strconv: clean up powers-of-10 table, tests

Both Eisel-Lemire and Ryu depend on a table of
truncated 128-bit mantissas of powers of 10,
and so will Dragonbox.

This CL:
 - Moves the table to a separate file, so it doesn't look tied to Eisel-Lemire.
 - Introduces a uint128 type in math.go for the table values,
   since .Hi and .Lo are clearer than [1] and [0].
 - Generates the table from a standalone generator pow10gen.go.
 - Adds a new pow10 function in math.go to handle table access details.
 - Factors a 64x128->192-bit multiply into umul192 in math.go.
 - Moves multiplication by log₁₀ 2 and log₂ 10 into math.go.
 - Introduces an import_test.go to avoid having to type differently
   cased names in test code versus regular code.
 - Introduces named constants for the floating-point size parameters.
   Previously these were only in the floatInfo global variables.
 - Changes the BenchmarkAppendUintVarlen subtest names
   to be more useful.

Change-Id: I9826ee5f41c5c19be3b6a7c3c5f277ec6c23b39a
Reviewed-on: https://go-review.googlesource.com/c/go/+/712661
Reviewed-by: Alan Donovan <adonovan@google.com>
LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com>
Reviewed-by: David Chase <drchase@google.com>
This commit is contained in:
Russ Cox 2025-10-14 23:24:19 -04:00
parent 7c9fa4d5e9
commit 1ff59f3dd3
14 changed files with 1035 additions and 844 deletions

View file

@ -460,7 +460,7 @@ func atof64exact(mantissa uint64, exp int, neg bool) (f float64, ok bool) {
// If possible to compute mantissa*10^exp to 32-bit float f exactly, // If possible to compute mantissa*10^exp to 32-bit float f exactly,
// entirely in floating-point math, do so, avoiding the machinery above. // entirely in floating-point math, do so, avoiding the machinery above.
func atof32exact(mantissa uint64, exp int, neg bool) (f float32, ok bool) { func atof32exact(mantissa uint64, exp int, neg bool) (f float32, ok bool) {
if mantissa>>float32info.mantbits != 0 { if mantissa>>float32MantBits != 0 {
return return
} }
f = float32(mantissa) f = float32(mantissa)

View file

@ -501,11 +501,11 @@ func TestAtoi(t *testing.T) {
} }
func bitSizeErrStub(name string, bitSize int) error { func bitSizeErrStub(name string, bitSize int) error {
return BitSizeError(name, "0", bitSize) return bitSizeError(name, "0", bitSize)
} }
func baseErrStub(name string, base int) error { func baseErrStub(name string, base int) error {
return BaseError(name, "0", base) return baseError(name, "0", base)
} }
func noErrStub(name string, arg int) error { func noErrStub(name string, arg int) error {

View file

@ -33,22 +33,22 @@ func eiselLemire64(man uint64, exp10 int, neg bool) (f float64, ok bool) {
} }
return f, true return f, true
} }
if exp10 < detailedPowersOfTenMinExp10 || detailedPowersOfTenMaxExp10 < exp10 { pow, exp2, ok := pow10(exp10)
if !ok {
return 0, false return 0, false
} }
// Normalization. // Normalization.
clz := bits.LeadingZeros64(man) clz := bits.LeadingZeros64(man)
man <<= uint(clz) man <<= uint(clz)
const float64ExponentBias = 1023 retExp2 := uint64(exp2+64-float64Bias) - uint64(clz)
retExp2 := uint64(217706*exp10>>16+64+float64ExponentBias) - uint64(clz)
// Multiplication. // Multiplication.
xHi, xLo := bits.Mul64(man, detailedPowersOfTen[exp10-detailedPowersOfTenMinExp10][1]) xHi, xLo := bits.Mul64(man, pow.Hi)
// Wider Approximation. // Wider Approximation.
if xHi&0x1FF == 0x1FF && xLo+man < man { if xHi&0x1FF == 0x1FF && xLo+man < man {
yHi, yLo := bits.Mul64(man, detailedPowersOfTen[exp10-detailedPowersOfTenMinExp10][0]) yHi, yLo := bits.Mul64(man, pow.Lo)
mergedHi, mergedLo := xHi, xLo+yHi mergedHi, mergedLo := xHi, xLo+yHi
if mergedLo < xLo { if mergedLo < xLo {
mergedHi++ mergedHi++
@ -84,7 +84,7 @@ func eiselLemire64(man uint64, exp10 int, neg bool) (f float64, ok bool) {
if retExp2-1 >= 0x7FF-1 { if retExp2-1 >= 0x7FF-1 {
return 0, false return 0, false
} }
retBits := retExp2<<52 | retMantissa&0x000FFFFFFFFFFFFF retBits := retExp2<<float64MantBits | retMantissa&(1<<float64MantBits-1)
if neg { if neg {
retBits |= 0x8000000000000000 retBits |= 0x8000000000000000
} }
@ -108,22 +108,22 @@ func eiselLemire32(man uint64, exp10 int, neg bool) (f float32, ok bool) {
} }
return f, true return f, true
} }
if exp10 < detailedPowersOfTenMinExp10 || detailedPowersOfTenMaxExp10 < exp10 { pow, exp2, ok := pow10(exp10)
if !ok {
return 0, false return 0, false
} }
// Normalization. // Normalization.
clz := bits.LeadingZeros64(man) clz := bits.LeadingZeros64(man)
man <<= uint(clz) man <<= uint(clz)
const float32ExponentBias = 127 retExp2 := uint64(exp2+64-float32Bias) - uint64(clz)
retExp2 := uint64(217706*exp10>>16+64+float32ExponentBias) - uint64(clz)
// Multiplication. // Multiplication.
xHi, xLo := bits.Mul64(man, detailedPowersOfTen[exp10-detailedPowersOfTenMinExp10][1]) xHi, xLo := bits.Mul64(man, pow.Hi)
// Wider Approximation. // Wider Approximation.
if xHi&0x3FFFFFFFFF == 0x3FFFFFFFFF && xLo+man < man { if xHi&0x3FFFFFFFFF == 0x3FFFFFFFFF && xLo+man < man {
yHi, yLo := bits.Mul64(man, detailedPowersOfTen[exp10-detailedPowersOfTenMinExp10][0]) yHi, yLo := bits.Mul64(man, pow.Lo)
mergedHi, mergedLo := xHi, xLo+yHi mergedHi, mergedLo := xHi, xLo+yHi
if mergedLo < xLo { if mergedLo < xLo {
mergedHi++ mergedHi++
@ -159,726 +159,9 @@ func eiselLemire32(man uint64, exp10 int, neg bool) (f float32, ok bool) {
if retExp2-1 >= 0xFF-1 { if retExp2-1 >= 0xFF-1 {
return 0, false return 0, false
} }
retBits := retExp2<<23 | retMantissa&0x007FFFFF retBits := retExp2<<float32MantBits | retMantissa&(1<<float32MantBits-1)
if neg { if neg {
retBits |= 0x80000000 retBits |= 0x80000000
} }
return math.Float32frombits(uint32(retBits)), true return math.Float32frombits(uint32(retBits)), true
} }
// detailedPowersOfTen{Min,Max}Exp10 is the power of 10 represented by the
// first and last rows of detailedPowersOfTen. Both bounds are inclusive.
const (
detailedPowersOfTenMinExp10 = -348
detailedPowersOfTenMaxExp10 = +347
)
// detailedPowersOfTen contains 128-bit mantissa approximations (rounded down)
// to the powers of 10. For example:
//
// - 1e43 ≈ (0xE596B7B0_C643C719 * (2 ** 79))
// - 1e43 = (0xE596B7B0_C643C719_6D9CCD05_D0000000 * (2 ** 15))
//
// The mantissas are explicitly listed. The exponents are implied by a linear
// expression with slope 217706.0/65536.0 ≈ log(10)/log(2).
//
// The table was generated by
// https://github.com/google/wuffs/blob/ba3818cb6b473a2ed0b38ecfc07dbbd3a97e8ae7/script/print-mpb-powers-of-10.go
var detailedPowersOfTen = [...][2]uint64{
{0x1732C869CD60E453, 0xFA8FD5A0081C0288}, // 1e-348
{0x0E7FBD42205C8EB4, 0x9C99E58405118195}, // 1e-347
{0x521FAC92A873B261, 0xC3C05EE50655E1FA}, // 1e-346
{0xE6A797B752909EF9, 0xF4B0769E47EB5A78}, // 1e-345
{0x9028BED2939A635C, 0x98EE4A22ECF3188B}, // 1e-344
{0x7432EE873880FC33, 0xBF29DCABA82FDEAE}, // 1e-343
{0x113FAA2906A13B3F, 0xEEF453D6923BD65A}, // 1e-342
{0x4AC7CA59A424C507, 0x9558B4661B6565F8}, // 1e-341
{0x5D79BCF00D2DF649, 0xBAAEE17FA23EBF76}, // 1e-340
{0xF4D82C2C107973DC, 0xE95A99DF8ACE6F53}, // 1e-339
{0x79071B9B8A4BE869, 0x91D8A02BB6C10594}, // 1e-338
{0x9748E2826CDEE284, 0xB64EC836A47146F9}, // 1e-337
{0xFD1B1B2308169B25, 0xE3E27A444D8D98B7}, // 1e-336
{0xFE30F0F5E50E20F7, 0x8E6D8C6AB0787F72}, // 1e-335
{0xBDBD2D335E51A935, 0xB208EF855C969F4F}, // 1e-334
{0xAD2C788035E61382, 0xDE8B2B66B3BC4723}, // 1e-333
{0x4C3BCB5021AFCC31, 0x8B16FB203055AC76}, // 1e-332
{0xDF4ABE242A1BBF3D, 0xADDCB9E83C6B1793}, // 1e-331
{0xD71D6DAD34A2AF0D, 0xD953E8624B85DD78}, // 1e-330
{0x8672648C40E5AD68, 0x87D4713D6F33AA6B}, // 1e-329
{0x680EFDAF511F18C2, 0xA9C98D8CCB009506}, // 1e-328
{0x0212BD1B2566DEF2, 0xD43BF0EFFDC0BA48}, // 1e-327
{0x014BB630F7604B57, 0x84A57695FE98746D}, // 1e-326
{0x419EA3BD35385E2D, 0xA5CED43B7E3E9188}, // 1e-325
{0x52064CAC828675B9, 0xCF42894A5DCE35EA}, // 1e-324
{0x7343EFEBD1940993, 0x818995CE7AA0E1B2}, // 1e-323
{0x1014EBE6C5F90BF8, 0xA1EBFB4219491A1F}, // 1e-322
{0xD41A26E077774EF6, 0xCA66FA129F9B60A6}, // 1e-321
{0x8920B098955522B4, 0xFD00B897478238D0}, // 1e-320
{0x55B46E5F5D5535B0, 0x9E20735E8CB16382}, // 1e-319
{0xEB2189F734AA831D, 0xC5A890362FDDBC62}, // 1e-318
{0xA5E9EC7501D523E4, 0xF712B443BBD52B7B}, // 1e-317
{0x47B233C92125366E, 0x9A6BB0AA55653B2D}, // 1e-316
{0x999EC0BB696E840A, 0xC1069CD4EABE89F8}, // 1e-315
{0xC00670EA43CA250D, 0xF148440A256E2C76}, // 1e-314
{0x380406926A5E5728, 0x96CD2A865764DBCA}, // 1e-313
{0xC605083704F5ECF2, 0xBC807527ED3E12BC}, // 1e-312
{0xF7864A44C633682E, 0xEBA09271E88D976B}, // 1e-311
{0x7AB3EE6AFBE0211D, 0x93445B8731587EA3}, // 1e-310
{0x5960EA05BAD82964, 0xB8157268FDAE9E4C}, // 1e-309
{0x6FB92487298E33BD, 0xE61ACF033D1A45DF}, // 1e-308
{0xA5D3B6D479F8E056, 0x8FD0C16206306BAB}, // 1e-307
{0x8F48A4899877186C, 0xB3C4F1BA87BC8696}, // 1e-306
{0x331ACDABFE94DE87, 0xE0B62E2929ABA83C}, // 1e-305
{0x9FF0C08B7F1D0B14, 0x8C71DCD9BA0B4925}, // 1e-304
{0x07ECF0AE5EE44DD9, 0xAF8E5410288E1B6F}, // 1e-303
{0xC9E82CD9F69D6150, 0xDB71E91432B1A24A}, // 1e-302
{0xBE311C083A225CD2, 0x892731AC9FAF056E}, // 1e-301
{0x6DBD630A48AAF406, 0xAB70FE17C79AC6CA}, // 1e-300
{0x092CBBCCDAD5B108, 0xD64D3D9DB981787D}, // 1e-299
{0x25BBF56008C58EA5, 0x85F0468293F0EB4E}, // 1e-298
{0xAF2AF2B80AF6F24E, 0xA76C582338ED2621}, // 1e-297
{0x1AF5AF660DB4AEE1, 0xD1476E2C07286FAA}, // 1e-296
{0x50D98D9FC890ED4D, 0x82CCA4DB847945CA}, // 1e-295
{0xE50FF107BAB528A0, 0xA37FCE126597973C}, // 1e-294
{0x1E53ED49A96272C8, 0xCC5FC196FEFD7D0C}, // 1e-293
{0x25E8E89C13BB0F7A, 0xFF77B1FCBEBCDC4F}, // 1e-292
{0x77B191618C54E9AC, 0x9FAACF3DF73609B1}, // 1e-291
{0xD59DF5B9EF6A2417, 0xC795830D75038C1D}, // 1e-290
{0x4B0573286B44AD1D, 0xF97AE3D0D2446F25}, // 1e-289
{0x4EE367F9430AEC32, 0x9BECCE62836AC577}, // 1e-288
{0x229C41F793CDA73F, 0xC2E801FB244576D5}, // 1e-287
{0x6B43527578C1110F, 0xF3A20279ED56D48A}, // 1e-286
{0x830A13896B78AAA9, 0x9845418C345644D6}, // 1e-285
{0x23CC986BC656D553, 0xBE5691EF416BD60C}, // 1e-284
{0x2CBFBE86B7EC8AA8, 0xEDEC366B11C6CB8F}, // 1e-283
{0x7BF7D71432F3D6A9, 0x94B3A202EB1C3F39}, // 1e-282
{0xDAF5CCD93FB0CC53, 0xB9E08A83A5E34F07}, // 1e-281
{0xD1B3400F8F9CFF68, 0xE858AD248F5C22C9}, // 1e-280
{0x23100809B9C21FA1, 0x91376C36D99995BE}, // 1e-279
{0xABD40A0C2832A78A, 0xB58547448FFFFB2D}, // 1e-278
{0x16C90C8F323F516C, 0xE2E69915B3FFF9F9}, // 1e-277
{0xAE3DA7D97F6792E3, 0x8DD01FAD907FFC3B}, // 1e-276
{0x99CD11CFDF41779C, 0xB1442798F49FFB4A}, // 1e-275
{0x40405643D711D583, 0xDD95317F31C7FA1D}, // 1e-274
{0x482835EA666B2572, 0x8A7D3EEF7F1CFC52}, // 1e-273
{0xDA3243650005EECF, 0xAD1C8EAB5EE43B66}, // 1e-272
{0x90BED43E40076A82, 0xD863B256369D4A40}, // 1e-271
{0x5A7744A6E804A291, 0x873E4F75E2224E68}, // 1e-270
{0x711515D0A205CB36, 0xA90DE3535AAAE202}, // 1e-269
{0x0D5A5B44CA873E03, 0xD3515C2831559A83}, // 1e-268
{0xE858790AFE9486C2, 0x8412D9991ED58091}, // 1e-267
{0x626E974DBE39A872, 0xA5178FFF668AE0B6}, // 1e-266
{0xFB0A3D212DC8128F, 0xCE5D73FF402D98E3}, // 1e-265
{0x7CE66634BC9D0B99, 0x80FA687F881C7F8E}, // 1e-264
{0x1C1FFFC1EBC44E80, 0xA139029F6A239F72}, // 1e-263
{0xA327FFB266B56220, 0xC987434744AC874E}, // 1e-262
{0x4BF1FF9F0062BAA8, 0xFBE9141915D7A922}, // 1e-261
{0x6F773FC3603DB4A9, 0x9D71AC8FADA6C9B5}, // 1e-260
{0xCB550FB4384D21D3, 0xC4CE17B399107C22}, // 1e-259
{0x7E2A53A146606A48, 0xF6019DA07F549B2B}, // 1e-258
{0x2EDA7444CBFC426D, 0x99C102844F94E0FB}, // 1e-257
{0xFA911155FEFB5308, 0xC0314325637A1939}, // 1e-256
{0x793555AB7EBA27CA, 0xF03D93EEBC589F88}, // 1e-255
{0x4BC1558B2F3458DE, 0x96267C7535B763B5}, // 1e-254
{0x9EB1AAEDFB016F16, 0xBBB01B9283253CA2}, // 1e-253
{0x465E15A979C1CADC, 0xEA9C227723EE8BCB}, // 1e-252
{0x0BFACD89EC191EC9, 0x92A1958A7675175F}, // 1e-251
{0xCEF980EC671F667B, 0xB749FAED14125D36}, // 1e-250
{0x82B7E12780E7401A, 0xE51C79A85916F484}, // 1e-249
{0xD1B2ECB8B0908810, 0x8F31CC0937AE58D2}, // 1e-248
{0x861FA7E6DCB4AA15, 0xB2FE3F0B8599EF07}, // 1e-247
{0x67A791E093E1D49A, 0xDFBDCECE67006AC9}, // 1e-246
{0xE0C8BB2C5C6D24E0, 0x8BD6A141006042BD}, // 1e-245
{0x58FAE9F773886E18, 0xAECC49914078536D}, // 1e-244
{0xAF39A475506A899E, 0xDA7F5BF590966848}, // 1e-243
{0x6D8406C952429603, 0x888F99797A5E012D}, // 1e-242
{0xC8E5087BA6D33B83, 0xAAB37FD7D8F58178}, // 1e-241
{0xFB1E4A9A90880A64, 0xD5605FCDCF32E1D6}, // 1e-240
{0x5CF2EEA09A55067F, 0x855C3BE0A17FCD26}, // 1e-239
{0xF42FAA48C0EA481E, 0xA6B34AD8C9DFC06F}, // 1e-238
{0xF13B94DAF124DA26, 0xD0601D8EFC57B08B}, // 1e-237
{0x76C53D08D6B70858, 0x823C12795DB6CE57}, // 1e-236
{0x54768C4B0C64CA6E, 0xA2CB1717B52481ED}, // 1e-235
{0xA9942F5DCF7DFD09, 0xCB7DDCDDA26DA268}, // 1e-234
{0xD3F93B35435D7C4C, 0xFE5D54150B090B02}, // 1e-233
{0xC47BC5014A1A6DAF, 0x9EFA548D26E5A6E1}, // 1e-232
{0x359AB6419CA1091B, 0xC6B8E9B0709F109A}, // 1e-231
{0xC30163D203C94B62, 0xF867241C8CC6D4C0}, // 1e-230
{0x79E0DE63425DCF1D, 0x9B407691D7FC44F8}, // 1e-229
{0x985915FC12F542E4, 0xC21094364DFB5636}, // 1e-228
{0x3E6F5B7B17B2939D, 0xF294B943E17A2BC4}, // 1e-227
{0xA705992CEECF9C42, 0x979CF3CA6CEC5B5A}, // 1e-226
{0x50C6FF782A838353, 0xBD8430BD08277231}, // 1e-225
{0xA4F8BF5635246428, 0xECE53CEC4A314EBD}, // 1e-224
{0x871B7795E136BE99, 0x940F4613AE5ED136}, // 1e-223
{0x28E2557B59846E3F, 0xB913179899F68584}, // 1e-222
{0x331AEADA2FE589CF, 0xE757DD7EC07426E5}, // 1e-221
{0x3FF0D2C85DEF7621, 0x9096EA6F3848984F}, // 1e-220
{0x0FED077A756B53A9, 0xB4BCA50B065ABE63}, // 1e-219
{0xD3E8495912C62894, 0xE1EBCE4DC7F16DFB}, // 1e-218
{0x64712DD7ABBBD95C, 0x8D3360F09CF6E4BD}, // 1e-217
{0xBD8D794D96AACFB3, 0xB080392CC4349DEC}, // 1e-216
{0xECF0D7A0FC5583A0, 0xDCA04777F541C567}, // 1e-215
{0xF41686C49DB57244, 0x89E42CAAF9491B60}, // 1e-214
{0x311C2875C522CED5, 0xAC5D37D5B79B6239}, // 1e-213
{0x7D633293366B828B, 0xD77485CB25823AC7}, // 1e-212
{0xAE5DFF9C02033197, 0x86A8D39EF77164BC}, // 1e-211
{0xD9F57F830283FDFC, 0xA8530886B54DBDEB}, // 1e-210
{0xD072DF63C324FD7B, 0xD267CAA862A12D66}, // 1e-209
{0x4247CB9E59F71E6D, 0x8380DEA93DA4BC60}, // 1e-208
{0x52D9BE85F074E608, 0xA46116538D0DEB78}, // 1e-207
{0x67902E276C921F8B, 0xCD795BE870516656}, // 1e-206
{0x00BA1CD8A3DB53B6, 0x806BD9714632DFF6}, // 1e-205
{0x80E8A40ECCD228A4, 0xA086CFCD97BF97F3}, // 1e-204
{0x6122CD128006B2CD, 0xC8A883C0FDAF7DF0}, // 1e-203
{0x796B805720085F81, 0xFAD2A4B13D1B5D6C}, // 1e-202
{0xCBE3303674053BB0, 0x9CC3A6EEC6311A63}, // 1e-201
{0xBEDBFC4411068A9C, 0xC3F490AA77BD60FC}, // 1e-200
{0xEE92FB5515482D44, 0xF4F1B4D515ACB93B}, // 1e-199
{0x751BDD152D4D1C4A, 0x991711052D8BF3C5}, // 1e-198
{0xD262D45A78A0635D, 0xBF5CD54678EEF0B6}, // 1e-197
{0x86FB897116C87C34, 0xEF340A98172AACE4}, // 1e-196
{0xD45D35E6AE3D4DA0, 0x9580869F0E7AAC0E}, // 1e-195
{0x8974836059CCA109, 0xBAE0A846D2195712}, // 1e-194
{0x2BD1A438703FC94B, 0xE998D258869FACD7}, // 1e-193
{0x7B6306A34627DDCF, 0x91FF83775423CC06}, // 1e-192
{0x1A3BC84C17B1D542, 0xB67F6455292CBF08}, // 1e-191
{0x20CABA5F1D9E4A93, 0xE41F3D6A7377EECA}, // 1e-190
{0x547EB47B7282EE9C, 0x8E938662882AF53E}, // 1e-189
{0xE99E619A4F23AA43, 0xB23867FB2A35B28D}, // 1e-188
{0x6405FA00E2EC94D4, 0xDEC681F9F4C31F31}, // 1e-187
{0xDE83BC408DD3DD04, 0x8B3C113C38F9F37E}, // 1e-186
{0x9624AB50B148D445, 0xAE0B158B4738705E}, // 1e-185
{0x3BADD624DD9B0957, 0xD98DDAEE19068C76}, // 1e-184
{0xE54CA5D70A80E5D6, 0x87F8A8D4CFA417C9}, // 1e-183
{0x5E9FCF4CCD211F4C, 0xA9F6D30A038D1DBC}, // 1e-182
{0x7647C3200069671F, 0xD47487CC8470652B}, // 1e-181
{0x29ECD9F40041E073, 0x84C8D4DFD2C63F3B}, // 1e-180
{0xF468107100525890, 0xA5FB0A17C777CF09}, // 1e-179
{0x7182148D4066EEB4, 0xCF79CC9DB955C2CC}, // 1e-178
{0xC6F14CD848405530, 0x81AC1FE293D599BF}, // 1e-177
{0xB8ADA00E5A506A7C, 0xA21727DB38CB002F}, // 1e-176
{0xA6D90811F0E4851C, 0xCA9CF1D206FDC03B}, // 1e-175
{0x908F4A166D1DA663, 0xFD442E4688BD304A}, // 1e-174
{0x9A598E4E043287FE, 0x9E4A9CEC15763E2E}, // 1e-173
{0x40EFF1E1853F29FD, 0xC5DD44271AD3CDBA}, // 1e-172
{0xD12BEE59E68EF47C, 0xF7549530E188C128}, // 1e-171
{0x82BB74F8301958CE, 0x9A94DD3E8CF578B9}, // 1e-170
{0xE36A52363C1FAF01, 0xC13A148E3032D6E7}, // 1e-169
{0xDC44E6C3CB279AC1, 0xF18899B1BC3F8CA1}, // 1e-168
{0x29AB103A5EF8C0B9, 0x96F5600F15A7B7E5}, // 1e-167
{0x7415D448F6B6F0E7, 0xBCB2B812DB11A5DE}, // 1e-166
{0x111B495B3464AD21, 0xEBDF661791D60F56}, // 1e-165
{0xCAB10DD900BEEC34, 0x936B9FCEBB25C995}, // 1e-164
{0x3D5D514F40EEA742, 0xB84687C269EF3BFB}, // 1e-163
{0x0CB4A5A3112A5112, 0xE65829B3046B0AFA}, // 1e-162
{0x47F0E785EABA72AB, 0x8FF71A0FE2C2E6DC}, // 1e-161
{0x59ED216765690F56, 0xB3F4E093DB73A093}, // 1e-160
{0x306869C13EC3532C, 0xE0F218B8D25088B8}, // 1e-159
{0x1E414218C73A13FB, 0x8C974F7383725573}, // 1e-158
{0xE5D1929EF90898FA, 0xAFBD2350644EEACF}, // 1e-157
{0xDF45F746B74ABF39, 0xDBAC6C247D62A583}, // 1e-156
{0x6B8BBA8C328EB783, 0x894BC396CE5DA772}, // 1e-155
{0x066EA92F3F326564, 0xAB9EB47C81F5114F}, // 1e-154
{0xC80A537B0EFEFEBD, 0xD686619BA27255A2}, // 1e-153
{0xBD06742CE95F5F36, 0x8613FD0145877585}, // 1e-152
{0x2C48113823B73704, 0xA798FC4196E952E7}, // 1e-151
{0xF75A15862CA504C5, 0xD17F3B51FCA3A7A0}, // 1e-150
{0x9A984D73DBE722FB, 0x82EF85133DE648C4}, // 1e-149
{0xC13E60D0D2E0EBBA, 0xA3AB66580D5FDAF5}, // 1e-148
{0x318DF905079926A8, 0xCC963FEE10B7D1B3}, // 1e-147
{0xFDF17746497F7052, 0xFFBBCFE994E5C61F}, // 1e-146
{0xFEB6EA8BEDEFA633, 0x9FD561F1FD0F9BD3}, // 1e-145
{0xFE64A52EE96B8FC0, 0xC7CABA6E7C5382C8}, // 1e-144
{0x3DFDCE7AA3C673B0, 0xF9BD690A1B68637B}, // 1e-143
{0x06BEA10CA65C084E, 0x9C1661A651213E2D}, // 1e-142
{0x486E494FCFF30A62, 0xC31BFA0FE5698DB8}, // 1e-141
{0x5A89DBA3C3EFCCFA, 0xF3E2F893DEC3F126}, // 1e-140
{0xF89629465A75E01C, 0x986DDB5C6B3A76B7}, // 1e-139
{0xF6BBB397F1135823, 0xBE89523386091465}, // 1e-138
{0x746AA07DED582E2C, 0xEE2BA6C0678B597F}, // 1e-137
{0xA8C2A44EB4571CDC, 0x94DB483840B717EF}, // 1e-136
{0x92F34D62616CE413, 0xBA121A4650E4DDEB}, // 1e-135
{0x77B020BAF9C81D17, 0xE896A0D7E51E1566}, // 1e-134
{0x0ACE1474DC1D122E, 0x915E2486EF32CD60}, // 1e-133
{0x0D819992132456BA, 0xB5B5ADA8AAFF80B8}, // 1e-132
{0x10E1FFF697ED6C69, 0xE3231912D5BF60E6}, // 1e-131
{0xCA8D3FFA1EF463C1, 0x8DF5EFABC5979C8F}, // 1e-130
{0xBD308FF8A6B17CB2, 0xB1736B96B6FD83B3}, // 1e-129
{0xAC7CB3F6D05DDBDE, 0xDDD0467C64BCE4A0}, // 1e-128
{0x6BCDF07A423AA96B, 0x8AA22C0DBEF60EE4}, // 1e-127
{0x86C16C98D2C953C6, 0xAD4AB7112EB3929D}, // 1e-126
{0xE871C7BF077BA8B7, 0xD89D64D57A607744}, // 1e-125
{0x11471CD764AD4972, 0x87625F056C7C4A8B}, // 1e-124
{0xD598E40D3DD89BCF, 0xA93AF6C6C79B5D2D}, // 1e-123
{0x4AFF1D108D4EC2C3, 0xD389B47879823479}, // 1e-122
{0xCEDF722A585139BA, 0x843610CB4BF160CB}, // 1e-121
{0xC2974EB4EE658828, 0xA54394FE1EEDB8FE}, // 1e-120
{0x733D226229FEEA32, 0xCE947A3DA6A9273E}, // 1e-119
{0x0806357D5A3F525F, 0x811CCC668829B887}, // 1e-118
{0xCA07C2DCB0CF26F7, 0xA163FF802A3426A8}, // 1e-117
{0xFC89B393DD02F0B5, 0xC9BCFF6034C13052}, // 1e-116
{0xBBAC2078D443ACE2, 0xFC2C3F3841F17C67}, // 1e-115
{0xD54B944B84AA4C0D, 0x9D9BA7832936EDC0}, // 1e-114
{0x0A9E795E65D4DF11, 0xC5029163F384A931}, // 1e-113
{0x4D4617B5FF4A16D5, 0xF64335BCF065D37D}, // 1e-112
{0x504BCED1BF8E4E45, 0x99EA0196163FA42E}, // 1e-111
{0xE45EC2862F71E1D6, 0xC06481FB9BCF8D39}, // 1e-110
{0x5D767327BB4E5A4C, 0xF07DA27A82C37088}, // 1e-109
{0x3A6A07F8D510F86F, 0x964E858C91BA2655}, // 1e-108
{0x890489F70A55368B, 0xBBE226EFB628AFEA}, // 1e-107
{0x2B45AC74CCEA842E, 0xEADAB0ABA3B2DBE5}, // 1e-106
{0x3B0B8BC90012929D, 0x92C8AE6B464FC96F}, // 1e-105
{0x09CE6EBB40173744, 0xB77ADA0617E3BBCB}, // 1e-104
{0xCC420A6A101D0515, 0xE55990879DDCAABD}, // 1e-103
{0x9FA946824A12232D, 0x8F57FA54C2A9EAB6}, // 1e-102
{0x47939822DC96ABF9, 0xB32DF8E9F3546564}, // 1e-101
{0x59787E2B93BC56F7, 0xDFF9772470297EBD}, // 1e-100
{0x57EB4EDB3C55B65A, 0x8BFBEA76C619EF36}, // 1e-99
{0xEDE622920B6B23F1, 0xAEFAE51477A06B03}, // 1e-98
{0xE95FAB368E45ECED, 0xDAB99E59958885C4}, // 1e-97
{0x11DBCB0218EBB414, 0x88B402F7FD75539B}, // 1e-96
{0xD652BDC29F26A119, 0xAAE103B5FCD2A881}, // 1e-95
{0x4BE76D3346F0495F, 0xD59944A37C0752A2}, // 1e-94
{0x6F70A4400C562DDB, 0x857FCAE62D8493A5}, // 1e-93
{0xCB4CCD500F6BB952, 0xA6DFBD9FB8E5B88E}, // 1e-92
{0x7E2000A41346A7A7, 0xD097AD07A71F26B2}, // 1e-91
{0x8ED400668C0C28C8, 0x825ECC24C873782F}, // 1e-90
{0x728900802F0F32FA, 0xA2F67F2DFA90563B}, // 1e-89
{0x4F2B40A03AD2FFB9, 0xCBB41EF979346BCA}, // 1e-88
{0xE2F610C84987BFA8, 0xFEA126B7D78186BC}, // 1e-87
{0x0DD9CA7D2DF4D7C9, 0x9F24B832E6B0F436}, // 1e-86
{0x91503D1C79720DBB, 0xC6EDE63FA05D3143}, // 1e-85
{0x75A44C6397CE912A, 0xF8A95FCF88747D94}, // 1e-84
{0xC986AFBE3EE11ABA, 0x9B69DBE1B548CE7C}, // 1e-83
{0xFBE85BADCE996168, 0xC24452DA229B021B}, // 1e-82
{0xFAE27299423FB9C3, 0xF2D56790AB41C2A2}, // 1e-81
{0xDCCD879FC967D41A, 0x97C560BA6B0919A5}, // 1e-80
{0x5400E987BBC1C920, 0xBDB6B8E905CB600F}, // 1e-79
{0x290123E9AAB23B68, 0xED246723473E3813}, // 1e-78
{0xF9A0B6720AAF6521, 0x9436C0760C86E30B}, // 1e-77
{0xF808E40E8D5B3E69, 0xB94470938FA89BCE}, // 1e-76
{0xB60B1D1230B20E04, 0xE7958CB87392C2C2}, // 1e-75
{0xB1C6F22B5E6F48C2, 0x90BD77F3483BB9B9}, // 1e-74
{0x1E38AEB6360B1AF3, 0xB4ECD5F01A4AA828}, // 1e-73
{0x25C6DA63C38DE1B0, 0xE2280B6C20DD5232}, // 1e-72
{0x579C487E5A38AD0E, 0x8D590723948A535F}, // 1e-71
{0x2D835A9DF0C6D851, 0xB0AF48EC79ACE837}, // 1e-70
{0xF8E431456CF88E65, 0xDCDB1B2798182244}, // 1e-69
{0x1B8E9ECB641B58FF, 0x8A08F0F8BF0F156B}, // 1e-68
{0xE272467E3D222F3F, 0xAC8B2D36EED2DAC5}, // 1e-67
{0x5B0ED81DCC6ABB0F, 0xD7ADF884AA879177}, // 1e-66
{0x98E947129FC2B4E9, 0x86CCBB52EA94BAEA}, // 1e-65
{0x3F2398D747B36224, 0xA87FEA27A539E9A5}, // 1e-64
{0x8EEC7F0D19A03AAD, 0xD29FE4B18E88640E}, // 1e-63
{0x1953CF68300424AC, 0x83A3EEEEF9153E89}, // 1e-62
{0x5FA8C3423C052DD7, 0xA48CEAAAB75A8E2B}, // 1e-61
{0x3792F412CB06794D, 0xCDB02555653131B6}, // 1e-60
{0xE2BBD88BBEE40BD0, 0x808E17555F3EBF11}, // 1e-59
{0x5B6ACEAEAE9D0EC4, 0xA0B19D2AB70E6ED6}, // 1e-58
{0xF245825A5A445275, 0xC8DE047564D20A8B}, // 1e-57
{0xEED6E2F0F0D56712, 0xFB158592BE068D2E}, // 1e-56
{0x55464DD69685606B, 0x9CED737BB6C4183D}, // 1e-55
{0xAA97E14C3C26B886, 0xC428D05AA4751E4C}, // 1e-54
{0xD53DD99F4B3066A8, 0xF53304714D9265DF}, // 1e-53
{0xE546A8038EFE4029, 0x993FE2C6D07B7FAB}, // 1e-52
{0xDE98520472BDD033, 0xBF8FDB78849A5F96}, // 1e-51
{0x963E66858F6D4440, 0xEF73D256A5C0F77C}, // 1e-50
{0xDDE7001379A44AA8, 0x95A8637627989AAD}, // 1e-49
{0x5560C018580D5D52, 0xBB127C53B17EC159}, // 1e-48
{0xAAB8F01E6E10B4A6, 0xE9D71B689DDE71AF}, // 1e-47
{0xCAB3961304CA70E8, 0x9226712162AB070D}, // 1e-46
{0x3D607B97C5FD0D22, 0xB6B00D69BB55C8D1}, // 1e-45
{0x8CB89A7DB77C506A, 0xE45C10C42A2B3B05}, // 1e-44
{0x77F3608E92ADB242, 0x8EB98A7A9A5B04E3}, // 1e-43
{0x55F038B237591ED3, 0xB267ED1940F1C61C}, // 1e-42
{0x6B6C46DEC52F6688, 0xDF01E85F912E37A3}, // 1e-41
{0x2323AC4B3B3DA015, 0x8B61313BBABCE2C6}, // 1e-40
{0xABEC975E0A0D081A, 0xAE397D8AA96C1B77}, // 1e-39
{0x96E7BD358C904A21, 0xD9C7DCED53C72255}, // 1e-38
{0x7E50D64177DA2E54, 0x881CEA14545C7575}, // 1e-37
{0xDDE50BD1D5D0B9E9, 0xAA242499697392D2}, // 1e-36
{0x955E4EC64B44E864, 0xD4AD2DBFC3D07787}, // 1e-35
{0xBD5AF13BEF0B113E, 0x84EC3C97DA624AB4}, // 1e-34
{0xECB1AD8AEACDD58E, 0xA6274BBDD0FADD61}, // 1e-33
{0x67DE18EDA5814AF2, 0xCFB11EAD453994BA}, // 1e-32
{0x80EACF948770CED7, 0x81CEB32C4B43FCF4}, // 1e-31
{0xA1258379A94D028D, 0xA2425FF75E14FC31}, // 1e-30
{0x096EE45813A04330, 0xCAD2F7F5359A3B3E}, // 1e-29
{0x8BCA9D6E188853FC, 0xFD87B5F28300CA0D}, // 1e-28
{0x775EA264CF55347D, 0x9E74D1B791E07E48}, // 1e-27
{0x95364AFE032A819D, 0xC612062576589DDA}, // 1e-26
{0x3A83DDBD83F52204, 0xF79687AED3EEC551}, // 1e-25
{0xC4926A9672793542, 0x9ABE14CD44753B52}, // 1e-24
{0x75B7053C0F178293, 0xC16D9A0095928A27}, // 1e-23
{0x5324C68B12DD6338, 0xF1C90080BAF72CB1}, // 1e-22
{0xD3F6FC16EBCA5E03, 0x971DA05074DA7BEE}, // 1e-21
{0x88F4BB1CA6BCF584, 0xBCE5086492111AEA}, // 1e-20
{0x2B31E9E3D06C32E5, 0xEC1E4A7DB69561A5}, // 1e-19
{0x3AFF322E62439FCF, 0x9392EE8E921D5D07}, // 1e-18
{0x09BEFEB9FAD487C2, 0xB877AA3236A4B449}, // 1e-17
{0x4C2EBE687989A9B3, 0xE69594BEC44DE15B}, // 1e-16
{0x0F9D37014BF60A10, 0x901D7CF73AB0ACD9}, // 1e-15
{0x538484C19EF38C94, 0xB424DC35095CD80F}, // 1e-14
{0x2865A5F206B06FB9, 0xE12E13424BB40E13}, // 1e-13
{0xF93F87B7442E45D3, 0x8CBCCC096F5088CB}, // 1e-12
{0xF78F69A51539D748, 0xAFEBFF0BCB24AAFE}, // 1e-11
{0xB573440E5A884D1B, 0xDBE6FECEBDEDD5BE}, // 1e-10
{0x31680A88F8953030, 0x89705F4136B4A597}, // 1e-9
{0xFDC20D2B36BA7C3D, 0xABCC77118461CEFC}, // 1e-8
{0x3D32907604691B4C, 0xD6BF94D5E57A42BC}, // 1e-7
{0xA63F9A49C2C1B10F, 0x8637BD05AF6C69B5}, // 1e-6
{0x0FCF80DC33721D53, 0xA7C5AC471B478423}, // 1e-5
{0xD3C36113404EA4A8, 0xD1B71758E219652B}, // 1e-4
{0x645A1CAC083126E9, 0x83126E978D4FDF3B}, // 1e-3
{0x3D70A3D70A3D70A3, 0xA3D70A3D70A3D70A}, // 1e-2
{0xCCCCCCCCCCCCCCCC, 0xCCCCCCCCCCCCCCCC}, // 1e-1
{0x0000000000000000, 0x8000000000000000}, // 1e0
{0x0000000000000000, 0xA000000000000000}, // 1e1
{0x0000000000000000, 0xC800000000000000}, // 1e2
{0x0000000000000000, 0xFA00000000000000}, // 1e3
{0x0000000000000000, 0x9C40000000000000}, // 1e4
{0x0000000000000000, 0xC350000000000000}, // 1e5
{0x0000000000000000, 0xF424000000000000}, // 1e6
{0x0000000000000000, 0x9896800000000000}, // 1e7
{0x0000000000000000, 0xBEBC200000000000}, // 1e8
{0x0000000000000000, 0xEE6B280000000000}, // 1e9
{0x0000000000000000, 0x9502F90000000000}, // 1e10
{0x0000000000000000, 0xBA43B74000000000}, // 1e11
{0x0000000000000000, 0xE8D4A51000000000}, // 1e12
{0x0000000000000000, 0x9184E72A00000000}, // 1e13
{0x0000000000000000, 0xB5E620F480000000}, // 1e14
{0x0000000000000000, 0xE35FA931A0000000}, // 1e15
{0x0000000000000000, 0x8E1BC9BF04000000}, // 1e16
{0x0000000000000000, 0xB1A2BC2EC5000000}, // 1e17
{0x0000000000000000, 0xDE0B6B3A76400000}, // 1e18
{0x0000000000000000, 0x8AC7230489E80000}, // 1e19
{0x0000000000000000, 0xAD78EBC5AC620000}, // 1e20
{0x0000000000000000, 0xD8D726B7177A8000}, // 1e21
{0x0000000000000000, 0x878678326EAC9000}, // 1e22
{0x0000000000000000, 0xA968163F0A57B400}, // 1e23
{0x0000000000000000, 0xD3C21BCECCEDA100}, // 1e24
{0x0000000000000000, 0x84595161401484A0}, // 1e25
{0x0000000000000000, 0xA56FA5B99019A5C8}, // 1e26
{0x0000000000000000, 0xCECB8F27F4200F3A}, // 1e27
{0x4000000000000000, 0x813F3978F8940984}, // 1e28
{0x5000000000000000, 0xA18F07D736B90BE5}, // 1e29
{0xA400000000000000, 0xC9F2C9CD04674EDE}, // 1e30
{0x4D00000000000000, 0xFC6F7C4045812296}, // 1e31
{0xF020000000000000, 0x9DC5ADA82B70B59D}, // 1e32
{0x6C28000000000000, 0xC5371912364CE305}, // 1e33
{0xC732000000000000, 0xF684DF56C3E01BC6}, // 1e34
{0x3C7F400000000000, 0x9A130B963A6C115C}, // 1e35
{0x4B9F100000000000, 0xC097CE7BC90715B3}, // 1e36
{0x1E86D40000000000, 0xF0BDC21ABB48DB20}, // 1e37
{0x1314448000000000, 0x96769950B50D88F4}, // 1e38
{0x17D955A000000000, 0xBC143FA4E250EB31}, // 1e39
{0x5DCFAB0800000000, 0xEB194F8E1AE525FD}, // 1e40
{0x5AA1CAE500000000, 0x92EFD1B8D0CF37BE}, // 1e41
{0xF14A3D9E40000000, 0xB7ABC627050305AD}, // 1e42
{0x6D9CCD05D0000000, 0xE596B7B0C643C719}, // 1e43
{0xE4820023A2000000, 0x8F7E32CE7BEA5C6F}, // 1e44
{0xDDA2802C8A800000, 0xB35DBF821AE4F38B}, // 1e45
{0xD50B2037AD200000, 0xE0352F62A19E306E}, // 1e46
{0x4526F422CC340000, 0x8C213D9DA502DE45}, // 1e47
{0x9670B12B7F410000, 0xAF298D050E4395D6}, // 1e48
{0x3C0CDD765F114000, 0xDAF3F04651D47B4C}, // 1e49
{0xA5880A69FB6AC800, 0x88D8762BF324CD0F}, // 1e50
{0x8EEA0D047A457A00, 0xAB0E93B6EFEE0053}, // 1e51
{0x72A4904598D6D880, 0xD5D238A4ABE98068}, // 1e52
{0x47A6DA2B7F864750, 0x85A36366EB71F041}, // 1e53
{0x999090B65F67D924, 0xA70C3C40A64E6C51}, // 1e54
{0xFFF4B4E3F741CF6D, 0xD0CF4B50CFE20765}, // 1e55
{0xBFF8F10E7A8921A4, 0x82818F1281ED449F}, // 1e56
{0xAFF72D52192B6A0D, 0xA321F2D7226895C7}, // 1e57
{0x9BF4F8A69F764490, 0xCBEA6F8CEB02BB39}, // 1e58
{0x02F236D04753D5B4, 0xFEE50B7025C36A08}, // 1e59
{0x01D762422C946590, 0x9F4F2726179A2245}, // 1e60
{0x424D3AD2B7B97EF5, 0xC722F0EF9D80AAD6}, // 1e61
{0xD2E0898765A7DEB2, 0xF8EBAD2B84E0D58B}, // 1e62
{0x63CC55F49F88EB2F, 0x9B934C3B330C8577}, // 1e63
{0x3CBF6B71C76B25FB, 0xC2781F49FFCFA6D5}, // 1e64
{0x8BEF464E3945EF7A, 0xF316271C7FC3908A}, // 1e65
{0x97758BF0E3CBB5AC, 0x97EDD871CFDA3A56}, // 1e66
{0x3D52EEED1CBEA317, 0xBDE94E8E43D0C8EC}, // 1e67
{0x4CA7AAA863EE4BDD, 0xED63A231D4C4FB27}, // 1e68
{0x8FE8CAA93E74EF6A, 0x945E455F24FB1CF8}, // 1e69
{0xB3E2FD538E122B44, 0xB975D6B6EE39E436}, // 1e70
{0x60DBBCA87196B616, 0xE7D34C64A9C85D44}, // 1e71
{0xBC8955E946FE31CD, 0x90E40FBEEA1D3A4A}, // 1e72
{0x6BABAB6398BDBE41, 0xB51D13AEA4A488DD}, // 1e73
{0xC696963C7EED2DD1, 0xE264589A4DCDAB14}, // 1e74
{0xFC1E1DE5CF543CA2, 0x8D7EB76070A08AEC}, // 1e75
{0x3B25A55F43294BCB, 0xB0DE65388CC8ADA8}, // 1e76
{0x49EF0EB713F39EBE, 0xDD15FE86AFFAD912}, // 1e77
{0x6E3569326C784337, 0x8A2DBF142DFCC7AB}, // 1e78
{0x49C2C37F07965404, 0xACB92ED9397BF996}, // 1e79
{0xDC33745EC97BE906, 0xD7E77A8F87DAF7FB}, // 1e80
{0x69A028BB3DED71A3, 0x86F0AC99B4E8DAFD}, // 1e81
{0xC40832EA0D68CE0C, 0xA8ACD7C0222311BC}, // 1e82
{0xF50A3FA490C30190, 0xD2D80DB02AABD62B}, // 1e83
{0x792667C6DA79E0FA, 0x83C7088E1AAB65DB}, // 1e84
{0x577001B891185938, 0xA4B8CAB1A1563F52}, // 1e85
{0xED4C0226B55E6F86, 0xCDE6FD5E09ABCF26}, // 1e86
{0x544F8158315B05B4, 0x80B05E5AC60B6178}, // 1e87
{0x696361AE3DB1C721, 0xA0DC75F1778E39D6}, // 1e88
{0x03BC3A19CD1E38E9, 0xC913936DD571C84C}, // 1e89
{0x04AB48A04065C723, 0xFB5878494ACE3A5F}, // 1e90
{0x62EB0D64283F9C76, 0x9D174B2DCEC0E47B}, // 1e91
{0x3BA5D0BD324F8394, 0xC45D1DF942711D9A}, // 1e92
{0xCA8F44EC7EE36479, 0xF5746577930D6500}, // 1e93
{0x7E998B13CF4E1ECB, 0x9968BF6ABBE85F20}, // 1e94
{0x9E3FEDD8C321A67E, 0xBFC2EF456AE276E8}, // 1e95
{0xC5CFE94EF3EA101E, 0xEFB3AB16C59B14A2}, // 1e96
{0xBBA1F1D158724A12, 0x95D04AEE3B80ECE5}, // 1e97
{0x2A8A6E45AE8EDC97, 0xBB445DA9CA61281F}, // 1e98
{0xF52D09D71A3293BD, 0xEA1575143CF97226}, // 1e99
{0x593C2626705F9C56, 0x924D692CA61BE758}, // 1e100
{0x6F8B2FB00C77836C, 0xB6E0C377CFA2E12E}, // 1e101
{0x0B6DFB9C0F956447, 0xE498F455C38B997A}, // 1e102
{0x4724BD4189BD5EAC, 0x8EDF98B59A373FEC}, // 1e103
{0x58EDEC91EC2CB657, 0xB2977EE300C50FE7}, // 1e104
{0x2F2967B66737E3ED, 0xDF3D5E9BC0F653E1}, // 1e105
{0xBD79E0D20082EE74, 0x8B865B215899F46C}, // 1e106
{0xECD8590680A3AA11, 0xAE67F1E9AEC07187}, // 1e107
{0xE80E6F4820CC9495, 0xDA01EE641A708DE9}, // 1e108
{0x3109058D147FDCDD, 0x884134FE908658B2}, // 1e109
{0xBD4B46F0599FD415, 0xAA51823E34A7EEDE}, // 1e110
{0x6C9E18AC7007C91A, 0xD4E5E2CDC1D1EA96}, // 1e111
{0x03E2CF6BC604DDB0, 0x850FADC09923329E}, // 1e112
{0x84DB8346B786151C, 0xA6539930BF6BFF45}, // 1e113
{0xE612641865679A63, 0xCFE87F7CEF46FF16}, // 1e114
{0x4FCB7E8F3F60C07E, 0x81F14FAE158C5F6E}, // 1e115
{0xE3BE5E330F38F09D, 0xA26DA3999AEF7749}, // 1e116
{0x5CADF5BFD3072CC5, 0xCB090C8001AB551C}, // 1e117
{0x73D9732FC7C8F7F6, 0xFDCB4FA002162A63}, // 1e118
{0x2867E7FDDCDD9AFA, 0x9E9F11C4014DDA7E}, // 1e119
{0xB281E1FD541501B8, 0xC646D63501A1511D}, // 1e120
{0x1F225A7CA91A4226, 0xF7D88BC24209A565}, // 1e121
{0x3375788DE9B06958, 0x9AE757596946075F}, // 1e122
{0x0052D6B1641C83AE, 0xC1A12D2FC3978937}, // 1e123
{0xC0678C5DBD23A49A, 0xF209787BB47D6B84}, // 1e124
{0xF840B7BA963646E0, 0x9745EB4D50CE6332}, // 1e125
{0xB650E5A93BC3D898, 0xBD176620A501FBFF}, // 1e126
{0xA3E51F138AB4CEBE, 0xEC5D3FA8CE427AFF}, // 1e127
{0xC66F336C36B10137, 0x93BA47C980E98CDF}, // 1e128
{0xB80B0047445D4184, 0xB8A8D9BBE123F017}, // 1e129
{0xA60DC059157491E5, 0xE6D3102AD96CEC1D}, // 1e130
{0x87C89837AD68DB2F, 0x9043EA1AC7E41392}, // 1e131
{0x29BABE4598C311FB, 0xB454E4A179DD1877}, // 1e132
{0xF4296DD6FEF3D67A, 0xE16A1DC9D8545E94}, // 1e133
{0x1899E4A65F58660C, 0x8CE2529E2734BB1D}, // 1e134
{0x5EC05DCFF72E7F8F, 0xB01AE745B101E9E4}, // 1e135
{0x76707543F4FA1F73, 0xDC21A1171D42645D}, // 1e136
{0x6A06494A791C53A8, 0x899504AE72497EBA}, // 1e137
{0x0487DB9D17636892, 0xABFA45DA0EDBDE69}, // 1e138
{0x45A9D2845D3C42B6, 0xD6F8D7509292D603}, // 1e139
{0x0B8A2392BA45A9B2, 0x865B86925B9BC5C2}, // 1e140
{0x8E6CAC7768D7141E, 0xA7F26836F282B732}, // 1e141
{0x3207D795430CD926, 0xD1EF0244AF2364FF}, // 1e142
{0x7F44E6BD49E807B8, 0x8335616AED761F1F}, // 1e143
{0x5F16206C9C6209A6, 0xA402B9C5A8D3A6E7}, // 1e144
{0x36DBA887C37A8C0F, 0xCD036837130890A1}, // 1e145
{0xC2494954DA2C9789, 0x802221226BE55A64}, // 1e146
{0xF2DB9BAA10B7BD6C, 0xA02AA96B06DEB0FD}, // 1e147
{0x6F92829494E5ACC7, 0xC83553C5C8965D3D}, // 1e148
{0xCB772339BA1F17F9, 0xFA42A8B73ABBF48C}, // 1e149
{0xFF2A760414536EFB, 0x9C69A97284B578D7}, // 1e150
{0xFEF5138519684ABA, 0xC38413CF25E2D70D}, // 1e151
{0x7EB258665FC25D69, 0xF46518C2EF5B8CD1}, // 1e152
{0xEF2F773FFBD97A61, 0x98BF2F79D5993802}, // 1e153
{0xAAFB550FFACFD8FA, 0xBEEEFB584AFF8603}, // 1e154
{0x95BA2A53F983CF38, 0xEEAABA2E5DBF6784}, // 1e155
{0xDD945A747BF26183, 0x952AB45CFA97A0B2}, // 1e156
{0x94F971119AEEF9E4, 0xBA756174393D88DF}, // 1e157
{0x7A37CD5601AAB85D, 0xE912B9D1478CEB17}, // 1e158
{0xAC62E055C10AB33A, 0x91ABB422CCB812EE}, // 1e159
{0x577B986B314D6009, 0xB616A12B7FE617AA}, // 1e160
{0xED5A7E85FDA0B80B, 0xE39C49765FDF9D94}, // 1e161
{0x14588F13BE847307, 0x8E41ADE9FBEBC27D}, // 1e162
{0x596EB2D8AE258FC8, 0xB1D219647AE6B31C}, // 1e163
{0x6FCA5F8ED9AEF3BB, 0xDE469FBD99A05FE3}, // 1e164
{0x25DE7BB9480D5854, 0x8AEC23D680043BEE}, // 1e165
{0xAF561AA79A10AE6A, 0xADA72CCC20054AE9}, // 1e166
{0x1B2BA1518094DA04, 0xD910F7FF28069DA4}, // 1e167
{0x90FB44D2F05D0842, 0x87AA9AFF79042286}, // 1e168
{0x353A1607AC744A53, 0xA99541BF57452B28}, // 1e169
{0x42889B8997915CE8, 0xD3FA922F2D1675F2}, // 1e170
{0x69956135FEBADA11, 0x847C9B5D7C2E09B7}, // 1e171
{0x43FAB9837E699095, 0xA59BC234DB398C25}, // 1e172
{0x94F967E45E03F4BB, 0xCF02B2C21207EF2E}, // 1e173
{0x1D1BE0EEBAC278F5, 0x8161AFB94B44F57D}, // 1e174
{0x6462D92A69731732, 0xA1BA1BA79E1632DC}, // 1e175
{0x7D7B8F7503CFDCFE, 0xCA28A291859BBF93}, // 1e176
{0x5CDA735244C3D43E, 0xFCB2CB35E702AF78}, // 1e177
{0x3A0888136AFA64A7, 0x9DEFBF01B061ADAB}, // 1e178
{0x088AAA1845B8FDD0, 0xC56BAEC21C7A1916}, // 1e179
{0x8AAD549E57273D45, 0xF6C69A72A3989F5B}, // 1e180
{0x36AC54E2F678864B, 0x9A3C2087A63F6399}, // 1e181
{0x84576A1BB416A7DD, 0xC0CB28A98FCF3C7F}, // 1e182
{0x656D44A2A11C51D5, 0xF0FDF2D3F3C30B9F}, // 1e183
{0x9F644AE5A4B1B325, 0x969EB7C47859E743}, // 1e184
{0x873D5D9F0DDE1FEE, 0xBC4665B596706114}, // 1e185
{0xA90CB506D155A7EA, 0xEB57FF22FC0C7959}, // 1e186
{0x09A7F12442D588F2, 0x9316FF75DD87CBD8}, // 1e187
{0x0C11ED6D538AEB2F, 0xB7DCBF5354E9BECE}, // 1e188
{0x8F1668C8A86DA5FA, 0xE5D3EF282A242E81}, // 1e189
{0xF96E017D694487BC, 0x8FA475791A569D10}, // 1e190
{0x37C981DCC395A9AC, 0xB38D92D760EC4455}, // 1e191
{0x85BBE253F47B1417, 0xE070F78D3927556A}, // 1e192
{0x93956D7478CCEC8E, 0x8C469AB843B89562}, // 1e193
{0x387AC8D1970027B2, 0xAF58416654A6BABB}, // 1e194
{0x06997B05FCC0319E, 0xDB2E51BFE9D0696A}, // 1e195
{0x441FECE3BDF81F03, 0x88FCF317F22241E2}, // 1e196
{0xD527E81CAD7626C3, 0xAB3C2FDDEEAAD25A}, // 1e197
{0x8A71E223D8D3B074, 0xD60B3BD56A5586F1}, // 1e198
{0xF6872D5667844E49, 0x85C7056562757456}, // 1e199
{0xB428F8AC016561DB, 0xA738C6BEBB12D16C}, // 1e200
{0xE13336D701BEBA52, 0xD106F86E69D785C7}, // 1e201
{0xECC0024661173473, 0x82A45B450226B39C}, // 1e202
{0x27F002D7F95D0190, 0xA34D721642B06084}, // 1e203
{0x31EC038DF7B441F4, 0xCC20CE9BD35C78A5}, // 1e204
{0x7E67047175A15271, 0xFF290242C83396CE}, // 1e205
{0x0F0062C6E984D386, 0x9F79A169BD203E41}, // 1e206
{0x52C07B78A3E60868, 0xC75809C42C684DD1}, // 1e207
{0xA7709A56CCDF8A82, 0xF92E0C3537826145}, // 1e208
{0x88A66076400BB691, 0x9BBCC7A142B17CCB}, // 1e209
{0x6ACFF893D00EA435, 0xC2ABF989935DDBFE}, // 1e210
{0x0583F6B8C4124D43, 0xF356F7EBF83552FE}, // 1e211
{0xC3727A337A8B704A, 0x98165AF37B2153DE}, // 1e212
{0x744F18C0592E4C5C, 0xBE1BF1B059E9A8D6}, // 1e213
{0x1162DEF06F79DF73, 0xEDA2EE1C7064130C}, // 1e214
{0x8ADDCB5645AC2BA8, 0x9485D4D1C63E8BE7}, // 1e215
{0x6D953E2BD7173692, 0xB9A74A0637CE2EE1}, // 1e216
{0xC8FA8DB6CCDD0437, 0xE8111C87C5C1BA99}, // 1e217
{0x1D9C9892400A22A2, 0x910AB1D4DB9914A0}, // 1e218
{0x2503BEB6D00CAB4B, 0xB54D5E4A127F59C8}, // 1e219
{0x2E44AE64840FD61D, 0xE2A0B5DC971F303A}, // 1e220
{0x5CEAECFED289E5D2, 0x8DA471A9DE737E24}, // 1e221
{0x7425A83E872C5F47, 0xB10D8E1456105DAD}, // 1e222
{0xD12F124E28F77719, 0xDD50F1996B947518}, // 1e223
{0x82BD6B70D99AAA6F, 0x8A5296FFE33CC92F}, // 1e224
{0x636CC64D1001550B, 0xACE73CBFDC0BFB7B}, // 1e225
{0x3C47F7E05401AA4E, 0xD8210BEFD30EFA5A}, // 1e226
{0x65ACFAEC34810A71, 0x8714A775E3E95C78}, // 1e227
{0x7F1839A741A14D0D, 0xA8D9D1535CE3B396}, // 1e228
{0x1EDE48111209A050, 0xD31045A8341CA07C}, // 1e229
{0x934AED0AAB460432, 0x83EA2B892091E44D}, // 1e230
{0xF81DA84D5617853F, 0xA4E4B66B68B65D60}, // 1e231
{0x36251260AB9D668E, 0xCE1DE40642E3F4B9}, // 1e232
{0xC1D72B7C6B426019, 0x80D2AE83E9CE78F3}, // 1e233
{0xB24CF65B8612F81F, 0xA1075A24E4421730}, // 1e234
{0xDEE033F26797B627, 0xC94930AE1D529CFC}, // 1e235
{0x169840EF017DA3B1, 0xFB9B7CD9A4A7443C}, // 1e236
{0x8E1F289560EE864E, 0x9D412E0806E88AA5}, // 1e237
{0xF1A6F2BAB92A27E2, 0xC491798A08A2AD4E}, // 1e238
{0xAE10AF696774B1DB, 0xF5B5D7EC8ACB58A2}, // 1e239
{0xACCA6DA1E0A8EF29, 0x9991A6F3D6BF1765}, // 1e240
{0x17FD090A58D32AF3, 0xBFF610B0CC6EDD3F}, // 1e241
{0xDDFC4B4CEF07F5B0, 0xEFF394DCFF8A948E}, // 1e242
{0x4ABDAF101564F98E, 0x95F83D0A1FB69CD9}, // 1e243
{0x9D6D1AD41ABE37F1, 0xBB764C4CA7A4440F}, // 1e244
{0x84C86189216DC5ED, 0xEA53DF5FD18D5513}, // 1e245
{0x32FD3CF5B4E49BB4, 0x92746B9BE2F8552C}, // 1e246
{0x3FBC8C33221DC2A1, 0xB7118682DBB66A77}, // 1e247
{0x0FABAF3FEAA5334A, 0xE4D5E82392A40515}, // 1e248
{0x29CB4D87F2A7400E, 0x8F05B1163BA6832D}, // 1e249
{0x743E20E9EF511012, 0xB2C71D5BCA9023F8}, // 1e250
{0x914DA9246B255416, 0xDF78E4B2BD342CF6}, // 1e251
{0x1AD089B6C2F7548E, 0x8BAB8EEFB6409C1A}, // 1e252
{0xA184AC2473B529B1, 0xAE9672ABA3D0C320}, // 1e253
{0xC9E5D72D90A2741E, 0xDA3C0F568CC4F3E8}, // 1e254
{0x7E2FA67C7A658892, 0x8865899617FB1871}, // 1e255
{0xDDBB901B98FEEAB7, 0xAA7EEBFB9DF9DE8D}, // 1e256
{0x552A74227F3EA565, 0xD51EA6FA85785631}, // 1e257
{0xD53A88958F87275F, 0x8533285C936B35DE}, // 1e258
{0x8A892ABAF368F137, 0xA67FF273B8460356}, // 1e259
{0x2D2B7569B0432D85, 0xD01FEF10A657842C}, // 1e260
{0x9C3B29620E29FC73, 0x8213F56A67F6B29B}, // 1e261
{0x8349F3BA91B47B8F, 0xA298F2C501F45F42}, // 1e262
{0x241C70A936219A73, 0xCB3F2F7642717713}, // 1e263
{0xED238CD383AA0110, 0xFE0EFB53D30DD4D7}, // 1e264
{0xF4363804324A40AA, 0x9EC95D1463E8A506}, // 1e265
{0xB143C6053EDCD0D5, 0xC67BB4597CE2CE48}, // 1e266
{0xDD94B7868E94050A, 0xF81AA16FDC1B81DA}, // 1e267
{0xCA7CF2B4191C8326, 0x9B10A4E5E9913128}, // 1e268
{0xFD1C2F611F63A3F0, 0xC1D4CE1F63F57D72}, // 1e269
{0xBC633B39673C8CEC, 0xF24A01A73CF2DCCF}, // 1e270
{0xD5BE0503E085D813, 0x976E41088617CA01}, // 1e271
{0x4B2D8644D8A74E18, 0xBD49D14AA79DBC82}, // 1e272
{0xDDF8E7D60ED1219E, 0xEC9C459D51852BA2}, // 1e273
{0xCABB90E5C942B503, 0x93E1AB8252F33B45}, // 1e274
{0x3D6A751F3B936243, 0xB8DA1662E7B00A17}, // 1e275
{0x0CC512670A783AD4, 0xE7109BFBA19C0C9D}, // 1e276
{0x27FB2B80668B24C5, 0x906A617D450187E2}, // 1e277
{0xB1F9F660802DEDF6, 0xB484F9DC9641E9DA}, // 1e278
{0x5E7873F8A0396973, 0xE1A63853BBD26451}, // 1e279
{0xDB0B487B6423E1E8, 0x8D07E33455637EB2}, // 1e280
{0x91CE1A9A3D2CDA62, 0xB049DC016ABC5E5F}, // 1e281
{0x7641A140CC7810FB, 0xDC5C5301C56B75F7}, // 1e282
{0xA9E904C87FCB0A9D, 0x89B9B3E11B6329BA}, // 1e283
{0x546345FA9FBDCD44, 0xAC2820D9623BF429}, // 1e284
{0xA97C177947AD4095, 0xD732290FBACAF133}, // 1e285
{0x49ED8EABCCCC485D, 0x867F59A9D4BED6C0}, // 1e286
{0x5C68F256BFFF5A74, 0xA81F301449EE8C70}, // 1e287
{0x73832EEC6FFF3111, 0xD226FC195C6A2F8C}, // 1e288
{0xC831FD53C5FF7EAB, 0x83585D8FD9C25DB7}, // 1e289
{0xBA3E7CA8B77F5E55, 0xA42E74F3D032F525}, // 1e290
{0x28CE1BD2E55F35EB, 0xCD3A1230C43FB26F}, // 1e291
{0x7980D163CF5B81B3, 0x80444B5E7AA7CF85}, // 1e292
{0xD7E105BCC332621F, 0xA0555E361951C366}, // 1e293
{0x8DD9472BF3FEFAA7, 0xC86AB5C39FA63440}, // 1e294
{0xB14F98F6F0FEB951, 0xFA856334878FC150}, // 1e295
{0x6ED1BF9A569F33D3, 0x9C935E00D4B9D8D2}, // 1e296
{0x0A862F80EC4700C8, 0xC3B8358109E84F07}, // 1e297
{0xCD27BB612758C0FA, 0xF4A642E14C6262C8}, // 1e298
{0x8038D51CB897789C, 0x98E7E9CCCFBD7DBD}, // 1e299
{0xE0470A63E6BD56C3, 0xBF21E44003ACDD2C}, // 1e300
{0x1858CCFCE06CAC74, 0xEEEA5D5004981478}, // 1e301
{0x0F37801E0C43EBC8, 0x95527A5202DF0CCB}, // 1e302
{0xD30560258F54E6BA, 0xBAA718E68396CFFD}, // 1e303
{0x47C6B82EF32A2069, 0xE950DF20247C83FD}, // 1e304
{0x4CDC331D57FA5441, 0x91D28B7416CDD27E}, // 1e305
{0xE0133FE4ADF8E952, 0xB6472E511C81471D}, // 1e306
{0x58180FDDD97723A6, 0xE3D8F9E563A198E5}, // 1e307
{0x570F09EAA7EA7648, 0x8E679C2F5E44FF8F}, // 1e308
{0x2CD2CC6551E513DA, 0xB201833B35D63F73}, // 1e309
{0xF8077F7EA65E58D1, 0xDE81E40A034BCF4F}, // 1e310
{0xFB04AFAF27FAF782, 0x8B112E86420F6191}, // 1e311
{0x79C5DB9AF1F9B563, 0xADD57A27D29339F6}, // 1e312
{0x18375281AE7822BC, 0xD94AD8B1C7380874}, // 1e313
{0x8F2293910D0B15B5, 0x87CEC76F1C830548}, // 1e314
{0xB2EB3875504DDB22, 0xA9C2794AE3A3C69A}, // 1e315
{0x5FA60692A46151EB, 0xD433179D9C8CB841}, // 1e316
{0xDBC7C41BA6BCD333, 0x849FEEC281D7F328}, // 1e317
{0x12B9B522906C0800, 0xA5C7EA73224DEFF3}, // 1e318
{0xD768226B34870A00, 0xCF39E50FEAE16BEF}, // 1e319
{0xE6A1158300D46640, 0x81842F29F2CCE375}, // 1e320
{0x60495AE3C1097FD0, 0xA1E53AF46F801C53}, // 1e321
{0x385BB19CB14BDFC4, 0xCA5E89B18B602368}, // 1e322
{0x46729E03DD9ED7B5, 0xFCF62C1DEE382C42}, // 1e323
{0x6C07A2C26A8346D1, 0x9E19DB92B4E31BA9}, // 1e324
{0xC7098B7305241885, 0xC5A05277621BE293}, // 1e325
{0xB8CBEE4FC66D1EA7, 0xF70867153AA2DB38}, // 1e326
{0x737F74F1DC043328, 0x9A65406D44A5C903}, // 1e327
{0x505F522E53053FF2, 0xC0FE908895CF3B44}, // 1e328
{0x647726B9E7C68FEF, 0xF13E34AABB430A15}, // 1e329
{0x5ECA783430DC19F5, 0x96C6E0EAB509E64D}, // 1e330
{0xB67D16413D132072, 0xBC789925624C5FE0}, // 1e331
{0xE41C5BD18C57E88F, 0xEB96BF6EBADF77D8}, // 1e332
{0x8E91B962F7B6F159, 0x933E37A534CBAAE7}, // 1e333
{0x723627BBB5A4ADB0, 0xB80DC58E81FE95A1}, // 1e334
{0xCEC3B1AAA30DD91C, 0xE61136F2227E3B09}, // 1e335
{0x213A4F0AA5E8A7B1, 0x8FCAC257558EE4E6}, // 1e336
{0xA988E2CD4F62D19D, 0xB3BD72ED2AF29E1F}, // 1e337
{0x93EB1B80A33B8605, 0xE0ACCFA875AF45A7}, // 1e338
{0xBC72F130660533C3, 0x8C6C01C9498D8B88}, // 1e339
{0xEB8FAD7C7F8680B4, 0xAF87023B9BF0EE6A}, // 1e340
{0xA67398DB9F6820E1, 0xDB68C2CA82ED2A05}, // 1e341
{0x88083F8943A1148C, 0x892179BE91D43A43}, // 1e342
{0x6A0A4F6B948959B0, 0xAB69D82E364948D4}, // 1e343
{0x848CE34679ABB01C, 0xD6444E39C3DB9B09}, // 1e344
{0xF2D80E0C0C0B4E11, 0x85EAB0E41A6940E5}, // 1e345
{0x6F8E118F0F0E2195, 0xA7655D1D2103911F}, // 1e346
{0x4B7195F2D2D1A9FB, 0xD13EB46469447567}, // 1e347
}

View file

@ -4,7 +4,27 @@
package strconv package strconv
type Uint128 = uint128
var ( var (
BitSizeError = bitSizeError BaseError = baseError
BaseError = baseError BitSizeError = bitSizeError
MulLog10_2 = mulLog10_2
MulLog2_10 = mulLog2_10
ParseFloatPrefix = parseFloatPrefix
Pow10 = pow10
Umul128 = umul128
Umul192 = umul192
) )
func NewDecimal(i uint64) *decimal {
d := new(decimal)
d.Assign(i)
return d
}
func SetOptimize(b bool) bool {
old := optimize
optimize = b
return old
}

View file

@ -12,15 +12,25 @@ package strconv
import "math" import "math"
// TODO: move elsewhere?
type floatInfo struct { type floatInfo struct {
mantbits uint mantbits uint
expbits uint expbits uint
bias int bias int
} }
var float32info = floatInfo{23, 8, -127} const (
var float64info = floatInfo{52, 11, -1023} float32MantBits = 23
float32ExpBits = 8
float32Bias = -127
float64MantBits = 52
float64ExpBits = 11
float64Bias = -1023
)
var (
float32info = floatInfo{float32MantBits, float32ExpBits, float32Bias}
float64info = floatInfo{float64MantBits, float64ExpBits, float64Bias}
)
// FormatFloat converts the floating-point number f to a string, // FormatFloat converts the floating-point number f to a string,
// according to the format fmt and precision prec. It rounds the // according to the format fmt and precision prec. It rounds the

View file

@ -40,8 +40,8 @@ func ryuFtoaFixed32(d *decimalSlice, mant uint32, exp int, prec int) {
// mant*(2^e2)*(10^q) >= 10^(prec-1) // mant*(2^e2)*(10^q) >= 10^(prec-1)
// Because mant >= 2^24, it is enough to choose: // Because mant >= 2^24, it is enough to choose:
// 2^(e2+24) >= 10^(-q+prec-1) // 2^(e2+24) >= 10^(-q+prec-1)
// or q = -mulByLog2Log10(e2+24) + prec - 1 // or q = -mulLog10_2(e2+24) + prec - 1
q := -mulByLog2Log10(e2+24) + prec - 1 q := -mulLog10_2(e2+24) + prec - 1
// Now compute mant*(2^e2)*(10^q). // Now compute mant*(2^e2)*(10^q).
// Is it an exact computation? // Is it an exact computation?
@ -107,11 +107,11 @@ func ryuFtoaFixed64(d *decimalSlice, mant uint64, exp int, prec int) {
// mant*(2^e2)*(10^q) >= 10^(prec-1) // mant*(2^e2)*(10^q) >= 10^(prec-1)
// Because mant >= 2^54, it is enough to choose: // Because mant >= 2^54, it is enough to choose:
// 2^(e2+54) >= 10^(-q+prec-1) // 2^(e2+54) >= 10^(-q+prec-1)
// or q = -mulByLog2Log10(e2+54) + prec - 1 // or q = -mulLog10_2(e2+54) + prec - 1
// //
// The minimal required exponent is -mulByLog2Log10(1025)+18 = -291 // The minimal required exponent is -mulLog10_2(1025)+18 = -291
// The maximal required exponent is mulByLog2Log10(1074)+18 = 342 // The maximal required exponent is mulLog10_2(1074)+18 = 342
q := -mulByLog2Log10(e2+54) + prec - 1 q := -mulLog10_2(e2+54) + prec - 1
// Now compute mant*(2^e2)*(10^q). // Now compute mant*(2^e2)*(10^q).
// Is it an exact computation? // Is it an exact computation?
@ -242,7 +242,7 @@ func ryuFtoaShortest(d *decimalSlice, mant uint64, exp int, flt *floatInfo) {
return return
} }
// Find 10^q *larger* than 2^-e2 // Find 10^q *larger* than 2^-e2
q := mulByLog2Log10(-e2) + 1 q := mulLog10_2(-e2) + 1
// We are going to multiply by 10^q using 128-bit arithmetic. // We are going to multiply by 10^q using 128-bit arithmetic.
// The exponent is the same for all 3 numbers. // The exponent is the same for all 3 numbers.
@ -326,26 +326,6 @@ func ryuFtoaShortest(d *decimalSlice, mant uint64, exp int, flt *floatInfo) {
d.dp -= q d.dp -= q
} }
// mulByLog2Log10 returns math.Floor(x * log(2)/log(10)) for an integer x in
// the range -1600 <= x && x <= +1600.
//
// The range restriction lets us work in faster integer arithmetic instead of
// slower floating point arithmetic. Correctness is verified by unit tests.
func mulByLog2Log10(x int) int {
// log(2)/log(10) ≈ 0.30102999566 ≈ 78913 / 2^18
return (x * 78913) >> 18
}
// mulByLog10Log2 returns math.Floor(x * log(10)/log(2)) for an integer x in
// the range -500 <= x && x <= +500.
//
// The range restriction lets us work in faster integer arithmetic instead of
// slower floating point arithmetic. Correctness is verified by unit tests.
func mulByLog10Log2(x int) int {
// log(10)/log(2) ≈ 3.32192809489 ≈ 108853 / 2^15
return (x * 108853) >> 15
}
// computeBounds returns a floating-point vector (l, c, u)×2^e2 // computeBounds returns a floating-point vector (l, c, u)×2^e2
// where the mantissas are 55-bit (or 26-bit) integers, describing the interval // where the mantissas are 55-bit (or 26-bit) integers, describing the interval
// represented by the input float64 or float32. // represented by the input float64 or float32.
@ -482,7 +462,7 @@ func ryuDigits32(d *decimalSlice, lower, central, upper uint32,
// mult64bitPow10 takes a floating-point input with a 25-bit // mult64bitPow10 takes a floating-point input with a 25-bit
// mantissa and multiplies it with 10^q. The resulting mantissa // mantissa and multiplies it with 10^q. The resulting mantissa
// is m*P >> 57 where P is a 64-bit element of the detailedPowersOfTen tables. // is m*P >> 57 where P is a 64-bit truncated power of 10.
// It is typically 31 or 32-bit wide. // It is typically 31 or 32-bit wide.
// The returned boolean is true if all trimmed bits were zero. // The returned boolean is true if all trimmed bits were zero.
// //
@ -495,23 +475,23 @@ func mult64bitPow10(m uint32, e2, q int) (resM uint32, resE int, exact bool) {
// P == 1<<63 // P == 1<<63
return m << 6, e2 - 6, true return m << 6, e2 - 6, true
} }
if q < detailedPowersOfTenMinExp10 || detailedPowersOfTenMaxExp10 < q { pow, exp2, ok := pow10(q)
if !ok {
// This never happens due to the range of float32/float64 exponent // This never happens due to the range of float32/float64 exponent
panic("mult64bitPow10: power of 10 is out of range") panic("mult64bitPow10: power of 10 is out of range")
} }
pow := detailedPowersOfTen[q-detailedPowersOfTenMinExp10][1]
if q < 0 { if q < 0 {
// Inverse powers of ten must be rounded up. // Inverse powers of ten must be rounded up.
pow += 1 pow.Hi++
} }
hi, lo := bits.Mul64(uint64(m), pow) hi, lo := bits.Mul64(uint64(m), pow.Hi)
e2 += mulByLog10Log2(q) - 63 + 57 e2 += exp2 - 63 + 57
return uint32(hi<<7 | lo>>57), e2, lo<<7 == 0 return uint32(hi<<7 | lo>>57), e2, lo<<7 == 0
} }
// mult128bitPow10 takes a floating-point input with a 55-bit // mult128bitPow10 takes a floating-point input with a 55-bit
// mantissa and multiplies it with 10^q. The resulting mantissa // mantissa and multiplies it with 10^q. The resulting mantissa
// is m*P >> 119 where P is a 128-bit element of the detailedPowersOfTen tables. // is m*P >> 119 where P is a 128-bit truncated power of 10.
// It is typically 63 or 64-bit wide. // It is typically 63 or 64-bit wide.
// The returned boolean is true is all trimmed bits were zero. // The returned boolean is true is all trimmed bits were zero.
// //
@ -524,23 +504,19 @@ func mult128bitPow10(m uint64, e2, q int) (resM uint64, resE int, exact bool) {
// P == 1<<127 // P == 1<<127
return m << 8, e2 - 8, true return m << 8, e2 - 8, true
} }
if q < detailedPowersOfTenMinExp10 || detailedPowersOfTenMaxExp10 < q { pow, exp2, ok := pow10(q)
if !ok {
// This never happens due to the range of float32/float64 exponent // This never happens due to the range of float32/float64 exponent
panic("mult128bitPow10: power of 10 is out of range") panic("mult128bitPow10: power of 10 is out of range")
} }
pow := detailedPowersOfTen[q-detailedPowersOfTenMinExp10]
if q < 0 { if q < 0 {
// Inverse powers of ten must be rounded up. // Inverse powers of ten must be rounded up.
pow[0] += 1 pow.Lo++
} }
e2 += mulByLog10Log2(q) - 127 + 119 e2 += exp2 - 127 + 119
// long multiplication hi, mid, lo := umul192(m, pow)
l1, l0 := bits.Mul64(m, pow[0]) return hi<<9 | mid>>55, e2, mid<<9 == 0 && lo == 0
h1, h0 := bits.Mul64(m, pow[1])
mid, carry := bits.Add64(l1, h0, 0)
h1 += carry
return h1<<9 | mid>>55, e2, mid<<9 == 0 && l0 == 0
} }
func divisibleByPower5(m uint64, k int) bool { func divisibleByPower5(m uint64, k int) bool {

View file

@ -1,31 +0,0 @@
// Copyright 2021 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package strconv_test
import (
"math"
. "strconv"
"testing"
)
func TestMulByLog2Log10(t *testing.T) {
for x := -1600; x <= +1600; x++ {
iMath := MulByLog2Log10(x)
fMath := int(math.Floor(float64(x) * math.Ln2 / math.Ln10))
if iMath != fMath {
t.Errorf("mulByLog2Log10(%d) failed: %d vs %d\n", x, iMath, fMath)
}
}
}
func TestMulByLog10Log2(t *testing.T) {
for x := -500; x <= +500; x++ {
iMath := MulByLog10Log2(x)
fMath := int(math.Floor(float64(x) * math.Ln10 / math.Ln2))
if iMath != fMath {
t.Errorf("mulByLog10Log2(%d) failed: %d vs %d\n", x, iMath, fMath)
}
}
}

View file

@ -0,0 +1,20 @@
// Copyright 2025 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package strconv_test
import . "strconv"
type uint128 = Uint128
var (
baseError = BaseError
bitSizeError = BitSizeError
mulLog10_2 = MulLog10_2
mulLog2_10 = MulLog2_10
parseFloatPrefix = ParseFloatPrefix
pow10 = Pow10
umul128 = Umul128
umul192 = Umul192
)

View file

@ -1,31 +0,0 @@
// Copyright 2009 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
// export access to strconv internals for tests
package strconv
func NewDecimal(i uint64) *decimal {
d := new(decimal)
d.Assign(i)
return d
}
func SetOptimize(b bool) bool {
old := optimize
optimize = b
return old
}
func ParseFloatPrefix(s string, bitSize int) (float64, int, error) {
return parseFloatPrefix(s, bitSize)
}
func MulByLog2Log10(x int) int {
return mulByLog2Log10(x)
}
func MulByLog10Log2(x int) int {
return mulByLog10Log2(x)
}

View file

@ -5,6 +5,7 @@
package strconv_test package strconv_test
import ( import (
"fmt"
. "strconv" . "strconv"
"testing" "testing"
) )
@ -230,7 +231,7 @@ func BenchmarkAppendIntSmall(b *testing.B) {
func BenchmarkAppendUintVarlen(b *testing.B) { func BenchmarkAppendUintVarlen(b *testing.B) {
for _, test := range varlenUints { for _, test := range varlenUints {
b.Run(test.out, func(b *testing.B) { b.Run(fmt.Sprint("digits=", len(test.out)), func(b *testing.B) {
dst := make([]byte, 0, 30) dst := make([]byte, 0, 30)
for j := 0; j < b.N; j++ { for j := 0; j < b.N; j++ {
dst = AppendUint(dst[:0], test.in, 10) dst = AppendUint(dst[:0], test.in, 10)

57
src/strconv/math.go Normal file
View file

@ -0,0 +1,57 @@
// Copyright 2025 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package strconv
import "math/bits"
// A uint128 is a 128-bit uint.
// The fields are exported to make them visible to package strconv_test.
type uint128 struct {
Hi uint64
Lo uint64
}
// umul128 returns the 128-bit product x*y.
func umul128(x, y uint64) uint128 {
hi, lo := bits.Mul64(x, y)
return uint128{hi, lo}
}
// umul192 returns the 192-bit product x*y in three uint64s.
func umul192(x uint64, y uint128) (hi, mid, lo uint64) {
mid1, lo := bits.Mul64(x, y.Lo)
hi, mid2 := bits.Mul64(x, y.Hi)
mid, carry := bits.Add64(mid1, mid2, 0)
return hi + carry, mid, lo
}
// pow10 returns the 128-bit mantissa and binary exponent of 10**e
// If e is out of range, pow10 returns ok=false.
func pow10(e int) (mant uint128, exp int, ok bool) {
if e < pow10Min || e > pow10Max {
return
}
return pow10Tab[e-pow10Min], mulLog2_10(e), true
}
// mulLog10_2 returns math.Floor(x * log(2)/log(10)) for an integer x in
// the range -1600 <= x && x <= +1600.
//
// The range restriction lets us work in faster integer arithmetic instead of
// slower floating point arithmetic. Correctness is verified by unit tests.
func mulLog10_2(x int) int {
// log(2)/log(10) ≈ 0.30102999566 ≈ 78913 / 2^18
return (x * 78913) >> 18
}
// mulLog2_10 returns math.Floor(x * log(10)/log(2)) for an integer x in
// the range -500 <= x && x <= +500.
//
// The range restriction lets us work in faster integer arithmetic instead of
// slower floating point arithmetic. Correctness is verified by unit tests.
func mulLog2_10(x int) int {
// log(10)/log(2) ≈ 3.32192809489 ≈ 108853 / 2^15
return (x * 108853) >> 15
}

80
src/strconv/math_test.go Normal file
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@ -0,0 +1,80 @@
// Copyright 2025 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package strconv_test
import (
"math"
. "strconv"
"testing"
)
var pow10Tests = []struct {
exp10 int
mant uint128
exp2 int
ok bool
}{
{-349, uint128{0, 0}, 0, false},
{-348, uint128{0xFA8FD5A0081C0288, 0x1732C869CD60E453}, -1157, true},
{0, uint128{0x8000000000000000, 0x0000000000000000}, 0, true},
{347, uint128{0xD13EB46469447567, 0x4B7195F2D2D1A9FB}, 1152, true},
{348, uint128{0, 0}, 0, false},
}
func TestPow10(t *testing.T) {
for _, tt := range pow10Tests {
mant, exp2, ok := Pow10(tt.exp10)
if mant != tt.mant || exp2 != tt.exp2 {
t.Errorf("pow10(%d) = %#016x, %#016x, %d, %v want %#016x,%#016x, %d, %v",
tt.exp10, mant.Hi, mant.Lo, exp2, ok,
tt.mant.Hi, tt.mant.Lo, tt.exp2, tt.ok)
}
}
}
func u128(hi, lo uint64) uint128 {
return uint128{Hi: hi, Lo: lo}
}
var umul192Tests = []struct {
x uint64
y uint128
hi uint64
mid uint64
lo uint64
}{
{0, u128(0, 0), 0, 0, 0},
{^uint64(0), u128(^uint64(0), ^uint64(0)), ^uint64(1), ^uint64(0), 1},
}
func TestUmul192(t *testing.T) {
for _, tt := range umul192Tests {
hi, mid, lo := Umul192(tt.x, tt.y)
if hi != tt.hi || mid != tt.mid || lo != tt.lo {
t.Errorf("umul192(%#x, {%#x,%#x}) = %#x, %#x, %#x, want %#x, %#x, %#x",
tt.x, tt.y.Hi, tt.y.Lo, hi, mid, lo, tt.hi, tt.mid, tt.lo)
}
}
}
func TestMulLog10_2(t *testing.T) {
for x := -1600; x <= +1600; x++ {
iMath := mulLog10_2(x)
fMath := int(math.Floor(float64(x) * math.Ln2 / math.Ln10))
if iMath != fMath {
t.Errorf("mulLog10_2(%d) failed: %d vs %d\n", x, iMath, fMath)
}
}
}
func TestMulLog2_10(t *testing.T) {
for x := -500; x <= +500; x++ {
iMath := mulLog2_10(x)
fMath := int(math.Floor(float64(x) * math.Ln10 / math.Ln2))
if iMath != fMath {
t.Errorf("mulLog2_10(%d) failed: %d vs %d\n", x, iMath, fMath)
}
}
}

91
src/strconv/pow10gen.go Normal file
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@ -0,0 +1,91 @@
// Copyright 2025 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
//go:build ignore
package main
import (
"bytes"
"fmt"
"go/format"
"log"
"math/big"
"os"
)
const (
minExp = -348
maxExp = 347
)
func main() {
log.SetPrefix("pow10gen: ")
log.SetFlags(0)
var (
one = big.NewInt(1)
ten = big.NewInt(10)
b1p64 = new(big.Int).Lsh(one, 64)
b1p128 = new(big.Int).Lsh(one, 128)
r2 = big.NewRat(2, 1)
r1p128 = new(big.Rat).SetInt(b1p128)
)
var out bytes.Buffer
fmt.Fprintf(&out, top, minExp, maxExp)
for e := int64(minExp); e <= maxExp; e++ {
var r *big.Rat
if e >= 0 {
r = new(big.Rat).SetInt(new(big.Int).Exp(ten, big.NewInt(e), nil))
} else {
r = new(big.Rat).SetFrac(one, new(big.Int).Exp(ten, big.NewInt(-e), nil))
}
be := 0
for r.Cmp(r1p128) < 0 {
r.Mul(r, r2)
be++
}
for r.Cmp(r1p128) >= 0 {
r.Quo(r, r2)
be--
}
d := new(big.Int).Div(r.Num(), r.Denom())
hi, lo := new(big.Int).DivMod(d, b1p64, new(big.Int))
fmt.Fprintf(&out, "\t{%#016x, %#016x}, // 1e%d * 2**%d\n", hi.Uint64(), lo.Uint64(), e, be)
}
fmt.Fprintf(&out, "}\n")
src, err := format.Source(out.Bytes())
if err != nil {
log.Fatal(err)
}
if err := os.WriteFile("pow10tab.go", src, 0666); err != nil {
log.Fatal(err)
}
}
var top = `// Copyright 2025 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
// Code generated by: go run pow10gen.go. DO NOT EDIT.
//
//go:generate go run pow10gen.go
package strconv
const (
pow10Min = %d
pow10Max = %d
)
// pow10Tab holds 128-bit mantissas of powers of 10.
// The values are scaled so the high bit is always set; there is no "implicit leading 1 bit".
var pow10Tab = [...]uint128{
`

715
src/strconv/pow10tab.go Normal file
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@ -0,0 +1,715 @@
// Copyright 2025 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
// Code generated by: go run pow10gen.go. DO NOT EDIT.
//
//go:generate go run pow10gen.go
package strconv
const (
pow10Min = -348
pow10Max = 347
)
// pow10Tab holds 128-bit mantissas of powers of 10.
// The values are scaled so the high bit is always set; there is no "implicit leading 1 bit".
var pow10Tab = [...]uint128{
{0xfa8fd5a0081c0288, 0x1732c869cd60e453}, // 1e-348 * 2**1284
{0x9c99e58405118195, 0x0e7fbd42205c8eb4}, // 1e-347 * 2**1280
{0xc3c05ee50655e1fa, 0x521fac92a873b261}, // 1e-346 * 2**1277
{0xf4b0769e47eb5a78, 0xe6a797b752909ef9}, // 1e-345 * 2**1274
{0x98ee4a22ecf3188b, 0x9028bed2939a635c}, // 1e-344 * 2**1270
{0xbf29dcaba82fdeae, 0x7432ee873880fc33}, // 1e-343 * 2**1267
{0xeef453d6923bd65a, 0x113faa2906a13b3f}, // 1e-342 * 2**1264
{0x9558b4661b6565f8, 0x4ac7ca59a424c507}, // 1e-341 * 2**1260
{0xbaaee17fa23ebf76, 0x5d79bcf00d2df649}, // 1e-340 * 2**1257
{0xe95a99df8ace6f53, 0xf4d82c2c107973dc}, // 1e-339 * 2**1254
{0x91d8a02bb6c10594, 0x79071b9b8a4be869}, // 1e-338 * 2**1250
{0xb64ec836a47146f9, 0x9748e2826cdee284}, // 1e-337 * 2**1247
{0xe3e27a444d8d98b7, 0xfd1b1b2308169b25}, // 1e-336 * 2**1244
{0x8e6d8c6ab0787f72, 0xfe30f0f5e50e20f7}, // 1e-335 * 2**1240
{0xb208ef855c969f4f, 0xbdbd2d335e51a935}, // 1e-334 * 2**1237
{0xde8b2b66b3bc4723, 0xad2c788035e61382}, // 1e-333 * 2**1234
{0x8b16fb203055ac76, 0x4c3bcb5021afcc31}, // 1e-332 * 2**1230
{0xaddcb9e83c6b1793, 0xdf4abe242a1bbf3d}, // 1e-331 * 2**1227
{0xd953e8624b85dd78, 0xd71d6dad34a2af0d}, // 1e-330 * 2**1224
{0x87d4713d6f33aa6b, 0x8672648c40e5ad68}, // 1e-329 * 2**1220
{0xa9c98d8ccb009506, 0x680efdaf511f18c2}, // 1e-328 * 2**1217
{0xd43bf0effdc0ba48, 0x0212bd1b2566def2}, // 1e-327 * 2**1214
{0x84a57695fe98746d, 0x014bb630f7604b57}, // 1e-326 * 2**1210
{0xa5ced43b7e3e9188, 0x419ea3bd35385e2d}, // 1e-325 * 2**1207
{0xcf42894a5dce35ea, 0x52064cac828675b9}, // 1e-324 * 2**1204
{0x818995ce7aa0e1b2, 0x7343efebd1940993}, // 1e-323 * 2**1200
{0xa1ebfb4219491a1f, 0x1014ebe6c5f90bf8}, // 1e-322 * 2**1197
{0xca66fa129f9b60a6, 0xd41a26e077774ef6}, // 1e-321 * 2**1194
{0xfd00b897478238d0, 0x8920b098955522b4}, // 1e-320 * 2**1191
{0x9e20735e8cb16382, 0x55b46e5f5d5535b0}, // 1e-319 * 2**1187
{0xc5a890362fddbc62, 0xeb2189f734aa831d}, // 1e-318 * 2**1184
{0xf712b443bbd52b7b, 0xa5e9ec7501d523e4}, // 1e-317 * 2**1181
{0x9a6bb0aa55653b2d, 0x47b233c92125366e}, // 1e-316 * 2**1177
{0xc1069cd4eabe89f8, 0x999ec0bb696e840a}, // 1e-315 * 2**1174
{0xf148440a256e2c76, 0xc00670ea43ca250d}, // 1e-314 * 2**1171
{0x96cd2a865764dbca, 0x380406926a5e5728}, // 1e-313 * 2**1167
{0xbc807527ed3e12bc, 0xc605083704f5ecf2}, // 1e-312 * 2**1164
{0xeba09271e88d976b, 0xf7864a44c633682e}, // 1e-311 * 2**1161
{0x93445b8731587ea3, 0x7ab3ee6afbe0211d}, // 1e-310 * 2**1157
{0xb8157268fdae9e4c, 0x5960ea05bad82964}, // 1e-309 * 2**1154
{0xe61acf033d1a45df, 0x6fb92487298e33bd}, // 1e-308 * 2**1151
{0x8fd0c16206306bab, 0xa5d3b6d479f8e056}, // 1e-307 * 2**1147
{0xb3c4f1ba87bc8696, 0x8f48a4899877186c}, // 1e-306 * 2**1144
{0xe0b62e2929aba83c, 0x331acdabfe94de87}, // 1e-305 * 2**1141
{0x8c71dcd9ba0b4925, 0x9ff0c08b7f1d0b14}, // 1e-304 * 2**1137
{0xaf8e5410288e1b6f, 0x07ecf0ae5ee44dd9}, // 1e-303 * 2**1134
{0xdb71e91432b1a24a, 0xc9e82cd9f69d6150}, // 1e-302 * 2**1131
{0x892731ac9faf056e, 0xbe311c083a225cd2}, // 1e-301 * 2**1127
{0xab70fe17c79ac6ca, 0x6dbd630a48aaf406}, // 1e-300 * 2**1124
{0xd64d3d9db981787d, 0x092cbbccdad5b108}, // 1e-299 * 2**1121
{0x85f0468293f0eb4e, 0x25bbf56008c58ea5}, // 1e-298 * 2**1117
{0xa76c582338ed2621, 0xaf2af2b80af6f24e}, // 1e-297 * 2**1114
{0xd1476e2c07286faa, 0x1af5af660db4aee1}, // 1e-296 * 2**1111
{0x82cca4db847945ca, 0x50d98d9fc890ed4d}, // 1e-295 * 2**1107
{0xa37fce126597973c, 0xe50ff107bab528a0}, // 1e-294 * 2**1104
{0xcc5fc196fefd7d0c, 0x1e53ed49a96272c8}, // 1e-293 * 2**1101
{0xff77b1fcbebcdc4f, 0x25e8e89c13bb0f7a}, // 1e-292 * 2**1098
{0x9faacf3df73609b1, 0x77b191618c54e9ac}, // 1e-291 * 2**1094
{0xc795830d75038c1d, 0xd59df5b9ef6a2417}, // 1e-290 * 2**1091
{0xf97ae3d0d2446f25, 0x4b0573286b44ad1d}, // 1e-289 * 2**1088
{0x9becce62836ac577, 0x4ee367f9430aec32}, // 1e-288 * 2**1084
{0xc2e801fb244576d5, 0x229c41f793cda73f}, // 1e-287 * 2**1081
{0xf3a20279ed56d48a, 0x6b43527578c1110f}, // 1e-286 * 2**1078
{0x9845418c345644d6, 0x830a13896b78aaa9}, // 1e-285 * 2**1074
{0xbe5691ef416bd60c, 0x23cc986bc656d553}, // 1e-284 * 2**1071
{0xedec366b11c6cb8f, 0x2cbfbe86b7ec8aa8}, // 1e-283 * 2**1068
{0x94b3a202eb1c3f39, 0x7bf7d71432f3d6a9}, // 1e-282 * 2**1064
{0xb9e08a83a5e34f07, 0xdaf5ccd93fb0cc53}, // 1e-281 * 2**1061
{0xe858ad248f5c22c9, 0xd1b3400f8f9cff68}, // 1e-280 * 2**1058
{0x91376c36d99995be, 0x23100809b9c21fa1}, // 1e-279 * 2**1054
{0xb58547448ffffb2d, 0xabd40a0c2832a78a}, // 1e-278 * 2**1051
{0xe2e69915b3fff9f9, 0x16c90c8f323f516c}, // 1e-277 * 2**1048
{0x8dd01fad907ffc3b, 0xae3da7d97f6792e3}, // 1e-276 * 2**1044
{0xb1442798f49ffb4a, 0x99cd11cfdf41779c}, // 1e-275 * 2**1041
{0xdd95317f31c7fa1d, 0x40405643d711d583}, // 1e-274 * 2**1038
{0x8a7d3eef7f1cfc52, 0x482835ea666b2572}, // 1e-273 * 2**1034
{0xad1c8eab5ee43b66, 0xda3243650005eecf}, // 1e-272 * 2**1031
{0xd863b256369d4a40, 0x90bed43e40076a82}, // 1e-271 * 2**1028
{0x873e4f75e2224e68, 0x5a7744a6e804a291}, // 1e-270 * 2**1024
{0xa90de3535aaae202, 0x711515d0a205cb36}, // 1e-269 * 2**1021
{0xd3515c2831559a83, 0x0d5a5b44ca873e03}, // 1e-268 * 2**1018
{0x8412d9991ed58091, 0xe858790afe9486c2}, // 1e-267 * 2**1014
{0xa5178fff668ae0b6, 0x626e974dbe39a872}, // 1e-266 * 2**1011
{0xce5d73ff402d98e3, 0xfb0a3d212dc8128f}, // 1e-265 * 2**1008
{0x80fa687f881c7f8e, 0x7ce66634bc9d0b99}, // 1e-264 * 2**1004
{0xa139029f6a239f72, 0x1c1fffc1ebc44e80}, // 1e-263 * 2**1001
{0xc987434744ac874e, 0xa327ffb266b56220}, // 1e-262 * 2**998
{0xfbe9141915d7a922, 0x4bf1ff9f0062baa8}, // 1e-261 * 2**995
{0x9d71ac8fada6c9b5, 0x6f773fc3603db4a9}, // 1e-260 * 2**991
{0xc4ce17b399107c22, 0xcb550fb4384d21d3}, // 1e-259 * 2**988
{0xf6019da07f549b2b, 0x7e2a53a146606a48}, // 1e-258 * 2**985
{0x99c102844f94e0fb, 0x2eda7444cbfc426d}, // 1e-257 * 2**981
{0xc0314325637a1939, 0xfa911155fefb5308}, // 1e-256 * 2**978
{0xf03d93eebc589f88, 0x793555ab7eba27ca}, // 1e-255 * 2**975
{0x96267c7535b763b5, 0x4bc1558b2f3458de}, // 1e-254 * 2**971
{0xbbb01b9283253ca2, 0x9eb1aaedfb016f16}, // 1e-253 * 2**968
{0xea9c227723ee8bcb, 0x465e15a979c1cadc}, // 1e-252 * 2**965
{0x92a1958a7675175f, 0x0bfacd89ec191ec9}, // 1e-251 * 2**961
{0xb749faed14125d36, 0xcef980ec671f667b}, // 1e-250 * 2**958
{0xe51c79a85916f484, 0x82b7e12780e7401a}, // 1e-249 * 2**955
{0x8f31cc0937ae58d2, 0xd1b2ecb8b0908810}, // 1e-248 * 2**951
{0xb2fe3f0b8599ef07, 0x861fa7e6dcb4aa15}, // 1e-247 * 2**948
{0xdfbdcece67006ac9, 0x67a791e093e1d49a}, // 1e-246 * 2**945
{0x8bd6a141006042bd, 0xe0c8bb2c5c6d24e0}, // 1e-245 * 2**941
{0xaecc49914078536d, 0x58fae9f773886e18}, // 1e-244 * 2**938
{0xda7f5bf590966848, 0xaf39a475506a899e}, // 1e-243 * 2**935
{0x888f99797a5e012d, 0x6d8406c952429603}, // 1e-242 * 2**931
{0xaab37fd7d8f58178, 0xc8e5087ba6d33b83}, // 1e-241 * 2**928
{0xd5605fcdcf32e1d6, 0xfb1e4a9a90880a64}, // 1e-240 * 2**925
{0x855c3be0a17fcd26, 0x5cf2eea09a55067f}, // 1e-239 * 2**921
{0xa6b34ad8c9dfc06f, 0xf42faa48c0ea481e}, // 1e-238 * 2**918
{0xd0601d8efc57b08b, 0xf13b94daf124da26}, // 1e-237 * 2**915
{0x823c12795db6ce57, 0x76c53d08d6b70858}, // 1e-236 * 2**911
{0xa2cb1717b52481ed, 0x54768c4b0c64ca6e}, // 1e-235 * 2**908
{0xcb7ddcdda26da268, 0xa9942f5dcf7dfd09}, // 1e-234 * 2**905
{0xfe5d54150b090b02, 0xd3f93b35435d7c4c}, // 1e-233 * 2**902
{0x9efa548d26e5a6e1, 0xc47bc5014a1a6daf}, // 1e-232 * 2**898
{0xc6b8e9b0709f109a, 0x359ab6419ca1091b}, // 1e-231 * 2**895
{0xf867241c8cc6d4c0, 0xc30163d203c94b62}, // 1e-230 * 2**892
{0x9b407691d7fc44f8, 0x79e0de63425dcf1d}, // 1e-229 * 2**888
{0xc21094364dfb5636, 0x985915fc12f542e4}, // 1e-228 * 2**885
{0xf294b943e17a2bc4, 0x3e6f5b7b17b2939d}, // 1e-227 * 2**882
{0x979cf3ca6cec5b5a, 0xa705992ceecf9c42}, // 1e-226 * 2**878
{0xbd8430bd08277231, 0x50c6ff782a838353}, // 1e-225 * 2**875
{0xece53cec4a314ebd, 0xa4f8bf5635246428}, // 1e-224 * 2**872
{0x940f4613ae5ed136, 0x871b7795e136be99}, // 1e-223 * 2**868
{0xb913179899f68584, 0x28e2557b59846e3f}, // 1e-222 * 2**865
{0xe757dd7ec07426e5, 0x331aeada2fe589cf}, // 1e-221 * 2**862
{0x9096ea6f3848984f, 0x3ff0d2c85def7621}, // 1e-220 * 2**858
{0xb4bca50b065abe63, 0x0fed077a756b53a9}, // 1e-219 * 2**855
{0xe1ebce4dc7f16dfb, 0xd3e8495912c62894}, // 1e-218 * 2**852
{0x8d3360f09cf6e4bd, 0x64712dd7abbbd95c}, // 1e-217 * 2**848
{0xb080392cc4349dec, 0xbd8d794d96aacfb3}, // 1e-216 * 2**845
{0xdca04777f541c567, 0xecf0d7a0fc5583a0}, // 1e-215 * 2**842
{0x89e42caaf9491b60, 0xf41686c49db57244}, // 1e-214 * 2**838
{0xac5d37d5b79b6239, 0x311c2875c522ced5}, // 1e-213 * 2**835
{0xd77485cb25823ac7, 0x7d633293366b828b}, // 1e-212 * 2**832
{0x86a8d39ef77164bc, 0xae5dff9c02033197}, // 1e-211 * 2**828
{0xa8530886b54dbdeb, 0xd9f57f830283fdfc}, // 1e-210 * 2**825
{0xd267caa862a12d66, 0xd072df63c324fd7b}, // 1e-209 * 2**822
{0x8380dea93da4bc60, 0x4247cb9e59f71e6d}, // 1e-208 * 2**818
{0xa46116538d0deb78, 0x52d9be85f074e608}, // 1e-207 * 2**815
{0xcd795be870516656, 0x67902e276c921f8b}, // 1e-206 * 2**812
{0x806bd9714632dff6, 0x00ba1cd8a3db53b6}, // 1e-205 * 2**808
{0xa086cfcd97bf97f3, 0x80e8a40eccd228a4}, // 1e-204 * 2**805
{0xc8a883c0fdaf7df0, 0x6122cd128006b2cd}, // 1e-203 * 2**802
{0xfad2a4b13d1b5d6c, 0x796b805720085f81}, // 1e-202 * 2**799
{0x9cc3a6eec6311a63, 0xcbe3303674053bb0}, // 1e-201 * 2**795
{0xc3f490aa77bd60fc, 0xbedbfc4411068a9c}, // 1e-200 * 2**792
{0xf4f1b4d515acb93b, 0xee92fb5515482d44}, // 1e-199 * 2**789
{0x991711052d8bf3c5, 0x751bdd152d4d1c4a}, // 1e-198 * 2**785
{0xbf5cd54678eef0b6, 0xd262d45a78a0635d}, // 1e-197 * 2**782
{0xef340a98172aace4, 0x86fb897116c87c34}, // 1e-196 * 2**779
{0x9580869f0e7aac0e, 0xd45d35e6ae3d4da0}, // 1e-195 * 2**775
{0xbae0a846d2195712, 0x8974836059cca109}, // 1e-194 * 2**772
{0xe998d258869facd7, 0x2bd1a438703fc94b}, // 1e-193 * 2**769
{0x91ff83775423cc06, 0x7b6306a34627ddcf}, // 1e-192 * 2**765
{0xb67f6455292cbf08, 0x1a3bc84c17b1d542}, // 1e-191 * 2**762
{0xe41f3d6a7377eeca, 0x20caba5f1d9e4a93}, // 1e-190 * 2**759
{0x8e938662882af53e, 0x547eb47b7282ee9c}, // 1e-189 * 2**755
{0xb23867fb2a35b28d, 0xe99e619a4f23aa43}, // 1e-188 * 2**752
{0xdec681f9f4c31f31, 0x6405fa00e2ec94d4}, // 1e-187 * 2**749
{0x8b3c113c38f9f37e, 0xde83bc408dd3dd04}, // 1e-186 * 2**745
{0xae0b158b4738705e, 0x9624ab50b148d445}, // 1e-185 * 2**742
{0xd98ddaee19068c76, 0x3badd624dd9b0957}, // 1e-184 * 2**739
{0x87f8a8d4cfa417c9, 0xe54ca5d70a80e5d6}, // 1e-183 * 2**735
{0xa9f6d30a038d1dbc, 0x5e9fcf4ccd211f4c}, // 1e-182 * 2**732
{0xd47487cc8470652b, 0x7647c3200069671f}, // 1e-181 * 2**729
{0x84c8d4dfd2c63f3b, 0x29ecd9f40041e073}, // 1e-180 * 2**725
{0xa5fb0a17c777cf09, 0xf468107100525890}, // 1e-179 * 2**722
{0xcf79cc9db955c2cc, 0x7182148d4066eeb4}, // 1e-178 * 2**719
{0x81ac1fe293d599bf, 0xc6f14cd848405530}, // 1e-177 * 2**715
{0xa21727db38cb002f, 0xb8ada00e5a506a7c}, // 1e-176 * 2**712
{0xca9cf1d206fdc03b, 0xa6d90811f0e4851c}, // 1e-175 * 2**709
{0xfd442e4688bd304a, 0x908f4a166d1da663}, // 1e-174 * 2**706
{0x9e4a9cec15763e2e, 0x9a598e4e043287fe}, // 1e-173 * 2**702
{0xc5dd44271ad3cdba, 0x40eff1e1853f29fd}, // 1e-172 * 2**699
{0xf7549530e188c128, 0xd12bee59e68ef47c}, // 1e-171 * 2**696
{0x9a94dd3e8cf578b9, 0x82bb74f8301958ce}, // 1e-170 * 2**692
{0xc13a148e3032d6e7, 0xe36a52363c1faf01}, // 1e-169 * 2**689
{0xf18899b1bc3f8ca1, 0xdc44e6c3cb279ac1}, // 1e-168 * 2**686
{0x96f5600f15a7b7e5, 0x29ab103a5ef8c0b9}, // 1e-167 * 2**682
{0xbcb2b812db11a5de, 0x7415d448f6b6f0e7}, // 1e-166 * 2**679
{0xebdf661791d60f56, 0x111b495b3464ad21}, // 1e-165 * 2**676
{0x936b9fcebb25c995, 0xcab10dd900beec34}, // 1e-164 * 2**672
{0xb84687c269ef3bfb, 0x3d5d514f40eea742}, // 1e-163 * 2**669
{0xe65829b3046b0afa, 0x0cb4a5a3112a5112}, // 1e-162 * 2**666
{0x8ff71a0fe2c2e6dc, 0x47f0e785eaba72ab}, // 1e-161 * 2**662
{0xb3f4e093db73a093, 0x59ed216765690f56}, // 1e-160 * 2**659
{0xe0f218b8d25088b8, 0x306869c13ec3532c}, // 1e-159 * 2**656
{0x8c974f7383725573, 0x1e414218c73a13fb}, // 1e-158 * 2**652
{0xafbd2350644eeacf, 0xe5d1929ef90898fa}, // 1e-157 * 2**649
{0xdbac6c247d62a583, 0xdf45f746b74abf39}, // 1e-156 * 2**646
{0x894bc396ce5da772, 0x6b8bba8c328eb783}, // 1e-155 * 2**642
{0xab9eb47c81f5114f, 0x066ea92f3f326564}, // 1e-154 * 2**639
{0xd686619ba27255a2, 0xc80a537b0efefebd}, // 1e-153 * 2**636
{0x8613fd0145877585, 0xbd06742ce95f5f36}, // 1e-152 * 2**632
{0xa798fc4196e952e7, 0x2c48113823b73704}, // 1e-151 * 2**629
{0xd17f3b51fca3a7a0, 0xf75a15862ca504c5}, // 1e-150 * 2**626
{0x82ef85133de648c4, 0x9a984d73dbe722fb}, // 1e-149 * 2**622
{0xa3ab66580d5fdaf5, 0xc13e60d0d2e0ebba}, // 1e-148 * 2**619
{0xcc963fee10b7d1b3, 0x318df905079926a8}, // 1e-147 * 2**616
{0xffbbcfe994e5c61f, 0xfdf17746497f7052}, // 1e-146 * 2**613
{0x9fd561f1fd0f9bd3, 0xfeb6ea8bedefa633}, // 1e-145 * 2**609
{0xc7caba6e7c5382c8, 0xfe64a52ee96b8fc0}, // 1e-144 * 2**606
{0xf9bd690a1b68637b, 0x3dfdce7aa3c673b0}, // 1e-143 * 2**603
{0x9c1661a651213e2d, 0x06bea10ca65c084e}, // 1e-142 * 2**599
{0xc31bfa0fe5698db8, 0x486e494fcff30a62}, // 1e-141 * 2**596
{0xf3e2f893dec3f126, 0x5a89dba3c3efccfa}, // 1e-140 * 2**593
{0x986ddb5c6b3a76b7, 0xf89629465a75e01c}, // 1e-139 * 2**589
{0xbe89523386091465, 0xf6bbb397f1135823}, // 1e-138 * 2**586
{0xee2ba6c0678b597f, 0x746aa07ded582e2c}, // 1e-137 * 2**583
{0x94db483840b717ef, 0xa8c2a44eb4571cdc}, // 1e-136 * 2**579
{0xba121a4650e4ddeb, 0x92f34d62616ce413}, // 1e-135 * 2**576
{0xe896a0d7e51e1566, 0x77b020baf9c81d17}, // 1e-134 * 2**573
{0x915e2486ef32cd60, 0x0ace1474dc1d122e}, // 1e-133 * 2**569
{0xb5b5ada8aaff80b8, 0x0d819992132456ba}, // 1e-132 * 2**566
{0xe3231912d5bf60e6, 0x10e1fff697ed6c69}, // 1e-131 * 2**563
{0x8df5efabc5979c8f, 0xca8d3ffa1ef463c1}, // 1e-130 * 2**559
{0xb1736b96b6fd83b3, 0xbd308ff8a6b17cb2}, // 1e-129 * 2**556
{0xddd0467c64bce4a0, 0xac7cb3f6d05ddbde}, // 1e-128 * 2**553
{0x8aa22c0dbef60ee4, 0x6bcdf07a423aa96b}, // 1e-127 * 2**549
{0xad4ab7112eb3929d, 0x86c16c98d2c953c6}, // 1e-126 * 2**546
{0xd89d64d57a607744, 0xe871c7bf077ba8b7}, // 1e-125 * 2**543
{0x87625f056c7c4a8b, 0x11471cd764ad4972}, // 1e-124 * 2**539
{0xa93af6c6c79b5d2d, 0xd598e40d3dd89bcf}, // 1e-123 * 2**536
{0xd389b47879823479, 0x4aff1d108d4ec2c3}, // 1e-122 * 2**533
{0x843610cb4bf160cb, 0xcedf722a585139ba}, // 1e-121 * 2**529
{0xa54394fe1eedb8fe, 0xc2974eb4ee658828}, // 1e-120 * 2**526
{0xce947a3da6a9273e, 0x733d226229feea32}, // 1e-119 * 2**523
{0x811ccc668829b887, 0x0806357d5a3f525f}, // 1e-118 * 2**519
{0xa163ff802a3426a8, 0xca07c2dcb0cf26f7}, // 1e-117 * 2**516
{0xc9bcff6034c13052, 0xfc89b393dd02f0b5}, // 1e-116 * 2**513
{0xfc2c3f3841f17c67, 0xbbac2078d443ace2}, // 1e-115 * 2**510
{0x9d9ba7832936edc0, 0xd54b944b84aa4c0d}, // 1e-114 * 2**506
{0xc5029163f384a931, 0x0a9e795e65d4df11}, // 1e-113 * 2**503
{0xf64335bcf065d37d, 0x4d4617b5ff4a16d5}, // 1e-112 * 2**500
{0x99ea0196163fa42e, 0x504bced1bf8e4e45}, // 1e-111 * 2**496
{0xc06481fb9bcf8d39, 0xe45ec2862f71e1d6}, // 1e-110 * 2**493
{0xf07da27a82c37088, 0x5d767327bb4e5a4c}, // 1e-109 * 2**490
{0x964e858c91ba2655, 0x3a6a07f8d510f86f}, // 1e-108 * 2**486
{0xbbe226efb628afea, 0x890489f70a55368b}, // 1e-107 * 2**483
{0xeadab0aba3b2dbe5, 0x2b45ac74ccea842e}, // 1e-106 * 2**480
{0x92c8ae6b464fc96f, 0x3b0b8bc90012929d}, // 1e-105 * 2**476
{0xb77ada0617e3bbcb, 0x09ce6ebb40173744}, // 1e-104 * 2**473
{0xe55990879ddcaabd, 0xcc420a6a101d0515}, // 1e-103 * 2**470
{0x8f57fa54c2a9eab6, 0x9fa946824a12232d}, // 1e-102 * 2**466
{0xb32df8e9f3546564, 0x47939822dc96abf9}, // 1e-101 * 2**463
{0xdff9772470297ebd, 0x59787e2b93bc56f7}, // 1e-100 * 2**460
{0x8bfbea76c619ef36, 0x57eb4edb3c55b65a}, // 1e-99 * 2**456
{0xaefae51477a06b03, 0xede622920b6b23f1}, // 1e-98 * 2**453
{0xdab99e59958885c4, 0xe95fab368e45eced}, // 1e-97 * 2**450
{0x88b402f7fd75539b, 0x11dbcb0218ebb414}, // 1e-96 * 2**446
{0xaae103b5fcd2a881, 0xd652bdc29f26a119}, // 1e-95 * 2**443
{0xd59944a37c0752a2, 0x4be76d3346f0495f}, // 1e-94 * 2**440
{0x857fcae62d8493a5, 0x6f70a4400c562ddb}, // 1e-93 * 2**436
{0xa6dfbd9fb8e5b88e, 0xcb4ccd500f6bb952}, // 1e-92 * 2**433
{0xd097ad07a71f26b2, 0x7e2000a41346a7a7}, // 1e-91 * 2**430
{0x825ecc24c873782f, 0x8ed400668c0c28c8}, // 1e-90 * 2**426
{0xa2f67f2dfa90563b, 0x728900802f0f32fa}, // 1e-89 * 2**423
{0xcbb41ef979346bca, 0x4f2b40a03ad2ffb9}, // 1e-88 * 2**420
{0xfea126b7d78186bc, 0xe2f610c84987bfa8}, // 1e-87 * 2**417
{0x9f24b832e6b0f436, 0x0dd9ca7d2df4d7c9}, // 1e-86 * 2**413
{0xc6ede63fa05d3143, 0x91503d1c79720dbb}, // 1e-85 * 2**410
{0xf8a95fcf88747d94, 0x75a44c6397ce912a}, // 1e-84 * 2**407
{0x9b69dbe1b548ce7c, 0xc986afbe3ee11aba}, // 1e-83 * 2**403
{0xc24452da229b021b, 0xfbe85badce996168}, // 1e-82 * 2**400
{0xf2d56790ab41c2a2, 0xfae27299423fb9c3}, // 1e-81 * 2**397
{0x97c560ba6b0919a5, 0xdccd879fc967d41a}, // 1e-80 * 2**393
{0xbdb6b8e905cb600f, 0x5400e987bbc1c920}, // 1e-79 * 2**390
{0xed246723473e3813, 0x290123e9aab23b68}, // 1e-78 * 2**387
{0x9436c0760c86e30b, 0xf9a0b6720aaf6521}, // 1e-77 * 2**383
{0xb94470938fa89bce, 0xf808e40e8d5b3e69}, // 1e-76 * 2**380
{0xe7958cb87392c2c2, 0xb60b1d1230b20e04}, // 1e-75 * 2**377
{0x90bd77f3483bb9b9, 0xb1c6f22b5e6f48c2}, // 1e-74 * 2**373
{0xb4ecd5f01a4aa828, 0x1e38aeb6360b1af3}, // 1e-73 * 2**370
{0xe2280b6c20dd5232, 0x25c6da63c38de1b0}, // 1e-72 * 2**367
{0x8d590723948a535f, 0x579c487e5a38ad0e}, // 1e-71 * 2**363
{0xb0af48ec79ace837, 0x2d835a9df0c6d851}, // 1e-70 * 2**360
{0xdcdb1b2798182244, 0xf8e431456cf88e65}, // 1e-69 * 2**357
{0x8a08f0f8bf0f156b, 0x1b8e9ecb641b58ff}, // 1e-68 * 2**353
{0xac8b2d36eed2dac5, 0xe272467e3d222f3f}, // 1e-67 * 2**350
{0xd7adf884aa879177, 0x5b0ed81dcc6abb0f}, // 1e-66 * 2**347
{0x86ccbb52ea94baea, 0x98e947129fc2b4e9}, // 1e-65 * 2**343
{0xa87fea27a539e9a5, 0x3f2398d747b36224}, // 1e-64 * 2**340
{0xd29fe4b18e88640e, 0x8eec7f0d19a03aad}, // 1e-63 * 2**337
{0x83a3eeeef9153e89, 0x1953cf68300424ac}, // 1e-62 * 2**333
{0xa48ceaaab75a8e2b, 0x5fa8c3423c052dd7}, // 1e-61 * 2**330
{0xcdb02555653131b6, 0x3792f412cb06794d}, // 1e-60 * 2**327
{0x808e17555f3ebf11, 0xe2bbd88bbee40bd0}, // 1e-59 * 2**323
{0xa0b19d2ab70e6ed6, 0x5b6aceaeae9d0ec4}, // 1e-58 * 2**320
{0xc8de047564d20a8b, 0xf245825a5a445275}, // 1e-57 * 2**317
{0xfb158592be068d2e, 0xeed6e2f0f0d56712}, // 1e-56 * 2**314
{0x9ced737bb6c4183d, 0x55464dd69685606b}, // 1e-55 * 2**310
{0xc428d05aa4751e4c, 0xaa97e14c3c26b886}, // 1e-54 * 2**307
{0xf53304714d9265df, 0xd53dd99f4b3066a8}, // 1e-53 * 2**304
{0x993fe2c6d07b7fab, 0xe546a8038efe4029}, // 1e-52 * 2**300
{0xbf8fdb78849a5f96, 0xde98520472bdd033}, // 1e-51 * 2**297
{0xef73d256a5c0f77c, 0x963e66858f6d4440}, // 1e-50 * 2**294
{0x95a8637627989aad, 0xdde7001379a44aa8}, // 1e-49 * 2**290
{0xbb127c53b17ec159, 0x5560c018580d5d52}, // 1e-48 * 2**287
{0xe9d71b689dde71af, 0xaab8f01e6e10b4a6}, // 1e-47 * 2**284
{0x9226712162ab070d, 0xcab3961304ca70e8}, // 1e-46 * 2**280
{0xb6b00d69bb55c8d1, 0x3d607b97c5fd0d22}, // 1e-45 * 2**277
{0xe45c10c42a2b3b05, 0x8cb89a7db77c506a}, // 1e-44 * 2**274
{0x8eb98a7a9a5b04e3, 0x77f3608e92adb242}, // 1e-43 * 2**270
{0xb267ed1940f1c61c, 0x55f038b237591ed3}, // 1e-42 * 2**267
{0xdf01e85f912e37a3, 0x6b6c46dec52f6688}, // 1e-41 * 2**264
{0x8b61313bbabce2c6, 0x2323ac4b3b3da015}, // 1e-40 * 2**260
{0xae397d8aa96c1b77, 0xabec975e0a0d081a}, // 1e-39 * 2**257
{0xd9c7dced53c72255, 0x96e7bd358c904a21}, // 1e-38 * 2**254
{0x881cea14545c7575, 0x7e50d64177da2e54}, // 1e-37 * 2**250
{0xaa242499697392d2, 0xdde50bd1d5d0b9e9}, // 1e-36 * 2**247
{0xd4ad2dbfc3d07787, 0x955e4ec64b44e864}, // 1e-35 * 2**244
{0x84ec3c97da624ab4, 0xbd5af13bef0b113e}, // 1e-34 * 2**240
{0xa6274bbdd0fadd61, 0xecb1ad8aeacdd58e}, // 1e-33 * 2**237
{0xcfb11ead453994ba, 0x67de18eda5814af2}, // 1e-32 * 2**234
{0x81ceb32c4b43fcf4, 0x80eacf948770ced7}, // 1e-31 * 2**230
{0xa2425ff75e14fc31, 0xa1258379a94d028d}, // 1e-30 * 2**227
{0xcad2f7f5359a3b3e, 0x096ee45813a04330}, // 1e-29 * 2**224
{0xfd87b5f28300ca0d, 0x8bca9d6e188853fc}, // 1e-28 * 2**221
{0x9e74d1b791e07e48, 0x775ea264cf55347d}, // 1e-27 * 2**217
{0xc612062576589dda, 0x95364afe032a819d}, // 1e-26 * 2**214
{0xf79687aed3eec551, 0x3a83ddbd83f52204}, // 1e-25 * 2**211
{0x9abe14cd44753b52, 0xc4926a9672793542}, // 1e-24 * 2**207
{0xc16d9a0095928a27, 0x75b7053c0f178293}, // 1e-23 * 2**204
{0xf1c90080baf72cb1, 0x5324c68b12dd6338}, // 1e-22 * 2**201
{0x971da05074da7bee, 0xd3f6fc16ebca5e03}, // 1e-21 * 2**197
{0xbce5086492111aea, 0x88f4bb1ca6bcf584}, // 1e-20 * 2**194
{0xec1e4a7db69561a5, 0x2b31e9e3d06c32e5}, // 1e-19 * 2**191
{0x9392ee8e921d5d07, 0x3aff322e62439fcf}, // 1e-18 * 2**187
{0xb877aa3236a4b449, 0x09befeb9fad487c2}, // 1e-17 * 2**184
{0xe69594bec44de15b, 0x4c2ebe687989a9b3}, // 1e-16 * 2**181
{0x901d7cf73ab0acd9, 0x0f9d37014bf60a10}, // 1e-15 * 2**177
{0xb424dc35095cd80f, 0x538484c19ef38c94}, // 1e-14 * 2**174
{0xe12e13424bb40e13, 0x2865a5f206b06fb9}, // 1e-13 * 2**171
{0x8cbccc096f5088cb, 0xf93f87b7442e45d3}, // 1e-12 * 2**167
{0xafebff0bcb24aafe, 0xf78f69a51539d748}, // 1e-11 * 2**164
{0xdbe6fecebdedd5be, 0xb573440e5a884d1b}, // 1e-10 * 2**161
{0x89705f4136b4a597, 0x31680a88f8953030}, // 1e-9 * 2**157
{0xabcc77118461cefc, 0xfdc20d2b36ba7c3d}, // 1e-8 * 2**154
{0xd6bf94d5e57a42bc, 0x3d32907604691b4c}, // 1e-7 * 2**151
{0x8637bd05af6c69b5, 0xa63f9a49c2c1b10f}, // 1e-6 * 2**147
{0xa7c5ac471b478423, 0x0fcf80dc33721d53}, // 1e-5 * 2**144
{0xd1b71758e219652b, 0xd3c36113404ea4a8}, // 1e-4 * 2**141
{0x83126e978d4fdf3b, 0x645a1cac083126e9}, // 1e-3 * 2**137
{0xa3d70a3d70a3d70a, 0x3d70a3d70a3d70a3}, // 1e-2 * 2**134
{0xcccccccccccccccc, 0xcccccccccccccccc}, // 1e-1 * 2**131
{0x8000000000000000, 0x0000000000000000}, // 1e0 * 2**127
{0xa000000000000000, 0x0000000000000000}, // 1e1 * 2**124
{0xc800000000000000, 0x0000000000000000}, // 1e2 * 2**121
{0xfa00000000000000, 0x0000000000000000}, // 1e3 * 2**118
{0x9c40000000000000, 0x0000000000000000}, // 1e4 * 2**114
{0xc350000000000000, 0x0000000000000000}, // 1e5 * 2**111
{0xf424000000000000, 0x0000000000000000}, // 1e6 * 2**108
{0x9896800000000000, 0x0000000000000000}, // 1e7 * 2**104
{0xbebc200000000000, 0x0000000000000000}, // 1e8 * 2**101
{0xee6b280000000000, 0x0000000000000000}, // 1e9 * 2**98
{0x9502f90000000000, 0x0000000000000000}, // 1e10 * 2**94
{0xba43b74000000000, 0x0000000000000000}, // 1e11 * 2**91
{0xe8d4a51000000000, 0x0000000000000000}, // 1e12 * 2**88
{0x9184e72a00000000, 0x0000000000000000}, // 1e13 * 2**84
{0xb5e620f480000000, 0x0000000000000000}, // 1e14 * 2**81
{0xe35fa931a0000000, 0x0000000000000000}, // 1e15 * 2**78
{0x8e1bc9bf04000000, 0x0000000000000000}, // 1e16 * 2**74
{0xb1a2bc2ec5000000, 0x0000000000000000}, // 1e17 * 2**71
{0xde0b6b3a76400000, 0x0000000000000000}, // 1e18 * 2**68
{0x8ac7230489e80000, 0x0000000000000000}, // 1e19 * 2**64
{0xad78ebc5ac620000, 0x0000000000000000}, // 1e20 * 2**61
{0xd8d726b7177a8000, 0x0000000000000000}, // 1e21 * 2**58
{0x878678326eac9000, 0x0000000000000000}, // 1e22 * 2**54
{0xa968163f0a57b400, 0x0000000000000000}, // 1e23 * 2**51
{0xd3c21bcecceda100, 0x0000000000000000}, // 1e24 * 2**48
{0x84595161401484a0, 0x0000000000000000}, // 1e25 * 2**44
{0xa56fa5b99019a5c8, 0x0000000000000000}, // 1e26 * 2**41
{0xcecb8f27f4200f3a, 0x0000000000000000}, // 1e27 * 2**38
{0x813f3978f8940984, 0x4000000000000000}, // 1e28 * 2**34
{0xa18f07d736b90be5, 0x5000000000000000}, // 1e29 * 2**31
{0xc9f2c9cd04674ede, 0xa400000000000000}, // 1e30 * 2**28
{0xfc6f7c4045812296, 0x4d00000000000000}, // 1e31 * 2**25
{0x9dc5ada82b70b59d, 0xf020000000000000}, // 1e32 * 2**21
{0xc5371912364ce305, 0x6c28000000000000}, // 1e33 * 2**18
{0xf684df56c3e01bc6, 0xc732000000000000}, // 1e34 * 2**15
{0x9a130b963a6c115c, 0x3c7f400000000000}, // 1e35 * 2**11
{0xc097ce7bc90715b3, 0x4b9f100000000000}, // 1e36 * 2**8
{0xf0bdc21abb48db20, 0x1e86d40000000000}, // 1e37 * 2**5
{0x96769950b50d88f4, 0x1314448000000000}, // 1e38 * 2**1
{0xbc143fa4e250eb31, 0x17d955a000000000}, // 1e39 * 2**-2
{0xeb194f8e1ae525fd, 0x5dcfab0800000000}, // 1e40 * 2**-5
{0x92efd1b8d0cf37be, 0x5aa1cae500000000}, // 1e41 * 2**-9
{0xb7abc627050305ad, 0xf14a3d9e40000000}, // 1e42 * 2**-12
{0xe596b7b0c643c719, 0x6d9ccd05d0000000}, // 1e43 * 2**-15
{0x8f7e32ce7bea5c6f, 0xe4820023a2000000}, // 1e44 * 2**-19
{0xb35dbf821ae4f38b, 0xdda2802c8a800000}, // 1e45 * 2**-22
{0xe0352f62a19e306e, 0xd50b2037ad200000}, // 1e46 * 2**-25
{0x8c213d9da502de45, 0x4526f422cc340000}, // 1e47 * 2**-29
{0xaf298d050e4395d6, 0x9670b12b7f410000}, // 1e48 * 2**-32
{0xdaf3f04651d47b4c, 0x3c0cdd765f114000}, // 1e49 * 2**-35
{0x88d8762bf324cd0f, 0xa5880a69fb6ac800}, // 1e50 * 2**-39
{0xab0e93b6efee0053, 0x8eea0d047a457a00}, // 1e51 * 2**-42
{0xd5d238a4abe98068, 0x72a4904598d6d880}, // 1e52 * 2**-45
{0x85a36366eb71f041, 0x47a6da2b7f864750}, // 1e53 * 2**-49
{0xa70c3c40a64e6c51, 0x999090b65f67d924}, // 1e54 * 2**-52
{0xd0cf4b50cfe20765, 0xfff4b4e3f741cf6d}, // 1e55 * 2**-55
{0x82818f1281ed449f, 0xbff8f10e7a8921a4}, // 1e56 * 2**-59
{0xa321f2d7226895c7, 0xaff72d52192b6a0d}, // 1e57 * 2**-62
{0xcbea6f8ceb02bb39, 0x9bf4f8a69f764490}, // 1e58 * 2**-65
{0xfee50b7025c36a08, 0x02f236d04753d5b4}, // 1e59 * 2**-68
{0x9f4f2726179a2245, 0x01d762422c946590}, // 1e60 * 2**-72
{0xc722f0ef9d80aad6, 0x424d3ad2b7b97ef5}, // 1e61 * 2**-75
{0xf8ebad2b84e0d58b, 0xd2e0898765a7deb2}, // 1e62 * 2**-78
{0x9b934c3b330c8577, 0x63cc55f49f88eb2f}, // 1e63 * 2**-82
{0xc2781f49ffcfa6d5, 0x3cbf6b71c76b25fb}, // 1e64 * 2**-85
{0xf316271c7fc3908a, 0x8bef464e3945ef7a}, // 1e65 * 2**-88
{0x97edd871cfda3a56, 0x97758bf0e3cbb5ac}, // 1e66 * 2**-92
{0xbde94e8e43d0c8ec, 0x3d52eeed1cbea317}, // 1e67 * 2**-95
{0xed63a231d4c4fb27, 0x4ca7aaa863ee4bdd}, // 1e68 * 2**-98
{0x945e455f24fb1cf8, 0x8fe8caa93e74ef6a}, // 1e69 * 2**-102
{0xb975d6b6ee39e436, 0xb3e2fd538e122b44}, // 1e70 * 2**-105
{0xe7d34c64a9c85d44, 0x60dbbca87196b616}, // 1e71 * 2**-108
{0x90e40fbeea1d3a4a, 0xbc8955e946fe31cd}, // 1e72 * 2**-112
{0xb51d13aea4a488dd, 0x6babab6398bdbe41}, // 1e73 * 2**-115
{0xe264589a4dcdab14, 0xc696963c7eed2dd1}, // 1e74 * 2**-118
{0x8d7eb76070a08aec, 0xfc1e1de5cf543ca2}, // 1e75 * 2**-122
{0xb0de65388cc8ada8, 0x3b25a55f43294bcb}, // 1e76 * 2**-125
{0xdd15fe86affad912, 0x49ef0eb713f39ebe}, // 1e77 * 2**-128
{0x8a2dbf142dfcc7ab, 0x6e3569326c784337}, // 1e78 * 2**-132
{0xacb92ed9397bf996, 0x49c2c37f07965404}, // 1e79 * 2**-135
{0xd7e77a8f87daf7fb, 0xdc33745ec97be906}, // 1e80 * 2**-138
{0x86f0ac99b4e8dafd, 0x69a028bb3ded71a3}, // 1e81 * 2**-142
{0xa8acd7c0222311bc, 0xc40832ea0d68ce0c}, // 1e82 * 2**-145
{0xd2d80db02aabd62b, 0xf50a3fa490c30190}, // 1e83 * 2**-148
{0x83c7088e1aab65db, 0x792667c6da79e0fa}, // 1e84 * 2**-152
{0xa4b8cab1a1563f52, 0x577001b891185938}, // 1e85 * 2**-155
{0xcde6fd5e09abcf26, 0xed4c0226b55e6f86}, // 1e86 * 2**-158
{0x80b05e5ac60b6178, 0x544f8158315b05b4}, // 1e87 * 2**-162
{0xa0dc75f1778e39d6, 0x696361ae3db1c721}, // 1e88 * 2**-165
{0xc913936dd571c84c, 0x03bc3a19cd1e38e9}, // 1e89 * 2**-168
{0xfb5878494ace3a5f, 0x04ab48a04065c723}, // 1e90 * 2**-171
{0x9d174b2dcec0e47b, 0x62eb0d64283f9c76}, // 1e91 * 2**-175
{0xc45d1df942711d9a, 0x3ba5d0bd324f8394}, // 1e92 * 2**-178
{0xf5746577930d6500, 0xca8f44ec7ee36479}, // 1e93 * 2**-181
{0x9968bf6abbe85f20, 0x7e998b13cf4e1ecb}, // 1e94 * 2**-185
{0xbfc2ef456ae276e8, 0x9e3fedd8c321a67e}, // 1e95 * 2**-188
{0xefb3ab16c59b14a2, 0xc5cfe94ef3ea101e}, // 1e96 * 2**-191
{0x95d04aee3b80ece5, 0xbba1f1d158724a12}, // 1e97 * 2**-195
{0xbb445da9ca61281f, 0x2a8a6e45ae8edc97}, // 1e98 * 2**-198
{0xea1575143cf97226, 0xf52d09d71a3293bd}, // 1e99 * 2**-201
{0x924d692ca61be758, 0x593c2626705f9c56}, // 1e100 * 2**-205
{0xb6e0c377cfa2e12e, 0x6f8b2fb00c77836c}, // 1e101 * 2**-208
{0xe498f455c38b997a, 0x0b6dfb9c0f956447}, // 1e102 * 2**-211
{0x8edf98b59a373fec, 0x4724bd4189bd5eac}, // 1e103 * 2**-215
{0xb2977ee300c50fe7, 0x58edec91ec2cb657}, // 1e104 * 2**-218
{0xdf3d5e9bc0f653e1, 0x2f2967b66737e3ed}, // 1e105 * 2**-221
{0x8b865b215899f46c, 0xbd79e0d20082ee74}, // 1e106 * 2**-225
{0xae67f1e9aec07187, 0xecd8590680a3aa11}, // 1e107 * 2**-228
{0xda01ee641a708de9, 0xe80e6f4820cc9495}, // 1e108 * 2**-231
{0x884134fe908658b2, 0x3109058d147fdcdd}, // 1e109 * 2**-235
{0xaa51823e34a7eede, 0xbd4b46f0599fd415}, // 1e110 * 2**-238
{0xd4e5e2cdc1d1ea96, 0x6c9e18ac7007c91a}, // 1e111 * 2**-241
{0x850fadc09923329e, 0x03e2cf6bc604ddb0}, // 1e112 * 2**-245
{0xa6539930bf6bff45, 0x84db8346b786151c}, // 1e113 * 2**-248
{0xcfe87f7cef46ff16, 0xe612641865679a63}, // 1e114 * 2**-251
{0x81f14fae158c5f6e, 0x4fcb7e8f3f60c07e}, // 1e115 * 2**-255
{0xa26da3999aef7749, 0xe3be5e330f38f09d}, // 1e116 * 2**-258
{0xcb090c8001ab551c, 0x5cadf5bfd3072cc5}, // 1e117 * 2**-261
{0xfdcb4fa002162a63, 0x73d9732fc7c8f7f6}, // 1e118 * 2**-264
{0x9e9f11c4014dda7e, 0x2867e7fddcdd9afa}, // 1e119 * 2**-268
{0xc646d63501a1511d, 0xb281e1fd541501b8}, // 1e120 * 2**-271
{0xf7d88bc24209a565, 0x1f225a7ca91a4226}, // 1e121 * 2**-274
{0x9ae757596946075f, 0x3375788de9b06958}, // 1e122 * 2**-278
{0xc1a12d2fc3978937, 0x0052d6b1641c83ae}, // 1e123 * 2**-281
{0xf209787bb47d6b84, 0xc0678c5dbd23a49a}, // 1e124 * 2**-284
{0x9745eb4d50ce6332, 0xf840b7ba963646e0}, // 1e125 * 2**-288
{0xbd176620a501fbff, 0xb650e5a93bc3d898}, // 1e126 * 2**-291
{0xec5d3fa8ce427aff, 0xa3e51f138ab4cebe}, // 1e127 * 2**-294
{0x93ba47c980e98cdf, 0xc66f336c36b10137}, // 1e128 * 2**-298
{0xb8a8d9bbe123f017, 0xb80b0047445d4184}, // 1e129 * 2**-301
{0xe6d3102ad96cec1d, 0xa60dc059157491e5}, // 1e130 * 2**-304
{0x9043ea1ac7e41392, 0x87c89837ad68db2f}, // 1e131 * 2**-308
{0xb454e4a179dd1877, 0x29babe4598c311fb}, // 1e132 * 2**-311
{0xe16a1dc9d8545e94, 0xf4296dd6fef3d67a}, // 1e133 * 2**-314
{0x8ce2529e2734bb1d, 0x1899e4a65f58660c}, // 1e134 * 2**-318
{0xb01ae745b101e9e4, 0x5ec05dcff72e7f8f}, // 1e135 * 2**-321
{0xdc21a1171d42645d, 0x76707543f4fa1f73}, // 1e136 * 2**-324
{0x899504ae72497eba, 0x6a06494a791c53a8}, // 1e137 * 2**-328
{0xabfa45da0edbde69, 0x0487db9d17636892}, // 1e138 * 2**-331
{0xd6f8d7509292d603, 0x45a9d2845d3c42b6}, // 1e139 * 2**-334
{0x865b86925b9bc5c2, 0x0b8a2392ba45a9b2}, // 1e140 * 2**-338
{0xa7f26836f282b732, 0x8e6cac7768d7141e}, // 1e141 * 2**-341
{0xd1ef0244af2364ff, 0x3207d795430cd926}, // 1e142 * 2**-344
{0x8335616aed761f1f, 0x7f44e6bd49e807b8}, // 1e143 * 2**-348
{0xa402b9c5a8d3a6e7, 0x5f16206c9c6209a6}, // 1e144 * 2**-351
{0xcd036837130890a1, 0x36dba887c37a8c0f}, // 1e145 * 2**-354
{0x802221226be55a64, 0xc2494954da2c9789}, // 1e146 * 2**-358
{0xa02aa96b06deb0fd, 0xf2db9baa10b7bd6c}, // 1e147 * 2**-361
{0xc83553c5c8965d3d, 0x6f92829494e5acc7}, // 1e148 * 2**-364
{0xfa42a8b73abbf48c, 0xcb772339ba1f17f9}, // 1e149 * 2**-367
{0x9c69a97284b578d7, 0xff2a760414536efb}, // 1e150 * 2**-371
{0xc38413cf25e2d70d, 0xfef5138519684aba}, // 1e151 * 2**-374
{0xf46518c2ef5b8cd1, 0x7eb258665fc25d69}, // 1e152 * 2**-377
{0x98bf2f79d5993802, 0xef2f773ffbd97a61}, // 1e153 * 2**-381
{0xbeeefb584aff8603, 0xaafb550ffacfd8fa}, // 1e154 * 2**-384
{0xeeaaba2e5dbf6784, 0x95ba2a53f983cf38}, // 1e155 * 2**-387
{0x952ab45cfa97a0b2, 0xdd945a747bf26183}, // 1e156 * 2**-391
{0xba756174393d88df, 0x94f971119aeef9e4}, // 1e157 * 2**-394
{0xe912b9d1478ceb17, 0x7a37cd5601aab85d}, // 1e158 * 2**-397
{0x91abb422ccb812ee, 0xac62e055c10ab33a}, // 1e159 * 2**-401
{0xb616a12b7fe617aa, 0x577b986b314d6009}, // 1e160 * 2**-404
{0xe39c49765fdf9d94, 0xed5a7e85fda0b80b}, // 1e161 * 2**-407
{0x8e41ade9fbebc27d, 0x14588f13be847307}, // 1e162 * 2**-411
{0xb1d219647ae6b31c, 0x596eb2d8ae258fc8}, // 1e163 * 2**-414
{0xde469fbd99a05fe3, 0x6fca5f8ed9aef3bb}, // 1e164 * 2**-417
{0x8aec23d680043bee, 0x25de7bb9480d5854}, // 1e165 * 2**-421
{0xada72ccc20054ae9, 0xaf561aa79a10ae6a}, // 1e166 * 2**-424
{0xd910f7ff28069da4, 0x1b2ba1518094da04}, // 1e167 * 2**-427
{0x87aa9aff79042286, 0x90fb44d2f05d0842}, // 1e168 * 2**-431
{0xa99541bf57452b28, 0x353a1607ac744a53}, // 1e169 * 2**-434
{0xd3fa922f2d1675f2, 0x42889b8997915ce8}, // 1e170 * 2**-437
{0x847c9b5d7c2e09b7, 0x69956135febada11}, // 1e171 * 2**-441
{0xa59bc234db398c25, 0x43fab9837e699095}, // 1e172 * 2**-444
{0xcf02b2c21207ef2e, 0x94f967e45e03f4bb}, // 1e173 * 2**-447
{0x8161afb94b44f57d, 0x1d1be0eebac278f5}, // 1e174 * 2**-451
{0xa1ba1ba79e1632dc, 0x6462d92a69731732}, // 1e175 * 2**-454
{0xca28a291859bbf93, 0x7d7b8f7503cfdcfe}, // 1e176 * 2**-457
{0xfcb2cb35e702af78, 0x5cda735244c3d43e}, // 1e177 * 2**-460
{0x9defbf01b061adab, 0x3a0888136afa64a7}, // 1e178 * 2**-464
{0xc56baec21c7a1916, 0x088aaa1845b8fdd0}, // 1e179 * 2**-467
{0xf6c69a72a3989f5b, 0x8aad549e57273d45}, // 1e180 * 2**-470
{0x9a3c2087a63f6399, 0x36ac54e2f678864b}, // 1e181 * 2**-474
{0xc0cb28a98fcf3c7f, 0x84576a1bb416a7dd}, // 1e182 * 2**-477
{0xf0fdf2d3f3c30b9f, 0x656d44a2a11c51d5}, // 1e183 * 2**-480
{0x969eb7c47859e743, 0x9f644ae5a4b1b325}, // 1e184 * 2**-484
{0xbc4665b596706114, 0x873d5d9f0dde1fee}, // 1e185 * 2**-487
{0xeb57ff22fc0c7959, 0xa90cb506d155a7ea}, // 1e186 * 2**-490
{0x9316ff75dd87cbd8, 0x09a7f12442d588f2}, // 1e187 * 2**-494
{0xb7dcbf5354e9bece, 0x0c11ed6d538aeb2f}, // 1e188 * 2**-497
{0xe5d3ef282a242e81, 0x8f1668c8a86da5fa}, // 1e189 * 2**-500
{0x8fa475791a569d10, 0xf96e017d694487bc}, // 1e190 * 2**-504
{0xb38d92d760ec4455, 0x37c981dcc395a9ac}, // 1e191 * 2**-507
{0xe070f78d3927556a, 0x85bbe253f47b1417}, // 1e192 * 2**-510
{0x8c469ab843b89562, 0x93956d7478ccec8e}, // 1e193 * 2**-514
{0xaf58416654a6babb, 0x387ac8d1970027b2}, // 1e194 * 2**-517
{0xdb2e51bfe9d0696a, 0x06997b05fcc0319e}, // 1e195 * 2**-520
{0x88fcf317f22241e2, 0x441fece3bdf81f03}, // 1e196 * 2**-524
{0xab3c2fddeeaad25a, 0xd527e81cad7626c3}, // 1e197 * 2**-527
{0xd60b3bd56a5586f1, 0x8a71e223d8d3b074}, // 1e198 * 2**-530
{0x85c7056562757456, 0xf6872d5667844e49}, // 1e199 * 2**-534
{0xa738c6bebb12d16c, 0xb428f8ac016561db}, // 1e200 * 2**-537
{0xd106f86e69d785c7, 0xe13336d701beba52}, // 1e201 * 2**-540
{0x82a45b450226b39c, 0xecc0024661173473}, // 1e202 * 2**-544
{0xa34d721642b06084, 0x27f002d7f95d0190}, // 1e203 * 2**-547
{0xcc20ce9bd35c78a5, 0x31ec038df7b441f4}, // 1e204 * 2**-550
{0xff290242c83396ce, 0x7e67047175a15271}, // 1e205 * 2**-553
{0x9f79a169bd203e41, 0x0f0062c6e984d386}, // 1e206 * 2**-557
{0xc75809c42c684dd1, 0x52c07b78a3e60868}, // 1e207 * 2**-560
{0xf92e0c3537826145, 0xa7709a56ccdf8a82}, // 1e208 * 2**-563
{0x9bbcc7a142b17ccb, 0x88a66076400bb691}, // 1e209 * 2**-567
{0xc2abf989935ddbfe, 0x6acff893d00ea435}, // 1e210 * 2**-570
{0xf356f7ebf83552fe, 0x0583f6b8c4124d43}, // 1e211 * 2**-573
{0x98165af37b2153de, 0xc3727a337a8b704a}, // 1e212 * 2**-577
{0xbe1bf1b059e9a8d6, 0x744f18c0592e4c5c}, // 1e213 * 2**-580
{0xeda2ee1c7064130c, 0x1162def06f79df73}, // 1e214 * 2**-583
{0x9485d4d1c63e8be7, 0x8addcb5645ac2ba8}, // 1e215 * 2**-587
{0xb9a74a0637ce2ee1, 0x6d953e2bd7173692}, // 1e216 * 2**-590
{0xe8111c87c5c1ba99, 0xc8fa8db6ccdd0437}, // 1e217 * 2**-593
{0x910ab1d4db9914a0, 0x1d9c9892400a22a2}, // 1e218 * 2**-597
{0xb54d5e4a127f59c8, 0x2503beb6d00cab4b}, // 1e219 * 2**-600
{0xe2a0b5dc971f303a, 0x2e44ae64840fd61d}, // 1e220 * 2**-603
{0x8da471a9de737e24, 0x5ceaecfed289e5d2}, // 1e221 * 2**-607
{0xb10d8e1456105dad, 0x7425a83e872c5f47}, // 1e222 * 2**-610
{0xdd50f1996b947518, 0xd12f124e28f77719}, // 1e223 * 2**-613
{0x8a5296ffe33cc92f, 0x82bd6b70d99aaa6f}, // 1e224 * 2**-617
{0xace73cbfdc0bfb7b, 0x636cc64d1001550b}, // 1e225 * 2**-620
{0xd8210befd30efa5a, 0x3c47f7e05401aa4e}, // 1e226 * 2**-623
{0x8714a775e3e95c78, 0x65acfaec34810a71}, // 1e227 * 2**-627
{0xa8d9d1535ce3b396, 0x7f1839a741a14d0d}, // 1e228 * 2**-630
{0xd31045a8341ca07c, 0x1ede48111209a050}, // 1e229 * 2**-633
{0x83ea2b892091e44d, 0x934aed0aab460432}, // 1e230 * 2**-637
{0xa4e4b66b68b65d60, 0xf81da84d5617853f}, // 1e231 * 2**-640
{0xce1de40642e3f4b9, 0x36251260ab9d668e}, // 1e232 * 2**-643
{0x80d2ae83e9ce78f3, 0xc1d72b7c6b426019}, // 1e233 * 2**-647
{0xa1075a24e4421730, 0xb24cf65b8612f81f}, // 1e234 * 2**-650
{0xc94930ae1d529cfc, 0xdee033f26797b627}, // 1e235 * 2**-653
{0xfb9b7cd9a4a7443c, 0x169840ef017da3b1}, // 1e236 * 2**-656
{0x9d412e0806e88aa5, 0x8e1f289560ee864e}, // 1e237 * 2**-660
{0xc491798a08a2ad4e, 0xf1a6f2bab92a27e2}, // 1e238 * 2**-663
{0xf5b5d7ec8acb58a2, 0xae10af696774b1db}, // 1e239 * 2**-666
{0x9991a6f3d6bf1765, 0xacca6da1e0a8ef29}, // 1e240 * 2**-670
{0xbff610b0cc6edd3f, 0x17fd090a58d32af3}, // 1e241 * 2**-673
{0xeff394dcff8a948e, 0xddfc4b4cef07f5b0}, // 1e242 * 2**-676
{0x95f83d0a1fb69cd9, 0x4abdaf101564f98e}, // 1e243 * 2**-680
{0xbb764c4ca7a4440f, 0x9d6d1ad41abe37f1}, // 1e244 * 2**-683
{0xea53df5fd18d5513, 0x84c86189216dc5ed}, // 1e245 * 2**-686
{0x92746b9be2f8552c, 0x32fd3cf5b4e49bb4}, // 1e246 * 2**-690
{0xb7118682dbb66a77, 0x3fbc8c33221dc2a1}, // 1e247 * 2**-693
{0xe4d5e82392a40515, 0x0fabaf3feaa5334a}, // 1e248 * 2**-696
{0x8f05b1163ba6832d, 0x29cb4d87f2a7400e}, // 1e249 * 2**-700
{0xb2c71d5bca9023f8, 0x743e20e9ef511012}, // 1e250 * 2**-703
{0xdf78e4b2bd342cf6, 0x914da9246b255416}, // 1e251 * 2**-706
{0x8bab8eefb6409c1a, 0x1ad089b6c2f7548e}, // 1e252 * 2**-710
{0xae9672aba3d0c320, 0xa184ac2473b529b1}, // 1e253 * 2**-713
{0xda3c0f568cc4f3e8, 0xc9e5d72d90a2741e}, // 1e254 * 2**-716
{0x8865899617fb1871, 0x7e2fa67c7a658892}, // 1e255 * 2**-720
{0xaa7eebfb9df9de8d, 0xddbb901b98feeab7}, // 1e256 * 2**-723
{0xd51ea6fa85785631, 0x552a74227f3ea565}, // 1e257 * 2**-726
{0x8533285c936b35de, 0xd53a88958f87275f}, // 1e258 * 2**-730
{0xa67ff273b8460356, 0x8a892abaf368f137}, // 1e259 * 2**-733
{0xd01fef10a657842c, 0x2d2b7569b0432d85}, // 1e260 * 2**-736
{0x8213f56a67f6b29b, 0x9c3b29620e29fc73}, // 1e261 * 2**-740
{0xa298f2c501f45f42, 0x8349f3ba91b47b8f}, // 1e262 * 2**-743
{0xcb3f2f7642717713, 0x241c70a936219a73}, // 1e263 * 2**-746
{0xfe0efb53d30dd4d7, 0xed238cd383aa0110}, // 1e264 * 2**-749
{0x9ec95d1463e8a506, 0xf4363804324a40aa}, // 1e265 * 2**-753
{0xc67bb4597ce2ce48, 0xb143c6053edcd0d5}, // 1e266 * 2**-756
{0xf81aa16fdc1b81da, 0xdd94b7868e94050a}, // 1e267 * 2**-759
{0x9b10a4e5e9913128, 0xca7cf2b4191c8326}, // 1e268 * 2**-763
{0xc1d4ce1f63f57d72, 0xfd1c2f611f63a3f0}, // 1e269 * 2**-766
{0xf24a01a73cf2dccf, 0xbc633b39673c8cec}, // 1e270 * 2**-769
{0x976e41088617ca01, 0xd5be0503e085d813}, // 1e271 * 2**-773
{0xbd49d14aa79dbc82, 0x4b2d8644d8a74e18}, // 1e272 * 2**-776
{0xec9c459d51852ba2, 0xddf8e7d60ed1219e}, // 1e273 * 2**-779
{0x93e1ab8252f33b45, 0xcabb90e5c942b503}, // 1e274 * 2**-783
{0xb8da1662e7b00a17, 0x3d6a751f3b936243}, // 1e275 * 2**-786
{0xe7109bfba19c0c9d, 0x0cc512670a783ad4}, // 1e276 * 2**-789
{0x906a617d450187e2, 0x27fb2b80668b24c5}, // 1e277 * 2**-793
{0xb484f9dc9641e9da, 0xb1f9f660802dedf6}, // 1e278 * 2**-796
{0xe1a63853bbd26451, 0x5e7873f8a0396973}, // 1e279 * 2**-799
{0x8d07e33455637eb2, 0xdb0b487b6423e1e8}, // 1e280 * 2**-803
{0xb049dc016abc5e5f, 0x91ce1a9a3d2cda62}, // 1e281 * 2**-806
{0xdc5c5301c56b75f7, 0x7641a140cc7810fb}, // 1e282 * 2**-809
{0x89b9b3e11b6329ba, 0xa9e904c87fcb0a9d}, // 1e283 * 2**-813
{0xac2820d9623bf429, 0x546345fa9fbdcd44}, // 1e284 * 2**-816
{0xd732290fbacaf133, 0xa97c177947ad4095}, // 1e285 * 2**-819
{0x867f59a9d4bed6c0, 0x49ed8eabcccc485d}, // 1e286 * 2**-823
{0xa81f301449ee8c70, 0x5c68f256bfff5a74}, // 1e287 * 2**-826
{0xd226fc195c6a2f8c, 0x73832eec6fff3111}, // 1e288 * 2**-829
{0x83585d8fd9c25db7, 0xc831fd53c5ff7eab}, // 1e289 * 2**-833
{0xa42e74f3d032f525, 0xba3e7ca8b77f5e55}, // 1e290 * 2**-836
{0xcd3a1230c43fb26f, 0x28ce1bd2e55f35eb}, // 1e291 * 2**-839
{0x80444b5e7aa7cf85, 0x7980d163cf5b81b3}, // 1e292 * 2**-843
{0xa0555e361951c366, 0xd7e105bcc332621f}, // 1e293 * 2**-846
{0xc86ab5c39fa63440, 0x8dd9472bf3fefaa7}, // 1e294 * 2**-849
{0xfa856334878fc150, 0xb14f98f6f0feb951}, // 1e295 * 2**-852
{0x9c935e00d4b9d8d2, 0x6ed1bf9a569f33d3}, // 1e296 * 2**-856
{0xc3b8358109e84f07, 0x0a862f80ec4700c8}, // 1e297 * 2**-859
{0xf4a642e14c6262c8, 0xcd27bb612758c0fa}, // 1e298 * 2**-862
{0x98e7e9cccfbd7dbd, 0x8038d51cb897789c}, // 1e299 * 2**-866
{0xbf21e44003acdd2c, 0xe0470a63e6bd56c3}, // 1e300 * 2**-869
{0xeeea5d5004981478, 0x1858ccfce06cac74}, // 1e301 * 2**-872
{0x95527a5202df0ccb, 0x0f37801e0c43ebc8}, // 1e302 * 2**-876
{0xbaa718e68396cffd, 0xd30560258f54e6ba}, // 1e303 * 2**-879
{0xe950df20247c83fd, 0x47c6b82ef32a2069}, // 1e304 * 2**-882
{0x91d28b7416cdd27e, 0x4cdc331d57fa5441}, // 1e305 * 2**-886
{0xb6472e511c81471d, 0xe0133fe4adf8e952}, // 1e306 * 2**-889
{0xe3d8f9e563a198e5, 0x58180fddd97723a6}, // 1e307 * 2**-892
{0x8e679c2f5e44ff8f, 0x570f09eaa7ea7648}, // 1e308 * 2**-896
{0xb201833b35d63f73, 0x2cd2cc6551e513da}, // 1e309 * 2**-899
{0xde81e40a034bcf4f, 0xf8077f7ea65e58d1}, // 1e310 * 2**-902
{0x8b112e86420f6191, 0xfb04afaf27faf782}, // 1e311 * 2**-906
{0xadd57a27d29339f6, 0x79c5db9af1f9b563}, // 1e312 * 2**-909
{0xd94ad8b1c7380874, 0x18375281ae7822bc}, // 1e313 * 2**-912
{0x87cec76f1c830548, 0x8f2293910d0b15b5}, // 1e314 * 2**-916
{0xa9c2794ae3a3c69a, 0xb2eb3875504ddb22}, // 1e315 * 2**-919
{0xd433179d9c8cb841, 0x5fa60692a46151eb}, // 1e316 * 2**-922
{0x849feec281d7f328, 0xdbc7c41ba6bcd333}, // 1e317 * 2**-926
{0xa5c7ea73224deff3, 0x12b9b522906c0800}, // 1e318 * 2**-929
{0xcf39e50feae16bef, 0xd768226b34870a00}, // 1e319 * 2**-932
{0x81842f29f2cce375, 0xe6a1158300d46640}, // 1e320 * 2**-936
{0xa1e53af46f801c53, 0x60495ae3c1097fd0}, // 1e321 * 2**-939
{0xca5e89b18b602368, 0x385bb19cb14bdfc4}, // 1e322 * 2**-942
{0xfcf62c1dee382c42, 0x46729e03dd9ed7b5}, // 1e323 * 2**-945
{0x9e19db92b4e31ba9, 0x6c07a2c26a8346d1}, // 1e324 * 2**-949
{0xc5a05277621be293, 0xc7098b7305241885}, // 1e325 * 2**-952
{0xf70867153aa2db38, 0xb8cbee4fc66d1ea7}, // 1e326 * 2**-955
{0x9a65406d44a5c903, 0x737f74f1dc043328}, // 1e327 * 2**-959
{0xc0fe908895cf3b44, 0x505f522e53053ff2}, // 1e328 * 2**-962
{0xf13e34aabb430a15, 0x647726b9e7c68fef}, // 1e329 * 2**-965
{0x96c6e0eab509e64d, 0x5eca783430dc19f5}, // 1e330 * 2**-969
{0xbc789925624c5fe0, 0xb67d16413d132072}, // 1e331 * 2**-972
{0xeb96bf6ebadf77d8, 0xe41c5bd18c57e88f}, // 1e332 * 2**-975
{0x933e37a534cbaae7, 0x8e91b962f7b6f159}, // 1e333 * 2**-979
{0xb80dc58e81fe95a1, 0x723627bbb5a4adb0}, // 1e334 * 2**-982
{0xe61136f2227e3b09, 0xcec3b1aaa30dd91c}, // 1e335 * 2**-985
{0x8fcac257558ee4e6, 0x213a4f0aa5e8a7b1}, // 1e336 * 2**-989
{0xb3bd72ed2af29e1f, 0xa988e2cd4f62d19d}, // 1e337 * 2**-992
{0xe0accfa875af45a7, 0x93eb1b80a33b8605}, // 1e338 * 2**-995
{0x8c6c01c9498d8b88, 0xbc72f130660533c3}, // 1e339 * 2**-999
{0xaf87023b9bf0ee6a, 0xeb8fad7c7f8680b4}, // 1e340 * 2**-1002
{0xdb68c2ca82ed2a05, 0xa67398db9f6820e1}, // 1e341 * 2**-1005
{0x892179be91d43a43, 0x88083f8943a1148c}, // 1e342 * 2**-1009
{0xab69d82e364948d4, 0x6a0a4f6b948959b0}, // 1e343 * 2**-1012
{0xd6444e39c3db9b09, 0x848ce34679abb01c}, // 1e344 * 2**-1015
{0x85eab0e41a6940e5, 0xf2d80e0c0c0b4e11}, // 1e345 * 2**-1019
{0xa7655d1d2103911f, 0x6f8e118f0f0e2195}, // 1e346 * 2**-1022
{0xd13eb46469447567, 0x4b7195f2d2d1a9fb}, // 1e347 * 2**-1025
}