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  • Linear Attribution Model : What Is It and How Does It Work ?

    16 février 2024, par Erin

    Want a more in-depth way to understand the effectiveness of your marketing campaigns ? Then, the linear attribution model could be the answer.

    Although you can choose from several different attribution models, a linear model is ideal for giving value to every touchpoint along the customer journey. It can help you identify your most effective marketing channels and optimise your campaigns. 

    So, without further ado, let’s explore what a linear attribution model is, when you should use it and how you can get started. 

    What is a linear attribution model ?

    A linear attribution model is a multi-touch method of marketing attribution where equal credit is given to each touchpoint. Every marketing channel used across the entire customer journey gets credit, and each is considered equally important. 

    So, if a potential customer has four interactions before converting, each channel gets 25% of the credit.

    The linear attribution model shares credit equally between each touchpoint

    Let’s look at how linear attribution works in practice using a hypothetical example of a marketing manager, Sally, who is looking for an alternative to Google Analytics. 

    Sally starts her conversion path by reading a Matomo article comparing Matomo to Google Analytics she finds when searching on Google. A few days later she signs up for a webinar she saw on Matomo’s LinkedIn page. Two weeks later, Sally gets a sign-off from her boss and decides to go ahead with Matomo. She visits the website and starts a free trial by clicking on one of the paid Google Ads. 

    Using a linear attribution model, we credit each of the channels Sally uses (organic traffic, organic social, and paid ads), ensuring no channel is overlooked in our marketing analysis. 

    Are there other types of attribution models ?

    Absolutely. There are several common types of attribution models marketing managers can use to measure the impact of channels in different ways. 

    Pros & Cons of Different Marketing Attribution Models
    • First interaction : Also called a first-touch attribution model, this method gives all the credit to the first channel in the customer journey. This model is great for optimising the top of your sales funnel.
    • Last interaction : Also called a last-touch attribution model, this approach gives all the credit to the last channel the customer interacts with. It’s a great model for optimising the bottom of your marketing funnel. 
    • Last non-direct interaction : This attribution model excludes direct traffic and credits the previous touchpoint. This is a fantastic alternative to a last-touch attribution model, especially if most customers visit your website before converting. 
    • Time decay attribution model : This model adjusts credit according to the order of the touchpoints. Those nearest the conversion get weighted the highest. 
    • Position-based attribution model : This model allocates 40% of the credit to the first and last touchpoints and splits the remaining 20% evenly between every other interaction.

    Why use a linear attribution model ?

    Marketing attribution is vital if you want to understand which parts of your marketing strategy are working. All of the attribution models described above can help you achieve this to some degree, but there are several reasons to choose a linear attribution model in particular. 

    It uses multi-touch attribution

    Unlike single-touch attribution models like first and last interaction, linear attribution is a multi-touch attribution model that considers every touchpoint. This is vital to get a complete picture of the modern customer journey, where customers interact with companies between 20 and 500 times

    Single-touch attribution models can be misleading by giving conversion credit to a single channel, especially if it was the customer’s last use. In our example above, Sally’s last interaction with our brand was through a paid ad, but it was hardly the most important. 

    It’s easy to understand

    Attribution models can be complicated, but linear attribution is easy to understand. Every touchpoint gets the same credit, allowing you to see how your entire marketing function works. This simplicity also makes it easy for marketers to take action. 

    It’s great for identifying effective marketing channels

    Because linear attribution is one of the few models that provides a complete view of the customer journey, it’s easy to identify your most common and influential touchpoints. 

    It accounts for the top and bottom of your funnel, so you can also categorise your marketing channels more effectively and make more informed decisions. For example, PPC ads may be a more common bottom-of-the-full touchpoint and should, therefore, not be used to target broad, top-of-funnel search terms.

    Are there any reasons not to use linear attribution ?

    Linear attribution isn’t perfect. Like all attribution models, it has its weaknesses. Specifically, linear attribution can be too simple, dilute conversion credit and unsuitable for long sales cycles.

    What are the reasons not to use linear attribution

    It can be too simple

    Linear attribution lacks nuance. It only considers touchpoints while ignoring other factors like brand image and your competitors. This is true for most attribution models, but it’s still important to point it out. 

    It can dilute conversion credit

    In reality, not every touchpoint impacts conversions to the same extent. In the example above, the social media post promoting the webinar may have been the most effective touchpoint, but we have no way of measuring this. 

    The risk with using a linear model is that credit can be underestimated and overestimated — especially if you have a long sales cycle. 

    It’s unsuitable for very long sales cycles

    Speaking of long sales cycles, linear attribution models won’t add much value if your customer journey contains dozens of different touchpoints. Credit will get diluted to the point where analysis becomes impossible, and the model will also struggle to measure the precise ways certain touchpoints impact conversions. 

    Should you use a linear attribution model ?

    A linear attribution model is a great choice for any company with shorter sales cycles or a reasonably straightforward customer journey that uses multiple marketing channels. In these cases, it helps you understand the contribution of each touchpoint and find your best channels. 

    It’s also a practical choice for small businesses and startups that don’t have a team of data scientists on staff or the budget to hire outside help. Because it’s so easy to set up and understand, anyone can start generating insights using this model. 

    How to set up a linear attribution model

    Are you sold on the idea of using a linear attribution model ? Then follow the steps below to get started :

    Set up marketing attribution in four steps

    Choose a marketing attribution tool

    Given the market is worth $3.1 billion, you won’t be surprised to learn there are plenty of tools to choose from. But choose carefully. The tool you pick can significantly impact your success with attribution modelling. 

    Take Google Analytics, for instance. While GA4 offers several marketing attribution models for free, including linear attribution, it lacks accuracy due to cookie consent rejection and data sampling. 

    Accurate marketing attribution is included as a feature in Matomo Cloud and is available as a plugin for Matomo On-Premise users. We support a full range of attribution models that use 100% accurate data because we don’t use data sampling, and cookie consent isn’t an issue (with the exception of Germany and the UK). That means you can trust our insights.

    Matomo’s marketing attribution is available out of the box, and we also provide access to raw data, allowing you to develop your custom attribution model. 

    Collect data

    The quality of your marketing attribution also depends on the quality and quantity of your data. It’s why you need to avoid a platform that uses data sampling. 

    This should include :

    • General data from your analytics platform, like pages visited and forms filled
    • Goals and conversions, which we’ll discuss in more detail in the next step
    • Campaign tracking data so you can monitor the behaviour of traffic from different referral channels
    • Behavioural data from features like Heatmaps or Session Recordings

    Set up goals and conversions

    You can’t assign conversion values to customer journey touchpoints if you don’t have conversion goals in place. That’s why the next step of the process is to set up conversion tracking in your web analytics platform. 

    Depending on your type of business and the product you sell, conversions could take one of the following forms :

    • A product purchase
    • Signing up for a webinar
    • Downloading an ebook
    • Filling in a form
    • Starting a free trial

    Setting up these kinds of goals is easy if you use Matomo. 

    Just head to the Goals section of the dashboard, click Manage Goals and then click the green Add A New Goal button. 

    Fill in the screen below, and add a Goal Revenue at the bottom of the page. Doing so will mean Matomo can automatically calculate the value of each touchpoint when using your attribution model. 

    A screenshot of Matomo's conversion dashboard

    If your analytics platform allows it, make sure you also set up Event Tracking, which will allow you to analyse how many users start to take a desired action (like filling in a form) but never complete the task. 

    Try Matomo for Free

    Get the web insights you need, without compromising data accuracy.

    No credit card required

    Test and validate

    As we’ve explained, linear attribution is a great model in some scenarios, but it can fall short if you have a long or complex sales funnel. Even if you’re sure it’s the right model for your company, testing and validating is important. 

    Ideally, your chosen attribution tool should make this process pretty straightforward. For example, Matomo’s Marketing Attribution feature makes comparing and contrasting three different attribution models easy. 

    Here we compare the performance of three attribution models—linear, first-touch, and last-non-direct—in Matomo’s Marketing Attribution dashboard, providing straightforward analysis.

    If you think linear attribution accurately reflects the value of your channels, you can start to analyse the insights it generates. If not, then consider using another attribution model.

    Don’t forget to take action from your marketing efforts, either. Linear attribution helps you spot the channels that contribute most to conversions, so allocate more resources to those channels and see if you can improve your conversion rate or boost your ROI. 

    Make the most of marketing attribution with Matomo

    A linear attribution model lets you measure every touchpoint in your customer journey. It’s an easy attribution model to start with and lets you identify and optimise your most effective marketing channels. 

    However, accurate data is essential if you want to benefit the most from marketing attribution data. If your web analytics solution doesn’t play nicely with cookies or uses sampled data, then your linear model isn’t going to tell you the whole story. 

    That’s why over 1 million sites trust Matomo’s privacy-focused web analytics, ensuring accurate data for a comprehensive understanding of customer journeys.

    Now you know what linear attribution modelling is, start employing the model today by signing up for a free 21-day trial, no credit card required. 

  • 10 Matomo Features You Possibly Didn’t Know About

    28 octobre 2022, par Erin

    Most users know Matomo as the privacy-focussed web analytics tool with data accuracy, superior to Google Analytics. 

    And we’re thrilled to be that — and more ! 

    At Matomo, our underlying product vision is to provide a full stack of accurate, user-friendly and privacy-mindful online marketing tools. 

    Over the years, we’ve expanded beyond baseline website statistics. Matomo Cloud users also get to benefit from additional powerful tools for audience segmentation, conversion optimisation, advanced event tracking and more. 

    Here are the top 10 advanced Matomo features you wish you knew about earlier (but won’t stop using now !). 

    Funnels

    At first glance, most customer journeys look sporadic. But every marketer will tell you that there is a method to almost every users’ madness. Or more precisely — there’s a method you can use to guide users towards conversions. 

    That’s called a customer journey — a schematic set of steps and actions people complete from developing awareness and interest in your solution to consideration and finally conversion.

    On average, 8 touchpoints are required to turn a prospect into a customer. Though the number can be significantly bigger in B2B sales and smaller for B2C Ecommerce websites. 

    With the Funnels feature, you can first map all the on-site touchpoints (desired actions) for different types of customers. Then examine the results you’re getting as prospects move through these checkbox steps.

    Funnel reports provide :

    • High-level metrics such as “Funnel conversion rate”, “Number of funnel conversions”, “Number of funnel entries”. 
    • Drilled-down reports for each funnel and each tracked action within it. This way you can track the success rates of each step and estimate their contribution to the cumulative effect.

    Segmented funnel reports for specific user cohorts (with Matomo Segmentation enabled).

    Funnels Report Matomo

    What makes funnels so fun (pun intended) ? The variety of use cases and configurations ! 

    You can build funnels to track conversion rates for :

    • Newsletter subscriptions
    • Job board applications 
    • Checkout or payment 
    • Product landing pages
    • Seasonal promo campaigns

    …. And pretty much any other page where users must complete a meaningful action. So go test this out. 

    Form Analytics

    On-site forms are a 101 tactic for lead generation. For most service businesses, a “contact request” or a “booking inquiry” submission means a new lead in your pipeline. 

    That said : the average on-site form conversion rates across industries stand at below 50% : 

    • Property – 37% 
    • Telecoms – 40%
    • Software — 46.83%

    That’s not bad, but it could be better. If only you could figure out why people abandon your forms….

    Oh wait, Matomo Form Analytics can supply you with answers. Form Analytics provide real-time information on key form metrics — total views, starter rate, submitter rate, conversions and more.

    Separately the average form hesitation time is also provided (in other words, the time a user contemplates if filling in a form is worth the effort). Plus, Matomo also tracks the time spent on form submission.

    You can review : 

    • Top drop-off fields – to understand where you are losing prospects. These fields should either be removed or simplified (e.g., with a dropdown menu) to increase conversions.
    • Most corrected-field – this will provide a clear indication of where your prospects are struggling with a form. Providing help text can simplify the process and increase conversions. 
    • Unesserary fields – with this metric, you’ll know which optional fields your leads aren’t interested in filling in and can remove them to help drive conversions. 

    With Form Analytics, you’ll be able to boost conversions and create a better on-site experience with accurate user data. 

    A/B testing

    Marketing is both an art and a science. A/B testing (or split testing) helps you statistically verify which creative ideas perform better. 

    A good conversion rate optimisation (CRO) practice is to test different elements and to do so often to find your top contenders.

    What can you split test ? Loads of things :

    • Page slogans and call-to-actions 
    • Button or submission form placements
    • Different landing page designs and layouts
    • Seasonal promo offers and banners
    • Pricing information 
    • Customer testimonial placements 

    More times than not, those small changes in page design or copy can lead to a double-digit lift in conversion rates. Accounting software Sage saw a 30% traffic boost after changing the homepage layout, copy and CTAs based on split test data. Depositphotos, in turn, got a 9.32% increase in account registration rate (CR) after testing a timed pop-up registration form. 

    The wrinkle ? A/B testing software isn’t exactly affordable, with tools averaging $119 – $1,995 per month. Plus, you then have to integrate a third-party tool with your website analytics for proper attribution — and this can get messy.

    Matomo saves you the hassle in both cases. An A/B testing tool is part of your Cloud subscription and plays nicely with other features — goal tracking, heatmaps, historic visitor profiles and more. 

    You can run split tests with Matomo on your websites or mobile apps — and find out if version A, B, C or D is the top performer. 

    Conversions Report Matomo

    Advertising Conversion Exports

    A well-executed search marketing or banner remarketing campaign can drive heaps of traffic to your website. But the big question is : How much of it will convert ?

    The AdTech industry has a major problem with proper attribution and, because of it, with ad fraud. 

    Globally, digital ad fraud will cost advertisers a hefty $8 billion by the end of 2022. That’s when another $74 million in ad budgets get wasted per quarter. 

    The reasons for ad budget waste may vary, but they often have a common denominator : lack of reliable conversion tracking data.

    Matomo helps you get a better sense of how you spend your cents with Advertising Conversion Reports. Unlike other MarTech analytics tools, you don’t need to embed any third-party advertising network trackers into your website or compromise user privacy.

    Instead, you can easily export accurate conversion data from Matomo (either manually via a CSV file or automated with an HTTPS link) into your Google Ads, Microsoft Advertising or Yandex Ads for cross-validation. This way you can get an objective view of the performance of different campaigns and optimise your budget allocations accordingly. 

    Find out more about tracking ad campaigns with Matomo.

    Matomo Tag Manager

    The marketing technology landscape is close to crossing 10,000 different solutions. Cross-platform advertising trackers and all sorts of customer data management tools comprise the bulk of that growing stack. 

    Remember : Each new tool embed adds extra “weight” to your web page. More tracking scripts equal slower page loading speed — and more frustration for your users. Likewise, extra embeds often means dialling up the developer (which takes time). Or tinkering with the site code yourself (which can result in errors and still raise the need to call a developer). 

    With Tag Manager, you can easily generate tags for :

    • Custom analytics reports 
    • Newsletter signups
    • Affiliates 
    • Form submission tracking 
    • Exit popups and surveys
    • Ads and more

    With Matomo Tag Manager, you can monitor, update or delete everything from one convenient interface. Finally, you can programme custom triggers — conditions when the tag gets activated — and specify data points (variables) it should collect. The latter is a great choice for staying privacy-focused and excluding any sensitive user information from processing. 

    With our tag management system (TMS), no rogue tags will mess up your analytics or conversion tracking. 

    Session recordings

    User experience (UX) plays a pivotal role in your conversion rates. 

    A five-year McKinsey study of 300 publicly listed companies found that companies with strong design practices have 32 percentage points higher revenue growth than their peers. 

    But what makes up a great website design and browsing experience ? Veteran UX designers name seven qualities :

    Source : Semantic Studios

    To figure out if your website meets all these criteria, you can use Session Recording — a tool for recording how users interact with your website. 

    By observing clicks, mouse moves, scrolls and form interactions you can determine problematic website design areas such as poor header navigation, subpar button placements or “boring” blocks of text. 

    Such observational studies are a huge part of the UX research process because they provide unbiased data on interaction. Or as Nielsen Norman Group puts it :

    “The way to get user data boils down to the basic rules of usability :

    • Watch what people actually do.
    • Do not believe what people say they do.
    • Definitely don’t believe what people predict they may do in the future.” 

    Most user behaviour analytics tools sell such functionality for a fee. With Matomo Cloud, this feature is included in your subscription. 

    Heatmaps

    While Session Replays provide qualitative insights, Heatmaps supply you with first-hand qualitative insights. Instead of individual user browsing sessions, you get consolidated data on where they click and how they scroll through your website. 

    Heatmaps Matomo

    Heatmaps are another favourite among UX designers and their CRO peers because you can :

    • Validate earlier design decisions around information architecture, page layout, button placements and so on. 
    • Develop new design hypotheses based on stats and then translate them into website design improvements. 
    • Identify distractive no-click elements that confuse users and remove them to improve conversions. 
    • Locate problematic user interface (UI) areas on specific devices or operating systems and improve them for a seamless experience.

    To get even more granular results, you can apply up to 100 Matomo segments to drill down on specific user groups, geographies or devices. 

    This way you can make data-based decisions for A/B testing, updating or redesigning your website pages. 

    Custom Alerts

    When it comes to your website, you don’t want to miss anything big — be it your biggest sales day or a sudden nosedive in traffic. 

    That’s when Custom Alerts come in handy. 

    Matomo Custom Alerts

    With a few clicks, you can set up email or text-based alerts about important website metrics. Once you hit that metric, Matomo will send a ping. 

    You can also set different types of Custom Alerts for your teams. For example, your website administrator can get alerted about critical technical performance issues such as a sudden spike in traffic. It can indicate a DDoS attack (in the worst case) — and timely resolution is crucial here. Or suggest that your website is going viral and you might need to provision extra computing resources to ensure optimal site performance.

    Your sales team, in turn, can get alerted about new form submissions, so that they can quickly move on to lead scoring and subsequent follow-ups. 

    Use cases are plentiful with this feature. 

    Custom Dashboards and Reports

    Did you know you can get a personalised view of the main Matomo dashboards ? 

    By design, we made different website stats available as separate widgets. Hence, you can cherry-pick which stats get a prominent spot. Moreover, you can create and embed custom widgets into your Matomo dashboard to display third-party insights (e.g., POS data).

    Set up custom dashboard views for different teams, business stakeholders or clients to keep them in the loop on relevant website metrics. 

    Custom Reports feature, in turn, lets you slice and dice your traffic analytics the way you please. You can combine up to three different data dimensions per report and then add any number of supported metrics to get a personalised analytics report.

    For example, to zoom in on your website performance in a specific target market you can apply “location” (e.g., Germany) and “action type” (e.g., app downloads) dimensions and then get segmented data on metrics such as total visits, conversion rates, revenue and more. 

    Get to know even more ways to customise Matomo deployment.

    Roll Up Report

    Need to get aggregated traffic analytics from multiple web properties, but not ready to pay $150K per year for Google Analytics 360 for that ?

    We’ve got you with Roll-Up Reporting. You can get a 360-degree view into important KPIs like global revenue, conversion rates or form performance across multiple websites, online stores, mobile apps and even Intranet properties.

    Roll-Up-Reporting in Matomo

    Setting up this feature takes minutes, but saves you hours on manually exporting and cross-mapping data from different web analytics tools. 

    Channel all those saved hours into more productive things like increasing your conversion rates or boosting user engagement

    Avoid Marketing Tool Sprawl with Matomo 

    With Matomo as your website analytics and conversion optimisation app, you don’t need to switch between different systems, interfaces or have multiple tracking codes embedded on your site.

    And you don’t need to cultivate a disparate (and expensive !) MarTech tool stack — and then figure out if each of your tools is compliant with global privacy laws.

    All the tools you need are conveniently housed under one roof. 

    Want to learn more about Matomo features ? Check out product training videos next ! 

  • ARM inline asm secrets

    6 juillet 2010, par Mans — ARM, Compilers

    Although I generally recommend against using GCC inline assembly, preferring instead pure assembly code in separate files, there are occasions where inline is the appropriate solution. Should one, at a time like this, turn to the GCC documentation for guidance, one must be prepared for a degree of disappointment. As it happens, much of the inline asm syntax is left entirely undocumented. This article attempts to fill in some of the blanks for the ARM target.

    Constraints

    Each operand of an inline asm block is described by a constraint string encoding the valid representations of the operand in the generated assembly. For example the “r” code denotes a general-purpose register. In addition to the standard constraints, ARM allows a number of special codes, only some of which are documented. The full list, including a brief description, is available in the constraints.md file in the GCC source tree. The following table is an extract from this file consisting of the codes which are meaningful in an inline asm block (a few are only useful in the machine description itself).

    f Legacy FPA registers f0-f7.
    t The VFP registers s0-s31.
    v The Cirrus Maverick co-processor registers.
    w The VFP registers d0-d15, or d0-d31 for VFPv3.
    x The VFP registers d0-d7.
    y The Intel iWMMX co-processor registers.
    z The Intel iWMMX GR registers.
    l In Thumb state the core registers r0-r7.
    h In Thumb state the core registers r8-r15.
    j A constant suitable for a MOVW instruction. (ARM/Thumb-2)
    b Thumb only. The union of the low registers and the stack register.
    I In ARM/Thumb-2 state a constant that can be used as an immediate value in a Data Processing instruction. In Thumb-1 state a constant in the range 0 to 255.
    J In ARM/Thumb-2 state a constant in the range -4095 to 4095. In Thumb-1 state a constant in the range -255 to -1.
    K In ARM/Thumb-2 state a constant that satisfies the I constraint if inverted. In Thumb-1 state a constant that satisfies the I constraint multiplied by any power of 2.
    L In ARM/Thumb-2 state a constant that satisfies the I constraint if negated. In Thumb-1 state a constant in the range -7 to 7.
    M In Thumb-1 state a constant that is a multiple of 4 in the range 0 to 1020.
    N Thumb-1 state a constant in the range 0 to 31.
    O In Thumb-1 state a constant that is a multiple of 4 in the range -508 to 508.
    Pa In Thumb-1 state a constant in the range -510 to +510
    Pb In Thumb-1 state a constant in the range -262 to +262
    Ps In Thumb-2 state a constant in the range -255 to +255
    Pt In Thumb-2 state a constant in the range -7 to +7
    G In ARM/Thumb-2 state a valid FPA immediate constant.
    H In ARM/Thumb-2 state a valid FPA immediate constant when negated.
    Da In ARM/Thumb-2 state a const_int, const_double or const_vector that can be generated with two Data Processing insns.
    Db In ARM/Thumb-2 state a const_int, const_double or const_vector that can be generated with three Data Processing insns.
    Dc In ARM/Thumb-2 state a const_int, const_double or const_vector that can be generated with four Data Processing insns. This pattern is disabled if optimizing for space or when we have load-delay slots to fill.
    Dn In ARM/Thumb-2 state a const_vector which can be loaded with a Neon vmov immediate instruction.
    Dl In ARM/Thumb-2 state a const_vector which can be used with a Neon vorr or vbic instruction.
    DL In ARM/Thumb-2 state a const_vector which can be used with a Neon vorn or vand instruction.
    Dv In ARM/Thumb-2 state a const_double which can be used with a VFP fconsts instruction.
    Dy In ARM/Thumb-2 state a const_double which can be used with a VFP fconstd instruction.
    Ut In ARM/Thumb-2 state an address valid for loading/storing opaque structure types wider than TImode.
    Uv In ARM/Thumb-2 state a valid VFP load/store address.
    Uy In ARM/Thumb-2 state a valid iWMMX load/store address.
    Un In ARM/Thumb-2 state a valid address for Neon doubleword vector load/store instructions.
    Um In ARM/Thumb-2 state a valid address for Neon element and structure load/store instructions.
    Us In ARM/Thumb-2 state a valid address for non-offset loads/stores of quad-word values in four ARM registers.
    Uq In ARM state an address valid in ldrsb instructions.
    Q In ARM/Thumb-2 state an address that is a single base register.

    Operand codes

    Within the text of an inline asm block, operands are referenced as %0, %1 etc. Register operands are printed as rN, memory operands as [rN, #offset], and so forth. In some situations, for example with operands occupying multiple registers, more detailed control of the output may be required, and once again, an undocumented feature comes to our rescue.

    Special code letters inserted between the % and the operand number alter the output from the default for each type of operand. The table below lists the more useful ones.

    c An integer or symbol address without a preceding # sign
    B Bitwise inverse of integer or symbol without a preceding #
    L The low 16 bits of an immediate constant
    m The base register of a memory operand
    M A register range suitable for LDM/STM
    H The highest-numbered register of a pair
    Q The least significant register of a pair
    R The most significant register of a pair
    P A double-precision VFP register
    p The high single-precision register of a VFP double-precision register
    q A NEON quad register
    e The low doubleword register of a NEON quad register
    f The high doubleword register of a NEON quad register
    h A range of VFP/NEON registers suitable for VLD1/VST1
    A A memory operand for a VLD1/VST1 instruction
    y S register as indexed D register, e.g. s5 becomes d2[1]