Correctly Rounded Arbitrary-Precision Floating-Point Summation

Vincent Lefèvre

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Correctly Rounded Arbitrary-Precision Floating-Point Summation

机译：正确舍入的任意精度浮点求和

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摘要

We present a fast algorithm together with its low-level implementation of correctly rounded arbitrary-precision floating-point summation. The arithmetic is the one used by the GNU MPFR library: radix 2; no subnormals; each variable (each input and the output) has its own precision. We also give a worst-case complexity of this algorithm and describe how the implementation is tested.

机译：我们提出了一种快速算法及其对正确舍入的任意精度浮点求和的低级实现。该算法是GNU MPFR库使用的一种算法：基数2；基数2。无异常每个变量（每个输入和输出）都有自己的精度。我们还给出了该算法的最坏情况复杂度，并描述了如何测试实现。

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《IEEE Transactions on Computers》 |2017年第12期|2111-2124|共14页
作者
Vincent Lefèvre;
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正文语种 eng
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关键词
Context awareness; Floating-point arithmetic; Complexity theory; Open area test sites;

机译：上下文感知;浮点算法;复杂性理论;开放区域测试站点;

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专利

1. Correct Rounding and a Hybrid Approach to Exact Floating-Point Summation [J] . Yong-Kang Zhu., Wayne B. Hayes. SIAM Journal on Scientific Computing . 2010,第4期

机译：正确舍入和精确浮点求和的混合方法
2. ACCURATE FLOATING-POINT SUMMATION PART II: SIGN,K-FOLD FAITHFUL AND ROUNDING TO NEAREST [J] . SIEGFRIED M. RUMP, TAKESHI OGITA, SHIN’ICHI OISHI SIAM Journal on Scientific Computing . 2010,第2期

机译：精确的浮点求和第二部分：标记，K折折叠和到周围的环绕
3. ACCURATE FLOATING-POINT SUMMATION PART I: FAITHFUL ROUNDING [J] . SIEGFRIED M. RUMP, TAKESHI OGITA, SHIN’ICHI OISHI SIAM Journal on Scientific Computing . 2010,第1期

机译：精确的浮点求和运算第一部分：故障环绕
4. Correctly Rounded Arbitrary-Precision Floating-Point Summation [C] . Vincent Lef#x00E8, vre IEEE Symposium on Computer Arithmetic . 2016

机译：正确舍入的任意精度浮点求和
5. Exact floating-point summation and its application in shadowing. [D] . Zhu, Yong-Kang. 2009

机译：精确的浮点求和及其在阴影中的应用。
6. Binocular visual performance and summation after correcting higher order aberrations [O] . Ramkumar Sabesan, Len Zheleznyak, Geunyoung Yoon 2012

机译：校正高阶像差后的双目视觉性能和总和
7. Accurate floating-point summation part I: Faithful rounding [O] . Siegfried M. Rump, Takeshi Ogita, Shin’ichi Oishi 2015

机译：准确的浮点求和第一部分：忠实的舍入
8. A Unified Approach to Floating-Point Rounding with Applications to Multiple-Precision Summation [R] . Virkkunen, V. E. J. 1980

机译：一种统一的浮点舍入方法及其在多精度求和中的应用

Correctly Rounded Arbitrary-Precision Floating-Point Summation

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