| 1 | /* Lookup table for double-precision log(x) vector function. |
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| 2 | |
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| 3 | Copyright (C) 2023-2024 Free Software Foundation, Inc. |
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| 4 | This file is part of the GNU C Library. |
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| 5 | |
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| 6 | The GNU C Library is free software; you can redistribute it and/or |
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| 7 | modify it under the terms of the GNU Lesser General Public |
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| 8 | License as published by the Free Software Foundation; either |
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| 9 | version 2.1 of the License, or (at your option) any later version. |
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| 10 | |
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| 11 | The GNU C Library is distributed in the hope that it will be useful, |
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| 12 | but WITHOUT ANY WARRANTY; without even the implied warranty of |
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| 13 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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| 14 | Lesser General Public License for more details. |
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| 15 | |
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| 16 | You should have received a copy of the GNU Lesser General Public |
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| 17 | License along with the GNU C Library; if not, see |
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| 18 | <https://www.gnu.org/licenses/>. */ |
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| 19 | |
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| 20 | #include "vecmath_config.h" |
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| 21 | |
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| 22 | const struct v_log_data __v_log_data = { |
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| 23 | /* Worst-case error: 1.17 + 0.5 ulp. |
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| 24 | Rel error: 0x1.6272e588p-56 in [ -0x1.fc1p-9 0x1.009p-8 ]. */ |
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| 25 | .poly = { -0x1.ffffffffffff7p-2, 0x1.55555555170d4p-2, -0x1.0000000399c27p-2, |
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| 26 | 0x1.999b2e90e94cap-3, -0x1.554e550bd501ep-3 }, |
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| 27 | .ln2 = 0x1.62e42fefa39efp-1, |
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| 28 | /* Algorithm: |
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| 29 | |
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| 30 | x = 2^k z |
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| 31 | log(x) = k ln2 + log(c) + poly(z/c - 1) |
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| 32 | |
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| 33 | where z is in [a;2a) which is split into N subintervals (a=0x1.69009p-1, |
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| 34 | N=128) and log(c) and 1/c for the ith subinterval comes from two lookup |
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| 35 | tables: |
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| 36 | |
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| 37 | table[i].invc = 1/c |
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| 38 | table[i].logc = (double)log(c) |
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| 39 | |
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| 40 | where c is near the center of the subinterval and is chosen by trying |
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| 41 | several floating point invc candidates around 1/center and selecting one |
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| 42 | for which the error in (double)log(c) is minimized (< 0x1p-74), except the |
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| 43 | subinterval that contains 1 and the previous one got tweaked to avoid |
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| 44 | cancellation. */ |
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| 45 | .table = { { .invc: 0x1.6a133d0dec120p+0, .logc: -0x1.62fe995eb963ap-2 }, |
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| 46 | { 0x1.6815f2f3e42edp+0, -0x1.5d5a48dad6b67p-2 }, |
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| 47 | { 0x1.661e39be1ac9ep+0, -0x1.57bde257d2769p-2 }, |
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| 48 | { 0x1.642bfa30ac371p+0, -0x1.52294fbf2af55p-2 }, |
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| 49 | { 0x1.623f1d916f323p+0, -0x1.4c9c7b598aa38p-2 }, |
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| 50 | { 0x1.60578da220f65p+0, -0x1.47174fc5ff560p-2 }, |
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| 51 | { 0x1.5e75349dea571p+0, -0x1.4199b7fa7b5cap-2 }, |
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| 52 | { 0x1.5c97fd387a75ap+0, -0x1.3c239f48cfb99p-2 }, |
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| 53 | { 0x1.5abfd2981f200p+0, -0x1.36b4f154d2aebp-2 }, |
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| 54 | { 0x1.58eca051dc99cp+0, -0x1.314d9a0ff32fbp-2 }, |
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| 55 | { 0x1.571e526d9df12p+0, -0x1.2bed85cca3cffp-2 }, |
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| 56 | { 0x1.5554d555b3fcbp+0, -0x1.2694a11421af9p-2 }, |
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| 57 | { 0x1.539015e2a20cdp+0, -0x1.2142d8d014fb2p-2 }, |
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| 58 | { 0x1.51d0014ee0164p+0, -0x1.1bf81a2c77776p-2 }, |
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| 59 | { 0x1.50148538cd9eep+0, -0x1.16b452a39c6a4p-2 }, |
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| 60 | { 0x1.4e5d8f9f698a1p+0, -0x1.11776ffa6c67ep-2 }, |
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| 61 | { 0x1.4cab0edca66bep+0, -0x1.0c416035020e0p-2 }, |
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| 62 | { 0x1.4afcf1a9db874p+0, -0x1.071211aa10fdap-2 }, |
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| 63 | { 0x1.495327136e16fp+0, -0x1.01e972e293b1bp-2 }, |
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| 64 | { 0x1.47ad9e84af28fp+0, -0x1.f98ee587fd434p-3 }, |
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| 65 | { 0x1.460c47b39ae15p+0, -0x1.ef5800ad716fbp-3 }, |
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| 66 | { 0x1.446f12b278001p+0, -0x1.e52e160484698p-3 }, |
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| 67 | { 0x1.42d5efdd720ecp+0, -0x1.db1104b19352ep-3 }, |
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| 68 | { 0x1.4140cfe001a0fp+0, -0x1.d100ac59e0bd6p-3 }, |
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| 69 | { 0x1.3fafa3b421f69p+0, -0x1.c6fced287c3bdp-3 }, |
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| 70 | { 0x1.3e225c9c8ece5p+0, -0x1.bd05a7b317c29p-3 }, |
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| 71 | { 0x1.3c98ec29a211ap+0, -0x1.b31abd229164fp-3 }, |
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| 72 | { 0x1.3b13442a413fep+0, -0x1.a93c0edadb0a3p-3 }, |
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| 73 | { 0x1.399156baa3c54p+0, -0x1.9f697ee30d7ddp-3 }, |
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| 74 | { 0x1.38131639b4cdbp+0, -0x1.95a2efa9aa40ap-3 }, |
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| 75 | { 0x1.36987540fbf53p+0, -0x1.8be843d796044p-3 }, |
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| 76 | { 0x1.352166b648f61p+0, -0x1.82395ecc477edp-3 }, |
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| 77 | { 0x1.33adddb3eb575p+0, -0x1.7896240966422p-3 }, |
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| 78 | { 0x1.323dcd99fc1d3p+0, -0x1.6efe77aca8c55p-3 }, |
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| 79 | { 0x1.30d129fefc7d2p+0, -0x1.65723e117ec5cp-3 }, |
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| 80 | { 0x1.2f67e6b72fe7dp+0, -0x1.5bf15c0955706p-3 }, |
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| 81 | { 0x1.2e01f7cf8b187p+0, -0x1.527bb6c111da1p-3 }, |
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| 82 | { 0x1.2c9f518ddc86ep+0, -0x1.491133c939f8fp-3 }, |
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| 83 | { 0x1.2b3fe86e5f413p+0, -0x1.3fb1b90c7fc58p-3 }, |
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| 84 | { 0x1.29e3b1211b25cp+0, -0x1.365d2cc485f8dp-3 }, |
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| 85 | { 0x1.288aa08b373cfp+0, -0x1.2d13758970de7p-3 }, |
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| 86 | { 0x1.2734abcaa8467p+0, -0x1.23d47a721fd47p-3 }, |
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| 87 | { 0x1.25e1c82459b81p+0, -0x1.1aa0229f25ec2p-3 }, |
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| 88 | { 0x1.2491eb1ad59c5p+0, -0x1.117655ddebc3bp-3 }, |
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| 89 | { 0x1.23450a54048b5p+0, -0x1.0856fbf83ab6bp-3 }, |
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| 90 | { 0x1.21fb1bb09e578p+0, -0x1.fe83fabbaa106p-4 }, |
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| 91 | { 0x1.20b415346d8f7p+0, -0x1.ec6e8507a56cdp-4 }, |
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| 92 | { 0x1.1f6fed179a1acp+0, -0x1.da6d68c7cc2eap-4 }, |
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| 93 | { 0x1.1e2e99b93c7b3p+0, -0x1.c88078462be0cp-4 }, |
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| 94 | { 0x1.1cf011a7a882ap+0, -0x1.b6a786a423565p-4 }, |
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| 95 | { 0x1.1bb44b97dba5ap+0, -0x1.a4e2676ac7f85p-4 }, |
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| 96 | { 0x1.1a7b3e66cdd4fp+0, -0x1.9330eea777e76p-4 }, |
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| 97 | { 0x1.1944e11dc56cdp+0, -0x1.8192f134d5ad9p-4 }, |
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| 98 | { 0x1.18112aebb1a6ep+0, -0x1.70084464f0538p-4 }, |
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| 99 | { 0x1.16e013231b7e9p+0, -0x1.5e90bdec5cb1fp-4 }, |
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| 100 | { 0x1.15b1913f156cfp+0, -0x1.4d2c3433c5536p-4 }, |
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| 101 | { 0x1.14859cdedde13p+0, -0x1.3bda7e219879ap-4 }, |
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| 102 | { 0x1.135c2dc68cfa4p+0, -0x1.2a9b732d27194p-4 }, |
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| 103 | { 0x1.12353bdb01684p+0, -0x1.196eeb2b10807p-4 }, |
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| 104 | { 0x1.1110bf25b85b4p+0, -0x1.0854be8ef8a7ep-4 }, |
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| 105 | { 0x1.0feeafd2f8577p+0, -0x1.ee998cb277432p-5 }, |
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| 106 | { 0x1.0ecf062c51c3bp+0, -0x1.ccadb79919fb9p-5 }, |
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| 107 | { 0x1.0db1baa076c8bp+0, -0x1.aae5b1d8618b0p-5 }, |
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| 108 | { 0x1.0c96c5bb3048ep+0, -0x1.89413015d7442p-5 }, |
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| 109 | { 0x1.0b7e20263e070p+0, -0x1.67bfe7bf158dep-5 }, |
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| 110 | { 0x1.0a67c2acd0ce3p+0, -0x1.46618f83941bep-5 }, |
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| 111 | { 0x1.0953a6391e982p+0, -0x1.2525df1b0618ap-5 }, |
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| 112 | { 0x1.0841c3caea380p+0, -0x1.040c8e2f77c6ap-5 }, |
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| 113 | { 0x1.07321489b13eap+0, -0x1.c62aad39f738ap-6 }, |
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| 114 | { 0x1.062491aee9904p+0, -0x1.847fe3bdead9cp-6 }, |
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| 115 | { 0x1.05193497a7cc5p+0, -0x1.43183683400acp-6 }, |
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| 116 | { 0x1.040ff6b5f5e9fp+0, -0x1.01f31c4e1d544p-6 }, |
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| 117 | { 0x1.0308d19aa6127p+0, -0x1.82201d1e6b69ap-7 }, |
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| 118 | { 0x1.0203beedb0c67p+0, -0x1.00dd0f3e1bfd6p-7 }, |
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| 119 | { 0x1.010037d38bcc2p+0, -0x1.ff6fe1feb4e53p-9 }, |
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| 120 | { 1.0, 0.0 }, |
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| 121 | { 0x1.fc06d493cca10p-1, 0x1.fe91885ec8e20p-8 }, |
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| 122 | { 0x1.f81e6ac3b918fp-1, 0x1.fc516f716296dp-7 }, |
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| 123 | { 0x1.f44546ef18996p-1, 0x1.7bb4dd70a015bp-6 }, |
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| 124 | { 0x1.f07b10382c84bp-1, 0x1.f84c99b34b674p-6 }, |
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| 125 | { 0x1.ecbf7070e59d4p-1, 0x1.39f9ce4fb2d71p-5 }, |
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| 126 | { 0x1.e91213f715939p-1, 0x1.7756c0fd22e78p-5 }, |
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| 127 | { 0x1.e572a9a75f7b7p-1, 0x1.b43ee82db8f3ap-5 }, |
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| 128 | { 0x1.e1e0e2c530207p-1, 0x1.f0b3fced60034p-5 }, |
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| 129 | { 0x1.de5c72d8a8be3p-1, 0x1.165bd78d4878ep-4 }, |
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| 130 | { 0x1.dae50fa5658ccp-1, 0x1.3425d2715ebe6p-4 }, |
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| 131 | { 0x1.d77a71145a2dap-1, 0x1.51b8bd91b7915p-4 }, |
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| 132 | { 0x1.d41c51166623ep-1, 0x1.6f15632c76a47p-4 }, |
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| 133 | { 0x1.d0ca6ba0bb29fp-1, 0x1.8c3c88ecbe503p-4 }, |
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| 134 | { 0x1.cd847e8e59681p-1, 0x1.a92ef077625dap-4 }, |
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| 135 | { 0x1.ca4a499693e00p-1, 0x1.c5ed5745fa006p-4 }, |
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| 136 | { 0x1.c71b8e399e821p-1, 0x1.e27876de1c993p-4 }, |
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| 137 | { 0x1.c3f80faf19077p-1, 0x1.fed104fce4cdcp-4 }, |
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| 138 | { 0x1.c0df92dc2b0ecp-1, 0x1.0d7bd9c17d78bp-3 }, |
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| 139 | { 0x1.bdd1de3cbb542p-1, 0x1.1b76986cef97bp-3 }, |
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| 140 | { 0x1.baceb9e1007a3p-1, 0x1.295913d24f750p-3 }, |
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| 141 | { 0x1.b7d5ef543e55ep-1, 0x1.37239fa295d17p-3 }, |
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| 142 | { 0x1.b4e749977d953p-1, 0x1.44d68dd78714bp-3 }, |
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| 143 | { 0x1.b20295155478ep-1, 0x1.52722ebe5d780p-3 }, |
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| 144 | { 0x1.af279f8e82be2p-1, 0x1.5ff6d12671f98p-3 }, |
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| 145 | { 0x1.ac5638197fdf3p-1, 0x1.6d64c2389484bp-3 }, |
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| 146 | { 0x1.a98e2f102e087p-1, 0x1.7abc4da40fddap-3 }, |
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| 147 | { 0x1.a6cf5606d05c1p-1, 0x1.87fdbda1e8452p-3 }, |
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| 148 | { 0x1.a4197fc04d746p-1, 0x1.95295b06a5f37p-3 }, |
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| 149 | { 0x1.a16c80293dc01p-1, 0x1.a23f6d34abbc5p-3 }, |
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| 150 | { 0x1.9ec82c4dc5bc9p-1, 0x1.af403a28e04f2p-3 }, |
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| 151 | { 0x1.9c2c5a491f534p-1, 0x1.bc2c06a85721ap-3 }, |
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| 152 | { 0x1.9998e1480b618p-1, 0x1.c903161240163p-3 }, |
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| 153 | { 0x1.970d9977c6c2dp-1, 0x1.d5c5aa93287ebp-3 }, |
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| 154 | { 0x1.948a5c023d212p-1, 0x1.e274051823fa9p-3 }, |
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| 155 | { 0x1.920f0303d6809p-1, 0x1.ef0e656300c16p-3 }, |
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| 156 | { 0x1.8f9b698a98b45p-1, 0x1.fb9509f05aa2ap-3 }, |
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| 157 | { 0x1.8d2f6b81726f6p-1, 0x1.04041821f37afp-2 }, |
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| 158 | { 0x1.8acae5bb55badp-1, 0x1.0a340a49b3029p-2 }, |
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| 159 | { 0x1.886db5d9275b8p-1, 0x1.105a7918a126dp-2 }, |
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| 160 | { 0x1.8617ba567c13cp-1, 0x1.1677819812b84p-2 }, |
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| 161 | { 0x1.83c8d27487800p-1, 0x1.1c8b405b40c0ep-2 }, |
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| 162 | { 0x1.8180de3c5dbe7p-1, 0x1.2295d16cfa6b1p-2 }, |
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| 163 | { 0x1.7f3fbe71cdb71p-1, 0x1.28975066318a2p-2 }, |
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| 164 | { 0x1.7d055498071c1p-1, 0x1.2e8fd855d86fcp-2 }, |
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| 165 | { 0x1.7ad182e54f65ap-1, 0x1.347f83d605e59p-2 }, |
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| 166 | { 0x1.78a42c3c90125p-1, 0x1.3a666d1244588p-2 }, |
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| 167 | { 0x1.767d342f76944p-1, 0x1.4044adb6f8ec4p-2 }, |
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| 168 | { 0x1.745c7ef26b00ap-1, 0x1.461a5f077558cp-2 }, |
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| 169 | { 0x1.7241f15769d0fp-1, 0x1.4be799e20b9c8p-2 }, |
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| 170 | { 0x1.702d70d396e41p-1, 0x1.51ac76a6b79dfp-2 }, |
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| 171 | { 0x1.6e1ee3700cd11p-1, 0x1.57690d5744a45p-2 }, |
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| 172 | { 0x1.6c162fc9cbe02p-1, 0x1.5d1d758e45217p-2 } } |
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| 173 | }; |
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| 174 | |
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