Finding Normal Binary Floating-Point Factors Efficiently
نویسندگان
چکیده
Abstract Solving the floating-point equation $$x \otimes y = z$$ x ⊗ y = z , where x and z belong to intervals, is a common task in automated reasoning for which no efficient algorithm known general. We show that it can be solved by computing constant number of factors, give fast successive normal factors numbers radix 2. This leads an procedure solving given equation, running time same order as multiplication.
منابع مشابه
On Floating-Point Normal Vectors
In this paper we analyze normal vector representations. We derive the error of the most widely used representation, namely 3D floating-point normal vectors. Based on this analysis, we show that, in theory, the discretization error inherent to single precision floating-point normals can be achieved by 250.2 uniformly distributed normals, addressable by 51 bits. We review common sphere parameteri...
متن کاملIA-64 Floating-Point Operations and the IEEE Standard for Binary Floating-Point Arithmetic
This paper examines the implementation of floating-point operations in the IA-64 architecture from the perspective of the IEEE Standard for Binary Floating-Point Arithmetic [1]. The floating-point data formats, operations, and special values are compared with the mandatory or recommended ones from the IEEE Standard, showing the potential gains in performance that result from specific choices. T...
متن کاملFinding Root Causes of Floating Point Error with Herbgrind
Floating point arithmetic plays a central role in science, engineering, and nance by enabling developers to approximately compute with real numbers. To address numerical issues in large oating-point applications, developers must identify root causes, which is dicult because oating point errors are generally silent, non-local, and non-compositional. is paper presents Herbgrind, a tool to he...
متن کاملEfficient Hybrid Method for Binary Floating Point Multiplication
This paper presents a high speed binary floating point multiplier based on Hybrid Method. To improve speed multiplication of mantissa is done using Hybrid method replacing existing multipliers like Carry Save Multiplier, Dadda Multiplier and Modified Booth Multiplier. Hybrid method is a combination of Dadda Multiplier and Modified Radix-8 Booth Multiplier. The design achieves high speed with ma...
متن کاملSolving Range Constraints for Binary Floating-Point Instructions
We present algorithms that solve the following problem: given three ranges of floating-point numbers Rx, Ry , Rz , a floating-point operation (op), and a rounding-mode (round), generate three floating-point numbers x̄, ȳ, z̄ such that x̄ ∈ Rx, ȳ ∈ Ry , z̄ ∈ Rz , and z̄ = round(x̄ op ȳ). This problem, although quite simple when dealing with intervals of real numbers, is much more complex when consider...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Automated Reasoning
سال: 2023
ISSN: ['0168-7433', '1573-0670']
DOI: https://doi.org/10.1007/s10817-023-09659-1