diff options
Diffstat (limited to 'absl/strings/internal')
| -rw-r--r-- | absl/strings/internal/pow10_helper.cc | 120 | ||||
| -rw-r--r-- | absl/strings/internal/pow10_helper.h | 36 | ||||
| -rw-r--r-- | absl/strings/internal/pow10_helper_test.cc | 120 |
3 files changed, 276 insertions, 0 deletions
diff --git a/absl/strings/internal/pow10_helper.cc b/absl/strings/internal/pow10_helper.cc new file mode 100644 index 000000000000..66be163f43fe --- /dev/null +++ b/absl/strings/internal/pow10_helper.cc @@ -0,0 +1,120 @@ +// Copyright 2018 The Abseil Authors. +// +// Licensed under the Apache License, Version 2.0 (the "License"); +// you may not use this file except in compliance with the License. +// You may obtain a copy of the License at +// +// http://www.apache.org/licenses/LICENSE-2.0 +// +// Unless required by applicable law or agreed to in writing, software +// distributed under the License is distributed on an "AS IS" BASIS, +// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +// See the License for the specific language governing permissions and +// limitations under the License. + +#include "absl/strings/internal/pow10_helper.h" + +#include <cmath> + +namespace absl { +namespace strings_internal { + +namespace { + +// The exact value of 1e23 falls precisely halfway between two representable +// doubles. Furthermore, the rounding rules we prefer (break ties by rounding +// to the nearest even) dictate in this case that the number should be rounded +// down, but this is not completely specified for floating-point literals in +// C++. (It just says to use the default rounding mode of the standard +// library.) We ensure the result we want by using a number that has an +// unambiguous correctly rounded answer. +constexpr double k1e23 = 9999999999999999e7; + +constexpr double kPowersOfTen[] = { + 0.0, 1e-323, 1e-322, 1e-321, 1e-320, 1e-319, 1e-318, 1e-317, 1e-316, + 1e-315, 1e-314, 1e-313, 1e-312, 1e-311, 1e-310, 1e-309, 1e-308, 1e-307, + 1e-306, 1e-305, 1e-304, 1e-303, 1e-302, 1e-301, 1e-300, 1e-299, 1e-298, + 1e-297, 1e-296, 1e-295, 1e-294, 1e-293, 1e-292, 1e-291, 1e-290, 1e-289, + 1e-288, 1e-287, 1e-286, 1e-285, 1e-284, 1e-283, 1e-282, 1e-281, 1e-280, + 1e-279, 1e-278, 1e-277, 1e-276, 1e-275, 1e-274, 1e-273, 1e-272, 1e-271, + 1e-270, 1e-269, 1e-268, 1e-267, 1e-266, 1e-265, 1e-264, 1e-263, 1e-262, + 1e-261, 1e-260, 1e-259, 1e-258, 1e-257, 1e-256, 1e-255, 1e-254, 1e-253, + 1e-252, 1e-251, 1e-250, 1e-249, 1e-248, 1e-247, 1e-246, 1e-245, 1e-244, + 1e-243, 1e-242, 1e-241, 1e-240, 1e-239, 1e-238, 1e-237, 1e-236, 1e-235, + 1e-234, 1e-233, 1e-232, 1e-231, 1e-230, 1e-229, 1e-228, 1e-227, 1e-226, + 1e-225, 1e-224, 1e-223, 1e-222, 1e-221, 1e-220, 1e-219, 1e-218, 1e-217, + 1e-216, 1e-215, 1e-214, 1e-213, 1e-212, 1e-211, 1e-210, 1e-209, 1e-208, + 1e-207, 1e-206, 1e-205, 1e-204, 1e-203, 1e-202, 1e-201, 1e-200, 1e-199, + 1e-198, 1e-197, 1e-196, 1e-195, 1e-194, 1e-193, 1e-192, 1e-191, 1e-190, + 1e-189, 1e-188, 1e-187, 1e-186, 1e-185, 1e-184, 1e-183, 1e-182, 1e-181, + 1e-180, 1e-179, 1e-178, 1e-177, 1e-176, 1e-175, 1e-174, 1e-173, 1e-172, + 1e-171, 1e-170, 1e-169, 1e-168, 1e-167, 1e-166, 1e-165, 1e-164, 1e-163, + 1e-162, 1e-161, 1e-160, 1e-159, 1e-158, 1e-157, 1e-156, 1e-155, 1e-154, + 1e-153, 1e-152, 1e-151, 1e-150, 1e-149, 1e-148, 1e-147, 1e-146, 1e-145, + 1e-144, 1e-143, 1e-142, 1e-141, 1e-140, 1e-139, 1e-138, 1e-137, 1e-136, + 1e-135, 1e-134, 1e-133, 1e-132, 1e-131, 1e-130, 1e-129, 1e-128, 1e-127, + 1e-126, 1e-125, 1e-124, 1e-123, 1e-122, 1e-121, 1e-120, 1e-119, 1e-118, + 1e-117, 1e-116, 1e-115, 1e-114, 1e-113, 1e-112, 1e-111, 1e-110, 1e-109, + 1e-108, 1e-107, 1e-106, 1e-105, 1e-104, 1e-103, 1e-102, 1e-101, 1e-100, + 1e-99, 1e-98, 1e-97, 1e-96, 1e-95, 1e-94, 1e-93, 1e-92, 1e-91, + 1e-90, 1e-89, 1e-88, 1e-87, 1e-86, 1e-85, 1e-84, 1e-83, 1e-82, + 1e-81, 1e-80, 1e-79, 1e-78, 1e-77, 1e-76, 1e-75, 1e-74, 1e-73, + 1e-72, 1e-71, 1e-70, 1e-69, 1e-68, 1e-67, 1e-66, 1e-65, 1e-64, + 1e-63, 1e-62, 1e-61, 1e-60, 1e-59, 1e-58, 1e-57, 1e-56, 1e-55, + 1e-54, 1e-53, 1e-52, 1e-51, 1e-50, 1e-49, 1e-48, 1e-47, 1e-46, + 1e-45, 1e-44, 1e-43, 1e-42, 1e-41, 1e-40, 1e-39, 1e-38, 1e-37, + 1e-36, 1e-35, 1e-34, 1e-33, 1e-32, 1e-31, 1e-30, 1e-29, 1e-28, + 1e-27, 1e-26, 1e-25, 1e-24, 1e-23, 1e-22, 1e-21, 1e-20, 1e-19, + 1e-18, 1e-17, 1e-16, 1e-15, 1e-14, 1e-13, 1e-12, 1e-11, 1e-10, + 1e-9, 1e-8, 1e-7, 1e-6, 1e-5, 1e-4, 1e-3, 1e-2, 1e-1, + 1e+0, 1e+1, 1e+2, 1e+3, 1e+4, 1e+5, 1e+6, 1e+7, 1e+8, + 1e+9, 1e+10, 1e+11, 1e+12, 1e+13, 1e+14, 1e+15, 1e+16, 1e+17, + 1e+18, 1e+19, 1e+20, 1e+21, 1e+22, k1e23, 1e+24, 1e+25, 1e+26, + 1e+27, 1e+28, 1e+29, 1e+30, 1e+31, 1e+32, 1e+33, 1e+34, 1e+35, + 1e+36, 1e+37, 1e+38, 1e+39, 1e+40, 1e+41, 1e+42, 1e+43, 1e+44, + 1e+45, 1e+46, 1e+47, 1e+48, 1e+49, 1e+50, 1e+51, 1e+52, 1e+53, + 1e+54, 1e+55, 1e+56, 1e+57, 1e+58, 1e+59, 1e+60, 1e+61, 1e+62, + 1e+63, 1e+64, 1e+65, 1e+66, 1e+67, 1e+68, 1e+69, 1e+70, 1e+71, + 1e+72, 1e+73, 1e+74, 1e+75, 1e+76, 1e+77, 1e+78, 1e+79, 1e+80, + 1e+81, 1e+82, 1e+83, 1e+84, 1e+85, 1e+86, 1e+87, 1e+88, 1e+89, + 1e+90, 1e+91, 1e+92, 1e+93, 1e+94, 1e+95, 1e+96, 1e+97, 1e+98, + 1e+99, 1e+100, 1e+101, 1e+102, 1e+103, 1e+104, 1e+105, 1e+106, 1e+107, + 1e+108, 1e+109, 1e+110, 1e+111, 1e+112, 1e+113, 1e+114, 1e+115, 1e+116, + 1e+117, 1e+118, 1e+119, 1e+120, 1e+121, 1e+122, 1e+123, 1e+124, 1e+125, + 1e+126, 1e+127, 1e+128, 1e+129, 1e+130, 1e+131, 1e+132, 1e+133, 1e+134, + 1e+135, 1e+136, 1e+137, 1e+138, 1e+139, 1e+140, 1e+141, 1e+142, 1e+143, + 1e+144, 1e+145, 1e+146, 1e+147, 1e+148, 1e+149, 1e+150, 1e+151, 1e+152, + 1e+153, 1e+154, 1e+155, 1e+156, 1e+157, 1e+158, 1e+159, 1e+160, 1e+161, + 1e+162, 1e+163, 1e+164, 1e+165, 1e+166, 1e+167, 1e+168, 1e+169, 1e+170, + 1e+171, 1e+172, 1e+173, 1e+174, 1e+175, 1e+176, 1e+177, 1e+178, 1e+179, + 1e+180, 1e+181, 1e+182, 1e+183, 1e+184, 1e+185, 1e+186, 1e+187, 1e+188, + 1e+189, 1e+190, 1e+191, 1e+192, 1e+193, 1e+194, 1e+195, 1e+196, 1e+197, + 1e+198, 1e+199, 1e+200, 1e+201, 1e+202, 1e+203, 1e+204, 1e+205, 1e+206, + 1e+207, 1e+208, 1e+209, 1e+210, 1e+211, 1e+212, 1e+213, 1e+214, 1e+215, + 1e+216, 1e+217, 1e+218, 1e+219, 1e+220, 1e+221, 1e+222, 1e+223, 1e+224, + 1e+225, 1e+226, 1e+227, 1e+228, 1e+229, 1e+230, 1e+231, 1e+232, 1e+233, + 1e+234, 1e+235, 1e+236, 1e+237, 1e+238, 1e+239, 1e+240, 1e+241, 1e+242, + 1e+243, 1e+244, 1e+245, 1e+246, 1e+247, 1e+248, 1e+249, 1e+250, 1e+251, + 1e+252, 1e+253, 1e+254, 1e+255, 1e+256, 1e+257, 1e+258, 1e+259, 1e+260, + 1e+261, 1e+262, 1e+263, 1e+264, 1e+265, 1e+266, 1e+267, 1e+268, 1e+269, + 1e+270, 1e+271, 1e+272, 1e+273, 1e+274, 1e+275, 1e+276, 1e+277, 1e+278, + 1e+279, 1e+280, 1e+281, 1e+282, 1e+283, 1e+284, 1e+285, 1e+286, 1e+287, + 1e+288, 1e+289, 1e+290, 1e+291, 1e+292, 1e+293, 1e+294, 1e+295, 1e+296, + 1e+297, 1e+298, 1e+299, 1e+300, 1e+301, 1e+302, 1e+303, 1e+304, 1e+305, + 1e+306, 1e+307, 1e+308, +}; + +} // namespace + +double Pow10(int exp) { + if (exp < -324) { + return 0.0; + } else if (exp > 308) { + return INFINITY; + } else { + return kPowersOfTen[exp + 324]; + } +} + +} // namespace strings_internal +} // namespace absl diff --git a/absl/strings/internal/pow10_helper.h b/absl/strings/internal/pow10_helper.h new file mode 100644 index 000000000000..39c153928de2 --- /dev/null +++ b/absl/strings/internal/pow10_helper.h @@ -0,0 +1,36 @@ +// +// Copyright 2018 The Abseil Authors. +// +// Licensed under the Apache License, Version 2.0 (the "License"); +// you may not use this file except in compliance with the License. +// You may obtain a copy of the License at +// +// http://www.apache.org/licenses/LICENSE-2.0 +// +// Unless required by applicable law or agreed to in writing, software +// distributed under the License is distributed on an "AS IS" BASIS, +// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +// See the License for the specific language governing permissions and +// limitations under the License. +// +// This test helper library contains a table of powers of 10, to guarantee +// precise values are computed across the full range of doubles. We can't rely +// on the pow() function, because not all standard libraries ship a version +// that is precise. +#ifndef ABSL_STRINGS_POW10_HELPER_H_ +#define ABSL_STRINGS_POW10_HELPER_H_ + +#include <vector> + +namespace absl { +namespace strings_internal { + +// Computes the precise value of 10^exp. (I.e. the nearest representable +// double to the exact value, rounding to nearest-even in the (single) case of +// being exactly halfway between.) +double Pow10(int exp); + +} // namespace strings_internal +} // namespace absl + +#endif // ABSL_STRINGS_POW10_HELPER_H_ diff --git a/absl/strings/internal/pow10_helper_test.cc b/absl/strings/internal/pow10_helper_test.cc new file mode 100644 index 000000000000..9a13d5240da7 --- /dev/null +++ b/absl/strings/internal/pow10_helper_test.cc @@ -0,0 +1,120 @@ +// Copyright 2018 The Abseil Authors. +// +// Licensed under the Apache License, Version 2.0 (the "License"); +// you may not use this file except in compliance with the License. +// You may obtain a copy of the License at +// +// http://www.apache.org/licenses/LICENSE-2.0 +// +// Unless required by applicable law or agreed to in writing, software +// distributed under the License is distributed on an "AS IS" BASIS, +// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +// See the License for the specific language governing permissions and +// limitations under the License. + +#include "absl/strings/internal/pow10_helper.h" + +#include <cmath> + +#include "gtest/gtest.h" +#include "absl/strings/str_format.h" + +namespace absl { +namespace strings_internal { + +namespace { + +struct TestCase { + int power; // Testing Pow10(power) + uint64_t significand; // Raw bits of the expected value + int radix; // significand is adjusted by 2^radix +}; + +TEST(Pow10HelperTest, Works) { + // The logic in pow10_helper.cc is so simple that theoretically we don't even + // need a test. However, we're paranoid and believe that there may be + // compilers that don't round floating-point literals correctly, even though + // it is specified by the standard. We check various edge cases, just to be + // sure. + constexpr TestCase kTestCases[] = { + // Subnormals + {-323, 0x2, -1074}, + {-322, 0x14, -1074}, + {-321, 0xca, -1074}, + {-320, 0x7e8, -1074}, + {-319, 0x4f10, -1074}, + {-318, 0x316a2, -1074}, + {-317, 0x1ee257, -1074}, + {-316, 0x134d761, -1074}, + {-315, 0xc1069cd, -1074}, + {-314, 0x78a42205, -1074}, + {-313, 0x4b6695433, -1074}, + {-312, 0x2f201d49fb, -1074}, + {-311, 0x1d74124e3d1, -1074}, + {-310, 0x12688b70e62b, -1074}, + {-309, 0xb8157268fdaf, -1074}, + {-308, 0x730d67819e8d2, -1074}, + // Values that are very close to rounding the other way. + // Comment shows difference of significand from the true value. + {-307, 0x11fa182c40c60d, -1072}, // -.4588 + {-290, 0x18f2b061aea072, -1016}, // .4854 + {-276, 0x11BA03F5B21000, -969}, // .4709 + {-259, 0x1899C2F6732210, -913}, // .4830 + {-252, 0x1D53844EE47DD1, -890}, // -.4743 + {-227, 0x1E5297287C2F45, -807}, // -.4708 + {-198, 0x1322E220A5B17E, -710}, // -.4714 + {-195, 0x12B010D3E1CF56, -700}, // .4928 + {-192, 0x123FF06EEA847A, -690}, // .4968 + {-163, 0x1708D0F84D3DE7, -594}, // -.4977 + {-145, 0x13FAAC3E3FA1F3, -534}, // -.4785 + {-111, 0x133D4032C2C7F5, -421}, // .4774 + {-106, 0x1D5B561574765B, -405}, // -.4869 + {-104, 0x16EF5B40C2FC77, -398}, // -.4741 + {-88, 0x197683DF2F268D, -345}, // -.4738 + {-86, 0x13E497065CD61F, -338}, // .4736 + {-76, 0x17288E1271F513, -305}, // -.4761 + {-63, 0x1A53FC9631D10D, -262}, // .4929 + {-30, 0x14484BFEEBC2A0, -152}, // .4758 + {-21, 0x12E3B40A0E9B4F, -122}, // -.4916 + {-5, 0x14F8B588E368F1, -69}, // .4829 + {23, 0x152D02C7E14AF6, 24}, // -.5000 (exactly, round-to-even) + {29, 0x1431E0FAE6D721, 44}, // -.4870 + {34, 0x1ED09BEAD87C03, 60}, // -.4721 + {70, 0x172EBAD6DDC73D, 180}, // .4733 + {105, 0x1BE7ABD3781ECA, 296}, // -.4850 + {126, 0x17A2ECC414A03F, 366}, // -.4999 + {130, 0x1CDA62055B2D9E, 379}, // .4855 + {165, 0x115D847AD00087, 496}, // -.4913 + {172, 0x14B378469B6732, 519}, // .4818 + {187, 0x1262DFEEBBB0F9, 569}, // -.4805 + {210, 0x18557F31326BBB, 645}, // -.4992 + {212, 0x1302CB5E6F642A, 652}, // -.4838 + {215, 0x1290BA9A38C7D1, 662}, // -.4881 + {236, 0x1F736F9B3494E9, 731}, // .4707 + {244, 0x176EC98994F489, 758}, // .4924 + {250, 0x1658E3AB795204, 778}, // -.4963 + {252, 0x117571DDF6C814, 785}, // .4873 + {254, 0x1B4781EAD1989E, 791}, // -.4887 + {260, 0x1A03FDE214CAF1, 811}, // .4784 + {284, 0x1585041B2C477F, 891}, // .4798 + {304, 0x1D2A1BE4048F90, 957}, // -.4987 + // Out-of-range values + {-324, 0x0, 0}, + {-325, 0x0, 0}, + {-326, 0x0, 0}, + {309, 1, 2000}, + {310, 1, 2000}, + {311, 1, 2000}, + }; + for (const TestCase& test_case : kTestCases) { + EXPECT_EQ(Pow10(test_case.power), + std::ldexp(test_case.significand, test_case.radix)) + << absl::StrFormat("Failure for Pow10(%d): %a vs %a", test_case.power, + Pow10(test_case.power), + std::ldexp(test_case.significand, test_case.radix)); + } +} + +} // namespace +} // namespace strings_internal +} // namespace absl |