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Google Keyword Rankings for : fast float reciprocal
1
https://stackoverflow.com/questions/9939322/fast-1-x-division-reciprocal
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https://stackoverflow.com/questions/9939322/fast-1-x-division-reciprocal
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2
https://pvk.ca/Blog/LowLevel/software-reciprocal.html
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https://pvk.ca/Blog/LowLevel/software-reciprocal.html
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3
https://en.wikipedia.org/wiki/Fast_inverse_square_root
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https://en.wikipedia.org/wiki/Fast_inverse_square_root
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4
http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Fowler.pdf
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http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Fowler.pdf
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5
https://codereview.stackexchange.com/questions/259771/fast-reciprocal-1-x
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https://codereview.stackexchange.com/questions/259771/fast-reciprocal-1-x
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6
https://www.emo.org.tr/ekler/1c1ce13987fd3b3_ek.pdf
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https://www.emo.org.tr/ekler/1c1ce13987fd3b3_ek.pdf
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7
https://www.appsloveworld.com/cplus/100/341/division-as-multiply-and-lut-fast-float-division-reciprocal
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https://www.appsloveworld.com/cplus/100/341/division-as-multiply-and-lut-fast-float-division-reciprocal
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8
https://www.reddit.com/r/cpp_questions/comments/uogmnd/is_multiplying_by_a_reciprocal_instead_of/
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https://www.reddit.com/r/cpp_questions/comments/uogmnd/is_multiplying_by_a_reciprocal_instead_of/
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9
https://www.physicsforums.com/threads/fast-reciprocal-square-root-algorithm.1001061/
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https://www.physicsforums.com/threads/fast-reciprocal-square-root-algorithm.1001061/
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10
https://ieeexplore.ieee.org/document/9660872
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https://ieeexplore.ieee.org/document/9660872
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11
https://hal.archives-ouvertes.fr/hal-00957379/document
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https://hal.archives-ouvertes.fr/hal-00957379/document
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12
https://homepage.divms.uiowa.edu/~jones/bcd/divide.html
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https://homepage.divms.uiowa.edu/~jones/bcd/divide.html
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13
https://inbetweennames.net/blog/2021-05-06-i76rsqrt/
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https://inbetweennames.net/blog/2021-05-06-i76rsqrt/
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14
https://sol.sbc.org.br/index.php/eradsp/article/download/13600/13448/
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https://sol.sbc.org.br/index.php/eradsp/article/download/13600/13448/
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15
https://people.ece.cornell.edu/land/courses/ece4760/Math/index.html
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https://people.ece.cornell.edu/land/courses/ece4760/Math/index.html
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16
https://www.geeksforgeeks.org/fast-inverse-square-root/
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https://www.geeksforgeeks.org/fast-inverse-square-root/
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17
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7827340/
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https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7827340/
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18
https://alexapta.medium.com/quake-iii-the-reciprocal-square-root-e61e0d0699c6
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https://alexapta.medium.com/quake-iii-the-reciprocal-square-root-e61e0d0699c6
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19
https://docs.nvidia.com/cuda/cuda-math-api/group__CUDA__MATH__INTRINSIC__SINGLE.html
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https://docs.nvidia.com/cuda/cuda-math-api/group__CUDA__MATH__INTRINSIC__SINGLE.html
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20
https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html
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https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html
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21
https://gcc.gnu.org/bugzilla/show_bug.cgi?id=31723
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https://gcc.gnu.org/bugzilla/show_bug.cgi?id=31723
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22
https://itecnote.com/tecnote/c-fast-1-x-division-reciprocal/
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https://itecnote.com/tecnote/c-fast-1-x-division-reciprocal/
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23
https://mdpi-res.com/d_attachment/computation/computation-09-00021/article_deploy/computation-09-00021-v3.pdf?version=1614249323
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https://mdpi-res.com/d_attachment/computation/computation-09-00021/article_deploy/computation-09-00021-v3.pdf?version=1614249323
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24
https://www.researchgate.net/publication/220804890_An_Efficient_Hardware_Implementation_for_a_Reciprocal_Unit
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https://www.researchgate.net/publication/220804890_An_Efficient_Hardware_Implementation_for_a_Reciprocal_Unit
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25
https://developer.arm.com/documentation/dui0774/k/Compiler-Command-line-Options/-ffp-mode
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https://developer.arm.com/documentation/dui0774/k/Compiler-Command-line-Options/-ffp-mode
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26
https://www.hilarispublisher.com/open-access/hardware-implementation-of-lowlatency-32bit-floatingpointreciprocal-2332-0796-1000278.pdf
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https://www.hilarispublisher.com/open-access/hardware-implementation-of-lowlatency-32bit-floatingpointreciprocal-2332-0796-1000278.pdf
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27
https://www.coranac.com/tonc/text/fixed.htm
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https://www.coranac.com/tonc/text/fixed.htm
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28
https://www.linkedin.com/pulse/fast-inverse-square-root-still-armin-kassemi-langroodi
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https://www.linkedin.com/pulse/fast-inverse-square-root-still-armin-kassemi-langroodi
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29
https://www.cse.scu.edu/~dlewis/book3/labs/Lab9G.pdf
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https://www.cse.scu.edu/~dlewis/book3/labs/Lab9G.pdf
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30
https://www.semanticscholar.org/paper/Design-and-Implementation-of-a-64%2F32-bit-Division%2C-Shuang-yan-Dong-hui/ec5e4c6d890f8c2bd2b0ee56a7d4de375c8b51c1
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https://www.semanticscholar.org/paper/Design-and-Implementation-of-a-64%2F32-bit-Division%2C-Shuang-yan-Dong-hui/ec5e4c6d890f8c2bd2b0ee56a7d4de375c8b51c1
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31
https://www.intel.com/content/dam/develop/external/us/en/documents/pdf/fp-consistency-121918.pdf
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https://www.intel.com/content/dam/develop/external/us/en/documents/pdf/fp-consistency-121918.pdf
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32
https://karmafx.net/docs/karmafx_floattricks.pdf
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https://karmafx.net/docs/karmafx_floattricks.pdf
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33
https://www.cs.uaf.edu/courses/cs301/2014-fall/notes/sse-performance/
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https://www.cs.uaf.edu/courses/cs301/2014-fall/notes/sse-performance/
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34
https://blog.segger.com/algorithms-for-division-part-4-using-newtons-method/
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https://blog.segger.com/algorithms-for-division-part-4-using-newtons-method/
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35
http://www.matrix67.com/data/InvSqrt.pdf
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http://www.matrix67.com/data/InvSqrt.pdf
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36
https://forums.ni.com/t5/LabVIEW/Fast-Reciprocal-Square-Root-with-Labview/td-p/3889359
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https://forums.ni.com/t5/LabVIEW/Fast-Reciprocal-Square-Root-with-Labview/td-p/3889359
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37
https://www.vishia.org/emc/html/Ctrl/Fixpoint_float.html
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https://www.vishia.org/emc/html/Ctrl/Fixpoint_float.html
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38
https://lemire.me/blog/2019/03/12/multiplying-by-the-inverse-is-not-the-same-as-the-division/
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https://lemire.me/blog/2019/03/12/multiplying-by-the-inverse-is-not-the-same-as-the-division/
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39
https://www.codee.com/run-floating-point-calculations-with-precision-and-speed/
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https://www.codee.com/run-floating-point-calculations-with-precision-and-speed/
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40
https://www.boost.org/doc/libs/develop/libs/math/doc/html/math_toolkit/powers/rsqrt.html
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https://www.boost.org/doc/libs/develop/libs/math/doc/html/math_toolkit/powers/rsqrt.html
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41
https://www.quora.com/Is-the-reciprocal-of-the-reciprocal-of-a-floating-point-number-always-the-original-number
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https://www.quora.com/Is-the-reciprocal-of-the-reciprocal-of-a-floating-point-number-always-the-original-number
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42
https://www.sciencedirect.com/topics/computer-science/reciprocal-square-root
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https://www.sciencedirect.com/topics/computer-science/reciprocal-square-root
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43
https://www.anycodings.com/1questions/4961551/division-as-multiply-and-lut-fast-float-division-reciprocal
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https://www.anycodings.com/1questions/4961551/division-as-multiply-and-lut-fast-float-division-reciprocal
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44
https://discourse.julialang.org/t/how-to-convert-the-binary-form-of-a-float-to-an-integer-and-vice-versa/70083
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https://discourse.julialang.org/t/how-to-convert-the-binary-form-of-a-float-to-an-integer-and-vice-versa/70083
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45
https://digitalsystemdesign.in/fast-computation-square-root-and-its-reciprocal/
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https://digitalsystemdesign.in/fast-computation-square-root-and-its-reciprocal/
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46
https://www.musicdsp.org/en/latest/Other/206-fast-cube-root-square-root-and-reciprocal-for-x86-sse-cpus.html
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https://www.musicdsp.org/en/latest/Other/206-fast-cube-root-square-root-and-reciprocal-for-x86-sse-cpus.html
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47
https://numpy.org/doc/stable/reference/generated/numpy.reciprocal.html
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https://numpy.org/doc/stable/reference/generated/numpy.reciprocal.html
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48
https://news.ycombinator.com/item?id=21342501
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https://news.ycombinator.com/item?id=21342501
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49
https://groups.google.com/a/groups.riscv.org/g/isa-dev/c/SLprSJzpgCQ/m/WdvNwTd0DAAJ
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https://groups.google.com/a/groups.riscv.org/g/isa-dev/c/SLprSJzpgCQ/m/WdvNwTd0DAAJ
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50
https://docs.xilinx.com/r/en-US/ug1483-model-composer-sys-gen-user-guide/Reciprocal
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https://docs.xilinx.com/r/en-US/ug1483-model-composer-sys-gen-user-guide/Reciprocal
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51
https://betterexplained.com/articles/understanding-quakes-fast-inverse-square-root/
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https://betterexplained.com/articles/understanding-quakes-fast-inverse-square-root/
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52
https://www.soa.org/news-and-publications/newsletters/compact/2014/may/com-2014-iss51/losing-my-precision-tips-for-handling-tricky-floating-point-arithmetic/
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https://www.soa.org/news-and-publications/newsletters/compact/2014/may/com-2014-iss51/losing-my-precision-tips-for-handling-tricky-floating-point-arithmetic/
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53
https://www.mathworks.com/help/simulink/slref/sqrt.html
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https://www.mathworks.com/help/simulink/slref/sqrt.html
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54
https://github.com/tomverbeure/math
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https://github.com/tomverbeure/math
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55
https://www.ibm.com/docs/SSGH4D_15.1.0/com.ibm.xlf151.aix.doc/proguide/fpperf.html
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https://www.ibm.com/docs/SSGH4D_15.1.0/com.ibm.xlf151.aix.doc/proguide/fpperf.html
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56
https://indico.cern.ch/event/166141/sessions/125686/attachments/201416/282784/Corden_FP_control.pdf
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https://indico.cern.ch/event/166141/sessions/125686/attachments/201416/282784/Corden_FP_control.pdf
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57
https://blog.llandsmeer.com/tech/2021/04/08/esp32-s2-fpu.html
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https://blog.llandsmeer.com/tech/2021/04/08/esp32-s2-fpu.html
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58
https://pages.cs.wisc.edu/~smoler/x86text/lect.notes/arith.flpt.html
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https://pages.cs.wisc.edu/~smoler/x86text/lect.notes/arith.flpt.html
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59
https://www.gamedev.net/forums/topic/704525-3-quick-ways-to-calculate-the-square-root-in-c/
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https://www.gamedev.net/forums/topic/704525-3-quick-ways-to-calculate-the-square-root-in-c/
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60
https://docs.racket-lang.org/math/bigfloat.html
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https://docs.racket-lang.org/math/bigfloat.html
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61
https://learn.microsoft.com/en-us/windows/win32/direct3dhlsl/rcp
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https://learn.microsoft.com/en-us/windows/win32/direct3dhlsl/rcp
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62
https://towardsdatascience.com/how-to-do-limitless-math-in-python-73f573570dfa
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https://towardsdatascience.com/how-to-do-limitless-math-in-python-73f573570dfa
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63
https://cppbenchmarks.wordpress.com/2020/11/10/float-division-vs-multiplication-speed/
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https://cppbenchmarks.wordpress.com/2020/11/10/float-division-vs-multiplication-speed/
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64
https://docs.unity3d.com/Packages/com.unity.shadergraph@10.10/manual/Reciprocal-Node.html
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https://docs.unity3d.com/Packages/com.unity.shadergraph@10.10/manual/Reciprocal-Node.html
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65
https://arxiv.org/pdf/2207.08420
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https://arxiv.org/pdf/2207.08420
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66
http://staffwww.fullcoll.edu/aclifton/cs241/lecture-floating-point-simd.html
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http://staffwww.fullcoll.edu/aclifton/cs241/lecture-floating-point-simd.html
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67
http://www.ti.com/lit/pdf/spru100
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http://www.ti.com/lit/pdf/spru100
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68
https://www.informit.com/articles/article.aspx?p=2103809&seqNum=3
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https://www.informit.com/articles/article.aspx?p=2103809&seqNum=3
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69
https://www.synopsys.com/dw/buildingblock.php
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https://www.synopsys.com/dw/buildingblock.php
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70
https://www.youtube.com/watch?v=p8u_k2LIZyo
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https://www.youtube.com/watch?v=p8u_k2LIZyo
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71
https://www.eetimes.com/the-basics-of-fpga-mathematics/
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https://www.eetimes.com/the-basics-of-fpga-mathematics/
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72
https://mlfbrown.com/fp.pdf
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https://mlfbrown.com/fp.pdf
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73
https://llvm.org/docs/LangRef.html
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https://llvm.org/docs/LangRef.html
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74
https://specbranch.com/posts/faster-div8/
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https://specbranch.com/posts/faster-div8/
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75
https://www.clear.rice.edu/comp422/resources/cuda/pdf/CUDA_Math_API.pdf
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https://www.clear.rice.edu/comp422/resources/cuda/pdf/CUDA_Math_API.pdf
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76
https://www.dsprelated.com/showthread/comp.dsp/108174-1.php
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https://www.dsprelated.com/showthread/comp.dsp/108174-1.php
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77
https://dl.acm.org/doi/fullHtml/10.1145/3001758
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https://dl.acm.org/doi/fullHtml/10.1145/3001758
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78
https://doc.rust-lang.org/std/primitive.f32.html
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https://doc.rust-lang.org/std/primitive.f32.html
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79
https://www.embeddedrelated.com/showthread/comp.arch.embedded/29854-1.php
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https://www.embeddedrelated.com/showthread/comp.arch.embedded/29854-1.php
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80
https://developer.apple.com/documentation/accelerate/simd_float3
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https://developer.apple.com/documentation/accelerate/simd_float3
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81
https://hackaday.com/2012/07/15/a-detailed-explanation-on-speeding-up-avr-division/
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https://hackaday.com/2012/07/15/a-detailed-explanation-on-speeding-up-avr-division/
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82
http://i.stanford.edu/pub/cstr/reports/csl/tr/96/711/CSL-TR-96-711.pdf
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http://i.stanford.edu/pub/cstr/reports/csl/tr/96/711/CSL-TR-96-711.pdf
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83
https://rc.dartmouth.edu/wp-content/uploads/2018/03/FP_Consistency_12.pdf
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https://rc.dartmouth.edu/wp-content/uploads/2018/03/FP_Consistency_12.pdf
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84
https://www.nccs.nasa.gov/images/FloatingPoint_consistency.pdf
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https://www.nccs.nasa.gov/images/FloatingPoint_consistency.pdf
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85
https://eigen.tuxfamily.org/dox/group__CoeffwiseMathFunctions.html
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https://eigen.tuxfamily.org/dox/group__CoeffwiseMathFunctions.html
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86
https://doc.lagout.org/science/0_Computer%20Science/3_Theory/Handbook%20of%20Floating%20Point%20Arithmetic.pdf
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https://doc.lagout.org/science/0_Computer%20Science/3_Theory/Handbook%20of%20Floating%20Point%20Arithmetic.pdf
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87
https://publik.tuwien.ac.at/files/publik_287602.pdf
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https://publik.tuwien.ac.at/files/publik_287602.pdf
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88
https://www.dline.info/ed/fulltext/v3n1/4.pdf
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https://www.dline.info/ed/fulltext/v3n1/4.pdf
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89
https://people.inf.ethz.ch/markusp/teaching/263-2300-ETH-spring11/slides/class17.pdf
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https://people.inf.ethz.ch/markusp/teaching/263-2300-ETH-spring11/slides/class17.pdf
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90
https://www.itu.dk/~sestoft/bachelor/IEEE754_article.pdf
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https://www.itu.dk/~sestoft/bachelor/IEEE754_article.pdf
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91
https://www.mdpi.com/2079-3197/9/2/21/htm
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https://www.mdpi.com/2079-3197/9/2/21/htm
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92
https://www.agner.org/optimize/instruction_tables.pdf
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https://www.agner.org/optimize/instruction_tables.pdf
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93
https://www.extremeoptimization.com/Documentation/Mathematics/Arbitrary-Precision-Arithmetic/Arbitrary-Precision-Floating-Point-Numbers.aspx
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https://www.extremeoptimization.com/Documentation/Mathematics/Arbitrary-Precision-Arithmetic/Arbitrary-Precision-Floating-Point-Numbers.aspx
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94
https://mospace.umsystem.edu/xmlui/bitstream/handle/10355/66752/research.pdf?sequence=1&isAllowed=y
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95
http://loyc.net/2019/unum-posits.html
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96
https://cr.yp.to/bib/1997/karp.pdf
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97
http://x86asm.net/articles/fixed-point-arithmetic-and-tricks/
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98
https://www.convict.lu/Jeunes/ultimate_stuff/exp_ln_2.htm
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