ST AN4044 APPLICATION NOTE

AN4044

Application note

Using floating-point unit (FPU) with STM32F405/07xx and STM32F415/417xx microcontrollers

Introduction

This application note explains how to use floating-point units (FPU) with STM32F405/07xx and STM32F415/417xx microcontrollers and provides a short overview of:

■Floating-point arithmetic

■STM32F405/07xx and STM32F415/417xx family floating-point unit

An application example is given at the end of this application note.

Table 1 lists the microcontrollers and development tools concerned by this application note.

Table 1. Applicable products and tools

Type	Applicable products

Microcontrollers

STM32F405/07xx and STM32F415/417xx high-performance MCUs with

DSP and FPU instructions

Development tools

STM3240G-EVAL evaluation board

March 2012

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Contents	AN4044

Contents

1	Floating-point arithmetic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		5
	1.1	Fixed-point or floating-point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	5
	1.2	Floating-point unit (FPU) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	6
2	IEEE standard for floating-point arithmetic (IEEE 754) . . . . . . . . . . . . .		7
	2.1	Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	7
	2.2	Number formats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	7

2.2.1 Normalized numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2.2 Denormalized numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2.3 Zeros . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2.4 Infinites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2.5 NaN (Not-a-Number) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.3 Rounding modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.4 Arithmetic operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.5 Number conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.6 Exception and exception handling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3	STM32F4 floating-point unit (FPU) . . . . . . . . . . . . . . . . . . . . . . . . . . . .		12
	3.1	Special operating modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	12
	3.2	Floating-point status and control register (FPSCR) . . . . . . . . . . . . . . . . .	12

3.2.1 Code condition bits: N, Z, C, V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.2.2 Mode bits: AHP, DN, FZ, RM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.2.3 Exception flags . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.3 Exception management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.4 Programmers model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.5 FPU instructions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.5.1 FPU arithmetic instructions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.5.2 FPU compare & convert instructions . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.5.3 FPU load/store instructions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

4

Application example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

15

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AN4044			Contents
	4.1	Julia set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	. . . . . 15
	4.2	Implementation on STM32F4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	. . . . . 16
	4.3	Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	. . . . 17
	4.4	Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	. . . . 18
5	Reference documents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		. . . . 19
6	Revision history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		. . . . 20

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List of tables	AN4044

List of tables

Table 1. Applicable products and tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Table 2. Integer numbers dynamic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Table 3. Floating-point numbers dynamic. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Table 4. Normalized numbers range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Table 5. Denormalized numbers range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Table 6. Value range for IEEE.754 number formats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Table 7. FPSCR register. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Table 8. Performance comparison with MDK-ARM version 4.22 . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Table 9. Reference documents. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Table 10. Document revision history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

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AN4044	Floating-point arithmetic

1 Floating-point arithmetic

Floating-point numbers are used to represent non-integer numbers. They are composed of 3 fields:

●the sign

●the exponent

●the mantissa

Such a representation allows a very wide range of number coding, making floating-point numbers the best way to deal with real numbers. Floating-point calculations can be accelerated using a Floating-point unit (FPU) integrated in the processor.

1.1Fixed-point or floating-point

One alternative to floating-point is fixed-point, where the exponent field is fixed. But if fixedpoint is giving better calculation speed on FPUless processors, the range of numbers and their dynamic is low. As a consequence, a developer using the fixed-point technique will have to check carefully any scaling/saturation issues in its algorithm.

Table 2.	Integer numbers dynamic
	Coding	Dynamic
Int8		48 dB
Int16		96 dB
Int32		192 dB
Int64		385 dB

The C language offers the float and the double types for floating-point operations. At a higher level, modelization tools, such as matlab or scilab, are generating C code mainly using float or double. No floating-point support means modifying the generated code to adapt it to fixed-point. And all the fixed-point operations have to be handcoded by the programmer.

Table 3.	Floating-point numbers dynamic
	Coding	Dynamic
half precision		180 dB
single precision		1529 dB
double precision		12318 dB

When used natively in code, floating-point operations will decrease the development time of a project. It is the most efficient way to implement any mathematical algorithm.

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Floating-point arithmetic	AN4044

1.2Floating-point unit (FPU)

Floating-point calculations require a lot of resources, as for any operation between two numbers. For example, we need to:

●align the two numbers (have them with the same exponent)

●perform the operation

●round out the result

●code the result

On an FPUless processor, all these operations are done by software through the C compiler library and are not visible to the programmer; but the performances are very low.

On a processor having an FPU, all of the operations are entirely done by hardware in a single cycle, for most of the instructions. The C compiler does not use its own floating-point library but directly generates FPU native instructions.

When implementing a mathematical algorithm on a microprocessor having an FPU, the programmer does not have to choose between performance and development time. The FPU brings reliability allowing to use directly any generated code through a high level tool, such as matlab or scilab, with the highest level of performance.

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AN4044	IEEE standard for floating-point arithmetic (IEEE 754)

2 IEEE standard for floating-point arithmetic (IEEE 754)

The usage of the floating-point arithmetic has always been a need in computer science since the early ages. At the end of the 30’s, when Konrad Zuse developed his Z series in Germany, floating-points were already in. But the complexity of implementing a hardware support for the floating-point arithmetic has discarded its usage for decades.

In the mid 50’s, IBM, with its 704, introduced the FPU in mainframes; and in the 70’s, various platforms were supporting floating-point operations but with their own coding techniques. The unification took place in 1985 when the IEEE published the standard 754 to define a common approach for floating-point arithmetic support.

2.1Overview

The various types of floating-point implementations over the years led the IEEE to standardize the following elements:

●number formats

●arithmetic operations

●number conversions

●special values coding

●4 rounding modes

●5 exceptions and their handling

2.2Number formats

All values are composed of three fields:

●Sign: s

●Biased exponent:

–sum of the exponent = e

–constant value = bias

●Fraction (or mantissa): f

The values can be coded on various lengths:

●16-bit: half precision format

●32-bit: single precision format

●64-bit: double precision format

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