A Correctly Rounded Mixed-Radix Fused-Multiply-Add
A Correctly Rounded Mixed-Radix Fused-Multiply-Add
复制标题
正确舍入的混合基融合乘加
DOI：
--
复制
发表时间：
2018
期刊：
影响因子：
--
通讯作者：
C. Lauter
中科院分区：
文献类型：
--
作者：
Clothilde Jeangoudoux;C. Lauter
IEEE 754-2008标准管理所有类型的计算机系统中的浮点算术。该标准规定了两个基数2和10。它规定了这些基数之间的转换操作，但不允许在计算运算中混合使用不同基数的浮点格式。相比之下，该标准确实规定了在一次操作中混合一个基数的格式。为了增强标准，使其在所有基本计算操作下都是封闭的，我们提出了一种正确舍入的混合基数融合乘加(FMA)算法。我们的算法采用IEEE754二进制64和十进制64数字的任意组合作为参数，并提供IEEE754二进制64和十进制64的结果，对于五种IEEE754舍入模式，根据ANY进行舍入。我们的实现不需要任何动态内存分配；它的运行时可以静态绑定。我们将我们的实现与基于GMP多精度库的基本混合基数FMA实现进行了比较。
The IEEE 754–2008 Standard governs Floating-Point Arithmetic in all types of Computer Systems. The Standard provides for two radices, 2 and 10. It specifies conversion operations between these radices, but does not allow floating-point formats of different radices to be mixed in computational operations. In contrast, the Standard does provide for mixing formats of one radix in one operation. In order to enhance the Standard and make it closed under all basic computational operations, we propose an algorithm for a correctly rounded mixed-radix Fused-Multiply-and-Add (FMA). Our algorithm takes any combination of IEEE754 binary64 and decimal64 numbers in argument and provides a result in IEEE754 binary64 and decimal64, rounded according to any for the five IEEE754 rounding modes. Our implementation does not require any dynamic memory allocation; its runtime can be bounded statically. We compare our implementation to a basic mixed-radix FMA implementation based on the GMP Multiple Precision library.