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406 lines
28 KiB
C++
406 lines
28 KiB
C++
/*
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Implements the Grisu3 algorithm for printing floating-point numbers.
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Follows Florian Loitsch's grisu3_59_56 implementation, available at
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http://florian.loitsch.com/publications, in bench.tar.gz, with
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minor modifications.
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*/
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/*
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Copyright (c) 2009 Florian Loitsch
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Permission is hereby granted, free of charge, to any person
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obtaining a copy of this software and associated documentation
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files (the "Software"), to deal in the Software without
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restriction, including without limitation the rights to use,
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copy, modify, merge, publish, distribute, sublicense, and/or sell
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copies of the Software, and to permit persons to whom the
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Software is furnished to do so, subject to the following
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conditions:
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The above copyright notice and this permission notice shall be
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included in all copies or substantial portions of the Software.
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
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EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
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OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
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NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
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HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
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WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
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OTHER DEALINGS IN THE SOFTWARE.
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*/
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#ifndef JSONCONS_GRISU3_HPP
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#define JSONCONS_GRISU3_HPP
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#pragma once
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#include <stdlib.h>
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#include <cinttypes>
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#include <cstdint>
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#include <cassert>
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#include <cmath>
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#include <cstring> // std::memmove
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namespace jsoncons { namespace detail {
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// diy_fp
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typedef struct diy_fp_t {
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uint64_t f;
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int e;
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} diy_fp_t;
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inline
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diy_fp_t minus(diy_fp_t x, diy_fp_t y)
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{
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assert(x.e == y.e);
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assert(x.f >= y.f);
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diy_fp_t r = { x.f = x.f - y.f, x.e = x.e };
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return r;
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}
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inline
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diy_fp_t multiply(diy_fp_t x, diy_fp_t y)
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{
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uint64_t a, b, c, d, ac, bc, ad, bd, tmp;
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diy_fp_t r; uint64_t M32 = 0xFFFFFFFF;
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a = x.f >> 32; b = x.f & M32;
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c = y.f >> 32; d = y.f & M32;
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ac = a * c; bc = b * c; ad = a * d; bd = b * d;
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tmp = (bd >> 32) + (ad & M32) + (bc & M32);
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tmp += 1U << 31; /// mult_round
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r.f = ac + (ad >> 32) + (bc >> 32) + (tmp >> 32);
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r.e = x.e + y.e + 64;
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return r;
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}
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// k_comp
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inline
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int k_comp(int e, int alpha, int /*gamma*/)
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{
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constexpr double d_1_log2_10 = 0.30102999566398114; // 1 / lg(10)
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return static_cast<int>(std::ceil((alpha - e + 63) * d_1_log2_10));
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}
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// powers_ten_round64
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constexpr int diy_significand_size = 64;
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static const uint64_t powers_ten[] = { 0xbf29dcaba82fdeae, 0xeef453d6923bd65a, 0x9558b4661b6565f8, 0xbaaee17fa23ebf76, 0xe95a99df8ace6f54, 0x91d8a02bb6c10594, 0xb64ec836a47146fa, 0xe3e27a444d8d98b8, 0x8e6d8c6ab0787f73, 0xb208ef855c969f50, 0xde8b2b66b3bc4724, 0x8b16fb203055ac76, 0xaddcb9e83c6b1794, 0xd953e8624b85dd79, 0x87d4713d6f33aa6c, 0xa9c98d8ccb009506, 0xd43bf0effdc0ba48, 0x84a57695fe98746d, 0xa5ced43b7e3e9188, 0xcf42894a5dce35ea, 0x818995ce7aa0e1b2, 0xa1ebfb4219491a1f, 0xca66fa129f9b60a7, 0xfd00b897478238d1, 0x9e20735e8cb16382, 0xc5a890362fddbc63, 0xf712b443bbd52b7c, 0x9a6bb0aa55653b2d, 0xc1069cd4eabe89f9, 0xf148440a256e2c77, 0x96cd2a865764dbca, 0xbc807527ed3e12bd, 0xeba09271e88d976c, 0x93445b8731587ea3, 0xb8157268fdae9e4c, 0xe61acf033d1a45df, 0x8fd0c16206306bac, 0xb3c4f1ba87bc8697, 0xe0b62e2929aba83c, 0x8c71dcd9ba0b4926, 0xaf8e5410288e1b6f, 0xdb71e91432b1a24b, 0x892731ac9faf056f, 0xab70fe17c79ac6ca, 0xd64d3d9db981787d, 0x85f0468293f0eb4e, 0xa76c582338ed2622, 0xd1476e2c07286faa, 0x82cca4db847945ca, 0xa37fce126597973d, 0xcc5fc196fefd7d0c, 0xff77b1fcbebcdc4f, 0x9faacf3df73609b1, 0xc795830d75038c1e, 0xf97ae3d0d2446f25, 0x9becce62836ac577, 0xc2e801fb244576d5, 0xf3a20279ed56d48a, 0x9845418c345644d7, 0xbe5691ef416bd60c, 0xedec366b11c6cb8f, 0x94b3a202eb1c3f39, 0xb9e08a83a5e34f08, 0xe858ad248f5c22ca, 0x91376c36d99995be, 0xb58547448ffffb2e, 0xe2e69915b3fff9f9, 0x8dd01fad907ffc3c, 0xb1442798f49ffb4b, 0xdd95317f31c7fa1d, 0x8a7d3eef7f1cfc52, 0xad1c8eab5ee43b67, 0xd863b256369d4a41, 0x873e4f75e2224e68, 0xa90de3535aaae202, 0xd3515c2831559a83, 0x8412d9991ed58092, 0xa5178fff668ae0b6, 0xce5d73ff402d98e4, 0x80fa687f881c7f8e, 0xa139029f6a239f72, 0xc987434744ac874f, 0xfbe9141915d7a922, 0x9d71ac8fada6c9b5, 0xc4ce17b399107c23, 0xf6019da07f549b2b, 0x99c102844f94e0fb, 0xc0314325637a193a, 0xf03d93eebc589f88, 0x96267c7535b763b5, 0xbbb01b9283253ca3, 0xea9c227723ee8bcb, 0x92a1958a7675175f, 0xb749faed14125d37, 0xe51c79a85916f485, 0x8f31cc0937ae58d3, 0xb2fe3f0b8599ef08, 0xdfbdcece67006ac9, 0x8bd6a141006042be, 0xaecc49914078536d, 0xda7f5bf590966849, 0x888f99797a5e012d, 0xaab37fd7d8f58179, 0xd5605fcdcf32e1d7, 0x855c3be0a17fcd26, 0xa6b34ad8c9dfc070, 0xd0601d8efc57b08c, 0x823c12795db6ce57, 0xa2cb1717b52481ed, 0xcb7ddcdda26da269, 0xfe5d54150b090b03, 0x9efa548d26e5a6e2, 0xc6b8e9b0709f109a, 0xf867241c8cc6d4c1, 0x9b407691d7fc44f8, 0xc21094364dfb5637, 0xf294b943e17a2bc4, 0x979cf3ca6cec5b5b, 0xbd8430bd08277231, 0xece53cec4a314ebe, 0x940f4613ae5ed137, 0xb913179899f68584, 0xe757dd7ec07426e5, 0x9096ea6f3848984f, 0xb4bca50b065abe63, 0xe1ebce4dc7f16dfc, 0x8d3360f09cf6e4bd, 0xb080392cc4349ded, 0xdca04777f541c568, 0x89e42caaf9491b61, 0xac5d37d5b79b6239, 0xd77485cb25823ac7, 0x86a8d39ef77164bd, 0xa8530886b54dbdec, 0xd267caa862a12d67, 0x8380dea93da4bc60, 0xa46116538d0deb78, 0xcd795be870516656, 0x806bd9714632dff6, 0xa086cfcd97bf97f4, 0xc8a883c0fdaf7df0, 0xfad2a4b13d1b5d6c, 0x9cc3a6eec6311a64, 0xc3f490aa77bd60fd, 0xf4f1b4d515acb93c, 0x991711052d8bf3c5, 0xbf5cd54678eef0b7, 0xef340a98172aace5, 0x9580869f0e7aac0f, 0xbae0a846d2195713, 0xe998d258869facd7, 0x91ff83775423cc06, 0xb67f6455292cbf08, 0xe41f3d6a7377eeca, 0x8e938662882af53e, 0xb23867fb2a35b28e, 0xdec681f9f4c31f31, 0x8b3c113c38f9f37f, 0xae0b158b4738705f, 0xd98ddaee19068c76, 0x87f8a8d4cfa417ca, 0xa9f6d30a038d1dbc, 0xd47487cc8470652b, 0x84c8d4dfd2c63f3b, 0xa5fb0a17c777cf0a, 0xcf79cc9db955c2cc, 0x81ac1fe293d599c0, 0xa21727db38cb0030, 0xca9cf1d206fdc03c, 0xfd442e4688bd304b, 0x9e4a9cec15763e2f, 0xc5dd44271ad3cdba, 0xf7549530e188c129, 0x9a94dd3e8cf578ba, 0xc13a148e3032d6e8, 0xf18899b1bc3f8ca2, 0x96f5600f15a7b7e5, 0xbcb2b812db11a5de, 0xebdf661791d60f56, 0x936b9fcebb25c996, 0xb84687c269ef3bfb, 0xe65829b3046b0afa, 0x8ff71a0fe2c2e6dc, 0xb3f4e093db73a093, 0xe0f218b8d25088b8, 0x8c974f7383725573, 0xafbd2350644eead0, 0xdbac6c247d62a584, 0x894bc396ce5da772, 0xab9eb47c81f5114f, 0xd686619ba27255a3, 0x8613fd0145877586, 0xa798fc4196e952e7, 0xd17f3b51fca3a7a1, 0x82ef85133de648c5, 0xa3ab66580d5fdaf6, 0xcc963fee10b7d1b3, 0xffbbcfe994e5c620, 0x9fd561f1fd0f9bd4, 0xc7caba6e7c5382c9, 0xf9bd690a1b68637b, 0x9c1661a651213e2d, 0xc31bfa0fe5698db8, 0xf3e2f893dec3f126, 0x986ddb5c6b3a76b8, 0xbe89523386091466, 0xee2ba6c0678b597f, 0x94db483840b717f0, 0xba121a4650e4ddec, 0xe896a0d7e51e1566, 0x915e2486ef32cd60, 0xb5b5ada8aaff80b8, 0xe3231912d5bf60e6, 0x8df5efabc5979c90, 0xb1736b96b6fd83b4, 0xddd0467c64bce4a1, 0x8aa22c0dbef60ee4, 0xad4ab7112eb3929e, 0xd89d64d57a607745, 0x87625f056c7c4a8b, 0xa93af6c6c79b5d2e, 0xd389b47879823479, 0x843610cb4bf160cc, 0xa54394fe1eedb8ff, 0xce947a3da6a9273e, 0x811ccc668829b887, 0xa163ff802a3426a9, 0xc9bcff6034c13053, 0xfc2c3f3841f17c68, 0x9d9ba7832936edc1, 0xc5029163f384a931, 0xf64335bcf065d37d, 0x99ea0196163fa42e, 0xc06481fb9bcf8d3a, 0xf07da27a82c37088, 0x964e858c91ba2655, 0xbbe226efb628afeb, 0xeadab0aba3b2dbe5, 0x92c8ae6b464fc96f, 0xb77ada0617e3bbcb, 0xe55990879ddcaabe, 0x8f57fa54c2a9eab7, 0xb32df8e9f3546564, 0xdff9772470297ebd, 0x8bfbea76c619ef36, 0xaefae51477a06b04, 0xdab99e59958885c5, 0x88b402f7fd75539b, 0xaae103b5fcd2a882, 0xd59944a37c0752a2, 0x857fcae62d8493a5, 0xa6dfbd9fb8e5b88f, 0xd097ad07a71f26b2, 0x825ecc24c8737830, 0xa2f67f2dfa90563b, 0xcbb41ef979346bca, 0xfea126b7d78186bd, 0x9f24b832e6b0f436, 0xc6ede63fa05d3144, 0xf8a95fcf88747d94, 0x9b69dbe1b548ce7d, 0xc24452da229b021c, 0xf2d56790ab41c2a3, 0x97c560ba6b0919a6, 0xbdb6b8e905cb600f, 0xed246723473e3813, 0x9436c0760c86e30c, 0xb94470938fa89bcf, 0xe7958cb87392c2c3, 0x90bd77f3483bb9ba, 0xb4ecd5f01a4aa828, 0xe2280b6c20dd5232, 0x8d590723948a535f, 0xb0af48ec79ace837, 0xdcdb1b2798182245, 0x8a08f0f8bf0f156b, 0xac8b2d36eed2dac6, 0xd7adf884aa879177, 0x86ccbb52ea94baeb, 0xa87fea27a539e9a5, 0xd29fe4b18e88640f, 0x83a3eeeef9153e89, 0xa48ceaaab75a8e2b, 0xcdb02555653131b6, 0x808e17555f3ebf12, 0xa0b19d2ab70e6ed6, 0xc8de047564d20a8c, 0xfb158592be068d2f, 0x9ced737bb6c4183d, 0xc428d05aa4751e4d, 0xf53304714d9265e0, 0x993fe2c6d07b7fac, 0xbf8fdb78849a5f97, 0xef73d256a5c0f77d, 0x95a8637627989aae, 0xbb127c53b17ec159, 0xe9d71b689dde71b0, 0x9226712162ab070e, 0xb6b00d69bb55c8d1, 0xe45c10c42a2b3b06, 0x8eb98a7a9a5b04e3, 0xb267ed1940f1c61c, 0xdf01e85f912e37a3, 0x8b61313bbabce2c6, 0xae397d8aa96c1b78, 0xd9c7dced53c72256, 0x881cea14545c7575, 0xaa242499697392d3, 0xd4ad2dbfc3d07788, 0x84ec3c97da624ab5, 0xa6274bbdd0fadd62, 0xcfb11ead453994ba, 0x81ceb32c4b43fcf5, 0xa2425ff75e14fc32, 0xcad2f7f5359a3b3e, 0xfd87b5f28300ca0e, 0x9e74d1b791e07e48, 0xc612062576589ddb, 0xf79687aed3eec551, 0x9abe14cd44753b53, 0xc16d9a0095928a27, 0xf1c90080baf72cb1, 0x971da05074da7bef, 0xbce5086492111aeb, 0xec1e4a7db69561a5, 0x9392ee8e921d5d07, 0xb877aa3236a4b449, 0xe69594bec44de15b, 0x901d7cf73ab0acd9, 0xb424dc35095cd80f, 0xe12e13424bb40e13, 0x8cbccc096f5088cc, 0xafebff0bcb24aaff, 0xdbe6fecebdedd5bf, 0x89705f4136b4a597, 0xabcc77118461cefd, 0xd6bf94d5e57a42bc, 0x8637bd05af6c69b6, 0xa7c5ac471b478423, 0xd1b71758e219652c, 0x83126e978d4fdf3b, 0xa3d70a3d70a3d70a, 0xcccccccccccccccd, 0x8000000000000000, 0xa000000000000000, 0xc800000000000000, 0xfa00000000000000, 0x9c40000000000000, 0xc350000000000000, 0xf424000000000000, 0x9896800000000000, 0xbebc200000000000, 0xee6b280000000000, 0x9502f90000000000, 0xba43b74000000000, 0xe8d4a51000000000, 0x9184e72a00000000, 0xb5e620f480000000, 0xe35fa931a0000000, 0x8e1bc9bf04000000, 0xb1a2bc2ec5000000, 0xde0b6b3a76400000, 0x8ac7230489e80000, 0xad78ebc5ac620000, 0xd8d726b7177a8000, 0x878678326eac9000, 0xa968163f0a57b400, 0xd3c21bcecceda100, 0x84595161401484a0, 0xa56fa5b99019a5c8, 0xcecb8f27f4200f3a, 0x813f3978f8940984, 0xa18f07d736b90be5, 0xc9f2c9cd04674edf, 0xfc6f7c4045812296, 0x9dc5ada82b70b59e, 0xc5371912364ce305, 0xf684df56c3e01bc7, 0x9a130b963a6c115c, 0xc097ce7bc90715b3, 0xf0bdc21abb48db20, 0x96769950b50d88f4, 0xbc143fa4e250eb31, 0xeb194f8e1ae525fd, 0x92efd1b8d0cf37be, 0xb7abc627050305ae, 0xe596b7b0c643c719, 0x8f7e32ce7bea5c70, 0xb35dbf821ae4f38c, 0xe0352f62a19e306f, 0x8c213d9da502de45, 0xaf298d050e4395d7, 0xdaf3f04651d47b4c, 0x88d8762bf324cd10, 0xab0e93b6efee0054, 0xd5d238a4abe98068, 0x85a36366eb71f041, 0xa70c3c40a64e6c52, 0xd0cf4b50cfe20766, 0x82818f1281ed44a0, 0xa321f2d7226895c8, 0xcbea6f8ceb02bb3a, 0xfee50b7025c36a08, 0x9f4f2726179a2245, 0xc722f0ef9d80aad6, 0xf8ebad2b84e0d58c, 0x9b934c3b330c8577, 0xc2781f49ffcfa6d5, 0xf316271c7fc3908b, 0x97edd871cfda3a57, 0xbde94e8e43d0c8ec, 0xed63a231d4c4fb27, 0x945e455f24fb1cf9, 0xb975d6b6ee39e437, 0xe7d34c64a9c85d44, 0x90e40fbeea1d3a4b, 0xb51d13aea4a488dd, 0xe264589a4dcdab15, 0x8d7eb76070a08aed, 0xb0de65388cc8ada8, 0xdd15fe86affad912, 0x8a2dbf142dfcc7ab, 0xacb92ed9397bf996, 0xd7e77a8f87daf7fc, 0x86f0ac99b4e8dafd, 0xa8acd7c0222311bd, 0xd2d80db02aabd62c, 0x83c7088e1aab65db, 0xa4b8cab1a1563f52, 0xcde6fd5e09abcf27, 0x80b05e5ac60b6178, 0xa0dc75f1778e39d6, 0xc913936dd571c84c, 0xfb5878494ace3a5f, 0x9d174b2dcec0e47b, 0xc45d1df942711d9a, 0xf5746577930d6501, 0x9968bf6abbe85f20, 0xbfc2ef456ae276e9, 0xefb3ab16c59b14a3, 0x95d04aee3b80ece6, 0xbb445da9ca61281f, 0xea1575143cf97227, 0x924d692ca61be758, 0xb6e0c377cfa2e12e, 0xe498f455c38b997a, 0x8edf98b59a373fec, 0xb2977ee300c50fe7, 0xdf3d5e9bc0f653e1, 0x8b865b215899f46d, 0xae67f1e9aec07188, 0xda01ee641a708dea, 0x884134fe908658b2, 0xaa51823e34a7eedf, 0xd4e5e2cdc1d1ea96, 0x850fadc09923329e, 0xa6539930bf6bff46, 0xcfe87f7cef46ff17, 0x81f14fae158c5f6e, 0xa26da3999aef774a, 0xcb090c8001ab551c, 0xfdcb4fa002162a63, 0x9e9f11c4014dda7e, 0xc646d63501a1511e, 0xf7d88bc24209a565, 0x9ae757596946075f, 0xc1a12d2fc3978937, 0xf209787bb47d6b85, 0x9745eb4d50ce6333, 0xbd176620a501fc00, 0xec5d3fa8ce427b00, 0x93ba47c980e98ce0, 0xb8a8d9bbe123f018, 0xe6d3102ad96cec1e, 0x9043ea1ac7e41393, 0xb454e4a179dd1877, 0xe16a1dc9d8545e95, 0x8ce2529e2734bb1d, 0xb01ae745b101e9e4, 0xdc21a1171d42645d, 0x899504ae72497eba, 0xabfa45da0edbde69, 0xd6f8d7509292d603, 0x865b86925b9bc5c2, 0xa7f26836f282b733, 0xd1ef0244af2364ff, 0x8335616aed761f1f, 0xa402b9c5a8d3a6e7, 0xcd036837130890a1, 0x802221226be55a65, 0xa02aa96b06deb0fe, 0xc83553c5c8965d3d, 0xfa42a8b73abbf48d, 0x9c69a97284b578d8, 0xc38413cf25e2d70e, 0xf46518c2ef5b8cd1, 0x98bf2f79d5993803, 0xbeeefb584aff8604, 0xeeaaba2e5dbf6785, 0x952ab45cfa97a0b3, 0xba756174393d88e0, 0xe912b9d1478ceb17, 0x91abb422ccb812ef, 0xb616a12b7fe617aa, 0xe39c49765fdf9d95, 0x8e41ade9fbebc27d, 0xb1d219647ae6b31c, 0xde469fbd99a05fe3, 0x8aec23d680043bee, 0xada72ccc20054aea, 0xd910f7ff28069da4, 0x87aa9aff79042287, 0xa99541bf57452b28, 0xd3fa922f2d1675f2, 0x847c9b5d7c2e09b7, 0xa59bc234db398c25, 0xcf02b2c21207ef2f, 0x8161afb94b44f57d, 0xa1ba1ba79e1632dc, 0xca28a291859bbf93, 0xfcb2cb35e702af78, 0x9defbf01b061adab, 0xc56baec21c7a1916, 0xf6c69a72a3989f5c, 0x9a3c2087a63f6399, 0xc0cb28a98fcf3c80, 0xf0fdf2d3f3c30b9f, 0x969eb7c47859e744, 0xbc4665b596706115, 0xeb57ff22fc0c795a, 0x9316ff75dd87cbd8, 0xb7dcbf5354e9bece, 0xe5d3ef282a242e82, 0x8fa475791a569d11, 0xb38d92d760ec4455, 0xe070f78d3927556b, 0x8c469ab843b89563, 0xaf58416654a6babb, 0xdb2e51bfe9d0696a, 0x88fcf317f22241e2, 0xab3c2fddeeaad25b, 0xd60b3bd56a5586f2, 0x85c7056562757457, 0xa738c6bebb12d16d, 0xd106f86e69d785c8, 0x82a45b450226b39d, 0xa34d721642b06084, 0xcc20ce9bd35c78a5, 0xff290242c83396ce, 0x9f79a169bd203e41, 0xc75809c42c684dd1, 0xf92e0c3537826146, 0x9bbcc7a142b17ccc, 0xc2abf989935ddbfe, 0xf356f7ebf83552fe, 0x98165af37b2153df, 0xbe1bf1b059e9a8d6, 0xeda2ee1c7064130c, 0x9485d4d1c63e8be8, 0xb9a74a0637ce2ee1, 0xe8111c87c5c1ba9a, 0x910ab1d4db9914a0, 0xb54d5e4a127f59c8, 0xe2a0b5dc971f303a, 0x8da471a9de737e24, 0xb10d8e1456105dad, 0xdd50f1996b947519, 0x8a5296ffe33cc930, 0xace73cbfdc0bfb7b, 0xd8210befd30efa5a, 0x8714a775e3e95c78, 0xa8d9d1535ce3b396, 0xd31045a8341ca07c, 0x83ea2b892091e44e, 0xa4e4b66b68b65d61, 0xce1de40642e3f4b9, 0x80d2ae83e9ce78f4, 0xa1075a24e4421731, 0xc94930ae1d529cfd, 0xfb9b7cd9a4a7443c, 0x9d412e0806e88aa6, 0xc491798a08a2ad4f, 0xf5b5d7ec8acb58a3, 0x9991a6f3d6bf1766, 0xbff610b0cc6edd3f, 0xeff394dcff8a948f, 0x95f83d0a1fb69cd9, 0xbb764c4ca7a44410, 0xea53df5fd18d5514, 0x92746b9be2f8552c, 0xb7118682dbb66a77, 0xe4d5e82392a40515, 0x8f05b1163ba6832d, 0xb2c71d5bca9023f8, 0xdf78e4b2bd342cf7, 0x8bab8eefb6409c1a, 0xae9672aba3d0c321, 0xda3c0f568cc4f3e9, 0x8865899617fb1871, 0xaa7eebfb9df9de8e, 0xd51ea6fa85785631, 0x8533285c936b35df, 0xa67ff273b8460357, 0xd01fef10a657842c, 0x8213f56a67f6b29c, 0xa298f2c501f45f43, 0xcb3f2f7642717713, 0xfe0efb53d30dd4d8, 0x9ec95d1463e8a507, 0xc67bb4597ce2ce49, 0xf81aa16fdc1b81db, 0x9b10a4e5e9913129, 0xc1d4ce1f63f57d73, 0xf24a01a73cf2dcd0, 0x976e41088617ca02, 0xbd49d14aa79dbc82, 0xec9c459d51852ba3, 0x93e1ab8252f33b46, 0xb8da1662e7b00a17, 0xe7109bfba19c0c9d, 0x906a617d450187e2, 0xb484f9dc9641e9db, 0xe1a63853bbd26451, 0x8d07e33455637eb3, 0xb049dc016abc5e60, 0xdc5c5301c56b75f7, 0x89b9b3e11b6329bb, 0xac2820d9623bf429, 0xd732290fbacaf134, 0x867f59a9d4bed6c0, 0xa81f301449ee8c70, 0xd226fc195c6a2f8c, 0x83585d8fd9c25db8, 0xa42e74f3d032f526, 0xcd3a1230c43fb26f, 0x80444b5e7aa7cf85, 0xa0555e361951c367, 0xc86ab5c39fa63441, 0xfa856334878fc151, 0x9c935e00d4b9d8d2, 0xc3b8358109e84f07, 0xf4a642e14c6262c9, 0x98e7e9cccfbd7dbe, 0xbf21e44003acdd2d, 0xeeea5d5004981478, 0x95527a5202df0ccb, 0xbaa718e68396cffe, 0xe950df20247c83fd, 0x91d28b7416cdd27e, 0xb6472e511c81471e, 0xe3d8f9e563a198e5, 0x8e679c2f5e44ff8f, 0xb201833b35d63f73, 0xde81e40a034bcf50, 0x8b112e86420f6192, 0xadd57a27d29339f6, 0xd94ad8b1c7380874, 0x87cec76f1c830549, 0xa9c2794ae3a3c69b, 0xd433179d9c8cb841, 0x849feec281d7f329, 0xa5c7ea73224deff3, 0xcf39e50feae16bf0, 0x81842f29f2cce376, 0xa1e53af46f801c53, 0xca5e89b18b602368, 0xfcf62c1dee382c42, 0x9e19db92b4e31ba9, 0xc5a05277621be294, 0xf70867153aa2db39, 0x9a65406d44a5c903, 0xc0fe908895cf3b44, 0xf13e34aabb430a15, 0x96c6e0eab509e64d, 0xbc789925624c5fe1, 0xeb96bf6ebadf77d9, 0x933e37a534cbaae8, 0xb80dc58e81fe95a1, 0xe61136f2227e3b0a, 0x8fcac257558ee4e6, 0xb3bd72ed2af29e20, 0xe0accfa875af45a8, 0x8c6c01c9498d8b89, 0xaf87023b9bf0ee6b, 0xdb68c2ca82ed2a06, 0x892179be91d43a44, 0xab69d82e364948d4 };
|
|
static const int powers_ten_e[] = { -1203, -1200, -1196, -1193, -1190, -1186, -1183, -1180, -1176, -1173, -1170, -1166, -1163, -1160, -1156, -1153, -1150, -1146, -1143, -1140, -1136, -1133, -1130, -1127, -1123, -1120, -1117, -1113, -1110, -1107, -1103, -1100, -1097, -1093, -1090, -1087, -1083, -1080, -1077, -1073, -1070, -1067, -1063, -1060, -1057, -1053, -1050, -1047, -1043, -1040, -1037, -1034, -1030, -1027, -1024, -1020, -1017, -1014, -1010, -1007, -1004, -1000, -997, -994, -990, -987, -984, -980, -977, -974, -970, -967, -964, -960, -957, -954, -950, -947, -944, -940, -937, -934, -931, -927, -924, -921, -917, -914, -911, -907, -904, -901, -897, -894, -891, -887, -884, -881, -877, -874, -871, -867, -864, -861, -857, -854, -851, -847, -844, -841, -838, -834, -831, -828, -824, -821, -818, -814, -811, -808, -804, -801, -798, -794, -791, -788, -784, -781, -778, -774, -771, -768, -764, -761, -758, -754, -751, -748, -744, -741, -738, -735, -731, -728, -725, -721, -718, -715, -711, -708, -705, -701, -698, -695, -691, -688, -685, -681, -678, -675, -671, -668, -665, -661, -658, -655, -651, -648, -645, -642, -638, -635, -632, -628, -625, -622, -618, -615, -612, -608, -605, -602, -598, -595, -592, -588, -585, -582, -578, -575, -572, -568, -565, -562, -558, -555, -552, -549, -545, -542, -539, -535, -532, -529, -525, -522, -519, -515, -512, -509, -505, -502, -499, -495, -492, -489, -485, -482, -479, -475, -472, -469, -465, -462, -459, -455, -452, -449, -446, -442, -439, -436, -432, -429, -426, -422, -419, -416, -412, -409, -406, -402, -399, -396, -392, -389, -386, -382, -379, -376, -372, -369, -366, -362, -359, -356, -353, -349, -346, -343, -339, -336, -333, -329, -326, -323, -319, -316, -313, -309, -306, -303, -299, -296, -293, -289, -286, -283, -279, -276, -273, -269, -266, -263, -259, -256, -253, -250, -246, -243, -240, -236, -233, -230, -226, -223, -220, -216, -213, -210, -206, -203, -200, -196, -193, -190, -186, -183, -180, -176, -173, -170, -166, -163, -160, -157, -153, -150, -147, -143, -140, -137, -133, -130, -127, -123, -120, -117, -113, -110, -107, -103, -100, -97, -93, -90, -87, -83, -80, -77, -73, -70, -67, -63, -60, -57, -54, -50, -47, -44, -40, -37, -34, -30, -27, -24, -20, -17, -14, -10, -7, -4, 0, 3, 6, 10, 13, 16, 20, 23, 26, 30, 33, 36, 39, 43, 46, 49, 53, 56, 59, 63, 66, 69, 73, 76, 79, 83, 86, 89, 93, 96, 99, 103, 106, 109, 113, 116, 119, 123, 126, 129, 132, 136, 139, 142, 146, 149, 152, 156, 159, 162, 166, 169, 172, 176, 179, 182, 186, 189, 192, 196, 199, 202, 206, 209, 212, 216, 219, 222, 226, 229, 232, 235, 239, 242, 245, 249, 252, 255, 259, 262, 265, 269, 272, 275, 279, 282, 285, 289, 292, 295, 299, 302, 305, 309, 312, 315, 319, 322, 325, 328, 332, 335, 338, 342, 345, 348, 352, 355, 358, 362, 365, 368, 372, 375, 378, 382, 385, 388, 392, 395, 398, 402, 405, 408, 412, 415, 418, 422, 425, 428, 431, 435, 438, 441, 445, 448, 451, 455, 458, 461, 465, 468, 471, 475, 478, 481, 485, 488, 491, 495, 498, 501, 505, 508, 511, 515, 518, 521, 524, 528, 531, 534, 538, 541, 544, 548, 551, 554, 558, 561, 564, 568, 571, 574, 578, 581, 584, 588, 591, 594, 598, 601, 604, 608, 611, 614, 617, 621, 624, 627, 631, 634, 637, 641, 644, 647, 651, 654, 657, 661, 664, 667, 671, 674, 677, 681, 684, 687, 691, 694, 697, 701, 704, 707, 711, 714, 717, 720, 724, 727, 730, 734, 737, 740, 744, 747, 750, 754, 757, 760, 764, 767, 770, 774, 777, 780, 784, 787, 790, 794, 797, 800, 804, 807, 810, 813, 817, 820, 823, 827, 830, 833, 837, 840, 843, 847, 850, 853, 857, 860, 863, 867, 870, 873, 877, 880, 883, 887, 890, 893, 897, 900, 903, 907, 910, 913, 916, 920, 923, 926, 930, 933, 936, 940, 943, 946, 950, 953, 956, 960, 963, 966, 970, 973, 976, 980, 983, 986, 990, 993, 996, 1000, 1003, 1006, 1009, 1013, 1016, 1019, 1023, 1026, 1029, 1033, 1036, 1039, 1043, 1046, 1049, 1053, 1056, 1059, 1063, 1066, 1069, 1073, 1076 };
|
|
|
|
inline
|
|
diy_fp_t cached_power(int k)
|
|
{
|
|
diy_fp_t res;
|
|
int index = 343 + k;
|
|
res.f = powers_ten[index];
|
|
res.e = powers_ten_e[index];
|
|
return res;
|
|
}
|
|
|
|
// double
|
|
|
|
typedef union {
|
|
double d;
|
|
uint64_t n;
|
|
} converter_t;
|
|
|
|
inline
|
|
uint64_t double_to_uint64(double d) { converter_t tmp; tmp.d = d; return tmp.n; }
|
|
|
|
inline
|
|
double uint64_to_double(uint64_t d64) { converter_t tmp; tmp.n = d64; return tmp.d; }
|
|
|
|
constexpr int dp_significand_size = 52;
|
|
constexpr int dp_exponent_bias = (0x3FF + dp_significand_size);
|
|
constexpr int dp_min_exponent = (-dp_exponent_bias);
|
|
constexpr uint64_t dp_exponent_mask = 0x7FF0000000000000;
|
|
constexpr uint64_t dp_significand_mask = 0x000FFFFFFFFFFFFF;
|
|
constexpr uint64_t dp_hidden_bit = 0x0010000000000000;
|
|
|
|
inline
|
|
diy_fp_t normalize_diy_fp(diy_fp_t in)
|
|
{
|
|
diy_fp_t res = in;
|
|
/* Normalize now */
|
|
/* the original number could have been a denormal. */
|
|
while (!(res.f & dp_hidden_bit))
|
|
{
|
|
res.f <<= 1;
|
|
res.e--;
|
|
}
|
|
/* do the final shifts in one go. Don't forget the hidden bit (the '-1') */
|
|
res.f <<= (diy_significand_size - dp_significand_size - 1);
|
|
res.e = res.e - (diy_significand_size - dp_significand_size - 1);
|
|
return res;
|
|
}
|
|
|
|
inline
|
|
diy_fp_t double2diy_fp(double d)
|
|
{
|
|
uint64_t d64 = double_to_uint64(d);
|
|
int biased_e = (d64 & dp_exponent_mask) >> dp_significand_size;
|
|
uint64_t significand = (d64 & dp_significand_mask);
|
|
diy_fp_t res;
|
|
if (biased_e != 0)
|
|
{
|
|
res.f = significand + dp_hidden_bit;
|
|
res.e = biased_e - dp_exponent_bias;
|
|
}
|
|
else
|
|
{
|
|
res.f = significand;
|
|
res.e = dp_min_exponent + 1;
|
|
}
|
|
return res;
|
|
}
|
|
|
|
inline
|
|
diy_fp_t normalize_boundary(diy_fp_t in)
|
|
{
|
|
diy_fp_t res = in;
|
|
/* Normalize now */
|
|
/* the original number could have been a denormal. */
|
|
while (!(res.f & (dp_hidden_bit << 1)))
|
|
{
|
|
res.f <<= 1;
|
|
res.e--;
|
|
}
|
|
/* do the final shifts in one go. Don't forget the hidden bit (the '-1') */
|
|
res.f <<= (diy_significand_size - dp_significand_size - 2);
|
|
res.e = res.e - (diy_significand_size - dp_significand_size - 2);
|
|
return res;
|
|
}
|
|
|
|
inline
|
|
void normalized_boundaries(double d, diy_fp_t *out_m_minus, diy_fp_t *out_m_plus)
|
|
{
|
|
diy_fp_t v = double2diy_fp(d);
|
|
diy_fp_t pl, mi;
|
|
bool significand_is_zero = v.f == dp_hidden_bit;
|
|
pl.f = (v.f << 1) + 1; pl.e = v.e - 1;
|
|
pl = normalize_boundary(pl);
|
|
if (significand_is_zero)
|
|
{
|
|
mi.f = (v.f << 2) - 1;
|
|
mi.e = v.e - 2;
|
|
} else
|
|
{
|
|
mi.f = (v.f << 1) - 1;
|
|
mi.e = v.e - 1;
|
|
}
|
|
mi.f <<= mi.e - pl.e;
|
|
mi.e = pl.e;
|
|
*out_m_plus = pl;
|
|
*out_m_minus = mi;
|
|
}
|
|
|
|
inline
|
|
double random_double()
|
|
{
|
|
uint64_t tmp = 0;
|
|
int i;
|
|
for (i = 0; i < 8; i++)
|
|
{
|
|
tmp <<= 8;
|
|
tmp += rand() % 256;
|
|
}
|
|
return uint64_to_double(tmp);
|
|
}
|
|
|
|
// fast_exponent
|
|
template <class Result>
|
|
void fill_exponent(int K, Result& result)
|
|
{
|
|
if (K < 0)
|
|
{
|
|
result.push_back('-');
|
|
K = -K;
|
|
}
|
|
else
|
|
{
|
|
result.push_back('+'); // compatibility with sprintf
|
|
}
|
|
if (K >= 100)
|
|
{
|
|
result.push_back((char)('0' + K / 100)); K %= 100;
|
|
result.push_back((char)('0' + K / 10)); K %= 10;
|
|
result.push_back((char)('0' + K));
|
|
}
|
|
else if (K >= 10)
|
|
{
|
|
result.push_back((char)('0' + K / 10)); K %= 10;
|
|
result.push_back((char)('0' + K));
|
|
}
|
|
else
|
|
{
|
|
result.push_back('0'); // compatibility with sprintf
|
|
result.push_back((char)('0' + K));
|
|
}
|
|
}
|
|
|
|
template <class Result>
|
|
void prettify_string(const char *buffer, size_t length, int k, int min_exp, int max_exp, Result& result)
|
|
{
|
|
int nb_digits = (int)length;
|
|
int offset;
|
|
/* v = buffer * 10^k
|
|
kk is such that 10^(kk-1) <= v < 10^kk
|
|
this way kk gives the position of the decimal point.
|
|
*/
|
|
int kk = nb_digits + k;
|
|
|
|
if (nb_digits <= kk && kk <= max_exp)
|
|
{
|
|
/* the first digits are already in. Add some 0s and call it a day. */
|
|
/* the max_exp is a personal choice. Only 16 digits could possibly be relevant.
|
|
* Basically we want to print 12340000000 rather than 1234.0e7 or 1.234e10 */
|
|
for (int i = 0; i < nb_digits; ++i)
|
|
{
|
|
result.push_back(buffer[i]);
|
|
}
|
|
for (int i = nb_digits; i < kk; ++i)
|
|
{
|
|
result.push_back('0');
|
|
}
|
|
result.push_back('.');
|
|
result.push_back('0');
|
|
}
|
|
else if (0 < kk && kk <= max_exp)
|
|
{
|
|
/* comma number. Just insert a '.' at the correct location. */
|
|
for (int i = 0; i < kk; ++i)
|
|
{
|
|
result.push_back(buffer[i]);
|
|
}
|
|
result.push_back('.');
|
|
for (int i = kk; i < nb_digits; ++i)
|
|
{
|
|
result.push_back(buffer[i]);
|
|
}
|
|
}
|
|
else if (min_exp < kk && kk <= 0)
|
|
{
|
|
offset = 2 - kk;
|
|
|
|
result.push_back('0');
|
|
result.push_back('.');
|
|
for (int i = 2; i < offset; ++i)
|
|
result.push_back('0');
|
|
for (int i = 0; i < nb_digits; ++i)
|
|
{
|
|
result.push_back(buffer[i]);
|
|
}
|
|
}
|
|
else if (nb_digits == 1)
|
|
{
|
|
result.push_back(buffer[0]);
|
|
result.push_back('e');
|
|
fill_exponent(kk - 1, result);
|
|
}
|
|
else
|
|
{
|
|
result.push_back(buffer[0]);
|
|
result.push_back('.');
|
|
for (int i = 1; i < nb_digits; ++i)
|
|
{
|
|
result.push_back(buffer[i]);
|
|
}
|
|
result.push_back('e');
|
|
fill_exponent(kk - 1, result);
|
|
}
|
|
}
|
|
|
|
// grisu3
|
|
|
|
inline
|
|
bool round_weed(char *buffer, int len,
|
|
uint64_t wp_W, uint64_t Delta,
|
|
uint64_t rest, uint64_t ten_kappa,
|
|
uint64_t ulp)
|
|
{
|
|
uint64_t wp_Wup = wp_W - ulp;
|
|
uint64_t wp_Wdown = wp_W + ulp;
|
|
while (rest < wp_Wup && /// round1
|
|
Delta - rest >= ten_kappa &&
|
|
(rest + ten_kappa < wp_Wup || /// closer
|
|
wp_Wup - rest >= rest + ten_kappa - wp_Wup))
|
|
{
|
|
buffer[len - 1]--; rest += ten_kappa;
|
|
}
|
|
if (rest < wp_Wdown && /// round2
|
|
Delta - rest >= ten_kappa &&
|
|
(rest + ten_kappa < wp_Wdown ||
|
|
wp_Wdown - rest > rest + ten_kappa - wp_Wdown)) return 0;
|
|
return 2 * ulp <= rest && rest <= Delta - 4 * ulp; /// weed
|
|
}
|
|
|
|
inline
|
|
bool digit_gen(diy_fp_t Wm, diy_fp_t W, diy_fp_t Wp,
|
|
char *buffer, int *len, int *K)
|
|
{
|
|
const uint32_t TEN2 = 100;
|
|
|
|
uint32_t div, p1; uint64_t p2, tmp, unit = 1;
|
|
int d, kappa;
|
|
diy_fp_t one, wp_W, Delta;
|
|
Delta = minus(Wp, Wm); Delta.f += 2 * unit;
|
|
wp_W = minus(Wp, W); wp_W.f += unit;
|
|
one.f = ((uint64_t)1) << -Wp.e; one.e = Wp.e;
|
|
p1 = static_cast<uint32_t>((Wp.f + 1) >> -one.e);
|
|
p2 = (Wp.f + 1) & (one.f - 1);
|
|
*len = 0; kappa = 3; div = TEN2;
|
|
while (kappa > 0)
|
|
{
|
|
d = p1 / div;
|
|
if (d || *len) buffer[(*len)++] = (char)('0' + d);
|
|
p1 %= div; kappa--;
|
|
tmp = (((uint64_t)p1) << -one.e) + p2;
|
|
if (tmp < Delta.f)
|
|
{
|
|
*K += kappa;
|
|
return round_weed(buffer, *len, wp_W.f, Delta.f, tmp,
|
|
((uint64_t)div) << -one.e, unit);
|
|
}
|
|
div /= 10;
|
|
}
|
|
while (1)
|
|
{
|
|
p2 *= 10; Delta.f *= 10; unit *= 10;
|
|
d = static_cast<int>(p2 >> -one.e);
|
|
if (d || *len) buffer[(*len)++] = (char)('0' + d);
|
|
p2 &= one.f - 1; kappa--;
|
|
if (p2 < Delta.f)
|
|
{
|
|
*K += kappa;
|
|
return round_weed(buffer, *len, wp_W.f * unit, Delta.f, p2,
|
|
one.f, unit);
|
|
}
|
|
}
|
|
}
|
|
|
|
inline
|
|
bool grisu3(double v, char *buffer, int *length, int *K)
|
|
{
|
|
diy_fp_t w_m, w_p;
|
|
int q = 64, alpha = -59, gamma = -56;
|
|
normalized_boundaries(v, &w_m, &w_p);
|
|
diy_fp_t w = normalize_diy_fp(double2diy_fp(v));
|
|
int mk = k_comp(w_p.e + q, alpha, gamma);
|
|
diy_fp_t c_mk = cached_power(mk);
|
|
diy_fp_t W = multiply(w, c_mk);
|
|
diy_fp_t Wp = multiply(w_p, c_mk);
|
|
diy_fp_t Wm = multiply(w_m, c_mk);
|
|
*K = -mk;
|
|
bool result = digit_gen(Wm, W, Wp, buffer, length, K);
|
|
buffer[*length] = 0;
|
|
return result;
|
|
}
|
|
|
|
}} // namespace detail namespace jsoncons
|
|
|
|
#endif
|