Philippe Négrel
email: p.negrel@brgm.fr

Wolfram Kloppmann
email: w.kloppmann@brgm.fr

Past Hydrological Conditions in a Fluvial Valley: Records from C-O Isotope Signatures of Holocene Sediments in the Loire River (France)

Keywords: River Loire, Holocene, fluvial dynamics, clay-mineralogy, stable isotopes

Multi-proxy indices (grainsize distribution, mineralogy, δ 18 O, δ 13 C) in sediments from a meander infill in the Middle Loire alluvial plain of central France are used to highlight some aspects of the basin evolution over the period from 0 to 10,000 years BP. During the Late-Glacial and Holocene period, the lacustrine carbonate substratum of the alluvial plain was incised by the Loire River, creating numerous oxbows and channels related to meander migration. The channel fills consist mainly of fine clayey sediments deposited during flooding of the river, with an almost total absence of coarse-clastic and sandy material, except in the basal part. The record of isotope ratio variations together with the distribution of particle sizes allows the evolution of the river dynamics to be constrained. The strong decrease of carbonate δ 13 C in the upper part of the record is ascribed to a progressive closure of the meander and, thus, an increasing control of the C-isotope signature by biological activity in a local environment. Variations in carbonate δ 18 O, rather, reflect paleohydrological/paleoclimatic changes at the basin scale. The isotope record of the river dynamics also agrees with the variations in clay mineralogy.

Introduction

Valley floors receive and record part of the erosive flux and act as archives of different types of events at the catchment scale [START_REF] Meade | Movement and storage of sediment in river systems[END_REF][START_REF] Runge | Holocene landscape history and palaeohydrology evidenced by stable carbon isotope (δ 13 C) analysis of alluvial sediments in the Mbari valley (5 • N/23 • E), Central African Republic[END_REF][START_REF] May | Properties of a 5500-year-old flood-plain in the Loup River Basin, Nebraska[END_REF][START_REF] Dhivert | Influence of fluvial environments on sediment archiving processes and temporal pollutant dynamics (Upper Loire River, France)[END_REF]. Lithology, relief, climate and human history [START_REF] Meade | Movement and storage of sediment in rivers of the United States and Canada[END_REF] are the factors that influence erosion rates and catchment input. The composition of sediments in rivers is used for interpreting continental erosion [START_REF] Gaillardet | Geochemistry of large river suspended sediments: Silicate weathering or recycling tracer? Geochim[END_REF]. Additionally, human activities can profoundly modify the sediment yield [START_REF] Meade | Movement and storage of sediment in rivers of the United States and Canada[END_REF]. Surface streams transport the chemical and mechanical weathering products as sediments, and about 90% of this load is stored in the alluvium for long-terms periods of up to 1000 years [START_REF] Dhivert | Influence of fluvial environments on sediment archiving processes and temporal pollutant dynamics (Upper Loire River, France)[END_REF]. Texture, sedimentary structure and geometry help distinguishing a wide variety of facies and their associations in aggradational sequences. These record the temporal evolution of fluvial, lacustrine and/or palustrine environments that result from aggradation, progradation, retrogradation and lateral-migration processes [START_REF] Meade | Movement and storage of sediment in river systems[END_REF][START_REF] Benito | Palaeoflood record of the Tagus River (Central Spain) during the Late Pleistocene and Holocene[END_REF].

The present-day mechanisms of trace-elements transfer in the Loire drainage basin (biologically induced calcite and Fe-Mn hydroxides precipitation), were unravelled [START_REF] Négrel | Changes in chemical and 87 Sr/ 86 Sr signature distribution patterns of suspended matter and bed sediments in the upper Loire River basin (France)[END_REF][START_REF] Négrel | The labile fraction of suspended matter in the Loire River (France): Multi-element chemistry and isotopic (Rb-Sr and C-O) systematics[END_REF][START_REF] Grosbois | An overview of dissolved and suspended matter fluxes in the Loire River basin: Natural and anthropogenic inputs[END_REF][START_REF] Négrel | Investigating the sources of the labile fraction in sediments from silicate-drained rocks using trace elements, and strontium and lead isotopes[END_REF] and the evolution of the Middle Loire basin was elucidated [START_REF] Garcin | Géométrie et âge des alluvions du lit majeur de la Loire moyenne, exemple du val d'Avaray (Loir-et-Cher, France)[END_REF][START_REF] Négrel | Strontium isotopic record of signatures of Holocene fluvial sediments in the Loire valley, France[END_REF][START_REF] Négrel | Lead isotope signatures of Holocene fluvial sediments from the Loire River valley[END_REF], better constraining the river dynamics. In this study, we present δ 18 O and δ 13 C data on carbonates, and granulometric and mineralogical proxy indices of the Holocene Loire River dynamics in sediments from a channel infill in the middle Loire alluvial plain. These data highlight some aspects of the basin evolution over the past 10,000 years. Classically, the stable O-and C-isotope ratio variations associated with particle-size distribution patterns allow the evolution of paleo-river or -lake dynamics to be constrained [START_REF] Fontes | Holocene environmental changes in Lake Bangong basin (Western Tibet). Part 1: Chronology and stable isotopes of carbonates of a Holocene lacustrine core[END_REF][START_REF] Makhnach | Stable oxygen and carbon isotopes in Late Glacial-Holocene freshwater carbonates from Belarus and their palaeoclimatic implications[END_REF][START_REF] Garzanti | Provenance versus weathering control on the composition of tropical river mud (southern Africa)[END_REF]. Isotope tracers establish the links between external drivers (climatic and tectonic evolution, human impact) and river response [START_REF] Mayer | A 15,000-year stable isotope record from sediments of lake Steisslingen, Southwest Germany[END_REF][START_REF] Lojen | C and O stable isotope variability in recent freshwater carbonates (River Krha, Croatia)[END_REF][START_REF] Schulte | Applications of stable water and carbon isotopes in watershed research: Weathering, carbon cycling, and water balances[END_REF][START_REF] Parrish | Stable and clumped isotopes in desert carbonate spring and lake deposits reveal palaeohydrology: A case study of the Lower Jurassic Navajo Sandstone, south-western USA[END_REF], as, due to low burial depths, diagenesis will only slightly alter the signals in river or lake sediments, contrary to many marine environments [START_REF] Reis | Evaluating the effects of diagenesis on the δ 13 C and δ 18 O compositions of carbonates in a mud-rich depositional environment: A case study from the Midland Basin, USA[END_REF]. Recently, it was demonstrated that carbonate O-and C isotopes from lake sediments or carbonate concretions are in some cases favourable paleo-flood proxies [START_REF] Kämpf | Stable oxygen and carbon isotopes of carbonates in lake sediments as a paleoflood proxy[END_REF] or a climatic record for sub-recent times [START_REF] Benjelloun | Geochemical study of carbonate concretions from the aqueduct of Nîmes (southern France): A climatic record for the first centuries AD?[END_REF].

Materials and Methods

Site Description

The Loire river (117,800 km 2 ) drains central France with a course of more than 1000 km in length (Figure 1, [START_REF] Négrel | Changes in chemical and 87 Sr/ 86 Sr signature distribution patterns of suspended matter and bed sediments in the upper Loire River basin (France)[END_REF]). Palaeozoic granite, gneiss and micaschist (500 to 300 Ma) and a large volcanic area constitute the bedrocks of the upstream section of the catchment. The marine and lacustrine carbonate deposits (200 to 6 Ma) of the Paris Basin constitute the intermediate part of the catchment. The bedrock at the sampling site in the Avaray Valley consists of limestone (Aquitanian lacustrine carbonates; Figure 1, [START_REF] Garcin | Géométrie et âge des alluvions du lit majeur de la Loire moyenne, exemple du val d'Avaray (Loir-et-Cher, France)[END_REF]). The site is located at a spot within the global drainage system of the Loire river where 40% of the total catchment is covered.

An oxbow infilling representing a sediment aggradation covering at least 8.5 ka with a sedimentation rate of around 0.6 mm•a -1 ( [START_REF] Garcin | Géométrie et âge des alluvions du lit majeur de la Loire moyenne, exemple du val d'Avaray (Loir-et-Cher, France)[END_REF][START_REF] Garcin | Radiocarbon dating and palynology of alluvial deposits in the Loire flood plain (Val d'Avaray, Loir et Cher, France)[END_REF]) was collected for geochemical investigations (cores M25B, M30 and M19, Figure 1). The chronology of the deposits was obtained through 20 radiocarbon dating on the M25B core, 4 on the M19 core, and 1 on the M30 core [START_REF] Négrel | Lead isotope signatures of Holocene fluvial sediments from the Loire River valley[END_REF]. In this study, 26 samples were collected from the M25B core, extracted from 6.3 m of Holocene sediments (Table 1), from 0.8 m depth-considered as the lower limit of agricultural reworking-to the bottom of the core. Two further samples were collected from a second core (M30, Figure 1) at a depth of 2.43 m (medium black sand, 11,460 ± 90 a BP, [START_REF] Garcin | Géométrie et âge des alluvions du lit majeur de la Loire moyenne, exemple du val d'Avaray (Loir-et-Cher, France)[END_REF]) and at 2.18 m depth (black clay). A sample of Aquitanian lacustrine carbonate was collected from a third core (M19) at 5 m depth. The description of the M25B core is as follows: (a) to (i) referring to identified units with 14 C dating [START_REF] Garcin | Géométrie et âge des alluvions du lit majeur de la Loire moyenne, exemple du val d'Avaray (Loir-et-Cher, France)[END_REF]; see also Figure 2. The evolution along the core is a classical sequence corresponding to a channel migration from the base of the channel to a more riparian environment.

(i) lower part (interval 6.3-4.9 m) of the core consists of coarse-and fine-to-medium grained micaceous sand; (h) 4.9-4.7 m: very fine black peat, the base is dated 8410 ± 70 a BP; (g) 4.7-3.5 m: black peat, becoming brownish towards the top, containing ligneous debris and gastropods (6840 ± 70 a BP at 3.58 m); (f) 3.5-2.9 m: black clay, rich in well-preserved gastropods, with ligneous debris dated as Atlantic; (e) 2.9-2.7 m: black clay with sparse gastropods and wood fragments (5350 ± 60 a BP at 2.77 m, end of Atlantic); (d) 2.7-2.2 m: grey to green clay, sparse shelly debris and very rare vegetal debris (Atlantic); (c) 2.2-1.0 m: compact green clay with blue spots and sparse gastropod debris (3360 ± 50 a BP at 2.16 m depth; Subboreal 2370 ± 50 a BP at 1.65 m depth, Subatlantic); (b) 1.0-0.9 m: brownish clay grading into loamy clay; (a) 0.9-0 m: brown clayey loam and soil. The sites where the cores were extracted are indicated, the meander structure and distribution of sediment bodies A-E (modified from Garcin et al. [START_REF] Garcin | Géométrie et âge des alluvions du lit majeur de la Loire moyenne, exemple du val d'Avaray (Loir-et-Cher, France)[END_REF]) are also shown. The bodies were identified on the basis of aerial photographs, lithological data, thickness and altitude of the Aquitanian limestone substratum provided by more than 200 boreholes in the area. Each body corresponds to a slight migration of the main river channel. Stage A is the oldest, corresponding to migration of a meander with frontal erosion and prograding sand bars, and was eroded by stage B. Bodies C and D have a slightly sinuous to rectilinear path and body E shows well-preserved sand-filled channels and islands. The sites where the cores were extracted are indicated, the meander structure and distribution of sediment bodies A-E (modified from Garcin et al. [START_REF] Garcin | Géométrie et âge des alluvions du lit majeur de la Loire moyenne, exemple du val d'Avaray (Loir-et-Cher, France)[END_REF]) are also shown. The bodies were identified on the basis of aerial photographs, lithological data, thickness and altitude of the Aquitanian limestone substratum provided by more than 200 boreholes in the area. Each body corresponds to a slight migration of the main river channel. Stage A is the oldest, corresponding to migration of a meander with frontal erosion and prograding sand bars, and was eroded by stage B. Bodies C and D have a slightly sinuous to rectilinear path and body E shows well-preserved sand-filled channels and islands.

Sample Pretreatment and Methods

After drying, each sample was homogenized by hand-crushing in an agate mortar. The mineralogical composition of the sediment sample was determined by X-ray diffraction (XRD) according to the procedure given by Négrel and Grosbois [START_REF] Négrel | Changes in chemical and 87 Sr/ 86 Sr signature distribution patterns of suspended matter and bed sediments in the upper Loire River basin (France)[END_REF] and reference therein. Each bulk sample was homogenized by hand-crushing with an agate mortar. A mix of 5 mg of powder and 3 mL of distilled water were placed on glass slides and air dried for 3 h. The mineralogical composition was determined by X-ray diffraction using a Rigaku analyser, Cu-K α ray with a Ni-K β filter and diffraction spectra allowing the qualitative mineralogical composition to be defined. For each mineral, the ratio of the height of its most intense peak against the sum of all the most intense mineral peaks was used to calculate the semi-quantitative percentages [START_REF] Grosbois | An overview of dissolved and suspended matter fluxes in the Loire River basin: Natural and anthropogenic inputs[END_REF].

The C and O isotopic ratios of the carbonate and bulk samples were analysed with a Finnigan MAT 252 mass spectrometer connected to an automatic carbonate-preparation Kiel device. They were reported in per-mil deviations from the international V-PDB standard with an average precision, based on replicate analyses of various samples and laboratory standards, of ±0.1‰ for δ 18 O and δ 13 C (2σ; [START_REF] Négrel | The labile fraction of suspended matter in the Loire River (France): Multi-element chemistry and isotopic (Rb-Sr and C-O) systematics[END_REF]). Gastropod shells were analysed after cleaning with distilled water and hand crushed for C and O isotopic ratios with the Finnigan MAT 252 mass spectrometer following manual preparation of the sample.

Results and Discussion

Clay Mineralogical Changes in the Loire River Reflecting Weathering Intensity

The channel fill consists of fine clayey overbank deposits corresponding to flooding of the river, as shown by the variation in the particle sizes (Figure 2a). The particle sizes and the semi-quantitative XRD analysis of the sediment showed that clay minerals constitute between 25% and 90% of the sediment (Table 1, Figure 2b). Quartz, feldspar and calcite range from less than 5% to 40%. The particle-size distribution is given in Figure 2a (Fµm stands for the fraction expressed in µm). It shows a total absence of coarse clastics and sand in the core, except in lowest part (±10% at 3 to 3.75 m depth). Particles in the range 20 < Fµm < 63 gently decrease upward in the core from 30% to around 20%. Particles with a size of up to 20 µm represent a mean of 76 ± 14% in the channel fill, separated in two fractions (4 < Fµm< 20 and Fµm < 4). The 4 < Fµm <20 fraction increases steadily upward from 20% at the base up to 40% at the top of the channel fill, whereas the Fµm <4 fraction remains relatively constant around 40% in the core.

The <4 µm fraction (Figure 2b) is dominated by mixed layer minerals illite/smectite (30%-90%), illite, illite/chlorite, chlorite and kaolinite making up the rest of the clay minerals. The distribution of the clays shows an up-core increase in illite/smectite and, conversely, a decrease in kaolinite and illite abundance. The increase of the illite/smectite abundance is large, starting around 25% at 4.75 m depth to reach over 85% at the top of the channel fill. Figure 2b shows the relative individual clay mineral contents compared to total clay content in the sample. This normalization allows excluding effects that might originate from changes in the depositional environment such as sudden changes in transport velocity. The clay minerals in soil are the result of weathering processes in the parent rocks [START_REF] Wilson | The origin and formation of clay minerals in soils: Past, present and future perspectives[END_REF][START_REF] Négrel | Geochemical fingerprinting and source discrimination of agricultural soils at continental scale[END_REF]. It is generally agreed that the differences in clay-mineral composition in soil or in river sediments reflect weathering intensity [START_REF] Garzanti | Provenance versus weathering control on the composition of tropical river mud (southern Africa)[END_REF] as well as weathering mechanisms (i.e., physical vs. chemical weathering). Clay mineral genesis reflects climatic variations, of both precipitation and temperature, and the lithological and morphological settings [START_REF] Liu | Climatic and tectonic controls on chemical weathering in tropical Southeast Asia (Malay Peninsula, Borneo, and Sumatra)[END_REF].

The weathering types and their intensity, at the basin scale, can be estimated from the clay minerals in riverine sediments [START_REF] Singer | The paleoclimatic interpretation of clay minerals in soils and weathering profiles[END_REF] when comparing the conditions of formation of each clay type [START_REF] Chamley | Clay Sedimentology[END_REF]. Kaolinite is formed by intensive hydrolysis in a warm and humid climate. Illite and chlorite are formed by weak hydrolysis and/or strong physical erosion of bedrock in a relatively dry climate, being primary minerals of weathering processes. Smectite formation in soil requires a warm and wet climate with poor drainage. Illite/chlorite also indicate the nature of the weathered bedrock, being more abundant during the weathering of felsic rather than mafic rocks [START_REF] Chamley | Clay Sedimentology[END_REF].

The clay-mineral assemblages of sediments help to constrain their sources and transport pathways, and provide information about the related paleoenvironmental and paleoclimatic conditions. For this purpose, a ternary diagram of the clay-mineral groups illite+chlorite, kaolinite, and smectite (Figure 3; [START_REF] Hu | Clay mineralogy of the riverine sediments of Hainan Island, South China Sea: Implications for weathering and provenance[END_REF]) illustrates the three parameters of sources, processes and pathways in the channel fill. As mentioned above, kaolinite is formed by chemical weathering, while illite/chlorite are mostly inherited from parent rocks by physical erosion. Thus, the kaolinite vs. illite/chlorite ratio indicates the types of weathering (chemical weathering vs. physical erosion) that affected the sediments, with the weathering intensity given by smectite.

Minerals 2020, 10, x FOR PEER REVIEW 5 of 13

The clay-mineral assemblages of sediments help to constrain their sources and transport pathways, and provide information about the related paleoenvironmental and paleoclimatic conditions. For this purpose, a ternary diagram of the clay-mineral groups illite+chlorite, kaolinite, and smectite (Figure 3; [START_REF] Hu | Clay mineralogy of the riverine sediments of Hainan Island, South China Sea: Implications for weathering and provenance[END_REF]) illustrates the three parameters of sources, processes and pathways in the channel fill. As mentioned above, kaolinite is formed by chemical weathering, while illite/chlorite are mostly inherited from parent rocks by physical erosion. Thus, the kaolinite vs. illite/chlorite ratio indicates the types of weathering (chemical weathering vs. physical erosion) that affected the sediments, with the weathering intensity given by smectite. [START_REF] Garcin | Géométrie et âge des alluvions du lit majeur de la Loire moyenne, exemple du val d'Avaray (Loir-et-Cher, France)[END_REF], see Table 1 for more details and text for the location of the 14 C dates. [START_REF] Garcin | Géométrie et âge des alluvions du lit majeur de la Loire moyenne, exemple du val d'Avaray (Loir-et-Cher, France)[END_REF], see Table 1 for more details and text for the location of the 14 C dates.

Table 1. Semi-quantitative X-ray diffraction (XRD) analysis of the sediment in the M25B core. Radiocarbon dates are issued from the interpretation given by [START_REF] Garcin | Géométrie et âge des alluvions du lit majeur de la Loire moyenne, exemple du val d'Avaray (Loir-et-Cher, France)[END_REF]. In Figure 3, the smectite values increase along the blue arrow, defining an up-core trend that suggests a less intense chemical weathering and a weak physical erosion for the younger sediments, and a more mafic (more basalt weathering) than felsic source for the clay-mineral origin.

Sample

These results give an insight into the changes that affected the Loire basin over the past 8500 years, and most likely indicate the dispersal of fine sediments during the yearly floods of the river. Over the same period, the weathering of basalt in the Massif Central has increased, as shown by lead isotopes [START_REF] Négrel | Lead isotope signatures of Holocene fluvial sediments from the Loire River valley[END_REF], while granite weathering has decreased. The authors demonstrate [START_REF] Négrel | Lead isotope signatures of Holocene fluvial sediments from the Loire River valley[END_REF] that the lead isotope has recorded the volcanic events (Vasset/Killian tephra event, 8300 BP) and also the increase of the erosion processes of volcanic material through soil cultivation in the mid to late Holocene. The decrease in physical erosion has favoured a relative increase in the importance of chemical weathering, agreeing with the gently up-core decrease of the 20 < Fµm < 63 fraction and the increase in the 4 < Fµm < 20 fraction, the latter being more easily transported by the river in terms of velocity capacities. This is also marked by a stability of the Fµm < 4 fraction in the channel fill as a mark of the final filling steps.

In Figure 3, the smectite values increase along the blue arrow, defining an up-core trend that suggests a less intense chemical weathering and a weak physical erosion for the younger sediments, and a more mafic (more basalt weathering) than felsic source for the clay-mineral origin.

These results give an insight into the changes that affected the Loire basin over the past 8500 years, and most likely indicate the dispersal of fine sediments during the yearly floods of the river. Over the same period, the weathering of basalt in the Massif Central has increased, as shown by lead isotopes [START_REF] Négrel | Lead isotope signatures of Holocene fluvial sediments from the Loire River valley[END_REF], while granite weathering has decreased. The authors demonstrate [START_REF] Négrel | Lead isotope signatures of Holocene fluvial sediments from the Loire River valley[END_REF] that the lead isotope has recorded the volcanic events (Vasset/Killian tephra event, 8300 BP) and also the increase of the erosion processes of volcanic material through soil cultivation in the mid to late Holocene. The decrease in physical erosion has favoured a relative increase in the importance of chemical weathering, agreeing with the gently up-core decrease of the 20 < Fµ m < 63 fraction and the increase in the 4 < Fµ m < 20 fraction, the latter being more easily transported by the river in terms of velocity capacities. This is also marked by a stability of the Fµ m < 4 fraction in the channel fill as a mark of the final filling steps.

Origin of Carbonate in the Flood Sediments

The study by Négrel et al. [START_REF] Négrel | Strontium isotopic record of signatures of Holocene fluvial sediments in the Loire valley, France[END_REF] on this channel infill suggests that the carbonates in the sediment record are authigenic rather than detrital in origin. Additionally, carbon-and oxygen-isotope compositions of fluvial and associated carbonate deposits provide environmental information on past temperature, humidity, soil and vegetation, as well as information on the CO2 source in carbonates-thus characterizing catchment areas-and on hydrological and physical features of underground and surface-water systems. A wide range of δ 13 C values and a narrower range in δ 18 O ones are commonly observed (Table 2). A narrower range in δ 18 O because carbonate deposits record variations in δ 18 O related to seasonal to decadal temperature changes, which generally are not parallel to δ 13 C variations that may integrate the role of aquatic vegetation as well as early diagenetic reactions during bacterial organic matter degradation [START_REF] Mayer | A 15,000-year stable isotope record from sediments of lake Steisslingen, Southwest Germany[END_REF].

Origin of Carbonate in the Flood Sediments

The study by Négrel et al. [START_REF] Négrel | Strontium isotopic record of signatures of Holocene fluvial sediments in the Loire valley, France[END_REF] on this channel infill suggests that the carbonates in the sediment record are authigenic rather than detrital in origin. Additionally, carbon-and oxygen-isotope compositions of fluvial and associated carbonate deposits provide environmental information on past temperature, humidity, soil and vegetation, as well as information on the CO 2 source in carbonates-thus characterizing catchment areas-and on hydrological and physical features of underground and surface-water systems. A wide range of δ 13 C values and a narrower range in δ 18 O ones are commonly observed (Table 2). A narrower range in δ 18 O because carbonate deposits record variations in δ 18 O related to seasonal to decadal temperature changes, which generally are not parallel to δ 13 C variations that may integrate the role of aquatic vegetation as well as early diagenetic reactions during bacterial organic matter degradation [START_REF] Mayer | A 15,000-year stable isotope record from sediments of lake Steisslingen, Southwest Germany[END_REF]. The range of δ values is wide for both δ 18 O (~-7.0‰ to -1.4‰) and δ 13 C (~-13.3‰ to -5.5‰). The stable-isotope record in Figure 4 shows several remarkable features: (1) From 0.75 m to 2.3 m δ 13 C strongly increases from -13.3‰ to -6.9‰ and then stabilises around -6‰; (2) The interval (4.55-3.45 m) is marked by a positive peak of δ 18 O values; (3) From 3.04 m upwards, the δ 18 O values evolve towards higher values. For the gastropod shells, analysed when they could be isolated from the rest of the sediment, the δ 18 O values more or less agree with those observed in the sediment, suggesting equilibrium both for carbonate precipitation in the sediment and in the organisms colonizing the meander. However, the δ 13 C in gastropod shells only matches the sediment carbonates at 1.40 m depth in the channel fill, the three other gastropod samples are depleted in 13 C by 2.7‰ to 5.7‰ compared to the sediment δ 13 C. Similar depletions in 13 C compared to equilibrium values (by 1‰ to 4‰) have been observed for certain species of freshwater gastropods, mainly lung-breathing, pulmonate gastropods, whereas gill-breathing species are close to equilibrium with dissolved inorganic carbon DIC [START_REF] Shanahan | Isotopic variability in the aragonite shells of freshwater gastropods living in springs with nearly constant temperature and isotopic composition[END_REF], highlighting the limitations for interpreting stable isotopic data from fossil gastropod shells.

Négrel et al. [START_REF] Négrel | The labile fraction of suspended matter in the Loire River (France): Multi-element chemistry and isotopic (Rb-Sr and C-O) systematics[END_REF] investigated the carbonate fraction of present-day suspended matter in the Loire River with stable carbon-and oxygen-isotope compositions (Figure 4). The recorded values varied from -3.1‰ to -7.6‰ for δ 13 C and from -1.7‰ to -9.4‰ for δ 18 O. The relationship between δ 18 O and δ 13 C (Figure 4) indicates that "winter" carbonate sampled during high-flow conditions is clearly different from "summer" carbonate sampled during low-flow conditions. The latter occupies a restricted area with δ 13 C = -7‰ and δ 18 O = -8‰. The 18 O content of the water and the 13 C content of the total DIC and their variations during changes of environmental conditions directly impact the isotope contents of authigenic carbonate. Calcite precipitation during low flow is in isotopic equilibrium with DIC which is derived in different proportions from atmospheric CO 2 , dissolved carbonates and from biogenic CO 2 produced during degradation of organic matter. During high flow, the relative contribution of atmospheric CO 2 and/or of erosive carbonates increases.

Minerals 2020, 10, x FOR PEER REVIEW 9 of 13 Négrel et al. [START_REF] Négrel | The labile fraction of suspended matter in the Loire River (France): Multi-element chemistry and isotopic (Rb-Sr and C-O) systematics[END_REF] investigated the carbonate fraction of present-day suspended matter in the Loire River with stable carbon-and oxygen-isotope compositions (Figure 4). The recorded values varied from -3.1‰ to -7.6‰ for  13 C and from -1.7‰ to -9.4‰ for  18 O. The relationship between  18 O and  13 C (Figure 4) indicates that "winter" carbonate sampled during high-flow conditions is clearly different from "summer" carbonate sampled during low-flow conditions. The latter occupies a restricted area with  13 C = -7‰ and  18 O = -8‰. The 18 O content of the water and the 13 C content of the total DIC and their variations during changes of environmental conditions directly impact the isotope contents of authigenic carbonate. Calcite precipitation during low flow is in isotopic equilibrium with DIC which is derived in different proportions from atmospheric CO2, dissolved carbonates and from biogenic CO2 produced during degradation of organic matter. During high flow, the relative contribution of atmospheric CO2 and/or of erosive carbonates increases. Fontes et al. [START_REF] Fontes | Holocene environmental changes in Lake Bangong basin (Western Tibet). Part 1: Chronology and stable isotopes of carbonates of a Holocene lacustrine core[END_REF] listed the factors that can control the evolution of  18 O and  13 C values in authigenic carbonate in lakes, which can be transposed to rivers. An increase in the  18 O values of authigenic carbonate may be due to: (1) enrichment of the heavy isotope in rain inputs (origin, type of condensation of air moisture, lower relative humidity); (2) increase in the average water temperature; (3) a longer residence time of the water in the water body (notably lakes) and/or lower relative humidity enhancing evaporative enrichment in heavy isotopes.

A decrease in the 13 C content of authigenic carbonates may be due to: (1) a lower isotope exchange of the total DIC with atmospheric CO2 through a shorter residence time of the water; (2) growth of vegetation cover in the catchment or in the vicinity of the site, (e.g., a riparian forest as last step in channel migration) and concomitant oxidation of organic matter; (3) an increase in partial pressure of soil CO2 in the catchment area or in the vicinity of the site, leading to a lower 13 C content in the total DIC. The carbonate fraction of present-day suspended matter in the Loire River over a one-year cycle, and six representative rock samples were analysed for their stable-isotope contents by Négrel et al. [START_REF] Négrel | The labile fraction of suspended matter in the Loire River (France): Multi-element chemistry and isotopic (Rb-Sr and C-O) systematics[END_REF]. Legend of the sedimentary deposits as in Figure 2.

Fontes et al. [START_REF] Fontes | Holocene environmental changes in Lake Bangong basin (Western Tibet). Part 1: Chronology and stable isotopes of carbonates of a Holocene lacustrine core[END_REF] listed the factors that can control the evolution of δ 18 O and δ 13 C values in authigenic carbonate in lakes, which can be transposed to rivers. An increase in the δ 18 O values of authigenic carbonate may be due to: (1) enrichment of the heavy isotope in rain inputs (origin, type of condensation of air moisture, lower relative humidity); (2) increase in the average water temperature;

(3) a longer residence time of the water in the water body (notably lakes) and/or lower relative humidity enhancing evaporative enrichment in heavy isotopes.

A decrease in the 13 C content of authigenic carbonates may be due to: (1) a lower isotope exchange of the total DIC with atmospheric CO 2 through a shorter residence time of the water; (2) growth of vegetation cover in the catchment or in the vicinity of the site, (e.g., a riparian forest as last step in channel migration) and concomitant oxidation of organic matter; (3) an increase in partial pressure of soil CO 2 in the catchment area or in the vicinity of the site, leading to a lower 13 C content in the total DIC.

The observed opposing trends in the upper part of the channel fill, from the Subboreal onwards, can be due to several causes, dependent or independent of the hydrological behaviour in the meander [START_REF] Li | δ 13 C-δ 18 O covariance as a paleohydrological indicator for closed-basin lakes[END_REF]. The rapid throughflow in the Loire River system implies that the 18 O content of water reflects the mean composition of precipitation at the catchment scale. Therefore, the 18 O variations of carbonates give a clue on the composition and patterns of regional precipitation as well as on the effect of the water temperature as evidenced in present-day suspended matter [START_REF] Mayer | A 15,000-year stable isotope record from sediments of lake Steisslingen, Southwest Germany[END_REF]. Additionally, such rapid throughflow also precludes causing an exchange of the total DIC with atmospheric CO 2 for the 13 C variations. To illustrate the opposite, but concomitant, variations in 18 O and 13 C contents, we plotted such data in a δ 18 O vs. δ 13 C diagram (Figure 5). There is no clear overall trend between δ 18 O and δ 13 C values, but it is worth noting that (1) the deeper samples agree with the range seen in the carbonate fraction of present-day suspended matter in the Loire River, and that (2) around 2.5-2.4 m depth a large decrease is seen in δ 13 C, which occurred around 4400 a BP. This decrease is accompanied by a smaller variation of the δ 18 O value.

Minerals 2020, 10, x FOR PEER REVIEW 10 of 13

The observed opposing trends in the upper part of the channel fill, from the Subboreal onwards, can be due to several causes, dependent or independent of the hydrological behaviour in the meander [START_REF] Li | δ 13 C-δ 18 O covariance as a paleohydrological indicator for closed-basin lakes[END_REF]. The rapid throughflow in the Loire River system implies that the 18 O content of water reflects the mean composition of precipitation at the catchment scale. Therefore, the 18 O variations of carbonates give a clue on the composition and patterns of regional precipitation as well as on the effect of the water temperature as evidenced in present-day suspended matter [START_REF] Mayer | A 15,000-year stable isotope record from sediments of lake Steisslingen, Southwest Germany[END_REF]. Additionally, such rapid throughflow also precludes causing an exchange of the total DIC with atmospheric CO2 for the 13 C variations. To illustrate the opposite, but concomitant, variations in 18 O and 13 C contents, we plotted such data in a  18 O vs.  13 C diagram (Figure 5). There is no clear overall trend between  18 O and  13 C values, but it is worth noting that (1) the deeper samples agree with the range seen in the carbonate fraction of present-day suspended matter in the Loire River, and that (2) around 2.5-2.4 m depth a large decrease is seen in δ 13 C, which occurred around 4400 a BP. This decrease is accompanied by a smaller variation of the  18 O value. The plants that colonized the meander are expected to be predominantly C3 so that sedimentary  13 C variations cannot be explained by a change in the relative proportions of C3 and C4 plants. Native C4 plants currently make up only 1.05% of the plant species in France [START_REF] Rowland | Tie channel sedimentation rates, oxbow formation age and channel migration rate from optically stimulated luminescence (OSL) analysis of floodplain deposits[END_REF] and during colder periods, this proportion would even have been less. Any significant contribution of C4 plants to the overall soil organic C budget would not be expected before the massive introduction of maize in the 20 th century. Even though, the opposing  13 C and  18 O trends can be ascribed to a progressive closure of the meander and the installation of C3 vegetation. This newly created non-permanent wetland [START_REF] Hammarlund | Rapid hydrological changes during the Holocene revealed by stable isotope records of lacustrine carbonates from Lake Igelsjön, southern Sweden[END_REF] was regularly destroyed by river floods during the winter months and by stagnant water in the The carbonate fraction of present-day suspended matter in the Loire River over a one-year cycle, and six representative rock samples were analysed for their stable-isotope contents by Négrel et al. [START_REF] Négrel | The labile fraction of suspended matter in the Loire River (France): Multi-element chemistry and isotopic (Rb-Sr and C-O) systematics[END_REF] and are shown in red and green, respectively. Numbers indicate the depth of the samples in the channel fill.

The plants that colonized the meander are expected to be predominantly C3 so that sedimentary δ 13 C variations cannot be explained by a change in the relative proportions of C3 and C4 plants. Native C4 plants currently make up only 1.05% of the plant species in France [START_REF] Rowland | Tie channel sedimentation rates, oxbow formation age and channel migration rate from optically stimulated luminescence (OSL) analysis of floodplain deposits[END_REF] and during colder periods, this proportion would even have been less. Any significant contribution of C4 plants to the overall soil organic C budget would not be expected before the massive introduction of maize in the 20th century. Even though, the opposing δ 13 C and δ 18 O trends can be ascribed to a progressive closure of the meander and the installation of C3 vegetation. This newly created non-permanent wetland [START_REF] Hammarlund | Rapid hydrological changes during the Holocene revealed by stable isotope records of lacustrine carbonates from Lake Igelsjön, southern Sweden[END_REF] was regularly destroyed by river floods during the winter months and by stagnant water in the meander. Thus, the C isotope signature was mainly controlled by a local environment with more negative δ 13 C values due to the oxidation of plant debris. This bacterially driven organic-matter mineralization means that organic C, with metabolic products, are released into the porewater, and nutrients are transformed into inorganic forms, allowing C to be fixed in authigenic carbonate.

Increasing contribution of local groundwater, dominated by carbonate dissolution would also contribute 13 C-depleted DIC, with a roughly equivalent contribution of biogenic carbon from C3 (< -26‰) and the palustrine rock carbonates of the Beauce aquifer (<0‰).

High δ 18 O values reflect a period of long residence time, induced by evaporation attributed to closure of the meander; this longer water-residence time conferred its signature to the carbonate and was less dependent of the meander evolution. Temperature variations explain most likely the high δ 18 O episode during the Atlantic. Whereas the δ 18 O value of authigenic carbonates decreases with increasing equilibrium temperature [START_REF] Négrel | The labile fraction of suspended matter in the Loire River (France): Multi-element chemistry and isotopic (Rb-Sr and C-O) systematics[END_REF][START_REF] Mayer | A 15,000-year stable isotope record from sediments of lake Steisslingen, Southwest Germany[END_REF], this effect can be overridden by long-term temperature effects on the precipitation [START_REF] Mayer | A 15,000-year stable isotope record from sediments of lake Steisslingen, Southwest Germany[END_REF]. The observed positive shift by 5‰ in our study is similar to that observed by Mayer and Schwark [START_REF] Mayer | A 15,000-year stable isotope record from sediments of lake Steisslingen, Southwest Germany[END_REF] in lake sediments in SW Germany at the end of the Boreal (from around -6‰ to -2‰), reflecting the temperature-driven changes in the δ 18 O value of rainfall at the basin scale, superposed to other effects, notably evaporation.

Conclusions

The stable O-and C-isotope ratio variations, the distribution of particle sizes and clay-mineral types, reflect the evolution of river dynamics. Our comprehensive study of a channel-fill system in the Middle Loire alluvial plain suggests that:

(1) The kaolinite vs. illite/chlorite ratio indicates the importance of chemical weathering vs. physical erosion that affected the sediments, with smectite content as weathering intensity proxy. Their variations might reflect a less-intense chemical weathering and a weak physical erosion in the case of the younger sediments, and a more mafic (basalt) than felsic source for the clay-mineral origin, likely related to the increase in the soil cultivation in the mid to late Holocene and a higher contribution of volcanic material to the alluvial deposits [START_REF] Négrel | Lead isotope signatures of Holocene fluvial sediments from the Loire River valley[END_REF]. (2) Variations of carbon and oxygen isotopes ratios over the last 10,000 years reveal a wide range.

The Atlantic climatic optimum is reflected by a positive δ 18 O shift. The opposite trends for δ 13 C and δ 18 O values observed in the Subboreal and the Subatlantic variations is ascribed to a progressive closure of the meander and the installation of vegetation in a non-permanent wetland. The closure is consistent with the decrease in particle size and reflects the progressive disconnection of the meander with its bed infill, changes in the C origin, and possible difference in oxygen availability affecting the degradation processes of organic matter.

The results of the present study complete previous interpretations, at the local and basin scales, and are consistent with observations from Sr and Pb isotopes [START_REF] Négrel | Strontium isotopic record of signatures of Holocene fluvial sediments in the Loire valley, France[END_REF][START_REF] Négrel | Lead isotope signatures of Holocene fluvial sediments from the Loire River valley[END_REF]. A different functioning of the past channels compared to present day conditions was shown by Sr isotopes [START_REF] Négrel | Strontium isotopic record of signatures of Holocene fluvial sediments in the Loire valley, France[END_REF], highlighting the role of local groundwater in the precipitation of authigenic carbonates in the meander. The Pb-isotope variation was related to natural input from erosion and to human impact (mining and smelting of Pb ore, agricultural development impacting the forest) during the past 10,000 years [START_REF] Négrel | Lead isotope signatures of Holocene fluvial sediments from the Loire River valley[END_REF]. The isotopic tools complement each other perfectly with a vision that stretches from the global basin scale with Pb and, partly, O-isotopes, down to the very local scale of a meander with Sr and stable O-and C isotopes. Our results prove an unambiguous isotopic imprint of a low-magnitude physical event (closure of the meander over a period of at least 2600 years) in the fluvial sedimentary record. Stable-isotope data are thus a meaningful complement to classic proxies (particle size, clay minerals); they have great potential in the reconstruction of the geomorphological evolution of rivers and are applicable to all streams and lakes with a known sedimentary record.

Figure 1 .

 1 Figure 1. (a) Location of the Loire River catchment in France. (b) Simplified geological map of the upper Loire river catchment (modified from Négrel et al. [9]); (c) map of the Val d'Avaray meander.The sites where the cores were extracted are indicated, the meander structure and distribution of sediment bodies A-E (modified from Garcin et al.[START_REF] Garcin | Géométrie et âge des alluvions du lit majeur de la Loire moyenne, exemple du val d'Avaray (Loir-et-Cher, France)[END_REF]) are also shown. The bodies were identified on the basis of aerial photographs, lithological data, thickness and altitude of the Aquitanian limestone substratum provided by more than 200 boreholes in the area. Each body corresponds to a slight migration of the main river channel. Stage A is the oldest, corresponding to migration of a meander with frontal erosion and prograding sand bars, and was eroded by stage B. Bodies C and D have a slightly sinuous to rectilinear path and body E shows well-preserved sand-filled channels and islands.

Figure 1 .

 1 Figure 1. (a) Location of the Loire River catchment in France. (b) Simplified geological map of the upper Loire river catchment (modified from Négrel et al. [9]); (c) map of the Val d'Avaray meander. The sites where the cores were extracted are indicated, the meander structure and distribution of sediment bodies A-E (modified from Garcin et al. [12]) are also shown. The bodies were identified on the basis of aerial photographs, lithological data, thickness and altitude of the Aquitanian limestone substratum provided by more than 200 boreholes in the area. Each body corresponds to a slight migration of the main river channel. Stage A is the oldest, corresponding to migration of a meander with frontal erosion and prograding sand bars, and was eroded by stage B. Bodies C and D have a slightly sinuous to rectilinear path and body E shows well-preserved sand-filled channels and islands.

Figure 2 .

 2 Figure 2. Variations of particle size (%, a) and clay content (%, b) in the M25B core. Radiocarbon dates are from[START_REF] Garcin | Géométrie et âge des alluvions du lit majeur de la Loire moyenne, exemple du val d'Avaray (Loir-et-Cher, France)[END_REF], see Table1for more details and text for the location of the 14 C dates.

Figure 2 .

 2 Figure 2. Variations of particle size (%, a) and clay content (%, b) in the M25B core. Radiocarbon dates are from[START_REF] Garcin | Géométrie et âge des alluvions du lit majeur de la Loire moyenne, exemple du val d'Avaray (Loir-et-Cher, France)[END_REF], see Table1for more details and text for the location of the 14 C dates.

Figure 3 .

 3 Figure 3. Ternary diagram of the major clay-mineral groups illite-chlorite, kaolinite, and smectite [31]. This clay-mineral assemblage reflects both source-rock lithology and past climate. Kaolinite and smectite abundances are proxies for weathering intensity, whereas the illite-chlorite abundance depends upon the lithology of source rocks.

Figure 3 .

 3 Figure 3. Ternary diagram of the major clay-mineral groups illite-chlorite, kaolinite, and smectite [31]. This clay-mineral assemblage reflects both source-rock lithology and past climate. Kaolinite and smectite abundances are proxies for weathering intensity, whereas the illite-chlorite abundance depends upon the lithology of source rocks.

Figure 4 .

 4 Figure 4. The Loire stable-isotope record:  18 O and  13 C values for the carbonate fraction and gastropod shells. The carbonate fraction of present-day suspended matter in the Loire River over a one-year cycle, and six representative rock samples were analysed for their stable-isotope contents by Négrel et al. [9]. Legend of the sedimentary deposits as in Figure 2.

Figure 4 .

 4 Figure 4. The Loire stable-isotope record: δ 18 O and δ 13 C values for the carbonate fraction and gastropod shells. The carbonate fraction of present-day suspended matter in the Loire River over a one-year cycle, and six representative rock samples were analysed for their stable-isotope contents by Négrel et al. [9]. Legend of the sedimentary deposits as in Figure 2.

Figure 5 .

 5 Figure 5. Isotopic compositions  18 O vs.  13 C of authigenic carbonates of the Loire channel fill. The carbonate fraction of present-day suspended matter in the Loire River over a one-year cycle, and six representative rock samples were analysed for their stable-isotope contents by Négrel et al. [9] and are shown in red and green, respectively. Numbers indicate the depth of the samples in the channel fill.

Figure 5 .

 5 Figure 5. Isotopic compositions δ 18 O vs. δ 13 C of authigenic carbonates of the Loire channel fill.The carbonate fraction of present-day suspended matter in the Loire River over a one-year cycle, and six representative rock samples were analysed for their stable-isotope contents by Négrel et al.[START_REF] Négrel | The labile fraction of suspended matter in the Loire River (France): Multi-element chemistry and isotopic (Rb-Sr and C-O) systematics[END_REF] and are shown in red and green, respectively. Numbers indicate the depth of the samples in the channel fill.

Table 2 .

 2 Carbon-and oxygen-isotope compositions of the sediment in the M25B and M30 cores; Z indicates the sampling below the soil surface.

	Sample	Z	age	δ 18 O	δ 13 C
		m	a BP	‰ vs. V-PDB	‰ vs. V-PDB
	M25B core
	M25B/A	0.80	1137	-4.2	-13.3
	M25B/B	0.91	1309	-4.3	-12.8
	M25B/C	1.20	1791	-2.6	-12.3
	M25B/Ca	1.30	1954	-4.2	-10.7
	M25B/D	1.40	2117	-2.8	-11.3
	M25B/E	1.60	2444	-2.7	-9
	M25B/F	1.80	2771	-3.5	-9.1
	M25B/Fa	1.91	2950	-2.6	-7.8
	M25B/G	2.30	3587	-5.3	-6.9
	M25B/Ga	2.41	3759	-5.2	-7.3
	M25B/H	2.50	3914	-4.7	-8.7
	M25B/Ha	2.70	4241	-4.4	-7.1
	M25B/I	2.80	4404	-6.7	-6.5
	M25B/J	3.04	4796	-7	-6.9
	M25B/K	3.25	5139	-5.7	-6.9
	M25B/L	3.45	5466	-6.9	-6.8
	M25B/Na	4.25	7721	-1.4	-6.8
	M25B/O	4.35	7870	-3.5	-6.1
	M25B/P	4.55	8166	-6.4	-6.1
	M25B/Pa	4.65	8315	-6.1	-5.6
	M25B/Q	4.75	8463	-4.1	-5.5
	M30B core
	M30A	2.43	11,460	-6.3	-5.6
	M30B	2.18	-	-6.8	-4.9
	Aquitanian carbonate
	M19/5	5.00	-	-2.4	-5.7
	gastropod shells
	M25B/Ds	1.40	-	-4.5	-10.1
	M25B/Gs	2.30	-	-4.5	-10.2
	M25B/Ks	3.25	-	-5.7	-9.6
	M25B/Ls	3.45	-	-5.6	-12.5

Minerals 2020, 10, x FOR PEER REVIEW

Acknowledgments: Isotopic analyses benefited from the collaboration of C. Fléhoc in the BRGM isotope laboratories. H.M. Kluijver edited the manuscript and proofread the English.

Funding: This research received no external funding. This work was financially supported by the BRGM Research Program.

Author Contributions: Conceptualization, methodology, investigation, P.N., W.K.; writing-original draft preparation, P.N.; writing-review and editing, W.K.; All authors have read and agreed to the published version of the manuscript.

Conflicts of Interest:

The authors declare no conflict of interest.


Pascal Benoit
email: pascal.benoit@lirmm.fr

Lionel Torres
email: lionel.torres@lirmm.fr

Gilles Sassatelli
email: gilles.sassatelli@lirmm.fr

Michel Robert
email: michel.robert@lirmm.fr

Nicolas Saint-Jean
email: nicolas.saint-jean@lirmm.fr

Run-time mapping for dynamic reconfiguration management in embedded systems

Keywords: reconfigurable computing, run-time resource management, self-adaptability, task relocation, task duplication, TD, task allocation and scheduling, hardware and software control, embedded systems

Dynamic reconfiguration provides attractive features such as hardware flexibility and adaptability. Unfortunately, the lack of programming tools to manage it has limited its use in current SoC. This paper presents a method to abstract dynamic reconfiguration management at design time. Dynamic hardware multiplexing is a generic principle based on a scheduler dedicated to the management of reconfigurable resources at run-time. Formal background, implementation, simulation results and validations are exposed to illustrate the contribution of this study.

Introduction

The explosion of standards in 3G and more generally in wireless systems goes along with a widening spectrum of applications that portable devices have to support.

Designing a chip for every single device tends to become less feasible (SoC complexity, lifecycle of multimedia product, increasing non-recurring engineering costs for deep-submicron technologies). A considered way to overcome these problems relies on flexibility, i.e., reusing the same chip for a range of products, applications, or even several generations of the same product. This approach allows sharing the non-recurring engineering costs, and the design stage comes down to a software customisation phase. Reconfigurable architectures provide this flexibility at the price of a silicon area overhead highly dependent on the level of flexibility.

Related works

Recently, FPGA cores integration has become a reality in embedded systems. Several companies as eASIC (http://www.easic.com/) and M2000 (http://www.m2000.fr/) offer dense customisable FPGA macros that can be used as configurable logic associated to a general purpose processor. Using reconfigurable logic provides an increased flexibility since it then becomes feasible to modify the configuration after the chip fabrication, to upgrade the device during its life cycle, at the price of a reduced silicon density. Dynamic reconfiguration is a third level of flexibility and consists in modifying the configuration of the device at run-time. For typical reconfigurable architectures such as FPGA, run-time reconfiguration is generally costly as it requires a large amount of data. To overcome this drawback, coarse grain reconfigurable architectures have been studied and developed (Table 1) for the past 15 years.

More recently, we have observed a growing interest in dynamic reconfiguration management techniques in the literature. Table 2 exposes a synthetic overview of different dynamic configuration management techniques. In the literature, most of the approaches target fine grain partially reconfigurable devices [XC6200 [START_REF] Shirazi | Run-time management of dynamically reconfigurable designs[END_REF][START_REF] Burns | A dynamic reconfiguration run-time system[END_REF][START_REF] Robinson | Modeling and synthesis of configuration controllers for dynamically reconfigurable logic systems using the DCS CAD framework[END_REF], Virtex-II Pro [START_REF] Curd | Dynamic reconfiguration of RocketIO MGT attributes[END_REF], Virtex II [START_REF] Blodget | A lightweight approach for embedded reconfiguration of FPGAs[END_REF][START_REF] Carvahlo | PADReH -a framework for the design and implementation of dynamically and partially reconfigurable systems[END_REF][START_REF] Huebner | Scalable application-dependent network on chip adaptability for dynamical reconfigurable real-time systems[END_REF][START_REF] Ullman | On-demand FPGA run-time system for dynamical reconfiguration with adaptive priorities[END_REF] or Altera-like architectures [START_REF] Danne | A heuristic approach to schedule periodic real-time tasks on reconfigurable hardware[END_REF]. Some of the proposed schemes provide a support for the relocation of tasks [START_REF] Burns | A dynamic reconfiguration run-time system[END_REF][START_REF] Robinson | Modeling and synthesis of configuration controllers for dynamically reconfigurable logic systems using the DCS CAD framework[END_REF][START_REF] Carvahlo | PADReH -a framework for the design and implementation of dynamically and partially reconfigurable systems[END_REF][START_REF] Danne | A heuristic approach to schedule periodic real-time tasks on reconfigurable hardware[END_REF][START_REF] Huebner | Scalable application-dependent network on chip adaptability for dynamical reconfigurable real-time systems[END_REF] where they are handled as a fixed-size or variable-size rectangle that can be placed on the FPGA resource. Each method may differ in the placement and scheduling, aiming at optimising cost functions. In the first methods [START_REF] Shirazi | Run-time management of dynamically reconfigurable designs[END_REF][START_REF] Burns | A dynamic reconfiguration run-time system[END_REF], the scheduling was performed statically by heuristics and in [START_REF] Robinson | Modeling and synthesis of configuration controllers for dynamically reconfigurable logic systems using the DCS CAD framework[END_REF], [START_REF] Carvahlo | PADReH -a framework for the design and implementation of dynamically and partially reconfigurable systems[END_REF], [START_REF] Huebner | Scalable application-dependent network on chip adaptability for dynamical reconfigurable real-time systems[END_REF] and [START_REF] Ullman | On-demand FPGA run-time system for dynamical reconfiguration with adaptive priorities[END_REF], this is processed dynamically. A configuration controller is then generally supposed to execute tasks as a loader in an operating system, according to a calculated scheduling. This one can be directly implemented in the reconfigurable logic on the FPGA [START_REF] Curd | Dynamic reconfiguration of RocketIO MGT attributes[END_REF][START_REF] Blodget | A lightweight approach for embedded reconfiguration of FPGAs[END_REF][START_REF] Carvahlo | PADReH -a framework for the design and implementation of dynamically and partially reconfigurable systems[END_REF][START_REF] Huebner | Scalable application-dependent network on chip adaptability for dynamical reconfigurable real-time systems[END_REF][START_REF] Ullman | On-demand FPGA run-time system for dynamical reconfiguration with adaptive priorities[END_REF]. Real-time scheduling of hardware tasks on FPGA has been studied in [START_REF] Danne | A heuristic approach to schedule periodic real-time tasks on reconfigurable hardware[END_REF] and in [START_REF] Huebner | Scalable application-dependent network on chip adaptability for dynamical reconfigurable real-time systems[END_REF], a dynamic placement of tasks is performed thanks to a NoC architecture. In [START_REF] Ullman | On-demand FPGA run-time system for dynamical reconfiguration with adaptive priorities[END_REF], an adaptive priority scheme allows a partial reconfiguration of relocatable tasks. An interesting solution for multi-tasking was also proposed in the SCORE project [START_REF] Caspi | Stream computations organized for reconfigurable execution (SCORE)[END_REF], a multi-threaded computational model and architecture that rely on a scalable dynamic scheduling. The RAW architecture [START_REF] Taylor | The raw microprocessor: a computational fabric for software circuits and general-purpose programs[END_REF] allows dynamic switching of tasks but with a compiled programme.

Table 1

Examples of dynamically reconfigurable architectures

Our approach

Dynamic reconfiguration management techniques become mandatory in a SoC context where next generation circuits will have to be able to handle several applications simultaneously in an adaptive manner. In the literature, most of the approaches target fine grain partially reconfigurable circuits. But a major drawback of fine grain architectures is the latency introduced by their reconfiguration time. Coarse grain reconfigurable architectures allow to significantly reduce the configuration time, then allowing an increased reactivity to dynamic environments. For these kinds of architectures, only compiler support has been proposed to manage the dynamic reconfiguration. Our purpose is to explore a dynamic reconfiguration technique based on a run-time controller support allowing an adaptive placement and scheduling of unpredictable task scenarios. The objective of this paper is then to present a technique to handle dynamic configuration with the hardware, allowing the application designer to abstract dynamic reconfiguration management constraints. This technique is based on a run-time scheduler implementing an algorithm called dynamic hardware multiplexing (DHM). Thanks to this approach, the configuration of each application is generated at design time. At run-time, the scheduler takes care of the placement and modifies the original configuration in order to adapt the computational resources to handle several applications or to implement different qualities of service. The efficiency of our approach is characterised by two-metrics showing the increase in the resource usage and multi-application management. The suggested method has been designed and validated on a coarse grain reconfigurable architecture.

This paper is organised as follows: Section 2 presents a context analysis to derive the formal framework and characterisation metrics; Section 3 describes the dynamic HW multiplexing algorithms; Section 4 illustrates the implementation of DHM carried out on a coarse grain reconfigurable architecture; simulation results are exposed in Section 5 and HW/SW DHM schedulers validations are discussed in Section 6; finally, conclusions and perspectives are drawn.

Context analysis and formalisation

Self-adaptability represents a real challenge in the SoC context. One promising approach to achieve it consists in using a reconfigurable co-processing unit as illustrated in Figure 1.

To achieve this objective of adaptability, it is necessary to provide a middleware layer to allow a smart configuration management (the 'configuration manager' in the figure). This unit must be able to communicate relevant information to the operating system so that it allows a local and a global supervision of the co-processor configurations. In this section, we develop a formal framework for this issue, in order to define a solution to multi-application handling through dynamic reconfiguration.

Execution scenario

We assume a set θ of random tasks potentially assignable to the reconfigurable co-processor as a hardware task (which assumes that this task is time-consuming in a software fashion implementation). The cardinal of this set represents the number of requests from the OS. We assume the system is running during n cycles (from 0 to n). Each task T k ∈ θ is executed during n k cycles (n k is a non-deterministic variable, e.g., depends on how long the user wants to run the application). At each cycle of [0, n], the co-processor is running a set of tasks Γ ⊆ θ. At cycle n, the co-processor has handled card ε tasks where ε is the set of executed tasks (ε ⊆ θ).

The reconfigurable co-processor is modelled as a set of homogenous processing elements P (further along, our model will consider the memory bandwidth between the coprocessor and the memory as a set of memory channels C). Each task T k is represented by a set of processing elements P k (and further along by a set of memory channels C k ). Figure 2 illustrates three possible scenarios (a, b, c) with four tasks, θ = {Task 1, Task 2, Task 3, Task 4}, and with different starting points. The co-processor has eight processing elements as depicted in Figure 1. The time is represented on the X-axis in Figure 2, and the resource utilisation (PE) on the Y-axis. In scenario (a), all requests are handled by the reconfigurable co-processor; there is no particular observation in this example: each new task starts after the completion of the previous task. In scenario (b), Task 3 is started before the completion of Task 1. There are three PE required and three are available. The task is potentially assignable but this requires a relocation of the initial configuration. In scenario (c), Task 2 is started before the completion of Task 1. However, Task 2 and Task 1 cannot be executed simultaneously as they require more than the total of available PE (the area above P 3.1 ). This entails that the system must be able to stall either the execution of Task 1 on the reconfigurable co-processor if Task 2 has a higher priority (pre-emption) and make it possible to execute Task 2 or Task 1 alternatively on another resource of the system (the CPU, i.e.).

Task configuration management

The management of the configurations depends on a set of conditions. From the previous observations, we define the three following lemmas: T k ∈ θ has a higher priority than at least one of the running tasks, then this task is temporarily stalled for lemma 1 and lemma 2 analyses. If both are verified, the stalled task is permanently removed from the co-processor and migrated to another resource of the system (the CPU, i.e.). Or else, another task with lower priority is also temporary stalled and so on. This step is done until the compatibility is found; otherwise the OS chooses an alternative resource to execute T k .

Lemma 1: A task T k ∈ θ
The critical part of previous propositions is to determine a new configuration from the initial one, to fit the current state of the reconfigurable co-processor resources. This process is commonly named 'relocation' of a hardware task. This has been studied in the literature for FPGA but from our knowledge, never deeply explored for coarse grain reconfigurable architectures. In this case, the relocation process can be formalised as follows: if f(T i ) is the function implemented by T i the function transform() must verify f(T k ) = f(transform(T k )), In other words, transform() is a relocation process able to generate a new configuration {P k , C k }, functionally equivalent to the configuration of T k . This function depends on the targeted architecture, i.e., the interconnection topology, the homogeneity of the PE, type of I/Os, memories, etc.

The example exposed in Figure 3 illustrates this proposition. The coarse grain reconfigurable architecture (a) is a four PE structure. Each PE has the same reconfigurable functionality, i.e., each one can implement the same predefined set of arithmetic functions. Assuming that this reconfigurable architecture has to compute the following function: f(a, b) = (a + b) * (a -b), one possible configuration can be the one exposed in (b). But the same functionality can be also achieved with the configuration in (c). This functionally equivalent configuration is actually obtained with a modulo relocation process, i.e.:

( ) ( ) , , (
) % 2 , i j i j t f P f P + =
where t is a translation of the functionality to the adjacent PE, and two because of the two parallel PE.

The modulo-relocation process can be adapted to any architecture based on a torus or a ring topology. Anyway, this methodology can also be applied to any architecture with respect to its properties in terms of PE functionality, interconnection topology, I/Os… Moreover, as we will see in the next section, the 'modulo relocation' process can be used for other purposes, such as task duplication (TD), i.e., to increase the intrinsic performances.

Characterisation metrics

In order to evaluate the quality of the configuration management, it is necessary to define metrics. The multi-tasking efficiency (MT eff ) computes the percentage of tasks handled by the reconfigurable co-processor compared to the number of OS requests:

( ) 100 ( ) eff card MT card ε θ = ⋅
This metric represents the task acceptance ratio and it is basically dependant on the system workload. The system workload is dependent on the load that each task of θ implies on a given architecture, during a given time. Thus, we define the metric WL as follows:

( )

100 ( ) k k k T card P n WL ncard P θ ∈ ⋅ = ⋅ ∑
We define another metric, R, to represent the time usage ratio:

100 k k T n R n ε ∈ = ⋅ ∑
The processing efficiency (P eff ) is defined to calculate the space and time utilisation percentage ratio of the co-processing resources:

( ) ( ) 100 ( ) k eff k k t P c a r dP n n card P ε ∈ = ⋅ ⋅ ⋅ ∑ Figure 4
depicts an example of a set of tasks θ = {T 0 , T 1 , T 2 , T 3 } handled by a reconfigurable architecture with P= {p 0,0 , p 0,1 , p 1,0 , p 1,1 , p 2,0 , p 2,1 }. This example shows that for this set of tasks, a multi-tasking efficiency of 75% is achieved with a 55% overall processing efficiency and relative P eff is 66% with a time usage ratio R = 83% (Figure 5). DHM is the proposed approach to address the objective of system-on-chip adaptability with reconfigurable hardware. It is based on a dedicated application design flow and a reconfigurable system platform with a so-called dynamic hardware multiplexer.

DHM design flow

The proposed design flow is depicted in Figure 6. It is based on a two-phase process: the first step is performed at design-time and the second one at run-time.

The application is represented as a task graph. A first analysis allows to partition the graph and to classify each task. The non-critical tasks are compiled as software tasks (SW). Each critical task (time/power consuming) is given a priority level. Then, they are both compiled as SW tasks and as HW configurations (configware or CW). A header is attached to each HW task: it contains information about the task priority level, the number of required operators, etc. The compiled SW tasks produce an object code, and the HW tasks a configuration bitstream. They are finally linked together in a unique executable which includes both object codes and configuration bitstreams.

The task allocation is performed at run-time under OS control. A dedicated system call is used for this purpose: each time a task has been assigned to HW, the header is sent to the OS which communicates a co-processing request to the DHM unit: this one analyses the task header and compares the task requirements and the state of reconfigurable hardware (number of available operators, priorities of running tasks, etc.). The DHM unit takes the decision either to accept or reject the co-processing request. In the first case, the configuration bitstream is loaded into the reconfigurable co-processor, in the second one; the task object code is scheduled by the OS on the CPU. The DHM unit acts as a dedicated service of the OS for HW management. This service is detailed in the following section.

DHM services: mapping analysis, relocation and replication

The DHM unit is implemented as an OS service allowing an adaptive task mapping on a given reconfigurable architecture. It is composed of two procedures: the first one is dedicated to the mapping analysis and relocation (simultaneous multi-tasking mapping algorithm), and the second one to the replication (TD mapping algorithm).

Mapping analysis and task relocation

The first function of the DHM unit is to perform a mapping analysis regarding the co-processing (OsTaskRequest) request through the header. The OsTaskRequest is structured as follows: This header allows to determine whether the task can be mapped. The number of required resources in terms of operators and memory channels (nOp for the number of processing units, card (Pi) as previously mentioned, and nChannels, the number of DMA channels required, card(Ci)) is first analysed in Proposition 1 (i.e., Lemma 1). Then, a topological compatibility test (Topology[N], or as previously mentioned {Pi, Ci}) is realised in Proposition 2 (i.e., Lemma 2). If both propositions are true, the task T k is directly allocated: the corresponding configuration bitstream is then loaded in the configuration memory without changes. If Proposition2 is not verified, the transform() function is executed to compute a new configuration with an equivalent functionality (as exposed in the previous section) until a compatible solution is found or all the equivalent configurations have been tested (TransformationIsPossible becomes false). Consequently, a map function is used to load the configuration and apply the required transformations on the topology. When a task needs more than the available resources or cannot be adapted to the current state of running tasks, tasks are sorted by priority levels and mapped accordingly. When a task has to be removed or when it cannot be handled by the co-processor, the DHM unit generates a CPU equivalent context (initial or current) and transmits it to the OS: the SW task is then executed by the CPU.

Task replication

Task replication has several advantages like increasing the processing efficiency (P eff ) or minimising power consumption (if a computational task is duplicated, the operating frequency can be divided by 2 with the same performance): this is the role of the TD mapping function (Figure 8). The principle is quite simple and similar to the task relocation: after sorting the running tasks by priority levels, it tries to map a second instance of each task on the free resources. This process is executed each time the SMT mapping is executed and when a new task request is pending, a background routine suspends all duplicated tasks.

DHM interaction with the OS micro kernel

The micro kernel is globally considered to operate as a classical pre-emptive and interrupt driven operating system. It manages the task-control by keeping track of the status or state of each task. In our approach, a task can typically be in any one of the following states: A task is said to be executing when it is actually running as SW code in the CPU. Tasks in the ready state are those that are ready to run but are not running. Tasks that are waiting on a particular resource, and thus are not ready, are said to be in the suspended or blocked state. A task identified as critical at design time is set as a HW task and can then be executed either as SW or CW code depending on the co-processing resource availability. When the micro kernel loads such a task, it generates a request to the DHM unit which performs a mapping analysis. During this time, the task is set to suspended mode in the micro kernel task list. When the analysis is completed, it generates an interrupt to the micro kernel which indicates whether the task can be implemented in SW or in CW fashion. In the first case, the task is set to ready and in the second one to co-executing.

When a process is killed, if the task is executing or ready, it is simply removed from the task list of scheduling and dispatching units of the OS. If it is suspended or co-executing, an OS request is sent to the reconfigurable co-processor to indicate that the task is being resumed. In this way, the resources involved are released and the task is removed from the OS task list.

Case study

Targeted architecture

The systolic ring is a customisable coarse grain reconfigurable model. It features a compact DSP-like coarse grain reconfigurable datapath, the Dnode, which is the building block of the architecture. The architecture is configured by a microinstruction code loaded from the memory to a local sequencer using dedicated registers as a configuration memory. Figure 9 describes this architecture. The specific structure of the operating layer is depicted in Figure 10. The ring topology allows an efficient implementation of pipelined datapath. The switch components establish a full connectivity between two layers. The systolic ring also provides an alternative connection bus network which proves useful for recursive operations, i.e. It allows to feedback data to previous layers implemented from each switch in the structure. Each switch in the architecture has a read access on each switch's bus.

Each configuration programme line is able to set the configuration of an entire Dnode layer (2 Dnodes on the 8 Dnodes systolic ring depicted in Figure 10) each cycle. Up to 12.5% of the Dnodes can be reconfigured at each cycle in the actual version, but this can be tailored, especially when d/l varies, d being the number of Dnodes per layer and l the number of layers. An assembler/simulator environment has been developed. This environment also generates the object code running on the global sequencer and dynamically managing the configuration.

With the formalism developed in Section 3, we can describe the architecture as

P = {{p 0,0 , p 0,1 , …, p 0,d-1 }, {p 1,0 , p 1,1 , …, p 1,d-1 },…, {p l-1,0 , p l-1,1 , …, p l-1,d-1 }}and C = {c 0 , c 1 , …, c 1 } with dim P = l × d and dim C = l.
The total number of processing elements of the architecture is then given by card P = l.d.

P 1 = {{1, 1}, {1, 1}, {0, 0}, {0, 0}}
Step 1.

Transform process implementation

The proposed DHM algorithms can be applied to any coarse grain reconfigurable architecture supporting run-time partial reconfiguration. The only architecture-dependent function is the transformation process applied to modify the configuration. This can be easily derived from the topology of the targeted architecture. For instance, the systolic ring architecture is based on a homogenous ring topology where each processing element is able to implement the same set F of arithmetic and logic functions. Thus, a simple rotation (an example is depicted in Figure 11) of the configuration following the dataflow direction (i) is functionally-equivalent. The following formula formalises this lemma and is used in the DHM algorithm in order to find equivalent implementations:

( ) ( ) ( ) ( ) , ( ) % , ( )% , [0.. 1] and [0.. 1],
and where

i j i r l j j ir l r i l j d f p f p f c f c f F + + ∀ ∈ - ∈ - = = ∈

Multi-tasking scenario with image processing kernels

Image processing is well known as a time consuming application field. Therefore, its implementation is often inefficient on general purpose processors making alternative approaches attractive. Several test benches have been implemented on the systolic ring in order to validate our purpose on real world applications. We focus here on the kernel acceleration which represents generally more than 80% of the CPU time required on a general purpose processor.

Figure 12 details the even-odd frequencies decomposition of a discrete cosine transform (DCT) [START_REF] Chen | A fast computational algorithm for the discrete cosine transform[END_REF] implementation. This decomposition splits the calculations into two matrix products. Once the first layer calculations have been carried out, the sums and differences of the samples are sent to the following layer which performs the multiplication-accumulation.

Several studies have proven that the wavelet transform is an efficient alternative to the classical DCT, and thus, it has been chosen for the JPEG2000 standard. Our implementation uses the lifting scheme [START_REF] Sweldens | The lifting scheme: a construction of second generation wavelets[END_REF] algorithm and operates a 2D direct transform on a 1,024 × 768 pixels 16 bits coded image. One pixel sample is computed each clock cycle, thanks to the use of 4 Dnodes, two based on local-mode implementation (Figure 13) and two global buses.

Block matching, and especially full search block matching (FSBM) algorithm is the most popular implementation, also recommended by several standard committees for motion estimation [START_REF] Park | Reconfiguration for power saving in real-time motion estimation[END_REF] . Figure 14 illustrates its implementation on the systolic ring.

Figure 15 depicts the scheduling and the mapping of previous tasks obtained thanks to the use of the DHM unit with the systolic ring on several scenarios. Thanks to the relocation scheme, the same task can be mapped on different processing elements with the same behaviour and functionality as expected at design time.

Figure 12 DCT implementation onto the systolic ring (see online version for colours)

+ Mac FIFO output FIFO input FIFO input - Mac FIFO output FIFO input FIFO input ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ + + + + ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ δ - β β - δ α α - α - α β - δ - δ β = ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ 4 3 5 2 6 1 7 0 6 4 2 0 1 1 1 1 x x x x x x x x z z z z α = cos (π/4) β = cos (π/8) δ = sin (π/8) ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ + + + + ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ δ - β β - δ α α - α - α β - δ - δ β = ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ 4 3 5 2 6 1 7 0 6 4 2 0 1 1 1 1 x x x x x x x x z z z z α = cos (π/4) β = cos (π/8) δ = sin (π/8) ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ - - - - ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ λ - γ μ - ν γ ν λ - μ μ - λ - ν - γ ν μ γ λ = ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ 4 3 5 2 6 1 7 0 7 5 3 1 x x x x x x x x z z z z λ = cos (π/16) γ = cos (3π/16) μ = sin (3π/16) ν = sin (π/16) ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ - - - - ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ λ - γ μ - ν γ ν λ - μ μ - λ - ν - γ ν μ γ λ = ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ 4 3 5 2 6 1 7 0 7 5 3 1 x x x x x x x x z z z z λ = cos (π/16) γ = cos (3π/16) μ = sin (3π/16) ν = sin (π/16) x N T N z ) ( 2 = x N T N z ) ( 2 =

Evaluation and experimental results

The DHM unit has been implemented and attached to the systolic ring, and then tested on three DSP kernels.

Simulations have demonstrated the run-time adaptability on different application scenarios. In order to generalise our approach on larger sets of scenarios, a simulation framework has been developed and is presented in this section.

Figure 16 depicts the simulation environment developed to explore and characterise the proposed approach. The generation of task scheduling and the DHM mapping is completely automated allowing to produce results on a large number of scenarios. The simulation framework is composed of a C++ programme with constants defined to tune the scenario characteristics or architecture generic parameters. This programme is interfaced with a spreadsheet programme calculating and probing the resulting task mapping. Also, the previous metrics are automatically computed and plotted for characterisation. For a given architecture, ten scenarios are generated with a random task sequence and a given range of scenario parameters. For each scenario, the parameters have been drawn lots: the task requirements in terms of processing elements and memory bandwidth, the workload (number of tasks from 2 to 80 (card θ ∈ [2, 80], on a given time n with variable task duration n k ), and the task sequence. Each generated scenario corresponds to a task scheduling. Three mapping procedures are then performed: one without the DHM capabilities, other ones with simultaneous multi-tasking procedure (DHM-SMT), and the last one with SMT and task duplication (DHM-SMT-TD). In order to extract statistical results, a total of 300 scenarios have been simulated for a given workload. Thus, the presented values in the following figures correspond to a mean value on 300 samples. Figure 17 depicts the resulting task scheduling (ten tasks) with a relative workload for both tested architectures (80% for 8-PE systolic ring, and 20% for 32-PE systolic ring). The Blue histogram represents the cumulated resource requirements at a given time. The size and shape of the tasks were inspired from the image processing kernels presented in the previous section. During a run-time duration equal to 5,000 seconds, ten tasks are run. We observe a maximum of 13 resources required and a mean value around six processing elements. We have depicted in Figure 18 and Figure 19 the resulting placement and scheduling on both 8-PE systolic ring and 32-PE systolic ring. In Figure 18, we notice that without any relocation possibility, the co-processor is underexploited and it rejects a lot of task requests. With DHM SMT, the resource utilisation is clearly higher. Because of its relocation feature, the task acceptance is improved. Thanks to the TD of DHM, we observe on the yellow histogram that the maximum of available resource can be reached while on the other ones it is either seldom (with SMT) or never. However, this technique does not increase the task acceptance. In Figure 19, with the same scenario, we show that the resulting placement/scheduling are exactly the same without any relocation feature. This results in a high under-usage of the available resources. With DHM SMT, all the task requests are accepted and thanks to the TD feature, a maximum of 26 parallel operations is reached. However, the systolic ring with 32-PE remains underused compared to the large number of available resources. This can be explained by the fact that resulting workload is four times lower. There are five different workload levels compared in this survey: from very low workloads (scenario #1) to very high workloads (scenario #5). Please, notice that in each case, the WL produced by these scenarios is always four times lower for 32-PE systolic ring. The histograms plotted here highlight the difference between two different instances of the systolic ring (8-PE in Figure 22, and 32-PE in Figure 23). The results presented above were done for a high workload scenario (scenario #4). We observe here the evolution in Peff and MTeff. Basically, Peff increases in both cases but grows quickly in the smallest systolic ring. It reaches a value between 80% to 90% for high and very high workloads, with a typical value around 70%. However, the MTeff decreases to a value around 60% for very high workloads. For the biggest systolic ring, the increase in Peff is slower but it reaches a value of 60% for the very high workloads, and still the task acceptance is higher than 90%. These results here emphasise the improvements obtained thanks to DHM through SMT and TD features. On the smallest systolic ring, the processing efficiency is clearly increased from 30% to almost 90%. The multi-tasking efficiency is also basically improved as it is more than doubled (from 30% to 70%) and the co-processor is used almost all the time (more than 95% of run-time). In Figure 21, we observe that all the tasks have been accepted (multi tasking efficiency equals 100%) and the systolic ring is used 100% of the run-time. But the processing efficiency is lower than the previous one as the set of tasks used for the simulation has a lower workload (20%).

When the set of tasks simulated is compounded with bigger sized tasks (Figure 24), the obtained results show an improved processing efficiency but the multi-tasking efficiency is lowered down.

HW and SW implementations

To evaluate the cost and performances of hardware and software implementations, we have designed both of them. In this section, we show the obtained results and we analyse the perspectives of each one.

HW DHM: Saturn ring system

The Saturn controller is a DHM unit implementation for the systolic ring architecture. This unit is a dedicated configuration processor. It is mainly composed of a programme counter (PC) that allows the generation of the programme memory addresses. Data coming from this memory are either headers or configuration words. Different logic blocks are used for topology matching analysis between the current state of the reconfigurable accelerator and the header fields. When a compatibility is found (after a configuration rotation or not), a configuration word is read from the memory and then modified accordingly. Dedicated registers are used to store the state of the systolic ring resources (e.g., Dnodes) at each cycle in order to allocate them if necessary. Saturn has been designed in behavioural VHDL and then synthesised with Cadence design flow as illustrated in Table 3. The design kit used is AMS 0.35 µ with four metal layers (3.3 V). The maximum accessible frequency in this technology for the synthesised hardware is 30 MHz.

SW DHM: the plasma processor

We have used a soft processor to implement the DHM algorithm with a software programme. This one is a MIPS-like processor. It is based on a 32 bits CPU, a local memory and an UART. The CPU is based on a three stage pipelined unit, an ALU, a shifter and a multiplier. The DHM programme is first compiled with a gcc cross compiler with the third level of optimisation allowing a gain on the performances around 20%. This code is then loaded into the local memory and executed indefinitely. Two different implementations have been tested: one optimised for memory, the other optimised for speed. The results are summarised in the table below. Several memories were synthesised from the manufacturer website following the size required for the code. The maximum accessible frequency for the synthesised processor is 30 MHz for an area equal to 1.44 mm 2 .

Performance comparisons

HW and SW-DHM controllers have been designed both for a systolic ring instance composed with 8 Dnodes. After synthesis, the designs have been validated by simulations.

For HW-DHM, the whole algorithm takes less than 25 cycles (0.8µs@30MHz) to dynamically modify and (re-)allocate a pre-defined configuration. The area overhead is about 0.4 mm 2 , which represents less than 10% of the systolic ring. For SW-DHM, the 32 bits processor has a silicon area of 1.44 mm 2 (about 36% of the systolic ring area) and implies in the worst case up to 65,902 cycles (2.1mms@100MHz) to perform the same allocation task. These results are listed in Table 5. Not surprisingly, these results clearly show the superiority of the dedicated approach with a global performance [1/AT (DeHon, 1998)] 10,000 times better than the SW-DHM. However, the HW-DHM requires much more design effort, while the SW-DHM can be easily changed by simply reprogramming the processor. Moreover, the software approach is far more scalable as it requires no area overhead for different instances. In terms of latency introduced by the mapping process, the quality of service obtained with hardware DHM is better than the software DHM as it is less than a microsecond, which certifies a very fast reconfiguration. However, for some applications, a maximum latency of 2 ms can be acceptable (i.e., audio applications require less than 8 ms).

Figure 2

 2 Figure 2 Execution scenarios of task processing and co-processor utilisation

Figure 3 Figure 4

 34 Figure 3 Coarse grain reconfigurable architecture example (a) and (b) (c) implementations of (a + b)*(a -b)

Figure 5

 5 Figure 5 Architecture characterisation with the proposed metrics

Figure 6

 6 Figure 6 DHM design flow

Figure 9 Figure 10

 910 Figure 9 Processing element architecture

Figure 11

 11 Figure 11 Task mapping with rotation-based transformation scheme

Figure 13 Figure 14 Figure 15

 131415 Figure 13 Wavelet transform implementation onto the systolic ring (see online version for colours)

Figure 16

 16 Figure 16The simulation environment (see online version for colours)

Figure 17

 17 Figure 17 Example of a generated task-scheduling

Figure 18 Figure 19 Figure 20

 181920 Figure 18 Task scheduling on 8-PE

Figure 21

 21 Figure 21 Characterisation with 32 PE

Figure 22

 22 Figure 22 Peff and MTEff on 8-PE with different task schedules

Figure 23

 23 Figure 23 Peff and MTEff on 32-PE with different task schedules

Figure 20 and

 20 Figure20and Figure21characterise both scenarios and architectures thanks to the metrics suggested in Section 3. These results here emphasise the improvements obtained thanks to DHM through SMT and TD features. On the smallest systolic ring, the processing efficiency is clearly increased from 30% to almost 90%. The multi-tasking efficiency is also basically improved as it is more than doubled (from 30% to 70%) and the co-processor is used almost all the time (more than 95% of run-time). In Figure21, we observe that all the tasks have been accepted (multi tasking efficiency equals 100%) and the systolic ring is used 100% of the run-time. But the processing efficiency is lower than the previous one as the set of tasks used for the simulation has a lower workload (20%).When the set of tasks simulated is compounded with bigger sized tasks (Figure24), the obtained results show an improved processing efficiency but the multi-tasking efficiency is lowered down.

Figure 24

 24 Figure 24 Task scheduling on 32-PE

Figure 25

 25 Figure 25 Task scheduling on 32 PE (see online version for colours)

  Simplified overview of the targeted SoC

	C entra l Processing Un it	C onfig uration	Manager	P E 0,0 P E 0,1	PE 1, 0 PE 1, 1	PE 2,0 PE 2,1	PE 3, 0 PE 3, 1	Data I/O
				Reconfigurable Coprocessor Bus	Bu s
								Arbi ter
		Proc essor / Memory B us				Bus
								Arb ite r
	Memory			D MA C ontro lle r		Timer	Peripherals Bus
							UAR T

Figure 1

  The On field is a Boolean that indicates if the task starts or ends up. The TaskId is a number attributed by the OS to identify the task. The ConfigTaskAddress is a pointer to the configuration bitstream memory location. The Header field is defined as follows:

	Header;
	* ConfigTaskAddress;
	}OsTaskRequest;
	typedef struct ConfigurationHeader {
	nOp;
	nChannels;
	Topology[N];
	Priority;
	}ConfigurationHeader;
	typedef struct OsTaskRequest {
	On;
	TaskId;

Table 3

 3 Performance and overhead of HW DHM

	Saturn	Area (mm²)	Min. lat (cycles)	Max. lat (cycles)	Power cons. (mW/MHz)
	DHM SMT	0.38	6	25	0.10
	DHM	0.40	6	25	0.12
	SMT-TD

Table 4

 4 Performance and overhead of SW DHM

	Plasma	Mem. (KB)	Min. lat. (cycles)	Max. lat. (cycles)	Power cons (mW/MHz)
	DHM1 SMT	23	3,806	65,902	1.25
	DHM1	25	3,806	65,902	1.36
	SMT-TD
	DHM2 SMT	16	1,200	188,359	1.12
	DHM2	18	1,200	188,359	1.16
	SMT-TD

Table 5

 5 Comparison of performance and overhead of HW and SW DHM

		HW-DHM scheduler	SW-DHM scheduler
	Area (mm 2 )	0.40	1.44
	Time (µs)	0.83	2,186.73
	1/(A.T)	3	3.10 -4

He is nominated as a member from the French University Institute in 1997, Advisor at the Research Ministry, and Scientific Co-Director from the STIC (Information and Communication Technology and Science) Department of CNRS (2002CNRS ( -2004)). He is currently the Vice President of CNFM (National Committee of Microelectronic Education) since 1999, and the Director of LIRMM since 2005.

Conclusions and future works

In this article, we have proposed and implemented a method for dynamic reconfiguration management. This method is based on a DHM algorithm allowing an abstraction, at design-time, of the dynamic reconfiguration management.

The DHM algorithm aims at exploiting more efficiently the processing resources thanks to an adaptive online scheduling technique. A case study on the systolic ring architecture has proven the feasibility of the proposed approach. The simulation results show an improved processing efficiency and dynamic reconfiguration is directly and automatically managed by the hardware. The HW-scheduler offers a clearly better performance/area trade-off, while the SW-DHM approach is attractive from the point of view of its flexibility. The features of our approach compared to related works are depicted in Table 6. A 'fine-grain' implementation could also be considered but we strongly believe that our method takes its whole sense on coarse grain architectures and proposed DHM is very easy to adapt to any processing element interconnection topology. The main limitation stands actually on the processing element programming. We are therefore exploring a new architectural support for DHM based on a mesh network of RISC processors that we can directly address with a C code.