Amélie Vantaux
email: amelie.vantaux@gmail.com

Saorin Kim

Eakpor Piv

Sophy Chy

Nimol Laura Berne

Nimol Khim

Dysoley Lek

Sovannaroth Siv

Mavuto Mukaka

Walter R Taylor

Didier Ménard

Significant efficacy of single low dose primaquine compared to stand alone artemisinin combination therapy in reducing gametocyte carriage in Cambodian patients with uncomplicated multidrug resistant Plasmodium falciparum malaria

Keywords: direct-membrane feeding assays, transmission-blocking, malaria, primaquine

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

Introduction

Malaria remains a major public health challenge with an estimated 228 million cases recorded in 2018 [START_REF]World malaria report 2019[END_REF]. While considerable progress has been made since 2010 when the estimated case burden was 251 million, the recent emergence and spread of both artemisinin and piperaquine resistant Plasmodium falciparum lineage (KEL1/PLA1) in the Eastern Greater Mekong subRegion (GMS), threaten this remarkable global achievement [START_REF] Noedl | Evidence of Artemisinin-Resistant Malaria in Western Cambodia[END_REF][START_REF] Dondorp | Artemisinin resistance in Plasmodium falciparum malaria[END_REF][START_REF] Saunders | Dihydroartemisinin-piperaquine failure in Cambodia[END_REF][START_REF] Leang | Evidence of Plasmodium falciparum malaria multidrug resistance to artemisinin and piperaquine in Western Cambodia: dihydroartemisinin-piperaquine open-label multicenter clinical assessment[END_REF][START_REF] Imwong | Spread of a single multidrug resistant malaria parasite lineage (PfPailin) to Vietnam[END_REF][START_REF] Van Der Pluijm | Determinants of dihydroartemisinin-piperaquine treatment failure in Plasmodium falciparum malaria in Cambodia, Thailand, and Vietnam: a prospective clinical, pharmacological, and genetic study[END_REF]. Eliminating rapidly multidrug resistant P. falciparum (MDRPf) is, therefore, the top priority for countries of the Greater Mekong Subregion (GMS). Implementation of novel tools and strategies or repurposing existing tools like primaquine that specifically aim at interrupting malaria transmission are essential to reach this goal.

Although artemisinin derivatives are the more potent compounds in artemisinin-based combination therapies (ACTs) and are active against early gametocyte stages (8-10) and reduce transmission [START_REF] Targett | Artesunate reduces but does not prevent posttreatment transmission of Plasmodium falciparum to Anopheles gambiae[END_REF][START_REF] Drakeley | Addition of artesunate to chloroquine for treatment of Plasmodium falciparum malaria in Gambian children causes a significant but short-lived reduction in infectiousness for mosquitoes[END_REF], the only currently available drug effective against the transmissible mature stage V gametocytes is primaquine. In 2012, the WHO recommended the addition of single low dose of primaquine (SLDPQ, target dose 0.25mg/kg) to ACTs to interrupt malaria transmission, primarily in low transmission areas of MDRPf like the GMS [START_REF]Single dose primaquine as gametocytocide in Plasmodium falciparum malaria[END_REF].

To date, several clinical studies conducted in Africa, Colombia and Cambodia, have assessed the safety and efficacy of SLDPQ [START_REF] Mwaiswelo | Safety of a single low-dose of primaquine in addition to standard artemether-lumefantrine regimen for treatment of acute uncomplicated Plasmodium falciparum malaria in Tanzania[END_REF][START_REF] Eziefula | Single dose primaquine for clearance of Plasmodium falciparum gametocytes in children with uncomplicated malaria in Uganda: a randomised, controlled, double-blind, dose-ranging trial[END_REF][START_REF] Dicko | Primaquine to reduce transmission of Plasmodium falciparum malaria in Mali: a single-blind, dose-ranging, adaptive randomised phase 2 trial[END_REF][START_REF] Goncalves | Single low dose primaquine to reduce gametocyte carriage and Plasmodium falciparum transmission after artemether-lumefantrine in children with asymptomatic infection: a randomised, double-blind, placebo-controlled trial[END_REF][START_REF] Chen | Safety of Single-Dose Primaquine in G6PD-Deficient and G6PD-Normal Males in Mali Without Malaria: An Open-Label, Phase 1, Dose-Adjustment Trial[END_REF][START_REF] Dicko | Efficacy and safety of primaquine and methylene blue for prevention of Plasmodium falciparum transmission in Mali: a phase 2, single-blind, randomised controlled trial[END_REF][START_REF] Bastiaens | Safety of single low-dose primaquine in glucose-6-phosphate dehydrogenase deficient falciparum-infected African males: Two openlabel, randomized, safety trials[END_REF][START_REF] Tine | Safety and Efficacy of Adding a Single Low Dose of Primaquine to the Treatment of Adult Patients With Plasmodium falciparum Malaria in Senegal, to Reduce Gametocyte Carriage: A Randomized Controlled Trial[END_REF][START_REF] Lin | Single dose primaquine to reduce gametocyte carriage and Plasmodium falciparum transmission in Cambodia: An open-label randomized trial[END_REF][START_REF] Arroyo-Arroyo | Efficacy of Different Primaquine Regimens to Control Plasmodium falciparum Gametocytemia in Colombia[END_REF][START_REF] Okebe | The gametocytocidal efficacy of different single doses of primaquine with dihydroartemisininpiperaquine in asymptomatic parasite carriers in the Gambia: a randomized controlled trial[END_REF], mainly by measuring gametocyte carriage [microscopy or Taqman reverse transcriptase polymerase chain reaction (RT-PCR)] as a surrogate marker of its transmission blocking efficacy. This is due to the challenging logistical requirements of carrying out mosquito infectivity studies. These studies showed that SLDPQ, dosed from 0.20 to 0.75 mg/kg, clearly reduced gametocyte carriage and increased their clearance in a dose dependent manner (15-17, 19, 21-25). A small number of studies have investigated human-to-mosquito transmission, based on infectivity measures, with variable results due to low pre-and/or post-SLDPQ infectivity [START_REF] Dicko | Primaquine to reduce transmission of Plasmodium falciparum malaria in Mali: a single-blind, dose-ranging, adaptive randomised phase 2 trial[END_REF][START_REF] Goncalves | Single low dose primaquine to reduce gametocyte carriage and Plasmodium falciparum transmission after artemether-lumefantrine in children with asymptomatic infection: a randomised, double-blind, placebo-controlled trial[END_REF][START_REF] Dicko | Efficacy and safety of primaquine and methylene blue for prevention of Plasmodium falciparum transmission in Mali: a phase 2, single-blind, randomised controlled trial[END_REF][START_REF] Lin | Single dose primaquine to reduce gametocyte carriage and Plasmodium falciparum transmission in Cambodia: An open-label randomized trial[END_REF][START_REF] Okebe | The gametocytocidal efficacy of different single doses of primaquine with dihydroartemisininpiperaquine in asymptomatic parasite carriers in the Gambia: a randomized controlled trial[END_REF]. Only two studies from Mali demonstrated conclusively the transmission-blocking efficacy of SLDPQ which produced a 92.6% to 100% within-person reduction in infectivity at Day 2 vs. baseline following 0.25 mg/kg of SLDPQ [START_REF] Dicko | Primaquine to reduce transmission of Plasmodium falciparum malaria in Mali: a single-blind, dose-ranging, adaptive randomised phase 2 trial[END_REF][START_REF] Dicko | Efficacy and safety of primaquine and methylene blue for prevention of Plasmodium falciparum transmission in Mali: a phase 2, single-blind, randomised controlled trial[END_REF].

In Cambodia, glucose-6-phosphate dehydrogenase deficiency (G6PDd) is a common X-linked disorder of the red blood cells with frequencies ranging from 10.8% to 29.6% in males ( 26) and a prevalence rate in malaria patients seen at health centers estimated at 13.9% [START_REF] Khim | G6PD deficiency in Plasmodium falciparum and Plasmodium vivax malaria-infected Cambodian patients[END_REF]. This is the main reason why Cambodian policy makers have been reluctant to deploy SLDPQ without local data on the safety and the efficacy of SLDPQ. Therefore, we conducted a trial assessing the tolerability and the safety of SLDPQ (0.25mg/kg) in Cambodia in 2015-2016 [START_REF] Dysoley | The tolerability of single low dose primaquine in glucose-6-phosphate deficient and normal falciparum-infected Cambodians[END_REF], which followed on from a safety trial of 0.75 mg/kg/week of PQ in vivax patients [START_REF] Kheng | Tolerability and safety of weekly primaquine against relapse of Plasmodium vivax in Cambodians with glucose-6-phosphate dehydrogenase deficiency[END_REF]. Here, we present our investigations on the transmission-blocking efficacy of this treatment through the evaluation of gametocyte prevalence dynamics as well as infectivity measures on a subset of patients using membrane-feeding assays with Anopheles minimus mosquitoes, one of the main malaria vectors in Southeast Asia.

Methods

Study design

This open-label randomized control trial assessing the tolerability and the safety of SLDPQ was carried out in Banlung, Rattanakiri province in northeastern Cambodia in 2015-2016 (NCT02434952), as described in Dysoley et al. [START_REF] Dysoley | The tolerability of single low dose primaquine in glucose-6-phosphate deficient and normal falciparum-infected Cambodians[END_REF]. Briefly, 109 non pregnant, non breast feeding patients aged ≥1 year with acute uncomplicated falciparum malaria (≥1 asexual parasite/500 white blood cells equivalent to 16 asexual parasites/µl) and a hemoglobin concentration ≥6g/dL were recruited to receive either dihydroartemisinin piperaquine (DP, Duo-Cotecxin®, D40 mg and P320 mg, Zhejiang Holley Nanhu Pharamaceutical Co. Ltd, Jiaxing, Zhejiang, China) alone or combined with SLDPQ (0.25mg/kg given with the first dose of DP, Thai Government Pharmaceutical Organization, 15mg of primaquine base). Clinical and laboratory assessments were performed on Days (D) 0, 1, 2, 3, 7, 14, 21 and 28. Anopheles minimus mosquitoes were fed on blood samples collected from a subset of 55 patients and on the days of recurrent (Drec) falciparum parasitaemia (defined by the WHO as late treatment failures) depending on mosquito availability using direct-membrane feeding assays (DMFA).

The sample size calculation was based on the primary outcome of a reduction in the mean D7 hemoglobin (Hb) concentration of 1 g/dL in the G6PDd DP+SLDPQ arm vs. G6PDn DP+SLDPQ arm. Assuming a mean and standard deviation of 11.27 (1.74) g/dL, calculated from a SE Asian database of ⁓6,800 ACT-treated, falciparum-infected patients of all ages (WRJT, unpublished), a two-sided alpha of 0.05, power of 80%, the sample size was 48/arm, rounded up to 50. G6PD status in the field was diagnosed initially using the fluorescent spot test to allow for the allocation of SLDPQ. The qualitative Carestart ® (AcessBio, Solerset, NJ) rapid diagnostic test was assessed in parallel.

Mosquito infection

DMFAs were carried out to assess individual malaria infectivity as described previously [START_REF] Vantaux | Contribution to malaria transmission of symptomatic and asymptomatic parasite carriers in Cambodia[END_REF].

Briefly, 3-to-5-day-old An. minimus females were fed through membranes on patient's blood.

Mosquitoes were starved for 24h before being provided a blood meal. Venous blood samples were collected in heparinized tubes and 400µl of blood were made available in membrane feeders maintained at 37°C. Females were fed only once on freshly drawn blood. Post-feeding, unfed females were discarded and fed females were kept in cages (20x20x20cm) with constant access to a 10% sucrose solution. Patient infectivity was determined by assessing infection prevalence (i.e.

proportion of infected females) and infection intensity (i.e. number of Plasmodium sp. oocysts in infected females). Midguts were dissected in a 1% Mercurochrome ® stain and the presence and the number of oocysts were determined under a microscope (20x magnification). Dissections were performed 7-day post-blood meal. The mean number of dissected females was 49 (range: 15-85, median: 50).

Biological investigations

Parasite RNA was extracted from the Trizol ® (Life Technologies Holdings Pte Ltd, Singapore) conserved whole blood samples using QIAamp RNA Blood Mini Kit® (Qiagen, Germany), following the protocol recommended by the manufacturer. A two-step semi-quantitative real time PCR was performed to detect malaria parasites, as previously described [START_REF] Canier | An innovative tool for moving malaria PCR detection of parasite reservoir into the field[END_REF]. Following PCR amplification, falciparum positive samples were analyzed for the presence of gametocytes by a Taqman RT-PCR, using primers spanning an exon-exon junction and targeting the "Plasmodium falciparum meiotic recombination protein DMC1-like protein" gene (AF356553), as described previously [START_REF] Lawaly | Heritability of the Human Infectious Reservoir of Malaria Parasites[END_REF]. Gametocyte dilution series based on in-vitro cultured local strain were used to estimate gametocyte blood concentrations.

Ethical statement

Results

One hundred nine patients with uncomplicated falciparum malaria were enrolled and treated with the standard 3-day DP alone (48.6%, 53/109) or DP+SLDPQ (51.4%, 56/109). Seven patients were lost to follow up (6.4%). Of the remaining 102 patients, 28 (27.4%) had PCR-proven P. falciparum recrudescences; 24 occurred within the 28-day follow up on Days 12 (1), 14 (1), 17

(2), 18 (1), 21 (2), 22 (2), 23 (1), 24 (2), 25 (1), 26 (2), 27 (1), 28 [START_REF] Adjuik | Artesunate combinations for treatment of malaria: meta-analysis[END_REF], and four on D44, 46, 52, and 124. Of the 28 recrudescent patients, 10 were retreated with the standard 3-day DP and 18 with quinine or quinine plus tetracycline; six of the 10 patients retreated with DP experienced a second recrudescence. At D0, gametocytes were detected in 47/109 patients (43.1%) by Taqman RT-PCR (Table 1; see 30 for further details), with no significant difference between arms (P=0.3057).

Gametocyte dynamics

Examining the dynamics of Taqman RT-PCR gametocyte carriage to D28, drug arm, baseline gametocytemia, recrudescence status, baseline hemoglobin and Day of follow up were all significant factors for gametocytemia in the univariate analysis (Table 2).

The DP recipients were more likely to be gametocytemic than DP+SLDPQ recipients during the follow-up, seen more clearly on D7 and D14 (Table 2; Figure 1) as were patients with baseline gametocytemia (Table 2; Figure 2) and recrudescent vs. cured patients (Table 2).

Baseline hemoglobin concentration and Day of follow-up were inversely associated with the probability of being gametocytemic during the follow-up (Table 2).

When the aforementioned factors were tested in a multivariable model, all except drug arm remained significant in the multivariate analysis (Table 3, model 1). However, when removing recrudescence from the multivariable model, drug arm was a significant explanatory factor again (Table 3, model 2).

Post-hoc calculation showed that there was a 99.1% power to detect a difference between the DP and DP-PPQ treatment with the study sample sizes (n=49 and n=56 on D7 for DP and DP-PPQ respectively.

Mosquito infectivity

A total of 55 patients were included in the DMFAs. Amongst the 292 feeding assays, only 113 of 14,444 (0.78%) dissected mosquitoes were infected (Table 4). Overall, 3 out of 48 (6.3 ± 6.8%) individuals infected at least one mosquito at baseline, one individual was infectious on D14 (DP) and two individuals with recrudescent infections (Tables 4 &5) who were repeat DP treatment failures: (i) at presentation on D124 (DP+SLDPQ), and (ii) D35 (7 days post DP started on D28).

The three individuals infectious on D0 were all gametocytemic by microscopy, received DP+SLDPQ and were not infectious on D1 or D3 post-treatment (Table 5).

Discussion

In 2012, the WHO recommended adding 0.25 mg/kg SLDPQ to first-line treatments (ACTs) to kill mature gametocytes and block human-to-mosquito transmission [START_REF]Single dose primaquine as gametocytocide in Plasmodium falciparum malaria[END_REF]. As no data were available at that time in Cambodia, we investigated the transmission-blocking efficacy of SLDPQ when given with DP (the recommended first line standard ACT in 2015) by evaluating gametocyte prevalence dynamics (Taqman RT-PCR) and Anopheles minimus infectivity by DMFA.

Our results show that SLDPQ, given on the first day of the 3-day standard ACT treatment, significantly decreased gametocyte carriage over time, starting on D3 and was least on D7 resulting in a 5.59 fold reduced risk, relative to DP alone, over 28 days in the univariate analysis. This is consistent with recent reports on the efficacy of PQ in reducing gametocyte carriage (15-17, 19, 21-25, 34) and earlier reports showing a lag between reduced gametocyte carriage and rapid mosquito infectivity. The multivariable analysis revealed the significant effect of recrudescent (resistant) infections on gametocyte carriage with a 3 fold reduction in gametocyte carriage in the absence of resistance.

Our patients had a high rate of baseline gametocytemia (19% by microscopy, just under 45% by Taqman RT-PCR), which is similar to that reported previously in 2010 in artemisinin resistant western Cambodia (~19%) but is three fold higher than the 6% reported earlier in Rattanakiri province [START_REF] Ashley | Spread of artemisinin resistance in Plasmodium falciparum malaria[END_REF]. Given the high prevalence of PfKelch13 mutant P. falciparum parasites (63%) in our study and the very high recrudescent rate (⁓28%), our high gametocyte carriage rate is consistent with the presence of ARPf, which has also led to piperaquine resistance [START_REF] Van Der Pluijm | Determinants of dihydroartemisinin-piperaquine treatment failure in Plasmodium falciparum malaria in Cambodia, Thailand, and Vietnam: a prospective clinical, pharmacological, and genetic study[END_REF]. This is consistent with another study in Cambodia which showed that DP treated patients from Oddar Meanchey province (northern Cambodia) also had prolonged gametocyte carriage, irrespective of the slow asexual parasite clearance time, due to ARPf, and in patients with recrudescent infections [START_REF] Lin | Single dose primaquine to reduce gametocyte carriage and Plasmodium falciparum transmission in Cambodia: An open-label randomized trial[END_REF][START_REF] Ashley | Spread of artemisinin resistance in Plasmodium falciparum malaria[END_REF].

However, prolonged gametocyte carriage has also been seen in DP treated African patients without ARPf who, nevertheless, had low human-to-mosquito transmission [START_REF] Dicko | Primaquine to reduce transmission of Plasmodium falciparum malaria in Mali: a single-blind, dose-ranging, adaptive randomised phase 2 trial[END_REF][START_REF] Ashley | Spread of artemisinin resistance in Plasmodium falciparum malaria[END_REF][START_REF] Sawa | Malaria transmission after artemetherlumefantrine and dihydroartemisinin-piperaquine: a randomized trial[END_REF]. Moreover, several comparative studies have found that gametocyte carriage is higher in DP compared to artemether lumefantrine [START_REF] Sawa | Malaria transmission after artemetherlumefantrine and dihydroartemisinin-piperaquine: a randomized trial[END_REF][START_REF] Bassat | Dihydroartemisinin-piperaquine and artemether-lumefantrine for treating uncomplicated malaria in African children: a randomised, non-inferiority trial[END_REF][START_REF] Onyamboko | Randomized comparison of the efficacies and tolerabilities of three artemisinin-based combination treatments for children with acute Plasmodium falciparum malaria in the Democratic Republic of the Congo[END_REF][START_REF] Wwarn Gametoctye | Gametocyte carriage in uncomplicated Plasmodium falciparum malaria following treatment with artemisinin combination therapy: a systematic review and meta-analysis of individual patient data[END_REF], suggesting reduced gametocytocidal activity of piperaquine compared to lumefantrine. Overall, we observed a biphasic pattern of gametocyte prevalence with a drop on D7, a rebound on D14, followed by a decrease on D21 and D28. However, this effect was mainly driven by the DP treated patients as their gametocyte carriage rate was similar over the 28-day follow-up whereas it decreased markedly in the DP+SLDPQ treated patients (Figure 1).

We were not able to assess the transmission-blocking efficacy of SLDPQ due to the very low infectivity rate observed in only three patients (~6%) at baseline and three infectious events during follow up. This is a major limitation of DFMAs, previously reported by Lin et al. [START_REF] Lin | Single dose primaquine to reduce gametocyte carriage and Plasmodium falciparum transmission in Cambodia: An open-label randomized trial[END_REF] at baseline using Anopheles dirus mosquitoes and on D7, without assessing baseline, by Okebe et al [START_REF] Okebe | The gametocytocidal efficacy of different single doses of primaquine with dihydroartemisininpiperaquine in asymptomatic parasite carriers in the Gambia: a randomized controlled trial[END_REF]. In another study in African children, despite a higher infectivity rate at enrollment after microscopy-based selection of gametocyte positive asymptomatic children (38%), Gonçalves et al. [START_REF] Goncalves | Single low dose primaquine to reduce gametocyte carriage and Plasmodium falciparum transmission after artemether-lumefantrine in children with asymptomatic infection: a randomised, double-blind, placebo-controlled trial[END_REF] were also unable to detect the added value of SLDPQ due to very low infectivity posttreatments in all arms. As our clinical trial aimed primarily at assessing SLDPQ tolerability and safety, we did not particularly select patent or high-density gametocyte carriers and thus would have needed substantially more individuals to assess transmission-blocking efficacy. Only two studies in Mali statistically confirmed high anti-infectivity efficacy (>90%) at 48h of SLDPQ, when dosed at baseline, after selecting gametocyte positive participants by microscopy [START_REF] Dicko | Primaquine to reduce transmission of Plasmodium falciparum malaria in Mali: a single-blind, dose-ranging, adaptive randomised phase 2 trial[END_REF][START_REF] Dicko | Efficacy and safety of primaquine and methylene blue for prevention of Plasmodium falciparum transmission in Mali: a phase 2, single-blind, randomised controlled trial[END_REF]. However, we observed that the three SLDPQ treated infectious patients on D0 did not infect mosquitoes on subsequent days despite the presence of gametocytes. Several reasons may explain this finding. Following primaquine, an anti-infectivity effect is rapid (≤ 24h) and precedes the decline in gametocytaemia [START_REF] Burgess | The effect of a single dose of primaquine on the gametocytes, gametogony and sporogony of Laverania falciparum[END_REF]. Male gametoctyes seem to be more sensitive to primaquine than female gametoctyes [START_REF] Delves | Male and female Plasmodium falciparum mature gametocytes show different responses to antimalarial drugs[END_REF] and P. falciparum sex ratio is biased towards females, potentially resulting in delayed gametocyte clearance. The relationship between gametocytemia and infectivity is nonlinear and is, thus, an indirect measure of infectivity [START_REF] White | Assessment of therapeutic responses to gametocytocidal drugs in Plasmodium falciparum malaria[END_REF][START_REF] Jeffery | Infectivity to mosquitoes of Plasmodium falciparum as related to gametocyte density and duration of infection[END_REF][START_REF] Churcher | Predicting mosquito infection from Plasmodium falciparum gametocyte density and estimating the reservoir of infection[END_REF].

To conclude, our study shows that the addition of SLDPQ to ACT treatment in symptomatic falciparum malaria decreases substantially gametocyte carriage in patients with MDRPf.

Although unable to reconfirm the elegant studies of Dicko et al. [START_REF] Dicko | Primaquine to reduce transmission of Plasmodium falciparum malaria in Mali: a single-blind, dose-ranging, adaptive randomised phase 2 trial[END_REF][START_REF] Dicko | Efficacy and safety of primaquine and methylene blue for prevention of Plasmodium falciparum transmission in Mali: a phase 2, single-blind, randomised controlled trial[END_REF], SLDPQ, dosed on the first day of treatment, is likely to further decrease the transmission potential of P. falciparum patients in our setting when combined with an effective ACT.

Owing to the high failure rate of DP, Cambodia has switched to artesunate-mefloquine treatment as first line treatment for uncomplicated P. falciparum and in January 2018 deployed SLDPQ in the whole country, based partly on the results of these findings and the good tolerability of SLDPQ in G6PDd patients [START_REF] Dysoley | The tolerability of single low dose primaquine in glucose-6-phosphate deficient and normal falciparum-infected Cambodians[END_REF]. An age based dosing regimen of SLDPQ, designed for Cambodia, will aid elimination efforts where weighing scales are unavailable [START_REF] Leang | An optimised age-based dosing regimen for single low-dose primaquine for blocking malaria transmission in Cambodia[END_REF].

Conflicts of interest.

All authors declare no conflicts of interest.

Tables

FiguresFigure 1 .

 1 Figures

  Gametocyte prevalence by Taqman RT-PCR by follow-up day and treatment group. Data show proportion ± 95% confidence intervals.

Figure 2 .

 2 Figure 2.

Table 1 .

 1 Baseline characteristics of the two study groups of patients

	DP	DP + SLDPQ

Table 2 .

 2 Independent factors associated with change in gametocytemia over 28 days by univariate analysis. Odds ratio < 1 indicates a negative association.

	Factor

Table 3 .

 3 Multivariable models (with and without recrudescence) of the factors associated with changes in gametocytemia over 28 days.

	Model	Factors	adjOR 95% CI	P-value
	Model 1	Treatment	2.39	0.81 , 7.08	0.1152
		D0 status	7.35	2.27 , 23.78 0.0009
		Recrudescence	6.02	1.70 , 21.26 0.0053
		D0 hemoglobin	0.57	0.42 , 0.77	0.0003
		Day of follow-up	0.93	0.90 , 0.96	<0.0001
	Model 2	Treatment	3.15	1.09 , 9.11	0.0344
		D0 status	6.63	2.10 , 20.87 0.0012
		D0 hemoglobin	0.55	0.41 , 0.75	0.0001
		Day of follow-up	0.93	0.90 , 0.96	<0.0001

Table 5 .

 5 Details of the five patients, infectious to A. minimus by direct-membrane feeding assays 489 during the 28-day follow-up. 490

Acknowledgements

We would like to thank the patients for taking part in this study and the invaluable help of the village malaria health workers in helping with patient recruitment. This work was supported by the Institut Pasteur of Cambodia, FEI 5% initiative (grant number 12INI211, 'Towards malaria elimination: effective strategies against transmission. The new challenges in South East Asia'), Rotary Club (grant number GG1523934, 'Amélioration des capacités en entomologie des acteurs luttant contre le paludisme et de de la compréhension de la transmission du paludisme'), USAID/PMI/CDC through Malaria Consortium ('The tolerability and safety of low dose primaquine for transmission blocking in symptomatic falciparum infected Cambodians') and Dedonder Clayton (grant number EC/MAM/N°325/14). AV was supported by a post-doctoral fellowship from the International Division, Institut Pasteur, Paris, France. The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Ethical approvals were obtained from the Cambodian National Ethics Committee for Health Research (0370NECHR) and the trial registered at the clinicaltrials.gov (NCT02434952). The protocols conformed to the Helsinki Declaration on ethical principles for medical research involving human subjects (version 2002) and informed written consent was obtained for all volunteers.

Statistical analyses

Initially, univariate Generalized Linear Mixed Models (GLMMs) with a binomial distribution were fitted to model the PCR measured, gametocyte prevalence rates. In these models, follow-up days (D1, 2, 3, 7, 14, 21 and 28), treatment (DP vs. DP+SLDPQ), presence of gametocytes prior to treatment on D0, recrudescence status (recrudescent vs. cured patient) and hemoglobin concentration prior to treatment on D0 were included in the model as fixed factors. Patient ID was coded as a random factor to account for repeated measures on the same individual. The univariate analyses were followed by a multivariable GLMM to model the dynamics of gametocyte prevalence post-treatment including all the significant factors from the univariate analysis.

Gametocyte clearance times were not compared in the study for three principal reasons: (i) of the 21 patients with microscopically detected D0 gametocytes, only 7 had complete follow up microscopy data, (ii) Taqman RT-PCR measured gametocyte densities were highly variable during the 28 days follow-up, and, (iii) by D28, 10/34 patients with gametocytes on D0 by Taqman RT-PCR were still gametocytemic (n=1, DP+SLDPQ arm). P-values <0.05 were deemed significant. All analyses were performed in R v.3.5.1 [START_REF] Team | R: A language and environment for statistical computing[END_REF]. Positive isolates are isolates which were able to infect at least one mosquito from directmembrane feeding assay (DFMA).


Marc Besson
email: marc.besson@ens-lyon.org.

Marc Metian

Paco Bustamante

Laetitia Hédouin

Metal(loid)s in superficial sediments from coral reefs of French Polynesia

Keywords: Contamination, metals, metalloids, Pacific Ocean, South Pacific Islands

Metal(loid)s in superficial sediments from coral reefs of

French Polynesia

However, such data is limited in French Polynesia, a region as vast as Europe in the South Pacific Ocean and composed of 118 islands with a wide diversity of island types from high islands (e.g. Tahiti and Mo'orea, Society archipelago) to atolls (e.g. Rangiroa, Tuamotu archipelago) [START_REF] Orstom | Office de la Recherche Scientifique et Technique Outre-Mer[END_REF]. Metal(loid) levels in the sediment were only investigated through two single cores performed at two sites in Tahiti, within the harbor of Papeete [START_REF] Fichez | Sediment records of past anthropogenic environmental changes in a barrier reef lagoon (Papeete, Tahiti, French Polynesia)[END_REF]. Moreover, while organic and metal(loid) contamination have also been examined in coral reef organisms at Mo'orea [START_REF] Fey | Does trophic level drive organic and metallic contamination in coral reef organisms?[END_REF][START_REF] Roche | Assessment of the pesticide pollution of coral reef communities from French Polynesia[END_REF], data related to the sediment are actually limited to the sedimentary organic matter at a single site [START_REF] Fey | Does trophic level drive organic and metallic contamination in coral reef organisms?[END_REF]. The current lack of information on the metal(loid) levels in the sediments of French Polynesia coral reefs represents significant hurdles to determine whether the increasing development of anthropogenic activities in this region [START_REF] Thiault | Space and time matter in social-ecological vulnerability assessments[END_REF] is associated with an increased contamination in metal(loid)s.

In this context, we measured the levels of ten metal(loid)s (Ag, As, Cd, Co, Cu, Fe, Mn, Ni, Pb, and Zn) in superficial sediments from 28 sites spread over the coral reefs of three contrasted islands of French Polynesia (Mo'orea,Rangiroa and Tahiti;Fig. 1). Tahiti is the most populated island of French Polynesia with 189,517 inhabitants (Insee/Ispf, 2017). It is located in the Society Archipelago and has two parts: a main island called Tahiti Nui and a peninsula called Tahiti Iti.

Industrial activities are mainly located in the vicinity of the capital (Papeete) on Tahiti nui. Most of the population also inhabit Tahiti nui (89 %, Insee/Ispf, 2017). Nonetheless, it has developed rapidly in the recent years, and predominantly associated with the construction of several goods and services establishments at Taravao (Tahiti Iti main city). Mo'orea is also located in the Society Archipelago, 17 km northwest of Tahiti. It is the second most urbanized island of French Polynesia, with 17,816 inhabitants (Insee/Ispf, 2017). Mo'orea is far less industrialized than Tahiti, restricted to some intensive agriculture activities (e.g. pineapple production), a fruit juice processing factory and most of the boat traffic related to ferries and daily transfers from Papeete to Vaiare harbor.

Rangiroa is the largest atoll of French Polynesia, located in the Tuamotu Archipelago at approximately 430 km northeast of Papeete. There is no industry on the island and limited anthropogenic activities (i.e. pearl production, fishing, and tourism, all operating on a small scale) with 3,657 inhabitants (Insee/Ispf, 2017). Sampling sites were selected along the coasts of Tahiti (10 sites), Mo'orea (13 sites) and Rangiroa (5 sites) (Fig. 1), by choosing sites with various anthropogenic inputs, i.e. potentially contaminated sites near the river mouth in the vicinity of cities, industries, harbors and marinas, and suitable reference sites close to remote beaches and reefs supposedly less contaminated (Table S1).

Sediment samples were collected from September to November 2012. At each site, three superficial sediment samples (i.e. triplicates), each of 50 to 75 g wet weight (ww), were collected in acid-washed plastic bags by scuba diving. Following collection, samples were stored in a freezer at -20 °C until being processed for contaminant analyses. Before analysis, each sample was screened through a 1 mm sieve to remove large particles (this <1 mm fraction constitutes 80-90% of the total sediment of each sample, and preliminary observations showed that the <63 mm fraction represented less than 0.2% of the total sediment). Aliquots of 150-250 mg were microwave digested in a mixture of 3 ml of suprapure nitric acid (VWR/Merck) and 1 ml of suprapure hydrochloric acid (VWR/Merck), and then diluted to 25 ml with MilliQ-quality water. Metal(oid)s were then analyzed by Inductively Coupled Plasma Atomic Emission Spectrometry (Varian Vista-Pro ICP-OES) and Mass Spectrometry (ThermoFisherScientific XSeries II ICP-MS). Certified Reference Materials (CRM) provided by the National Research Council Canada were treated and analyzed in a similar way as the samples. The CRM were dogfish liver DOLT-4, lobster hepatopancreas TORT-2 and marine sediment MESS-3 and the results from their analysis indicated a recovery ranging from 80 to 107% (Table S2).

The concentrations of metal(loid)s measured in superficial sediments from 28 sites in French Polynesia coral reefs ranged from 0.01 to 1.18 µg g -1 dw (dry weight) for Ag, 0.21 to 27.3 µg g -1 dw for As, 0.01 to 0.20 µg g -1 dw for Cd, 0.46 to 42.2 µg g -1 dw for Co, 0.14 to 35.1 µg g -1 dw for Cu, 10.4 to 32,513 µg g -1 dw for Fe, 0.11 to 549 µg g -1 dw for Mn, 0.04 to 325 µg g -1 dw for Ni, 0.02 to 21.5 µg g -1 dw for Pb and 3.03 to 194 µg g -1 dw for Zn (Table 1).

Table 1. Metal(loid) concentrations in superficial sediments from coral reefs of French

Polynesia. Data are expressed in µg g -1 dw (dry weight), and correspond to the mean (sd) of n = 3 samples for each site (i.e. triplicates). § indicates sd <0.005. Sites are indicated by the initial of the island, followed by the site name as in Fig. 1.

Site

Ag

As first group comprises Ag, As and Cd and drives the contamination in Mo'orea (Fig. 2A). The second group comprises Cu, Pb and Zn, and the third group comprises Co, Fe, Mn and Ni, and these groups differ on PC3 (Fig S2A -B) and drive the contamination in Tahiti, in particular at T-FAR for the second group. Strong positive (r> 0.63, Fig. 2C) and significant (P <0.001, Table S5) correlations were indeed observed between Ag and Cd, between Cu, Pb and Zn, and between Co, Fe, Mn and Ni (Fig. 2C, Table S5).

The degree of contamination of the different sites was examined using the Pollution Load Index (PLI) described by [START_REF] Tomlinson | Problems in the assessment of heavy-metal levels in estuaries and the formation of a pollution index[END_REF]. PLI was determined as the n th root of the product of , where Ci is the concentration of the metal(loid) i, and Cb is the background concentration of this metal(loid).

Since the concentrations measured in sediments from Rangiroa are lower than those generally used as background values [START_REF] Bowen | Environmental Chemistry of the Elements[END_REF], the means of these concentrations for each metal(loid) were used as background values in the PLI calculations performed in this study. Pollution Load Index (PLI) varied across sites (χ 27 2 = 15617, P <0.001; Gamma Generalized Linear Mixed-Effects Model, Supplementary Text 2, [START_REF] Bolker | Generalized linear mixed models: a practical guide for ecology and evolution[END_REF], with the same trends and clusters as in Fig. 2 and Fig. S1. M-OP1, M-OP2 and T-FAR exhibited the highest PLI, followed by T-TAA, T-TNU, T-VEN and T-LAG, and then by M-VA1 and M-VA2 (Fig. 3). Other sites showed a PLI under the average PLI (when combining all sites), and the lowest PLI were observed for sites at Rangiroa (Fig. 3). This study provides the first large-scale baseline of metal(loid) levels in superficial sediments from coral reefs of three islands of French Polynesia, highlighting various degrees of contamination across and within islands. Our results highlight a clear gradient of contamination in metal(loid)s in superficial sediments of French Polynesia, from pristine coral reef sites (e.g. Rangiroa) to sites with higher river discharge and anthropogenic influence (e.g. Mo'orea and Tahiti). In Rangiroa, none of the metal(loid) levels exceeded any of the sediment quality guidelines. These levels were lower than those reported in most other tropical areas [START_REF] Denton | Trace metals in sediments of four harbours in Guam[END_REF][START_REF] Morrison | Elemental composition and mineralogical characteristics of coastal marine sediments of Tutuila, American Samoa[END_REF], in particular at similar remote and non-polluted sites [START_REF] Denton | Contaminant assessment of surface sediments from Tanapag Lagoon, Saipan, Commonwealth of the Northern Mariana Islands[END_REF][START_REF] Denton | Trace metals in sediments of four harbours in Guam[END_REF][START_REF] Denton | The impact of a rudimentary landfill on the trace metal status of Pago Bay, Guam[END_REF]. Further, they are lower than the classically used background values [START_REF] Bowen | Environmental Chemistry of the Elements[END_REF], and therefore represent important baseline values of metal(loid) levels for sediments of French Polynesia but also for coral reef areas in general. Evaluating the levels of metal(loid)s in reef sediments from such remote environments is topical when one wants to assess the environmental effects of anthropogenic activities in more urbanized areas [START_REF] Kadhum | Evaluation and assessment of baseline metal contamination in surface sediments from the Bernam River, Malaysia[END_REF].

In Mo'orea, a few sites also exhibited low levels of metal(loid) contamination and similar PLI as Rangiroa sites, while two other sites (M-OP1 and M-OP2, where no coral cover was present)

showed the highest PLI of this study. In particular, Ni levels at M-OP1 and M-OP2 exceeded ERM and levels of Ag and As exceeded levels recorded in sediments from other coral reef regions [START_REF] Bastidas | Sedimentation rates and metal content of sediments in a Venezuelan coral reef[END_REF][START_REF] Denton | Trace metals in sediments of four harbours in Guam[END_REF][START_REF] Guzmán | Contamination of coral reefs by heavy metals along the Caribbean coast of Central America (Costa Rica and Panama)[END_REF][START_REF] Haynes | Organochlorine, Heavy Metal and Polyaromatic Hydrocarbon Pollutant Concentrations in the Great Barrier Reef (Australia) Environment: a Review[END_REF]Hédouin et al., 2011bHédouin et al., , 2009b;;[START_REF] Metian | Accumulation of nine metals and one metalloid in the tropical scallop Comptopallium radula from coral reefs in New Caledonia[END_REF][START_REF] Morrison | Elemental composition and mineralogical characteristics of coastal marine sediments of Tutuila, American Samoa[END_REF]. Sediment contamination rapidly dropped further away in Opunohu Bay, as evidenced by the low levels of contamination recorded at M-OP3 and M-OP4, and the same decreasing contamination gradient was observed in

Vaiare Bay (M-VA1 to M-VA4). These gradients are therefore probably linked to the discharge of sediments from the Opunohu and Vaiare streams but also to salinity shifts in Opunohu and

Vaiare bays, which are known to affect metal(loid) solubilization, speciation, precipitation, diffusion and advection [START_REF] Barletta | Distribution, sources and consequences of nutrients, persistent organic pollutants, metals and microplastics in South American estuaries[END_REF][START_REF] Coynel | Spatial distribution of trace elements in the surface sediments of a major European estuary (Loire Estuary, France): Source identification and evaluation of anthropogenic contribution[END_REF][START_REF] De Souza Machado | Metal fate and effects in estuaries: A review and conceptual model for better understanding of toxicity[END_REF].

In Tahiti, the highest levels of contamination were observed in the sediments collected in Papeete (T-FAR, Table S1), the capital of French Polynesia. This site was the only one monitored in a previous study [START_REF] Fichez | Sediment records of past anthropogenic environmental changes in a barrier reef lagoon (Papeete, Tahiti, French Polynesia)[END_REF], and we observed moderate increases in the levels of all the elements that examined in both this previous study and the current study. High levels of Co, Cu, Fe, Mn, Ni, and Zn were observed at 5 sites in Tahiti, with Ni levels exceeding the ERM and constituting a potential threat to marine organisms if bioavailable [START_REF] Gissi | A review of nickel toxicity to marine and estuarine tropical biota with particular reference to the South East Asian and Melanesian region[END_REF].

PCA and correlation analyses can highlight which elements may originate from the same source [START_REF] Yongming | Multivariate Analysis of Heavy Metal Contamination in Urban Dusts of Multivariate analysis of heavy metal contamination in urban dusts of Xi'an, Central China[END_REF], but identifying those sources would require further research and additional data on sediment grain size, total organic carbon content, total nitrogen content, mineralogy, and origin (e.g. terrestrial vs. marine). Indeed, metal(loid) contamination can be influenced by the structure and composition of the sediment itself, as well as by the geological characteristics of the island (Hédouin et al., 2009b). For instance, and in contrast with Rangiroa [START_REF] Chevalier | Geomorphology and geology of coral reefs in French Polynesia[END_REF], high levels of Fe and Mn are expected in basaltic-rich volcanic islands with high terrestrial inputs such as Mo'orea and Tahiti [START_REF] Fichez | Sediment records of past anthropogenic environmental changes in a barrier reef lagoon (Papeete, Tahiti, French Polynesia)[END_REF]. The overall higher levels of metal(loid)s in the sediments from Tahiti and Mo'orea vs. Rangiroa could therefore be related to their river network and higher land surface areas [START_REF] Orstom | Office de la Recherche Scientifique et Technique Outre-Mer[END_REF]. Contamination levels can also be associated with anthropogenic inputs, and our results are consistent with the fact that high levels of Co, Cu, Ni, and Zn are often associated with domestic discharges and industrial activities such as the presence of harbors and marinas [START_REF] Fichez | Sediment records of past anthropogenic environmental changes in a barrier reef lagoon (Papeete, Tahiti, French Polynesia)[END_REF][START_REF] Harris | Using geochronology to reconstruct the evolution of particulate phosphorus inputs during the past century in the Papeete Lagoon (French Polynesia)[END_REF].

Figure 1 .

 1 Figure 1. Location of the sampling sites in Mo'orea, Rangiroa and Tahiti. A: Location of the three islands in French Polynesia. B-D: Location of the sampling sites in Mo'orea, Rangiroa and Tahiti, respectively. Gray zones indicate land areas and blue zones indicate coral reef areas. Site codes used in the other figures and tables of this manuscript correspond to the island initial followed by the site names presented in B-D.

  the n Contamination Factor (CF) of the n elements: PLI = (∏ 𝐶𝐹 𝑖 𝑛 𝑖 ) 1/𝑛 , and 𝐶𝐹 𝑖 = 𝐶 𝑖 𝐶 𝑏

Figure 2 .

 2 Figure 2. Site and metal(loid) grouping based on the levels measured in the sediment. A: Principal Component Analysis (PCA) of sites (as individuals) and metal(loid)s (as variables) according to metal(loid) concentrations in the 28 sites from Mo'orea, Rangiroa and Tahiti. The three main groups of metal(loid)s and sites have been added. B: Cluster classification of sites based on metal(loid) concentrations. The number of clusters was measured using the gap statistic. Sites are indicated by the initial of the island, followed by the site name as in Fig. 1. C: Correlation plot of metal(loid)s based on their concentrations across sites. Data indicate the Spearman r correlation coefficients.

Figure 3 .

 3 Figure 3. Pollution Load Index (PLI) of reef superficial sediments 28 sites across French Polynesia. Sites from Mo'orea, Rangiroa and Tahiti are indicated by orange, blue and green bars, respectively. Sites are indicated by the initial of the island, followed by the site name as in Fig. 1. Bars and error bars indicate mean ± se (n = 3). The dashed line indicates the mean PLI value of all sites. Letters on the right of each bar indicate statistically different groups according to Tukey posthoc-test following Gamma Generalized Linear Mixed-Effect Model.

  While highlighting the opportunity for further research regarding the sources of contamination, our study provides critical baseline values for the vast region of French Polynesia, and for coral reef areas in general. Our results emphasize the necessity to minimize the levels of metal(loid)s discharged in the marine environment of the most populated Islands in French Polynesia, where levels of certain metal(loid)s already exceed sediment quality guidelines, potentially threatening the health of coral reef organisms. This need is critical, especially as local stressors such as metal(loid) pollution may reduce the capacity of coral reefs to face the unprecedented changes associated with global warming and ocean acidification.

Figure S2 .

 S2 Figure S2. Site and metal(loid) grouping based on the levels measured in the sediment. A: Principal Component Analysis (PCA) with PC1 and PC3 of sites (as individuals) and metal(loid)s (as variables) according to the metal(loid) levels at the 28 sites from Mo'orea, Rangiroa and Tahiti. B: Principal Component Analysis (PCA) with PC2 and PC3 of sites (as individuals) and metal(loid)s (as variables) according to the metal(loid) levels at the 28 sites from Mo'orea, Rangiroa and Tahiti. The three main clusters of metal(loid)s have been added to each PCA.

Table S3 . Eigenvalues and percentage of explained variance of the Principal Component Analysis (PCA) on the metal(loid) levels in the 28 sites of French Polynesia.

 S3

	PC	Eigenvalue	Explained variance (%)	Cumulative explained variance (%)
	1	5.556	55.561	55.561
	2	1.938	19.383	74.944
	3	1.199	11.993	86.937
	4	0.854	8.541	95.477
	5	0.239	2.394	97.871
	6	0.098	0.983	98.855
	7	0.071	0.714	99.569
	8	0.034	0.342	99.911
	9	0.005	0.055	99.966
	10	0.003	0.034	100.000

Table S4 . PCA loading factors.

 S4

	Element	PC1	PC2	PC3
	Ag	0.26	0.54	-0.12
	As	0.18	0.20	0.17
	Cd	0.28	0.50	0.03
	Co	0.28	-0.36	-0.41
	Cu	0.38	0.05	0.25
	Fe	0.40	0.01	-0.19
	Mn	0.40	0.05	-0.22
	Ni	0.31	-0.38	-0.36
	Pb	0.24	-0.34	0.60
	Zn	0.35	-0.17	0.40

Table S5 . Metal(loid)s correlation analysis associated p-values.

 S5 Values in bold indicate P values < 0.05.

	Ag	As	Cd	Co	Cu	Fe	Mn	Ni	Pb	Zn
	Ag	0.009	<0.001	0.524	<0.001	0.001	<0.001	0.654	0.726	0.1302
	As		0.082	0.857	0.103	0.031	0.030	0.370	0.191	0.321
		Cd		0.564	<0.001	0.001	<0.001	0.630	0.663	0.022
			Co		0.014	<0.001 <0.001 <0.001	0.076	0.012
				Cu		<0.001 <0.001	0.009	<0.001 <0.001
					Fe		<0.001 <0.001	0.045	<0.001
						Mn		<0.001	0.085	<0.001
							Ni		0.026	0.005
								Pb		<0.001
									Zn

Acknowledgments

This work was funded by the French National Research Agency (R-ECOLOGS, ANR-10-PDOC-0013). We thank S. Planes, C. Churlaud, and J. Carlot for their help in conceiving, analyzing and formatting the data presented in this study. We thank the Contrat de Projet Etat-Région and the Fonds Européen de Développement Régional for funding the ICPs of LIENSs laboratory, and the National Center of Scientific Research and the Ecole Pratique des Hautes Etudes for their support.

The IAEA is grateful for the support provided to its Environment Laboratories by the Government of the Principality of Monaco. The Institut Universitaire de France is acknowledged for its support to P.B. as a Senior Member.

Supplementary material

Table S1. Site location, code and description. Sites are indicated by the initial of the island, followed by the site name as in Fig. 1.

Island

Site Description

Supplementary Text 2. Statistical analyses.

A Gamma Generalised Linear Mixed-Effects Model [START_REF] Bolker | Generalized linear mixed models: a practical guide for ecology and evolution[END_REF] was run to assess whether the site location influenced sediment contamination in metal(loid)s. PLI was used as the dependant variable and followed a gamma distribution. Replicate identity was included as a random factor to account for potential differences only due to technical issues. A top-down approach using Likelihood Ratio Tests and the Akaike Information Criterion (AIC) was used to assess the explanatory power of

Supplementary References

Bates, D., Mächler, M., Bolker, B.M., Walker, S.C., 2015. Fitting


David Defour
email: david.defour@upvd.fr

Pablo De

Oliveira Castro
email: pablo.oliveira@uvsq.fr

Matei Istoan
email: matei.istoan@uvsq.fr

Matei Is ¸toan * † Eric Petit
email: eric.petit@intel.com

Pablo De Oliveira Castro

Custom-Precision Mathematical Library Explorations for Code Profiling and Optimization

Keywords: HPC, libm, floating-point, custom-precision, optimization, specialization

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

I. INTRODUCTION

A growing interest to adapt floating-point formats to the real needs of applications is becoming ever more ubiquitous. This process has been successfully conducted by the AI community which has settled on the BF16 [START_REF] Intel | White paper: Bfloat16 hardware numerics definition[END_REF] and fp16 [START_REF] Nvidia | White paper: Training with mixed precision[END_REF] formats, in order to increase performance and efficiency. Similar benefits have been achieved in other domains [START_REF] Chatelain | Automatic exploration of reduced floating-point representations in iterative methods[END_REF], [START_REF] Haidar | The design of fast and energy-efficient linear solvers: On the potential of half-precision arithmetic and iterative refinement techniques[END_REF] by reducing the precision of basic operations (+, -, * , /) and harnessing hardware-support for multiple internal floating-point formats.

Oberman et al. [START_REF] Oberman | Design issues in division and other floating-point operations[END_REF] demonstrate that neglecting optimizations of infrequent operations, such as division and square root, can severely impact performance. We believe that elementary functions should not be neglected either when optimizing for mixed-precision. Even though elementary functions are not widely available in hardware and infrequently used in applications, their impact can be important. HPC Patmos neutronic solver [START_REF] Brun | Patmos: A prototype Monte Carlo transport code to test high performance architectures[END_REF] spends 70% of the execution time in the mathematical library (libm) functions. This confirms similar observations by CERN [START_REF] Piparo | Speeding up HEP experiment software with a library of fast and auto-vectorisable mathematical functions[END_REF] on their HPC codes.

Various mathematical libraries specialize evaluation schemes for different accuracy/performance trade-offs [START_REF]Intel® math kernel library, developer reference[END_REF]. Recent developments such as metalibm [START_REF] Brunie | Code generators for mathematical functions[END_REF] automatically generate elementary functions to best fit the hardware and accuracy constraints. These works highlight that a trade-off can be explored between performance, accuracy and precision.

In this paper, we propose a tool for collecting input intervals and output required precision profiles from real applications in order to guide the design of specialized mathematical libraries. Indeed, considering limited input data ranges and application-focused output accuracy could drastically influence the implementation performance. We demonstrate the tool's capabilities on SGP4, a satellite tracking application. The profile data shows the potential for specialization and provides insight into where it is useful to provide variable-precision designs for elementary function evaluation.

II. RELATED WORKS

Contrary to basic operations, properties of elementary function are not standardized mainly because the correctly rounded property is difficult to achieve [START_REF] Black | The need for an industry standard of accuracy for elementary-function programs[END_REF], [START_REF] Defour | Proposal for a standardization of mathematical function implementation in floating-point arithmetic[END_REF]. As a consequence, there are numerous available implementations of such functions, either in software or hardware, each representing a different trade-off between, accuracy, performance, hardware requirements and programming language. The most notable mathematical library embedding different trade-offs are the Vector Mathematical Functions from Intel's MKL library [START_REF]Intel® math kernel library, developer reference[END_REF], which offers three accuracy modes: High-/Low-accuracy and Enhanced Performance. Another example are Nvidia's GPUs, which embed dedicated hardware for fast approximation of some functions and software implementation of more accurate and larger input range versions [START_REF] Collange | Graphic processors to speedup simulations for the design of high performance solar receptors[END_REF]. This has led to the OpenCL 2.2 standard which defines the requirements in terms of accuracy of mathematical functions from half to double [START_REF] Group | The OpenCL C specification version: 2.2[END_REF].

Developing and maintaining multiple implementations for each function is a daunting endeavor. Several tools have been proposed to automate this task either, for hardware or software implementation of such functions [START_REF] Brunie | Code generators for mathematical functions[END_REF], [START_REF] Dinechin | Floating-point exponential functions for DSP-enabled FPGAs[END_REF].

Porting the concept of memoization to mathematical functions has been explored in [START_REF] Collange | Fonctions élémentaires sur GPU exploitant la localité de valeurs[END_REF], [START_REF] Suresh | Intercepting functions for memoization[END_REF] where the authors investigated how considering real input-data profile can be used to optimize the evaluation. However, they did not evaluate the potential decrease in accuracy.

III. SIMULATING VARIABLE PRECISION AND RANGE FOR MATHEMATICAL FUNCTIONS

Our approach to simulate mathematical functions with reduced range/precision is twofold: first we transparently interpose calls to mathematical functions, then the VPREC-libm library computes the result in a reduced precision.

A. Library Call Interposition

In Linux, the dynamic loader offers the possibility to intercept dynamic library calls, so that a custom library is called instead. This is achieved by setting the LD_PRELOAD environment variable. This interception method works out-ofthe-box with a compiled binary and is transparent to the user.

We use it to replace standard calls to the libm with custom calls to our own VPREC-libm library which simulates nonstandard precisions and range. This approach is flexible, but has two limitations:

• it is not applicable to statically linked programs: for those, the user must manually re-link the program against the VPREC-libm; • it only intercepts library calls; to ensure that we intercept all operations we disable compiler optimizations which replace calls by hardware instrinsics (such as sqrtsd assembly instruction in IA-64). Fortunately, the -fno-builtin flag disables these optimizations in most standard compilers.

B. Implementation of the VPREC-libm

The interposed mathematical call is handled by VPREC-libm, which returns the result in the target floating-point format. For example in double precision, one can customize the bit length of the pseudo-exponent r ∈ [START_REF] Intel | White paper: Bfloat16 hardware numerics definition[END_REF][START_REF] Defour | Proposal for a standardization of mathematical function implementation in floating-point arithmetic[END_REF] and the pseudo-mantissa p ∈ [0, 52].

VPREC-libm operates in two steps. First, it computes a binary128 result z by calling the corresponding mathematical function from the GCC's libquadmath.

Then, z is converted to the target format using Verificarlo-VPREC [START_REF] Chatelain | Automatic exploration of reduced floating-point representations in iterative methods[END_REF]. If z is representable in the target range, a faithfully rounded result at target precision p is returned. If z is outside the target range, VPREC returns ±∞ for overflows and ±0 for underflows. Rounding is achieved by adding a ulp at precision p + 1 followed by a truncation (⌊ z + 2 ez-p-1 ⌋ p ).

C. Exploring Precision Requirements Using VPREC-libm

VPREC-libm can be used in two modes: profiling, and execution. In profiling mode, VPREC-libm creates a profile of the executed code. For each call, it updates the boundaries of the operands and output intervals, the number of occurrences for the unique program address and stack trace from which the call is made. This information is aggregated and processed to produce execution statistics.

In execution mode, VPREC-libm accepts a configuration file which specifies the floating-point formats to use at each call-site. An initial config file is generated automatically after a profiling run, containing information for all encountered callsites, which the user can later modify as it is required.

Taking advantage of this functionality, we developed a method for exploring the optimization potential of a given floating-point code. On a broad scale, we perform a dichotomic search for the minimal output precision of the VPREC-libm functions which meets the user-specified correctness criteria. This search is applied sequentially per call-site and converges in logarithmic time, in the size of the mantissa. As we are dealing with a vast search-space, the order in which this optimization is performed is quite important. According to Amdahl's law, optimizing the code in which most of the time is spent results in the biggest performance gains. Therefore we prioritize the call-site exploration by call frequency as a heuristic. Figure 1 summarizes this process.

IV. EXPERIMENTAL RESULTS

The example discussed throughout this section illustrates the potential of our proposed method, applied to a real-world astrophysics application used to predict the position and the velocity of Earth-orbiting objects (most notably satellites).

A. Satellite Tracker: SGP4

In order to track the position and the velocity of satellites, a common technique is to use simplified general perturbations (SGP) models, which predict the influence of drag, the Earth's shape, as well as that of the sun and the moon on the trajectory. Work on SGP started in the 1960's, but at the beginning of the 1980s NORAD 1 released the equations and the source code to predict satellite positions [START_REF] Hoots | Spacetrack Report No. 3: Models for propagation of NORAD element sets[END_REF]. NORAD maintains and periodically refines data sets on all resident space objects, ensuring the accuracy of trajectory predictions. The data-sets were made available to users, through NASA, being the only source of readily available orbital data.

However, a user could not just go ahead and use any prediction model she wished, she had to use the same model employed to generate the data-set, even if the user's choice might have had better performance, an aspect highlighted in [START_REF] Hoots | Spacetrack Report No. 3: Models for propagation of NORAD element sets[END_REF]. This made SGP, especially its SGP4/SDP4 variants, commonplace among users wishing to use NORAD's orbital data, distributed as two-line element (TLE) sets. Near-Earth objects (period less than 225 minutes) are tracked using SGP4, while deep-space objects (period over 225 minutes) are tracked using SDP4, which also models the gravitational effects of the moon and the sun and certain Earth harmonics.

In the period following the original release of SGP, a multitude of code variations came to exist, making interoperability and compatibility an issue. For experimental purposes, we will use the SGP4 version documented in [START_REF] Vallado | [END_REF], which is a community effort to keep a version up to date with the models and TLE data-sets used by NORAD. The mathematical models used throughout are those presented in [START_REF] Hoots | History of Analytical Orbit Modeling in the U. S. Space Surveillance System[END_REF]. The C++ version used for the experiments is the one provided by CelesTrak, available online2 . Only minimal changes were made, in order to ensure that the program runs correctly on Linux. This has not affected the program outputs, as verified against the provided test-suites.

B. Results

We applied our method to the data-set sgp4-all.tle discussed in [START_REF] Vallado | [END_REF]. Figure 2 illustrates our profiling and precision exploration results for the 50 libm call-sites with the most calls. At the top we show the number of occurrences for different libm call-sites. In the middle graph we show for each call-site the dynamic range of the input data, as used in the original code, extracted from the profile produced by VPREC-libm. Finally, in the bottom graph we show for each call-site the required precision of the outputs determined by our exploration with the VPREC-libm method.

We can observe that the second and third call-sites are almost twice more frequent than the next ten entries. The output precision cannot be significantly decreased for the two first call-sites, as shown in the bottom sub-figure. Indeed they occur at the very end of the algorithm, directly influencing the outputs. On the other hand, the dynamic range of the input is quite reduced at these two call-sites.

Analyzing the code, we notice that these calls to sin() and cos() take the same argument, as they are part of a rotation. Therefore, they could be replaced with a call to sincos(), effectively reducing their combined workload by almost a factor of two, similar to what is done in [START_REF] Markstein | Accelerating sine and cosine evaluation with compiler assistance[END_REF].

Analyzing the rest of the call-sites, we can observe two general trends. The first are call-sites where the required precision is close to the default one; here we only manage to save 5 -6bits. The second are call-sites where the required precision hovers around the 28-bits mark. A plausible explanation for these results can be found through a bit of computer-science archaeology. SGP4 was first developed in FortranIV3 , on a Honeywell-6000 4 series computer [START_REF] Hoots | Spacetrack Report No. 3: Models for propagation of NORAD element sets[END_REF]. This machine had 36bit words, so floating-point numbers had a 8-bit exponent and a 28or 64-bit significand, for single-or double-precision, respectively. As noted in [START_REF] Vallado | [END_REF], the code originally used a mix of single-and double-precision computations. With the evolution of the underlying hardware, the code was moved to doubleprecision throughout, which made for a smoother behavior, but did not improve the accuracy. These observations are indeed coherent with our findings on optimizing the precision of the outputs of the mathematical functions.

Figure 3 shows the results of our method on to a data-set containing just the satelite number 5, which is the first satellite in the sgp4-all.tle dataset. This is a near-Earth satellite, which means that its trajectory is tracked using SGP4, not SDP4. Its period, perigee and eccentricity ensure that no corner case is triggered in the model. The only particularity of this example is that it uses the TEME 5 coordinate system, which requires a conversion to a more standard coordinate systems. Indeed, avoiding exceptional cases in the model shows that considerably lower precisions can be used throughout. The trends for the precision of the math functions' output remains mostly the same. We notice, that over a third of the functions could be evaluated in single-precision, requiring at most 23bits of precision at the output.

It should be noted that the x-axis indices in Fig. 2 and3 do not necessarily match, as the execution paths can differ, due to the different nature of the two data-sets.

V. CONCLUSION AND FUTURE WORK

In this paper, we focus on providing a software tool and methodology to profile the mathematical library usage in a full scale application. The objective is to measure the potential and drive future ad-hoc optimizations of the math library.

Usually, elementary functions are implemented following a four step scheme [START_REF] Lauter | Semi-automatic floating-point implementation of special functions[END_REF]: special-case handling, argument reduction, reduced domain splitting and interpolation (e.g. polynomial or iterative).

When limiting the input domain, the first two steps can be optimized. Furthermore, reducing the required accuracy and input domain may lower the interpolation complexity. It can also diminish the implementation cost in special purpose architecture designs or re-programmable architectures (FPGA).

Rewriting ad-hoc custom elementary functions with a target accuracy on a given input interval is a costly and error prone task. We propose to explore existing tools to assist or automate these optimizations and measure emprical speedup on real use cases. An easy first step would be to automatically select the best fitting implementation among existing libraries, such as Intel MKL VML [START_REF]Intel® math kernel library, developer reference[END_REF]. Finally, approaches such as metalibm [START_REF] Brunie | Code generators for mathematical functions[END_REF] for math function code generation could be leveraged to produce specialized libraries.

To conclude, the work presented in this paper shows promising results on co-designing mathematical libraries from application profiles. One weakness of the approach is that the profile is data-input dependent; further experiments on a larger set of use-cases will be done to demonstrate the generalization of the approach and how one can deal with the speculative aspect of profile-guided optimization for math libraries.

P O W 6 F M O D 7 F M O D 8 F M O D 9 F M O D 1 0 F M O D 1 1 A T A N 2 1 2 A T A N 2 1 3 F M O D 1 4 F M O D 1 5 F M O D 1 6 S Q R T 1 7 S IN 1 8 C O S 1 9 S IN 2 0 C O S 2 1 S IN 2 2 S Q R T 2 3 C O S 2 4 S IN 2 5 C O S 2 6 S IN 2 7 C O S 2 8 S Q R T 2 9 S Q R T 3 0 A C O S 3 1 S IN 3 2 F L O O R 3 3 S Q R T 3 4 S Q R T 3 5 F L O O R 3 6 S Q R T 3 7 S Q R T 3 8 F A B S 3 9 S Q R T 4 0 S Q R T 4 1 S Q R T 4 2 F A B S 4 3 A C O S 4 4 F A B S 4 5 S Q R T 4 6 S Q R T 4 7 F L O O R 4

Fig. 1 :

 1 Fig. 1: VPREC-libm optimization process overview

Fig. 3 :

 3 Fig. 3: Analysis of calls to libm for satellite 5 data-set

North American Space Defense Command

httsp://celestrak.com/publications/AIAA/2006-6753/

https://en.wikipedia.org/wiki/Fortran#FORTRAN IV

https://en.wikipedia.org/wiki/Honeywell 6000 series


Marc Pierrot Deseilligny

Fast computation of distances in a tree

come

Motivation

Computation of distance between two submits of a graph is a basic well known problem of graph theory for which there exist efficient methods. This is even easier in the case where the graph is known to be tree or a forest (i.e. no cycle), in this case the time of basic algorithm are proportionnal to N where N is the number of submits. However there are cases where this operation has to be done a huge number of time and for which these linear performance may be limitative.

This problem can occur for example in photogrammetry in the computation of global orientation from a set of relative orientations (see for example [Govindu, Venu 2006]) . We give a short description, illustrated by figure 1 : -we want to orientate a set of N images ; -for certain pairs of images I, J we have computed the relative orientation r i,j of I relatively to J using some photogtrammetric method after computing tie-points; -now we want to compute a global solution correspond to equation 1.

R i " r i,j R J (1)
Figure 1 -A graph with relative rotations; a random tree extracted from previous graph

E " ÿ pR i ´ri,j R J q 2 (2)
As there is more constraints than unkown, the standard method is to minimize some criterion E like equation 2. Before doing that, we need to get an initial solution and remove the outlier. A possible way to do it this one :

-generate a "huge" quantity of random tree; -for each tree , set arbitrarily R 1 " Id and generate by propagation the unique solution satisfying 1; -use equation 1 to compute by accumulation the reliable r i,j . Suppose we generate M tree, and note R k i solution tree k, with k P r1, M s, a basic way to compute the reliability/quality Q i,j of r i,j is :

Q i,j " M ř k"1 |R k i ´ri,j R k j | M (3)
However we see that formula 3 is not completely satisfying :

-when r i,j belongs to the tree , obviously residual of equation 1 is zero, but this has no signification; -more generally, the highest is the distance between i and j in the tree, the longest is the chain of propagation and the highest is naturally expected to be the residual of equation 1; -for example in figure 1, the distance between R 1 and R 6 is 4, and this reflect that the chain that goes from one to the other is r 1,4 Ñ r 4,3 Ñ r 3,5 Ñ r 5,6 ; So the formula of equation should be replaced by another one taking into account the distance in the tree; for example, something like equation 4 :

Q i,j " ÿ |R k i ´rk i,j R k J | b D k i,j ´1 (4)
There is much more to say, and formula 4 should probably need more attention. However the fact is that to test formula like 4 we need a way to compute for a given tree the distance D k i,j of many pair of submits inside this tree.

In this paper we present an efficient method with the following performance :

-pre-computation in OpN logpN qq ; -for each pair S 1 , S 2 , the cost of computation is OplogpN qq in the worst case ; -the cost of computation on all pair is OpN 2 q, so in average the cost for one pair is in Op1q.

We give also an implementation in C++ of the algorithm in a single file that aims to be easily integrated in user code.

Recursive split

Figure 2 illustrate the notion used for the computation : -let A be a any submit (we will see in next section how chosing it); -starting from A we can easily compute for each submit the distance to A and also propagate a labeling of the connected components we would obtain if we would supress all edges connected to A from the tree; -left image of figure 2 present the tree and the name of submit we will use; -middle image present the distance to submit A; -right image present the labeling L A of connected components of the graph we would obtain if were supressing all edges starting from A. The presented method is based on the elementary remark that if two submit B and G do not belong to the same component, then the shortest past from B to G cross A, and DpB, Gq " DpB, Aq `DpA, Gq. This is formalized by equation 5 :

L A pBq ‰ L A pGq ñ DpB, Gq " DpB, Aq `DpA, Gq (5)
The following, recursive, split algorithm can then be formulated : we first make a recursrive precomputation for the whole graphe (using algorithm 1), we then use this precomputation to compute distance between pairs using the algorithm 4 : Untill now we have not discussed how we select the pivot submit. Obviously this may have a main influence on the efficiency of algorithm 1. This is illustrated on figure 3. On this figure we see that the choice of A as pivot does not decrease so much the size of the biggest remaining graph, while the choice of C seems much more pertinent leading to sub-graph which maximal size is 3. In the extreme case where the tree is a chain, we see that :

-if we make systematically the "bad" choice and select an extremity to split the graphe, we will have to compute N level; -on the other hand, if we make systematically the "good" choice and select the middle of the chain, we will only have to compute logpN q level.

Criteria for spliting

To answer to the question of the pivot selection, we must must solve two issues :

-define a criteria on each submit that caracterize how good it would be to choose it as pivot; -ensure that this criteria can be computed fastly enough .

For the first issue we want, after split, to avoid having too big connected component. So we simply take as criteria to select A as pivot, the maximum size of all connected components after supression of A. Once computed on all G, we will select the submit minimizing this criteria. If "naive" definition of algorithm 4 is satifying, we cannot simply compute it for each submit, as the cost would be N for each submit, which would result in N 2 for all the graph. This is why in next section, we describe a recursive modification approach leading to a global cost of N for the computation of pivot quality on the whole graph.

Fast computation

Figure 4 illustrate the fast computation. In a first step, we select an arbitray submit, A here, and consider the oriented tree with A as head, an compute the function H A pSq which, for each submit, contain the size of the subtree under S. This computation can easily be done in linear time. 1. PivotQuality(A) can be easily computed from H A , as it simply the max of H A pN q for all neighoor of A;

2. for all neighboor N of A , H N can easily be computed from H A ;

For second property, we see for example, that if we want to compute H C knowing H A , we have only two operation to do :

1. H C pCq " H A pAq " N , in fact this is always the same value (the number of submit of the graph);

The implementation

Attached to this note is an implementation in C++ of this algorithm. The "librairy" is contained in a single file TreeDist.h that can be include. The file TreeDist.cpp can generate an executable program that run the test, using the following command (on Gnu/Linux) :

g++ TreeDist.cpp -std=c++11

The main interface for user is the class cFastTreeDist. The usage of the class consist of essentially of 3 methods :

-cFastTreeDist(int NbSom) : the constructor, allocate the memory; void MakeDist(const std::vector<int> & aVS1,const std::vector<int> & aVS2); : make all the pre-computation for a given graph ,see comment in the code for graph representation; 1 int Dist(int aI1,int aI2) const; compute the distance bewteen two submit once the precomputation has been done (correspond to algorithm 4).

Theoreticall and empiricall analyse of complexity

To analyse the complexity, we must first compute the maximal level of recursion that can be reached.

By the definition we use of pivot quality, we are ensured that at each decomposition the connected component have a size inferior to half of the graph. Let prove it, illustrated by figure 5 : -let N be the number of submit of G , N " G; -let p be the pivot; -let C `be the connected componet of G ´tpu with maximal number of submit and m the submit connecting C `to p; -if we had " C `ą N 2 , then if we were taking m as pivot , connected of G ´tmu would be : -one component C p " G ´C`a nd C p ď N 2 ; -other components c i each being included in C `´tmu so c i ă C so m would be a better pivot than p which is a contradiction. As each component, in the recursive split, has a size inferior to the initial size, the maximal number of level is log 2 pN q. At each level the computation is linear. So :

-the pre-computaion has a complexity of N logpN q; -the computation of each distance, in algorithm 4 is in worst case equal to the maximum level, so logpN q is the cost for computation of distance in worst case; The computation of distance in average case is more complex to analyse. We can make the following, not 100% formal, reasoning in algoritm 4:

-the probabilty that Lab 1 pIq " Lab 1 pJq is inferior to 1 2 because size of maximal component is inferior to 1 2 ; -the probabilty that Lab 2 pIq " Lab 2 pJq is inferior to 1 4 because size of maximal component is inferior to Figure 6 present the experimental computation time we obtain using the command StatTimeBenchFastTreeDist, that generate random trees and evaluate the average level reached in algorithm 4 , this level beign proportionnal to the time. The line AvgT correspond to the average, on all pair of the graph, we see that this time if almost constant .

By the way, in some situaion the average on all pair may be unrealistic and too optimistic. In all case, the pair corresponding to low distances are generally splited at higher level and correspond to a longer time of computation. For example in the case of photogrammetry exposed in [Govindu, Venu 2006], it will be current that, due to spatial correlation, the majority of edges will correspond to low distances and that the average time is more important that predicted when taking all the pair. This is the reason of the two last lines :

-AvgLowT this line present an average on the pair corresponding to "low" distances, here the threshold is arbitrarily 3, we clearly see the time is growing with the number of submit; -Low/Log is the previous line divided by logpN bSomq, we see that it is almost constant and validate that the time for low distance a modelisation in logpN q, like worst case, is coherent.

Figure 2 -

 2 Figure 2 -Notation for a Tree; Distance to submit A; labeling of component after suppressing A

Figure 3 -

 3 Figure 3 -Two possible split of the same tree : arround A and arround C

Algorithm 3

 3 NaivePivotQual (S) Qual=0 for all CC connected component of G ´tSu do Qual = Max(Qual,CardCC) end for return Qual

Figure 4 -

 4 Figure 4 -Using tree of figure 2, function H A (left) and H C (right) representing sizes of subtree fonction with A and C as head

Figure 5 -

 5 Figure 5 -Notation for analyzing the cardinal when pivot change from p to m