circom/c/buildasm/montgomery.asm.ejs

<%
//////////////////////
// montgomeryTemplate
//////////////////////
// This function creates functions with the montgomery transformation
// applied
// the round hook allows to add diferent code in the iteration
//
//  All the montgomery functions modifies:
//  r8, r9, 10, r11, rax, rcx
//////////////////////
function montgomeryTemplate(fnName, round) {
    let r0, r1, r2;
    function setR(step) {
        if ((step % 3) == 0) {
            r0 = "r8";
            r1 = "r9";
            r2 = "r10";
        } else if ((step % 3) == 1) {
            r0 = "r9";
            r1 = "r10";
            r2 = "r8";
        } else {
            r0 = "r10";
            r1 = "r8";
            r2 = "r9";
        }
    }

    const base = bigInt.one.shiftLeft(64);
    const np64 = base.minus(q.modInv(base));
%>
<%=fnName%>:
        sub     rsp, <%= n64*8 %>  ; Reserve space for ms
        mov     rcx, rdx            ; rdx is needed for multiplications so keep it in cx
        mov     r11, 0x<%= np64.toString(16) %> ; np
        xor     r8,r8
        xor     r9,r9
        xor     r10,r10
<%
    // Main loop
    for (let i=0; i<n64*2; i++) {
        setR(i);
        round(i, r0, r1, r2);
%>

<%
        for (let j=i-1; j>=0; j--) { // All ms
            if (((i-j)<n64)&&(j<n64)) {
%>
        mov     rax, [rsp + <%= j*8 %>]
        mul     qword [q + <%= (i-j)*8 %>]
        add     <%= r0 %>, rax
        adc     <%= r1 %>, rdx
        adc     <%= r2 %>, 0x0
<%
            }
        } // ms
%>

<%
        if (i<n64) {
%>
        mov     rax, <%= r0 %>
        mul     r11
        mov     [rsp + <%= i*8 %>], rax
        mul     qword [q]
        add     <%= r0 %>, rax
        adc     <%= r1 %>, rdx
        adc     <%= r2 %>, 0x0
<%
        } else {
%>
        mov     [rdi + <%= (i-n64)*8 %> ], <%= r0 %>
        xor     <%= r0 %>,<%= r0 %>
<%
        }
%>

<%
    }   // Main Loop
%>
        test    <%= r1 %>, <%= r1 %>
        jnz     <%=fnName%>_mulM_sq
        ; Compare with q
<%
    for (let i=0; i<n64; i++) {
%>
        mov rax, [rdi + <%= (n64-i-1)*8 %>]
        cmp rax, [q + <%= (n64-i-1)*8 %>]
        jc <%=fnName%>_mulM_done        ; q is bigget so done.
        jnz <%=fnName%>_mulM_sq         ; q is lower
<%
    }
%>
        ; If equal substract q

<%=fnName%>_mulM_sq:
<%
    for (let i=0; i<n64; i++) {
%>
        mov rax, [q + <%= i*8 %>]
        <%= i==0 ? "sub" : "sbb" %> [rdi + <%= i*8 %>], rax
<%
    }
%>

<%=fnName%>_mulM_done:
        mov rdx, rcx            ; recover rdx to its original place.
        add rsp, <%= n64*8 %>   ; recover rsp
        ret

<%
}   // Template
%>

;;;;;;;;;;;;;;;;;;;;;;
; rawMontgomeryMul
;;;;;;;;;;;;;;;;;;;;;;
; Multiply two elements in montgomery form
; Params:
;   rsi <= Pointer to the long data of element 1
;   rdx <= Pointer to the long data of element 2
;   rdi <= Pointer to the long data of result
; Modified registers:
;    r8, r9, 10, r11, rax, rcx
;;;;;;;;;;;;;;;;;;;;;;
<%
montgomeryTemplate("rawMontgomeryMul", function(i, r0, r1, r2) {
    // Same Digit
    for (let o1=Math.max(0, i-n64+1); (o1<=i)&&(o1<n64); o1++) {
    const o2= i-o1;
%>
        mov     rax, [rsi + <%= 8*o1 %>]
        mul     qword [rcx + <%= 8*o2 %>]
        add     <%= r0 %>, rax
        adc     <%= r1 %>, rdx
        adc     <%= r2 %>, 0x0
<%
    } // Same digit
})
%>

;;;;;;;;;;;;;;;;;;;;;;
; rawMontgomerySquare
;;;;;;;;;;;;;;;;;;;;;;
; Square an element
; Params:
;   rsi <= Pointer to the long data of element 1
;   rdi <= Pointer to the long data of result
; Modified registers:
;    r8, r9, 10, r11, rax, rcx
;;;;;;;;;;;;;;;;;;;;;;
<%
montgomeryTemplate("rawMontgomerySquare", function(i, r0, r1, r2) {
    // Same Digit
    for (let o1=Math.max(0, i-n64+1); (o1<((i+1)>>1) )&&(o1<n64); o1++) {
    const o2= i-o1;
%>
        mov     rax, [rsi + <%= 8*o1 %>]
        mul     qword [rsi + <%= 8*o2 %>]
        add     <%= r0 %>, rax
        adc     <%= r1 %>, rdx
        adc     <%= r2 %>, 0x0
        add     <%= r0 %>, rax
        adc     <%= r1 %>, rdx
        adc     <%= r2 %>, 0x0
<%
    } // Same digit
%>

<%  if (i%2 == 0) { %>
        mov     rax, [rsi + <%= 8*(i/2) %>]
        mul     rax
        add     <%= r0 %>, rax
        adc     <%= r1 %>, rdx
        adc     <%= r2 %>, 0x0
<%  } %>

<%
})
%>


;;;;;;;;;;;;;;;;;;;;;;
; rawMontgomeryMul1
;;;;;;;;;;;;;;;;;;;;;;
; Multiply two elements in montgomery form
; Params:
;   rsi <= Pointer to the long data of element 1
;   rdx <= second operand
;   rdi <= Pointer to the long data of result
; Modified registers:
;    r8, r9, 10, r11, rax, rcx
;;;;;;;;;;;;;;;;;;;;;;
<%
montgomeryTemplate("rawMontgomeryMul1", function(i, r0, r1, r2) {
    // Same Digit
    if (i<n64) {
%>
        mov     rax, [rsi + <%= 8*i %>]
        mul     rcx
        add     <%= r0 %>, rax
        adc     <%= r1 %>, rdx
        adc     <%= r2 %>, 0x0
<%
    } // Same digit
})
%>


;;;;;;;;;;;;;;;;;;;;;;
; rawFromMontgomery
;;;;;;;;;;;;;;;;;;;;;;
; Multiply two elements in montgomery form
; Params:
;   rsi <= Pointer to the long data of element 1
;   rdi <= Pointer to the long data of result
; Modified registers:
;    r8, r9, 10, r11, rax, rcx
;;;;;;;;;;;;;;;;;;;;;;
<%
montgomeryTemplate("rawFromMontgomery", function(i, r0, r1, r2) {
    // Same Digit
    if (i<n64) {
%>
        add     <%= r0 %>, [rdi + <%= 8*i %>]
        adc     <%= r1 %>, 0x0
        adc     <%= r2 %>, 0x0
<%
    } // Same digit
})
%>

;;;;;;;;;;;;;;;;;;;;;;
; toMontgomery
;;;;;;;;;;;;;;;;;;;;;;
; Convert a number to Montgomery
;   rdi <= Pointer element to convert
; Modified registers:
;    r8, r9, 10, r11, rax, rcx
;;;;;;;;;;;;;;;;;;;;
<%=name%>_toMontgomery:
    mov     rax, [rdi]
    bts     rax, 62                     ; check if montgomery
    jc      toMontgomery_doNothing
    bts     rax, 63
    jc      toMontgomeryLong

toMontgomeryShort:
    mov     [rdi], rax
    add     rdi, 8
    push    rsi
    lea     rsi, [R2]
    movsx   rdx, eax
    cmp     rdx, 0
    js      negMontgomeryShort
posMontgomeryShort:
    call    rawMontgomeryMul1
    pop     rsi
    sub     rdi, 8
    ret

negMontgomeryShort:
    neg     rdx              ; Do the multiplication positive and then negate the result.
    call    rawMontgomeryMul1
    mov     rsi, rdi
    call    rawNegL
    pop     rsi
    sub     rdi, 8
    ret


toMontgomeryLong:
    mov     [rdi], rax
    add     rdi, 8
    push    rsi
    mov     rdx, rdi
    lea     rsi, [R2]
    call    rawMontgomeryMul
    pop     rsi
    sub     rdi, 8

toMontgomery_doNothing:
    ret

;;;;;;;;;;;;;;;;;;;;;;
; toNormal
;;;;;;;;;;;;;;;;;;;;;;
; Convert a number from Montgomery
;   rdi <= Pointer element to convert
; Modified registers:
;    r8, r9, 10, r11, rax, rcx
;;;;;;;;;;;;;;;;;;;;
<%=name%>_toNormal:
    mov     rax, [rdi]
    btc     rax, 62                     ; check if montgomery
    jnc     toNormal_doNothing
    bt      rax, 63                     ; if short, it means it's converted
    jnc     toNormal_doNothing

toNormalLong:
    mov     [rdi], rax
    add     rdi, 8
    call    rawFromMontgomery
    sub     rdi, 8

toNormal_doNothing:
    ret

;;;;;;;;;;;;;;;;;;;;;;
; toLongNormal
;;;;;;;;;;;;;;;;;;;;;;
; Convert a number to long normal
;   rdi <= Pointer element to convert
; Modified registers:
;    r8, r9, 10, r11, rax, rcx
;;;;;;;;;;;;;;;;;;;;
<%=name%>_toLongNormal:
    mov     rax, [rdi]
    bt      rax, 62                     ; check if montgomery
    jc      toLongNormal_fromMontgomery
    bt      rax, 63                     ; check if long
    jnc     toLongNormal_fromShort
    ret                                 ; It is already long

toLongNormal_fromMontgomery:
    add     rdi, 8
    call    rawFromMontgomery
    sub     rdi, 8
    ret

toLongNormal_fromShort:
    mov     r8, rsi                     ; save rsi
    movsx   rsi, eax
    call    rawCopyS2L
    mov     rsi, r8                     ; recover rsi