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#ifdef __GNUC__
#if defined(__x86_64__) || defined(_M_X64)
#pragma once
#include <inttypes.h>
// Computes the addition of four-element f1 with value in f2
// and returns the carry (if any)
static inline void
add_scalar(uint64_t *out, uint64_t *f1, uint64_t f2)
{
__asm__ volatile(
// Clear registers to propagate the carry bit
" xor %%r8d, %%r8d;"
" xor %%r9d, %%r9d;"
" xor %%r10d, %%r10d;"
" xor %%r11d, %%r11d;"
" xor %%eax, %%eax;"
// Begin addition chain
" addq 0(%2), %0;"
" movq %0, 0(%1);"
" adcxq 8(%2), %%r8;"
" movq %%r8, 8(%1);"
" adcxq 16(%2), %%r9;"
" movq %%r9, 16(%1);"
" adcxq 24(%2), %%r10;"
" movq %%r10, 24(%1);"
// Return the carry bit in a register
" adcx %%r11, %%rax;"
: "+&r"(f2)
: "r"(out), "r"(f1)
: "%rax", "%r8", "%r9", "%r10", "%r11", "memory", "cc");
}
// Computes the field addition of two field elements
static inline void
fadd(uint64_t *out, uint64_t *f1, uint64_t *f2)
{
__asm__ volatile(
// Compute the raw addition of f1 + f2
" movq 0(%0), %%r8;"
" addq 0(%2), %%r8;"
" movq 8(%0), %%r9;"
" adcxq 8(%2), %%r9;"
" movq 16(%0), %%r10;"
" adcxq 16(%2), %%r10;"
" movq 24(%0), %%r11;"
" adcxq 24(%2), %%r11;"
/////// Wrap the result back into the field //////
// Step 1: Compute carry*38
" mov $0, %%rax;"
" mov $38, %0;"
" cmovc %0, %%rax;"
// Step 2: Add carry*38 to the original sum
" xor %%ecx, %%ecx;"
" add %%rax, %%r8;"
" adcx %%rcx, %%r9;"
" movq %%r9, 8(%1);"
" adcx %%rcx, %%r10;"
" movq %%r10, 16(%1);"
" adcx %%rcx, %%r11;"
" movq %%r11, 24(%1);"
// Step 3: Fold the carry bit back in; guaranteed not to carry at this point
" mov $0, %%rax;"
" cmovc %0, %%rax;"
" add %%rax, %%r8;"
" movq %%r8, 0(%1);"
: "+&r"(f2)
: "r"(out), "r"(f1)
: "%rax", "%rcx", "%r8", "%r9", "%r10", "%r11", "memory", "cc");
}
// Computes the field substraction of two field elements
static inline void
fsub(uint64_t *out, uint64_t *f1, uint64_t *f2)
{
__asm__ volatile(
// Compute the raw substraction of f1-f2
" movq 0(%1), %%r8;"
" subq 0(%2), %%r8;"
" movq 8(%1), %%r9;"
" sbbq 8(%2), %%r9;"
" movq 16(%1), %%r10;"
" sbbq 16(%2), %%r10;"
" movq 24(%1), %%r11;"
" sbbq 24(%2), %%r11;"
/////// Wrap the result back into the field //////
// Step 1: Compute carry*38
" mov $0, %%rax;"
" mov $38, %%rcx;"
" cmovc %%rcx, %%rax;"
// Step 2: Substract carry*38 from the original difference
" sub %%rax, %%r8;"
" sbb $0, %%r9;"
" sbb $0, %%r10;"
" sbb $0, %%r11;"
// Step 3: Fold the carry bit back in; guaranteed not to carry at this point
" mov $0, %%rax;"
" cmovc %%rcx, %%rax;"
" sub %%rax, %%r8;"
// Store the result
" movq %%r8, 0(%0);"
" movq %%r9, 8(%0);"
" movq %%r10, 16(%0);"
" movq %%r11, 24(%0);"
:
: "r"(out), "r"(f1), "r"(f2)
: "%rax", "%rcx", "%r8", "%r9", "%r10", "%r11", "memory", "cc");
}
// Computes a field multiplication: out <- f1 * f2
// Uses the 8-element buffer tmp for intermediate results
static inline void
fmul(uint64_t *out, uint64_t *f1, uint64_t *f2, uint64_t *tmp)
{
__asm__ volatile(
/////// Compute the raw multiplication: tmp <- src1 * src2 //////
// Compute src1[0] * src2
" movq 0(%0), %%rdx;"
" mulxq 0(%1), %%r8, %%r9;"
" xor %%r10d, %%r10d;"
" movq %%r8, 0(%2);"
" mulxq 8(%1), %%r10, %%r11;"
" adox %%r9, %%r10;"
" movq %%r10, 8(%2);"
" mulxq 16(%1), %%rbx, %%r13;"
" adox %%r11, %%rbx;"
" mulxq 24(%1), %%r14, %%rdx;"
" adox %%r13, %%r14;"
" mov $0, %%rax;"
" adox %%rdx, %%rax;"
// Compute src1[1] * src2
" movq 8(%0), %%rdx;"
" mulxq 0(%1), %%r8, %%r9;"
" xor %%r10d, %%r10d;"
" adcxq 8(%2), %%r8;"
" movq %%r8, 8(%2);"
" mulxq 8(%1), %%r10, %%r11;"
" adox %%r9, %%r10;"
" adcx %%rbx, %%r10;"
" movq %%r10, 16(%2);"
" mulxq 16(%1), %%rbx, %%r13;"
" adox %%r11, %%rbx;"
" adcx %%r14, %%rbx;"
" mov $0, %%r8;"
" mulxq 24(%1), %%r14, %%rdx;"
" adox %%r13, %%r14;"
" adcx %%rax, %%r14;"
" mov $0, %%rax;"
" adox %%rdx, %%rax;"
" adcx %%r8, %%rax;"
// Compute src1[2] * src2
" movq 16(%0), %%rdx;"
" mulxq 0(%1), %%r8, %%r9;"
" xor %%r10d, %%r10d;"
" adcxq 16(%2), %%r8;"
" movq %%r8, 16(%2);"
" mulxq 8(%1), %%r10, %%r11;"
" adox %%r9, %%r10;"
" adcx %%rbx, %%r10;"
" movq %%r10, 24(%2);"
" mulxq 16(%1), %%rbx, %%r13;"
" adox %%r11, %%rbx;"
" adcx %%r14, %%rbx;"
" mov $0, %%r8;"
" mulxq 24(%1), %%r14, %%rdx;"
" adox %%r13, %%r14;"
" adcx %%rax, %%r14;"
" mov $0, %%rax;"
" adox %%rdx, %%rax;"
" adcx %%r8, %%rax;"
// Compute src1[3] * src2
" movq 24(%0), %%rdx;"
" mulxq 0(%1), %%r8, %%r9;"
" xor %%r10d, %%r10d;"
" adcxq 24(%2), %%r8;"
" movq %%r8, 24(%2);"
" mulxq 8(%1), %%r10, %%r11;"
" adox %%r9, %%r10;"
" adcx %%rbx, %%r10;"
" movq %%r10, 32(%2);"
" mulxq 16(%1), %%rbx, %%r13;"
" adox %%r11, %%rbx;"
" adcx %%r14, %%rbx;"
" movq %%rbx, 40(%2);"
" mov $0, %%r8;"
" mulxq 24(%1), %%r14, %%rdx;"
" adox %%r13, %%r14;"
" adcx %%rax, %%r14;"
" movq %%r14, 48(%2);"
" mov $0, %%rax;"
" adox %%rdx, %%rax;"
" adcx %%r8, %%rax;"
" movq %%rax, 56(%2);"
// Line up pointers
" mov %2, %0;"
" mov %3, %2;"
/////// Wrap the result back into the field //////
// Step 1: Compute dst + carry == tmp_hi * 38 + tmp_lo
" mov $38, %%rdx;"
" mulxq 32(%0), %%r8, %%r13;"
" xor %k1, %k1;"
" adoxq 0(%0), %%r8;"
" mulxq 40(%0), %%r9, %%rbx;"
" adcx %%r13, %%r9;"
" adoxq 8(%0), %%r9;"
" mulxq 48(%0), %%r10, %%r13;"
" adcx %%rbx, %%r10;"
" adoxq 16(%0), %%r10;"
" mulxq 56(%0), %%r11, %%rax;"
" adcx %%r13, %%r11;"
" adoxq 24(%0), %%r11;"
" adcx %1, %%rax;"
" adox %1, %%rax;"
" imul %%rdx, %%rax;"
// Step 2: Fold the carry back into dst
" add %%rax, %%r8;"
" adcx %1, %%r9;"
" movq %%r9, 8(%2);"
" adcx %1, %%r10;"
" movq %%r10, 16(%2);"
" adcx %1, %%r11;"
" movq %%r11, 24(%2);"
// Step 3: Fold the carry bit back in; guaranteed not to carry at this point
" mov $0, %%rax;"
" cmovc %%rdx, %%rax;"
" add %%rax, %%r8;"
" movq %%r8, 0(%2);"
: "+&r"(f1), "+&r"(f2), "+&r"(tmp)
: "r"(out)
: "%rax", "%rbx", "%rdx", "%r8", "%r9", "%r10", "%r11", "%r13", "%r14", "memory", "cc");
}
// Computes two field multiplications:
// out[0] <- f1[0] * f2[0]
// out[1] <- f1[1] * f2[1]
// Uses the 16-element buffer tmp for intermediate results:
static inline void
fmul2(uint64_t *out, uint64_t *f1, uint64_t *f2, uint64_t *tmp)
{
__asm__ volatile(
/////// Compute the raw multiplication tmp[0] <- f1[0] * f2[0] //////
// Compute src1[0] * src2
" movq 0(%0), %%rdx;"
" mulxq 0(%1), %%r8, %%r9;"
" xor %%r10d, %%r10d;"
" movq %%r8, 0(%2);"
" mulxq 8(%1), %%r10, %%r11;"
" adox %%r9, %%r10;"
" movq %%r10, 8(%2);"
" mulxq 16(%1), %%rbx, %%r13;"
" adox %%r11, %%rbx;"
" mulxq 24(%1), %%r14, %%rdx;"
" adox %%r13, %%r14;"
" mov $0, %%rax;"
" adox %%rdx, %%rax;"
// Compute src1[1] * src2
" movq 8(%0), %%rdx;"
" mulxq 0(%1), %%r8, %%r9;"
" xor %%r10d, %%r10d;"
" adcxq 8(%2), %%r8;"
" movq %%r8, 8(%2);"
" mulxq 8(%1), %%r10, %%r11;"
" adox %%r9, %%r10;"
" adcx %%rbx, %%r10;"
" movq %%r10, 16(%2);"
" mulxq 16(%1), %%rbx, %%r13;"
" adox %%r11, %%rbx;"
" adcx %%r14, %%rbx;"
" mov $0, %%r8;"
" mulxq 24(%1), %%r14, %%rdx;"
" adox %%r13, %%r14;"
" adcx %%rax, %%r14;"
" mov $0, %%rax;"
" adox %%rdx, %%rax;"
" adcx %%r8, %%rax;"
// Compute src1[2] * src2
" movq 16(%0), %%rdx;"
" mulxq 0(%1), %%r8, %%r9;"
" xor %%r10d, %%r10d;"
" adcxq 16(%2), %%r8;"
" movq %%r8, 16(%2);"
" mulxq 8(%1), %%r10, %%r11;"
" adox %%r9, %%r10;"
" adcx %%rbx, %%r10;"
" movq %%r10, 24(%2);"
" mulxq 16(%1), %%rbx, %%r13;"
" adox %%r11, %%rbx;"
" adcx %%r14, %%rbx;"
" mov $0, %%r8;"
" mulxq 24(%1), %%r14, %%rdx;"
" adox %%r13, %%r14;"
" adcx %%rax, %%r14;"
" mov $0, %%rax;"
" adox %%rdx, %%rax;"
" adcx %%r8, %%rax;"
// Compute src1[3] * src2
" movq 24(%0), %%rdx;"
" mulxq 0(%1), %%r8, %%r9;"
" xor %%r10d, %%r10d;"
" adcxq 24(%2), %%r8;"
" movq %%r8, 24(%2);"
" mulxq 8(%1), %%r10, %%r11;"
" adox %%r9, %%r10;"
" adcx %%rbx, %%r10;"
" movq %%r10, 32(%2);"
" mulxq 16(%1), %%rbx, %%r13;"
" adox %%r11, %%rbx;"
" adcx %%r14, %%rbx;"
" movq %%rbx, 40(%2);"
" mov $0, %%r8;"
" mulxq 24(%1), %%r14, %%rdx;"
" adox %%r13, %%r14;"
" adcx %%rax, %%r14;"
" movq %%r14, 48(%2);"
" mov $0, %%rax;"
" adox %%rdx, %%rax;"
" adcx %%r8, %%rax;"
" movq %%rax, 56(%2);"
/////// Compute the raw multiplication tmp[1] <- f1[1] * f2[1] //////
// Compute src1[0] * src2
" movq 32(%0), %%rdx;"
" mulxq 32(%1), %%r8, %%r9;"
" xor %%r10d, %%r10d;"
" movq %%r8, 64(%2);"
" mulxq 40(%1), %%r10, %%r11;"
" adox %%r9, %%r10;"
" movq %%r10, 72(%2);"
" mulxq 48(%1), %%rbx, %%r13;"
" adox %%r11, %%rbx;"
" mulxq 56(%1), %%r14, %%rdx;"
" adox %%r13, %%r14;"
" mov $0, %%rax;"
" adox %%rdx, %%rax;"
// Compute src1[1] * src2
" movq 40(%0), %%rdx;"
" mulxq 32(%1), %%r8, %%r9;"
" xor %%r10d, %%r10d;"
" adcxq 72(%2), %%r8;"
" movq %%r8, 72(%2);"
" mulxq 40(%1), %%r10, %%r11;"
" adox %%r9, %%r10;"
" adcx %%rbx, %%r10;"
" movq %%r10, 80(%2);"
" mulxq 48(%1), %%rbx, %%r13;"
" adox %%r11, %%rbx;"
" adcx %%r14, %%rbx;"
" mov $0, %%r8;"
" mulxq 56(%1), %%r14, %%rdx;"
" adox %%r13, %%r14;"
" adcx %%rax, %%r14;"
" mov $0, %%rax;"
" adox %%rdx, %%rax;"
" adcx %%r8, %%rax;"
// Compute src1[2] * src2
" movq 48(%0), %%rdx;"
" mulxq 32(%1), %%r8, %%r9;"
" xor %%r10d, %%r10d;"
" adcxq 80(%2), %%r8;"
" movq %%r8, 80(%2);"
" mulxq 40(%1), %%r10, %%r11;"
" adox %%r9, %%r10;"
" adcx %%rbx, %%r10;"
" movq %%r10, 88(%2);"
" mulxq 48(%1), %%rbx, %%r13;"
" adox %%r11, %%rbx;"
" adcx %%r14, %%rbx;"
" mov $0, %%r8;"
" mulxq 56(%1), %%r14, %%rdx;"
" adox %%r13, %%r14;"
" adcx %%rax, %%r14;"
" mov $0, %%rax;"
" adox %%rdx, %%rax;"
" adcx %%r8, %%rax;"
// Compute src1[3] * src2
" movq 56(%0), %%rdx;"
" mulxq 32(%1), %%r8, %%r9;"
" xor %%r10d, %%r10d;"
" adcxq 88(%2), %%r8;"
" movq %%r8, 88(%2);"
" mulxq 40(%1), %%r10, %%r11;"
" adox %%r9, %%r10;"
" adcx %%rbx, %%r10;"
" movq %%r10, 96(%2);"
" mulxq 48(%1), %%rbx, %%r13;"
" adox %%r11, %%rbx;"
" adcx %%r14, %%rbx;"
" movq %%rbx, 104(%2);"
" mov $0, %%r8;"
" mulxq 56(%1), %%r14, %%rdx;"
" adox %%r13, %%r14;"
" adcx %%rax, %%r14;"
" movq %%r14, 112(%2);"
" mov $0, %%rax;"
" adox %%rdx, %%rax;"
" adcx %%r8, %%rax;"
" movq %%rax, 120(%2);"
// Line up pointers
" mov %2, %0;"
" mov %3, %2;"
/////// Wrap the results back into the field //////
// Step 1: Compute dst + carry == tmp_hi * 38 + tmp_lo
" mov $38, %%rdx;"
" mulxq 32(%0), %%r8, %%r13;"
" xor %k1, %k1;"
" adoxq 0(%0), %%r8;"
" mulxq 40(%0), %%r9, %%rbx;"
" adcx %%r13, %%r9;"
" adoxq 8(%0), %%r9;"
" mulxq 48(%0), %%r10, %%r13;"
" adcx %%rbx, %%r10;"
" adoxq 16(%0), %%r10;"
" mulxq 56(%0), %%r11, %%rax;"
" adcx %%r13, %%r11;"
" adoxq 24(%0), %%r11;"
" adcx %1, %%rax;"
" adox %1, %%rax;"
" imul %%rdx, %%rax;"
// Step 2: Fold the carry back into dst
" add %%rax, %%r8;"
" adcx %1, %%r9;"
" movq %%r9, 8(%2);"
" adcx %1, %%r10;"
" movq %%r10, 16(%2);"
" adcx %1, %%r11;"
" movq %%r11, 24(%2);"
// Step 3: Fold the carry bit back in; guaranteed not to carry at this point
" mov $0, %%rax;"
" cmovc %%rdx, %%rax;"
" add %%rax, %%r8;"
" movq %%r8, 0(%2);"
// Step 1: Compute dst + carry == tmp_hi * 38 + tmp_lo
" mov $38, %%rdx;"
" mulxq 96(%0), %%r8, %%r13;"
" xor %k1, %k1;"
" adoxq 64(%0), %%r8;"
" mulxq 104(%0), %%r9, %%rbx;"
" adcx %%r13, %%r9;"
" adoxq 72(%0), %%r9;"
" mulxq 112(%0), %%r10, %%r13;"
" adcx %%rbx, %%r10;"
" adoxq 80(%0), %%r10;"
" mulxq 120(%0), %%r11, %%rax;"
" adcx %%r13, %%r11;"
" adoxq 88(%0), %%r11;"
" adcx %1, %%rax;"
" adox %1, %%rax;"
" imul %%rdx, %%rax;"
// Step 2: Fold the carry back into dst
" add %%rax, %%r8;"
" adcx %1, %%r9;"
" movq %%r9, 40(%2);"
" adcx %1, %%r10;"
" movq %%r10, 48(%2);"
" adcx %1, %%r11;"
" movq %%r11, 56(%2);"
// Step 3: Fold the carry bit back in; guaranteed not to carry at this point
" mov $0, %%rax;"
" cmovc %%rdx, %%rax;"
" add %%rax, %%r8;"
" movq %%r8, 32(%2);"
: "+&r"(f1), "+&r"(f2), "+&r"(tmp)
: "r"(out)
: "%rax", "%rbx", "%rdx", "%r8", "%r9", "%r10", "%r11", "%r13", "%r14", "memory", "cc");
}
// Computes the field multiplication of four-element f1 with value in f2
// Requires f2 to be smaller than 2^17
static inline void
fmul_scalar(uint64_t *out, uint64_t *f1, uint64_t f2)
{
register uint64_t f2_r __asm__("rdx") = f2;
__asm__ volatile(
// Compute the raw multiplication of f1*f2
" mulxq 0(%2), %%r8, %%rcx;" // f1[0]*f2
" mulxq 8(%2), %%r9, %%rbx;" // f1[1]*f2
" add %%rcx, %%r9;"
" mov $0, %%rcx;"
" mulxq 16(%2), %%r10, %%r13;" // f1[2]*f2
" adcx %%rbx, %%r10;"
" mulxq 24(%2), %%r11, %%rax;" // f1[3]*f2
" adcx %%r13, %%r11;"
" adcx %%rcx, %%rax;"
/////// Wrap the result back into the field //////
// Step 1: Compute carry*38
" mov $38, %%rdx;"
" imul %%rdx, %%rax;"
// Step 2: Fold the carry back into dst
" add %%rax, %%r8;"
" adcx %%rcx, %%r9;"
" movq %%r9, 8(%1);"
" adcx %%rcx, %%r10;"
" movq %%r10, 16(%1);"
" adcx %%rcx, %%r11;"
" movq %%r11, 24(%1);"
// Step 3: Fold the carry bit back in; guaranteed not to carry at this point
" mov $0, %%rax;"
" cmovc %%rdx, %%rax;"
" add %%rax, %%r8;"
" movq %%r8, 0(%1);"
: "+&r"(f2_r)
: "r"(out), "r"(f1)
: "%rax", "%rbx", "%rcx", "%r8", "%r9", "%r10", "%r11", "%r13", "memory", "cc");
}
// Computes p1 <- bit ? p2 : p1 in constant time
static inline void
cswap2(uint64_t bit, uint64_t *p1, uint64_t *p2)
{
__asm__ volatile(
// Transfer bit into CF flag
" add $18446744073709551615, %0;"
// cswap p1[0], p2[0]
" movq 0(%1), %%r8;"
" movq 0(%2), %%r9;"
" mov %%r8, %%r10;"
" cmovc %%r9, %%r8;"
" cmovc %%r10, %%r9;"
" movq %%r8, 0(%1);"
" movq %%r9, 0(%2);"
// cswap p1[1], p2[1]
" movq 8(%1), %%r8;"
" movq 8(%2), %%r9;"
" mov %%r8, %%r10;"
" cmovc %%r9, %%r8;"
" cmovc %%r10, %%r9;"
" movq %%r8, 8(%1);"
" movq %%r9, 8(%2);"
// cswap p1[2], p2[2]
" movq 16(%1), %%r8;"
" movq 16(%2), %%r9;"
" mov %%r8, %%r10;"
" cmovc %%r9, %%r8;"
" cmovc %%r10, %%r9;"
" movq %%r8, 16(%1);"
" movq %%r9, 16(%2);"
// cswap p1[3], p2[3]
" movq 24(%1), %%r8;"
" movq 24(%2), %%r9;"
" mov %%r8, %%r10;"
" cmovc %%r9, %%r8;"
" cmovc %%r10, %%r9;"
" movq %%r8, 24(%1);"
" movq %%r9, 24(%2);"
// cswap p1[4], p2[4]
" movq 32(%1), %%r8;"
" movq 32(%2), %%r9;"
" mov %%r8, %%r10;"
" cmovc %%r9, %%r8;"
" cmovc %%r10, %%r9;"
" movq %%r8, 32(%1);"
" movq %%r9, 32(%2);"
// cswap p1[5], p2[5]
" movq 40(%1), %%r8;"
" movq 40(%2), %%r9;"
" mov %%r8, %%r10;"
" cmovc %%r9, %%r8;"
" cmovc %%r10, %%r9;"
" movq %%r8, 40(%1);"
" movq %%r9, 40(%2);"
// cswap p1[6], p2[6]
" movq 48(%1), %%r8;"
" movq 48(%2), %%r9;"
" mov %%r8, %%r10;"
" cmovc %%r9, %%r8;"
" cmovc %%r10, %%r9;"
" movq %%r8, 48(%1);"
" movq %%r9, 48(%2);"
// cswap p1[7], p2[7]
" movq 56(%1), %%r8;"
" movq 56(%2), %%r9;"
" mov %%r8, %%r10;"
" cmovc %%r9, %%r8;"
" cmovc %%r10, %%r9;"
" movq %%r8, 56(%1);"
" movq %%r9, 56(%2);"
: "+&r"(bit)
: "r"(p1), "r"(p2)
: "%r8", "%r9", "%r10", "memory", "cc");
}
// Computes the square of a field element: out <- f * f
// Uses the 8-element buffer tmp for intermediate results
static inline void
fsqr(uint64_t *out, uint64_t *f, uint64_t *tmp)
{
__asm__ volatile(
/////// Compute the raw multiplication: tmp <- f * f //////
// Step 1: Compute all partial products
" movq 0(%0), %%rdx;" // f[0]
" mulxq 8(%0), %%r8, %%r14;"
" xor %%r15d, %%r15d;" // f[1]*f[0]
" mulxq 16(%0), %%r9, %%r10;"
" adcx %%r14, %%r9;" // f[2]*f[0]
" mulxq 24(%0), %%rax, %%rcx;"
" adcx %%rax, %%r10;" // f[3]*f[0]
" movq 24(%0), %%rdx;" // f[3]
" mulxq 8(%0), %%r11, %%rbx;"
" adcx %%rcx, %%r11;" // f[1]*f[3]
" mulxq 16(%0), %%rax, %%r13;"
" adcx %%rax, %%rbx;" // f[2]*f[3]
" movq 8(%0), %%rdx;"
" adcx %%r15, %%r13;" // f1
" mulxq 16(%0), %%rax, %%rcx;"
" mov $0, %%r14;" // f[2]*f[1]
// Step 2: Compute two parallel carry chains
" xor %%r15d, %%r15d;"
" adox %%rax, %%r10;"
" adcx %%r8, %%r8;"
" adox %%rcx, %%r11;"
" adcx %%r9, %%r9;"
" adox %%r15, %%rbx;"
" adcx %%r10, %%r10;"
" adox %%r15, %%r13;"
" adcx %%r11, %%r11;"
" adox %%r15, %%r14;"
" adcx %%rbx, %%rbx;"
" adcx %%r13, %%r13;"
" adcx %%r14, %%r14;"
// Step 3: Compute intermediate squares
" movq 0(%0), %%rdx;"
" mulx %%rdx, %%rax, %%rcx;" // f[0]^2
" movq %%rax, 0(%1);"
" add %%rcx, %%r8;"
" movq %%r8, 8(%1);"
" movq 8(%0), %%rdx;"
" mulx %%rdx, %%rax, %%rcx;" // f[1]^2
" adcx %%rax, %%r9;"
" movq %%r9, 16(%1);"
" adcx %%rcx, %%r10;"
" movq %%r10, 24(%1);"
" movq 16(%0), %%rdx;"
" mulx %%rdx, %%rax, %%rcx;" // f[2]^2
" adcx %%rax, %%r11;"
" movq %%r11, 32(%1);"
" adcx %%rcx, %%rbx;"
" movq %%rbx, 40(%1);"
" movq 24(%0), %%rdx;"
" mulx %%rdx, %%rax, %%rcx;" // f[3]^2
" adcx %%rax, %%r13;"
" movq %%r13, 48(%1);"
" adcx %%rcx, %%r14;"
" movq %%r14, 56(%1);"
// Line up pointers
" mov %1, %0;"
" mov %2, %1;"
/////// Wrap the result back into the field //////
// Step 1: Compute dst + carry == tmp_hi * 38 + tmp_lo
" mov $38, %%rdx;"
" mulxq 32(%0), %%r8, %%r13;"
" xor %%ecx, %%ecx;"
" adoxq 0(%0), %%r8;"
" mulxq 40(%0), %%r9, %%rbx;"
" adcx %%r13, %%r9;"
" adoxq 8(%0), %%r9;"
" mulxq 48(%0), %%r10, %%r13;"
" adcx %%rbx, %%r10;"
" adoxq 16(%0), %%r10;"
" mulxq 56(%0), %%r11, %%rax;"
" adcx %%r13, %%r11;"
" adoxq 24(%0), %%r11;"
" adcx %%rcx, %%rax;"
" adox %%rcx, %%rax;"
" imul %%rdx, %%rax;"
// Step 2: Fold the carry back into dst
" add %%rax, %%r8;"
" adcx %%rcx, %%r9;"
" movq %%r9, 8(%1);"
" adcx %%rcx, %%r10;"
" movq %%r10, 16(%1);"
" adcx %%rcx, %%r11;"
" movq %%r11, 24(%1);"
// Step 3: Fold the carry bit back in; guaranteed not to carry at this point
" mov $0, %%rax;"
" cmovc %%rdx, %%rax;"
" add %%rax, %%r8;"
" movq %%r8, 0(%1);"
: "+&r"(f), "+&r"(tmp)
: "r"(out)
: "%rax", "%rbx", "%rcx", "%rdx", "%r8", "%r9", "%r10", "%r11", "%r13", "%r14", "%r15", "memory", "cc");
}
// Computes two field squarings:
// out[0] <- f[0] * f[0]
// out[1] <- f[1] * f[1]
// Uses the 16-element buffer tmp for intermediate results
static inline void
fsqr2(uint64_t *out, uint64_t *f, uint64_t *tmp)
{
__asm__ volatile(
// Step 1: Compute all partial products
" movq 0(%0), %%rdx;" // f[0]
" mulxq 8(%0), %%r8, %%r14;"
" xor %%r15d, %%r15d;" // f[1]*f[0]
" mulxq 16(%0), %%r9, %%r10;"
" adcx %%r14, %%r9;" // f[2]*f[0]
" mulxq 24(%0), %%rax, %%rcx;"
" adcx %%rax, %%r10;" // f[3]*f[0]
" movq 24(%0), %%rdx;" // f[3]
" mulxq 8(%0), %%r11, %%rbx;"
" adcx %%rcx, %%r11;" // f[1]*f[3]
" mulxq 16(%0), %%rax, %%r13;"
" adcx %%rax, %%rbx;" // f[2]*f[3]
" movq 8(%0), %%rdx;"
" adcx %%r15, %%r13;" // f1
" mulxq 16(%0), %%rax, %%rcx;"
" mov $0, %%r14;" // f[2]*f[1]
// Step 2: Compute two parallel carry chains
" xor %%r15d, %%r15d;"
" adox %%rax, %%r10;"
" adcx %%r8, %%r8;"
" adox %%rcx, %%r11;"
" adcx %%r9, %%r9;"
" adox %%r15, %%rbx;"
" adcx %%r10, %%r10;"
" adox %%r15, %%r13;"
" adcx %%r11, %%r11;"
" adox %%r15, %%r14;"
" adcx %%rbx, %%rbx;"
" adcx %%r13, %%r13;"
" adcx %%r14, %%r14;"
// Step 3: Compute intermediate squares
" movq 0(%0), %%rdx;"
" mulx %%rdx, %%rax, %%rcx;" // f[0]^2
" movq %%rax, 0(%1);"
" add %%rcx, %%r8;"
" movq %%r8, 8(%1);"
" movq 8(%0), %%rdx;"
" mulx %%rdx, %%rax, %%rcx;" // f[1]^2
" adcx %%rax, %%r9;"
" movq %%r9, 16(%1);"
" adcx %%rcx, %%r10;"
" movq %%r10, 24(%1);"
" movq 16(%0), %%rdx;"
" mulx %%rdx, %%rax, %%rcx;" // f[2]^2
" adcx %%rax, %%r11;"
" movq %%r11, 32(%1);"
" adcx %%rcx, %%rbx;"
" movq %%rbx, 40(%1);"
" movq 24(%0), %%rdx;"
" mulx %%rdx, %%rax, %%rcx;" // f[3]^2
" adcx %%rax, %%r13;"
" movq %%r13, 48(%1);"
" adcx %%rcx, %%r14;"
" movq %%r14, 56(%1);"
// Step 1: Compute all partial products
" movq 32(%0), %%rdx;" // f[0]
" mulxq 40(%0), %%r8, %%r14;"
" xor %%r15d, %%r15d;" // f[1]*f[0]
" mulxq 48(%0), %%r9, %%r10;"
" adcx %%r14, %%r9;" // f[2]*f[0]
" mulxq 56(%0), %%rax, %%rcx;"
" adcx %%rax, %%r10;" // f[3]*f[0]
" movq 56(%0), %%rdx;" // f[3]
" mulxq 40(%0), %%r11, %%rbx;"
" adcx %%rcx, %%r11;" // f[1]*f[3]
" mulxq 48(%0), %%rax, %%r13;"
" adcx %%rax, %%rbx;" // f[2]*f[3]
" movq 40(%0), %%rdx;"
" adcx %%r15, %%r13;" // f1
" mulxq 48(%0), %%rax, %%rcx;"
" mov $0, %%r14;" // f[2]*f[1]
// Step 2: Compute two parallel carry chains
" xor %%r15d, %%r15d;"
" adox %%rax, %%r10;"
" adcx %%r8, %%r8;"
" adox %%rcx, %%r11;"
" adcx %%r9, %%r9;"
" adox %%r15, %%rbx;"
" adcx %%r10, %%r10;"
" adox %%r15, %%r13;"
" adcx %%r11, %%r11;"
" adox %%r15, %%r14;"
" adcx %%rbx, %%rbx;"
" adcx %%r13, %%r13;"
" adcx %%r14, %%r14;"
// Step 3: Compute intermediate squares
" movq 32(%0), %%rdx;"
" mulx %%rdx, %%rax, %%rcx;" // f[0]^2
" movq %%rax, 64(%1);"
" add %%rcx, %%r8;"
" movq %%r8, 72(%1);"
" movq 40(%0), %%rdx;"
" mulx %%rdx, %%rax, %%rcx;" // f[1]^2
" adcx %%rax, %%r9;"
" movq %%r9, 80(%1);"
" adcx %%rcx, %%r10;"
" movq %%r10, 88(%1);"
" movq 48(%0), %%rdx;"
" mulx %%rdx, %%rax, %%rcx;" // f[2]^2
" adcx %%rax, %%r11;"
" movq %%r11, 96(%1);"
" adcx %%rcx, %%rbx;"
" movq %%rbx, 104(%1);"
" movq 56(%0), %%rdx;"
" mulx %%rdx, %%rax, %%rcx;" // f[3]^2
" adcx %%rax, %%r13;"
" movq %%r13, 112(%1);"
" adcx %%rcx, %%r14;"
" movq %%r14, 120(%1);"
// Line up pointers
" mov %1, %0;"
" mov %2, %1;"
// Step 1: Compute dst + carry == tmp_hi * 38 + tmp_lo
" mov $38, %%rdx;"
" mulxq 32(%0), %%r8, %%r13;"
" xor %%ecx, %%ecx;"
" adoxq 0(%0), %%r8;"
" mulxq 40(%0), %%r9, %%rbx;"
" adcx %%r13, %%r9;"
" adoxq 8(%0), %%r9;"
" mulxq 48(%0), %%r10, %%r13;"
" adcx %%rbx, %%r10;"
" adoxq 16(%0), %%r10;"
" mulxq 56(%0), %%r11, %%rax;"
" adcx %%r13, %%r11;"
" adoxq 24(%0), %%r11;"
" adcx %%rcx, %%rax;"
" adox %%rcx, %%rax;"
" imul %%rdx, %%rax;"
// Step 2: Fold the carry back into dst
" add %%rax, %%r8;"
" adcx %%rcx, %%r9;"
" movq %%r9, 8(%1);"
" adcx %%rcx, %%r10;"
" movq %%r10, 16(%1);"
" adcx %%rcx, %%r11;"
" movq %%r11, 24(%1);"
// Step 3: Fold the carry bit back in; guaranteed not to carry at this point
" mov $0, %%rax;"
" cmovc %%rdx, %%rax;"
" add %%rax, %%r8;"
" movq %%r8, 0(%1);"
// Step 1: Compute dst + carry == tmp_hi * 38 + tmp_lo
" mov $38, %%rdx;"
" mulxq 96(%0), %%r8, %%r13;"
" xor %%ecx, %%ecx;"
" adoxq 64(%0), %%r8;"
" mulxq 104(%0), %%r9, %%rbx;"
" adcx %%r13, %%r9;"
" adoxq 72(%0), %%r9;"
" mulxq 112(%0), %%r10, %%r13;"
" adcx %%rbx, %%r10;"
" adoxq 80(%0), %%r10;"
" mulxq 120(%0), %%r11, %%rax;"
" adcx %%r13, %%r11;"
" adoxq 88(%0), %%r11;"
" adcx %%rcx, %%rax;"
" adox %%rcx, %%rax;"
" imul %%rdx, %%rax;"
// Step 2: Fold the carry back into dst
" add %%rax, %%r8;"
" adcx %%rcx, %%r9;"
" movq %%r9, 40(%1);"
" adcx %%rcx, %%r10;"
" movq %%r10, 48(%1);"
" adcx %%rcx, %%r11;"
" movq %%r11, 56(%1);"
// Step 3: Fold the carry bit back in; guaranteed not to carry at this point
" mov $0, %%rax;"
" cmovc %%rdx, %%rax;"
" add %%rax, %%r8;"
" movq %%r8, 32(%1);"
: "+&r"(f), "+&r"(tmp)
: "r"(out)
: "%rax", "%rbx", "%rcx", "%rdx", "%r8", "%r9", "%r10", "%r11", "%r13", "%r14", "%r15", "memory", "cc");
}
#endif /* defined(__x86_64__) || defined(_M_X64) */
#endif /* __GNUC__ */