12/03/2025

Barium No-Boot (4): measurements, rev up iMX8MP

Introduction

In previous posts we've made minimal but enough for studying and playing basic application which is able to output debug information. It sets some PLLs and clocks except, maybe, for most of us, the most interesting one — ARM PLL, or PLL which controls the speed of ALU. And we will do such research in this part. The announce of this post is partial, this is on a purpose — it will be more interesting for you to read without knowing the complete plan of this post.

The research plan

We can't measure ALU clock directly because it has no outputs outside of SoC. So, how should we act if we want to know if it is at least changed? We need to do something that depends on ALU speed, and what we can measure. What could it be? UART? No. We configure UART to output data on a particular baud rate, but that has nothing in common with ALU speed. UART configuration affects its TX and RX pins but impulses UART makes while transceiving data are irrelevant with ALU clock. Thus, we need different «interface» with SoC which can give us possibility to measure its clock. Let's turn to theory for a little. So-called ALU «cycle» is one tick of ALU clock, but single clock tick is not equal to an instruction, instruction may take from one to thousands of cycles. (Instruction that take zero cycles are out of scope of this post). But we know that any particular instruction takes the same amount of cycles at any ALU speed. Thus, real execution time of any block of instructions will directly vary according to different ALU speeds. We just need to have some measurable points of some «reference» block of instructions. The most obvious block of instructions is empty loop which translates into branch back to itself (even leaving link register intact) until the countdown variable reaches zero. What could be the rest of our setup? The most clear way to measure something on a SoC is GPIO. Hence, in this post we will initialise IOMUX Controller, one of pads of particular GPIO bank and put GPIO toggling function among with some empty loop (generating measured impulse length) into an infinite loop. After that we'll be able to measure impulses with a scope, change ALU PLL speed, leaving reference code intact and measure impulses again.

As we've reviewed the workflow on embedded systems without any BSP, bootloader, kernel — bare-metal, in previous posts, I'll not provide such details in this and further parts. You'll see what and how is done in the code. Some code lines have comments referencing datasheet page numbers. If you'll ever need to change, for example, GPIO number you can look datasheet around page numbers that you'll see in code and make necessary changes according to appropriate sections of datasheet.

The practice

This time we need a GPIO. As we've noticed in previous posts, GPIO is one of AFs (alternative functions) of a pad or ball. AFs are configured by IOMUX Controller. Therefore, we start with IOMUXC. First, as we did in previous posts, we check the section 6.1.4.2 — «Boot block activation» (p.706) and check if IOMUXC is configured by BROM or not. And we see that we are lucky today because it is initialised by BROM. Thus, we omit initialisation and configuration of this hardware block and proceed straight to GPIO.

Now, we have to see what GPIOs are available and choose one we will use. I'm working on DEBIX Model A SBC. In (most probably fantastic) case you have the same SBC, you can use the picture below and/or the same GPIO as we will use in this post. If you have another SBC, you have to find similar picture for your SBC. What you need is called «pinout» or «header pinout» or «gpio header». This information usually is included in your SBC datasheet or user manual. But sometimes it is easier and faster to search the Internet for something like «_your_sbc_name_ gpio pinout». Let's see what pinout we have:

 DEBIX Model-A GPIO header pinout

There is a handy GPIO on this board — GPIO number 11 on bank 1 (pin 29). Today we will add two new files to our project — gpio.c and gpio.h. So, we add GPIO initialisation and set its direction to barium_main() function:


/* Init GPIO and set 11th of first bank as output */ gpio_init(); gpio_set_dir(GPIO_BANK1, 11, GPIO_OUT);

After that we add our measurement code — the reference code we have mentioned earlier:


/* Generate impulses for measurements */ loop_meas: gpio_toggle_val(GPIO_BANK1, 11); for (lVal = 0; lVal < IMPULSE_LEN; lVal++); goto loop_meas;

IMPULSE_LEN can have any value, but I've chosen 1 000 000 to fit the loop to comfortable scope view settings.

Build, write to SD-card, connect scope, start the board and see:

Measure at default ARM PLL settings 

Here we see that period is approximately 570ms. The period width is uninformative itself. This is just how many time our SoC spends executing our reference cycle on the default ARM PLL settings. From «PLL setting by ROM» we remember that ARM PLL is set at 1GHz. Let's reconfigure it and see what measurements we'll have. ARM cores of iMX8MP are driven by so-called PLL1416x. I could not find any documentation describing it, so we will cope with SoC's datasheet (ARM PLL), see the registers we need to write values to and generate the exact values using the sheet I've managed to create from information I've gathered from around and got from my experiments. You'll see the sheet file in the repository and can play with it. The methodology is simple — you change the Main divider (the biggest number in the most left column) with step of 25 and see column «Clock (MHz)». The rest will be done by the sheet formulas. The table will display register value in hexadecimal and decimal, and two values — Pre div and Scaler. We can configure iMX8MP ARM PLL by using three values — Main div, Pre div and Scaler in formula, or just write the exact value from the most right columns.

iMX8MP ARM PLL Settings

The whole code is added to files clocks.c and clocks.h. And I utilise three values formula instead of a exact single value. That's because I used to do it this way while I was on my researches. Let's rev our SoC up to 1.8GHz — its stated maximum (p. 95). According to sheet we will use 225, 3, 0 coefficients:


raw_writel((225 << 12) | (3 << 4) | (0), CCM_ANALOG_ARM_PLL_FDIV_CTL0);

Now build, write to SD-card, start the board and see:

Measure at 1.8GHz 

And what we see here? 507ms. The period has narrowed, but not as we expected — 570ms@1GHz expected to be 570/1.8 what is 316ms@1.8GHz! What is going on here? To make long story short (it still is not the most interesting part of this post) I'll tell that I've measured different speeds and all periods appeared to be non-proportional to ARM clock. The short summary is shown in following table. I've made a little calculations also:

Non-linearity of ARM ALU clock speed  

We see clocks we set, periods we have measured and two rows as values should be if reference (real true value) was at the slowest or at the fastest clock. Being calculated in any direction the calculated values have linear relation with clock speed. But measured values are non-linear and look like barely related to clock speed at all. The table displays that something is really unclear or even wrong here.

What could go wrong? NXP PLL1416x is undisclosed, thus, we don't know how it exactly works — we can't be sure what speeds it really sets. Another reason could lead to such results — our reference code was modified. But we can't examine PLL and we are sure our code stays intact between builds. So let's try to find some different cause of such ARM ALU behavior. We remember that at this stage ALU works on OCRAM — the slowest one of all RAMs. Let's assume that nonlinearity of our clock speed and period measurements is caused by OCRAM — its access speed. What can we do now? We can use caches. According to specification iMX8MP has 32kB of instruction cache and the same amount of data cache. Therefore our tiny 1-2kB application will fit in SoC's cache entirely. Let's turn on both caches by adding this code to our start_64.s file:


# Load System Control Register (EL3): mrs x3, SCTLR_EL3 # Turn on Data Cache: orr x3, x3, #(1 << 2) # Turn on Instruction Cache: orr x3, x3, #(1 << 12) # Set System Control Register (EL3): msr SCTLR_EL3, x3

Let's check what we get on default 1GHz now:

ARM ALU at 1GHz with caches on

The changes appeared to be so dramatic, that I had to tune my scope to make pretty-looking picture! Now our reference code executes in 36ms at 1GHz instead of 570ms with caches turned off at the same ALU clock speed! And here is new resulting table, showing that not only is everything faster, but it is also linear in both directions:

Linearity of ARM ALU clock speed (caches on)

Now everything is in order and clear — be it calculated from the lowest value (big to small) or from the highest (small to big) — the values check with each other and correlation is absolutely linear: 200MHz * 3 (600MHZ is three times slower than 200MHz) = 180ms/3 = 60ms; 1800MHz * 9 (1800MHz is nine times faster than 200MHZ) = 1800ms/9 = 20ms and so on. The hypothesis is confirmed — OCRAM timings was messing ARM ALU speeds and now we have formula to set ARM ALU clock speed, we have measurement tool and nice and clean results.

But there is more to explore. As I mentioned earlier, we have a tool for calculating ARM PLL speeds — the spreadsheet. And maybe you noticed that picture above («iMX8MP ARM PLL Settings») shows some clock speeds far above of 1.8GHz. Yes, let's check that and here is the result we've got:

Linearity of ARM ALU clock speed (caches on)

The table contains columns with 1.2GHz and 1.6GHz and this is on a purpose. The thing is that NXP's documentation claims that even 1.8GHz is so-called «overdrive» of this SoC's ALU. And my Linux system (NXP's BSP) confirms that — it works on two speeds only — 1.2GHz and 1.6GHz. These speeds are marked green  — as normal or standard. I've measured both standard speeds and the highest I've managed to make SoC to work on (2.2GHz) to show the difference between really used clock speed and maximum I've got out of this SoC's ALU in single core mode.

The result


Barium No-Boot V0.2 (iMX8MP) Build: 22:00:00, Mar 12 2025 Initial PC: 0000000000920000 BootROM SP: 0000000000916ED0 Current EL: 0000000000000003 Running at: 2200MHz

In previous posts we were reading, planning, preparing, learning, today we've learned how to use GPIO on this SoC, how to configure ARM PLL speed. But today is a special day — we've some nice and exceptional result, which is a real practical result — we've significantly revved up (overclocked) iMX8MP and maybe invented the only one iMX8MP running at 2.2GHz! Disclosing undocumented features is another one benefit of bare-metal studying (or exploring).

You can clone the final repository from Barium No-Boot (iMX8MP) (see «Stage III» directory).

12/02/2025

The real «Hello World» from embedder (3): result, play — the birth of Barium No-Boot!

Chapter 3

Result, play — the birth of Barium No-Boot!

Finally...

Well, we've discussed goals and benefits of bare-metal development, have gathered all the information we need to work on a specific SoC, and now we are ready to start writing code. In this post, we will practice. We will go thru the whole process of bare-metal coding, compiling, linking, stripping and, finally, will get a real stand-alone application for a real specific ARMv8-A SoC. Can you imagine  it will be slightly bigger than 1kB in size (including all necessary headers)! But this tiny sprout of digital life, as a result, will perform the minimal task — output strings via UART. And even more — it will read from UART and output those bytes! Also we will add some functionality to our application, do some interesting stuff and perform some experiments.

The plan

The plan we need to carry out to reach the final result looks like:
1. Organise our code
— .s and .c files.
2. CPU start code
— assembly code.
3. Initialise the stack pointer
— assembly code.
4. Initialise PLLs, clocks
, pads, UART hardware-block — C-code.
5. Write some payload code
— write to and read from UART.
6. Compile and link our code into binary file.
7. Make our binary acceptable by our SoC as boot-image.
8. Put our boot-block in a proper place.
9. Configure the board for booting from media we need.
10. Power on and play!

Hands-on code

Let's get it started.

1. Organise our code — .s and .c files.

This is bare-metal — we don't have bootloader and/or kernel behind us. Thus, there are some routines we have to do in assembly language before writing any C-code. So, we will have assembly files. Actually two. They can be combined into a single .s-file, but we will stick to traditions. These files are (common names on 64-bit platforms) start_64.s and crt0_64.s. But what exactly should be done in assembly files (language) on bare-metal? The answer is the things we can't do in C. We can access registers of hardware-blocks via volatile pointers as this is done via so-called memory-mapped input/output (MMIO). But we can't access CPU registers in C directly, thus start_64.s file contains the very first code that cannot be done in C. Specifically CPU start-up code — applying erratas, switching modes, exception levels, setting interrupt vector tables, etc. Now let's go on with crt0. You probably are familiar with it (or, at least, heard of it) — so called «C-runtime zero». In user-space, usually, this is some object file, which is implicitly added to our code by linker prior to file containing main() function written in any high-level language. In user-space crt0 prepares argv and argc which are passed to developer's main() function, makes pointers to environment variables code starts with, etc. As you can assume, this file is unnecessary if we are about to write in assembly language only. Its content is to prepare the environment (be it a user-space program or bare-metal code) for C-code, in our case — set stack pointer to some valid address. After all necessary assembly code routines are done, we will break out to C-code and realise application payload — read from and write to UART. Assembly language files are for startup code and stay as the window to ARMv8-A architecture, our sandbox — one of our goals.

2. CPU start code — assembly code.

CPU start code. In this example we don't need to do anything here, but let's save some values for further research — (believe me) it'll be interesting to explore. According to AAPCS64 (AArch64 Procedure Call Standard — routine calling convention for 64-bit ARM machines), x0 will be the first parameter of called function, x1 the second, x2 — the third, etc. Let's save initial program counter (PC), stack pointer (SP) and exception level (EL) while they are intact by our code — at the very beginning of it. We will save initial PC, SP and EL by storing them in x0, x1 and x2 registers. Later you will see how they will get into our main C-function and will be output to UART. So, start_64.s will look like:


.arch armv8-a .globl _start_64 _start_64: # Store the address of the very first instruction. This will be the # address BROM puts our code to. According to AAPCS64 x0 will be the # first parameter of called function. So, save current PC to x0: adr x0, . # Store initial stack pointer address as the second parameter: mov x1, sp # Save Current EL to x2, and it will get to third parameter: mrs x2, CurrentEL # Branch to crt0's main: b _crt0_main_64

3. Initialise the stack pointer — assembly code.

In our case, there is the only thing we have to do in crt0 to get prepared for C-code — set stack pointer. Stack pointer is set by just writing memory address value to SP register. We want our x0, x1 and x2 registers to pass thru this file to C-function, so we avoid using these registers here. So, crt0_64.s will look like:


.arch armv8-a .globl _crt0_main_64 _crt0_main_64: # Set stack pointer at the top of OCRAM 97FFFFh # Internal ROM and RAM memory map (NXP IMX8MPRM, Figure 6-2, p.706): # Move the address to x3 without last Fh (aligned to 16): mov x3, 0xFFF0 movk x3, 0x0097, lsl #16 # Set stack pointer: mov sp, x3 # Finally, break out to C-code: b barium_main

From here on, you will see links to documents in brackets. The format is as follows: (document name, section, table, figure name or number, page number).

4. Initialise PLLs, clocks, pads, UART hardware-block — C-code.

After that, we have to initialise PLLs, clocks, pads and UART controller.

We begin with ccm_plls_init() function. The only thing we have to do here is to enable div 5 of PLL2 because we decided to drive UART HW block via PLL2 div 5 output. Therefore, this function looks like:


void ccm_plls_init(void) { /* Enable div 5 output of PLL2 as we dicided to clock UART via this output. * Actually, this is unneeded - it appears to be enabled. */ setbits_le32(CCM_ANALOG_SYS_PLL2_GEN_CTRL, PLL_DIV5_CLKE); return; }

After that we proceed with uart_init() function:


uart_init();

The most interesting part of this routine is the initialisation of pads, which looks like:


... /* Set UART2 TXD Alternative function */ iomux_set_pad(UART2_TXD_ALT, UART2_TXD_MUX); /* Set UART2 TXD Pad properties */ iomux_set_pad(UART2_TXD_PAD, UART2_TXD_MUX + ALT_PAD_STEP); /* Set UART2 RXD Alternative function */ iomux_set_alt(UART2_RXD_ALT, UART2_RXD_MUX); /* Set UART2 RXD Pad properties */ iomux_set_pad(UART2_RXD_PAD, UART2_RXD_MUX + ALT_PAD_STEP); /* Select UART2 RXD input (Daisy Chain) */ iomux_select_input(UART2_RXD_DSY, UART2_RXD_SEL); ...

As we discussed earlier, we set alternative functions of pads, their properties and input type of UART2 RXD pad — its so-called «daisy chain».

The rest of uart_init() function initialises UART hardware block. This is not interesting enough to list it here. You can see it in the code.

5. Write some payload code — write to and read from UART.

Payload code. Since we have initialised all the hardware and have some high-level functions, the code becomes self-explanatory. The only thing I want to explain is the uart_chars_counter variable and UART_FIFO_MAX define. On each output we increment special counter and when it reaches maximum length of FIFO we wait for real transfer to finish by waiting for TXDC bit in UART Status Register. We have to check this because without this we can get in situation where UART can skip symbols being output. This is done in uart.c file. You can see the payload functionality in barium_main() function located in barium.c file.

6. Compile and link our code into binary file.

Compile and link. Compilation and even cross-compilation is not something new — as usual, we compile separate source files, link them in a single ELF-file then perform the only extra step — dump pure code of it into a binary file. You'll see a linker script in the repository. Actually, you can build the project without it. I've used it just to remove some unneeded section that GCC adds to ELF. But we should bear in mind that this is bare-metal — that means that machine starts from the very first instruction it finds in our code. Actually, BootROM branches to the address it loads our application to. Thus, we have to put our start function in the very first place. This is done by respecting the order of object files when linking to resulting code. In our case it is done via PRODUCT_SRC variable in our Makefile. Thereby, we set the file containing our starting code in a first place and the function we want SoC to start as the first function in that file.

7. Make our binary acceptable by our SoC as boot-image.

Making binary acceptable by a SoC is very important step, but I'll not bother you with all that details — what information, where and how to find it to know the fields we have to fill for our SoC. I've made host tool named mkbb_imx8. It is derived from NXP's mkimage_imx8. It gathers some information, fills necessary structures and writes them to proprietary header and adds it to specified binary. The only interesting thing here is the address to load image to. This field tells BootROM where to put loaded application (and jump to after loading it). In my tool it is defined as DEFAULT_LOAD_ADDR in source code or can be passed as third, optional parameter to mkbb_imx8. Command line parameter takes priority over define. If you ever need to develop such tool for particular SoC, you can follow the same way as I have made. No tricks here, all you need — just to find the structure of proprietary header for specific SoC. Usually this information can be found in vendor's BSP build system — host tool, often named mkimage_XXX. You will see mkbb_imx8 code in separate directory in the repository.

8. Put our boot-block in a proper place.

The result of mkbb_imx8 is a binary file which will be accepted by iMX8MP BootROM as boot-image. The last thing we have to do on our host machine is to put our boot-block in a proper place. iMX8MP expects it to be on media with offset of 32kB. Thus, we will write our application to SD-card with the following command:


dd if=./barium of=/dev/sdX bs=1k seek=32 ; sync

I said it'll about 1kB in size. The code (with its data) I've got with my compiler (ARM GNU Toolchain 14.3.Rel1) is 980 bytes, and it appeared to be 1044 bytes with iMX headers. Maybe we've made one of the most beautiful kilobytes all over the world...

9. Configure the board for booting from media we need.

If you are reading this, perhaps, you have some board (proprietary or kit) with iMX8MP SoC. If so, you may already have it configured to boot from SD-card or already know how to do it. If not, you need to configure the board for booting from SD-card. From iMX8MP SoC perspective boot device selection is described in section 6.1.5 — «Boot devices (internal boot)» (p.713). Refer to your product manual to see how it is done on a particular board.

10. Power on and play!

Insert SD-card into your board, connect your UART converter to UART2 interface of the board, start your favourite serial communication program and power on (or reset) the board. You'll see:


Barium No-Boot V0.1 (iMX8MP) Build: 18:00:00, Feb 12 2025 Initial PC: 0000000000920000 BootROM SP: 0000000000916ED0 Current EL: 0000000000000003 Awaiting commands from UART: Received: 20h

What's about naming? «Barium» stands for «Bare», because barium, besides consonance with «bare», is a metal element. Thus, bare-metal is replaced with «Barium». «No-Boot» means it does not boot any kernel or anything at all (but runs when and where boot loader usually does).

Well, what we see here. First, initial PC is 920000h. This is our DEFAULT_LOAD_ADDR (in our Makefile address is passed via command line argument). You can play with it, set it here and there according to OCRAM memory map (p.707). Datasheet claims that OCRAM free area starts from 918000h, but the lowest address I've managed to put application to is 920000h. BootROM does not allow to put it to 918000h.

But what is more interesting — the stack pointer BootROM leaves for us. It does not allow to place our application in its reserved area, but leaves SP at 916ED0h. This can be used — we can leave SP intact and have stack from 916ED0h to 900000h which is pretty enough space and is actually restricted for our code by BootROM unusable anyway.

And we see that we run in third exception level, EL3 — the highest one. We have carte blanche to do whatever we want on this machine.

What conclusion can be drawn from this? First Platform Loader (BootROM) of iMX8MP leaves SoC in condition where we can omit any initialisation which is usually done in assembly language — as we mentioned earlier, stack pointer is already set to some valid address. While setting stack pointer is the only crucial thing we have to do in assembly code for such simple example, we can skip this step by excluding all .s-files. Nothing else should be changed, just don't forget to set main .c-file (in our case — barium.c) as the first one in your objects list. And main function (in our case — barium_main()) should be the first function in this file. Keep in mind — this is bare-metal, and the first function in your code is the entry-point regardless what ENTRY() linker directive points to. (You won't even see it in our .lds-file at all). Despite our goal was exact opposite, the whole bare-metal project can work without a single .s-file on iMX8MP! You can try it. Thus, we can call iMX8MP very high level SoC, or some kind of a «C-SoC».

You can clone the final repository from Barium No-Boot (iMX8MP) (see «Stage I» directory).

That's all. Finally we have a good window to learn ARMv8 aka ARM64 aka AArch64 on a real hardware — we have assembly files and C-files to play with, we have build system for this project — Makefile, linker script, we have host tool to make proper boot image, and we have some kind of a debug interface — UART. That looks like sufficient setup for further studying.

16/01/2025

The real «Hello World» from embedder (2): practice, prepare

Chapter 2

Practice, prepare

Between theory and code

In the previous post we've reviewed bare-metal development: what it is, the theory of it, its workflow, what information we need and where to get this information, its profits, bottlenecks and limitations. This — how SoC is organised and how it works, most of all somehow know from theory (school or university) and/or practice (working on a high level or via some HAL). The next post will describe the well known to all of us process — coding. But what is between that areas of theory and practice? What is between the knowing how PLLs and clocks work, knowing that UART is configured by writing some values to some registers and process of writing device-tree nodes and calling functions of HAL? How does that magic of making certain SoC functioning really arise? The process of preparing to code is described in this post — the practice of getting information, gathering it and planning tasks. Excuse me for not feeling sorry for you — not a single line of code will be written in this post, but I will describe this (middle) part of job up to the single bit. This is to let you know clear enough how it is done.

The plan

The plan we need to carry out to reach our goals looks like:
1. Choose the SoC we will work on and get its documentation.
2. Find out the condition BROM leaves SoC in, and see what is initialised for us and what is not
.
3. Find out what exactly PLLs and clocks we have to configure to start up hardware-blocks.
4. Configure UART TX and RX pads.
5. Configure UART hardware-block.
6. Output some string.
7. Finish with infinite loop outputting characters received from UART.
8. Make proper boot image and put it in the place BROM of our SoC expects it to be.

The practice

Let's get it started.

1. Choose the SoC we will work on and get its documentation.

We will work on NXP i.MX 8M Plus (iMX8MP). This is multi-core (mine is quad-core) ARM Cortex-A53 (ARMv8-A), SoC (with additional Cortex-M7 core). Some kind of what we need and interesting to play with. Remember and bear in mind what we were talking about in previous post — bare-metal development is strongly tied to certain SoC. Thus, if you are about to develop stand-alone application for any other SoC, then the practice, we will do in this post, is not for you. You can read it as an example of workflow only. Once, we have chosen SoC, we download datasheet describing it. In our case it is «i.MX 8M Plus Applications Processor Reference Manual» (IMX8MPRM.pdf, I have Rev. 3, 08/2024). And, to entertain you a little, here is the SoC itself:

NXP iMX 8M Plus

2. Find out the condition BROM leaves SoC in, and see what is initialised for us and what is not.

To find out the condition BROM leaves SoC in we look for section, which describes what BROM enables and what does not. This is section 6.1.4.2 «Boot block activation» (p. 748). This section claims that BROM of iMX8MP activates (in addition to some others) these blocks: Clock Control Module (CCM), Input/Output Multiplexer Controller (IOMUXC). We will boot from SD-Card, thus Ultra-Secure Digital Host Controller (USDHC) will be enabled also (but this is obvious). Let's proceed to clocks BROM has initialised for us. In the next section 6.1.4.3 «Clocks at boot time» (p. 749), table 6-3 «PLL setting by ROM» we see which PLLs are enabled: ARM PLL at 1GHz, System PLL1 at 800MHz and System PLL2 at 1GHz.  Let's remember PLLs we have enabled: System PLL1 and System PLL2. We don't care about ARM PLL at this point, as it controls ALU only and is enabled and configured already by BROM. Proceed to Table 6-6 «CCGR setting by ROM» (p. 750), and see which clocks are enabled and which are not. Scrolling down to UARTs (p. 752) and see that BROM enables none of UARTs. iMX8MP boards usually use second UART (UART2) for debug, thus, let's remember that its clock number is 74 (CCM_CCGR74).

3. Find out what exactly PLLs and clocks we have to configure to start up hardware-blocks.

From the previous paragraph we see that none of UARTs hardware-blocks is enabled by BROM. Well, we have to find out how to enable it by ourselves. Let's start with CCM structure, it is described in section 5.1 «Clock Control Module (CCM)» (p. 227). Looking at Figure 5-1 «CCM Block Diagram» (p. 228) we see that clock ticks pass from clock generators (on the left side) via PLLs (or bypassing them), then to CCM's Clock Root Generator which has clock slices, then clock slices form out clock roots and, finally, come out to hardware-blocks (on the right side). Well, this scheme looks more complicated than that we've discussed in the previous post. The idea of Clock Roots becomes more clear if we look at section 5.1.2 «Clock Root Selects» (p. 228). Let's scroll down to Slice Index №95 (p. 241). 95 is the slice Clock Root of UART2. In the column «Source Select» we see that it can be driven by few outputs. We will drive our UART by SYSTEM_PLL2_DIV5. Let's remember its value 010b. As we know already, System PLL2 is enabled at 1GHz. Here we need to configure its outputs — ensure its DIV5 (1GHz div 5 is 200MHz — we'll need this value later) output is enabled. This is done by configuring System PLL2 General Function Control Register which is described in section 5.1.8.32 «SYS PLL2 General Function Control Register» (p. 509). We will set all PLL_DIVx_CLKE bits and PLL_CLKE. The address of this register is ANAMIX base + 104h. After we have enabled PLL outputs we have to select proper clock root for UART2 hardware block. This is done by configuring CCM_TARGET_ROOT №95. It is described in section 5.1.7.10 «Target Register (CCM_TARGET_ROOTn)» (p. 412). We see that here we need to set enable (28th) bit to 1 and MUX (24th-26th) bits to the value we've remembered earlier 010b. The address of this register is CCM base + 8000h + 95 (slice index we need) * 80h. The resulting value we have to write to the register is 12000000h.

4. Configure UART TX and RX pads.

Well, PLLs and clocks are configured and enabled. Now we have to find out how to configure UART pads. First, let's set proper AF for our UART. Alternative functions are described in table 8.1.1.1 «Muxing Options» (p. 1287). Let's scroll to UART2 (p. 1307). Here we see that UART2_RX port can be routed to one of these pads: UART2_RXD, SD2_DATA0, SD1_DATA3 and SAI3_TXFS. The first one is what we need. UART2_TX port can be routed to one of these pads: UART2_TXD, SD2_DATA1, SD1_DATA2 and SAI3_TXC. The first one is what we need. Both UART2_TXD and UART2_RXD have mode called ALT0. Let's proceed to section 8.2.4 «IOMUXC Memory Map/Register Definition» (p. 1344). In this table we need to find our UART2_RXD and UART2_TXD they are on the bottom of page 1350 and on the top of page 1351 correspondingly. Here we see that their reset values both are 5h (remember that value for a while) and absolute addresses are 30330228h for UART2_RXD, and 3033022Ch for UART2_TXD. Then click on the link in the right column. From section 8.2.4.134 «SW_MUX_CTL_PAD_UART2_RXD SW MUX Control Register» (p. 1540) and section 8.2.4.135 «SW_MUX_CTL_PAD_UART2_TXD SW MUX Control Register» (p. 1542) we see that MUX_MODE is represented by lowest 3 bits of this registers. Also, we see that 5h (the value we've remembered recently) corresponds to 101b. That means that both pads we need are routed to pads we don't need  GPIO5 24 and GPIO5 25 in this case. Thus, we have to configure those pads correctly for our needs — set both to zero (ALT0). To achieve that, we need to write zeroes to 30330228h and 3033022Ch to set proper alternative functions for that pads. But that's not all we have to do to make UART pads functioning correctly. In addition to setting AF, we need to configure physical parameters of that pads. This is done by setting two SW_PAD_CTL Registers: UART2 RXD pad control register, section 8.2.4.286 «SW_PAD_CTL_PAD_UART3_RXD SW PAD Control Register» (p. 1837) and UART2 TXD pad control register, section 8.2.4.287 — «SW_PAD_CTL_PAD_UART2_TXD SW PAD Control Register» (p. 1839). After inspecting these descriptions, we conclude that zero is a good value for both of them. And the last one step we have left to do. UART RX is a little special, because it works as an input function. Thus, we need to select input for it. This is done by configuring DAISY Register, which is represented in section 8.2.4.376 «UART2_UART_RXD_MUX_SELECT_INPUT DAISY Register» (p. 1922). Here we see that 110b «SELECT_UART2_RXD_ALT0 — Selecting Pad: UART2_RXD for Mode: ALT0» (p. 1923) is what we need. Thus, we'll write 6h to 303305F0h.

5. Configure UART hardware-block.

The last thing we have left is to configure UART hardware-block. It is done by familiar steps like — reading registers values (optional), modifying that values (optional) or forming out them from scratch, writing values to registers, waiting for conditions flags (optional). Actually, UART is a simple hardware-block, thus, I will not explain the specific process of configuring it — you will see it in the code, which will be presented in the next post.

6. Output some string.

After UART is configured and running, the game starts. Now we are prepared and ready to output some strings. This is also done by writing a byte to some address (UART register) and controlling TX empty flag to avoid buffer overrun. Here I'll skip detailed description of this process too — see it in the code.

7. Finish with infinite loop outputting characters received from UART.

We will finish with infinite loop outputting characters received from UART. This is done by controlling RX empty flag and reading received byte (UART register) when flag becomes unset.

8. Make proper boot image and put it in the place BROM of our SoC expects it to be.

To make our application load and run on the SoC we've chosen, we have to prepare proper boot image and put it in the place BROM of our SoC expects it to be. This is done by a tool (mkbb_imx8), which is derived from standard NXPs mkimage_imx8. I will not explain how it works and how it was developed at all, but will show how to use it to generate boot block (and how and where to place it) for our SoC in the next post.

Conclusion

We've made it. Now we have gathered all the information we need to start writing code for iMX8MP SoC and we are ready to proceed. And now you know what lies between the theory and the daily routine of embedded developer. In the next post we will develop the application — we will write in assembly language and C-code, compile, link objects to binary, strip it, make a bootable image of it, and put it in the right place on a storage media. It'll be a very small program that will run on the iMX8MP and on this SoC only. But it will give a platform for learning ARM64 machine. You'll be able to play with the ARMv8 machine from the ground-up, as in assembly language as in C-code — start (kick) or not start its cores, switch or not switch exception levels, output values of registers, and so on. Finally, we'll have a wide-open window to ARM64 machine!

17/12/2024

The real «Hello World» from embedder (1): preface, theory

Chapter 1

Preface, theory 

Preface

Any learning process eventually comes up to some examples, some practice. In the case of software development, practice starts from so-called «Hello World». «Hello World» is the very first code every software developer on every platform, API, or framework should do on his very first days as his very first steps. Embedded software engineers are not an exception.

There is a lot of «Hello Worlds» out there on the Internet and in books. Those «Hello Worlds» are in any kind of programmings languages, APIs, and frameworks. But the vast majority of those «any kinds» are in pure software — Java, JavaScript, C++, etc. Thus, embedded software developers, those of them who want to study machine architecture, get in touch and play with it, suffer from a lack of examples — they have no starting point.

You can argue with that — there are examples in assembly language for all types of architectures, assembly language should let us study machine architecture and its behaviour. Yes, there is a lot of examples in assembly language, but those examples are for very high (more precisely — top) levels of runtime environment — Linux and Mac user-space. This approach to learning machine architecture doesn't lead to understanding of how it works and how it is organised.

Actually, it gives us a very narrow slit to machine architecture. Even in kernel-space, we are very limited in abilities to learn the machine. That's because all the hardware initialisation is already done for (and before) us by bootloader and kernel itself. The second problem is so-called «concepts and abstractions of operating systems». Those «abstractions» hide a lot of machine architecture from us while «concepts» arise a lot of software that serve an OS itself and make it what it is from user's point of view. Thus, even working in kernel-space, we learn more about these concepts and principles rather than about a machine.

Let's go on and discuss our last chance — MCUs (Micro-Controller Unit), which are cheap, popular, easy to start up and do let us be as close to the machine as possible. MCUs always had a crucial difference with full-fledged CPUs and SoCs (System on Chip) — they have no MMU (Memory Management Unit) and usually are single-core ALUs. After the beginning of the ARM64-era — the times when not only phones and tablets but also desktops (and even servers) and laptops are running on ARM64, MCUs eventually have got another one drawback ARM32 (the most common architecture of worth anything at all MCUs) architecture became outdated even as a single-core platform for studying. Now we are living in the days when it's almost useless to learn ARM32 architecture. It's more a waste of time because the difference between actual and almost omnipresent ARM64 and rapidly becoming obsolete ARM32 is enormous.

Thus, we come to the point where we need a comfortable, big enough window (let's say — better a door or a nice gate) to the machine that represents modern ARM64 architecture. Usually it is done by programming for an emulator. Developing for an emulator is like a game because of its abstraction. Games (and gaming) give you minimal or even zero risks by the price of insignificant wins. To get real valuable practice and results, as well as satisfaction, we need a real «Hello World» on real hardware.

Learning a machine architecture (and its behaviour) is done by so-called «Bare Metal» development. «Bare» means that we are working on a machine without an OS, without a kernel, and even without a bootloader. Actually, we develop code that works instead of a bootloader or runs where and when the very first part of user bootloader (SPL — Second Platform Loader) usually does. «Metal» stands for hardware or machine and means that we work on a real hardware — not a virtual machine or an emulator.

In these topics we'll cut a good window for studying modern ARM64 machine. This will be the «Hello World» from embedded engineer and a nice toy for embedded developer.

Theory

Let's start with a little overview of a computing machine, specifically about its heart — CPU or SoC. SoC provides a set of functions (functionalities); each functionality is provided by an according and separate hardware-block. Thus, SoC consists of hardware-blocks or represents a set of hardware-blocks. Each hardware-block is driven by a clock; each clock is derived from PLL, Phase Lock Loop — a small circuit that generates one or more frequencies from an input clock source — an oscillator. So, turning a hardware-block on, besides powering it, is just enabling the clock it is connected to. Actually, you will not find such element like «clock» on your board. «Clock», as an element — is just a concept of embedded developers. Really, «clock» — is one of the outputs of PLL, which can be enabled or disabled by software. Real clocking sources are oscillators and outputs of PLLs. You can see overview of clock generating scheme below.

Clock generating scheme

But enabling clock is not enough to start using functionality of hardware-block. In most cases there are two more things. The first — usually, SoCs provide more functionalities than they have pins, or, in terms of embedded software, more often we say — pads. It leads to so-called «alternative function» (AF) concept. This means that some pads, as we say in software theory — can be configured to specific (alternative) function — I2C SDA or UART TX, for example. Configuring of AFs is done by Input/Output Multiplexing Controller (IOMUXC) or, more commonly called Pin Multiplexer (PINMUX). PINMUX is a built-in hardware-block. So, it has to be turned on (clocked) too, like other hardware-blocks. From the hardware point of view, PINMUX simply routes signals from SoC's pads to inputs/outputs of specified internal hardware-block — to I2C bus controller or to UART controller in example above. In other words, PINMUX switches signals between hardware-blocks inside of a SoC on one end and SoCs pins/balls (or pads) that we can see on the chip package. You can see example of alternative functions multiplexing scheme below.

Alternative functions multiplexing scheme

Second thing is configuration of hardware-block. This is done by code. After hardware-block is clocked (enabled) it stays in some default condition. We need to write specific values to specific registers to make it function according to our needs.

Clocks for hardware-blocks and corresponding PLLs are enabled by code. Hardware-blocks are configured by code too. But no program can run on a non-clocked CPU. So who and how starts the main PLLs and clocks that drive the ALU? This functionality is hardcoded into so-called BootROM, or BROM. BROM is microcode of SoC itself; it is located inside SoC. BROM initialises the essential hardware minimum required to start user code. It starts up a minimal amount of hardware-blocks and after that performs as FPL (see below). BROMs are very different in functionality — some of them just start code from built-in memory, not even loading it into RAM (like BROMs of MCUs do), some of them initialise a bunch of hardware-blocks and can even operate filesystems (like BROM of Raspberry's Broadcom does). The most common condition BROM leaves SoCs in is: one ALU core is started, SRAM (or OCRAM — OnChip RAM) initialised, and one of the boot sources initialised. Initialisation of the rest functionality is left for user code.

Any SoC uses its own, proprietary FPL (First Platform Loader). FPL is a part of BROM we've discussed earlier. To run our code on a SoC we need so-called «boot image», which is made out of our code. We need to say few words about contents of boot image. It is not a regular file we get from compiler. And the architecture mismatch is not the only reason. Usually compiler builds ELF (Executable and Linkable Format) file. ELF-file contains a lot of extra information which is used by OS or some other environment code is run in. For example, ELF-file can include debug information, symbol names, etc. But while working on bare-metal we have to get rid of all OS-specific, debug and other environmental information. This is because SoC will execute raw code only and treat any data as straight, linear stream of code (with some addition of data). Bare-metal needs raw code to function correctly. If we try to load whole ELF-file as a bare-metal application, most probably we'll get some kind of illegal instruction exception because that extra information in ELF-file will not match with correct instructions codes. The process of making raw code, or raw binary from ELF-file is called stripping.

Now, let's proceed with FPL. Any FPL expects boot-image in a specific format and in a specific place. Thus, after we've compiled our source code to (set of) object files, linked that objects into single binary, and stripped it down to pure machine code, we have to pack it and make it comply with specific requirements of a particular SoC and its BROM. This is done by a tool, which usually is named «mkimage», sometimes like «mkimage_XXX», where XXX is replaced by the name of SoC or the name of a family of SoCs. Usually, mkimage adds some headers, which BROM reads, and sometimes CRCs, to machine code. BROM uses this information to verify the boot image. Then we have to put this image in a particular place — usually on a SD-Card or eMMC with some offset from zero. Offset is needed to make bootable media also usable as storage media — it leaves space for partition table and filesystems.

This is what we have about hardware. Let's proceed to software. There's not too much to do and discuss here. We can work in assembly language forever — this is interesting and can be useful. By limiting ourself to assembly language only we can omit using stack. But anyway, at some point we want to dive out into C-code. At this point we'll need stack because C-compiler will use it intensively. Thus, we have to initialise it — that's all we need to know at the moment. Initialisation of the stack is done by setting the stack pointer register to a value representing a valid memory address. Stack (more often) grows down, so we have to choose an address for it according to its behaviour — to prevent it from touching the bottom of RAM and from destroying our application in case it is set above. And, of course, we can't set it higher than the top of accessible RAM.

Now let's proceed to our specific task. Let's say we want to make our SBC (Single-Board Computer) output a «Hello World». How can we do that? Let's confess that outputting (drawing) strings on a display is a little complicated task for a bare-metal beginner. So we'll output our «Hello World» via the most common debug interface all over the world — UART. UART functionality is provided by a particular hardware-block. So we need to start clocking that hardware-block, set its pads and configure it.

First, to enable a clock for UART we have to know which clock exactly we need to enable on the exact SoC. As we mentioned earlier, every clock is derived from a particular PLL. Hence, we need to find out what PLL provides the clock we need. All this information is presented in a datasheet and is rigidly tied to a certain SoC. The second part is to set AF — to configure pads for UART — its TX and RX. Here we need to turn on PINMUX (PLL, clock) and configure pads we need to functions we need. And the last part — configuration is done by writing values to a memory location mapped to an address of hardware-block — PINMUX (pads) and UART (baud rate, parity, etc.) in our case. What configuration must be written is described in a datasheet and, again, is rigidly tied to a certain SoC.

After writing this code we have to compile, link and strip the resulting file to raw machine code, make boot-image by forming out BROM header and adding it to machine code we've got on the previous stage. Then put our boot-image to specific place on a specific media and power on SBC.

Theory ends at this point. In the next part, we'll choose specific SoC, gather information needed to design the «Hello World» for the chosen SoC. With this information we will form out the plan of steps for third part.

28/07/2024

Kernel-Space: asm _ko Hello!

Long time no see, confreres.

This time we will do some crazy (or maybe even mad) things.

As we all know, Linux kernel is a cross-platform software. It supports a very large variety of hardware platforms. Thus it’s written in the most «inter-platform» language in the world — Plain C. The secret of cross-platformness is a compiler used to build the kernel itself and its modules. Exceptions are small parts that provide the only hardware specific functionality that cannot be written in C — SoCs/CPUs start-up and configuration routines. These small parts of kernel are written in assembly languages.


But today I’ll present some sort of skeleton of the whole kernel module written in assembly language — not a single .c-file is used. I had this idea for a long time, I’ve searched the Internet a lot of times for some examples or at least a starting point or a discussion. But had no luck — no examples for ARM nor x86 or any other architecture. This fact proves the craziness of my idea (possibly also it explains why you should not do this in your practice). But I’ve managed to do this.


This module’s functionality will be limited to some kind of «Hello World» — it will be able to be loaded and unloaded correctly and do the only thing — print messages on these events. I’ve mentioned that no .c-files are used in this module, but this module looks like a usual kernel module (except the language it is written in) and is built and works like any other module — thus it is a regular code which you can work with like your everyday routine — no any sort of magic nor discomfort. We will talk about ARM64 (or AArch64) but it can be easily rewritten for any other architecture.


I said that there is no magic in this module, but… we know that any object file must have some sections, information and has to be built — compiled and linked according to strict rules. Kernel module is no exception. That was the «magic» I had to reveal to achieve the goal of my idea — regular-looking and developer-friendly kernel module in assembly language.


There is a lot of «magic» in kernel build system. But my idea was to write a template of a kernel module that will look, feel, act and work like a regular one, as regular part of kernel source tree. Thus today we will not talk about kernel’s build system, differences between linking user-space objects and linking kernel-space objects — but about template of a kernel module in assembly language only (and Makefile for it, of course). Building — compiling and linking will be done by standard kernel build system.


Kernel module project consists of two parts — Makefile and source code. Let's start with Makefile. Everything is clear enough here — you just set source file name to your assembly (.s or .S) file and set obj-m variable. That's all — the rest of the job will be done by kernel build system. Here is our Makefile:


ifeq ($(KERNEL_SRC),)
$(error Specify KERNEL_SRC directory)
endif

export ARCH := arm64
export CROSS_COMPILE ?= aarch64-linux-gnu-
PWD := $(shell pwd)

PROJECT_NAME := asm_ko_hello
$(PROJECT_NAME)-src := $(PROJECT_NAME).S
obj-m += $(PROJECT_NAME).o
AFLAGS_$(PROJECT_NAME).o := -DPROJECT_NAME=$(PROJECT_NAME)

all:
	make -C $(KERNEL_SRC) M=$(PWD) modules

clean:
	make -C $(KERNEL_SRC) M=$(PWD) clean


Now, let's have a look at asm_ko_hello.S (capitalised extension means that this file will be passed via preprocessor):


#include "linux/kern_levels.h"

Here you can see something familiar to kernel modules you have worked with and guess that we will have standard levels of output and you are right — we will have all that standard KERN_XXXX output levels in our assembly code.

#if !defined (PROJECT_NAME)
	#error You must define project name for this template. Stopping build.
#endif

#define MAKE_FN_NAME(x, y) x##_##y
#define FN_NAME(project, func) MAKE_FN_NAME(project, func)


The above lines serve project's template and are not related to today's topic.

.section .text
FN_NAME(PROJECT_NAME, init):
	stp x29, x30, [sp, -16]!
	adrp x0, .loaded
	mov x29, sp
	add x0, x0, :lo12:.loaded
	bl _printk
	mov w0, 0
	ldp x29, x30, [sp], 16
	ret

FN_NAME(PROJECT_NAME, exit):
	stp x29, x30, [sp, -16]!
	adrp x0, .unloaded
	mov x29, sp
	add x0, x0, :lo12:.unloaded
	bl _printk
	ldp x29, x30, [sp], 16
	ret


This is the code of common «Hello World» kernel module. It is put into standard .text section. FN_NAME macro will produce functions names. And after go two functions bodies in standard/usual ARM64 assembly language. As you can see we preserve registers, load string address and call (in term of ARM it's called «branch with link») printk() function, restore registers and, in case of _init(), return value (which actually is an abstraction).

The code looks clear and familiar, but this is kernel module and there is a little difference with user-space program. We should let the system know where are the entry and leave points (or load/unload functions) of our module. In C it's done by two macros module_init() and module_exit(). In our case it would look like:

module_init(asm_ko_init);
module_exit(asm_ko_exit);


But how should we specify these functions in assembly language? What's covered under those macros? Actually nothing too complicated. We just need to declare global functions (symbols) init_module and cleanup_module. To give them proper payload (symbol itself is just a symbol in object file) we specify aliases to our _init() and _exit() functions with .set directive. The whole part of this code is in snippet below:

.global init_module
.global cleanup_module
.set init_module, FN_NAME(PROJECT_NAME, init)
.set cleanup_module, FN_NAME(PROJECT_NAME, exit)


We can't omit the .data section. This one is absolutely standard. Here is our section with strings used for our output:

.section .data
.unloaded:
	.string KERN_INFO MODULE_NAME": unloaded.\n"

.loaded:
	.string KERN_INFO MODULE_NAME": successfully loaded.\n"


There is something that the kernel will not accept our module without. This is something new for developers working in user-space and familiar for kernel-space developers. For Linux kernel we have to specify one mandatory parameter that cannot be omitted — the license. In C it is done by MODULE_LICENSE() macro and would look like:

MODULE_LICENSE("GPL");


Let's see how it is done in assembly language. Maybe you've expected something serious here — some special codes or sequences. But it's easy too — this is just .modinfo section containing information about module in a very simple (and unexpectedly ridiculous) format. See self-explaining snippet below:

#define MODULE_NAME	"Kernel Module in Assembly"
#define MODULE_VER	"1.0"
#define MODULE_AUTHOR	"Daft Soft, 2024"

.section .modinfo, "a"
	.string "author=" MODULE_AUTHOR
	.string "version=" MODULE_VER
	.string "description=" MODULE_NAME
	.string "license=GPL"


That's all about code. The repository is here. According to our Makefile, if you cross-compiler is aarch64-linux-gnu-, you build module as follows:

make KERNEL_SRC="PATAH/TO/YOUR/KERNEL/lib/modules/VERSION/build" clean all


Test it:

modinfo ./asm_ko_hello.ko  
filename:       ./asm_ko_hello.ko 
author:         Daft Soft, 2024
version:        1.0
description:    Kernel Module in Assembly
license:        GPL
srcversion:     48259120F9222D4D7B9D8E7
depends:         
name:           asm_ko_hello
vermagic:       6.1.55 SMP preempt mod_unload modversions aarch64

insmod ./asm_ko_hello.ko  
Kernel Module in Assembly: successfully loaded. 

lsmod 
Module                  Size  Used by 
asm_ko_hello           16384  0 

rmmod asm_ko_hello
Kernel Module in Assembly: unloaded.



P.S.
High level programming languages do a lot of job for developer and prevent a lot of mistakes. Actually not prevent but don't allow to make mistakes — you don't have enough tools to do most dummy things. When you write in assembly language in user-space it's a risk, but it's a funny walk in comparison to working in kernel-space. So you have to be extremely cautious working in assembly language in kernel-space because your any typo will be compiled and executed. For example, slight shift of stack pointer may lead to huge troubles — broken file system is a case. You have been warned — it's your decision how hard you wanna play.

18/10/2022

Оптимизация кода (1): О вызовах функций

Недавно я увидел следующую рекомендацию по рефакторингу кода с целью оптимизации:

Изначальный вариантОптимизированный вариант
return pow (base, exp/2) * pow (base, exp/2);let result = pow (base, exp/2); return result * result;

В книге было написано, что результатом такого рефакторинга будет увеличение скорости работы представленного участка кода. Но почему такой рефакторинг должен привести к ускорению работы этого кода? Большинство авторов/советчиков/специалистов не раскрывают суть своих советов и не дают понимания почему что-либо нужно делать так или иначе. Если вам интересно действительно ли здесь произошло ускорение работы и за счёт чего, то читайте — эта заметка для вас. В ней я рассмотрю, что происходит на вычислительной машине в данной ситуации, чем достигается результат, поясню как именно происходит оптимизация и дам информацию для некоторого понимания «масштаба» этой оптимизации. Пояснения в этой заметке раскрывают суть подобной оптимизации не только в данном случае — а в общем. Вы сможете применять это во множестве подобных ситуаций в вашей практике.

По синтаксису можно предположить, что представленный участок кода написан на JavaScript'е. Я же буду работать на общепринятых языках ИТ/ВТ — С, Aseembler x86_64 и стандартном ABI x86_64.

Для начала мы видим, что автор, ценой добавления ещё одной переменной, сократила вызовы функции pow () в два раза. Рассмотрим, что происходит при вызове функции pow (). Её прототип выглядит следующим образом:

double pow (double x, double y);

Из прототипа понятно, что функция работает с параметрами с плавающей точкой и возвращает такой же результат, а это значит, что она будет задействовать сопроцессор (FPU).

Сокращение вызовов функции pow () действительно даёт оптимизацию, и вот почему. Вызов любой функции требует ощутимых накладных расходов. Рассмотрим, что происходит на центральном процессоре при вызове функции в общем, и в частности при вызове функции pow (). В скобках, рядом с командами процессора, стоит приблизительное количество «циклов» (микроопераций) процессора на команду. Рассматриваем на примере x86-ой машины:

1. (При необходимости) вычисление или каким-то иным образом получение всех входных параметров, передаваемых функции (в данном примере это вычисление выражения exp/2). Здесь возможна работа с памятью (а она медленная) и вызовы других, вложенных функций. Если они есть, то стоит пройти все их начиная с этого же пункта.

2. «Раскладывание» параметров, вычисленных или полученных на предыдущем этапе в соответствии с ABI. После вычисления их, они могут оказаться в «местах» (память, регистры), не соответствующих сигнатуре рассматриваемой функции. Это некоторое количество команд mov (~1).

3. Вызов команды call (~10), которая, в свою очередь, сохраняет адрес возврата в стеке, затем осуществляет переход потока выполнения на (указанный адрес) рассматриваемой нами функции.

4. Сама функция pow (), как и любая другая, имеет в себе «преамбулу» (или «пролог»). В этой секции кода происходит сохранение регистров общего назначения путём выполнения нескольких команд семейства push, резервирование пространства в стеке для внутренних нужд функции несколькими манипуляциями с указателем стека. Напомним, что всё это уже происходит один раз в нашей, вызывающей функции.

5. Так как pow () работает с числами с плавающей точкой, она должна сохранить регистры и состояние сопроцессора — так называемую «среду сопроцессора», включающую в себя стек сопроцессора, регистры его состояния, управления, тегов, указатели данных и команд. Так же функция должна сбросить состояние FPU при входе, так как неизвестно в каком состоянии он будет к этому моменту. К счастью у нас есть простые команды для сохранения всей среды сопроцессора — fsave/fnsave (120-150 и более) и finit/fninit (15-20 и более) — для сброса его состояния. Как эти, так и описанные ниже команды восстановления среды FPU, достаточно тяжёлые, так как работают с достаточно большим объёмом информации — всей средой сопроцессора и с памятью (а она, не забываем, у нас — медленная).

6. pow (), вероятно, имеет множество проверок и инициализацию локальных переменных в своей реализации, а они нам здесь не нужны.

7. Реализация самих вычислений функции. При работе с FPU, есть вероятность необходимости вызова команды fwait — дождаться выполнения операции на FPU (на x86 FPU работает параллельно с CPU).

8. После завершения своей работы, функции нужно восстановить регистры FPU и его состояние (что так же уже, возможно, делается в нашей функции). Это команда frstor (~100).

9. В конце функции есть «эпилог», включающий в себя восстановление состояния стека — некоторые манипуляции с указателем стека и регистров общего назначения CPU при выходе — выполнение нескольких команд семейства pop.

10. По завершению вызывается команда ret (15-25), которая извлекает адрес возврата из стека и изменяет указатель текущей инструкции процессора на этот адрес. Таким образом, модуль выборки команд x86, после окончания обработки команды ret, начнёт загружать и выполнять команды с адреса, хранящегося в указателе текущей инструкции.

На ARM'е накладные расходы будут схожими.

Таким образом, мы видим, что основные накладные расходы, исключением которых достигнута оптимизация в этом примере, заключаются в управлении потоком исполнения, исключении некоторых проверок, встроенных в вызываемую функцию (что, в данной ситуации, нужно лишь для вычисления значения, которое уже есть).

Но есть и ещё один нюанс. Мы никогда не знаем сколько раз операционная система переключит контекст нашего приложения (в данной ситуации — функции), пока оно работает. А любая, современная операционная система работает по принципу вытесняющей многозадачности. Следовательно, чем меньше список команд, требуемый для получения результата — тем больше вероятность, что наш код будет прерван меньшее количество раз — наша задача будет делиться на меньшее количество квантов выделяемого времени. В критических ко времени вычислениях, когда результат зависит от внешних обстоятельств, например — поток данных, приходящих по сети, такая оптимизация может глобально улучшить результат работы приложения (либо и вовсе спасти код/алгоритм от признания непригодным).

Из этого можно сделать вывод, что такая оптимизация особенно желательна в критичных местах — в «верхних половинах» kernel-space (там лучше вообще не делать никаких вычислений, но мы рассматриваем оптимизацию через сокращение количества вызовов функций в общем), в обработчиках прерываний на Bare-Metal/RTOS.

Теперь опишем, что происходит в оптимизированном варианте. Умножая, в данной ситуации, число само на себя, без вызова функции, мы всего лишь пишем одну команду из семейства fmul, которая в упрощённом варианте (при правильном использовании) умножает два верхних регистра FPU и кладёт результат в самый верхний — ST(0). Который по правилам ABI x86_64, в свою очередь, является возвращаемым значением функции, работающей с числами с плавающей точкой. А если мы пойдём дальше, и сами будем писать код этих операций, то мы сделаем так, чтобы к моменту этого умножения, у нас операнды были уже в двух верхних регистрах FPU, в правильной последовательности. Вот какая оптимизация происходит — практически автоматическая работа процессора на нас.

Кто-то может возразить, что x86-ая машина имеет множество оптимизаций и, что, благодаря им, многие операции из рассмотренного участка кода будут выполнены в параллель, на опережение, или вовсе опущены. Да, это так. Но зачем нам грузить вычислительную машину лишними операциями, когда мы можем избежать их на этапе написания кода? Пусть она использует свои возможности для оптимизации чего-то другого.

P.S.
По описанным выше причинам, предостерегу вас от достаточно очевидного манёвра с этим участком кода. А именно, использовать вместо умножения вызов всё той же функции pow () с result в качестве первого параметра и двойкой — в качестве второго. Умножение числа на само себя — есть возведение его в квадрат. Математически и идеологически, кому-то это может показаться правильнее или «красивее», но технически — правильнее так, как мы рассмотрели. В противном случае это будет «пример плохого кода».

P.P.S.
А вот, например, сократить количество машинных операций, передавая в функцию выражение exp/2 вычисленное заранее извне — хороший вариант. Во-первых, внутри функции не будет заниматься лишнее место на стеке (для проведения этой операции). Во-вторых, при множественном вызове такой функции, с одинаковым значением какого-то из параметров, сократится время на вычисления — он будет вычислен единожды в вызывающей функции и затем повторно использоваться. А если у нас exp/2 будет равно двойке, то и вовсе проще дважды умножить base на себя и выйти, вернув этот результат.