Md Adnan Zaman
email: mdadnanz@mail.usf.edu

Rajeev Joshi
email: rajeevjoshi@mail.usf.edu

Srinivas Katkoori
email: katkoori@mail.usf.edu

Optimizing Performance and Energy Overheads Due to Fanout In In-Memory Computing Systems

Keywords: Memristor, In-memory computing, Fanout, MAGIC, crossbar, logic synthesis, resistive memory

For NOR-NOT based memristor crossbar architectures, we propose a novel approach to address the fanout overhead problem. Instead of copying the logic value as inputs to the driven memristors, we propose that the controller reads the logic value and then applies it in parallel to the driven memristors. We consider two different cases based on the initialization of the memristors to logic-1 at the locations where we want keep the first input memristor of the driven gates. If the memristors are initialized, it falls under case 1, otherwise case 2. In comparison to recently published works, experimental evaluation on ISCAS85 benchmarks resulted in average performance improvements of 51.08%, 38.66%, and 63.18% for case 1 and 50.94%, 42.08%, and 60.65% for case 2 considering three different mapping scenarios (average, best, and worst). In regards to energy dissipation, we have also obtained average improvements of 91.30%, 88.53%, and 74.04% for case 1 and 86.03%, 78.97%, and 51.89% for case 2 considering the aforementioned scenarios.

Introduction

Von Neumann architecture suffers from memory wall problem due to bandwidth mismatch between slower memory and faster CPU [START_REF] Wulf | Hitting the memory wall: implications of the obvious[END_REF]. To overcome memory wall problem, non von-Neumann architecture is being actively considered where storage and computing can be performed in the same location. This computing inside memory is known as in-memory computing. Emerging non-volatile resistive memory technology such as memristor can enable such non von-Neumann computing paradigm. A Memory Processing Unit (MPU) has been proposed [START_REF] Hur | Memristive memory processing unit (MPU) controller for in-memory processing[END_REF], where memristive memory is used as storage in conjunction with logical operations.

Due to high speed, low power consumption, scalability, data retention, endurance, and compatibility with conventional CMOS, many memristor based logic families and circuits have been proposed [START_REF] Kvatinsky | The Desired Memristor for Circuit Designers[END_REF]. Based on logic state variable, memristor based logic families can be classified into stateful (logic value represented with memristor resistance) and non-stateful logic families [START_REF] Lehtonen | Memristive stateful logic[END_REF]. In this work, we employ a stateful logic family, known as Memristor-Aided loGIC (MAGIC) [5]. In this logic style, for a given logic gate, input values and output value(s) are stored as memristor states. Memristors can be fabricated on a crossbar array, which offers high storage density and low power consumption [6]. With MAGIC, only NOR and NOT gates can be directly mapped to crossbar array.

In recent years, researchers have proposed a few in-memory logic synthesis approaches based on MAGIC logic style, where a given circuit netlist consisting of only NOR and NOT gates is mapped to a memristor crossbar. In [5], a detailed procedure to map NOR/NOT logic gates to crossbar has been discussed and also transpose crossbar concept has been introduced to allow gates to be mapped along the rows as well as columns in a crossbar architecture. In [START_REF] Hur | Simple magic: Synthesis and in-memory Mapping of logic execution for memristor-aided logic[END_REF], a synthesis tool has been proposed that maps arbitrary logical functions within the memristive memory in an optimal manner. In [8], a scalable design flow for in-memory computing has been proposed that allows a given circuit netlist to be implemented in transpose crossbar. In both of these approaches, a given gate netlist is first converted into a netlist of NOR/NOT gates using an existing logic synthesis tool [START_REF]Berkeley Logic Synthesis and Verification Group, ABC: A System for Sequential Synthesis and Verification[END_REF] and mapped to the crossbar architecture. While mapping, we come across fanout where a single output (driving) memristor of a logic gate has to be used as input (driven) memristors of multiple gates connected to it. For a fanout of two or more leaf memristors, current methods (previous approaches) perform the copy operation for a number of times equal to the number of driven memristors that are not on the same row or column as of the driving memristor. Such copy style requires two NOT operations which in turn requires two extra cycles. With the increment of fanouts in a given netlist, the number of extra cycles increases hence energy as well. To the best of our knowledge, no other previous works attempted to reduce the additional cycle count of a copy operation inherent to a fanout.

In this work, we propose a novel approach that will reduce the performance and energy overheads originated from fanout in a given circuit netlist. Instead of copying the value, the proposed controller can read the value and apply in parallel to the driven memristors. We consider two different cases based on the initialization of the memristors at the copy locations. The locations on the crossbar where we want to keep the first input memristors of the driven gates can be defined as the copy locations. In our prior work [START_REF] Zaman | Minimizing Performance and Energy Overheads Due to Fanout In Memristor based Logic Implementations[END_REF] which discusses case 1, like the previous works [START_REF] Hur | Simple magic: Synthesis and in-memory Mapping of logic execution for memristor-aided logic[END_REF]8], we consider that the memristors at the copy locations are initilaized to logic-1 which provides an added advantage to decide whether to write the read value or not to the driven memristors. As proposed in MAGIC logic style, the output memristors are initialized to logic-1 prior to logic execution and it allows the controller to skip write cycle if the read value is one. We have compared our work with a recently published work [8] for three different mapping scenarios. We obtain average improvements of 51.08%, 38.66%, and 63.18% and 91.30%, 88.53%, and 74.04% in performance and energy dissipation respectively. For case 2, we consider that the memristors at the copy locations are not initialized to logic-1 which dictates the use of initialization cycles with the previous approach. We obtain average improvements of 50.94%, 42.08%, and 60.65% and 86.03%, 78.97%, and 51.89% in performance and energy dissipation respectively.

The rest of the chapter is organized as follows: Section 2 presents background and related work. Section 3 describes the proposed approach to reduce the number of cycles and energy dissipations related to fanout. Section 4 reports experimental results. Section 5 draws conclusions.

Background and Related work

In this section, we discuss the basic working principle of a memristor, relevant logic design styles, crossbar architecture, and in-memory computing. We also review some of the recent works on memristor based in-memory logic synthesis for a given gate-level netlist with particular concentration on fanout.

Memristor

Memristor is a two terminal device that can remember its previous state and change its resistance based on a given potential across the device. Chua [START_REF] Chua | Memristor-The missing circuit element[END_REF] first proposed memristor that links flux (φ) and charge (q) to its memristance (M ) according to,

dφ = M dq (1)
Structurally, memristor can be thought of as a thin semiconductor film with thickness (D) sandwiched between two contacts. We can change the overall resistance by changing its doped region width, w [START_REF] Strukov | The missing memristor found[END_REF].

D w

Doped Undoped R ON R OFF

Fig. 1. Physical and circuit model of memristor [START_REF] Hur | Memristive memory processing unit (MPU) controller for in-memory processing[END_REF].

Memristor Aided LoGIC (MAGIC)

Our proposed methodology is based on MAGIC logic style [5]. As shown in Fig.

IN 1 IN 2 OUT V G IN 1 IN 2 OUT V G R C1 C2 C3 IN 1 IN 2 OUT (a) (c) (b)
Fig. 2. NOR gate implementation using MAGIC on crossbar.

In-memory Computation Using Memristor Crossbar

A Memory Processing Unit (MPU) based on in-memory computing architecture is as shown in Fig. 3 [START_REF] Hur | Memristive memory processing unit (MPU) controller for in-memory processing[END_REF]. It consists of a controller, crossbar memory, and analog multiplexers. The analog multiplexers' outputs are connected to the bitlines and wordlines of the memristive memory and the voltage select lines of the multiplexers are connected to the controller. To carry out a regular read or write operation, controller sends suitable signals to the addressed memristor cells through multiplexers. We have also shown two signals, V SET and V RESET that can enable writing logic-1 and logic-0 to the memristor cells respectively.

The suitability of the crossbar architecture can be better explained by NOR operation as shown in Fig. 2. We, first, initialize the output memristor (OU T ) to logic-1 and connect it to the ground (0V) and then we apply execution voltage V G to the input memristors (IN 1 and IN 2 ). This voltage may corrupt data on other memristors on the same row/column, to avoid this, an isolation voltage V iso needs to be applied to the columns and rows that we want to unselect. Parallel execution of NOR/NOT gates on the crossbar requires the alignment of the inputs and outputs of the respective gates. Since we are considering transpose memory here, gates can be aligned either by rows or columns.

Fanout

Fanout occurs when an output memristor at any circuit depth (excluding primary output) has to drive multiple memristors. It can degrade performance as circuit depth increases and incurs additional energy overheads by introduction of extra cycles. For a given gate-level netlist, a single memristor cell can only be

Memristive

Crossbar Memory used either as an input or output of a gate. Therefore, the value that is stored in the output memristor if needed can work as input to multiple following memristors. A naïve approach can perform this fanout operation by multiple copies of the logic value as equal to number of the driven memristors (on different rows or columns than driving memristor). This copy operation introduces additional cycles, as proposed in MAGIC logic style where each copy operation requires cascade of two NOT operations. Therefore, it will require two extra memristors as well as two extra cycles for a single copy operation. As the number of fanout increases for a specific gate output, the number of copy operations, hence additional cycles also increases linearly. Moreover, the energy dissipation also increases due to the extra NOT operations. Works [START_REF] Hur | Simple magic: Synthesis and in-memory Mapping of logic execution for memristor-aided logic[END_REF]8] based in-memory logic synthesis did not address these performance related issues.

Controller Wordlines Bitlines Valid Read Data V SET V RESET V READ V G Voltage Select MUX V ISO (a) (b)

Proposed Approach

In this work, we propose a novel approach that will reduce the performance and energy overheads due to fanout in memristor based in-memory computing. The controller will apply relevant signals in proper sequence to the rows and columns in a crossbar architecture. Here, we consider two different cases based on the initialization of the output memristors at the copy locations.

-Case 1: Here, we maintain the same assumption as of works [8] and [START_REF] Strukov | The missing memristor found[END_REF]. We consider that the output memristors at the copy locations are initialized to logic-1 which allows us to use a multiplexer through which controller can skip write cycle if the read value is one. With our approach, we have assumed on average 50% of the time, the sensed logic value is 1 which allows us to skip the write cycle. The equations for total cycle counts and energy consumption are formed considering this factor. -Case 2: Here, we consider that the output memristors at the copy locations are not initialized to logic-1. With our proposed approach, we exclude the multiplexer circuit hence removing the ability to skip write cycle (cycle 2) on average 50% of the time. We calculate the total cycle counts and energy requirement and compare with the previous work [8]. Previous works rely on copy operation which requires cascade of two NOT executions which in turn requires initialization of the output memristors of NOT gates to logic-1. Whereas with our approach, we do not need to initialize the output memristors at the copy locations to logic-1. This comparison demonstrates the trade-off between copy operation and direct read-write operation.

Overall Approach: Case 1

It will carry out the proposed method according to the following steps:

-Cycle 1: Controller reads the logic value of the output memristor which has fanout of two or more. -Cycle 2: Controller writes the logic value as inputs to the driven memristors only if the sensed value is zero, otherwise, it can skip the cycle 2.

Previous works [START_REF] Hur | Simple magic: Synthesis and in-memory Mapping of logic execution for memristor-aided logic[END_REF]8] utilized a controller that produces a similar state diagram as shown in Fig. 4(a). For regular memory read and write operations, it goes to the read and write states respectively and for executing a logic function, it goes to the execution state. Execution state consists of micro operations where the controller executes the logic function in multiple cycles.

With our proposed approach, the number of state transitions will increase as shown in the Fig. 4(b) but the number of states will remain the same. While executing the micro operations in the execution state, whenever there is a fanout event, the controller will go to the read state and depending on the read value, it will decide whether to go to the write state or not. We can achieve this by modifying the controller circuit. The sensed bit can act as selector for a 2:1 multiplexer and depending on the select bit, controller will determine whether to write to the memory or not. If the read value is 1, the multiplexer will pass the input signal r e1 to the controller to go the execution state skipping the write state, otherwise, it will go to the write state and then to the execution state. This allows us to avoid writing logic-1 if the sensed logic value is 1.

Mapping Scenario Analysis: Case 1

We have made the following assumptions for three different mapping scenarios of a logic function on a memristor crossbar.

We only assume that a single copy of primary input is stored in a single memristor cell and following a fanout scenario from this cell, one can do the copy operation on-demand. Previous works assume that multiple copies of primary inputs are already available depending on the number of gates they are driving. Hence, their assumptions underestimate the cycles required as they are able to eliminate the copy cycles produced from the fanouts of primary inputs. Like the previous works [8,[START_REF] Ali | Efficient Algorithms for In-Memory Fixed Point Multiplication Using MAGIC[END_REF], we have considered the output memristors are initialized to logic value one at the beginning of the execution process which is a requirement for MAGIC logic style.

The work [8] has also initialized the output memristors to logic-1 required for copy operations (which eventually become the first input memristors of the driven gates). With our proposed approach, we are only considering fanout event related metrics not the whole synthesis procedure. Therefore, in our result analyses, we are not accounting the initialization cycles and energy consumption generated from initializing the output memristors. For fair comparison, we have maintained the same assumption while comparing with work [8]. In our work, the added consideration is, we can avoid writing logic value one. After reading the logic value of the driving memristor, if the controller finds the value as one, it can skip the write operation as the memristors are already initialized to one.

To demonstrate the efficacy of the approach, we have considered three different mapping scenarios (average, best, and worst) depending on the location of the second input memristors of the driven gates. To explain three scenarios, we consider the gate-level netlist shown in Fig. 5(a). We observe that there is a fanout of 4 from the node h. We also consider the logic value of h to be mapped on the location (1, 1) in the memristor crossbar architecture.

Scenario 1 Here, we consider that all the second input memristors are aligned along the same row or same column. The mapped variable h in Fig. 5 variables a, i, j, and g are mapped as second input memristors on the second column of the crossbar. With the previous approach, it requires 4 cycles to copy logic value of h and now with all the input memristors of the driven gates in aligned position, it is possible to execute the gates in one cycle. The following equation can be used to estimate the total cycles required for copy operations with previous approach:

N n=2 [n * f req(n)] (2)
where, n denotes different fanouts (i.e., number of gates it is driving), N is maximum fanout degree, and f req(n) is the number of times, a fanout of n is found in a netlist.

With the proposed approach, we need 1 cycle to read the logic value and one cycle to write multiple copies of h along the same row or column (given that the read value is logic-0). We consider that on average 50% of the time the read value is 0 which allows us to consider only half of the write cycles to the total cycle count. Therefore, we can estimate the total cycles required with the equation given below:

1.5 N n=2 [f req(n)] (3)
It should be noted that with our proposed approach, we require at most two cycles (read and write) for each fanout event and this is true for all scenarios considered here. Therefore, for all three scenarios, we can reuse Equation 13to estimate the total cycle counts.

We are providing a general formula to estimate the energy dissipation with both the previous and proposed approach due to the fanout only. According to the work [8], 52.49 fJ is the energy required for one NOT execution. Therefore, with previous approach, we can estimate the total energy dissipation by multiplying 52.49 fJ with the total cycle count (same as total NOT executions required for copy operations). The following equation gives us the total energy dissipation with this approach: 52.49

N n=2 [n * f req(n)] (4)
Whereas, for the proposed approach, the total energy required for a specific benchmark circuit can be estimated as:

N n=2 [{(RE m + (n -1) * W E)} * f req(n)] (5)
Where, RE m denotes the total energy needed to read the variable and to decide (using multiplexer) whether to go to the write state or not. For fanout of n, we need to write (n -1) memristors in a single cycle. Here, W E denotes the write energy required for writing a single memristor. Fig. 6. Scenario 2: (a) previous approach, (b) proposed approach. Scenario 3: (c) regular approach, (d) proposed approach. Here, same color notation as Fig. 5 is maintained, the additional colors, orange, purple, and dark green represent different execution cycles and each composed of all the participating gates in that same cycle.

Scenario 2

We consider here some of the second input memristors are aligned on the same row as of the first input memristor (h) and some are scattered throughout the crossbar. Here, we divide different fanouts (n) according to the number of second input memristors residing on the same row. For example, for fanout of 3, 4, 5, and 6, we have considered 2 second input memristors are on the same row as first input memristor. From Fig. 6(a), it can be seen that the logic variables a and i that are mapped to the second input memristors of the gates 4 and 5 are aligned on the same row and variables j and g are in random locations. With the previous approach, h needs to be copied two times (3 NOT executions) to use it as an inputs of gates 6 and 7. We can evaluate the following equation for the previous approach:

2 + M i=1 4i+2 n=4i-1 [{n -(2i -1)}f req(n)] (6)
where, 2 cycles are required for fanout of 2. Here, i denotes the number of sub-divisions made on the different fanout and M denotes maximum degree of sub-division. For example, fanout of 4 falls under first sub-division (i=1) which requires 3 cycles (given by the term {n -(2i -1)}) to make two copies of the driving memristor. In this way, we find cycle count for each division and add together to get the total cycle counts. As discussed earlier, with the proposed approach, we will get the cycle counts from Equation 13.

With the previous approach, as in Scenario 1, by simply multiplying the total cycle count with energy requirement of one NOT execution, we can estimate the total energy dissipation:

52.49 * [2 + M i=1 4i+2 n=4i-1 [{n -(2i -1)}f req(n)]] (7)
and for the proposed approach:

(RE m + W E) + M i=1 4i+2 n=4i-1 [{RE m + (n -2i) * W E}f req(n)] (8)
Where, first term (RE m + W E) is the energy required for fanout of 2. The term (n -2i) gives us the number of memristors that needs to be written in a single write cycle. Scenario 3 For the third scenario, we consider that the second input memristors are scattered throughout the crossbar i.e., aligned neither horizontally nor vertically. From Fig. 6(c), we can see that variables a, i, j, and g are mapped on the memristors that are scattered on the crossbar. With the previous approach, it requires (n + 1) copy cycles for a specific fanout of n and the total cycles required can be estimated as:

N n=2 [(n + 1)f req(n)] (9)
For the proposed approach, we use Equation 13which gives us the same cycle counts as of scenario 1 and 2.

By maintaining the same procedure as of Scenarios 1 and 2, the total energy dissipation for the previous approach can be obtained. For the proposed approach, we need to write n memristors in a single write cycle for a fanout of n and the term (n * W E) gives us the write energy required for this operation. For the previous and proposed approach, the energy dissipation can be estimated by the following two equations respectively:

52.49 * N n=2 [(n + 1)f req(n)] ( 10
) N n=2 [{RE m + (n * W E)}f req(n)] (11)

Overall Approach: Case 2

It will carry out the proposed method according to the following steps:

-Cycle 1: Controller reads the logic value of the output memristor which has fanout of two or more. -Cycle 2: Controller writes the logic value as inputs to the driven memristors without considering whether the sensed logic value is one or not.

Previous works [START_REF] Hur | Simple magic: Synthesis and in-memory Mapping of logic execution for memristor-aided logic[END_REF]8] utilized a controller that produces a similar state diagram as shown in Fig. 7(a) and maintain the same operation as explained in section 3.1.

With our proposed approach, While executing the micro operations in the execution state, whenever there is a fanout event, the controller will go to the read state and then go to the write state to write the value to the driven memristors without considering whether the read logic value is one or not. Here, we do not use the 2:1 multiplexer, so, controller does not have the capacity to determine whether to skip cycle 2 or not. Controller will always go to the read state and then to the write state irrespective of the read logic value. We do not initialize the output memristors at the copy locations to logic-1 which saves us the initialization cycles and energy required for this operation.

Mapping Scenario Analysis: Case 2

We maintain the same assumption as discussed in the section 3.2 except the third assumption that assume the output memristors at the copy locations are initialized to logic-1. With the exclusion of this assumption, controller now does not have the ability to skip the write cycle as considered in case 1. Here, we discuss three different mapping scenarios of a logic function on a memristor crossbar.

Scenario 1 Here, we consider that all the second input memristors are aligned along the same row or same column. The mapped variable h in Fig. 5(b) needs to be copied 3 times to use as first input memristors of the driven gates and the variables a, i, j, and g are mapped as second input memristors on the second column of the crossbar. In case 2, we consider that output memristors at the copy locations are not initialized to logic-1. Hence, with the previous approach, it requires at least 1 cycle to initialize the memristors at the copy locations and 4 cycles to copy logic value of h. The following equation can be used to estimate the total cycles required for copy operations with previous approach:

N n=2 [(n + 1)f req(n)] (12)
where, n denotes different fanouts (i.e., number of gates it is driving), N is maximum fanout degree, and f req(n) is the number of times, a fanout of n is found in a netlist.

With the proposed approach, we need one cycle to read the logic value and one cycle to write multiple copies of h along the same row or column. Therefore, we can estimate the total cycles required with the equation given below:

2 N n=2 [f req(n)] (13)
It should be noted that with our proposed approach, we require two cycles (read and write) for each fanout event and this is true for all scenarios considered here. Therefore, for all three scenarios, we can reuse Equation 13 to estimate the total cycle counts.

We are providing a general formula to estimate the energy dissipation with both the previous and proposed approach due to the fanout only. For case 2, we have to consider both the energy dissipation due to NOT execution and initialization of the output memristors at the copy locations. According to the work [8], 52.49 fJ is the energy required for one NOT execution, we can denote it by N Ex and the energy required to set a memristor to logic 1 is 66.09 fJ, we can denote it by init 1. For fanout of n, we need to initialize n number of memristors. The following equation gives us the total energy dissipation with this approach:

(N Ex + init 1) N n=2 [n * f req(n)] (14)
Whereas, for the proposed approach, the total energy required for a specific benchmark circuit can be estimated as:

N n=2 [{(RE + (n -1) * W E)} * f req(n)] (15)
Where, RE denotes the energy needed to read the variable. For fanout of n, we need to write (n -1) memristors in a single cycle. Here, W E denotes the write energy required for writing a single memristor.

Scenario 2

We consider here the same mapping scenario as discussed in section 3.2, i.e. some of the second input memristors are aligned on the same row as of the first input memristor (h) and some are scattered throughout the crossbar. For details of this mapping scenario, we can refer to section 3.2 (scenario 2). Referring to Fig. 6(a), with the previous approach, first, an initialization cycle is needed to initialize the three output memristors at the copy locations and then h needs to be copied two times (3 NOT executions) to use it as an inputs of gates 6 and 7. We can evaluate the following equation for the previous approach:

3 + M i=1 4i+2 n=4i-1 [{n -2(i -1)}f req(n)] (16)
where, 3 cycles are required for fanout of 2. Here, i denotes the number of sub-divisions made on the different fanout and M denotes maximum degree of sub-division. For a specific fanout of n, the term {n -2(i -1)} gives us the total cycle count which includes the copy cycles and the initialization cycle. In this way, we find cycle count for each division and add together to get the total cycle counts. As discussed earlier, with the proposed approach, we will get the cycle counts from Equation 13.

With the previous approach, as in Scenario 1, we can estimate the total energy dissipation by the following equation:

(N Ex + init 1)[2 + M i=1 4i+2 n=4i-1 [{n -(2i -1)}f req(n)]] (17)
and for the proposed approach:

(RE + W E) + M i=1 4i+2 n=4i-1 [{RE + (n -2i) * W E}f req(n)] (18)
Where, first term (RE + W E) is the energy required for fanout of 2. The term (n -2i) gives us the number of memristors that needs to be written in a single write cycle. Scenario 3 For the third scenario, we consider that the second input memristors are scattered throughout the crossbar i.e., aligned neither horizontally nor vertically. From Fig. 6(c), we can see that variables a, i, j, and g are mapped on the memristors that are scattered on the crossbar. With the previous approach, it requires 1 initialization cycle and (n + 1) copy cycles for a specific fanout of n and the total cycles required can be estimated as:

N n=2 [(n + 2)f req(n)] (19)
For the proposed approach, we use Equation 13which gives us the same cycle counts as of scenario 1 and 2.

By maintaining the same procedure as of Scenarios 1 and 2, the total energy dissipation for the previous approach can be obtained. For the proposed approach, we need to write n memristors in a single write cycle for a fanout of n and the term (n * W E) gives us the write energy required for this operation. For the previous and proposed approach, the energy dissipation can be estimated by the following two equations respectively:

(N Ex + init 1) N n=2 [(n + 1)f req(n)] ( 20
) N n=2 [{RE + (n * W E)}f req(n)] (21)

Experimental Results

To validate the proposed approach, we performed a set of experiments on IS-CAS'85 benchmark circuits and compared our results with a recently published work [8]. While doing so, we maintained the assumptions as stated in Section 3.

In a given NOR/NOT based synthesized netlist, total number of gate executions consist of regular execution of gates pertaining only to the netlist and the extra NOT executions required for copy operations produced by fanout. We estimated the total number of extra NOT executions over the total number of gate executions for a specific benchmark circuit and then averaged over all the benchmark circuits. An average of 47.41%, 41.82%, and 54.40% additional cycle count due to NOT operations has been measured for scenario 1, scenario 2, and scenario 3 respectively. With our proposed approach, we are able to reduce performance and energy overheads produced by these aforementioned additional cycles.

-Case 1: Previous works such as [START_REF] Hur | Simple magic: Synthesis and in-memory Mapping of logic execution for memristor-aided logic[END_REF]8] have only considered energy dissipation due to gate executions, but as energy consumptions from read cycle, write cycle, and 2:1 multiplexer are inherent in our proposed approach, we have included these in our analysis. Performance and energy overheads for the multiplexer are obtained for a 45nm CMOS process technology from PTM using HSPICE and our circuit level evaluation shows that the delay introduced by a multiplexer is in the picosecond range. The work [8] has used the VTEAM model [START_REF] Kvatinsky | VTEAM: A General Model for Voltage-Controlled Memristors[END_REF] to find the maximum latency for MAGIC NOR operations (when either of the inputs is at logic-1) and also to find the read time.

We consider these times as the cycle time and read time of the system respectively. According to [START_REF] Talati | Practical challenges in delivering the promises of real processing-in-memory machines[END_REF], the latency introduced by MAGIC operations are much higher than that of read and write operations. Hence, the effective delay produced by the sense circuit and the multiplexer still stays below 1 cycle time. Therefore, in our analysis, we will not consider any performance overhead due to this added multiplexer. -Case 2: In case 2, we do not initialize the output memristors at the copy locations to logic-1. This removes the 2:1 multiplexer from the system, as the controller is not aware of the logic value stored in the output memristors at the copy locations. In our result analysis, for the proposed approach, we exclude the energy consumed by the multiplexer and in case of previous approach, we add the energy required for initializing the memristor to logic-1.

From [8], the energy required to write logic-1 to a memristor is 66.09 fJ. Therefore, with the previous approach, the total cycle count comes from the addition of initialization cycle and the copy cycles. With the proposed approach, we always need two cycles, one to read the logic value of the driving memristor and other to write the logic value to the driven memristors.

Experimental Setup

The experimental methodology we follow to validate our approach is as follows:

1. A given gate-level netlist is first synthesized with ABC tool [START_REF]Berkeley Logic Synthesis and Verification Group, ABC: A System for Sequential Synthesis and Verification[END_REF] and target library of NOR and NOT gates. 2. For three different scenarios, number of fanout events has been found and cycle counts and energy dissipations estimation have been performed with the proposed method and compared with [8].

Results and Analysis

Table 1, Table 2, and Table 3 report the improvements over recently published work with respect to the number of cycles due to fanout in average, best, and worst scenarios respectively. For case 1, we observe average improvements of 51.08%, 38.66%, and 63.18% in cycle reduction considering three mapping scenarios.

In case 2, we consider that the memristors at the copy locations are not initialized to logic-1 which dictates the need of adding initialization cycle to the total cycle counts. With the proposed approach, we need two cycles to read the driving memristor and then write the logic variable to the driven memristors in parallel. We observe average improvements of 50.94%, 42.08%, and 60.65% in cycle reduction. Table 4, Table 5, and Table 6 report the improvements in energy consumption. For estimating the energy requirement, we have taken the same parameter values as discussed in [8]. The energy required for NOT execution is 52.49 fJ. The energy required to read logic-0 is 0.03 fJ, while that for logic-1 is 3.34 fJ. For our estimation purpose, we have averaged these two values and considered the read energy as 1.685 fJ. The energy required to write logic-1 to a memristor which is termed as SET operation is 66.09 fJ and through RESET operation, we can write logic-0 to a memristor and the energy required is 17.60 fJ. For case 1, as discussed in Section 3, we do not need to write logic-1 with our proposed approach, thus, no energy is consumed. Therefore, the average energy considered for SET and RESET operation is 8.8 fJ. For a specific benchmark circuit, we find all different fanout occurrences and add the energies required to estimate the total energy dissipation. We observe average improvements of 91.30%, 88.53%, and 74.04% by experimental evaluation on ISCAS'85 benchmark circuits. This improvement can be primarily attributed to the fact that we were able to eliminate the need for writing logic-1.

For case 2, with the previous approach, the memristors at the copy locations need to be initialized to logic-1. Therefore, this initialization energy needs to be accounted for in the total energy calculation. With the proposed approach, we exclude energy consumption produced by the multiplexer that is required in case 1. The only energies required are the energy to read the driving memristor and energy to write the driven memristors. We observe average improvements of 86.03%, 78.97%, and 51.89% in energy saving.

Conclusions

In this work, we outline an effective approach that would significantly reduce the performance and energy overheads due to fanout while mapping a logic function in memristor based crossbar architecture. Comparison has been made with a recently published work and shows significant average improvements in average, best, mapping scenarios in performance and energy dissipation. Future research direction would be to implement the entire logic synthesis process utilizing the fanout optimization discussed here.

Fig. 3 .

 3 Fig. 3. (a) Memory processing unit (MPU), (b) Analog mux.

Fig. 4 .

 4 Fig. 4. Controller state diagram (Case 1). (a) Previous approach and (b) Proposed approach. The states are given as: I = Initial state, R = Read state, W = Write state, and Ex = Execution state; The different inputs denote the followings: r = read, rc = read complete, w = write, wc = write complete, e = execution, ec = execution complete, f = fanout event, re1 = read logic-1, re0 = read logic-0, and wce = write complete and go to execution state.

Fig. 5 .

 5 Fig. 5. Scenario 1 with Previous and Proposed Approach. (a) NOR/NOT based synthesized netlist. Regular Approach: (b) 1 st cycle: 1 st NOT execution to initiate the copy operation, (c) 2 nd cycle: 2 nd NOT execution to complete the first copy operation, (d) 3 rd & 4 th cycles: two NOT executions to complete all the copy operations, (e) execution of all the NOR gates in parallel. Proposed Approach: (f) 1 st cycle: read operation to sense the logic variable h, (g) 2 nd cycle: write operation to write h required number of times in one cycle, (h) 3 rd cycle: execution of all NOR gates in parallel. Here, black arrows denote the NOT execution required for copy operation, blue arrow denotes the read operation, green arrows denote the write operations and red arrows denote the execution of NOR gates.

Fig. 7 .

 7 Fig. 7. Controller state diagram (Case 2). (a) Previous approach and (b) Proposed approach. The states are given as: I = Initial state, R = Read state, W = Write state, and Ex = Execution state; The different inputs denote the followings: r = read, rc = read complete, w = write, wc = write complete, e = execution, ec = execution complete, f = fanout event, rw = go to write state after reading logic value, and wce = write complete and go to execution state.

  2, memristors' resistances of the IN 1 and IN 2 are considered as input values and we can determine the output logic value by measuring OU T memristor resistance. An execution voltage V G is applied to both input memristors and the output value is stored in the output memristor.

Table 1 .

 1 Comparison of Number of Cycles (Average Scenario) with the Regular and Proposed Approach.

Table 2 .

 2 Comparison of Number of Cycles (Best Scenario) with the Regular and Proposed Approach.

Table 4 .

 4 Comparison of Energy Dissipation (Average Scenario) With the Regular and Proposed Approach.


Evgeniya Vorontsova

Interval Computations in Julia programming language

Keywords: Numerical Computing, Interval Arithmetic, Julia Programming Language, JuliaIntervals, Octave Interval Package

Introduction

The general-purpose Julia programming language [START_REF] Bezanson | Julia: A fresh approach to numerical computing[END_REF] was designed for speed, efficiency, and high performance.

It is a flexible, optionally-typed, and dynamic computing language for scientific, numerical and technical computing applications. Julia is open source language with all sources free available on GitHub. The language was developed and incubated at MIT [START_REF] Bezanson | Why we created julia[END_REF]. Currently, after Julia 1.0 was officially released to the public in August 2018, the language is becoming increasingly popular. Julia has been downloaded more than 8.4 million times, as of May 2019 [2], and is used at more than 1,500 universities.

So, it is very important for researchers, working in a field of interval analysis, to have fast, efficient and robust publicly available software packages for performing computations with interval arithmetic written in Julia.

IntervalArithmetic.jl

In this paper, we review and compare a recently developed Julia package for performing Validated Numerics, i.e. rigorous computations with finite-precision floating-point arithmetic, IntervalArithmetic.jl [START_REF] Benet | JuliaIntervals.jl Package -Rigorous numerics with interval arithmetic & applications[END_REF], with performance of GNU Octave interval package for real-valued interval arithmetic [START_REF] Heimlich | GNU Octave interval package, version 3.2.0[END_REF]. This Octave toolbox was chosen for comparison because of several important reasons. First of all, it is a free, open-source software, unlike INTLAB [START_REF] Rump | Intlab -interval laboratory[END_REF], a Matlab/Octave toolbox for Reliable Computing. The other fundamental difference between INTLAB and GNU Octave interval package is non-conformance of INT-LAB to IEEE 1788-2015 -IEEE Standard for Interval Arithmetic [START_REF]IEEE Std 1788-2015 -IEEE Standard for Interval Arithmetic[END_REF]. On the other hand GNU Octave interval package's main goal is to be compliant with the Standard. Likewise, authors of IntervalArithmetic.jl wrote [START_REF] Benet | JuliaIntervals.jl Package -Rigorous numerics with interval arithmetic & applications[END_REF] that they were working towards having the package be conforming with the Standard. So, all calculations in these packages are performed using interval arithmetic: all quantities are treated as intervals. The final result is also an interval contained the correct answer.

In next section we would like to show some practical examples with interval arithmetic in Julia.

Examples

Getting Started

The basic object in the IntervalArithmetic.jl package is the parameterized type Interval. By default, Interval objects contain Float64 s. Intervals are created using the @interval macro:

using IntervalArithmetic a = @interval (1 , 2) b = @interval (3 , 4) print ( a + b , a -b , a * b , a / b )
The output of this code is

[4 , 6] [ -3 , -1] [3 , 8] [0.25 , 0.666667]
As you may have noticed, the package permits to write quite clear and intuitive code for interval computations.

Matrix Multiplication

In this section we present the results of experiments comparing the IntervalArithmetic.jl library with the GNU Octave interval package. In summary, we show that Julia interval library is significantly faster than the Octave library.

In our first experiment we measured the time to evaluate the interval matrix multiplication. The Julia code is:

function MultMatr (A , B ) return A * B end n = 10 M1 = 10* rand (n , n ) M2 = 10* rand (n , n ) iM1 = map ( Interval , M1 ) iM2 = map ( Interval , M2 ) A = iM1 .± 5 B = iM2 .± 5 @benchmark MultMatr (A,B )
Here we use BenchmarkTools package by Jarrett Revels [START_REF] Revels | BenchmarkTools Julia package[END_REF], a framework for writing and running groups of benchmarks.

And Octave code for MultMatr function is: 1. This experiment shows that performance of Julia interval package for that problem is significantly better.

pkg load interval function [ t ] = MultMatr ( n ) A = infsupdec ( rand ( n ) , 10* rand ( n ) + 1); B = infsupdec ( rand ( n ) , 10* rand ( n ) + 1); tic C = A * B ; t = toc ;

Elementary functions

In our second experiment we compared the times for evaluation of the elementary functions (exp, sin, cos, etc.) for random interval arguments. The design of the experiment is taken from [START_REF] Mascarenhas | Moore: Interval Arithmetic in Modern C++[END_REF]. The results of the second setting are summarized in Table 2. We may see that these calculations in Julia are almost two orders of magnitude faster.

Plotting

In this section, we will illustrate how to visualize the interval extension of a given function over an interval. The process of splitting the interval into many smaller adjacent pieces for range evaluations of the given function is called mincing.

Figures 12show visualization of mincing process for one function (Julia code was adapted from [START_REF] Sanders | Métodos numéricos para sistemas dinámicos[END_REF]). For implementation The IntervalBox type constructed from an array of Interval was used.

Figure 1 :

 1 Figure 1: Function cos(x) + 0.5 sin(2x), 10 sub-intervals.

Figure 2 :

 2 Figure 2: Function cos(x) + 0.5 sin(2x), 50 sub-intervals.

Table 1 :

 1 end Time for interval matrix multiplications

	Matrix size,	Julia,	Octave,
	rows	ms	ms
	10	0.095	13.317
	100	111.91	849.61
	1000	125870	863340
	For Octave we create 10 random interval

Table 2 :

 2 Time for 10 5 evaluations of the ele-

	mentary functions
	Function Julia, s Octave, s
	exp	0.49	102.7
	sin	0.749	147.85
	cos	0.638	230.2
	tan	0.49	126.13
	arcsin	0.858	119.01
	arccos	1.132	169.02
	arctan	1.318	127.01

Acknowledgement

The work was supported by the Russian Foundation for Basic Research, project no. 18-29-03071 mk.

Conclusion

Public available Julia package for interval arithmetic has been investigated. Experimental comparison of Octave and Julia packages for interval arithmetic shows that Julia Inter-valArithmetic.jl package is significantly faster then Octave interval package. In addition, the implementation process of interval arithmetic computations in this Julia package is easy and convenient, due to intuitive syntax of the language and the package.


De Carlo
email: steeve.comeau@obs-vlfr.fr

Similar controls on calcification under ocean acidification across unrelated coral reef taxa Running head: Calcification physiology in coral reef taxa

Keywords: pH, Dissolved inorganic carbon, Calcifying fluid, Calcium, Physiology, Coral, Coralline alga

Ocean acidification (OA) is a major threat to marine ecosystems, particularly coral reefs which are heavily reliant on calcareous species. OA decreases seawater pH and calcium carbonate saturation state (Ω), and increases the concentration of dissolved inorganic carbon (DIC). Intense scientific effort has attempted to determine the mechanisms via which ocean acidification (OA) influences calcification, led by early hypotheses that calcium carbonate saturation state (Ω) is the main driver. We grew corals and coralline algae for 8 to 21 weeks, under treatments where the seawater parameters Ω, pH and DIC were manipulated to examine their differential effects on calcification rates and calcifying fluid chemistry (Ω cf , pH cf , and DIC cf ). Here, using long duration experiments, we provide geochemical evidence that differing physiological controls on carbonate chemistry at the site of calcification, rather than seawater Ω, are the main determinants of calcification. We found that changes in seawater pH and DIC rather than Ω had the greatest effects on calcification and calcifying fluid chemistry, though the effects of seawater carbonate chemistry were limited. Our results demonstrate the capacity of organisms from taxa with vastly different calcification mechanisms to regulate their internal chemistry under extreme chemical conditions. These findings provide an explanation for the resilience of some species to OA, while also demonstrating how changes in seawater DIC and pH under OA influence calcification of key coral reef taxa.

Introduction

Over the last decade there has been intensive scientific effort to better understand the impacts of ocean acidification (OA) on calcifying organisms that are responsible for building and sustaining coral reefs. OA is expected to cause a reduction in calcification of both corals and coralline algae [START_REF] Kroeker | Meta-analysis reveals negative yet variable effects of ocean acidification on marine organisms[END_REF] that are key reef formers and cementing species in coral reefs [START_REF] Chan | Sensitivity of coral calcification to ocean acidification: a meta-analysis[END_REF][START_REF] Mccoy | Coralline algae (Rhodophyta) in a changing world: integrating ecological, physiological, and geochemical responses to global change[END_REF]. The reduction of calcification with OA has often been linked to the decrease in seawater Ω, because the precipitation of CaCO 3 ultimately requires both Ca 2+ and CO 3 2-. Because [Ca 2+ ] is constant in the oceans and will not be affected by OA, the decrease in calcification with OA has been attributed to the associated decrease in [CO 3 2-]. However, the capacity of organisms to transport seawater CO 3 2-across membranes has not been proven, which led to the alternate hypothesis that the ratio between seawater [DIC] and [H + ] controls calcification [START_REF] Bach | Dissecting the impact of CO2 and pH on the mechanisms of photosynthesis and calcification in the coccolithophore Emiliania huxleyi[END_REF][START_REF] Jokiel | Coral reef calcification: carbonate, bicarbonate and proton flux under conditions of increasing ocean acidification[END_REF]. This hypothesis is based on the principle that skeletal accretion requires the import of DIC that is consumed, and export of H + that are produced during the mineralization process in the calcifying fluid (i.e., the site of calcification). Under this hypothesis, the decline in calcification under OA is caused by higher [H + ] in seawater that increases the gradient against which H + need to be exported from the calcifying fluid [START_REF] Jokiel | Coral reef calcification: carbonate, bicarbonate and proton flux under conditions of increasing ocean acidification[END_REF][START_REF] Jokiel | Ocean Acidification and Control of Reef Coral Calcification by Boundary Layer Limitation of Proton Flux[END_REF].

This steeper gradient could either reduce the capacity of the organisms to maintain elevated pH in the calcifying fluid (pH cf ), or increase the energy expenditure needed to maintain constant elevated pH cf [START_REF] Mcculloch | Coral resilience to ocean acidification and global warming through pH up-regulation[END_REF][START_REF] Venn | Impact of seawater acidification on pH at the tissue-skeleton interface and calcification in reef corals[END_REF]. The role of DIC is more complex because the species of DIC involved (CO 3 2-, HCO 3 -, or CO 2 ), the mechanisms via which it is transported to the site of calcification in different taxa [START_REF] Zoccola | Bicarbonate transporters in corals point towards a key step in the evolution of cnidarian calcification[END_REF], and its origin (metabolic or inorganic) remain controversial [START_REF] Furla | Sources and mechanisms of inorganic carbon transport for coral calcification and photosynthesis[END_REF].

Attempts to disentangle the effects of these parameters of carbonate chemistry on calcification have collectively demonstrated that decreasing seawater DIC, pH,

[DIC] / [H + ] and Ω can all reduce calcification for various marine calcifiers [START_REF] Comeau | Coral calcifying fluid pH is modulated by seawater carbonate chemistry not solely seawater pH[END_REF][START_REF] Comeau | Coral reef calcifiers buffer their response to ocean acidification using both bicarbonate and carbonate[END_REF][START_REF] Herfort | Bicarbonate Stimulation of Calcification and Photosynthesis in Two Hermatypic Corals(1)[END_REF]. However, results are inconsistent, indicating changes in [CO 3 2-],

[HCO 3 -], Ω, [DIC] / [H + ], and [Ca 2+ ] could all influence calcification rates to varying extents [START_REF] Comeau | Coral calcifying fluid pH is modulated by seawater carbonate chemistry not solely seawater pH[END_REF][START_REF] Comeau | Coral reef calcifiers buffer their response to ocean acidification using both bicarbonate and carbonate[END_REF][START_REF] Herfort | Bicarbonate Stimulation of Calcification and Photosynthesis in Two Hermatypic Corals(1)[END_REF][START_REF] Jury | Effects of variations in carbonate chemistry on the calcification rates of Madracis auretenra (= Madracis mirabilis sensu Wells, 1973): bicarbonate concentrations best predict calcification rates[END_REF][START_REF] Marubini | Coral calcification responds to seawater acidification: a working hypothesis towards a physiological mechanism[END_REF][START_REF] Marubini | Suppression of skeletal growth in scleractinian corals by decreasing ambient carbonate-ion concentration: a cross-family comparison[END_REF][START_REF] Schneider | The effect of carbonate chemistry on calcification and photosynthesis in the hermatypic coral Acropora eurystoma[END_REF]. The difficulty with testing these hypotheses is that [DIC] / [H + ] and Ω are correlated, leading to an inability to test the role of one over the other [START_REF] Comeau | Coral reef calcifiers buffer their response to ocean acidification using both bicarbonate and carbonate[END_REF][START_REF] Jokiel | Ocean Acidification and Control of Reef Coral Calcification by Boundary Layer Limitation of Proton Flux[END_REF].

Therefore, here we examine the underlying role of seawater carbonate chemistry parameters in the calcification process by testing the independent effects of [DIC],

[H + ], [DIC] / [H + ] and Ω on calcification rates and calcifying fluid chemistry on multiple coral and coralline algal species. We choose to work on two different taxa (coral and coralline alga) to investigate if organisms with different physiologies and calcification mechanisms would respond similarly to large modification of the carbonate chemistry.

Past studies that have examined the separate effects of the different species of the carbonate system have had three limitations that we seek to overcome: 1) no test of the treatment conditions on multiple species representing a range of taxa, 2) short duration times (≤ 2 weeks, but mostly ~ 1 or 2 hours) where specimens are subject to "shock" responses, and most importantly 3) they have not determined the underlying processes responsible for the observed effects on calcification: specifically how pH, DIC, and Ω within the calcifying fluid where precipitation occurs is affected by the prescribed treatments.

To test these hypotheses, we grew the subtropical coral species Pocillopora damicornis and Acropora yongei for 13 and 8 weeks, and the coralline algal species Neogoniolithon sp. and Sporolithon for 21 weeks under 5 treatments (Figure 1 and Table S1) designed specifically to determine the effects: 1) of DIC at constant pH

Materials and Methods

Organism collection

The experiment was performed in two phases, the first in April-June 2016 and the second in August-October 2016. The first phase focused on the coral P.

damicornis and the second phase on the coral A. yongei.

Treatments and regulation of pH

Our experiment consisted of five treatments that were created in duplicate ~ 20 L black tanks for a total of 10 experimental tanks. Each experimental tank was attached to an individual header tank where seawater carbonate chemistry was manipulated as per Fig. 3a from [START_REF] Cornwall | Experimental design in ocean acidification research: problems and solutions[END_REF]. Header tanks consisted of 220 L drums. The five treatments were specifically chosen to test the two hypotheses mentioned in the introduction. Combinations of CO 2 -free air, pure CO 2 , 2 M HCl, and 2 M NaOH were used to manipulate the seawater to the desired conditions. To avoid exposing organisms directly to large changes in seawater chemistry resulting from the addition of HCl and NaOH, seawater (pumped from 12-m depth 150-m off the shore) was first manipulated in the header tanks. Modified seawater was pumped into the experimental tanks every 3 hours for 15 min from each header tank to their respective incubation tanks to ensure the delivery of ~60 L of manipulated seawater per day, 3 times the experimental tank volume. Manipulations of the carbonate chemistry in the header tanks was done twice per week on new seawater by adjusting first the total alkalinity (A T ) using additions HCl or NaOH (Table S1). pH was then adjusted to the desired value using pH-controllers (AquaController, Neptune systems, USA) that controlled the bubbling of either pure CO 2 or CO 2 -free air. During the 3 -6 hours necessary to equilibrate the seawater to the target pH, the delivery of seawater from the header tanks to the experimental tanks was suspended. pH was also continuously adjusted in each experimental tank using pH-controllers that controlled the bubbling of either CO 2 -free air or pure CO 2 .

Light was provided by 150W LED (Malibu LED, Ledzeal) that followed a natural diel cycle. Light was ramped up in the morning from 6:30 h until 10:30 h to a maximum of ~200 -250 µmol quanta m -2 s -1 (for corals) or 30 -40 µmol quanta m -2 s -1 (for CCA) that was maintained for 4 h before ramping down until total darkness at 18:30 h. Temperature was kept constant at ~20° C, which is the average annual seawater temperature in Salmon Bay [START_REF] Ross | Perennial growth of hermatypic corals at Rottnest Island, Western Australia (32°S)[END_REF] where organisms were collected. Two submersible water pumps (Tunze) provided turbulent water motion in each incubation tank. This simulated more than 3 cm s -1 unidirectional seawater velocities. To avoid any nutritional stress, the corals were fed with freshly hatched brine shrimp twice per week.

Carbonate chemistry

Seawater pH and temperature were measured at 09:00 h every ~2 d in each incubation tank and after each water change in the drums, using a pH meter calibrated before each use on the total scale using Tris/HCl buffers, made following the protocol of [START_REF] Dickson | Guide to best practices for Ocean CO2 measurements[END_REF]. A T was measured twice per week in each incubation tank. A T was calculated using a modified Gran function, as described in [START_REF] Dickson | Guide to best practices for Ocean CO2 measurements[END_REF], and titrations of certified reference materials of the certified value. A T , pH T , temperature, and salinity were used to calculate the carbonate chemistry parameters using the seacarb package running in R software (R Foundation for Statistical Computing).

Calcification rates

Prior to the incubation, the skeletons of the organisms were stained by placing the organisms during 18 hours in seawater enriched with the fluorescent dye calcein at 50 mg L -1 with a pH adjusted to ~8.1 by the addition of NaOH. Three individuals of each species were placed in random order within each of the 10 incubation tanks, and calcification was measured over the incubation periods using buoyant weighing. We acknowledge that housing organisms in the same tank is not ideal, but these experimental treatments are logistically challenging to maintain for a long duration, and this level of replication equals or exceeds that used previously in these types of manipulations. Our experimental design also allows us to assess linear relationships between the different parameters of seawater carbonate chemistry and responses in multiple tanks, avoiding some of the pitfalls of traditional factorial approaches if they also implemented two tanks per treatment. The difference in buoyant weight between the beginning and end of incubation was converted to dry weight of aragonite and was used to calculate net calcification. Some Neogonioltihon sp. individuals died over the course of the experimental duration, so calcification rates at the 100 day mark where used for individuals that died between then and the end of the experiment. Mortality was similar across treatments. Calcification rates were normalized to surface area of the coral or CCA (mg cm -2 d -1 ) determined using the aluminum foil method. The duration of the experiment was 21 weeks for the CCA, 13 weeks for P. damicornis and 8 weeks for A. yongei.

Net photosynthesis

Photosynthetic rates were determined on A. yongei after 6 weeks and on S.

durum after 18 weeks in the experimental treatments. Each individual was placed into in a sealed incubation chamber filled with seawater originating from its respective tank. Light and temperature were adjusted to match the respective conditions in the tanks and a magnetic stirring bar was placed inside the incubation chambers to provide flow. Incubations lasted ~ 1.5 -2h and dissolved oxygen (measured using an A323 dissolved oxygen portable meter, Orion Star, Thermo Scientific, USA) and temperature were recorded at the start and end of each incubation to calculate net photosynthesis. Controls with tank seawater were run during each incubation.

pH cf , DIC cf , and Ca cf

Calcifying fluid pH (pH cf ) for all organisms and DIC (DIC cf ) for corals was calculated using the δ 11 B proxy method for pH cf [START_REF] Trotter | Quantifying the pH 'vital effect' in the temperate zooxanthellate coral Cladocora caespitosa: Validation of the boron seawater pH proxy[END_REF] and the δ 11 B and B/Ca method for DIC cf [START_REF] Holcomb | Factors affecting B/Ca ratios in synthetic aragonite[END_REF][START_REF] Mcculloch | Coral calcification in a changing World and the interactive dynamics of pH and DIC upregulation[END_REF]. Measurements of the skeleton geochemistry were done on the tip of the branches of corals (first 1-2 mm) that corresponded to material deposited during the incubation (as confirmed by the calcein staining). The selected portions of the skeleton were sampled by sectioning apical tips and then were crushed in a mortar and pestle. Coralline algal sample preparation followed the methods of (Cornwall, Comeau, & McCulloch, 2017). Briefly, samples were placed for 24 hours in 6.25 % NaClO, rinsed in mQ water. Sections of corallines were then cut to determine the distance of the calcein stain from the surface of individual samples, and examined under a fluorescence compound microscope. To ensure that skeleton grown during the experimental trial was sampled, individuals were only further processed if the stain was more than 0.5 mm from the surface. Due to uneven calcification, this meant that some individuals did not have regions that could be sampled, while for other individuals only small areas could be sampled. A diamond studded rounded tip attached to a dental drill was used to remove surface material.

All powders were processed subsequently in the clean laboratory of the Advanced Geochemical Facility for Indian Ocean Research [AGFIOR, University of Western Australia (UWA)] for dissolution and dilution to 10-ppm Ca solutions. Ten mg of each sample was placed in 6.25 % NaClO for 15 mins, rinsed in MilQ water then dried for 24 h. Samples were then dissolved in 0.51 N HNO 3 , and the boron was quantitatively separated on ion exchange columns and δ 11 B was measured on a multicollector inductively coupled plasma mass spectrometry (NU II). Measurements of the international carbonate standard JCP-1 yielded a mean value of 24.47 ± 0.06 ‰ (mean ± SE, n = 7), which was similar to the 24.33 ± 0.11 ‰ (SE) reported previously. Calculations of pH cf based on δ 11 B were made using the calculations of [START_REF] Trotter | Quantifying the pH 'vital effect' in the temperate zooxanthellate coral Cladocora caespitosa: Validation of the boron seawater pH proxy[END_REF]:

pH !" = pK ! -log (! !! ! !" ! ! !! ! !"#$ ) ! !"!!" ! !! ! !"#$ !! !! ! !" !!""" ! !"!!" !! (1)
where pK B is the dissociation constant dependent on temperature and salinity, δ 11 B sw = 39.61 [START_REF] Foster | Boron and magnesium isotopic composition of seawater[END_REF], and α B3 -B4 is the boron isotopic fractionation factor for the pH dependent equilibrium of the borate (B(OH) 4 -)

relative to the boric acid (B(OH) 3 ) species in the calcifying fluid, with a value of 1.0272 [START_REF] Klochko | Experimental measurement of boron isotope fractionation in seawater[END_REF].

B/Ca ratios, measured on the same material, and δ 11 B was utilized to determine [CO 3 2-] and then [DIC] at the site of calcification [DIC] cf following [START_REF] Mcculloch | Coral calcification in a changing World and the interactive dynamics of pH and DIC upregulation[END_REF]. B/Ca ratios were determined on the same aliquot of the solution used for pH cf estimates and DIC cf was calculated from estimates of carbonate ion concentrations using the following equations described in [START_REF] Mcculloch | Coral calcification in a changing World and the interactive dynamics of pH and DIC upregulation[END_REF]:

CO ! !! !" = K ! B OH ! ! !" B Ca !"!" ! (2)
Where

K D = K D.0 exp(-k KD [H + ] T ) with = 2.97 ± 0.17×10 -3 ( ± 95% CI),
= 0.0202 ± 0.042. The concentration of DIC cf was then calculated from estimates of pH cf and [CO 3 2-] cf .

[Ca 2+ ] cf was calculated as:

Ca !! !" = Ω !" * ! !" CO ! !! !" (1)
where [CO ! !! ] cf and Ω Ar are derived from boron systematics and Raman spectroscopy (see below), respectively [START_REF] Decarlo | Coral calcifying fluid aragonite saturation states derived from Raman spectroscopy[END_REF]. Ca !" !! Ca !" !! ratios were calculated by normalizing to [Ca 2+ ] sw , which was estimated from salinity as 10.58 mmol kg -1 .

Raman spectroscopy

We utilized confocal Raman spectroscopy to determine sample mineralogy and as a proxy of calcifying fluid Ω. Measurements were conducted on a WITec Alpha300RA+ using a 785 nm infrared laser following [START_REF] Decarlo | Coral calcifying fluid aragonite saturation states derived from Raman spectroscopy[END_REF]. The instrument is configured with a 1200 mm -1 grating that gives a spectral resolution of approximately 1.3 cm -1 and we used a 20x objective with 0.5 numerical aperture.

Repeated analyses of a silicon chip for wavenumber calibration showed the primary Si peak located at ~522.9 cm -1 . Skeleton samples were placed on glass slides (powders for corals, and cut sections for CCA) and topography maps were made with the TrueSurface module. The automated stage followed the topography while conducting Raman measurements so that the optics were always in focus on the sample surfaces. For corals, 36 spectra were collected per sample in a 300 µm by 300 µm grid using 1 s integrations, whereas for CCA 100 spectra were collected in a 1 mm by 1 mm grid using 2 s integrations. Spectra with poor signal (< 100 intensity units) or contaminated by cosmic rays were excluded.

Sample mineralogy was determined by ( 1) the presence of a v 1 peak at ~1085-1090 cm -1 indicative of CaCO 3 , and (2) the shape of the v 4 peak between 700-720 cm -1 where a double peak < 710 cm -1 is found in aragonite and a single peak > 710

D,0 K D K k
cm -1 is found in calcite [START_REF] Kamenos | Coralline algae in a naturally acidified ecosystem persist by maintaining control of skeletal mineralogy and size[END_REF][START_REF] Urmos | Characterization of some biogenic carbonates with Raman spectroscopy[END_REF]. Identifying mineralogy is key for CCA because aragonite and/or gypsum has been found in their skeletons under naturally low-pH conditions [START_REF] Kamenos | Coralline algae in a naturally acidified ecosystem persist by maintaining control of skeletal mineralogy and size[END_REF] and mixtures of high-Mg calcite with these other mineral phases would complicate the interpretations of boron systematics. We found only aragonite in our coral samples and only high-Mg calcite in our CCA samples, confirming the mineralogy expected for each species (Figure S2). [START_REF] Pauly | Coralline algal Mg-O bond strength as a marine pCO2 proxy[END_REF]. The abiogenic calibrations of [START_REF] Perrin | Raman characterization of synthetic magnesian calcites[END_REF] were used to first estimate [Mg] from v 1 wavenumber (following corrections based on comparing our Si chip wavenumber measurements to those reported by [START_REF] Perrin | Raman characterization of synthetic magnesian calcites[END_REF], and then to account for the effect of [Mg] on v 1 FWHM. We consider the residual v 1 FWHM a proxy measure of calcifying fluid Ω.

Statistical analysis

The assumptions of normality and equality of variance were evaluated through graphical analyses of residuals using the R software. Treatment effects were determined using one-way ANOVAs. The effect of seawater pH, DIC and saturation sates of aragonite or calcite (for corals and CCA respectively) on calcification, photosynthesis, pH cf , DIC cf , and Ω a were examined using linear models when possible. Proportions of the variation (R 2 ) explained by pH, DIC and saturation sates of aragonite or calcite were calculated using multiple linear regressions and the R package relaimpo. All statistical analysis were done with R.

Results

Our results show that only the calcification rates of A. yongei were affected by our treatments (Table S2), where calcification decreased as seawater pH declined (Figure 2, Table S3). In the three treatments where Ω was held constant, calcification was similar in the Low DIC -High pH and the Ambient treatment and lower in the High DIC -Low pH treatment. Calcification of P. damicornis, S. durum and Neogoniolithon sp. was not significantly affected by any parameter of the seawater chemistry over the ranges we tested (Figure 2, Table S2 andS3).

Our treatments had a greater impact on calcifying fluid chemistry (Figure 3).

pH cf , estimated from δ 11 B, declined significantly with both decreasing seawater pH and increasing seawater DIC for three of four species (Figure 4; Table S3; both corals and S. durum). Ω of seawater did not affect pH cf in any species. In the treatment with similar Ω, pH cf was mostly driven by seawater pH (highest pH cf in the high seawater pH).

We utilized aragonite-specific proxies to quantify the calcifying fluid DIC (DIC cf ) of the two coral species. DIC cf derived from B/Ca and δ 11 B [START_REF] Holcomb | Factors affecting B/Ca ratios in synthetic aragonite[END_REF][START_REF] Mcculloch | Coral calcification in a changing World and the interactive dynamics of pH and DIC upregulation[END_REF] of both coral species was significantly positively correlated with increasing DIC and decreasing pH in seawater (Figure 5a, Table S3). Seawater Ω did not influenced DIC cf in A. yongei. In the three treatments with similar Ω, DIC cf was the highest (and B/Ca the lowest for CCA) in the treatment with elevated DIC.

Calcifying fluid Ω a derived from peak widths in Raman spectra [START_REF] Decarlo | Coral calcifying fluid aragonite saturation states derived from Raman spectroscopy[END_REF] did not significantly change in response to seawater pH or DIC for either coral species (Figure 6). It marginally decreased with seawater Ω for P. damicornis.

While there are no published data of B/Ca or Raman spectroscopy for abiogenic high-Mg calcites, both have been interpreted as carbonate system proxies in CCA [START_REF] Donald | Boron isotope sensitivity to seawater pH change in a species of Neogoniolithon coralline red alga[END_REF][START_REF] Kamenos | Coralline algal structure is more sensitive to rate, rather than the magnitude, of ocean acidification[END_REF]. We interpret B/Ca and Raman spectra as indicative of calcifying fluid DIC and calcite saturation state (Ω Cal cf ) respectively (Figure 6) based on their systematics in aragonite. However, without the abiogenic high-Mg calcite calibrations, we quantify the response of B/Ca and Raman peak width directly, rather than converting them to carbonate system parameters as we can for the aragonitic corals. We therefore assume that there is both an inverse relationship between B/Ca and DIC cf , and a positive relationship between FWHM and mineral-specific saturation state in the calcifying fluid, as is the case in aragonite precipitating from seawater-like solutions [START_REF] Holcomb | Factors affecting B/Ca ratios in synthetic aragonite[END_REF][START_REF] Decarlo | Coral calcifying fluid aragonite saturation states derived from Raman spectroscopy[END_REF]. B/Ca of S. durum declined significantly (indicating a potential increase in DIC cf ) as seawater pH decreased and as seawater DIC increased (Figure 5; Table S3).

B/Ca was lowest in S. durum in the High DIC -Low pH treatment, and highest in the Low DIC -High pH treatment (though the latter was not statistically different). This was the opposite trend of the pH cf . Ω of seawater did not affect B/Ca of any species.

Raman peak width significantly increased with seawater DIC for Neogoniolithon sp., but did not change with seawater treatments for S. durum (Figure 6).

We utilized Ω cf and [CO 3 2-] cf estimates to calculate [Ca 2+ ] cf in the two coral species. There was a treatment effect on [Ca 2+ ] cf of P. damicornis (Table S2, Fig. S1),

while [Ca 2+ ] cf of A. yongei was not affected. In P. damicornis [Ca 2+ ] cf was significantly elevated in the High DIC -Low pH treatment compared to most others.

Photosynthetic rates were only determined on the coral A. yongei and the coralline S. durum. Photosynthesis increased significantly with increasing DIC and decreasing pH for A. yongei (Fig. S2, Table S2). There was no relationship between photosynthesis and Ω for of A. yongei. Photosynthesis of S. durum was not affected by the treatments (Table S2) and was not correlated to any parameter of the carbonate chemistry (Fig. S2).

Discussion

Here we demonstrate that two coral and two coralline algal species have the ability to control their calcification physiology under a large range of carbonate chemistry conditions that extend well beyond their natural range. Even when calcifying fluid carbonate chemistry was altered by our treatments, this only translated to shifts in calcification rates for one of the four species. Seawater pH and DIC were the primary drivers of changes in calcifying fluid chemistry, not the saturation state of seawater. Our findings were highly similar for corals and coralline algae and can be summarized into two pathways via which the calcifying fluid is impacted by seawater carbonate chemistry: 1) Seawater pH is the primary driver of changes in pH cf ; 2) seawater DIC is the primary driver of DIC cf and can also influence pH cf . Conversely, our Raman spectroscopy analyses indicate that three of the four species maintain a constant saturation state irrespective of the external seawater conditions, apart from Neogonioltihon sp., which exhibited a slight sensitivity to seawater DIC. This supports the notion that calcifiers must achieve threshold levels of Ω cf for CaCO 3 precipitation, and suggests that both corals and CCA have the ability to manipulate their calcifying fluid chemistry to reach these species-specific Ω cf thresholds when assessed over longer time periods, such as here. Notably, these results provide a mechanistic understanding of the resilience to ocean acidification found during in situ studies on coralline algae [START_REF] Kamenos | Coralline algae in a naturally acidified ecosystem persist by maintaining control of skeletal mineralogy and size[END_REF] Past attempts to disentangle the effects of different carbonate system parameters on calcification processes have been hampered by a number of limitations.

The majority of the past studies that have aimed to separate the different parameters of the seawater carbonate chemistry are based on very short-term incubations where the organisms were exposed to the manipulated seawater only during the few hours necessary to perform the physiological measurements (Table S4). While those studies are valuable, they mainly provide information on shock responses of organisms not acclimated to the treatments. These treatments are often extremely different from seawater carbonate chemistry encountered previously by the organisms. The present study shows that organisms have a greater capacity over much longer time periods (8-13 weeks for corals and 21 weeks for CCA) to adjust the chemistry in their calcifying fluid and therefore maintain their calcification when exposed to a large range of conditions. This is especially demonstrated by the low correlation (R 2 ) between seawater carbonate chemistry and all the physiological parameters measured here.

However, such adjustments require the involvement of physiological mechanisms (gene expressions for carbonic anhydrase, H + /Ca 2+ transporters, etc. [START_REF] Zoccola | Bicarbonate transporters in corals point towards a key step in the evolution of cnidarian calcification[END_REF] that necessitate time to be expressed. Another limitation of past studies was that conditions in the calcifying fluid were unknown (or only known in the growing margin for pH cf [START_REF] Comeau | Coral calcifying fluid pH is modulated by seawater carbonate chemistry not solely seawater pH[END_REF] , which did not allow past research to clearly establish the mechanisms responsible, beyond more easily measurable calcification and photosynthetic rates. Here, we overcome this problem by determining the relevant chemistry in the calcifying fluid for numerous taxa, and show that seawater pH and DIC differentially affect conditions in the calcifying fluid.

The magnitude of the effects of seawater carbonate chemistry on the different metabolic processes (pH cf , DIC cf , Ω cf , photosynthesis and calcification) are speciesspecific, but the ability to achieve a threshold level of Ω cf to maintain constant calcification is relatively consistent across taxa. For example, calcification rates of P.

damicornis are known to be insensitive to low seawater pH (Comeau, Cornwall, & McCulloch, 2017), while Neogoniolithon sp. calcification and pH cf do not decline over larger ranges in seawater pH than examined here (i.e. to 7.64) [START_REF] Cornwall | Coralline algae elevate pH at the site of calcification under ocean acidification[END_REF]. This is in contrast to more dramatic declines in calcification under OA observed for A. yongei or S. durum, particularly when pH is much lower than employed here (Comeau, Cornwall, & McCulloch, 2017;Cornwall, Comeau, & McCulloch, 2017). This suite of responses to seawater pH were repeated again here.

However, while species-specific effects were observed, the general trends persisted across taxa. This indicates an evolutionary convergence of the calcification mechanisms of the two taxa (Scleractinian corals and Rhodophyte CCA), where organisms are able to control their pH cf , DIC cf , and Ca 2+ cf to achieve a certain Ω cf threshold necessary for calcification. For both taxa, organisms have developed the necessary physiological mechanisms (proton pumping, carbonic anhydrase, calcium pumping, etc.) to create internal conditions favorable for the mineralization process under a large range of external carbonate chemistry conditions. This is likely the result of the large past variations in oceanic carbonate chemistry conditions that these taxa evolved in. Over geological time, pH and DIC have been at levels even more extreme than that employed in our study [START_REF] Hönisch | The Geological Record of Ocean Acidification[END_REF].

It is not unexpected that pH and DIC in seawater are the main drivers of pH cf and DIC cf respectively. Declines in pH cf as seawater pH decreases are speciesspecific, and sometimes result in concomitant drops in calcification rates (Cornwall et al., 2017;[START_REF] Holcomb | Coral calcifying fluid pH dictates response to ocean acidification[END_REF][START_REF] Mcculloch | Coral resilience to ocean acidification and global warming through pH up-regulation[END_REF][START_REF] Venn | Impact of seawater acidification on pH at the tissue-skeleton interface and calcification in reef corals[END_REF]. The fact that P. damicornis did not decrease its calcification with declining pH cf supports past findings (Comeau, Cornwall, &McCulloch, 2017). Therefore, the fact that pH cf is often impacted by seawater pH should not be taken as explicit evidence for the DIC/H + hypothesis. This is because changes in pH cf do not always impact calcification rates. It is possible that declining seawater pH does not increase the energy required to export H + out of the calcifying fluid because pumping remains constant (M. [START_REF] Mcculloch | Coral resilience to ocean acidification and global warming through pH up-regulation[END_REF], and/or that other physiological mechanisms can counter declines in pH cf for some species (e.g. increases in Ca 2+ and DIC in the calcifying fluid). Additionally, the decrease in pH cf with increasing seawater DIC found here is partly contradictory to results measured by confocal microscopy on the coral S. pistillata [START_REF] Comeau | Coral calcifying fluid pH is modulated by seawater carbonate chemistry not solely seawater pH[END_REF]. It is possible that this is due to differences in treatments employed here, as the response to low DIC at ambient pH was similar between studies. Another possibility is that the duration we used was sufficiently long to rule out shock responses that may have occurred in shorter term experiments (Table S4), or that the effects observed previously were species-specific.

When we compare the three treatments with constant pH, seawater DIC had a positive effect on S. durum and A. yongei calcification. A similar effect was observed in other species (corals Porites rus, Stylophora pistilata and Madracis auretenra, and the CCA Porolithon onkodes) which increased calcification under elevated DIC when pH was kept constant [START_REF] Comeau | Coral calcifying fluid pH is modulated by seawater carbonate chemistry not solely seawater pH[END_REF][START_REF] Comeau | Coral reef calcifiers buffer their response to ocean acidification using both bicarbonate and carbonate[END_REF][START_REF] Jury | Effects of variations in carbonate chemistry on the calcification rates of Madracis auretenra (= Madracis mirabilis sensu Wells, 1973): bicarbonate concentrations best predict calcification rates[END_REF][START_REF] Marubini | Coral calcification responds to seawater acidification: a working hypothesis towards a physiological mechanism[END_REF]. However, here seawater DIC did not significantly affect calcification rates of CCA or corals when all the treatments were considered because of the larger effects of pH. While seawater DIC did not have a linear effect on calcification rates, we still consider it could be important in some circumstances.

The elevation of DIC cf compared to seawater, and increases in DIC cf with seawater DIC, indicates that corals actively concentrate DIC in the calcifying fluid, but that this process is influenced by seawater [DIC]. Increasing DIC cf could result from additional external DIC transported with seawater to the site of calcification [START_REF] Gagnon | Seawater transport during coral biomineralization[END_REF], or from an increase of the active transport of bicarbonate using specific transporters [START_REF] Zoccola | Bicarbonate transporters in corals point towards a key step in the evolution of cnidarian calcification[END_REF]. Additional DIC cf could also be the result of increasing photosynthetic activity with seawater DIC measured in A. yongei.

Increasing photosynthetic rates and metabolic activity could be associated with an increase in light respiration rates that would favor the transport of respiratory CO 2 to the site of calcification. The control of seawater DIC observed in coral DIC cf were mirrored in the CCA B/Ca, likely indicative of consistent DIC cf responses among corals and CCA.

In conclusion, we propose an alternate explanation to both the Ω and DIC/H + . Characteristic Raman spectra of coral and CCA analyzed in this study. The peaks in the region of ~700-720 cm -1 can be used to distinguish calcite and aragonite. Aragonite (blue) has a double peak < 710 cm -1 whereas high-Mg calcite (red) has a single broad peak > 710 cm -1 .

[

  H + ], 2) of pH at constant[DIC], and 3) of changes in both [DIC] and pH at constant Ω. These treatments allowed us to isolate the effects of Ω from both[DIC] and [H + ] on calcification rates and calcifying fluid chemistry. We purposely selected treatments that were not extreme, and within the ranges of past and realistic future seawater Ω expected over the next 100 years. The effects of these treatments on the chemistry at the site of calcification were assessed using newly developed suite of skeletal proxies of the carbonate chemistry of the calcifying fluid (δ 11 B, B/Ca, and FWHM measured by Raman spectroscopy).

(

  CRM) provided by A.G. Dickson (batch 151) yielded A T values within 3 µmol kg -1

Fig. 1 .

 1 Figures LegendFig. 1. The two corals (Acropora yongei and Pocillopora damicornis) and the two crustose coralline algae (Neogoniolithon sp. and Sporolithon durum) were incubated under five seawater treatments obtained by manipulating pH T and the dissolved inorganic carbon concentration [DIC]. Here we employ treatments with similar DIC and different pH and Ω, similar pH with different DIC and Ω, and similar Ω with different pH and DIC. These treatment combinations allow us to separate out the effects of seawater DIC, pH and Ω, without the need for additional treatments. The shade of greys represents the seawater aragonite saturation state.

Fig. 2 .

 2 Fig. 2. Effects of seawater DIC, pH T and saturation state on the surface areanormalized net calcification of the tested organisms. The first row shows calcification for the coral Acropora yongei (circles) and Pocillopora damicornis (squares). The second row shows calcification for the coralline algae Neogoniolithon sp. (triangles) and Sporolithon durum (diamonds). The colors represent the different treatments: Low DIC-High pH (dark green), Low DIC-Ambient pH (light green), Ambient (blue), High DIC-Low pH (orange), and High DIC -Ambient pH (red). See Fig. 1 for treatment seawater carbonate chemistry. The dotted line represents the linear relationship with a significant slope p-value.

Fig. 3 .

 3 Fig. 3. Proportions of the variation (R 2 ) of the estimated variables explained by seawater DIC (green), pH (red) and saturation state (blue) in multiple linear regressions on calcification, pH in the calcifying fluid (pH cf ), dissolved inorganic carbon in the calcifying fluid (DIC cf ), aragonite saturation state in the calcifying fluid (Ω cf ), and a proxy for calcite saturation state in the calcifying fluid (FWHM). The photos show the organisms used during the experiment.

Fig. 4 .Fig. 5 .

 45 Fig. 4. Estimates of pH in the calcifying fluid (pH cf ) obtained using δ 11 B. The first row shows pH cf determined on the coral Acropora yongei (circles) and Pocillopora damicornis (squares) as a function of seawater DIC, pH and aragonite saturation state. The second row shows pH cf determined on the crustose coralline algae Neogoniolithon sp. (triangles) and Sporolithon durum (diamonds). The colors represent the different treatments: Low DIC-High pH (dark green), Low DIC-

Fig. 6 .

 6 Fig. 6. Estimates of corals calcifying fluid Ω ar and coralline algae FWHM (indicating the calcifying fluid Ω cal ) obtained using Raman spectroscopy. Measurements were done on the coral Acropora yongei (circles) and Pocillopora damicornis (squares) and the crustose coralline algae Neogoniolithon sp. (triangles) and Sporolithon durum (diamonds). The colors represent the different treatments: Low DIC-High pH (dark green), Low DIC-Ambient pH (light green), Ambient (blue), High DIC-Low pH (orange), and High DIC -Ambient pH (red).

Fig. S2 .

 S2 Fig. S2. Photosynthetic rates (mean ± SE, n = 6) of the coral Acropora yongei and the coralline alga Sporolithon durum exposed to the five seawater treatments. The colors represent the different treatments: Low DIC-High pH (dark green), Low DIC-Ambient pH (light green), Ambient (blue), High DIC-Low pH (orange), and High DIC -Ambient pH (red).A. youngei

  The two CCA species were grown throughout both phases of the experiment, because their calcification rates are much slower than the coral, hence taking a longer period of time to grow the carbonate material needed for further geochemical analyses mentioned below. The experiment was carried out in the Indian Ocean Marine Research Centre at

Watermans Bay, Western Australia, Australia. Organisms were collected 7 to 15 d prior to the beginning of the experiment from Salmon Bay, Rottnest Island, Western Australia, at ~ 1-2-m depth. After collection, the branches (~5 cm) were glued to plastic bases (4 x 4 cm) with Z-Spar (A788 epoxy) to facilitate handling of the nubbins without contact with the tissues.

  The widths of the v 1 peaks were used as proxy measures of calcifying fluid Ω[START_REF] Decarlo | Coral calcifying fluid aragonite saturation states derived from Raman spectroscopy[END_REF]. CaCO 3 minerals precipitating from more supersaturated solutions incorporate more impurities and are more disordered, which causes Raman

peak broadening due to greater distributions of C-O bond lengths

[START_REF] Decarlo | Coral calcifying fluid aragonite saturation states derived from Raman spectroscopy[END_REF]

. We used the abiogenic aragonite calibration equation of

[START_REF] Decarlo | Coral calcifying fluid aragonite saturation states derived from Raman spectroscopy[END_REF]

to calculate Ω a for the two coral species from the v 1 full width at half maximum intensity (FWHM). Although v 1 peak width has been applied to investigate CCA responses to ocean acidification in several studies

[START_REF] Kamenos | Coralline algae in a naturally acidified ecosystem persist by maintaining control of skeletal mineralogy and size[END_REF][START_REF] Kamenos | Coralline algal structure is more sensitive to rate, rather than the magnitude, of ocean acidification[END_REF]

, there is no abiogenic high-Mg calcite Ω calibration. We therefore used v 1 FWHM as a qualitative proxy of CCA calcifying fluid Ω. However, the high concentrations of Mg in CCA are known to broaden the Raman peaks independent of Ω, meaning that standardization to [Mg] is required when comparing v 1 FWHM among high-Mg calcite samples

[START_REF] Decarlo | Coral calcifying fluid aragonite saturation states derived from Raman spectroscopy[END_REF]

,

(Pauly, Kamenos, Donohue,

  [START_REF] Decarlo | Coral resistance to ocean acidification linked to increased calcium at the site of calcification[END_REF]. These results also suggest that the correlation between seawater saturation state and calcification measured during [Ca 2+ ] manipulations could have been the result of changes in[Ca 2+ ] cf caused by differences in seawater [Ca 2+ ] and not saturation state per se. However, further research is required to verify this.

	compared to [CO 3	2-] in the oceans, and unlike [CO 3	2-] will not be affected by OA. Our
	results also support the hypothesis that seawater [DIC]/[H + ] ratios, and its covariate
	Ω, are not the sole driver of calcification. This is demonstrated by the different
	calcification rates, pH cf , and DIC cf measured in the three treatments where seawater Ω
	([DIC]/[H + ] ratios) were similar but [DIC] and pH differed. Thus, while seawater pH
	and DIC independently control the conditions within the calcifying fluid of all four
	species examined here, only pH was found to be the dominant driver of calcification.
	Furthermore, we also found that [Ca 2+ ] cf was increased well above seawater [Ca 2+ ]

and corals

(Barkley et al. 2015(Barkley et al. , 2017) )

at naturally acidified sites.

Our results give support to some of the principles behind the [DIC]/[H + ] hypothesis. However, the idea that [DIC]/[H + ] ratios linearly drive calcification is also simplistic. This was also demonstrated in past

[Ca 2+

] manipulation experiments that yielded treatments with similar [DIC]/[H + ] ratios but different saturation states

[START_REF] Gattuso | Effect of calcium carbonate saturation of seawater on coral calcification[END_REF][START_REF] Marshall | Effect of increased calcium concentration in sea water on calcification and photosynthesis in the scleractinian coral Galaxea fascicularis[END_REF]

. Calcification decreased under low

[Ca 2+

] in these experiments despite

[DIC]/[H + ] ratios being at ambient levels. However, the role of calcium is complex because the decrease in calcification at lower [Ca 2+ ] (and therefore Ω) could result from the disruption of the numerous physiological pathways in which [Ca 2+ ] is involved. Furthermore, [Ca 2+ ] is significantly (at least ten-fold) more abundant only in P. damicornis in the treatment with the lowest pH cf . This result suggest that upregulation of

[Ca 2+

] cf in some coral species (and possibly CCA) could be a mechanism that enables constant Ω cf when pH cf decreases

(DeCarlo, Comeau,

Table 1 :

 1 Mean carbonate chemistry in the incubations tanks. Dissolved inorganic carbon (DIC), pCO 2 , and the saturation state of aragonite and calcite were calculated using measured pH T , total alkalinity (A T ), temperature, and a salinity of 35.2 (SE < 0.1).

	• A. yongei
	P. damicornis
	•	•	•
	•
			•

Table 2 .

 2 Summary of the ANOVA examining the effects of seawater treatments on the calcification, pH cf , DIC cf, (B/Ca for the coralline algae) and Ω cf (FWHM for the coralline algae). Post hoc results shows the significant differences between the treatments with L D H P = Low DIC-High pH, L D A P = Low DIC-Ambient pH, A = Ambient, H D L P = High DIC-Low pH, and H D A P = High DIC -Ambient pH.

	Species	Physiological parameter	dF	F	p-value	Post-hoc
	Acropora	Calcification	4,26 4.07	0.010 L D H P >H D L P
		pH cf	4,26 9.39	<0.001 L D H P = A >H D L P =
						H D A P
		DIC cf	4,26 13.75 <0.001 H D L P = H D A P > A=
						L D H P = L D A P
		Ω cf	4,26 1.094	0.380
		Ca cf	4,	1.946	0.134
			26
		Photosynthesis	4,26 6.473	0.001 H D L P > L D A P =
						L D H P
	Pocillopora	Calcification	4,22 0.449	0.772
		pH cf	4,22 33.88 <0.001 L D H P > L D A P = A =
						H D A P > H D L P
		DIC cf	4,22 8.69	<0.001 H D A P = H D L P > A =
						L D H P = L D A P
		Ω cf	4,25 1.83	0.154
		Ca cf	4,	6.172	0.002 H D L P > A = H D A P =
			22			L D H P
	Neogoniolithon Calcification	4,17 0.443	0.776
		pH cf	4,10 3.329	0.056
		B/Ca	4,10 3.609	0.045 H D L P >A
		FWHM	4,8	1.433	0.307
	Sporolithon	Calcification	4,19 1.276	0.312
		pH cf	4,20 6.315 0.002	L D H P > A = H D A P =
						L D H P = L D A P
		B/Ca	4,20 2.039	0.129
		FWHM	4,20 0.147	0.962
		Photosynthesis	4,15 1.003	0.436

Table 3 .

 3 Linear regressions with p-value of the slopes < 0.05. P values < 0.017 bolded based on Bonferroni corrections. Only parameters that describe more than 10 % of the variability are listed

	Species	Physiological	Seawa	Equation	Slope p-	R 2
		parameter	ter		value
			param
			eter
	Acropora	Calcification	pH	Y= -12.7 +1.77 x 0.008	0.21
		pH cf	Ω arag DIC	Y = 1.24 + 0.08 x 0.034 5 x Y = 8.68 -5.91 10 -<0.001	0.14 0.40
			pH	Y = 6.0 + 0.32 x	<0.001	0.33
			Ω arag	Y = 8.65 -0.04 x	0.05	0.12
		DIC cf	DIC	Y = 2461 + 0.38 x <0.001	0.61
			pH	Y = 15846 -1565	0.002	0.29
				x
		Photosynthesis	DIC	Y = 12.0 + 0.01 x 0.002	0.28
			pH	Y = 492.4 -57.6 x <0.001	0.32
	Pocillopora	pH cf	DIC	8.62 -4.3 x	<0.001	0.45
			pH	Y = 5.87 +0.33 x <0.001	0.73
		DIC cf	DIC	2687 + 0.23 x	<0.001	0.5
			pH	12894 -1211 x	<0.001	0.37
			Ω arag	2777 + 148 x	0.044	0.15
		Ω cf	Ω arag	Y = 13.19-0.27 x 0.034	0.15
	Sporolithon	pH cf	DIC	8.90 -6.57 10-5 x 0.003	0.32
			pH	4.92 + 0.48 x	<0.001	0.53
		B/Ca	DIC	463 -0.02 x	0.017	0.23
			pH	-640 + 132 x	0.010	0.27
	Neogoniolithon FWHM	DIC	-1.90 + 2.13 x	0.024	0.38

B Moore, A-M Comeau-Nisumaa and V Schoepf provided vital laboratory support. MTM was supported by an ARC Laureate Fellowship (LF120100049), S. C. was supported by an ARC DECRA (DE160100668). The authors acknowledge the facilities, and the scientific and technical assistance of the Australian Microscopy & Microanalysis Research Facility at the Centre for Microscopy, Characterisation & Analysis, The University of Western Australia, a facility funded by the University, State and Commonwealth Governments.

Author contributions

SC, CEC, and MTM designed the research. SC and CEC wrote the paper.

TMD and MTM edited the paper. SC, CEC and EK ran the experiment. SC, CEC, and TMD performed geochemical and statistical analysis. 4. Summary of the studies that have manipulated the carbonate chemistry to isolate the effect of species of the carbonate system on the physiology of corals and coralline algae.

Supplementary Table

Study

Species Time in the treatment

Main driver

Physiological parameter

Manipulation