Lecture（Ⅲ）：Floating Point

最新推荐文章于 2024-01-24 14:02:54 发布

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博客围绕IEEE浮点标准展开，介绍了分数二进制数背景、IEEE浮点标准定义、示例与特性，还提及了舍入、加法、乘法运算，以及C语言中的浮点运算，最后进行了总结并给出额外幻灯片内容。

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p3	---What is 1011.101(2)?
p4	---Representation
p5	---Value Representation ---Observations
p6	---Limitation #1 ---Limitation #2

p8	IEEE Floating Point ---IEEE Standard 754 ---Driven by numerical concerns
p9	---Numerical Form ---Encoding
p10	Precision options ---Single precision: 32 bits ---Double precision: 64 bits ---Extended precision: 80 bits (Intel only)
p11	“Normalized” Values
p12	Normalized Encoding Example ---Value: float F = 15213.0; ---Significand ---Exponent ---Result:
p13	Denormalized Values
p14	Special Values
p15	Visualization: Floating Point Encodings

p17	Tiny Floating Point Example ---8-bit Floating Point Representation ---Same general form as IEEE Format
p18	Dynamic Range (Positive Only)
p19	Distribution of Values ---6-bit IEEE-like format ---Notice how the distribution gets denser toward zero.
p20	Distribution of Values (close-up view) --6-bit IEEE-like format
p21	Special Properties of the IEEE Encoding ---FP Zero Same as Integer Zero ---Can (Almost) Use Unsigned Integer Comparison

p23	Floating Point Opera.ons: Basic Idea
p24	Rounding Modes (illustrate with $ rounding)
p25	Closer Look at Round-To-Even ---Default Rounding Mode ---Applying to Other Decimal Places / Bit Positions
p26	Rounding Binary Numbers ---Binary Fractional Numbers ---Examples
p27	FP Multiplication
p28	Floating Point Addition
p29	Mathematical Properties of FP Add ---Compare to those of Abelian Group ---Monotonicity
p30	Mathematical Properties of FP Mult ---Compare to Commutative Ring ---Monotonicity

p32

Floating Point in C
---C Guarantees Two Levels

---Conversions/Casting

p33

Floating Point Puzzles
---For each of the following C expressions, either:

p34	---IEEE Floating Point has clear mathematical properties ---Represents numbers of form M x 2E ---One can reason about operations independent of ---Not the same as real arithmetic

p36	Creating Floating Point Number ---Steps ---Case Study
p37	Normalize ---Requirement
p38	Rounding ---Round up conditions
p39	Postnormalize ---Issue
p40	Interesting Numbers