Bruno Ferres

Frédéric Olivier Muller

Frédéric Rousseau

Rousseau Chisel Usecase

Chisel Usecase: Designing General Matrix Multiply for FPGA

Keywords: Chisel, FPGA, GEMM, Methodology

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

As FPGA usage for application acceleration increases in the industry, notably in the domain of Cloud computing [START_REF] Caulfield | A Cloud-Scale Acceleration Architecture[END_REF] [START_REF] Ouyang | SDA: Softwaredefined accelerator for large-scale DNN systems[END_REF], RTL based design methodology -i.e. the standard methodology in industry -can be questionned on criteria such as efficiency, reusability, or accessibility.

The last decade has witnessed the appearance of new technologies easing hardware development, with higher levels of abstraction. The most known of those are High Level Synthesis, which goal is to bring the power of dedicated hardware acceleration to hardware-agnostic software developers. Nevertheless, HLS still has to cope with some flaws, including fine tuning on the code to infer efficient hardware, as well as lack of control on the generated hardware.

On the other hand, more hardware aware iniatives have appeared in the scientific community, like Chisel [START_REF] Bachrach | Chisel: constructing hardware in a Scala embedded language[END_REF]. Chisel (Constructing Hardware In a Scala Embedded Language) is an open source Scala based language dedicated to hardware generation, with high level programming functionalities, and an ever growing community. It can be used to generate Verilog code, insuring compatibilty with the standard flow, and ease design reutilisation thanks to the software constructs it embeds.

Google used Chisel for the design of their Edge TPU [START_REF] Alon | Invited: Open-Source EDA Tools and IP, A View from the Trenches[END_REF], and two RISC-V implementations have been proposed -Rocket Chip and BOOM -showing that the initiative can be integrated in both industrial and academic worlds. Works like [START_REF] Koenig | A Hardware Accelerator for Computing an Exact Dot Product[END_REF] showed that Chisel can be used to explore different implementations of a circuit, here designed for BLAS (Basic Linear Algebra Subroutines) dot product acceleration.

BLAS introduces a set of linear algebra operations that can be used to evaluate implementation performances on this kind of applications [START_REF] Dongarra | A set of level 3 basic linear algebra subprograms[END_REF]. In particular, it includes the General Matrix Multiply (GEMM) algorithm, a highly indicative application for all algebra computations [START_REF] Pedram | A high-performance, low-power linear algebra core[END_REF], which has been deployed to various platforms before, including FPGA [START_REF] De Matteis | FBLAS: Streaming Linear Algebra on FPGA[END_REF] and GPU [START_REF] Garg | A Portable and High-Performance General Matrix-Multiply (GEMM) Library for GPUs and Single-Chip CPU/GPU Systems[END_REF]. GEMM is usually implemented with variations on the type and length of elements used, SGEMM and DGEMM respectively representing simple and double precision floating points, and other implementations targeting fixed point or integer representations.

This paper introduces a methodology for designing, testing and evaluating an application using Chisel, demonstrating its usage on a GEMM case study. Through this usecase, we show that our methodology allows to deeply control the generated hardware, producing accelerators that are not only comparable to the state of the art, but behave as they are designed to. Resource usage can be fully explained by targeted architecture, as no hardware inference has to be made by the compile pass. On the other hand, this flow allows to easily explore multiple architectures, studying the influence of application and target parameters on the produced designs. It enables changing the type and width of the operands, the capacities of communication or even the dimension of the applicative problem. Section 2 introduces the aim and steps of this methodology, while section 3 demonstrates its usage on a GEMM usecase. Section 4 presents the results of this usecase, as well as the functionalities of our tool flow, and section 5 discusses the contribution of our work.

High level methodology

To efficiently implement an application, one must take into account the application temporal behavior, as well as the environment target, in order to take advantage of the available resources. For example, targeting a FPGA requires the developer to consider the different kind of memory and computational resources embedded, the communication links, the reachable clock frequency, and other factors that will impact the choices of implementations.

On the other hand, to maximize the reusability of the developed design, you need to think about genericity before implementation, so generated designs can be adapted to new implementation constraints if needed, including target change.

This section describes the chosen technology for our methodology, as well as its steps, from application and target specifities to implementation.

High level description

To improve productivity when it comes to hardware development, developers must be able to define architectures in a generic way, to be able to generate different implementations by varying application specific and non-specific parameters (e.g. I/O size, element type, ...). Such generic implementation would allow to explore different trade-offs, and be able to suggest the most efficient architecture, the most performant or the less costly, for example.

To do so, we choose to use Chisel in our architecture generator flow, since the language offers higher level generic features, compared to the ones proposed by standard RTL languages (such as Verilog, SystemVerilog or VHDL).

Replacing RTL Although Chisel remains a RTL language, we identified three main features of it that can ease the developement of such generator, compared to standard RTL languages such as VHDL or Verilog.

Table 1 compares Chisel and standard RTL features when it comes to parametrized design generation. We can notice that the third feature -high level generation -is also available in both Verilog and VHDL languages, but that the two other features require external tools and complex constructs to be included in these languages. HLS vs Chisel Choosing Chisel over standard RTL languages for design implementation can thus be motivated by a need for higher abstraction level when it comes to hardware development. However, as stated in introduction, High Level Synthesis technology aims at easing accelerators development by synthetyzing algorithmic description to hardware circuit, meaning that it is a good candidate for increasing developers productivity, as well as easing design reusability. Yet, HLS requires, by design, inference from the compilation tool to generate functioning circuits. This means that one can not control easily the hardware generated, which allows software or application developers to use it with no hardware knowledge, but also means that experienced hardware developers can not directly control the generation flow, and can only try to tune the code and the tool to orientate the compilation toward an acceptable architecture.

Zhao et al. [START_REF] Zhao | Using Vivado-HLS for Structural Design: a NoC Case Study[END_REF] state that HLS generated circuits can be compared to RTL written ones, but only with hard code discipline and fine pragma tuning. It can be complex, and might need to be repeted each time you change the generation constraints, meaning that evolving your design can be time consuming.

Since we aim at reusing code and generating multiple accelerators with different constraints, we chose to use the open-source, highly promising technology of Chisel.

From application to architecture

Using a language like Chisel, we propose a more generic development methodology, relying on hardware knowledge about the chosen target family (e.g. does it propose external memory, which kind of computing units are available, ...), and an architectural study of the application. This methodology does not require specific adjustment of code for a particular target board, but rather a generic design for a class of target, making it more target-agnostic. Figure 1 presents this methodology. As can be observed, we consider three entry points when implementing an application to dedicated hardware: obviously, the target and the application itself, but also the target class, which is defined by generic characteristics we aim at using for this specific application (e.g. memory type and capacity, available operators, communication links, ...).

To use this methodology, one has to distinguish two main steps: implementing a generic design of the application using Chisel, and instanciating this design with parameter variations for a particular target. Doing this, the generic design -that uses some particular constructs, like embedded memory or DSP unitscan be used to implement the application on various boards which includes those constructs. The methodology needs 3 main manual steps:

-Analysis of both application and target class, to define the parameters used for circuit parametrization -Implementation of a generic architecture using Chisel -Analysis of the target board, to define the parameter sets used for architecture instanciation, with respect to the target characteristics (e.g. the band width, the problem dimension, ...)

Elaboration and logic synthesis steps are done automatically, for each parameter set defined in this third step.

Methodology Usecase

In order to demonstrate both usability and advantages of the proposed methodology, we defined and implemented a generic GEMM architecture. It illustrates how preliminary reflexions on application and target class -communication model, available memory and computing units, temporal behavior, ... -can, with the help of Chisel, improve both productivity and code reusability with generic designs. GEMM The General Matrix Multiply (GEMM) algorithm is a generalization of the matrix product algorithm. Let A, B and C be square matrices of dimension n × n (M n ), and (α, β) ∈ N N N 2 . GEMM is defined as the following f function:

f : N N N × N N N × M n × M n × M n → M n (α, β, A, B, C) → α • A × B + β • C (1)
Target characteristics For this implementation, we assume that the developer is targeting Xilinx FPGA technology. More precisely, this means that the developed design can take advantage of embedded operators for multiplication (DSP block ) and only embedded memory (Block RAMs).

Application study GEMM computation complexity is O(n 3 ) while its communication complexity is only O(n 2 ). Since, in a generic context, matrices need to be sent to the design anyway, we can assume that O(n 2 ) -i.e. the communication complexity -is a temporal complexity bound.

If one wants to reach this bound, it means that the implemented design needs to be able to compute matrix product in a temporal complexity of n 2 . This defines the architecture parallelism level, as it requires to compute n scalar products (

n k=0 a i,k × b k,j for j ∈ [[0; n -1]]
) in parallel to comply with it. Figure 2 introduces the targeted temporal behavior for the implementation. It has been defined with respect to software considerations, as matrices are not interleaved nor transformed, except for B which has to be transposed for bycolumn access. Matrices are sent by blocks of size b (as defined in section 3).

As one can observe on the figure 2, the input bus utilization is almost optimal (i.e. the input bus is almost used for the whole computation time), as results can be computed on-the-fly while A matrix is being streamed. This way, we can ensure that the induced design will be communication efficient. e the matrix element size (in bits) n the matrix dimension

We assume that a GEMM kernel performs ρ = 2 × n 3 operations [START_REF] Underwood | Chapter 31 -the implications of floating point for fpgas[END_REF]. Let ∆ c be the number of cycles needed to compute the result of the GEMM algorithm -i.e. the delta cycle between sending α coefficient and receiving the last bit of the result matrix. We can state that ∆ c ≥ 3 × n 2 × b e , b e being the number of elements sent per cycle, as three matrices must be sent.

Thus, the theoretical maximum throughput T , in number of operation per second (OPs), is given by

T = ρ × f ∆ c ≤ 2 × n 3 × f 3 × n 2 × b e = 2 3 × f × n × e b (2)
GEMM parametrization As specified in section 2, the developer must think its architecture genericity before starting the implementation, to allow both exploration and design reutilization.

For GEMM application, we decided, after application and target class analysis, to define three parameters according to section 3:

b -bus bandwidth for input/output n -size of matrices type of elements (which bitwidth is defined as e)

Results

To study the usability and performances of our methodology, we implemented it as a tool flow, and used it to analyze and compare multiple GEMM architectures. This way, we can illustrate both hardware controlability and generation abilities of our methodology. We generate 80 different architectures, varying input bandwidth b (64, 128, 256 and 512 bits/cycle), element bitwidth e (4, 8, 16, 32 and 64 bits) and matrix dimension n (64 × 64, 128 × 128, 256 × 256 and 512×512), and we study the impact of those parameters on the performance and resource usage of generated designs. The architectures are generated, simulated and synthesized in less than 24 hours, thanks to our tool flow (see figure 1).

Experimental setup

For the experimentations, we targeted a Xilinx VC709 board which includes Block RAMs and integer DSPs, as specified in section 3. It embeds a xc7vx690 FPGA with 433k LUT6s, 866 FFs, 3600 DSPs and 1470 BRAMs (6.45 MB).

We developed a tool flow implementing the methodology proposed in section 2, based on Chisel (latest 3.2 version) as entry point to generate multiple Verilog designs with respect to the parameters defined in section 3. The flow simulates generated designs behavior using verilator to ensure functionality, comparing it to a software reference defined in Scala. It also uses simulation to extract design latency ∆ c as defined in the temporal behavior model (figure 2). After generation and simulation steps, we use Xilinx vivado (2017.3 version) to synthesize designs and extract performance and resource metrics. For performance evaluation, we use the estimated post-synthesis clock frequency and the simulation latency. We evaluate resource usage (LUT, Flip Flop, DSP and BRAM usage) thanks to post-synthesis resource report. All results presented in this section are given after vivado synthesis step.

Remark: We are only considering designs that can physically fit for this section, implying that tables 2, 3 and figure 3a only include those designs. Figure 3b represents non-fittable designs as hatched.

Control of generated hardware

This section presents our designs achieved performance, demonstrating that this methodology allows to control generated accelerators composition.

GEMM implementation As stated in section 1, GEMM algorithm can be implemented using various types and precision, SGEMM and DGEMM (using respectively IEEE-754 simple and double precision) are the most used version, as it has been widely used for performance comparison.

However, since we are targeting Xilinx FPGAs, which does not include dedicated floating point units, we chose to implement a fixed-point GEMM version here. Since the design generator includes type parameters, one could -with few changes to the control flow -target SGEMM and/or DGEMM variants once he implemented basic floating operations on Xilinx boards, as stated in section 2.1. 2 presents the influence of type precision on achieved throughput for GEMM implementation. For each element bitwidth e, we selected the most performant generated design, i.e. the design that offers the higher throughput, with the generation parameters (b, n) associated. We compared the throughput estimation (based on simulation) with the maximal theoretical throughput as defined in equation ( 2), indicating the functioning frequency of the generated designs in the last column, for information purpose.

Impact of type precision Table

By computing the theoretical differentials between achieved and theoretical throughputs, we can note that generated designs achieve at least 92% of maximal throughput -for the 8 bits version -meaning that the input bus utilization is almost maximal, and that the behavior can be finely controled from architecture design to generation.

We showed that our flow can be used to design, implement and analyze designs with high controlability on generated hardware, and demonstrated it on an analysis of type precision influence on the performances of GEMM implementations.

Element Table 2: Impact of element bitwidth on GEMM throughput.

Architecture exploration: dimensioning the application

We have shown that type precision has a considerable impact on the achievable throughput of generated designs. As type precision also impacts applicative performance metrics a developer can not always act on the type precision, that can be fixed by application specific needs.

In this section, we chose to target 32 bits fixed point GEMM implementation, though it is not comparable to SGEMM subroutine on 32 bits floating points because of the complexity of floating point operations (even with dedicated DSPs), to demonstrate the ability of our methodology to explore multiple parameter sets with no changes to the original Chisel description.

Figures 3a and3b respectively compare generated designs throughput and efficiency for various sizes of input matrices, and various I/O bandwidths. Efficiency e is defined as ρ f ×∆c ×

1 %resource = 2×n 3
f ×∆c× %resource , i.e. perf ormance resource ratio1 , unified with respect to computational complexity specified in section 3. Using a n 3 factor allows to compare solution of different dimensions, since computing GEMM in M n space is equivalent to 8 computations in M n 2 . We can observe that for 32 bits implementations, the most efficient version (figure 3b) is to operate on matrix kernels of size 256 × 256, using 2 × 128 bits/cycle I/O, with an achieved throughput of 224 GOP/s -among the 80 architectures generated. For this design, clock frequency reach 331.4 MHz, the theoretical optimal bit rate is thus 2.8 GB/s. On the other hand, figure 3a shows that the most performant design is to operate on kernels of size 128 × 128, with 2 × 128 bits/cycle I/O, achieving a throughput of 226 GOP/s.

By generating and comparing those GEMM architectures, we showed that our generation flow allows to determine which architecture is the most performant or the most efficient, with respect to constraints one might have on integration. fBLAS [START_REF] De Matteis | FBLAS: Streaming Linear Algebra on FPGA[END_REF] implements both SGEMM and DGEMM variants, using HLS on two Intel Altera FPGAs. It is important to note that Intel Altera FPGAs embed dedicated floating point DSP, while Xilinx FPGAs does not include any floating point dedicated units.

Garg et al. [START_REF] Garg | A Portable and High-Performance General Matrix-Multiply (GEMM) Library for GPUs and Single-Chip CPU/GPU Systems[END_REF] propose hybrid CPU-GPU SGEMM and DGEMM implementations based on Intel Ivy Bridge and AMD Richland platforms.

Our custom solutions present the most performant designs we generated for precision on 16, 32 and 64 bits. As VC709 target does not include floating point units, SGEMM and DGEMM will be compared respectively to fixed point solutions on 32 and 64 bits. We also choose to study results on 16 bits fixed point, since applicative accuracy needs might be compatible with lower precision type.

For each solution in table 3, we can observe different implementations -variation of platform, target and type precision -and the associated achieved performances, given as implementation throughput. We can see that both our 32 and 64 bits custom versions are comparable in term of performance with the hybrid solution of [START_REF] Garg | A Portable and High-Performance General Matrix-Multiply (GEMM) Library for GPUs and Single-Chip CPU/GPU Systems[END_REF], and with the fBLAS solution on Intel Altera Arria 10, if a fixed point solution is acceptable for a given application needs. Stratix 10 board being way wider than a VC709, we can not compare solutions fairly. Table 3: Throughput for GEMM implementations on different platforms

Analysis and contribution

With those experiments, we show that with a tool flow based on Chisel and a particular methodology, we are able to easily define a generic GEMM accelerator kernel, which presents multiple advantages when compared to HLS generated or RTL written ones. We demonstrate that using Chisel allows a high controlability on generated hardware, and that, with a sufficient knowledge on hardware development, one can easily describe a precise architecture, with no worry on which inferences the tool flow could make when generating the circuit.

We also show that using generic architectures can be useful when it comes to evaluation of parameters influences, and that using higher level of abstractions, hardware developers can easily compare architectural trade-offs for a given application, in order to take the best of the available resources.

Conclusion

In this paper, we introduce a design methodology associated to a toolflow that can be used to implement computation kernels on FPGAs with higher abstraction level.

We demonstrate the functionality of this new tool through a use case on GEMM algorithm, which is highly representative for all algebra computations. We show that we can define generic architecture descriptions with parametrization, thanks to Chisel, allowing architecture generation and comparison.

Generated GEMM implementations performances are comparable to designs generated with HLS methodology, as well as CPU and/or GPU solutions proposed in the litterature.

We now aim at reusing developed GEMM kernels to implement efficient, configurable and highly generic CNNs using the presented framework. We also want to implement other computation kernels to study influence of applications and target environments on resource usage and achieved performances.

Fig. 1 :

 1 Fig. 1: Proposed methodology for design development. Dashed rectangles presents an example of application to the GEMM usecase.

Fig. 2 :

 2 Fig. 2: Targeted chronogram for GEMM efficient implementation (Eq. 1) Application-specific parameters With such temporal behavior, we can compute the maximum throughput of a design implementing it, as a function of b the input (or output) bandwidth (in bits/cycle) f the clock frequency (in Hz)

Fig. 3 :

 3 Fig. 3: Metric comparison on 32 bits GEMM versions 4.4 Existing solutions GEMM implementations have been widely used to compare platform performances, as well as implementation choices. We propose to compare our implementations to GEMM instances on various platforms.

Table 1 :

 1 Feature comparison between Chisel and standard RTL languages for design generation

	Chisel programming feature	RTL equivalent (Verilog and/or VHDL)
		Black boxing type specific operators +
	Type genericity	string replacement in RTL code (i.e. using sed)
		N.B. generic can be used for width genericity only
	Procedural programming	Multiple version of the same code to change functionalities and/or behavior
	High level generation	for or generate loops if statements

Resource metric is defined as the maximum usage percentage for the 4 considered resources: LUTs, Flip Flops, BRAMs and DSPs.

Fixed point precision is used instead of floating point, as stated earlier.


Michaël Flacandji

Mariana Vlad

THE RELATIONSHIP BETWEEN RETAILER APP USE, PERCEIVED SHOPPING VALUE AND LOYALTY: THE MODERATING ROLE OF DEAL-PRONENESS

Keywords: Deal proneness, retailer app, app use, loyalty to the retailer, perceived shopping value, omnichannel

The relationship between retailer app use, perceived shopping value and loyalty: the moderating role of deal proneness

Michaël Flacandji, Mariana Vlad

Introduction

Consumers increasingly use their mobile phones while shopping (Grewal et al., 2018;Fuentes et al., 2017) and retailers need to adapt accordingly [START_REF] Holmes | Mobile shopping behaviour: insights into attitudes, shopping process involvement and location[END_REF] as mobile device technology transforms the retail shopping experience [START_REF] Rippé | Under the sway of a mobile device during an in-store shopping experience[END_REF]. Customers may use their mobiles in stores for several reasons (price comparisons, payment, etc.). Some uses, such as the Yuka app, are beyond a firm's control [START_REF] Becker | Customer experience: fundamental premises and implications for research[END_REF]. Conversely, in response to the increasingly competitive environment, retailers are developing their own apps -which can be viewed as a firm-controlled touchpoint.

Retailer apps provide customers with numerous services to enhance their shopping experience, enabling them to obtain product information, compare products, buy, share information on social networks, redeem coupons and locate stores, among other things [START_REF] Molinillo | The impact of affective and cognitive app experiences on loyalty towards retailers[END_REF]. Mobile app adoption is also changing the way customers interact with retailers [START_REF] Kim | The effects of adopting and using a brand's mobile application on customers' subsequent purchase behavior[END_REF][START_REF] Mclean | Examining consumer attitudes towards retailers' m-commerce mobile applications -an initial adoption vs. continuous use perspective[END_REF]. App adopters buy more items, more frequently, and spend more than non-adopters in the post app introduction period [START_REF] Narang | Mobile app introduction and online and offline purchases and product returns[END_REF]. Despite all the opportunities offered by retailers' apps, only 20% of French customers use such apps when grocery shopping, even though all the main retailers offer one (Nielsen study, 2019 1 ). While the penetration rate of shopping apps varies across countries in the same way as digital use as a whole (Hootsuite, 2021 2 ), more research is needed to help retailers exploit the potential of apps as a sales and engagement channel [START_REF] Molinillo | The impact of affective and cognitive app experiences on loyalty towards retailers[END_REF]. This is all the more necessary for at least two reasons. Firstly, the role of mobile phones strengthened with the pandemic when self-service technologies were unavailable for security reasons.

1 https://www.nielsen.com/fr/fr/insights/article/2019/apps-get-settled-in-everyday-races/ 2 https://wearesocial.com/digital-2021 Secondly, the introduction of 5G technology should offer new potentialities for retailers to enrich app use (e.g., augmented reality).

To date, mobile app studies have mainly focused on services, payment and banking, investigating topics related to app adoption [START_REF] Japutra | Influence of customer application experience and value in use on loyalty toward retailers[END_REF][START_REF] Newman | Bricks or clicks? Understanding consumer usage of retail mobile apps[END_REF], purchase behavior [START_REF] Kim | The effects of adopting and using a brand's mobile application on customers' subsequent purchase behavior[END_REF][START_REF] Liu | The Impact of mobile app adoption on cross-buying: The moderating roles of product category characteristics and adoption timing[END_REF][START_REF] Wang | On the go: how mobile shopping affects customer purchase bahavior[END_REF] and satisfaction with apps [START_REF] Molinillo | The impact of affective and cognitive app experiences on loyalty towards retailers[END_REF][START_REF] Molinillo | The impact of affective and cognitive app experiences on loyalty towards retailers[END_REF][START_REF] Iyer | Investigating the effectiveness of retailers' mobile applications in determining customer satisfaction and repatronage intentions? A congruency perspective[END_REF]. While a few studies have examined retailers' apps [START_REF] Hew | Hall of fame for mobile commerce and its applications: a bibliometric evaluation of a decade and a half (2000-2015)[END_REF], little attention has been paid to how retailer app use influences customer-retailer relations, especially loyalty towards the retailer. Some studies have noted the interest of investigating this process, especially the impact of apps on customer loyalty, with satisfaction used as a mediating variable [START_REF] Al-Nabhani | Examining consumers' continuous usage of multichannel retailers' mobile applications[END_REF][START_REF] Iyer | Investigating the effectiveness of retailers' mobile applications in determining customer satisfaction and repatronage intentions? A congruency perspective[END_REF][START_REF] Molinillo | The impact of affective and cognitive app experiences on loyalty towards retailers[END_REF][START_REF] Japutra | Influence of customer application experience and value in use on loyalty toward retailers[END_REF].

In the present study, we examine shopping value as a mediating variable between app use and loyalty towards the retailer since perceived value is considered a better predictor of loyalty than satisfaction [START_REF] James | Is customer satisfaction really a catch-all? The discrepancy between financial performance and survey results[END_REF][START_REF] Jones | Hedonic and utilitarian shopping value: investigating differential effects on retail outcomes[END_REF][START_REF] Mencarelli | Influences of the perceived value on actual repurchasing behavior: Empirical exploration in a retailing context[END_REF][START_REF] Overby | The effects of utilitarian and hedonic online shopping value on consumer preference and intentions[END_REF]. To our knowledge, no previous studies on retailer apps have examined shopping value as an antecedent of loyalty, despite [START_REF] Voropanova | Conceptualizing smart shopping with a smartphone: implications of the use of mobile devices for shopping productivity and value[END_REF] call for more research to examine the impact of retailer app use on key variables for retailers such as shopping value and loyalty. The positive relationship between perceived value and loyalty was first empirically supported in traditional brick-and-mortar retail settings where the main focus was on store loyalty (e.g., [START_REF] Adapa | Examining the antecedents and consequences of perceived shopping value through smart retail technology[END_REF]Diallo et al., 2015;[START_REF] Mencarelli | Influences of the perceived value on actual repurchasing behavior: Empirical exploration in a retailing context[END_REF]. Other studies, such as [START_REF] Parasuraman | E-S-QUAL: A multiple-item scale for assessing electronic service quality[END_REF], argue that the perceived value of an internet retailer has a significant and positive impact on customer loyalty intention towards the retailer in question. While [START_REF] Bui | E-tail emotion regulation: examining online hedonic product purchases[END_REF] show that hedonic shopping value influences repeat purchase intention for online music, more research is needed in the omnichannel area to capture the impact of perceived value on loyalty towards retailers. This would help retailers to provide their customers with a seamless shopping experience by allowing them to shape their own consumption experience [START_REF] Le | A moderated mediating mechanism of omnichannel customer experiences[END_REF].

To address these research gaps, the present study aims to: 1) investigate how in-store retailer app use affects loyalty to retailers directly or indirectly via the mediation of perceived shopping value and 2) investigate whether the impact of retail app use on perceived shopping value is greater for deal-prone consumers. The context of hypermarket and supermarket grocery shopping experiences provides an interesting setting in which to examine these relations as the sector is highly competitive and grocery shopping is often perceived as a chore for consumers [START_REF] Smith | Grocery shopping behavior A comparison of involved and uninvolved consumers[END_REF]. In this context consumers have varying price sensitivity and deals play a major role in creating value [START_REF] Shukla | Effects of consumer psychographics and store characteristics in influencing shopping value and store switching[END_REF][START_REF] Kwon | Heterogeneity of deal proneness: Value-mining, pricemining, and encounters[END_REF]. Pursuant to [START_REF] Oh | An exploratory study of sales promotions for multichannel holiday shopping[END_REF]'s study on consumer responses to price promotions in stores and on internet channels, it is important to understand whether consumers respond differently in an omnichannel context in which they can use their mobile in-store.

Overall, this study contributes to our understanding of the impact of apps on retailercustomer relations, potentially helping to guide businesses in developing and implementing appropriate app-related strategies in the post-Covid area. It extends the literature pertaining to perceived value as a means to predict loyalty towards the retailer and underscores the importance of the simultaneous consideration of hedonic and utilitarian value in consumption.

We also highlight the role played by deal proneness. Understanding value creation at the intersection of the physical store and retailer apps, together with its impact on loyalty, is crucial to understanding and adapting to technology-driven customers in the omnichannel context.

Conceptual framework

Customer loyalty and mobile apps

Customer loyalty is a crucial issue for retailers. Loyalty towards retailers reflects customers' willingness to consider the retailer as their first choice, give the retailer positive reviews and recommend the retailer to other people (Zeithaml et al., 1996). Despite numerous studies, retailers need more insights into loyalty antecedents and the building mechanisms, especially in the omnichannel context (Molinillo et al., 2019;[START_REF] Rokonuzzaman | An investigation into the link between product involvement and store loyalty: the roles of shopping value goals and information search as the mediating factors[END_REF].

A key feature of retailer apps is their capacity to provide anytime anyway information [START_REF] Narang | Mobile app introduction and online and offline purchases and product returns[END_REF]. Information searches develop consumer knowledge and engagement and reduce perceived risk, thereby improving loyalty intentions [START_REF] Rokonuzzaman | An investigation into the link between product involvement and store loyalty: the roles of shopping value goals and information search as the mediating factors[END_REF]. Mobile use during in-store shopping activity increases customer satisfaction (Grewal et al., 2018) and also has a positive and direct impact on store loyalty (Collin Lachaud and Diallo, 2021).

At the post-purchase stage, mobile apps offer customers more flexibility and control of retailer rewards programs and can have a positive impact on customer loyalty [START_REF] Roggeveen | Customer-interfacing retail technologies in 2020 and beyond: an integrative framework and research directions[END_REF]. Mobile apps can help consumers to take control of their omnichannel shopping experience (de Haan et al., 2018) and make it frictionless, with a positive impact on loyalty in the context of online grocery shopping [START_REF] Singh | Why do online grocery shoppers switch or stay? An exploratory analysis of consumers' response to online grocery shopping experience[END_REF]. In view of previous studies, we can assume that: H1: Retailer app use during the shopping experience (versus no use) has a positive effect on customer loyalty intention.

Shopping value and its mediation effect on loyalty

Customer perceived value has its roots in equity theory, which considers that consumers will feel fairly treated if their outcome/input correlates with the service provider's outcome/input (Oliver and De Sarbo, 1988). Perceived value is the result of consumers' overall assessment of what they receive in exchange for what they give, including monetary payment and non-monetary sacrifices [START_REF] Zeithaml | Consumer perceptions of price, quality, and value: A means-end model and synthesis of evidence[END_REF]. Perceived value as a key outcome variable in the general model of consumer experience, called shopping value, results from the interaction between the consumer and the shopping environment [START_REF] Babin | Work and/or fun: measuring hedonic and utilitarian shopping value[END_REF][START_REF] Jones | Hedonic and utilitarian shopping value: investigating differential effects on retail outcomes[END_REF]. The literature often identifies two dimensions of shopping value. The same act of purchase can combine these two dimensions in higher or lower proportions [START_REF] Babin | Work and/or fun: measuring hedonic and utilitarian shopping value[END_REF]. Utilitarian shopping value involves fulfilment of the instrumental expectations consumers may have for a product or service. It can be associated with rational motives related to time, place and possession. As a result, it is often linked to shopping efficiency, and utilitarian shoppers are viewed as rational problem solvers and value seekers [START_REF] Parsad | Do promotion and prevention focus influence impulse buying: The role of mood regulation, shopping values, and impulse buying tendency[END_REF]. [START_REF] Holbrook | The experiential aspects of consumption: Consumer fantasies, feelings, and fun[END_REF] raised the issue of human needs as variety, novelty and surprise factors. Hedonic shopping helps to fulfill fantasies and provides a sense of fun during the purchase process rather than simply buying for its own sake [START_REF] Holbrook | The experiential aspects of consumption: Consumer fantasies, feelings, and fun[END_REF]. Hedonic value is therefore more subjective and personal. Shopping value is essential in explaining loyalty behavior [START_REF] Mencarelli | Influences of the perceived value on actual repurchasing behavior: Empirical exploration in a retailing context[END_REF][START_REF] Parasuraman | The impact of technology on the quality-valueloyalty chain: A research agenda[END_REF]. This positive relationship has frequently been empirically supported in traditional brick-and-mortar retail settings (e.g., [START_REF] Jones | Hedonic and utilitarian shopping value: investigating differential effects on retail outcomes[END_REF]Diallo et al., 2015;[START_REF] Mencarelli | Influences of the perceived value on actual repurchasing behavior: Empirical exploration in a retailing context[END_REF][START_REF] Vieira | A meta-analytic review of hedonic and utilitarian shopping values[END_REF].

Smartphones offer consumers both utilitarian and hedonic benefits (Ha and Park, 2013).

In the retailing context, [START_REF] Voropanova | Conceptualizing smart shopping with a smartphone: implications of the use of mobile devices for shopping productivity and value[END_REF] suggests that the use of a mobile during shopping improves aspects of shopping productivity (time/effort savings, money savings, right purchase, and emotional benefits from shopping), which in turn lead to higher shopping value. Molinillo et al. (2019) and Hamouda (2021) conceptualize the consumer app experience around two dimensions (i.e., cognitive and affective). As some studies note that customer experience overlaps with outcome variables such as value [START_REF] Becker | Customer experience: fundamental premises and implications for research[END_REF], we consider that retailer app use can improve utilitarian and hedonic shopping value. In the context of mobile apps, [START_REF] Picot-Coupey | Still work and/or fun? Corroboration of the hedonic and utilitarian shopping value scale[END_REF] suggest that despite changes in purchasing behavior, the search for utilitarian and hedonic value in consumer experiences persists.

Collin-Lachaud and Diallo (2021) investigate the relationship between in-store smartphone use, store value and store loyalty, arguing that this effect is significantly mediated by the store's hedonic value dimension, but not by its utilitarian value. [START_REF] Van Heerde | Engaging the unengaged customer: the value of a retailer mobile app[END_REF] confirm the utilitarian value of retailer apps and their role as a segmentation strategy to enhance customer engagement. As retailer apps differ from other apps due to their firm-controlled touchpoint, we can expect both dimensions of shopping value to mediate the relationship between retailer app use and retailer loyalty. In the case of smart retail technologies, [START_REF] Adapa | Examining the antecedents and consequences of perceived shopping value through smart retail technology[END_REF] argue that both utilitarian and hedonic benefits drive consumers towards shopping activities and that perceived shopping value has a positive influence on retail store loyalty. We thus hypothesize that: H2. Retailer app use during the shopping experience has a positive effect on customer loyalty intention through the mediation of perceived utilitarian value.

H3. Retailer app use during the shopping experience has a positive effect on customer loyalty

intention through the mediation of perceived hedonic value.

Deal proneness

The omnichannel environment leads to channel proliferation for promotions. The grocery industry uses promotions extensively. Apps are the primary source of deals used by the "mobile-to-store deal shoppers" segment and physical stores are the primary channel for their usage [START_REF] Valentini | Identifying omnichannel deal prone segments, their antecedents, and their consequences[END_REF]. Deal proneness is defined as responsiveness to promotions and deals [START_REF] Blattberg | Sales promotion: concepts, methods, and strategies[END_REF]) such as coupons, rebates and sales [START_REF] Kwon | Heterogeneity of deal proneness: Value-mining, pricemining, and encounters[END_REF].

It is often conceptualized at a deal-specific level (e.g., coupon proneness, flyer proneness) or at a general level [START_REF] Lichtenstein | An examination of deal proneness across sales promotion types: A consumer segmentation perspective[END_REF]. We conceptualize it at a general level since customers who modify their purchase behavior for one type of promotion are likely to do the same for other promotions [START_REF] Price | Couponing behaviors of the market maven: Profile of a super couponer[END_REF].

Deal proneness influences mobile service adoption such as payment [START_REF] Handarkho | Intention to adopt mobile payment in physical stores: individual switching behavior perspective based on Push-Pull-Mooring (PPM) theory[END_REF] and M-coupon applications [START_REF] Liu | Roles of perceived value and individual differences in the acceptance of mobile coupon applications[END_REF]. Consumers with higher coupon proneness appear to be more likely to use M-coupon applications. [START_REF] Shukla | Effects of consumer psychographics and store characteristics in influencing shopping value and store switching[END_REF] examine deal proneness as an antecedent of value creation.

Considering deal proneness at store level to be associated with both exposure and usage of promotions, they show a positive impact of deal proneness on utilitarian value, but no impact on hedonic value. They thus call for further examination of the relation between deal proneness and shopping value. However, while [START_REF] Arnold | Hedonic shopping motivations[END_REF] suggest there is a positive link between price sensitivity and hedonic value, [START_REF] Lee | Shopping value in online auctions: Their antecedents and outcomes[END_REF] point to a negative relationship between the two. Furthermore, [START_REF] Lee | Shopping value in online auctions: Their antecedents and outcomes[END_REF] observe no relationship between price sensitivity and utilitarian value. These contrasting findings argue in favor of new research on the impact of deal proneness on perceived shopping value.

The grocery shopping activity is often described as stressful and unpleasant [START_REF] Smith | Grocery shopping behavior A comparison of involved and uninvolved consumers[END_REF]. As a result, retailer app use may confer both utilitarian and hedonic value on consumers who are sensitive to deals. While deal-prone segments are often described as heavy users, lower income or non-loyal to retailers, [START_REF] Valentini | Identifying omnichannel deal prone segments, their antecedents, and their consequences[END_REF] identify other variables to describe them. For example, customers can be motivated by quality upgrade, exploration or entertainment, which are associated with hedonic motives to a greater extent. This confirms the different levels of hedonic (opportunities for value expression, entertainment and exploration) and utilitarian benefits (savings, better product quality and improved shopping convenience) of promotions identified by Chandon et al. (2000). Many consumers spend considerable time and effort hunting for deals and enjoy getting bargains as well as the price savings [START_REF] Talukdar | An empirical analysis of the extreme cherry picking behavior of consumers in the frequently purchased goods market[END_REF]. This suggests that buying items on promotion has psychological benefits, irrespective of the utilitarian outcomes. Deal proneness can therefore be a moderator of customer experience and its consequences as suggested by [START_REF] Verhoef | Customer experience creation: Determinants, dynamics and management strategies[END_REF]. In their conceptual framework of customer experience management, these authors show that price sensitivity can be a moderator of customer experience and its consequences. We thus hypothesize that:

H4. When customers are sensitive to deals, retail app use significantly increases utilitarian shopping value.

H5. When customers are sensitive to deals, retail app use significantly increases hedonic shopping value.

Our proposed research model is presented in Figure 1 and is tested empirically in the grocery retailing sector where all the main retailers offer such apps to their customers.

[Insert Figure 1 here]

Method

A total of 455 French consumers took part in an online survey enquiring about a recent shopping experience (appendix A). The invitation with the URL link to the online survey was posted on social networks and sent by email to consumers who had previously given their consent to participate in academic research. Following [START_REF] Molinillo | The impact of affective and cognitive app experiences on loyalty towards retailers[END_REF], a snowball sampling procedure was used because it facilitated the distribution of the survey among the target population. The data were collected in January 2021. All participation was voluntary, and no credits were given. We excluded 28 participants for failing the attention checks (e.g., "If you are reading this, please select disagree"), resulting in the final sample made up of 427 participants (68.5% female; 59.6% over 25 years of age). Half of the participants declared that they used the retailer's mobile app when visiting the store. The sample frame primarily included Millennials, consistent with the retail environment where these customers are most likely to use retailer apps [START_REF] Iyer | Investigating the effectiveness of retailers' mobile applications in determining customer satisfaction and repatronage intentions? A congruency perspective[END_REF]. In the same vein, women are over-represented as it is still predominantly women (63%) who manage the shopping activity in France (In-Store Media -Ipsos Barometer, 2019).

We used previously validated scales to measure each investigated construct. The measures are presented in full in appendix B. Utilitarian value was measured with 3 items (α = 0.71) and hedonic value with 8 items (α = 0.94) adapted from Picot-Coupey et al. (2020) who recently validated the seminal scale of [START_REF] Babin | Work and/or fun: measuring hedonic and utilitarian shopping value[END_REF] in the context of mobile apps.

To measure loyalty intention towards the retailer (α = 0.87), we adopted the scale developed by Zeithaml et al. (1996), validated in the French context by [START_REF] Mencarelli | Influences of the perceived value on actual repurchasing behavior: Empirical exploration in a retailing context[END_REF]. Deal proneness (α = 0.86) was measured by the scale of [START_REF] Shukla | Effects of consumer psychographics and store characteristics in influencing shopping value and store switching[END_REF]. All the question items employed seven-point Likert-type scales (1 = strongly disagree, and 7 = strongly agree).

Findings

Preliminary analysis

The two groups (use of retailer's app versus no use of the app during the shopping experience) can be considered as comparable (appendix A) insofar as no difference was observable between them at the 5% threshold in terms of gender (χ2 = 0.31, p = 0.58), age (χ2 = 1.23, p = 0.74), social classification (χ2 = 1.00, p = 0.80), education level (χ2 = 0.13, p = 0.93), retailer (χ2 = 1.46, p = 0.917), store visit frequency (χ2 = 1.34, p = 0.51) and timeframe (χ2 = 32.74, p = 0.25).

The first step was to determine whether app use or not during the shopping experience affected the dependent measures differently. We conducted an independent t-test with the two different scenarios as independent variables and utilitarian value, hedonic value, deal proneness and customer loyalty as dependent variables. The results showed a significant difference for hedonic value, deal proneness and customer loyalty when the customers used the retailer's mobile app during their shopping experience (Table I).

[Insert Table I here] We used a linear regression analysis to investigate whether retailer app use during the shopping experience (versus no use) affected customers' loyalty intention (H1). The antecedent variable (app use) was scored using two values (0 = no use, 1 = use). The model was significant, R = 0.24, R² = 0.06, F(1,425)= 26.30, p < .001, meaning that retailer app use during the shopping experience affected loyalty towards the retailer both directly and positively. Therefore, H1 was supported.

Testing mediation effects

Hypotheses 2 and 3 suggest that retailer app use has a positive effect on customers' loyalty intention through the mediation of perceived utilitarian value (H2) and hedonic value (H3). The bootstrapping method of 5000 resamples using Hayes (2018)'s PROCESS macro for SPSS with Model 4 was employed to investigate the mediation effects. The results show that app use significantly and positively influences both perceived utilitarian value (B = 0.31, t(1, 425) = 2.63, p < 0.01) and perceived hedonic value (B = 0.80, t(1, 425) = 5.77, p < 0.001) (Table II).

The total effect (i.e., the effect of X on Y before including the mediators in the model) of app use on loyalty intentions was significant (B = 0.64, t(1,425) = 5.13, p < 0.001, 95% CI [0.39, 0.88]) (c path). After including the mediators in the model, the direct effect of app use on loyalty intention remains significant (B = 0.31, t(1, 425) = 2.95, p < 0.01, 95% CI [0.10, 0.52]) (c′ path) (see Table II for the respective direct effects and regression coefficients). There is a significant indirect effect of app use on loyalty intention through perceived utilitarian value as CI values do not include zero (B = 0.16, 95% CI [0.03, 0.29]). H2 is therefore supported.

There is also a significant indirect effect of app use on loyalty intention through perceived hedonic value (B = 0.17, 95% CI [0.09, 0.26]). As a result, H3 is supported. Lastly, the indirect effect contrast indicates that the indirect effect through utilitarian value is not significantly different from the indirect effect through hedonic value (B = -0.01, 95% CI [-0.15, 0.15]).

To confirm the robustness of the results, a check incrementally added consumer characteristics as control variables. The results remain significant, with gender not affecting utilitarian value (B = -0.12, t(1, 425) = -0.93, p = 0.35), hedonic value (B = -0.11, t(1, 425) = -0.73, p = 0.46) or loyalty intention (B = 0.09, t(1, 425) = 0.84, p = 0.40). The same lack of effect was observed with age (BUtilitarian = -0.04, t(1, 425) = -0.70, p = 0.48; BHedonic = 0.06, t(1, 425) = 0.80, p = 0.43; BLoyalty = -0.03, t(1, 425) = -0.63, p = 0.53) or social classification (BUtilitarian = 0.02, t(1, 425) = 0.27, p = 0.78; BHedonic = 0.05, t(1, 425) = -0.60, p = 0.55; BLoyalty = -0.01, t(1, 425) = -0.02, p = 0.98).

Testing moderated mediation effects

H4 and H5 respectively suggest that deal proneness moderates the mediation effect of utilitarian and hedonic value between app use during the shopping experience and customer loyalty. The bootstrapping method of 5000 resamples using Hayes (2018)'s PROCESS macro for SPSS with Model 7 was employed to investigate the moderated mediation effect. To probe the moderation of the indirect effect, the bootstrap method provides estimates of the conditional indirect effect of app use (X) on customer loyalty (Y) through utilitarian value (Med1) and hedonic value (Med2) at various values of deal proneness (Mod). First, our analysis reveals a significant interaction effect (B = 0.18, 95% CI [0.01, 0.35], t(1, 425) = 2.11, p = 0.03), indicating that deal proneness moderates the relationship between app use and perceived utilitarian value, which supports H4. Second, the analysis also reveals that deal proneness moderates the relationship between app use and perceived hedonic value, supporting H5 (B = 0.20, 95% CI [0.02, 0.38],

t(1, 425) = 2.13, p = 0.03). To further clarify the two-way interaction, spotlight analyses were conducted at one standard deviation above and below the mean deal proneness score. As

Table III shows, we found a significant indirect effect of app use on customer loyalty through utilitarian value only when the deal proneness level is equal to the mean (B = 0.29, 95% CI [0.05, 0.53], t(1, 425) = 2.38, p = 0.02) or one standard deviation above the mean (B = 0.47, 95% CI [0.16, 0.79], t(1, 425) = 2.94, p = 0.01). We also found that hedonic value is a significant mediator between app use and customer loyalty only when the deal proneness level is equal to the mean (B = 0.57, 95% CI [0.31, 0.83], t(1, 425) = 4.35, p < 0.001) or one standard deviation above the mean (B = 0.77, 95% CI [0.43,1.11], t(1, 425) = 4.46, p < 0.001). In short, we observe an additive effect of app use and deal proneness on both utilitarian and hedonic values as, when customers use a retailer app while shopping, the more they are deal prone, the higher their utilitarian and hedonic values.

[Insert Table II here] [Insert Table III here] consistent with previous studies in both offline and online contexts (Diallo et al., 2015;Mencarelli and Lombard, 2017;[START_REF] Parasuraman | E-S-QUAL: A multiple-item scale for assessing electronic service quality[END_REF] and the work of Collin-Lachaud and Diallo (2021) on app use. Positive emotional responses (fun, pleasure, evasion, excitement) tend to lead to stronger consumer commitment to the retailer [START_REF] Jones | Hedonic and utilitarian shopping value: investigating differential effects on retail outcomes[END_REF]. Thus, this study contributes to our understanding of shopping value in an omnichannel context as it empirically demonstrates the effects of retailer app use on shopping value.

Our results also enrich the literature on deal proneness. Deal proneness plays a central moderating role between retailer app use, shopping value and loyalty. For customers who are most sensitive to promotions, app use can deliver greater utilitarian and hedonic value, which in turn leads to stronger loyalty towards the retailer. These results contradict those of [START_REF] Shukla | Effects of consumer psychographics and store characteristics in influencing shopping value and store switching[END_REF] who only suggest a positive relationship between deal proneness and utilitarian value. The difference can be explained by the fact that these authors were only interested in the store environment and not in retailer app use which can provide customers with both information and entertainment [START_REF] Van Heerde | Engaging the unengaged customer: the value of a retailer mobile app[END_REF].

Practical implications

Our findings offer important insights for managers and retail owners. We show that a retailer app can be a powerful tool in increasing customer loyalty to the retailer both directly and indirectly through the mediation effect of not only utilitarian but also hedonic shopping values, adding the benefits of online shopping to the in-store shopping experience. As a result, retailers should not be afraid to invest in such an app with the objective to improve its penetration rate among their customers. Moreover, it is also important to note that when customers are using the retailer's app, it reduces the likelihood of third-party apps being used, such as Yuka or Open Food Facts which are beyond a firm's control [START_REF] Becker | Customer experience: fundamental premises and implications for research[END_REF]. Finally, this allows retailers to regain control over the in-store shopping experience and is in line with omnichannel literature which suggests that retailers should integrate touchpoints across channels to promote seamless experiences Retailers obviously need to offer apps that meet basic functions such as managing promotional coupons, finding information, organizing shopping lists and allowing customers to have fun and enjoy positive emotions, as previously argued by [START_REF] Iyer | Investigating the effectiveness of retailers' mobile applications in determining customer satisfaction and repatronage intentions? A congruency perspective[END_REF]. As a result, managers should use gamification tactics in order to offer a more immersive shopping experience to app users. Nevertheless, such apps must meet the usability condition (in terms of ease of use, usefulness, personalization and enjoyment) as this plays a critical role in developing customer loyalty [START_REF] Baek | Branded app usability: conceptualization, measurement, and prediction of consumer loyalty[END_REF][START_REF] Mclean | Examining consumer attitudes towards retailers' m-commerce mobile applications -an initial adoption vs. continuous use perspective[END_REF].

Finally, retailers could encourage their customers to use their app by rewarding them via a loyalty program. The strong moderating effect of deal proneness suggests that managers should not consider consumers as a homogeneous group. Both utilitarian and hedonic shopping values of retailer app use are greater for promotion-sensitive customers. This finding invites managers to ensure they understand the personas of their customers well. Van Heerde et al.

(2019) highlighted the role of retailer apps as a segmentation strategy to enhance customer engagement. Exclusive offers could be proposed only on the app to improve the utilitarian value for shoppers looking for easy savings. The app could also improve hedonic value for customers interested in exploration [START_REF] Valentini | Identifying omnichannel deal prone segments, their antecedents, and their consequences[END_REF]. Lastly, much the same as Carrefour's app, which gives its customers the option to choose the product categories where they can get promotions, the present study suggests that retailers can benefit from customizing promotions to match consumers' shopping interests [START_REF] Büttner | Purchase intention through mobile applications: a customer experience lens[END_REF].

Limitations and future research

We believe our study offers useful insights in the field of retailer apps. Nonetheless, some limitations need to be acknowledged that we present in this section along with several suggestions for future research. First, the study was carried out in France. A cross-cultural comparison would therefore be interesting as cultural differences may be significant, both in terms of app use (Hootsuite, 2021) and deal proneness [START_REF] Sharma | Deal proneness and national culture: evidence from the USA, Thailand and Kenya[END_REF]. In addition, we only looked at whether or not customers used the retailer's app during their shopping experience. However, we did not include other uses they might make of it (i.e., consulting the balance of points, benefiting from a promotion, scanning products, consulting a shopping list, paying, playing, etc.). [START_REF] Holmes | Mobile shopping behaviour: insights into attitudes, shopping process involvement and location[END_REF] suggest that use of mobiles may vary at different stages of a consumer's decision-making process. Moreover, not all retailer apps offer the same services. Overall, future research could contribute further by identifying and investigating specific situations in which retailer app use has a positive effect on shopping value. Finally, our perception of shopping value takes the two most frequently used dimensions into account but does not consider the social interactions that take place in an omnichannel context [START_REF] Huré | Understanding omni-channel shopping value: A mixed-method study[END_REF]. A future study could address social value as a third dimension of shopping value. effectiveness of monetary and nonmonetary promotions", European Journal of Marketing,Vol. 49 No. 1/2, pp. 170-189. https://doi.org/10.1108/EJM-01-2012-0044 Chandon, P., Wansink, B. and Laurent, G. (2000), "A benefit congruency framework of sales promotion effectiveness", Journal of Marketing,Vol. 64 No. 4, https://doi.org/10.1509/jmkg.64.

  Fuentes, C., Bäckström, K. and Svingsted, A. (2017), "Smartphones and the reconfiguration of

Discussion and conclusions

Theoretical contributions

The aim of this study was to investigate how retailer app use influences customer loyalty directly and indirectly through the mediation effect of shopping value dimensions. We provide a first contribution to the literature on in-store smartphone use and, more specifically, on existing research both on retailer app use and customer loyalty in an omnichannel retail context (Grewal et al., 2018;[START_REF] Van Heerde | Engaging the unengaged customer: the value of a retailer mobile app[END_REF].

Our findings confirm that retailer app use affects customers' loyalty towards the retailer both directly and indirectly through the mediation of both utilitarian and hedonic values.

The direct effect can be explained by the cognitive benefit of apps evoked by previous authors such as [START_REF] Narang | Mobile app introduction and online and offline purchases and product returns[END_REF] or Fuentes et al. (2017). This extended access to information develops customer knowledge, reduces perceived risk due to information asymmetry and improves engagement towards the retailer [START_REF] Rokonuzzaman | An investigation into the link between product involvement and store loyalty: the roles of shopping value goals and information search as the mediating factors[END_REF].

The findings concerning the indirect effect of app use on loyalty show no significant difference between utilitarian and hedonic values. However, retailer app use has a greater effect on hedonic value, while utilitarian value has a greater effect on customer loyalty. Our findings differ from Collin Lachaud and Diallo (2021) who noted a low mediating impact of utilitarian value on store loyalty. However, they did not investigate the specific case of retailer app use which can offer promotions compared to other apps such as Yuka.

The positive indirect effect between app use and loyalty through hedonic value suggests that customers who enjoy a pleasant shopping experience when using a retailer app are more likely to subsequently stay loyal to the retailer. Contrary to Picot Coupey et al. (2020)'s suggestion that customers do not look for experiential experiences when using mobile apps, we consider in-store retailer app use to have a significant impact on hedonic value. This is