
| BigDivisor * static_cast[uint32_t](q) | |
| ## r = zi % BigDivisor | |
| ## 0 <= r < 1000 | |
| if r < delta: ## likely ~50% ?! | |
| ## (r > deltai) | |
| ## Exclude the right endpoint if necessary | |
| if r != 0 or accept_upper or not IsIntegralEndpoint(two_fr, e2, minus_k): | |
| return (q, minus_k + Kappa + 1) | |
| DRAGONBOX_ASSERT(q != 0) | |
| dec(q) | |
| r = BigDivisor | |
| elif r == delta: ## unlikely | |
| ## Compare fractional parts. | |
| ## Check conditions in the order different from the paper | |
| ## to take advantage of short-circuiting | |
| if (accept_lower and IsIntegralEndpoint(two_fl, e2, minus_k)) or | |
| MulParity(two_fl, pow10, beta_minus_1): | |
| return (q, minus_k + Kappa + 1) | |
| else: | |
| discard | |
| ## | |
| ## Step 3: | |
| ## Find the significand with the smaller divisor | |
| ## | |
| q = q * 10 | |
| ## 1 hmul | |
| ## 0 <= r <= 1000 | |
| var dist: uint32_t = r - (delta div 2) + (SmallDivisor div 2) | |
| var dist_q: uint32_t = dist div 100 | |
| ## 1 mul | |
| ## const uint32_t dist_r = dist % 100; | |
| inc(q, dist_q) | |
| ## if /*likely*/ (dist_r == 0) | |
| if dist == dist_q * 100: | |
| ## const bool approx_y_parity = ((dist ^ (SmallDivisor / 2)) & 1) != 0; | |
| var approx_y_parity: bool = (dist and 1) != 0 | |
| ## Check z^(f) >= epsilon^(f) | |
| ## We have either yi == zi - epsiloni or yi == (zi - epsiloni) - 1, | |
| ## where yi == zi - epsiloni if and only if z^(f) >= epsilon^(f) | |
| ## Since there are only 2 possibilities, we only need to care about the | |
| ## parity. Also, zi and r should have the same parity since the divisor | |
| ## is an even number | |
| if MulParity(two_fc, pow10, beta_minus_1) != approx_y_parity: | |
| dec(q) | |
| elif q mod 2 != 0 and IsIntegralMidpoint(two_fc, e2, minus_k): | |
| dec(q) | |
| return (q, minus_k + Kappa) | |
| ## ================================================================================================== | |
| ## ToChars | |
| ## ================================================================================================== | |
| proc Utoa_2Digits*(buf: cstring; digits: uint32_t) {.inline.} = | |
| var Digits100: array[200, char] = ['0', '0', '0', '1', '0', '2', '0', '3', '0', '4', '0', '5', | |
| '0', '6', '0', '7', '0', '8', '0', '9', '1', '0', '1', '1', | |
| '1', '2', '1', '3', '1', '4', '1', '5', '1', '6', '1', '7', | |
| '1', '8', '1', '9', '2', '0', '2', '1', '2', '2', '2', '3', | |
| '2', '4', '2', '5', '2', '6', '2', '7', '2', '8', '2', '9', | |
| '3', '0', '3', '1', '3', '2', '3', '3', '3', '4', '3', '5', | |
| '3', '6', '3', '7', '3', '8', '3', '9', '4', '0', '4', '1', | |
| '4', '2', '4', '3', '4', '4', '4', '5', '4', '6', '4', '7', | |
| '4', '8', '4', '9', '5', '0', '5', '1', '5', '2', '5', '3', | |
| '5', '4', '5', '5', '5', '6', '5', '7', '5', '8', '5', '9', | |
| '6', '0', '6', '1', '6', '2', '6', '3', '6', '4', '6', '5', | |
| '6', '6', '6', '7', '6', '8', '6', '9', '7', '0', '7', '1', | |
| '7', '2', '7', '3', '7', '4', '7', '5', '7', '6', '7', '7', | |
| '7', '8', '7', '9', '8', '0', '8', '1', '8', '2', '8', '3', | |
| '8', '4', '8', '5', '8', '6', '8', '7', '8', '8', '8', '9', | |
| '9', '0', '9', '1', '9', '2', '9', '3', '9', '4', '9', '5', | |
| '9', '6', '9', '7', '9', '8', '9', '9'] | |
| DRAGONBOX_ASSERT(digits <= 99) | |
| memcpy(buf, addr(Digits100[2 * digits]), 2 * sizeof((char))) | |
| proc TrailingZeros_2Digits*(digits: uint32_t): int32_t {.inline.} = | |
| var TrailingZeros100: array[100, int8_t] = [2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, | |
| 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, | |
| 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, | |
| 0, 0, 0, 0, 0, 0, 0] | |
| DRAGONBOX_ASSERT(digits <= 99) | |
| return TrailingZeros100[digits] | |
| proc Utoa_8Digits_skip_trailing_zeros*(buf: cstring; digits: uint32_t): int32_t {. | |
| inline.} = | |
| DRAGONBOX_ASSERT(digits >= 1) | |
| DRAGONBOX_ASSERT(digits <= 99999999) | |
| var q: uint32_t = digits div 10000 | |
| var r: uint32_t = digits mod 10000 | |
| var qH: uint32_t = q div 100 | |
| var qL: uint32_t = q mod 100 | |
| Utoa_2Digits(buf + 0, qH) | |
| Utoa_2Digits(buf + 2, qL) | |
| if r == 0: | |
| return TrailingZeros_2Digits(if qL == 0: qH else: qL) + (if qL == 0: 6 else: 4) | |
| else: | |
| var rH: uint32_t = r div 100 | |
| var rL: uint32_t = r mod 100 | |
| Utoa_2Digits(buf + 4, rH) | |
| Utoa_2Digits(buf + 6, rL) | |
| return TrailingZeros_2Digits(if rL == 0: rH else: rL) + (if rL == 0: 2 else: 0) | |
| proc PrintDecimalDigitsBackwards*(buf: cstring; output64: uint64_t): int32_t {.inline.} = | |
| var tz: int32_t = 0 | |
| ## number of trailing zeros removed. | |
| var nd: int32_t = 0 | |
| ## number of decimal digits processed. | |
| ## At most 17 digits remaining | |
| if output64 >= 100000000: | |
| var q: uint64_t = output64 div 100000000 | |
| var r: uint32_t = static_cast[uint32_t](output64 mod 100000000) | |
| output64 = q | |
| dec(buf, 8) | |
| if r != 0: | |
| tz = Utoa_8Digits_skip_trailing_zeros(buf, r) | |
| DRAGONBOX_ASSERT(tz >= 0) | |
| DRAGONBOX_ASSERT(tz <= 7) | |
| else: | |
| tz = 8 | |
| nd = 8 | |
| DRAGONBOX_ASSERT(output64 <= UINT32_MAX) | |
| var output: uint32_t = static_cast[uint32_t](output64) | |
| if output >= 10000: | |
| var q: uint32_t = output div 10000 | |
| var r: uint32_t = output mod 10000 | |
| output = q | |
| dec(buf, 4) | |
| if r != 0: | |
| var rH: uint32_t = r div 100 | |
| var rL: uint32_t = r mod 100 | |
| Utoa_2Digits(buf + 0, rH) | |
| Utoa_2Digits(buf + 2, rL) | |
| if tz == nd: | |
| inc(tz, TrailingZeros_2Digits(if rL == 0: rH else: rL) + | |
| (if rL == 0: 2 else: 0)) | |
| else: | |
| if tz == nd: | |
| inc(tz, 4) | |
| else: | |
| memset(buf, '0', 4) | |
| ## (actually not required...) | |
| inc(nd, 4) | |
| if output >= 100: | |
| var q: uint32_t = output div 100 | |
| var r: uint32_t = output mod 100 | |
| output = q | |
| dec(buf, 2) | |
| Utoa_2Digits(buf, r) | |
| if tz == nd: | |
| inc(tz, TrailingZeros_2Digits(r)) | |
| inc(nd, 2) | |
| if output >= 100: | |
| var q2: uint32_t = output div 100 | |
| var r2: uint32_t = output mod 100 | |
| output = q2 | |
| dec(buf, 2) | |
| Utoa_2Digits(buf, r2) | |
| if tz == nd: | |
| inc(tz, TrailingZeros_2Digits(r2)) | |
| inc(nd, 2) | |
| DRAGONBOX_ASSERT(output >= 1) | |
| DRAGONBOX_ASSERT(output <= 99) | |
| if output >= 10: | |
| var q: uint32_t = output | |
| dec(buf, 2) | |
| Utoa_2Digits(buf, q) | |
| if tz == nd: | |
| inc(tz, TrailingZeros_2Digits(q)) | |
| else: | |
| var q: uint32_t = output | |
| DRAGONBOX_ASSERT(q >= 1) | |
| DRAGONBOX_ASSERT(q <= 9) | |
| dec(buf)[] = static_cast[char]('0' + q) | |
| return tz | |
| proc DecimalLength*(v: uint64_t): int32_t {.inline.} = | |
| DRAGONBOX_ASSERT(v >= 1) | |
| DRAGONBOX_ASSERT(v <= 99999999999999999'i64) | |
| if static_cast[uint32_t](v shr 32) != 0: | |
| if v >= 10000000000000000'i64: | |
| return 17 | |
| if v >= 1000000000000000'i64: | |
| return 16 | |
| if v >= 100000000000000'i64: | |
| return 15 | |
| if v >= 10000000000000'i64: | |
| return 14 | |
| if v >= 1000000000000'i64: | |
| return 13 | |
| if v >= 100000000000'i64: | |
| return 12 | |
| if v >= 10000000000'i64: | |
| return 11 | |
| return 10 | |
| var v32: uint32_t = static_cast[uint32_t](v) | |
| if v32 >= 1000000000: | |
| return 10 | |
| if v32 >= 100000000: | |
| return 9 | |
| if v32 >= 10000000: | |
| return 8 | |
| if v32 >= 1000000: | |
| return 7 | |
| if v32 >= 100000: | |
| return 6 | |
| if v32 >= 10000: | |
| return 5 | |
| if v32 >= 1000: | |
| return 4 | |
| if v32 >= 100: | |
| return 3 | |
| if v32 >= 10: | |
| return 2 | |
| return 1 | |
| proc FormatDigits*(buffer: cstring; digits: uint64_t; decimal_exponent: int32_t; | |
| force_trailing_dot_zero: bool = false): cstring {.inline.} = | |
| var MinFixedDecimalPoint: int32_t = -6 | |
| var MaxFixedDecimalPoint: int32_t = 17 | |
| static_assert(MinFixedDecimalPoint <= -1, "internal error") | |
| static_assert(MaxFixedDecimalPoint >= 17, "internal error") | |
| DRAGONBOX_ASSERT(digits >= 1) | |
| DRAGONBOX_ASSERT(digits <= 99999999999999999'i64) | |
| DRAGONBOX_ASSERT(decimal_exponent >= -999) | |
| DRAGONBOX_ASSERT(decimal_exponent <= 999) | |
| var num_digits: int32_t = DecimalLength(digits) | |
| var decimal_point: int32_t = num_digits + decimal_exponent | |
| var use_fixed: bool = MinFixedDecimalPoint <= decimal_point and | |
| decimal_point <= MaxFixedDecimalPoint | |
| ## Prepare the buffer. | |
| ## Avoid calling memset/memcpy with variable arguments below... | |
| memset(buffer + 0, '0', 16) | |
| memset(buffer + 16, '0', 16) | |
| static_assert(MinFixedDecimalPoint >= -30, "internal error") | |
| static_assert(MaxFixedDecimalPoint <= 32, "internal error") | |
| var decimal_digits_position: int32_t | |
| if use_fixed: | |
| if decimal_point <= 0: | |
| ## 0.[000]digits | |
| decimal_digits_position = 2 - decimal_point | |
| else: | |
| ## dig.its | |
| ## digits[000] | |
| decimal_digits_position = 0 | |
| else: | |
| ## dE+123 or d.igitsE+123 | |
| decimal_digits_position = 1 | |
| var digits_end: cstring = buffer + decimal_digits_position + num_digits | |
| var tz: int32_t = PrintDecimalDigitsBackwards(digits_end, digits) | |
| dec(digits_end, tz) | |
| dec(num_digits, tz) | |
| ## decimal_exponent += tz; // => decimal_point unchanged. | |
| if use_fixed: | |
| if decimal_point <= 0: | |
| ## 0.[000]digits | |
| buffer[1] = '.' | |
| buffer = digits_end | |
| elif decimal_point < num_digits: | |
| ## dig.its | |
| when defined(_MSC_VER) and not defined(__clang__): | |
| ## VC does not inline the memmove call below. (Even if compiled with /arch:AVX2.) | |
| ## However, memcpy will be inlined. | |
| var tmp: array[16, uint8_t] | |
| var src: cstring = buffer + decimal_point | |
| var dst: cstring = src + 1 | |
| memcpy(tmp, src, 16) | |
| memcpy(dst, tmp, 16) | |
| else: | |
| memmove(buffer + decimal_point + 1, buffer + decimal_point, 16) | |
| buffer[decimal_point] = '.' | |
| buffer = digits_end + 1 | |
| else: | |
| ## digits[000] | |
| inc(buffer, decimal_point) | |
| if force_trailing_dot_zero: | |
| memcpy(buffer, ".0", 2) | |
| inc(buffer, 2) | |
| else: | |
| ## Copy the first digit one place to the left. | |
| buffer[0] = buffer[1] | |
| if num_digits == 1: | |
| ## dE+123 | |
| inc(buffer) | |
| else: | |
| ## d.igitsE+123 | |
| buffer[1] = '.' | |
| buffer = digits_end | |
| var scientific_exponent: int32_t = decimal_point - 1 | |
| ## SF_ASSERT(scientific_exponent != 0); | |
| memcpy(buffer, if scientific_exponent < 0: "e-" else: "e+", 2) | |
| inc(buffer, 2) | |
| var k: uint32_t = static_cast[uint32_t](if scientific_exponent < 0: -scientific_exponent else: scientific_exponent) | |
| if k < 10: | |
| inc(buffer)[] = static_cast[char]('0' + k) | |
| elif k < 100: | |
| Utoa_2Digits(buffer, k) | |
| inc(buffer, 2) | |
| else: | |
| var q: uint32_t = k div 100 | |
| var r: uint32_t = k mod 100 | |
| inc(buffer)[] = static_cast[char]('0' + q) | |
| Utoa_2Digits(buffer, r) | |
| inc(buffer, 2) | |
| return buffer | |
| proc ToChars*(buffer: cstring; value: cdouble; force_trailing_dot_zero: bool = false): cstring {. | |
| inline.} = | |
| proc v(a1: value): Double | |
| var significand: uint64_t = v.PhysicalSignificand() | |
| var exponent: uint64_t = v.PhysicalExponent() | |
| if exponent != MaxIeeeExponent: | |
| ## Finite | |
| buffer[0] = '-' | |
| inc(buffer, v.SignBit()) | |
| if exponent != 0 or significand != 0: | |
| ## != 0 | |
| var dec: auto = ToDecimal64(significand, exponent) | |
| return FormatDigits(buffer, dec.significand, dec.exponent, | |
| force_trailing_dot_zero) | |
| else: | |
| memcpy(buffer, "0.0 ", 4) | |
| inc(buffer, if force_trailing_dot_zero: 3 else: 1) | |
| return buffer | |
| if significand == 0: | |
| buffer[0] = '-' | |
| inc(buffer, v.SignBit()) | |
| memcpy(buffer, "inf ", 4) | |
| return buffer + 3 | |
| else: | |
| memcpy(buffer, "nan ", 4) | |
| return buffer + 3 | |
| ## ================================================================================================== | |
| ## | |
| ## ================================================================================================== | |
| proc Dtoa*(buffer: cstring; value: cdouble): cstring = | |
| return ToChars(buffer, value) | |
| proc nim_dragonbox_Dtoa*(buffer: cstring; value: cdouble): cstring = | |
| return ToChars(buffer, value) |
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