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swift-mirror/test/stdlib/PrintFloat.swift.gyb
tbkka 1cc1832b96 SR-3131: Adjust choice of decimal vs. exponential format (#15805) 
Merge SR-3131 fix:

For each floating-point type, there is a range of integers which
can be exactly represented in that type.  Adjust the formatting
logic so that we use decimal format for integers within this
range, exponential format for numbers outside of this range.

For example, Double has a 53-bit significand so can exactly
represent every integer from `-(2^53)...(2^53)`.  With this
change, we now use decimal format for these integers and
exponential format for values outside of this range.  This is
a relatively small change from the previous logic -- we've
basically just moved the cutoff from 10^15 to 2^53 (about 10^17).

The decision for using exponential format for small numbers is
not changed.
2018-04-12 09:35:49 -07:00

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// RUN: %empty-directory(%t)
// RUN: %gyb %s -o %t/FloatingPointPrinting.swift
// RUN: %line-directive %t/FloatingPointPrinting.swift -- %target-build-swift %t/FloatingPointPrinting.swift -o %t/main.out
// RUN: %line-directive %t/FloatingPointPrinting.swift -- %target-run %t/main.out
// RUN: %line-directive %t/FloatingPointPrinting.swift -- %target-run %t/main.out --locale ru_RU.UTF-8
// REQUIRES: executable_test
%{
from gyb_stdlib_unittest_support import TRACE, stackTrace, trace
}%
import StdlibUnittest
#if os(Linux) || os(FreeBSD) || os(PS4) || os(Android)
import Glibc
#else
import Darwin
#endif
// It takes about an hour to run the Float formatter over all 2 billion
// positive values to verify that it's correct. Of course, we don't want
// to do that for the Swift standard library.
//
// Instead, I ran the same test against a version of the Float formatter that
// used only 45 bits precision (instead of 59) and collected all the values that
// failed with that reduced precision. This should catch any future mistakes
// that inadvertently damage the accuracy of the formatter's internal
// calculations.
fileprivate let generatedCases_Float: [(Float, String)] = [
(0x1.ab510cp-126, "1.9621416e-38"),
(0x1.b2171p-126 , "1.993244e-38"),
(0x1.b2171p-125 , "3.986488e-38"),
(0x1.b2171p-124 , "7.972976e-38"),
(0x1.1c01b4p-122, "2.0865513e-37"),
(0x1.e41e3p-122 , "3.5567368e-37"),
(0x1.070866p-120, "7.7298394e-37"),
(0x1.0a4cap-120 , "7.825834e-37"),
(0x1.2e92dep-118, "3.5567368e-36"),
(0x1.225e0ap-117, "6.826503e-36"),
(0x1.288e84p-117, "6.9720146e-36"),
(0x1.732b26p-117, "8.726131e-36"),
(0x1.ab8e9cp-117, "1.0051818e-35"),
(0x1.ea228ap-117, "1.15230165e-35"),
(0x1.fc5bb8p-117, "1.1951446e-35"),
(0x1.9cfcbcp-113, "1.5534853e-34"),
(0x1.e11c02p-112, "3.619465e-34"),
(0x1.56f96cp-110, "1.0321008e-33"),
(0x1.9d393ep-110, "1.2434995e-33"),
(0x1.e11c02p-109, "2.895572e-33"),
(0x1.0186b2p-107, "6.199717e-33"),
(0x1.e11c02p-107, "1.1582288e-32"),
(0x1.87454cp-106, "1.8838998e-32"),
(0x1.a337f6p-105, "4.0369282e-32"),
(0x1.71515ap-105, "3.556401e-32"),
(0x1.5d594ep-101, "5.382571e-31"),
(0x1.0d7e9ep-100, "8.304443e-31"),
(0x1.5d594ep-100, "1.0765142e-30"),
(0x1.fd0eacp-99 , "3.137308e-30"),
(0x1.356bf6p-98 , "3.813917e-30"),
(0x1.356bf6p-97 , "7.627834e-30"),
(0x1.6256f8p-97 , "8.7351485e-30"),
(0x1.6c524ep-97 , "8.9812184e-30"),
(0x1.993d5p-97 , "1.0088533e-29"),
(0x1.c62854p-97 , "1.11958476e-29"),
(0x1.fd0eacp-97 , "1.2549232e-29"),
(0x1.e41a56p-96 , "2.3868115e-29"),
(0x1.266f8p-94 , "5.806717e-29"),
(0x1.765118p-94 , "7.382097e-29"),
(0x1.cb25fep-94 , "9.055106e-29"),
(0x1.778decp-93 , "1.4813009e-28"),
(0x1.23f5d8p-92 , "2.303161e-28"),
(0x1.23f5d8p-90 , "9.212644e-28"),
(0x1.a1f86p-90 , "1.3188814e-27"),
(0x1.3db25cp-87 , "8.019793e-27"),
(0x1.bbb4e2p-87 , "1.1200729e-26"),
(0x1.83be04p-84 , "7.8303923e-26"),
(0x1.5c87fap-84 , "7.038531e-26"),
(0x1.b35478p-84 , "8.7914184e-26"),
(0x1.54279p-83 , "1.3738732e-25"),
(0x1.210beap-82 , "2.3348993e-25"),
(0x1.98040cp-82 , "3.2959255e-25"),
(0x1.d3801cp-81 , "7.552877e-25"),
(0x1.296c54p-80 , "9.610261e-25"),
(0x1.7ee2ccp-80 , "1.2371711e-24"),
(0x1.d3801cp-80 , "1.5105754e-24"),
(0x1.e8c296p-78 , "6.3170763e-24"),
(0x1.09a3c4p-77 , "6.8666256e-24"),
(0x1.7e7638p-77 , "9.886406e-24"),
(0x1.d3ecbp-77 , "1.2095566e-23"),
(0x1.5eada8p-76 , "1.8129645e-23"),
(0x1.21517ap-74 , "5.9829616e-23"),
(0x1.ab6668p-74 , "8.8384254e-23"),
(0x1.91172cp-74 , "8.2943575e-23"),
(0x1.be075ap-74 , "9.223658e-23"),
(0x1.aeaacap-70 , "1.424958e-21"),
(0x1.35db3cp-69 , "2.0504575e-21"),
(0x1.74df2p-67 , "9.869829e-21"),
(0x1.f5fa7ap-66 , "2.6574517e-20"),
(0x1.aa969ep-64 , "9.0333597e-20"),
(0x1.c77c72p-64 , "9.6452936e-20"),
(0x1.7f3dep-64 , "8.1154587e-20"),
(0x1.036eeap-57 , "7.0319526e-18"),
(0x1.46b2fap-57 , "8.855198e-18"),
(0x1.796e1ep-57 , "1.0230265e-17"),
(0x1.ce5b7ap-57 , "1.25322205e-17"),
(0x1.dee466p-57 , "1.2980399e-17"),
(0x1.5b3fep-55 , "3.7648867e-17"),
(0x1.3d11a2p-54 , "6.875335e-17"),
(0x1.796e1ep-54 , "8.184212e-17"),
(0x1.bbe57cp-54 , "9.625469e-17"),
(0x1.d624acp-54 , "1.01946067e-16"),
(0x1.f841f8p-54 , "1.0934346e-16"),
(0x1.3d11a2p-53 , "1.375067e-16"),
(0x1.b20fd8p-52 , "3.7648867e-16"),
(0x1.928636p-47 , "1.1172293e-14"),
(0x1.ba8a18p-47 , "1.2282937e-14"),
(0x1.e28dfap-47 , "1.3393581e-14"),
(0x1.374dcap-44 , "6.912334e-14"),
(0x1.a0efd4p-44 , "9.257857e-14"),
(0x1.7c8658p-44 , "8.4493474e-14"),
(0x1.e62862p-44 , "1.07948705e-13"),
(0x1.89537ap-40 , "1.397375e-12"),
(0x1.981532p-39 , "2.8996026e-12"),
(0x1.3e8744p-38 , "4.5265606e-12"),
(0x1.431bf6p-37 , "9.183316e-12"),
(0x1.525f7ep-37 , "9.6171395e-12"),
(0x1.7a0ff2p-37 , "1.07451764e-11"),
(0x1.cf8bp-37 , "1.3174684e-11"),
(0x1.f637d2p-37 , "1.4273895e-11"),
(0x1.4cc72ap-34 , "7.566495e-11"),
(0x1.86e8aep-34 , "8.8882395e-11"),
(0x1.9093e2p-34 , "9.1080816e-11"),
(0x1.eef76ap-34 , "1.12542343e-10"),
(0x1.f637d2p-34 , "1.1419116e-10"),
(0x1.2cc742p+59 , "6.772926e+17"),
(0x1.426638p+59 , "7.259787e+17"),
(0x1.ac1062p+60 , "1.9278289e+18"),
(0x1.3fb25ap+61 , "2.8795718e+18"),
(0x1.28aacp+68 , "3.4203376e+20"),
(0x1.21de92p+69 , "6.683934e+20"),
(0x1.077b62p+69 , "6.0754804e+20"),
(0x1.6dd68ep+69 , "8.435652e+20"),
(0x1.5b7194p+69 , "8.0115055e+20"),
(0x1.72d57p+71 , "3.4203376e+21"),
(0x1.3f1b66p+74 , "2.3545942e+22"),
(0x1.cf8accp+74 , "3.4203376e+22"),
(0x1.15204ep+76 , "8.179321e+22"),
(0x1.69167ep+76 , "1.0657433e+23"),
(0x1.a3dfccp+77 , "2.4784999e+23"),
(0x1.25ee82p+79 , "6.940265e+23"),
(0x1.6d4a0cp+79 , "8.6251485e+23"),
(0x1.9b811cp+79 , "9.716371e+23"),
(0x1.45ee1ep+84 , "2.4626585e+25"),
(0x1.84615ep+84 , "2.934519e+25"),
(0x1.1b492p+87 , "1.7123566e+26"),
(0x1.61594ap+87 , "2.1358624e+26"),
(0x1.1c0b3ep+89 , "6.8677604e+26"),
(0x1.3e5134p+89 , "7.696438e+26"),
(0x1.cd7a02p+89 , "1.1157819e+27"),
(0x1.621b68p+90 , "1.7123566e+27"),
(0x1.baa242p+93 , "1.7123566e+28"),
(0x1.d40dfp+94 , "3.6213959e+28"),
(0x1.10287cp+96 , "8.422887e+28"),
(0x1.8da532p+99 , "9.845221e+29"),
(0x1.f58b6cp+100, "2.4835287e+30"),
(0x1.e11158p+102, "9.5285285e+30"),
(0x1.b61814p+103, "1.7354693e+31"),
(0x1.0502cp+104 , "2.0679402e+31"),
(0x1.772604p+106, "1.188893e+32"),
(0x1.fe44a2p+106, "1.6171041e+32"),
(0x1.9c7f7ap+108, "5.229033e+32"),
(0x1.2c7314p+109, "7.6173e+32"),
(0x1.19c658p+109, "7.143839e+32"),
(0x1.89d2cp+109 , "9.984605e+32"),
(0x1.af2c36p+109, "1.0931527e+33"),
(0x1.c1d8f2p+109, "1.1404988e+33"),
(0x1.89d2cp+110 , "1.996921e+33"),
(0x1.97d44cp+110, "2.0679402e+33"),
(0x1.89d2cp+111 , "3.993842e+33"),
(0x1.2c7314p+112, "6.09384e+33"),
(0x1.368a68p+112, "6.2985127e+33"),
(0x1.89d2cp+112 , "7.987684e+33"),
(0x1.5b22eap+112, "7.040762e+33"),
(0x1.b88294p+112, "8.934606e+33"),
(0x1.e7326ap+112, "9.881528e+33"),
(0x1.672f5ap+114, "2.9140547e+34"),
(0x1.103662p+115, "4.4168992e+34"),
(0x1.4fd77p+116 , "1.0898681e+35"),
(0x1.cf198ap+116, "1.5028446e+35"),
(0x1.347374p+118, "4.0039227e+35"),
(0x1.7ced98p+118, "4.9447295e+35"),
(0x1.aa03cp+119 , "1.1059973e+36"),
(0x1.3b315cp+122, "6.5462986e+36"),
(0x1.3e2542p+122, "6.607624e+36"),
(0x1.c4fb6p+122 , "9.408067e+36"),
(0x1.f062b6p+122, "1.03095254e+37"),
(0x1.2db58cp+123, "1.2532508e+37"),
(0x1.a345d8p+126, "1.393273e+38"),
(0x1.a345d8p+127, "2.786546e+38")
]
// Of course, exhaustive testing of Double (or Float80!) is not
// practical, so I used another approach to generate test cases
// for those:
// The Errol paper details a method for enumerating cases where the optimal
// base-10 form might be extremely close to the midpoint between two binary
// Doubles, and therefore at risk of being handled incorrectly by Grisu-style
// formatters that use fixed-precision arithmetic. These are the extreme cases
// for our algorithm, so if we get these right, we have pretty high confidence
// that we get everything right.
// I took that list and ran it through a reduced-precision version of the Double
// formatter to identify these worst-case values:
fileprivate let generatedCases_Double: [(Double, String)] = [
(0x1.379f099a86228p-317, "4.559093100884257e-96"),
(0x1.7c3fba45c1271p-307, "5.696647848853893e-93"),
(0x1.4f14348a4c5dcp-299, "1.285104507361864e-90"),
(0x1.4f14348a4c5dcp-298, "2.570209014723728e-90"),
(0x1.a8c931c19b77ap-298, "3.258302752792233e-90"),
(0x1.4f14348a4c5dcp-297, "5.140418029447456e-90"),
(0x1.a8c931c19b77ap-297, "6.516605505584466e-90"),
(0x1.97a2a205f591fp-294, "5.002799281833755e-89"),
(0x1.387cf9cb4ad4fp-261, "3.294312317590731e-79"),
(0x1.ddc7e975c5045p-247, "8.252392874408775e-75"),
(0x1.ddc7e975c5045p-246, "1.650478574881755e-74"),
(0x1.ddc7e975c5045p-245, "3.30095714976351e-74"),
(0x1.ddc7e975c5045p-244, "6.60191429952702e-74"),
(0x1.ddc7e975c5045p-243, "1.320382859905404e-73"),
(0x1.ddc7e975c5045p-242, "2.640765719810808e-73"),
(0x1.ddc7e975c5045p-241, "5.281531439621616e-73"),
(0x1.9190e30e46c1ep-235, "2.840978519032327e-71"),
(0x1.0ed9bd6bfd003p-234, "3.832399419240467e-71"),
(0x1.9190e30e46c1ep-234, "5.681957038064654e-71"),
(0x1.3b28b27523ea6p-229, "1.426989259361117e-69"),
(0x1.3b28b27523ea6p-228, "2.853978518722234e-69"),
(0x1.aedaa0fc32ac8p-222, "2.497072464210591e-67"),
(0x1.aedaa0fc32ac8p-221, "4.994144928421182e-67"),
(0x1.48050091c3c25p-219, "1.520865118855779e-66"),
(0x1.48050091c3c25p-218, "3.041730237711558e-66"),
(0x1.f5a18504dfaadp-215, "3.721305106071689e-65"),
(0x1.f5a18504dfaadp-214, "7.442610212143378e-65"),
(0x1.eef5e1f90ac34p-196, "1.925091640472375e-59"),
(0x1.eef5e1f90ac34p-195, "3.85018328094475e-59"),
(0x1.eef5e1f90ac34p-194, "7.7003665618895e-59"),
(0x1.b20c2f4f8d49fp-138, "4.865841847892019e-42"),
(0x1.25d342b1e33e6p-128, "3.372948296445563e-39"),
(0x1.4faba79ea92edp-122, "2.466117547186101e-37"),
(0x1.4faba79ea92edp-121, "4.932235094372202e-37"),
(0x1.78cfcab31064dp-89 , "2.378016066134295e-27"),
(0x1.78cfcab31064dp-88 , "4.75603213226859e-27"),
(0x1.78cfcab31064dp-87 , "9.51206426453718e-27"),
(0x1.78cfcab31064dp-86 , "1.902412852907436e-26"),
(0x1.78cfcab31064dp-85 , "3.804825705814872e-26"),
(0x1.56d589dc3d0e3p-78 , "4.431027338341785e-24"),
(0x1.cd230a7ff47c4p+145, "8.034137530808823e+43"),
(0x1.30d9a1c3890bp+151 , "3.399192475886301e+45"),
(0x1.fc1562f08f125p+151, "5.665320793143835e+45"),
(0x1.a32ac316fb3acp+186, "1.605929046641989e+56"),
(0x1.a32ac316fb3acp+187, "3.211858093283978e+56"),
(0x1.8862481ccada3p+188, "6.013265967485603e+56"),
(0x1.a32ac316fb3acp+188, "6.423716186567956e+56"),
(0x1.5564fb098c956p+201, "4.285935458457607e+60"),
(0x1.f20b1a0d7f626p+207, "4.001624164855121e+62"),
(0x1.f20b1a0d7f626p+208, "8.003248329710242e+62"),
(0x1.a53bb31b369a2p+219, "1.386282306169174e+66"),
(0x1.a53bb31b369a2p+220, "2.772564612338348e+66"),
(0x1.a53bb31b369a2p+221, "5.545129224676696e+66"),
(0x1.66a00a69c6c34p+224, "3.776763733298609e+67"),
(0x1.e2785c3a2a20ap+227, "4.064803033949531e+68"),
(0x1.e2785c3a2a20ap+228, "8.129606067899062e+68"),
(0x1.454b1aef62c8dp+231, "4.384946084578497e+69"),
(0x1.0fde34c996086p+233, "1.465909318208761e+70"),
(0x1.0fde34c996086p+234, "2.931818636417522e+70"),
(0x1.9a2c2a34ac2fap+234, "4.423291694721855e+70"),
(0x1.9a2c2a34ac2fap+235, "8.84658338944371e+70"),
(0x1.9a2c2a34ac2fap+236, "1.769316677888742e+71"),
(0x1.9a2c2a34ac2fap+237, "3.538633355777484e+71"),
(0x1.9a2c2a34ac2fap+238, "7.077266711554968e+71"),
(0x1.ca9bade45b94ap+260, "3.318949537676913e+78"),
(0x1.ca9bade45b94ap+261, "6.637899075353826e+78"),
(0x1.b3a29c72cab91p+269, "1.614179517443508e+81"),
(0x1.b3a29c72cab91p+270, "3.228359034887016e+81"),
(0x1.b3a29c72cab91p+271, "6.456718069774032e+81"),
(0x1.c84c524ab5ebp+277 , "4.328301679886463e+83"),
(0x1.71760b3c0bc14p+287, "3.588703015985849e+86"),
(0x1.11926d079e00ap+304, "3.482974734743573e+91"),
(0x1.9d8f9fc2808d3p+321, "6.901257826767179e+96"),
(0x1.63ed4a60c9c91p+324, "4.751595491707413e+97")
]
#if !os(Windows) && (arch(i386) || arch(x86_64))
// Float80 found via Errol technique.
//
// As with Double, except for Float80. The original list in this
// case had 23 million test cases. I filtered that against
// a Float80 formatter with 129 bits precision.
fileprivate let generatedCases_Float80: [(Float80, String)] = [
(0xf.8f06b25f79a0ad9p-329, "1.4226714622425547106e-98"),
(0xb.a14796a877c6939p-303, "7.136593768505787697e-91"),
(0xf.8e473d72ad52a71p-296, "1.2218360180048428346e-88"),
(0xb.c6f5bb0c6811badp-289, "1.1840575897174935119e-86"),
(0xc.c2111d383f1adfp-236 , "1.1553302055733876345e-70"),
(0xc.c2111d383f1adfp-233 , "9.242641644587101076e-70"),
(0xf.be3d87da323be87p-156, "1.7235014706998294962e-46"),
(0xb.d809f3772d38a59p-150, "8.298420730548195494e-45"),
(0xb.61d88e478a80191p-136, "1.3066137006059396529e-40"),
(0x8.7e6e301b42330f6p-115, "2.044824541427335683e-34"),
(0xe.280cfad818ffc45p-115, "3.408040902378892805e-34"),
(0x8.7e6e301b42330f6p-114, "4.089649082854671366e-34"),
(0xe.280cfad818ffc45p-114, "6.81608180475778561e-34"),
(0x8.7e6e301b42330f6p-113, "8.179298165709342732e-34"),
(0xe.280cfad818ffc45p-113, "1.363216360951557122e-33"),
(0xe.280cfad818ffc45p-112, "2.726432721903114244e-33"),
(0xe.280cfad818ffc45p-111, "5.452865443806228488e-33"),
(0xe.280cfad818ffc45p-110, "1.0905730887612456976e-32"),
(0xc.09de12b2b8b462p+169 , "9.008308715099773956e+51"),
(0xc.eb461a5ceb157bep+196, "1.2975058974374774429e+60"),
(0xd.f29472fdfc52a5ep+202, "8.965157263531703087e+61"),
(0x9.63a86496b5f39b5p+206, "9.656322849684964617e+62"),
(0xf.aab4e43915de71bp+239, "1.3840439837858165139e+73"),
(0xf.135bf3c301b911ap+239, "1.3318159089259743813e+73"),
(0xe.7c03034ced93b19p+239, "1.2795878340661322487e+73"),
(0xd.e4aa12d6d96e518p+239, "1.2273597592062901161e+73"),
(0xd.4d512260c548f17p+239, "1.1751316843464479835e+73"),
(0xc.b5f831eab123916p+239, "1.1229036094866058509e+73"),
(0xc.1e9f41749cfe315p+239, "1.0706755346267637183e+73"),
(0xa.efed608874b3713p+239, "9.662193849070794531e+72"),
(0xa.58947012608e112p+239, "9.139913100472373205e+72"),
(0x9.c13b7f9c4c68b11p+239, "8.617632351873951879e+72"),
(0x9.29e28f26384351p+239 , "8.095351603275530553e+72"),
(0x8.92899eb0241df0fp+239, "7.573070854677109227e+72"),
(0xa.58947012608e112p+240, "1.827982620094474641e+73"),
(0xa.58947012608e112p+241, "3.655965240188949282e+73"),
(0xa.58947012608e112p+242, "7.311930480377898564e+73"),
(0xd.4d512260c548f17p+242, "9.401053474771583868e+73"),
(0xc.9240ee0f9d5e4d6p+252, "9.097859174935622588e+76"),
]
#endif
let PrintTests = TestSuite("FloatingPointPrinting")
% for FloatType in ['Float', 'Double', 'Float80']:
% if FloatType == 'Float80':
#if !os(Windows) && (arch(i386) || arch(x86_64))
% end
// Verify that a particular value provides a specific description string.
// Also check that the generated strings actually satisfy our
// accuracy requirements.
fileprivate func expectDescription(_ expected: String, _ object: ${FloatType}, ${TRACE}) {
expectEqual(expected, object.description, ${trace})
expectEqual(expected, object.debugDescription, ${trace})
expectAccurateDescription(object, ${trace})
}
// Verify our key requirements:
//
// * Accurate. A formatted float should parse back to exactly the original
// value.
//
// * Short. The formatted value should use the minimum number of digits needed
// to be accurate.
//
// * Close. If there is more than one accurate and short value, we want the one
// that is closest (as an infinitely-precise real number) to the original
// binary float (interpreted as an infinitely-precise real number).
fileprivate func expectAccurateDescription(_ object: ${FloatType}, ${TRACE}) {
if !object.isFinite {
return
}
// Following checks all return early on failure, since it makes no sense to
// check shortness if the result is inaccurate, etc.
// Verify round-trip accuracy:
let text = object.debugDescription
if let roundTrip = ${FloatType}(text) {
if object != roundTrip {
expectationFailure("Round-trip inaccuracy: \(object) != \(roundTrip)", trace: ${trace})
return
}
} else {
expectationFailure("Failed to parse \(text)", trace: ${trace})
return
}
// TODO: Verify shortness by trimming the last digit and checking
// that the result does NOT round-trip.
// TODO: Verify closeness by fuzzing the last digit and checking
// that the result is not closer. Note this requires higher-precision
// arithmetic.
}
% if FloatType == 'Float80':
#endif
% end
% end
// Special helper for NaN values
fileprivate func expectNaN<T>(_ expected: String, _ object: T, ${TRACE}) where T: FloatingPoint & CustomDebugStringConvertible & CustomStringConvertible {
// Regular description always returns "nan"
expectEqual("nan", object.description, ${trace})
// Debug description returns a more detailed form:
expectEqual(expected, object.debugDescription, ${trace})
}
// Foundation's String(format:) isn't available here, so
// build up "1e-234" manually:
fileprivate func exponentialPowerOfTen(_ power: Int) -> String {
let digits = ["0", "1", "2", "3", "4", "5", "6", "7", "8", "9"]
var s = "1e"
var p = power
if p < 0 {
s += "-"
p = -p
} else {
s += "+"
}
if (p > 999) {
s += digits[ (p / 1000) % 10]
}
if (p > 99) {
s += digits[ (p / 100) % 10]
}
s += digits[ (p / 10) % 10]
s += digits[ p % 10]
return s
}
// An earlier version of Swift's floating-point `.description` logic
// used potentially locale-sensitive C library functions, hence
// this logic to help verify that the output does not depend on
// the C locale.
PrintTests.setUp {
if let localeArgIndex = CommandLine.arguments.index(of: "--locale") {
let locale = CommandLine.arguments[localeArgIndex + 1]
expectEqual("ru_RU.UTF-8", locale)
setlocale(LC_ALL, locale)
} else {
setlocale(LC_ALL, "")
}
}
// Check that all floating point types
// are CustomStringConvertible
PrintTests.test("CustomStringConvertible") {
func hasDescription(_ any: Any) {
expectTrue(any is CustomStringConvertible)
}
hasDescription(Float(1.0))
hasDescription(Double(1.0))
#if !os(Windows) && (arch(i386) || arch(x86_64))
hasDescription(Float80(1.0))
#endif
hasDescription(CFloat(1.0))
hasDescription(CDouble(1.0))
}
// Check that all floating point types
// are CustomDebugStringConvertible
PrintTests.test("CustomDebugStringConvertible") {
func hasDebugDescription(_ any: Any) {
expectTrue(any is CustomDebugStringConvertible)
}
hasDebugDescription(Float(1.0))
hasDebugDescription(Double(1.0))
#if !os(Windows) && (arch(i386) || arch(x86_64))
hasDebugDescription(Float80(1.0))
#endif
hasDebugDescription(CFloat(1.0))
hasDebugDescription(CDouble(1.0))
}
PrintTests.test("Printable_CFloat") {
// Basic check for CFloat: Since it's a synonym for Float, we don't
// need more detailed verification, just basic sanity.
expectDescription("1.0", CFloat(1.0))
expectDescription("1.1", CFloat(1.1))
expectDescription("-1.0", CFloat(-1.0))
}
PrintTests.test("Printable_CDouble") {
// Likewise for CDouble
expectDescription("1.0", CDouble(1.0))
expectDescription("1.1", CDouble(1.1))
expectDescription("-1.0", CDouble(-1.0))
}
PrintTests.test("Printable_Float") {
func asFloat32(_ f: Float32) -> Float32 { return f }
// Basic sanity checks:
let f = 100.125 as Float
expectEqual("f = 100.125", "f = \(f)")
expectDescription("0.0", asFloat32(0.0))
expectDescription("-0.0", -asFloat32(0.0))
expectDescription("0.1", asFloat32(0.1))
expectDescription("-0.1", asFloat32(-0.1))
expectDescription("1.0", asFloat32(1.0))
expectDescription("-1.0", asFloat32(-1.0))
expectDescription("1.1", asFloat32(1.1))
expectDescription("100.125", asFloat32(100.125))
expectDescription("-100.125", asFloat32(-100.125))
// Standard special numbers:
expectDescription("inf", Float.infinity)
expectDescription("-inf", -Float.infinity)
expectDescription("3.1415925", Float.pi)
expectDescription("3.4028235e+38", Float.greatestFiniteMagnitude)
expectDescription("1e-45", Float.leastNonzeroMagnitude)
expectDescription("1.1754944e-38", Float.leastNormalMagnitude)
// Special cases for the underlying algorithms:
// Smallest Float that requires 9 digits to print accurately
expectDescription("1.00000075e-36", 1.00000075e-36 as Float)
// Worst case for shortness:
// Float for which the shortest accurate decimal form is
// closest to the midpoint between two binary floats
expectDescription("7.0385313e-26", 7.0385313e-26 as Float)
// Second-worst case for shortness:
expectDescription("7.038531e-26", 7.038531e-26 as Float)
// NaNs require special care in testing:
// NaN is printed with additional detail to debugDescription, but not description
expectNaN("nan", Float.nan)
expectNaN("nan(0xffff)", Float(nan: 65535, signaling: false))
expectNaN("nan(0x1fffff)", Float(bitPattern: 0x7fff_ffff))
expectNaN("nan(0x1fffff)", Float(bitPattern: 0x7fdf_ffff))
#if !arch(arm)
// ARM doesn't have negative Float nans
expectNaN("-nan", -Float.nan)
expectNaN("-nan(0xffff)", -Float(nan: 65535, signaling: false)) // fail
#endif
#if !arch(i386) && !arch(arm)
// 32-bit i386 and ARM lack signaling Float nans
expectNaN("snan", Float.signalingNaN)
expectNaN("-snan", -Float.signalingNaN)
expectNaN("snan(0xffff)", Float(nan: 65535, signaling: true))
expectNaN("-snan(0xffff)", -Float(nan: 65535, signaling: true))
expectNaN("snan(0x1fffff)", Float(bitPattern: 0x7fbf_ffff))
#endif
// Every power of 10 should print with only a single digit '1'
for power in -45 ... 38 {
let s: String
if power < -4 || power > 7 { // Exponential form
s = exponentialPowerOfTen(power)
} else if power < 0 { // Fractional decimal form
s = "0." + String(repeating: "0", count: -power - 1) + "1"
} else { // Decimal form
s = "1" + String(repeating: "0", count: power) + ".0"
}
let f = Float(s)!
expectDescription(s, f)
}
// Test the 170 "worst cases" listed above.
for (f,s) in generatedCases_Float {
expectAccurateDescription(f.nextDown)
expectDescription(s, f)
expectAccurateDescription(f.nextUp)
}
// Float can represent all integers -(2^24)...(2^24)
let maxDecimalForm = Float(1 << 24)
expectDescription("16777216.0", maxDecimalForm)
expectDescription("-16777216.0", -maxDecimalForm)
// Outside of that range, use exponential form
expectDescription("1.6777218e+07", maxDecimalForm.nextUp)
expectDescription("-1.6777218e+07", -maxDecimalForm.nextUp)
expectDescription("1.00001", asFloat32(1.00001))
expectDescription("1.25e+17", asFloat32(125000000000000000.0))
expectDescription("1.25e+16", asFloat32(12500000000000000.0))
expectDescription("1.25e+15", asFloat32(1250000000000000.0))
expectDescription("1.25e+14", asFloat32(125000000000000.0))
expectDescription("1.25e+13", asFloat32(12500000000000.0))
expectDescription("1.25e+12", asFloat32(1250000000000.0))
expectDescription("1.25e+11", asFloat32(125000000000.0))
expectDescription("1.25e+10", asFloat32(12500000000.0))
expectDescription("1.25e+09", asFloat32(1250000000.0))
expectDescription("1.25e+08", asFloat32(125000000.0))
expectDescription("12500000.0", asFloat32(12500000.0))
expectDescription("1250000.0", asFloat32(1250000.0))
expectDescription("125000.0", asFloat32(125000.0))
expectDescription("12500.0", asFloat32(12500.0))
expectDescription("1250.0", asFloat32(1250.0))
expectDescription("125.0", asFloat32(125.0))
expectDescription("12.5", asFloat32(12.5))
expectDescription("1.25", asFloat32(1.25))
expectDescription("0.125", asFloat32(0.125))
expectDescription("0.0125", asFloat32(0.0125))
expectDescription("0.00125", asFloat32(0.00125))
expectDescription("0.000125", asFloat32(0.000125))
expectDescription("1.25e-05", asFloat32(0.0000125))
expectDescription("1.25e-06", asFloat32(0.00000125))
expectDescription("1.25e-07", asFloat32(0.000000125))
expectDescription("1.25e-08", asFloat32(0.0000000125))
expectDescription("1.25e-09", asFloat32(0.00000000125))
expectDescription("1.25e-10", asFloat32(0.000000000125))
expectDescription("1.25e-11", asFloat32(0.0000000000125))
expectDescription("1.25e-12", asFloat32(0.00000000000125))
expectDescription("1.25e-13", asFloat32(0.000000000000125))
expectDescription("1.25e-14", asFloat32(0.0000000000000125))
expectDescription("1.25e-15", asFloat32(0.00000000000000125))
expectDescription("1.25e-16", asFloat32(0.000000000000000125))
expectDescription("1.25e-17", asFloat32(0.0000000000000000125))
}
PrintTests.test("Printable_Double") {
func asFloat64(_ f: Float64) -> Float64 { return f }
// Sanity check
let f = 100.125 as Double
expectEqual("f = 100.125", "f = \(f)")
expectDescription("0.0", asFloat64(0.0))
expectDescription("-0.0", asFloat64(-0.0))
expectDescription("0.1", asFloat64(0.1))
expectDescription("-0.1", asFloat64(-0.1))
expectDescription("1.0", asFloat64(1.0))
expectDescription("-1.0", asFloat64(-1.0))
expectDescription("1.1", asFloat64(1.1))
expectDescription("100.125", asFloat64(100.125))
expectDescription("-100.125", asFloat64(-100.125))
// Special values
expectDescription("3.141592653589793", Double.pi)
expectDescription("1.7976931348623157e+308", Double.greatestFiniteMagnitude)
expectDescription("5e-324", Double.leastNonzeroMagnitude)
expectDescription("2.2250738585072014e-308", Double.leastNormalMagnitude)
expectDescription("inf", Double.infinity)
expectDescription("-inf", -Double.infinity)
// Worst case for Double shortness:
expectDescription("2.311989689387339e-82", 2.311989689387339e-82)
// Verify NaNs
expectNaN("nan", Double.nan)
expectNaN("-nan", -Double.nan)
#if arch(i386)
expectNaN("nan", Double(nan: 65535, signaling: false))
expectNaN("nan", Float64(bitPattern: 0x7fff_ffff_ffff_ffff))
expectNaN("nan", Float64(bitPattern: 0x7ffb_ffff_ffff_ffff))
expectNaN("-nan", -Double(nan: 65535, signaling: false))
if _isDebugAssertConfiguration() {
expectNaN("nan", Double.signalingNaN)
expectNaN("-nan", -Double.signalingNaN)
expectNaN("nan", Double(nan: 65535, signaling: true))
expectNaN("-nan", -Double(nan: 65535, signaling: true))
expectNaN("nan", Float64(bitPattern: 0x7ff7_ffff_ffff_ffff))
}
#else
// 32-bit i386 lacks signaling Double nans or payloads on NaNs
expectNaN("nan(0xffff)", Double(nan: 65535, signaling: false))
expectNaN("nan(0x3ffffffffffff)", Float64(bitPattern: 0x7fff_ffff_ffff_ffff))
expectNaN("nan(0x3ffffffffffff)", Float64(bitPattern: 0x7ffb_ffff_ffff_ffff))
expectNaN("-nan(0xffff)", -Double(nan: 65535, signaling: false))
expectNaN("snan", Double.signalingNaN)
expectNaN("-snan", -Double.signalingNaN)
expectNaN("snan(0xffff)", Double(nan: 65535, signaling: true))
expectNaN("-snan(0xffff)", -Double(nan: 65535, signaling: true))
expectNaN("snan(0x3ffffffffffff)", Float64(bitPattern: 0x7ff7_ffff_ffff_ffff))
#endif
// We know how every power of 10 should print
for power in -323 ... 308 {
let s: String
if power < -4 || power > 15 { // Exponential form
s = exponentialPowerOfTen(power)
} else if power < 0 { // Fractional decimal form
s = "0." + String(repeating: "0", count: -power - 1) + "1"
} else { // Decimal form
s = "1" + String(repeating: "0", count: power) + ".0"
}
let f = Double(s)!
expectDescription(s, f)
}
// Verify 74 extreme values generated using a technique from the Errol paper,
// plus many nearby values.
for (d, s) in generatedCases_Double {
expectDescription(s, d)
// Also check nearby values.
var upCase = d
var downCase = d
for _ in 0..<10 {
upCase = upCase.nextUp
expectAccurateDescription(upCase)
downCase = downCase.nextDown
expectAccurateDescription(downCase)
}
}
// Double can represent all integers -(2^53)...(2^53)
let maxDecimalForm = Double((1 as Int64) << 53)
expectDescription("9007199254740992.0", maxDecimalForm)
expectDescription("-9007199254740992.0", -maxDecimalForm)
// Outside of that range, we use exponential form:
expectDescription("9.007199254740994e+15", maxDecimalForm.nextUp)
expectDescription("-9.007199254740994e+15", -maxDecimalForm.nextUp)
expectDescription("1.00000000000001", asFloat64(1.00000000000001))
expectDescription("1.25e+17", asFloat64(125000000000000000.0))
expectDescription("1.25e+16", asFloat64(12500000000000000.0))
expectDescription("1250000000000000.0", asFloat64(1250000000000000.0))
expectDescription("125000000000000.0", asFloat64(125000000000000.0))
expectDescription("12500000000000.0", asFloat64(12500000000000.0))
expectDescription("1250000000000.0", asFloat64(1250000000000.0))
expectDescription("125000000000.0", asFloat64(125000000000.0))
expectDescription("12500000000.0", asFloat64(12500000000.0))
expectDescription("1250000000.0", asFloat64(1250000000.0))
expectDescription("125000000.0", asFloat64(125000000.0))
expectDescription("12500000.0", asFloat64(12500000.0))
expectDescription("1250000.0", asFloat64(1250000.0))
expectDescription("125000.0", asFloat64(125000.0))
expectDescription("12500.0", asFloat64(12500.0))
expectDescription("1250.0", asFloat64(1250.0))
expectDescription("125.0", asFloat64(125.0))
expectDescription("12.5", asFloat64(12.5))
expectDescription("1.25", asFloat64(1.25))
expectDescription("0.125", asFloat64(0.125))
expectDescription("0.0125", asFloat64(0.0125))
expectDescription("0.00125", asFloat64(0.00125))
expectDescription("0.000125", asFloat64(0.000125))
expectDescription("1.25e-05", asFloat64(0.0000125))
expectDescription("1.25e-06", asFloat64(0.00000125))
expectDescription("1.25e-07", asFloat64(0.000000125))
expectDescription("1.25e-08", asFloat64(0.0000000125))
expectDescription("1.25e-09", asFloat64(0.00000000125))
expectDescription("1.25e-10", asFloat64(0.000000000125))
expectDescription("1.25e-11", asFloat64(0.0000000000125))
expectDescription("1.25e-12", asFloat64(0.00000000000125))
expectDescription("1.25e-13", asFloat64(0.000000000000125))
expectDescription("1.25e-14", asFloat64(0.0000000000000125))
expectDescription("1.25e-15", asFloat64(0.00000000000000125))
expectDescription("1.25e-16", asFloat64(0.000000000000000125))
expectDescription("1.25e-17", asFloat64(0.0000000000000000125))
}
PrintTests.test("Printable_Float80") {
#if !os(Windows) && (arch(i386) || arch(x86_64))
func asFloat80(_ f: Swift.Float80) -> Swift.Float80 { return f }
// Sanity
let f = 100.125 as Float80
expectEqual("f = 100.125", "f = \(f)")
expectDescription("0.0", asFloat80(0.0))
expectDescription("-0.0", -asFloat80(0.0))
expectDescription("0.1", asFloat80(0.1))
expectDescription("-0.1", asFloat80(-0.1))
expectDescription("1.0", asFloat80(1.0))
expectDescription("-1.0", asFloat80(-1.0))
expectDescription("1.1", asFloat80(1.1))
expectDescription("100.125", asFloat80(100.125))
expectDescription("-100.125", asFloat80(-100.125))
// Special values
expectDescription("3.1415926535897932385", Float80.pi)
expectDescription("1.189731495357231765e+4932", Float80.greatestFiniteMagnitude)
expectDescription("4e-4951", Float80.leastNonzeroMagnitude)
expectDescription("3.3621031431120935063e-4932", Float80.leastNormalMagnitude)
expectDescription("inf", Float80.infinity)
expectDescription("-inf", -Float80.infinity)
// NaNs
expectNaN("nan", Float80.nan)
expectNaN("nan(0xffff)", Float80(nan: 65535, signaling: false))
expectNaN("nan(0x1fffffffffffffff)", Float80(sign: .plus, exponentBitPattern: 0x7fff, significandBitPattern: 0xffff_ffff_ffff_ffff))
expectNaN("nan(0x1fffffffffffffff)", Float80(sign: .plus, exponentBitPattern: 0x7fff, significandBitPattern: 0xdfff_ffff_ffff_ffff))
expectNaN("-nan", -Float80.nan)
expectNaN("-nan(0xffff)", -Float80(nan: 65535, signaling: false))
expectNaN("snan", Float80.signalingNaN)
expectNaN("-snan", -Float80.signalingNaN)
expectNaN("snan(0xffff)", Float80(nan: 65535, signaling: true))
expectNaN("-snan(0xffff)", -Float80(nan: 65535, signaling: true))
expectNaN("snan(0x1fffffffffffffff)", Float80(sign: .plus, exponentBitPattern: 0x7fff, significandBitPattern: 0xbfff_ffff_ffff_ffff))
// We know how every power of 10 should print
for power in -4950 ... 4932 {
let s: String
if power < -4 || power > 19 { // Exponential form
s = exponentialPowerOfTen(power)
} else if power < 0 { // Fractional decimal form
s = "0." + String(repeating: "0", count: -power - 1) + "1"
} else { // Decimal form
s = "1" + String(repeating: "0", count: power) + ".0"
}
let f = Float80(s)!
expectDescription(s, f)
}
// Verify the extreme cases generated via the Errol technique.
for (d, s) in generatedCases_Float80 {
expectDescription(s, d)
var upCase = d
var downCase = d
for _ in 0..<10 {
upCase = upCase.nextUp
expectAccurateDescription(upCase)
downCase = downCase.nextDown
expectAccurateDescription(downCase)
}
}
// Float80 can represent all integers -(2^64)...(2^64):
let maxDecimalForm = Float80(UInt64.max) + 1.0
expectDescription("18446744073709551616.0", maxDecimalForm)
expectDescription("-18446744073709551616.0", -maxDecimalForm)
// Outside of that range, use exponential form
expectDescription("1.8446744073709551618e+19", maxDecimalForm.nextUp)
expectDescription("-1.8446744073709551618e+19", -maxDecimalForm.nextUp)
expectDescription("1.00000000000000001", asFloat80(1.00000000000000001))
expectDescription("1.25e+21", asFloat80(1250000000000000000000.0))
expectDescription("1.25e+20", asFloat80(125000000000000000000.0))
expectDescription("12500000000000000000.0", asFloat80(12500000000000000000.0))
expectDescription("1250000000000000000.0", asFloat80(1250000000000000000.0))
expectDescription("125000000000000000.0", asFloat80(125000000000000000.0))
expectDescription("12500000000000000.0", asFloat80(12500000000000000.0))
expectDescription("1250000000000000.0", asFloat80(1250000000000000.0))
expectDescription("125000000000000.0", asFloat80(125000000000000.0))
expectDescription("12500000000000.0", asFloat80(12500000000000.0))
expectDescription("1250000000000.0", asFloat80(1250000000000.0))
expectDescription("125000000000.0", asFloat80(125000000000.0))
expectDescription("12500000000.0", asFloat80(12500000000.0))
expectDescription("1250000000.0", asFloat80(1250000000.0))
expectDescription("125000000.0", asFloat80(125000000.0))
expectDescription("12500000.0", asFloat80(12500000.0))
expectDescription("1250000.0", asFloat80(1250000.0))
expectDescription("125000.0", asFloat80(125000.0))
expectDescription("12500.0", asFloat80(12500.0))
expectDescription("1250.0", asFloat80(1250.0))
expectDescription("125.0", asFloat80(125.0))
expectDescription("12.5", asFloat80(12.5))
expectDescription("1.25", asFloat80(1.25))
expectDescription("0.125", asFloat80(0.125))
expectDescription("0.0125", asFloat80(0.0125))
expectDescription("0.00125", asFloat80(0.00125))
expectDescription("0.000125", asFloat80(0.000125))
expectDescription("1.25e-05", asFloat80(0.0000125))
expectDescription("1.25e-06", asFloat80(0.00000125))
expectDescription("1.25e-07", asFloat80(0.000000125))
expectDescription("1.25e-08", asFloat80(0.0000000125))
expectDescription("1.25e-09", asFloat80(0.00000000125))
expectDescription("1.25e-10", asFloat80(0.000000000125))
expectDescription("1.25e-11", asFloat80(0.0000000000125))
expectDescription("1.25e-12", asFloat80(0.00000000000125))
expectDescription("1.25e-13", asFloat80(0.000000000000125))
expectDescription("1.25e-14", asFloat80(0.0000000000000125))
expectDescription("1.25e-15", asFloat80(0.00000000000000125))
expectDescription("1.25e-16", asFloat80(0.000000000000000125))
expectDescription("1.25e-17", asFloat80(0.0000000000000000125))
#endif
}
runAllTests()
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