How deeply does 100 Go Mistakes and How to Avoid Them cover FP32?

Defines FP32 representation and demonstrates rounding, but stops short of fully explaining decimal conversion.

FP32

As explained in 100 Go Mistakes and How to Avoid Them

float32 is Go's 32-bit floating-point type with an 8-bit exponent, a 23-bit mantissa, and a sign bit.

Treating float32 as exact real arithmetic causes surprising results. Go stores values approximately because infinitely many real numbers must fit into 32 bits. FP32 follows IEEE-754: one sign bit, an 8-bit exponent, and a 23-bit mantissa. section 3.3

A multiplication that loses digits

var n float32 = 1.0001 fmt.Println(n * n) The mathematical result is 1.00020001, but the stored FP32 approximation produces 1.0002 on most x86 processors. The value stored for 1.0001 is approximately 1.000100016593933, not the exact decimal. section 3.3

var n float32 = 1.0001
fmt.Println(n * n)

Run the minimal Go example to observe FP32 rounding directly. section 3.3

Keep these consequences in mind:

Floating-point arithmetic approximates real arithmetic, so precision can be lost. section 3.3
The representation uses the form sign × 2^exponent × mantissa; conversion internals are intentionally not developed further. section 3.3

How 100 Go Mistakes and How to Avoid Them covers it

Cover of 100 Go Mistakes and How to Avoid Them

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Also explained in

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Rust in Action: Systems programming concepts and techniquesA single-precision floating-point type is a floating-point type represented with the precision associated with Rust's f32 type.
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Learn Go with Pocket-Sized Projectsfloat32 is Go's 32-bit floating-point type, typically providing approximately six to seven decimal significant digits of precision.

Compare how 3 books explain FP32 →

Related concepts

64-bit floating-point numbercontrasts with · A 64-bit floating-point number is a numeric value represented using the IEEE 754 binary64 format, which occupies 64 bits.
floating-point arithmetickind of · Floating-point arithmetic is computation using finite-precision representations of real numbers, which can introduce rounding and range errors.
mixed precisionused by · Mixed precision is a computational technique that uses multiple numerical precisions for different values or operations to balance resource efficiency and numerical accuracy or stability.
float16contrasts with · Float16 is a 16-bit floating-point numeric format that represents values with less precision and storage than single-precision formats such as float32.
float64alternative to · Float64 is a 64-bit floating-point numeric type, commonly represented using the IEEE 754 binary64 format.
IEEE 754implements · IEEE 754 is an international standard specifying floating-point formats, arithmetic operations, rounding rules, and exceptional values.

This explainer was generated by Manning's knowledge graph from the text of 100 Go Mistakes and How to Avoid Them. The section links point to the parts of the book it draws on.