blob: 74570cbe3124d303b0444d021bbe188b8019ce3f [file] [log] [blame]
// SPDX-License-Identifier: GPL-2.0 OR MIT
/*
* Copyright (C) 2020 Jason A. Donenfeld <Jason@zx2c4.com>. All Rights Reserved.
* Copyright (c) 2016-2020 INRIA, CMU and Microsoft Corporation
*/
static __always_inline u64 eq_mask(u64 a, u64 b)
{
u64 x = a ^ b;
u64 minus_x = ~x + (u64)1U;
u64 x_or_minus_x = x | minus_x;
u64 xnx = x_or_minus_x >> (u32)63U;
return xnx - (u64)1U;
}
static __always_inline u64 gte_mask(u64 a, u64 b)
{
u64 x = a;
u64 y = b;
u64 x_xor_y = x ^ y;
u64 x_sub_y = x - y;
u64 x_sub_y_xor_y = x_sub_y ^ y;
u64 q = x_xor_y | x_sub_y_xor_y;
u64 x_xor_q = x ^ q;
u64 x_xor_q_ = x_xor_q >> (u32)63U;
return x_xor_q_ - (u64)1U;
}
/* Computes the addition of four-element f1 with value in f2
* and returns the carry (if any) */
static inline u64 add_scalar(u64 *out, const u64 *f1, u64 f2)
{
u64 carry_r;
asm volatile(
/* Clear registers to propagate the carry bit */
" xor %%r8, %%r8;"
" xor %%r9, %%r9;"
" xor %%r10, %%r10;"
" xor %%r11, %%r11;"
" xor %1, %1;"
/* Begin addition chain */
" addq 0(%3), %0;"
" movq %0, 0(%2);"
" adcxq 8(%3), %%r8;"
" movq %%r8, 8(%2);"
" adcxq 16(%3), %%r9;"
" movq %%r9, 16(%2);"
" adcxq 24(%3), %%r10;"
" movq %%r10, 24(%2);"
/* Return the carry bit in a register */
" adcx %%r11, %1;"
: "+&r" (f2), "=&r" (carry_r)
: "r" (out), "r" (f1)
: "%r8", "%r9", "%r10", "%r11", "memory", "cc"
);
return carry_r;
}
/* Computes the field addition of two field elements */
static inline void fadd(u64 *out, const u64 *f1, const u64 *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 %%rcx, %%rcx;"
" 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(u64 *out, const u64 *f1, const u64 *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(u64 *out, const u64 *f1, const u64 *f2, u64 *tmp)
{
asm volatile(
/* Compute the raw multiplication: tmp <- src1 * src2 */
/* Compute src1[0] * src2 */
" movq 0(%1), %%rdx;"
" mulxq 0(%3), %%r8, %%r9;" " xor %%r10, %%r10;" " movq %%r8, 0(%0);"
" mulxq 8(%3), %%r10, %%r11;" " adox %%r9, %%r10;" " movq %%r10, 8(%0);"
" mulxq 16(%3), %%r12, %%r13;" " adox %%r11, %%r12;"
" mulxq 24(%3), %%r14, %%rdx;" " adox %%r13, %%r14;" " mov $0, %%rax;"
" adox %%rdx, %%rax;"
/* Compute src1[1] * src2 */
" movq 8(%1), %%rdx;"
" mulxq 0(%3), %%r8, %%r9;" " xor %%r10, %%r10;" " adcxq 8(%0), %%r8;" " movq %%r8, 8(%0);"
" mulxq 8(%3), %%r10, %%r11;" " adox %%r9, %%r10;" " adcx %%r12, %%r10;" " movq %%r10, 16(%0);"
" mulxq 16(%3), %%r12, %%r13;" " adox %%r11, %%r12;" " adcx %%r14, %%r12;" " mov $0, %%r8;"
" mulxq 24(%3), %%r14, %%rdx;" " adox %%r13, %%r14;" " adcx %%rax, %%r14;" " mov $0, %%rax;"
" adox %%rdx, %%rax;" " adcx %%r8, %%rax;"
/* Compute src1[2] * src2 */
" movq 16(%1), %%rdx;"
" mulxq 0(%3), %%r8, %%r9;" " xor %%r10, %%r10;" " adcxq 16(%0), %%r8;" " movq %%r8, 16(%0);"
" mulxq 8(%3), %%r10, %%r11;" " adox %%r9, %%r10;" " adcx %%r12, %%r10;" " movq %%r10, 24(%0);"
" mulxq 16(%3), %%r12, %%r13;" " adox %%r11, %%r12;" " adcx %%r14, %%r12;" " mov $0, %%r8;"
" mulxq 24(%3), %%r14, %%rdx;" " adox %%r13, %%r14;" " adcx %%rax, %%r14;" " mov $0, %%rax;"
" adox %%rdx, %%rax;" " adcx %%r8, %%rax;"
/* Compute src1[3] * src2 */
" movq 24(%1), %%rdx;"
" mulxq 0(%3), %%r8, %%r9;" " xor %%r10, %%r10;" " adcxq 24(%0), %%r8;" " movq %%r8, 24(%0);"
" mulxq 8(%3), %%r10, %%r11;" " adox %%r9, %%r10;" " adcx %%r12, %%r10;" " movq %%r10, 32(%0);"
" mulxq 16(%3), %%r12, %%r13;" " adox %%r11, %%r12;" " adcx %%r14, %%r12;" " movq %%r12, 40(%0);" " mov $0, %%r8;"
" mulxq 24(%3), %%r14, %%rdx;" " adox %%r13, %%r14;" " adcx %%rax, %%r14;" " movq %%r14, 48(%0);" " mov $0, %%rax;"
" adox %%rdx, %%rax;" " adcx %%r8, %%rax;" " movq %%rax, 56(%0);"
/* Line up pointers */
" mov %0, %1;"
" mov %2, %0;"
/* Wrap the result back into the field */
/* Step 1: Compute dst + carry == tmp_hi * 38 + tmp_lo */
" mov $38, %%rdx;"
" mulxq 32(%1), %%r8, %%r13;"
" xor %3, %3;"
" adoxq 0(%1), %%r8;"
" mulxq 40(%1), %%r9, %%r12;"
" adcx %%r13, %%r9;"
" adoxq 8(%1), %%r9;"
" mulxq 48(%1), %%r10, %%r13;"
" adcx %%r12, %%r10;"
" adoxq 16(%1), %%r10;"
" mulxq 56(%1), %%r11, %%rax;"
" adcx %%r13, %%r11;"
" adoxq 24(%1), %%r11;"
" adcx %3, %%rax;"
" adox %3, %%rax;"
" imul %%rdx, %%rax;"
/* Step 2: Fold the carry back into dst */
" add %%rax, %%r8;"
" adcx %3, %%r9;"
" movq %%r9, 8(%0);"
" adcx %3, %%r10;"
" movq %%r10, 16(%0);"
" adcx %3, %%r11;"
" movq %%r11, 24(%0);"
/* 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(%0);"
: "+&r" (tmp), "+&r" (f1), "+&r" (out), "+&r" (f2)
:
: "%rax", "%rdx", "%r8", "%r9", "%r10", "%r11", "%r12", "%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(u64 *out, const u64 *f1, const u64 *f2, u64 *tmp)
{
asm volatile(
/* Compute the raw multiplication tmp[0] <- f1[0] * f2[0] */
/* Compute src1[0] * src2 */
" movq 0(%1), %%rdx;"
" mulxq 0(%3), %%r8, %%r9;" " xor %%r10, %%r10;" " movq %%r8, 0(%0);"
" mulxq 8(%3), %%r10, %%r11;" " adox %%r9, %%r10;" " movq %%r10, 8(%0);"
" mulxq 16(%3), %%r12, %%r13;" " adox %%r11, %%r12;"
" mulxq 24(%3), %%r14, %%rdx;" " adox %%r13, %%r14;" " mov $0, %%rax;"
" adox %%rdx, %%rax;"
/* Compute src1[1] * src2 */
" movq 8(%1), %%rdx;"
" mulxq 0(%3), %%r8, %%r9;" " xor %%r10, %%r10;" " adcxq 8(%0), %%r8;" " movq %%r8, 8(%0);"
" mulxq 8(%3), %%r10, %%r11;" " adox %%r9, %%r10;" " adcx %%r12, %%r10;" " movq %%r10, 16(%0);"
" mulxq 16(%3), %%r12, %%r13;" " adox %%r11, %%r12;" " adcx %%r14, %%r12;" " mov $0, %%r8;"
" mulxq 24(%3), %%r14, %%rdx;" " adox %%r13, %%r14;" " adcx %%rax, %%r14;" " mov $0, %%rax;"
" adox %%rdx, %%rax;" " adcx %%r8, %%rax;"
/* Compute src1[2] * src2 */
" movq 16(%1), %%rdx;"
" mulxq 0(%3), %%r8, %%r9;" " xor %%r10, %%r10;" " adcxq 16(%0), %%r8;" " movq %%r8, 16(%0);"
" mulxq 8(%3), %%r10, %%r11;" " adox %%r9, %%r10;" " adcx %%r12, %%r10;" " movq %%r10, 24(%0);"
" mulxq 16(%3), %%r12, %%r13;" " adox %%r11, %%r12;" " adcx %%r14, %%r12;" " mov $0, %%r8;"
" mulxq 24(%3), %%r14, %%rdx;" " adox %%r13, %%r14;" " adcx %%rax, %%r14;" " mov $0, %%rax;"
" adox %%rdx, %%rax;" " adcx %%r8, %%rax;"
/* Compute src1[3] * src2 */
" movq 24(%1), %%rdx;"
" mulxq 0(%3), %%r8, %%r9;" " xor %%r10, %%r10;" " adcxq 24(%0), %%r8;" " movq %%r8, 24(%0);"
" mulxq 8(%3), %%r10, %%r11;" " adox %%r9, %%r10;" " adcx %%r12, %%r10;" " movq %%r10, 32(%0);"
" mulxq 16(%3), %%r12, %%r13;" " adox %%r11, %%r12;" " adcx %%r14, %%r12;" " movq %%r12, 40(%0);" " mov $0, %%r8;"
" mulxq 24(%3), %%r14, %%rdx;" " adox %%r13, %%r14;" " adcx %%rax, %%r14;" " movq %%r14, 48(%0);" " mov $0, %%rax;"
" adox %%rdx, %%rax;" " adcx %%r8, %%rax;" " movq %%rax, 56(%0);"
/* Compute the raw multiplication tmp[1] <- f1[1] * f2[1] */
/* Compute src1[0] * src2 */
" movq 32(%1), %%rdx;"
" mulxq 32(%3), %%r8, %%r9;" " xor %%r10, %%r10;" " movq %%r8, 64(%0);"
" mulxq 40(%3), %%r10, %%r11;" " adox %%r9, %%r10;" " movq %%r10, 72(%0);"
" mulxq 48(%3), %%r12, %%r13;" " adox %%r11, %%r12;"
" mulxq 56(%3), %%r14, %%rdx;" " adox %%r13, %%r14;" " mov $0, %%rax;"
" adox %%rdx, %%rax;"
/* Compute src1[1] * src2 */
" movq 40(%1), %%rdx;"
" mulxq 32(%3), %%r8, %%r9;" " xor %%r10, %%r10;" " adcxq 72(%0), %%r8;" " movq %%r8, 72(%0);"
" mulxq 40(%3), %%r10, %%r11;" " adox %%r9, %%r10;" " adcx %%r12, %%r10;" " movq %%r10, 80(%0);"
" mulxq 48(%3), %%r12, %%r13;" " adox %%r11, %%r12;" " adcx %%r14, %%r12;" " mov $0, %%r8;"
" mulxq 56(%3), %%r14, %%rdx;" " adox %%r13, %%r14;" " adcx %%rax, %%r14;" " mov $0, %%rax;"
" adox %%rdx, %%rax;" " adcx %%r8, %%rax;"
/* Compute src1[2] * src2 */
" movq 48(%1), %%rdx;"
" mulxq 32(%3), %%r8, %%r9;" " xor %%r10, %%r10;" " adcxq 80(%0), %%r8;" " movq %%r8, 80(%0);"
" mulxq 40(%3), %%r10, %%r11;" " adox %%r9, %%r10;" " adcx %%r12, %%r10;" " movq %%r10, 88(%0);"
" mulxq 48(%3), %%r12, %%r13;" " adox %%r11, %%r12;" " adcx %%r14, %%r12;" " mov $0, %%r8;"
" mulxq 56(%3), %%r14, %%rdx;" " adox %%r13, %%r14;" " adcx %%rax, %%r14;" " mov $0, %%rax;"
" adox %%rdx, %%rax;" " adcx %%r8, %%rax;"
/* Compute src1[3] * src2 */
" movq 56(%1), %%rdx;"
" mulxq 32(%3), %%r8, %%r9;" " xor %%r10, %%r10;" " adcxq 88(%0), %%r8;" " movq %%r8, 88(%0);"
" mulxq 40(%3), %%r10, %%r11;" " adox %%r9, %%r10;" " adcx %%r12, %%r10;" " movq %%r10, 96(%0);"
" mulxq 48(%3), %%r12, %%r13;" " adox %%r11, %%r12;" " adcx %%r14, %%r12;" " movq %%r12, 104(%0);" " mov $0, %%r8;"
" mulxq 56(%3), %%r14, %%rdx;" " adox %%r13, %%r14;" " adcx %%rax, %%r14;" " movq %%r14, 112(%0);" " mov $0, %%rax;"
" adox %%rdx, %%rax;" " adcx %%r8, %%rax;" " movq %%rax, 120(%0);"
/* Line up pointers */
" mov %0, %1;"
" mov %2, %0;"
/* Wrap the results back into the field */
/* Step 1: Compute dst + carry == tmp_hi * 38 + tmp_lo */
" mov $38, %%rdx;"
" mulxq 32(%1), %%r8, %%r13;"
" xor %3, %3;"
" adoxq 0(%1), %%r8;"
" mulxq 40(%1), %%r9, %%r12;"
" adcx %%r13, %%r9;"
" adoxq 8(%1), %%r9;"
" mulxq 48(%1), %%r10, %%r13;"
" adcx %%r12, %%r10;"
" adoxq 16(%1), %%r10;"
" mulxq 56(%1), %%r11, %%rax;"
" adcx %%r13, %%r11;"
" adoxq 24(%1), %%r11;"
" adcx %3, %%rax;"
" adox %3, %%rax;"
" imul %%rdx, %%rax;"
/* Step 2: Fold the carry back into dst */
" add %%rax, %%r8;"
" adcx %3, %%r9;"
" movq %%r9, 8(%0);"
" adcx %3, %%r10;"
" movq %%r10, 16(%0);"
" adcx %3, %%r11;"
" movq %%r11, 24(%0);"
/* 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(%0);"
/* Step 1: Compute dst + carry == tmp_hi * 38 + tmp_lo */
" mov $38, %%rdx;"
" mulxq 96(%1), %%r8, %%r13;"
" xor %3, %3;"
" adoxq 64(%1), %%r8;"
" mulxq 104(%1), %%r9, %%r12;"
" adcx %%r13, %%r9;"
" adoxq 72(%1), %%r9;"
" mulxq 112(%1), %%r10, %%r13;"
" adcx %%r12, %%r10;"
" adoxq 80(%1), %%r10;"
" mulxq 120(%1), %%r11, %%rax;"
" adcx %%r13, %%r11;"
" adoxq 88(%1), %%r11;"
" adcx %3, %%rax;"
" adox %3, %%rax;"
" imul %%rdx, %%rax;"
/* Step 2: Fold the carry back into dst */
" add %%rax, %%r8;"
" adcx %3, %%r9;"
" movq %%r9, 40(%0);"
" adcx %3, %%r10;"
" movq %%r10, 48(%0);"
" adcx %3, %%r11;"
" movq %%r11, 56(%0);"
/* 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(%0);"
: "+&r" (tmp), "+&r" (f1), "+&r" (out), "+&r" (f2)
:
: "%rax", "%rdx", "%r8", "%r9", "%r10", "%r11", "%r12", "%r13", "%r14", "memory", "cc"
);
}
/* Computes the field multiplication of four-element f1 with value in f2 */
static inline void fmul_scalar(u64 *out, const u64 *f1, u64 f2)
{
register u64 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, %%r12;" /* f1[1]*f2 */
" add %%rcx, %%r9;"
" mov $0, %%rcx;"
" mulxq 16(%2), %%r10, %%r13;" /* f1[2]*f2 */
" adcx %%r12, %%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", "%rcx", "%r8", "%r9", "%r10", "%r11", "%r12", "%r13", "memory", "cc"
);
}
/* Computes p1 <- bit ? p2 : p1 in constant time */
static inline void cswap2(u64 bit, const u64 *p1, const u64 *p2)
{
asm volatile(
/* Invert the polarity of bit to match cmov expectations */
" 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(u64 *out, const u64 *f, u64 *tmp)
{
asm volatile(
/* Compute the raw multiplication: tmp <- f * f */
/* Step 1: Compute all partial products */
" movq 0(%1), %%rdx;" /* f[0] */
" mulxq 8(%1), %%r8, %%r14;" " xor %%r15, %%r15;" /* f[1]*f[0] */
" mulxq 16(%1), %%r9, %%r10;" " adcx %%r14, %%r9;" /* f[2]*f[0] */
" mulxq 24(%1), %%rax, %%rcx;" " adcx %%rax, %%r10;" /* f[3]*f[0] */
" movq 24(%1), %%rdx;" /* f[3] */
" mulxq 8(%1), %%r11, %%r12;" " adcx %%rcx, %%r11;" /* f[1]*f[3] */
" mulxq 16(%1), %%rax, %%r13;" " adcx %%rax, %%r12;" /* f[2]*f[3] */
" movq 8(%1), %%rdx;" " adcx %%r15, %%r13;" /* f1 */
" mulxq 16(%1), %%rax, %%rcx;" " mov $0, %%r14;" /* f[2]*f[1] */
/* Step 2: Compute two parallel carry chains */
" xor %%r15, %%r15;"
" adox %%rax, %%r10;"
" adcx %%r8, %%r8;"
" adox %%rcx, %%r11;"
" adcx %%r9, %%r9;"
" adox %%r15, %%r12;"
" adcx %%r10, %%r10;"
" adox %%r15, %%r13;"
" adcx %%r11, %%r11;"
" adox %%r15, %%r14;"
" adcx %%r12, %%r12;"
" adcx %%r13, %%r13;"
" adcx %%r14, %%r14;"
/* Step 3: Compute intermediate squares */
" movq 0(%1), %%rdx;" " mulx %%rdx, %%rax, %%rcx;" /* f[0]^2 */
" movq %%rax, 0(%0);"
" add %%rcx, %%r8;" " movq %%r8, 8(%0);"
" movq 8(%1), %%rdx;" " mulx %%rdx, %%rax, %%rcx;" /* f[1]^2 */
" adcx %%rax, %%r9;" " movq %%r9, 16(%0);"
" adcx %%rcx, %%r10;" " movq %%r10, 24(%0);"
" movq 16(%1), %%rdx;" " mulx %%rdx, %%rax, %%rcx;" /* f[2]^2 */
" adcx %%rax, %%r11;" " movq %%r11, 32(%0);"
" adcx %%rcx, %%r12;" " movq %%r12, 40(%0);"
" movq 24(%1), %%rdx;" " mulx %%rdx, %%rax, %%rcx;" /* f[3]^2 */
" adcx %%rax, %%r13;" " movq %%r13, 48(%0);"
" adcx %%rcx, %%r14;" " movq %%r14, 56(%0);"
/* Line up pointers */
" mov %0, %1;"
" mov %2, %0;"
/* Wrap the result back into the field */
/* Step 1: Compute dst + carry == tmp_hi * 38 + tmp_lo */
" mov $38, %%rdx;"
" mulxq 32(%1), %%r8, %%r13;"
" xor %%rcx, %%rcx;"
" adoxq 0(%1), %%r8;"
" mulxq 40(%1), %%r9, %%r12;"
" adcx %%r13, %%r9;"
" adoxq 8(%1), %%r9;"
" mulxq 48(%1), %%r10, %%r13;"
" adcx %%r12, %%r10;"
" adoxq 16(%1), %%r10;"
" mulxq 56(%1), %%r11, %%rax;"
" adcx %%r13, %%r11;"
" adoxq 24(%1), %%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(%0);"
" adcx %%rcx, %%r10;"
" movq %%r10, 16(%0);"
" adcx %%rcx, %%r11;"
" movq %%r11, 24(%0);"
/* 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(%0);"
: "+&r" (tmp), "+&r" (f), "+&r" (out)
:
: "%rax", "%rcx", "%rdx", "%r8", "%r9", "%r10", "%r11", "%r12", "%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(u64 *out, const u64 *f, u64 *tmp)
{
asm volatile(
/* Step 1: Compute all partial products */
" movq 0(%1), %%rdx;" /* f[0] */
" mulxq 8(%1), %%r8, %%r14;" " xor %%r15, %%r15;" /* f[1]*f[0] */
" mulxq 16(%1), %%r9, %%r10;" " adcx %%r14, %%r9;" /* f[2]*f[0] */
" mulxq 24(%1), %%rax, %%rcx;" " adcx %%rax, %%r10;" /* f[3]*f[0] */
" movq 24(%1), %%rdx;" /* f[3] */
" mulxq 8(%1), %%r11, %%r12;" " adcx %%rcx, %%r11;" /* f[1]*f[3] */
" mulxq 16(%1), %%rax, %%r13;" " adcx %%rax, %%r12;" /* f[2]*f[3] */
" movq 8(%1), %%rdx;" " adcx %%r15, %%r13;" /* f1 */
" mulxq 16(%1), %%rax, %%rcx;" " mov $0, %%r14;" /* f[2]*f[1] */
/* Step 2: Compute two parallel carry chains */
" xor %%r15, %%r15;"
" adox %%rax, %%r10;"
" adcx %%r8, %%r8;"
" adox %%rcx, %%r11;"
" adcx %%r9, %%r9;"
" adox %%r15, %%r12;"
" adcx %%r10, %%r10;"
" adox %%r15, %%r13;"
" adcx %%r11, %%r11;"
" adox %%r15, %%r14;"
" adcx %%r12, %%r12;"
" adcx %%r13, %%r13;"
" adcx %%r14, %%r14;"
/* Step 3: Compute intermediate squares */
" movq 0(%1), %%rdx;" " mulx %%rdx, %%rax, %%rcx;" /* f[0]^2 */
" movq %%rax, 0(%0);"
" add %%rcx, %%r8;" " movq %%r8, 8(%0);"
" movq 8(%1), %%rdx;" " mulx %%rdx, %%rax, %%rcx;" /* f[1]^2 */
" adcx %%rax, %%r9;" " movq %%r9, 16(%0);"
" adcx %%rcx, %%r10;" " movq %%r10, 24(%0);"
" movq 16(%1), %%rdx;" " mulx %%rdx, %%rax, %%rcx;" /* f[2]^2 */
" adcx %%rax, %%r11;" " movq %%r11, 32(%0);"
" adcx %%rcx, %%r12;" " movq %%r12, 40(%0);"
" movq 24(%1), %%rdx;" " mulx %%rdx, %%rax, %%rcx;" /* f[3]^2 */
" adcx %%rax, %%r13;" " movq %%r13, 48(%0);"
" adcx %%rcx, %%r14;" " movq %%r14, 56(%0);"
/* Step 1: Compute all partial products */
" movq 32(%1), %%rdx;" /* f[0] */
" mulxq 40(%1), %%r8, %%r14;" " xor %%r15, %%r15;" /* f[1]*f[0] */
" mulxq 48(%1), %%r9, %%r10;" " adcx %%r14, %%r9;" /* f[2]*f[0] */
" mulxq 56(%1), %%rax, %%rcx;" " adcx %%rax, %%r10;" /* f[3]*f[0] */
" movq 56(%1), %%rdx;" /* f[3] */
" mulxq 40(%1), %%r11, %%r12;" " adcx %%rcx, %%r11;" /* f[1]*f[3] */
" mulxq 48(%1), %%rax, %%r13;" " adcx %%rax, %%r12;" /* f[2]*f[3] */
" movq 40(%1), %%rdx;" " adcx %%r15, %%r13;" /* f1 */
" mulxq 48(%1), %%rax, %%rcx;" " mov $0, %%r14;" /* f[2]*f[1] */
/* Step 2: Compute two parallel carry chains */
" xor %%r15, %%r15;"
" adox %%rax, %%r10;"
" adcx %%r8, %%r8;"
" adox %%rcx, %%r11;"
" adcx %%r9, %%r9;"
" adox %%r15, %%r12;"
" adcx %%r10, %%r10;"
" adox %%r15, %%r13;"
" adcx %%r11, %%r11;"
" adox %%r15, %%r14;"
" adcx %%r12, %%r12;"
" adcx %%r13, %%r13;"
" adcx %%r14, %%r14;"
/* Step 3: Compute intermediate squares */
" movq 32(%1), %%rdx;" " mulx %%rdx, %%rax, %%rcx;" /* f[0]^2 */
" movq %%rax, 64(%0);"
" add %%rcx, %%r8;" " movq %%r8, 72(%0);"
" movq 40(%1), %%rdx;" " mulx %%rdx, %%rax, %%rcx;" /* f[1]^2 */
" adcx %%rax, %%r9;" " movq %%r9, 80(%0);"
" adcx %%rcx, %%r10;" " movq %%r10, 88(%0);"
" movq 48(%1), %%rdx;" " mulx %%rdx, %%rax, %%rcx;" /* f[2]^2 */
" adcx %%rax, %%r11;" " movq %%r11, 96(%0);"
" adcx %%rcx, %%r12;" " movq %%r12, 104(%0);"
" movq 56(%1), %%rdx;" " mulx %%rdx, %%rax, %%rcx;" /* f[3]^2 */
" adcx %%rax, %%r13;" " movq %%r13, 112(%0);"
" adcx %%rcx, %%r14;" " movq %%r14, 120(%0);"
/* Line up pointers */
" mov %0, %1;"
" mov %2, %0;"
/* Step 1: Compute dst + carry == tmp_hi * 38 + tmp_lo */
" mov $38, %%rdx;"
" mulxq 32(%1), %%r8, %%r13;"
" xor %%rcx, %%rcx;"
" adoxq 0(%1), %%r8;"
" mulxq 40(%1), %%r9, %%r12;"
" adcx %%r13, %%r9;"
" adoxq 8(%1), %%r9;"
" mulxq 48(%1), %%r10, %%r13;"
" adcx %%r12, %%r10;"
" adoxq 16(%1), %%r10;"
" mulxq 56(%1), %%r11, %%rax;"
" adcx %%r13, %%r11;"
" adoxq 24(%1), %%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(%0);"
" adcx %%rcx, %%r10;"
" movq %%r10, 16(%0);"
" adcx %%rcx, %%r11;"
" movq %%r11, 24(%0);"
/* 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(%0);"
/* Step 1: Compute dst + carry == tmp_hi * 38 + tmp_lo */
" mov $38, %%rdx;"
" mulxq 96(%1), %%r8, %%r13;"
" xor %%rcx, %%rcx;"
" adoxq 64(%1), %%r8;"
" mulxq 104(%1), %%r9, %%r12;"
" adcx %%r13, %%r9;"
" adoxq 72(%1), %%r9;"
" mulxq 112(%1), %%r10, %%r13;"
" adcx %%r12, %%r10;"
" adoxq 80(%1), %%r10;"
" mulxq 120(%1), %%r11, %%rax;"
" adcx %%r13, %%r11;"
" adoxq 88(%1), %%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(%0);"
" adcx %%rcx, %%r10;"
" movq %%r10, 48(%0);"
" adcx %%rcx, %%r11;"
" movq %%r11, 56(%0);"
/* 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(%0);"
: "+&r" (tmp), "+&r" (f), "+&r" (out)
:
: "%rax", "%rcx", "%rdx", "%r8", "%r9", "%r10", "%r11", "%r12", "%r13", "%r14", "%r15", "memory", "cc"
);
}
static void point_add_and_double(u64 *q, u64 *p01_tmp1, u64 *tmp2)
{
u64 *nq = p01_tmp1;
u64 *nq_p1 = p01_tmp1 + (u32)8U;
u64 *tmp1 = p01_tmp1 + (u32)16U;
u64 *x1 = q;
u64 *x2 = nq;
u64 *z2 = nq + (u32)4U;
u64 *z3 = nq_p1 + (u32)4U;
u64 *a = tmp1;
u64 *b = tmp1 + (u32)4U;
u64 *ab = tmp1;
u64 *dc = tmp1 + (u32)8U;
u64 *x3;
u64 *z31;
u64 *d0;
u64 *c0;
u64 *a1;
u64 *b1;
u64 *d;
u64 *c;
u64 *ab1;
u64 *dc1;
fadd(a, x2, z2);
fsub(b, x2, z2);
x3 = nq_p1;
z31 = nq_p1 + (u32)4U;
d0 = dc;
c0 = dc + (u32)4U;
fadd(c0, x3, z31);
fsub(d0, x3, z31);
fmul2(dc, dc, ab, tmp2);
fadd(x3, d0, c0);
fsub(z31, d0, c0);
a1 = tmp1;
b1 = tmp1 + (u32)4U;
d = tmp1 + (u32)8U;
c = tmp1 + (u32)12U;
ab1 = tmp1;
dc1 = tmp1 + (u32)8U;
fsqr2(dc1, ab1, tmp2);
fsqr2(nq_p1, nq_p1, tmp2);
a1[0U] = c[0U];
a1[1U] = c[1U];
a1[2U] = c[2U];
a1[3U] = c[3U];
fsub(c, d, c);
fmul_scalar(b1, c, (u64)121665U);
fadd(b1, b1, d);
fmul2(nq, dc1, ab1, tmp2);
fmul(z3, z3, x1, tmp2);
}
static void point_double(u64 *nq, u64 *tmp1, u64 *tmp2)
{
u64 *x2 = nq;
u64 *z2 = nq + (u32)4U;
u64 *a = tmp1;
u64 *b = tmp1 + (u32)4U;
u64 *d = tmp1 + (u32)8U;
u64 *c = tmp1 + (u32)12U;
u64 *ab = tmp1;
u64 *dc = tmp1 + (u32)8U;
fadd(a, x2, z2);
fsub(b, x2, z2);
fsqr2(dc, ab, tmp2);
a[0U] = c[0U];
a[1U] = c[1U];
a[2U] = c[2U];
a[3U] = c[3U];
fsub(c, d, c);
fmul_scalar(b, c, (u64)121665U);
fadd(b, b, d);
fmul2(nq, dc, ab, tmp2);
}
static void montgomery_ladder(u64 *out, const u8 *key, u64 *init1)
{
u64 tmp2[16U] = { 0U };
u64 p01_tmp1_swap[33U] = { 0U };
u64 *p0 = p01_tmp1_swap;
u64 *p01 = p01_tmp1_swap;
u64 *p03 = p01;
u64 *p11 = p01 + (u32)8U;
u64 *x0;
u64 *z0;
u64 *p01_tmp1;
u64 *p01_tmp11;
u64 *nq10;
u64 *nq_p11;
u64 *swap1;
u64 sw0;
u64 *nq1;
u64 *tmp1;
memcpy(p11, init1, (u32)8U * sizeof(init1[0U]));
x0 = p03;
z0 = p03 + (u32)4U;
x0[0U] = (u64)1U;
x0[1U] = (u64)0U;
x0[2U] = (u64)0U;
x0[3U] = (u64)0U;
z0[0U] = (u64)0U;
z0[1U] = (u64)0U;
z0[2U] = (u64)0U;
z0[3U] = (u64)0U;
p01_tmp1 = p01_tmp1_swap;
p01_tmp11 = p01_tmp1_swap;
nq10 = p01_tmp1_swap;
nq_p11 = p01_tmp1_swap + (u32)8U;
swap1 = p01_tmp1_swap + (u32)32U;
cswap2((u64)1U, nq10, nq_p11);
point_add_and_double(init1, p01_tmp11, tmp2);
swap1[0U] = (u64)1U;
{
u32 i;
for (i = (u32)0U; i < (u32)251U; i = i + (u32)1U) {
u64 *p01_tmp12 = p01_tmp1_swap;
u64 *swap2 = p01_tmp1_swap + (u32)32U;
u64 *nq2 = p01_tmp12;
u64 *nq_p12 = p01_tmp12 + (u32)8U;
u64 bit = (u64)(key[((u32)253U - i) / (u32)8U] >> ((u32)253U - i) % (u32)8U & (u8)1U);
u64 sw = swap2[0U] ^ bit;
cswap2(sw, nq2, nq_p12);
point_add_and_double(init1, p01_tmp12, tmp2);
swap2[0U] = bit;
}
}
sw0 = swap1[0U];
cswap2(sw0, nq10, nq_p11);
nq1 = p01_tmp1;
tmp1 = p01_tmp1 + (u32)16U;
point_double(nq1, tmp1, tmp2);
point_double(nq1, tmp1, tmp2);
point_double(nq1, tmp1, tmp2);
memcpy(out, p0, (u32)8U * sizeof(p0[0U]));
memzero_explicit(tmp2, sizeof(tmp2));
memzero_explicit(p01_tmp1_swap, sizeof(p01_tmp1_swap));
}
static void fsquare_times(u64 *o, const u64 *inp, u64 *tmp, u32 n1)
{
u32 i;
fsqr(o, inp, tmp);
for (i = (u32)0U; i < n1 - (u32)1U; i = i + (u32)1U)
fsqr(o, o, tmp);
}
static void finv(u64 *o, const u64 *i, u64 *tmp)
{
u64 t1[16U] = { 0U };
u64 *a0 = t1;
u64 *b = t1 + (u32)4U;
u64 *c = t1 + (u32)8U;
u64 *t00 = t1 + (u32)12U;
u64 *tmp1 = tmp;
u64 *a;
u64 *t0;
fsquare_times(a0, i, tmp1, (u32)1U);
fsquare_times(t00, a0, tmp1, (u32)2U);
fmul(b, t00, i, tmp);
fmul(a0, b, a0, tmp);
fsquare_times(t00, a0, tmp1, (u32)1U);
fmul(b, t00, b, tmp);
fsquare_times(t00, b, tmp1, (u32)5U);
fmul(b, t00, b, tmp);
fsquare_times(t00, b, tmp1, (u32)10U);
fmul(c, t00, b, tmp);
fsquare_times(t00, c, tmp1, (u32)20U);
fmul(t00, t00, c, tmp);
fsquare_times(t00, t00, tmp1, (u32)10U);
fmul(b, t00, b, tmp);
fsquare_times(t00, b, tmp1, (u32)50U);
fmul(c, t00, b, tmp);
fsquare_times(t00, c, tmp1, (u32)100U);
fmul(t00, t00, c, tmp);
fsquare_times(t00, t00, tmp1, (u32)50U);
fmul(t00, t00, b, tmp);
fsquare_times(t00, t00, tmp1, (u32)5U);
a = t1;
t0 = t1 + (u32)12U;
fmul(o, t0, a, tmp);
}
static void store_felem(u64 *b, u64 *f)
{
u64 f30 = f[3U];
u64 top_bit0 = f30 >> (u32)63U;
u64 carry0;
u64 f31;
u64 top_bit;
u64 carry;
u64 f0;
u64 f1;
u64 f2;
u64 f3;
u64 m0;
u64 m1;
u64 m2;
u64 m3;
u64 mask;
u64 f0_;
u64 f1_;
u64 f2_;
u64 f3_;
u64 o0;
u64 o1;
u64 o2;
u64 o3;
f[3U] = f30 & (u64)0x7fffffffffffffffU;
carry0 = add_scalar(f, f, (u64)19U * top_bit0);
f31 = f[3U];
top_bit = f31 >> (u32)63U;
f[3U] = f31 & (u64)0x7fffffffffffffffU;
carry = add_scalar(f, f, (u64)19U * top_bit);
f0 = f[0U];
f1 = f[1U];
f2 = f[2U];
f3 = f[3U];
m0 = gte_mask(f0, (u64)0xffffffffffffffedU);
m1 = eq_mask(f1, (u64)0xffffffffffffffffU);
m2 = eq_mask(f2, (u64)0xffffffffffffffffU);
m3 = eq_mask(f3, (u64)0x7fffffffffffffffU);
mask = ((m0 & m1) & m2) & m3;
f0_ = f0 - (mask & (u64)0xffffffffffffffedU);
f1_ = f1 - (mask & (u64)0xffffffffffffffffU);
f2_ = f2 - (mask & (u64)0xffffffffffffffffU);
f3_ = f3 - (mask & (u64)0x7fffffffffffffffU);
o0 = f0_;
o1 = f1_;
o2 = f2_;
o3 = f3_;
b[0U] = o0;
b[1U] = o1;
b[2U] = o2;
b[3U] = o3;
}
static void encode_point(u8 *o, const u64 *i)
{
const u64 *x = i;
const u64 *z = i + (u32)4U;
u64 tmp[4U] = { 0U };
u64 tmp_w[16U] = { 0U };
finv(tmp, z, tmp_w);
fmul(tmp, tmp, x, tmp_w);
store_felem((u64 *)o, tmp);
}
static void curve25519_ever64(u8 *out, const u8 *priv, const u8 *pub)
{
u64 init1[8U] = { 0U };
u64 tmp[4U] = { 0U };
u64 tmp3;
u64 *x;
u64 *z;
{
u32 i;
for (i = (u32)0U; i < (u32)4U; i = i + (u32)1U) {
u64 *os = tmp;
const u8 *bj = pub + i * (u32)8U;
u64 u = *(u64 *)bj;
u64 r = u;
u64 x0 = r;
os[i] = x0;
}
}
tmp3 = tmp[3U];
tmp[3U] = tmp3 & (u64)0x7fffffffffffffffU;
x = init1;
z = init1 + (u32)4U;
z[0U] = (u64)1U;
z[1U] = (u64)0U;
z[2U] = (u64)0U;
z[3U] = (u64)0U;
x[0U] = tmp[0U];
x[1U] = tmp[1U];
x[2U] = tmp[2U];
x[3U] = tmp[3U];
montgomery_ladder(init1, priv, init1);
encode_point(out, init1);
}
/* The below constants were generated using this sage script:
*
* #!/usr/bin/env sage
* import sys
* from sage.all import *
* def limbs(n):
* n = int(n)
* l = ((n >> 0) % 2^64, (n >> 64) % 2^64, (n >> 128) % 2^64, (n >> 192) % 2^64)
* return "0x%016xULL, 0x%016xULL, 0x%016xULL, 0x%016xULL" % l
* ec = EllipticCurve(GF(2^255 - 19), [0, 486662, 0, 1, 0])
* p_minus_s = (ec.lift_x(9) - ec.lift_x(1))[0]
* print("static const u64 p_minus_s[] = { %s };\n" % limbs(p_minus_s))
* print("static const u64 table_ladder[] = {")
* p = ec.lift_x(9)
* for i in range(252):
* l = (p[0] + p[2]) / (p[0] - p[2])
* print(("\t%s" + ("," if i != 251 else "")) % limbs(l))
* p = p * 2
* print("};")
*
*/
static const u64 p_minus_s[] = { 0x816b1e0137d48290ULL, 0x440f6a51eb4d1207ULL, 0x52385f46dca2b71dULL, 0x215132111d8354cbULL };
static const u64 table_ladder[] = {
0xfffffffffffffff3ULL, 0xffffffffffffffffULL, 0xffffffffffffffffULL, 0x5fffffffffffffffULL,
0x6b8220f416aafe96ULL, 0x82ebeb2b4f566a34ULL, 0xd5a9a5b075a5950fULL, 0x5142b2cf4b2488f4ULL,
0x6aaebc750069680cULL, 0x89cf7820a0f99c41ULL, 0x2a58d9183b56d0f4ULL, 0x4b5aca80e36011a4ULL,
0x329132348c29745dULL, 0xf4a2e616e1642fd7ULL, 0x1e45bb03ff67bc34ULL, 0x306912d0f42a9b4aULL,
0xff886507e6af7154ULL, 0x04f50e13dfeec82fULL, 0xaa512fe82abab5ceULL, 0x174e251a68d5f222ULL,
0xcf96700d82028898ULL, 0x1743e3370a2c02c5ULL, 0x379eec98b4e86eaaULL, 0x0c59888a51e0482eULL,
0xfbcbf1d699b5d189ULL, 0xacaef0d58e9fdc84ULL, 0xc1c20d06231f7614ULL, 0x2938218da274f972ULL,
0xf6af49beff1d7f18ULL, 0xcc541c22387ac9c2ULL, 0x96fcc9ef4015c56bULL, 0x69c1627c690913a9ULL,
0x7a86fd2f4733db0eULL, 0xfdb8c4f29e087de9ULL, 0x095e4b1a8ea2a229ULL, 0x1ad7a7c829b37a79ULL,
0x342d89cad17ea0c0ULL, 0x67bedda6cced2051ULL, 0x19ca31bf2bb42f74ULL, 0x3df7b4c84980acbbULL,
0xa8c6444dc80ad883ULL, 0xb91e440366e3ab85ULL, 0xc215cda00164f6d8ULL, 0x3d867c6ef247e668ULL,
0xc7dd582bcc3e658cULL, 0xfd2c4748ee0e5528ULL, 0xa0fd9b95cc9f4f71ULL, 0x7529d871b0675ddfULL,
0xb8f568b42d3cbd78ULL, 0x1233011b91f3da82ULL, 0x2dce6ccd4a7c3b62ULL, 0x75e7fc8e9e498603ULL,
0x2f4f13f1fcd0b6ecULL, 0xf1a8ca1f29ff7a45ULL, 0xc249c1a72981e29bULL, 0x6ebe0dbb8c83b56aULL,
0x7114fa8d170bb222ULL, 0x65a2dcd5bf93935fULL, 0xbdc41f68b59c979aULL, 0x2f0eef79a2ce9289ULL,
0x42ecbf0c083c37ceULL, 0x2930bc09ec496322ULL, 0xf294b0c19cfeac0dULL, 0x3780aa4bedfabb80ULL,
0x56c17d3e7cead929ULL, 0xe7cb4beb2e5722c5ULL, 0x0ce931732dbfe15aULL, 0x41b883c7621052f8ULL,
0xdbf75ca0c3d25350ULL, 0x2936be086eb1e351ULL, 0xc936e03cb4a9b212ULL, 0x1d45bf82322225aaULL,
0xe81ab1036a024cc5ULL, 0xe212201c304c9a72ULL, 0xc5d73fba6832b1fcULL, 0x20ffdb5a4d839581ULL,
0xa283d367be5d0fadULL, 0x6c2b25ca8b164475ULL, 0x9d4935467caaf22eULL, 0x5166408eee85ff49ULL,
0x3c67baa2fab4e361ULL, 0xb3e433c67ef35cefULL, 0x5259729241159b1cULL, 0x6a621892d5b0ab33ULL,
0x20b74a387555cdcbULL, 0x532aa10e1208923fULL, 0xeaa17b7762281dd1ULL, 0x61ab3443f05c44bfULL,
0x257a6c422324def8ULL, 0x131c6c1017e3cf7fULL, 0x23758739f630a257ULL, 0x295a407a01a78580ULL,
0xf8c443246d5da8d9ULL, 0x19d775450c52fa5dULL, 0x2afcfc92731bf83dULL, 0x7d10c8e81b2b4700ULL,
0xc8e0271f70baa20bULL, 0x993748867ca63957ULL, 0x5412efb3cb7ed4bbULL, 0x3196d36173e62975ULL,
0xde5bcad141c7dffcULL, 0x47cc8cd2b395c848ULL, 0xa34cd942e11af3cbULL, 0x0256dbf2d04ecec2ULL,
0x875ab7e94b0e667fULL, 0xcad4dd83c0850d10ULL, 0x47f12e8f4e72c79fULL, 0x5f1a87bb8c85b19bULL,
0x7ae9d0b6437f51b8ULL, 0x12c7ce5518879065ULL, 0x2ade09fe5cf77aeeULL, 0x23a05a2f7d2c5627ULL,
0x5908e128f17c169aULL, 0xf77498dd8ad0852dULL, 0x74b4c4ceab102f64ULL, 0x183abadd10139845ULL,
0xb165ba8daa92aaacULL, 0xd5c5ef9599386705ULL, 0xbe2f8f0cf8fc40d1ULL, 0x2701e635ee204514ULL,
0x629fa80020156514ULL, 0xf223868764a8c1ceULL, 0x5b894fff0b3f060eULL, 0x60d9944cf708a3faULL,
0xaeea001a1c7a201fULL, 0xebf16a633ee2ce63ULL, 0x6f7709594c7a07e1ULL, 0x79b958150d0208cbULL,
0x24b55e5301d410e7ULL, 0xe3a34edff3fdc84dULL, 0xd88768e4904032d8ULL, 0x131384427b3aaeecULL,
0x8405e51286234f14ULL, 0x14dc4739adb4c529ULL, 0xb8a2b5b250634ffdULL, 0x2fe2a94ad8a7ff93ULL,
0xec5c57efe843faddULL, 0x2843ce40f0bb9918ULL, 0xa4b561d6cf3d6305ULL, 0x743629bde8fb777eULL,
0x343edd46bbaf738fULL, 0xed981828b101a651ULL, 0xa401760b882c797aULL, 0x1fc223e28dc88730ULL,
0x48604e91fc0fba0eULL, 0xb637f78f052c6fa4ULL, 0x91ccac3d09e9239cULL, 0x23f7eed4437a687cULL,
0x5173b1118d9bd800ULL, 0x29d641b63189d4a7ULL, 0xfdbf177988bbc586ULL, 0x2959894fcad81df5ULL,
0xaebc8ef3b4bbc899ULL, 0x4148995ab26992b9ULL, 0x24e20b0134f92cfbULL, 0x40d158894a05dee8ULL,
0x46b00b1185af76f6ULL, 0x26bac77873187a79ULL, 0x3dc0bf95ab8fff5fULL, 0x2a608bd8945524d7ULL,
0x26449588bd446302ULL, 0x7c4bc21c0388439cULL, 0x8e98a4f383bd11b2ULL, 0x26218d7bc9d876b9ULL,
0xe3081542997c178aULL, 0x3c2d29a86fb6606fULL, 0x5c217736fa279374ULL, 0x7dde05734afeb1faULL,
0x3bf10e3906d42babULL, 0xe4f7803e1980649cULL, 0xe6053bf89595bf7aULL, 0x394faf38da245530ULL,
0x7a8efb58896928f4ULL, 0xfbc778e9cc6a113cULL, 0x72670ce330af596fULL, 0x48f222a81d3d6cf7ULL,
0xf01fce410d72caa7ULL, 0x5a20ecc7213b5595ULL, 0x7bc21165c1fa1483ULL, 0x07f89ae31da8a741ULL,
0x05d2c2b4c6830ff9ULL, 0xd43e330fc6316293ULL, 0xa5a5590a96d3a904ULL, 0x705edb91a65333b6ULL,
0x048ee15e0bb9a5f7ULL, 0x3240cfca9e0aaf5dULL, 0x8f4b71ceedc4a40bULL, 0x621c0da3de544a6dULL,
0x92872836a08c4091ULL, 0xce8375b010c91445ULL, 0x8a72eb524f276394ULL, 0x2667fcfa7ec83635ULL,
0x7f4c173345e8752aULL, 0x061b47feee7079a5ULL, 0x25dd9afa9f86ff34ULL, 0x3780cef5425dc89cULL,
0x1a46035a513bb4e9ULL, 0x3e1ef379ac575adaULL, 0xc78c5f1c5fa24b50ULL, 0x321a967634fd9f22ULL,
0x946707b8826e27faULL, 0x3dca84d64c506fd0ULL, 0xc189218075e91436ULL, 0x6d9284169b3b8484ULL,
0x3a67e840383f2ddfULL, 0x33eec9a30c4f9b75ULL, 0x3ec7c86fa783ef47ULL, 0x26ec449fbac9fbc4ULL,
0x5c0f38cba09b9e7dULL, 0x81168cc762a3478cULL, 0x3e23b0d306fc121cULL, 0x5a238aa0a5efdcddULL,
0x1ba26121c4ea43ffULL, 0x36f8c77f7c8832b5ULL, 0x88fbea0b0adcf99aULL, 0x5ca9938ec25bebf9ULL,
0xd5436a5e51fccda0ULL, 0x1dbc4797c2cd893bULL, 0x19346a65d3224a08ULL, 0x0f5034e49b9af466ULL,
0xf23c3967a1e0b96eULL, 0xe58b08fa867a4d88ULL, 0xfb2fabc6a7341679ULL, 0x2a75381eb6026946ULL,
0xc80a3be4c19420acULL, 0x66b1f6c681f2b6dcULL, 0x7cf7036761e93388ULL, 0x25abbbd8a660a4c4ULL,
0x91ea12ba14fd5198ULL, 0x684950fc4a3cffa9ULL, 0xf826842130f5ad28ULL, 0x3ea988f75301a441ULL,
0xc978109a695f8c6fULL, 0x1746eb4a0530c3f3ULL, 0x444d6d77b4459995ULL, 0x75952b8c054e5cc7ULL,
0xa3703f7915f4d6aaULL, 0x66c346202f2647d8ULL, 0xd01469df811d644bULL, 0x77fea47d81a5d71fULL,
0xc5e9529ef57ca381ULL, 0x6eeeb4b9ce2f881aULL, 0xb6e91a28e8009bd6ULL, 0x4b80be3e9afc3fecULL,
0x7e3773c526aed2c5ULL, 0x1b4afcb453c9a49dULL, 0xa920bdd7baffb24dULL, 0x7c54699f122d400eULL,
0xef46c8e14fa94bc8ULL, 0xe0b074ce2952ed5eULL, 0xbea450e1dbd885d5ULL, 0x61b68649320f712cULL,
0x8a485f7309ccbdd1ULL, 0xbd06320d7d4d1a2dULL, 0x25232973322dbef4ULL, 0x445dc4758c17f770ULL,
0xdb0434177cc8933cULL, 0xed6fe82175ea059fULL, 0x1efebefdc053db34ULL, 0x4adbe867c65daf99ULL,
0x3acd71a2a90609dfULL, 0xe5e991856dd04050ULL, 0x1ec69b688157c23cULL, 0x697427f6885cfe4dULL,
0xd7be7b9b65e1a851ULL, 0xa03d28d522c536ddULL, 0x28399d658fd2b645ULL, 0x49e5b7e17c2641e1ULL,
0x6f8c3a98700457a4ULL, 0x5078f0a25ebb6778ULL, 0xd13c3ccbc382960fULL, 0x2e003258a7df84b1ULL,
0x8ad1f39be6296a1cULL, 0xc1eeaa652a5fbfb2ULL, 0x33ee0673fd26f3cbULL, 0x59256173a69d2cccULL,
0x41ea07aa4e18fc41ULL, 0xd9fc19527c87a51eULL, 0xbdaacb805831ca6fULL, 0x445b652dc916694fULL,
0xce92a3a7f2172315ULL, 0x1edc282de11b9964ULL, 0xa1823aafe04c314aULL, 0x790a2d94437cf586ULL,
0x71c447fb93f6e009ULL, 0x8922a56722845276ULL, 0xbf70903b204f5169ULL, 0x2f7a89891ba319feULL,
0x02a08eb577e2140cULL, 0xed9a4ed4427bdcf4ULL, 0x5253ec44e4323cd1ULL, 0x3e88363c14e9355bULL,
0xaa66c14277110b8cULL, 0x1ae0391610a23390ULL, 0x2030bd12c93fc2a2ULL, 0x3ee141579555c7abULL,
0x9214de3a6d6e7d41ULL, 0x3ccdd88607f17efeULL, 0x674f1288f8e11217ULL, 0x5682250f329f93d0ULL,
0x6cf00b136d2e396eULL, 0x6e4cf86f1014debfULL, 0x5930b1b5bfcc4e83ULL, 0x047069b48aba16b6ULL,
0x0d4ce4ab69b20793ULL, 0xb24db91a97d0fb9eULL, 0xcdfa50f54e00d01dULL, 0x221b1085368bddb5ULL,
0xe7e59468b1e3d8d2ULL, 0x53c56563bd122f93ULL, 0xeee8a903e0663f09ULL, 0x61efa662cbbe3d42ULL,
0x2cf8ddddde6eab2aULL, 0x9bf80ad51435f231ULL, 0x5deadacec9f04973ULL, 0x29275b5d41d29b27ULL,
0xcfde0f0895ebf14fULL, 0xb9aab96b054905a7ULL, 0xcae80dd9a1c420fdULL, 0x0a63bf2f1673bbc7ULL,
0x092f6e11958fbc8cULL, 0x672a81e804822fadULL, 0xcac8351560d52517ULL, 0x6f3f7722c8f192f8ULL,
0xf8ba90ccc2e894b7ULL, 0x2c7557a438ff9f0dULL, 0x894d1d855ae52359ULL, 0x68e122157b743d69ULL,
0xd87e5570cfb919f3ULL, 0x3f2cdecd95798db9ULL, 0x2121154710c0a2ceULL, 0x3c66a115246dc5b2ULL,
0xcbedc562294ecb72ULL, 0xba7143c36a280b16ULL, 0x9610c2efd4078b67ULL, 0x6144735d946a4b1eULL,
0x536f111ed75b3350ULL, 0x0211db8c2041d81bULL, 0xf93cb1000e10413cULL, 0x149dfd3c039e8876ULL,
0xd479dde46b63155bULL, 0xb66e15e93c837976ULL, 0xdafde43b1f13e038ULL, 0x5fafda1a2e4b0b35ULL,
0x3600bbdf17197581ULL, 0x3972050bbe3cd2c2ULL, 0x5938906dbdd5be86ULL, 0x34fce5e43f9b860fULL,
0x75a8a4cd42d14d02ULL, 0x828dabc53441df65ULL, 0x33dcabedd2e131d3ULL, 0x3ebad76fb814d25fULL,
0xd4906f566f70e10fULL, 0x5d12f7aa51690f5aULL, 0x45adb16e76cefcf2ULL, 0x01f768aead232999ULL,
0x2b6cc77b6248febdULL, 0x3cd30628ec3aaffdULL, 0xce1c0b80d4ef486aULL, 0x4c3bff2ea6f66c23ULL,
0x3f2ec4094aeaeb5fULL, 0x61b19b286e372ca7ULL, 0x5eefa966de2a701dULL, 0x23b20565de55e3efULL,
0xe301ca5279d58557ULL, 0x07b2d4ce27c2874fULL, 0xa532cd8a9dcf1d67ULL, 0x2a52fee23f2bff56ULL,
0x8624efb37cd8663dULL, 0xbbc7ac20ffbd7594ULL, 0x57b85e9c82d37445ULL, 0x7b3052cb86a6ec66ULL,
0x3482f0ad2525e91eULL, 0x2cb68043d28edca0ULL, 0xaf4f6d052e1b003aULL, 0x185f8c2529781b0aULL,
0xaa41de5bd80ce0d6ULL, 0x9407b2416853e9d6ULL, 0x563ec36e357f4c3aULL, 0x4cc4b8dd0e297bceULL,
0xa2fc1a52ffb8730eULL, 0x1811f16e67058e37ULL, 0x10f9a366cddf4ee1ULL, 0x72f4a0c4a0b9f099ULL,
0x8c16c06f663f4ea7ULL, 0x693b3af74e970fbaULL, 0x2102e7f1d69ec345ULL, 0x0ba53cbc968a8089ULL,
0xca3d9dc7fea15537ULL, 0x4c6824bb51536493ULL, 0xb9886314844006b1ULL, 0x40d2a72ab454cc60ULL,
0x5936a1b712570975ULL, 0x91b9d648debda657ULL, 0x3344094bb64330eaULL, 0x006ba10d12ee51d0ULL,
0x19228468f5de5d58ULL, 0x0eb12f4c38cc05b0ULL, 0xa1039f9dd5601990ULL, 0x4502d4ce4fff0e0bULL,
0xeb2054106837c189ULL, 0xd0f6544c6dd3b93cULL, 0x40727064c416d74fULL, 0x6e15c6114b502ef0ULL,
0x4df2a398cfb1a76bULL, 0x11256c7419f2f6b1ULL, 0x4a497962066e6043ULL, 0x705b3aab41355b44ULL,
0x365ef536d797b1d8ULL, 0x00076bd622ddf0dbULL, 0x3bbf33b0e0575a88ULL, 0x3777aa05c8e4ca4dULL,
0x392745c85578db5fULL, 0x6fda4149dbae5ae2ULL, 0xb1f0b00b8adc9867ULL, 0x09963437d36f1da3ULL,
0x7e824e90a5dc3853ULL, 0xccb5f6641f135cbdULL, 0x6736d86c87ce8fccULL, 0x625f3ce26604249fULL,
0xaf8ac8059502f63fULL, 0x0c05e70a2e351469ULL, 0x35292e9c764b6305ULL, 0x1a394360c7e23ac3ULL,
0xd5c6d53251183264ULL, 0x62065abd43c2b74fULL, 0xb5fbf5d03b973f9bULL, 0x13a3da3661206e5eULL,
0xc6bd5837725d94e5ULL, 0x18e30912205016c5ULL, 0x2088ce1570033c68ULL, 0x7fba1f495c837987ULL,
0x5a8c7423f2f9079dULL, 0x1735157b34023fc5ULL, 0xe4f9b49ad2fab351ULL, 0x6691ff72c878e33cULL,
0x122c2adedc5eff3eULL, 0xf8dd4bf1d8956cf4ULL, 0xeb86205d9e9e5bdaULL, 0x049b92b9d975c743ULL,
0xa5379730b0f6c05aULL, 0x72a0ffacc6f3a553ULL, 0xb0032c34b20dcd6dULL, 0x470e9dbc88d5164aULL,
0xb19cf10ca237c047ULL, 0xb65466711f6c81a2ULL, 0xb3321bd16dd80b43ULL, 0x48c14f600c5fbe8eULL,
0x66451c264aa6c803ULL, 0xb66e3904a4fa7da6ULL, 0xd45f19b0b3128395ULL, 0x31602627c3c9bc10ULL,
0x3120dc4832e4e10dULL, 0xeb20c46756c717f7ULL, 0x00f52e3f67280294ULL, 0x566d4fc14730c509ULL,
0x7e3a5d40fd837206ULL, 0xc1e926dc7159547aULL, 0x216730fba68d6095ULL, 0x22e8c3843f69cea7ULL,
0x33d074e8930e4b2bULL, 0xb6e4350e84d15816ULL, 0x5534c26ad6ba2365ULL, 0x7773c12f89f1f3f3ULL,
0x8cba404da57962aaULL, 0x5b9897a81999ce56ULL, 0x508e862f121692fcULL, 0x3a81907fa093c291ULL,
0x0dded0ff4725a510ULL, 0x10d8cc10673fc503ULL, 0x5b9d151c9f1f4e89ULL, 0x32a5c1d5cb09a44cULL,
0x1e0aa442b90541fbULL, 0x5f85eb7cc1b485dbULL, 0xbee595ce8a9df2e5ULL, 0x25e496c722422236ULL,
0x5edf3c46cd0fe5b9ULL, 0x34e75a7ed2a43388ULL, 0xe488de11d761e352ULL, 0x0e878a01a085545cULL,
0xba493c77e021bb04ULL, 0x2b4d1843c7df899aULL, 0x9ea37a487ae80d67ULL, 0x67a9958011e41794ULL,
0x4b58051a6697b065ULL, 0x47e33f7d8d6ba6d4ULL, 0xbb4da8d483ca46c1ULL, 0x68becaa181c2db0dULL,
0x8d8980e90b989aa5ULL, 0xf95eb14a2c93c99bULL, 0x51c6c7c4796e73a2ULL, 0x6e228363b5efb569ULL,
0xc6bbc0b02dd624c8ULL, 0x777eb47dec8170eeULL, 0x3cde15a004cfafa9ULL, 0x1dc6bc087160bf9bULL,
0x2e07e043eec34002ULL, 0x18e9fc677a68dc7fULL, 0xd8da03188bd15b9aULL, 0x48fbc3bb00568253ULL,
0x57547d4cfb654ce1ULL, 0xd3565b82a058e2adULL, 0xf63eaf0bbf154478ULL, 0x47531ef114dfbb18ULL,
0xe1ec630a4278c587ULL, 0x5507d546ca8e83f3ULL, 0x85e135c63adc0c2bULL, 0x0aa7efa85682844eULL,
0x72691ba8b3e1f615ULL, 0x32b4e9701fbe3ffaULL, 0x97b6d92e39bb7868ULL, 0x2cfe53dea02e39e8ULL,
0x687392cd85cd52b0ULL, 0x27ff66c910e29831ULL, 0x97134556a9832d06ULL, 0x269bb0360a84f8a0ULL,
0x706e55457643f85cULL, 0x3734a48c9b597d1bULL, 0x7aee91e8c6efa472ULL, 0x5cd6abc198a9d9e0ULL,
0x0e04de06cb3ce41aULL, 0xd8c6eb893402e138ULL, 0x904659bb686e3772ULL, 0x7215c371746ba8c8ULL,
0xfd12a97eeae4a2d9ULL, 0x9514b7516394f2c5ULL, 0x266fd5809208f294ULL, 0x5c847085619a26b9ULL,
0x52985410fed694eaULL, 0x3c905b934a2ed254ULL, 0x10bb47692d3be467ULL, 0x063b3d2d69e5e9e1ULL,
0x472726eedda57debULL, 0xefb6c4ae10f41891ULL, 0x2b1641917b307614ULL, 0x117c554fc4f45b7cULL,
0xc07cf3118f9d8812ULL, 0x01dbd82050017939ULL, 0xd7e803f4171b2827ULL, 0x1015e87487d225eaULL,
0xc58de3fed23acc4dULL, 0x50db91c294a7be2dULL, 0x0b94d43d1c9cf457ULL, 0x6b1640fa6e37524aULL,
0x692f346c5fda0d09ULL, 0x200b1c59fa4d3151ULL, 0xb8c46f760777a296ULL, 0x4b38395f3ffdfbcfULL,
0x18d25e00be54d671ULL, 0x60d50582bec8aba6ULL, 0x87ad8f263b78b982ULL, 0x50fdf64e9cda0432ULL,
0x90f567aac578dcf0ULL, 0xef1e9b0ef2a3133bULL, 0x0eebba9242d9de71ULL, 0x15473c9bf03101c7ULL,
0x7c77e8ae56b78095ULL, 0xb678e7666e6f078eULL, 0x2da0b9615348ba1fULL, 0x7cf931c1ff733f0bULL,
0x26b357f50a0a366cULL, 0xe9708cf42b87d732ULL, 0xc13aeea5f91cb2c0ULL, 0x35d90c991143bb4cULL,
0x47c1c404a9a0d9dcULL, 0x659e58451972d251ULL, 0x3875a8c473b38c31ULL, 0x1fbd9ed379561f24ULL,
0x11fabc6fd41ec28dULL, 0x7ef8dfe3cd2a2dcaULL, 0x72e73b5d8c404595ULL, 0x6135fa4954b72f27ULL,
0xccfc32a2de24b69cULL, 0x3f55698c1f095d88ULL, 0xbe3350ed5ac3f929ULL, 0x5e9bf806ca477eebULL,
0xe9ce8fb63c309f68ULL, 0x5376f63565e1f9f4ULL, 0xd1afcfb35a6393f1ULL, 0x6632a1ede5623506ULL,
0x0b7d6c390c2ded4cULL, 0x56cb3281df04cb1fULL, 0x66305a1249ecc3c7ULL, 0x5d588b60a38ca72aULL,
0xa6ecbf78e8e5f42dULL, 0x86eeb44b3c8a3eecULL, 0xec219c48fbd21604ULL, 0x1aaf1af517c36731ULL,
0xc306a2836769bde7ULL, 0x208280622b1e2adbULL, 0x8027f51ffbff94a6ULL, 0x76cfa1ce1124f26bULL,
0x18eb00562422abb6ULL, 0xf377c4d58f8c29c3ULL, 0x4dbbc207f531561aULL, 0x0253b7f082128a27ULL,
0x3d1f091cb62c17e0ULL, 0x4860e1abd64628a9ULL, 0x52d17436309d4253ULL, 0x356f97e13efae576ULL,
0xd351e11aa150535bULL, 0x3e6b45bb1dd878ccULL, 0x0c776128bed92c98ULL, 0x1d34ae93032885b8ULL,
0x4ba0488ca85ba4c3ULL, 0x985348c33c9ce6ceULL, 0x66124c6f97bda770ULL, 0x0f81a0290654124aULL,
0x9ed09ca6569b86fdULL, 0x811009fd18af9a2dULL, 0xff08d03f93d8c20aULL, 0x52a148199faef26bULL,
0x3e03f9dc2d8d1b73ULL, 0x4205801873961a70ULL, 0xc0d987f041a35970ULL, 0x07aa1f15a1c0d549ULL,
0xdfd46ce08cd27224ULL, 0x6d0a024f934e4239ULL, 0x808a7a6399897b59ULL, 0x0a4556e9e13d95a2ULL,
0xd21a991fe9c13045ULL, 0x9b0e8548fe7751b8ULL, 0x5da643cb4bf30035ULL, 0x77db28d63940f721ULL,
0xfc5eeb614adc9011ULL, 0x5229419ae8c411ebULL, 0x9ec3e7787d1dcf74ULL, 0x340d053e216e4cb5ULL,
0xcac7af39b48df2b4ULL, 0xc0faec2871a10a94ULL, 0x140a69245ca575edULL, 0x0cf1c37134273a4cULL,
0xc8ee306ac224b8a5ULL, 0x57eaee7ccb4930b0ULL, 0xa1e806bdaacbe74fULL, 0x7d9a62742eeb657dULL,
0x9eb6b6ef546c4830ULL, 0x885cca1fddb36e2eULL, 0xe6b9f383ef0d7105ULL, 0x58654fef9d2e0412ULL,
0xa905c4ffbe0e8e26ULL, 0x942de5df9b31816eULL, 0x497d723f802e88e1ULL, 0x30684dea602f408dULL,
0x21e5a278a3e6cb34ULL, 0xaefb6e6f5b151dc4ULL, 0xb30b8e049d77ca15ULL, 0x28c3c9cf53b98981ULL,
0x287fb721556cdd2aULL, 0x0d317ca897022274ULL, 0x7468c7423a543258ULL, 0x4a7f11464eb5642fULL,
0xa237a4774d193aa6ULL, 0xd865986ea92129a1ULL, 0x24c515ecf87c1a88ULL, 0x604003575f39f5ebULL,
0x47b9f189570a9b27ULL, 0x2b98cede465e4b78ULL, 0x026df551dbb85c20ULL, 0x74fcd91047e21901ULL,
0x13e2a90a23c1bfa3ULL, 0x0cb0074e478519f6ULL, 0x5ff1cbbe3af6cf44ULL, 0x67fe5438be812dbeULL,
0xd13cf64fa40f05b0ULL, 0x054dfb2f32283787ULL, 0x4173915b7f0d2aeaULL, 0x482f144f1f610d4eULL,
0xf6210201b47f8234ULL, 0x5d0ae1929e70b990ULL, 0xdcd7f455b049567cULL, 0x7e93d0f1f0916f01ULL,
0xdd79cbf18a7db4faULL, 0xbe8391bf6f74c62fULL, 0x027145d14b8291bdULL, 0x585a73ea2cbf1705ULL,
0x485ca03e928a0db2ULL, 0x10fc01a5742857e7ULL, 0x2f482edbd6d551a7ULL, 0x0f0433b5048fdb8aULL,
0x60da2e8dd7dc6247ULL, 0x88b4c9d38cd4819aULL, 0x13033ac001f66697ULL, 0x273b24fe3b367d75ULL,
0xc6e8f66a31b3b9d4ULL, 0x281514a494df49d5ULL, 0xd1726fdfc8b23da7ULL, 0x4b3ae7d103dee548ULL,
0xc6256e19ce4b9d7eULL, 0xff5c5cf186e3c61cULL, 0xacc63ca34b8ec145ULL, 0x74621888fee66574ULL,
0x956f409645290a1eULL, 0xef0bf8e3263a962eULL, 0xed6a50eb5ec2647bULL, 0x0694283a9dca7502ULL,
0x769b963643a2dcd1ULL, 0x42b7c8ea09fc5353ULL, 0x4f002aee13397eabULL, 0x63005e2c19b7d63aULL,
0xca6736da63023beaULL, 0x966c7f6db12a99b7ULL, 0xace09390c537c5e1ULL, 0x0b696063a1aa89eeULL,
0xebb03e97288c56e5ULL, 0x432a9f9f938c8be8ULL, 0xa6a5a93d5b717f71ULL, 0x1a5fb4c3e18f9d97ULL,
0x1c94e7ad1c60cdceULL, 0xee202a43fc02c4a0ULL, 0x8dafe4d867c46a20ULL, 0x0a10263c8ac27b58ULL,
0xd0dea9dfe4432a4aULL, 0x856af87bbe9277c5ULL, 0xce8472acc212c71aULL, 0x6f151b6d9bbb1e91ULL,
0x26776c527ceed56aULL, 0x7d211cb7fbf8faecULL, 0x37ae66a6fd4609ccULL, 0x1f81b702d2770c42ULL,
0x2fb0b057eac58392ULL, 0xe1dd89fe29744e9dULL, 0xc964f8eb17beb4f8ULL, 0x29571073c9a2d41eULL,
0xa948a18981c0e254ULL, 0x2df6369b65b22830ULL, 0xa33eb2d75fcfd3c6ULL, 0x078cd6ec4199a01fULL,
0x4a584a41ad900d2fULL, 0x32142b78e2c74c52ULL, 0x68c4e8338431c978ULL, 0x7f69ea9008689fc2ULL,
0x52f2c81e46a38265ULL, 0xfd78072d04a832fdULL, 0x8cd7d5fa25359e94ULL, 0x4de71b7454cc29d2ULL,
0x42eb60ad1eda6ac9ULL, 0x0aad37dfdbc09c3aULL, 0x81004b71e33cc191ULL, 0x44e6be345122803cULL,
0x03fe8388ba1920dbULL, 0xf5d57c32150db008ULL, 0x49c8c4281af60c29ULL, 0x21edb518de701aeeULL,
0x7fb63e418f06dc99ULL, 0xa4460d99c166d7b8ULL, 0x24dd5248ce520a83ULL, 0x5ec3ad712b928358ULL,
0x15022a5fbd17930fULL, 0xa4f64a77d82570e3ULL, 0x12bc8d6915783712ULL, 0x498194c0fc620abbULL,
0x38a2d9d255686c82ULL, 0x785c6bd9193e21f0ULL, 0xe4d5c81ab24a5484ULL, 0x56307860b2e20989ULL,
0x429d55f78b4d74c4ULL, 0x22f1834643350131ULL, 0x1e60c24598c71fffULL, 0x59f2f014979983efULL,
0x46a47d56eb494a44ULL, 0x3e22a854d636a18eULL, 0xb346e15274491c3bULL, 0x2ceafd4e5390cde7ULL,
0xba8a8538be0d6675ULL, 0x4b9074bb50818e23ULL, 0xcbdab89085d304c3ULL, 0x61a24fe0e56192c4ULL,
0xcb7615e6db525bcbULL, 0xdd7d8c35a567e4caULL, 0xe6b4153acafcdd69ULL, 0x2d668e097f3c9766ULL,
0xa57e7e265ce55ef0ULL, 0x5d9f4e527cd4b967ULL, 0xfbc83606492fd1e5ULL, 0x090d52beb7c3f7aeULL,
0x09b9515a1e7b4d7cULL, 0x1f266a2599da44c0ULL, 0xa1c49548e2c55504ULL, 0x7ef04287126f15ccULL,
0xfed1659dbd30ef15ULL, 0x8b4ab9eec4e0277bULL, 0x884d6236a5df3291ULL, 0x1fd96ea6bf5cf788ULL,
0x42a161981f190d9aULL, 0x61d849507e6052c1ULL, 0x9fe113bf285a2cd5ULL, 0x7c22d676dbad85d8ULL,
0x82e770ed2bfbd27dULL, 0x4c05b2ece996f5a5ULL, 0xcd40a9c2b0900150ULL, 0x5895319213d9bf64ULL,
0xe7cc5d703fea2e08ULL, 0xb50c491258e2188cULL, 0xcce30baa48205bf0ULL, 0x537c659ccfa32d62ULL,
0x37b6623a98cfc088ULL, 0xfe9bed1fa4d6aca4ULL, 0x04d29b8e56a8d1b0ULL, 0x725f71c40b519575ULL,
0x28c7f89cd0339ce6ULL, 0x8367b14469ddc18bULL, 0x883ada83a6a1652cULL, 0x585f1974034d6c17ULL,
0x89cfb266f1b19188ULL, 0xe63b4863e7c35217ULL, 0xd88c9da6b4c0526aULL, 0x3e035c9df0954635ULL,
0xdd9d5412fb45de9dULL, 0xdd684532e4cff40dULL, 0x4b5c999b151d671cULL, 0x2d8c2cc811e7f690ULL,
0x7f54be1d90055d40ULL, 0xa464c5df464aaf40ULL, 0x33979624f0e917beULL, 0x2c018dc527356b30ULL,
0xa5415024e330b3d4ULL, 0x73ff3d96691652d3ULL, 0x94ec42c4ef9b59f1ULL, 0x0747201618d08e5aULL,
0x4d6ca48aca411c53ULL, 0x66415f2fcfa66119ULL, 0x9c4dd40051e227ffULL, 0x59810bc09a02f7ebULL,
0x2a7eb171b3dc101dULL, 0x441c5ab99ffef68eULL, 0x32025c9b93b359eaULL, 0x5e8ce0a71e9d112fULL,
0xbfcccb92429503fdULL, 0xd271ba752f095d55ULL, 0x345ead5e972d091eULL, 0x18c8df11a83103baULL,
0x90cd949a9aed0f4cULL, 0xc5d1f4cb6660e37eULL, 0xb8cac52d56c52e0bULL, 0x6e42e400c5808e0dULL,
0xa3b46966eeaefd23ULL, 0x0c4f1f0be39ecdcaULL, 0x189dc8c9d683a51dULL, 0x51f27f054c09351bULL,
0x4c487ccd2a320682ULL, 0x587ea95bb3df1c96ULL, 0xc8ccf79e555cb8e8ULL, 0x547dc829a206d73dULL,
0xb822a6cd80c39b06ULL, 0xe96d54732000d4c6ULL, 0x28535b6f91463b4dULL, 0x228f4660e2486e1dULL,
0x98799538de8d3abfULL, 0x8cd8330045ebca6eULL, 0x79952a008221e738ULL, 0x4322e1a7535cd2bbULL,
0xb114c11819d1801cULL, 0x2016e4d84f3f5ec7ULL, 0xdd0e2df409260f4cULL, 0x5ec362c0ae5f7266ULL,
0xc0462b18b8b2b4eeULL, 0x7cc8d950274d1afbULL, 0xf25f7105436b02d2ULL, 0x43bbf8dcbff9ccd3ULL,
0xb6ad1767a039e9dfULL, 0xb0714da8f69d3583ULL, 0x5e55fa18b42931f5ULL, 0x4ed5558f33c60961ULL,
0x1fe37901c647a5ddULL, 0x593ddf1f8081d357ULL, 0x0249a4fd813fd7a6ULL, 0x69acca274e9caf61ULL,
0x047ba3ea330721c9ULL, 0x83423fc20e7e1ea0ULL, 0x1df4c0af01314a60ULL, 0x09a62dab89289527ULL,
0xa5b325a49cc6cb00ULL, 0xe94b5dc654b56cb6ULL, 0x3be28779adc994a0ULL, 0x4296e8f8ba3a4aadULL,
0x328689761e451eabULL, 0x2e4d598bff59594aULL, 0x49b96853d7a7084aULL, 0x4980a319601420a8ULL,
0x9565b9e12f552c42ULL, 0x8a5318db7100fe96ULL, 0x05c90b4d43add0d7ULL, 0x538b4cd66a5d4edaULL,
0xf4e94fc3e89f039fULL, 0x592c9af26f618045ULL, 0x08a36eb5fd4b9550ULL, 0x25fffaf6c2ed1419ULL,
0x34434459cc79d354ULL, 0xeeecbfb4b1d5476bULL, 0xddeb34a061615d99ULL, 0x5129cecceb64b773ULL,
0xee43215894993520ULL, 0x772f9c7cf14c0b3bULL, 0xd2e2fce306bedad5ULL, 0x715f42b546f06a97ULL,
0x434ecdceda5b5f1aULL, 0x0da17115a49741a9ULL, 0x680bd77c73edad2eULL, 0x487c02354edd9041ULL,
0xb8efeff3a70ed9c4ULL, 0x56a32aa3e857e302ULL, 0xdf3a68bd48a2a5a0ULL, 0x07f650b73176c444ULL,
0xe38b9b1626e0ccb1ULL, 0x79e053c18b09fb36ULL, 0x56d90319c9f94964ULL, 0x1ca941e7ac9ff5c4ULL,
0x49c4df29162fa0bbULL, 0x8488cf3282b33305ULL, 0x95dfda14cabb437dULL, 0x3391f78264d5ad86ULL,
0x729ae06ae2b5095dULL, 0xd58a58d73259a946ULL, 0xe9834262d13921edULL, 0x27fedafaa54bb592ULL,
0xa99dc5b829ad48bbULL, 0x5f025742499ee260ULL, 0x802c8ecd5d7513fdULL, 0x78ceb3ef3f6dd938ULL,
0xc342f44f8a135d94ULL, 0x7b9edb44828cdda3ULL, 0x9436d11a0537cfe7ULL, 0x5064b164ec1ab4c8ULL,
0x7020eccfd37eb2fcULL, 0x1f31ea3ed90d25fcULL, 0x1b930d7bdfa1bb34ULL, 0x5344467a48113044ULL,
0x70073170f25e6dfbULL, 0xe385dc1a50114cc8ULL, 0x2348698ac8fc4f00ULL, 0x2a77a55284dd40d8ULL,
0xfe06afe0c98c6ce4ULL, 0xc235df96dddfd6e4ULL, 0x1428d01e33bf1ed3ULL, 0x785768ec9300bdafULL,
0x9702e57a91deb63bULL, 0x61bdb8bfe5ce8b80ULL, 0x645b426f3d1d58acULL, 0x4804a82227a557bcULL,
0x8e57048ab44d2601ULL, 0x68d6501a4b3a6935ULL, 0xc39c9ec3f9e1c293ULL, 0x4172f257d4de63e2ULL,
0xd368b450330c6401ULL, 0x040d3017418f2391ULL, 0x2c34bb6090b7d90dULL, 0x16f649228fdfd51fULL,
0xbea6818e2b928ef5ULL, 0xe28ccf91cdc11e72ULL, 0x594aaa68e77a36cdULL, 0x313034806c7ffd0fULL,
0x8a9d27ac2249bd65ULL, 0x19a3b464018e9512ULL, 0xc26ccff352b37ec7ULL, 0x056f68341d797b21ULL,
0x5e79d6757efd2327ULL, 0xfabdbcb6553afe15ULL, 0xd3e7222c6eaf5a60ULL, 0x7046c76d4dae743bULL,
0x660be872b18d4a55ULL, 0x19992518574e1496ULL, 0xc103053a302bdcbbULL, 0x3ed8e9800b218e8eULL,
0x7b0b9239fa75e03eULL, 0xefe9fb684633c083ULL, 0x98a35fbe391a7793ULL, 0x6065510fe2d0fe34ULL,
0x55cb668548abad0cULL, 0xb4584548da87e527ULL, 0x2c43ecea0107c1ddULL, 0x526028809372de35ULL,
0x3415c56af9213b1fULL, 0x5bee1a4d017e98dbULL, 0x13f6b105b5cf709bULL, 0x5ff20e3482b29ab6ULL,
0x0aa29c75cc2e6c90ULL, 0xfc7d73ca3a70e206ULL, 0x899fc38fc4b5c515ULL, 0x250386b124ffc207ULL,
0x54ea28d5ae3d2b56ULL, 0x9913149dd6de60ceULL, 0x16694fc58f06d6c1ULL, 0x46b23975eb018fc7ULL,
0x470a6a0fb4b7b4e2ULL, 0x5d92475a8f7253deULL, 0xabeee5b52fbd3adbULL, 0x7fa20801a0806968ULL,
0x76f3faf19f7714d2ULL, 0xb3e840c12f4660c3ULL, 0x0fb4cd8df212744eULL, 0x4b065a251d3a2dd2ULL,
0x5cebde383d77cd4aULL, 0x6adf39df882c9cb1ULL, 0xa2dd242eb09af759ULL, 0x3147c0e50e5f6422ULL,
0x164ca5101d1350dbULL, 0xf8d13479c33fc962ULL, 0xe640ce4d13e5da08ULL, 0x4bdee0c45061f8baULL,
0xd7c46dc1a4edb1c9ULL, 0x5514d7b6437fd98aULL, 0x58942f6bb2a1c00bULL, 0x2dffb2ab1d70710eULL,
0xccdfcf2fc18b6d68ULL, 0xa8ebcba8b7806167ULL, 0x980697f95e2937e3ULL, 0x02fbba1cd0126e8cULL
};
static void curve25519_ever64_base(u8 *out, const u8 *priv)
{
u64 swap = 1;
int i, j, k;
u64 tmp[16 + 32 + 4];
u64 *x1 = &tmp[0];
u64 *z1 = &tmp[4];
u64 *x2 = &tmp[8];
u64 *z2 = &tmp[12];
u64 *xz1 = &tmp[0];
u64 *xz2 = &tmp[8];
u64 *a = &tmp[0 + 16];
u64 *b = &tmp[4 + 16];
u64 *c = &tmp[8 + 16];
u64 *ab = &tmp[0 + 16];
u64 *abcd = &tmp[0 + 16];
u64 *ef = &tmp[16 + 16];
u64 *efgh = &tmp[16 + 16];
u64 *key = &tmp[0 + 16 + 32];
memcpy(key, priv, 32);
((u8 *)key)[0] &= 248;
((u8 *)key)[31] = (((u8 *)key)[31] & 127) | 64;
x1[0] = 1, x1[1] = x1[2] = x1[3] = 0;
z1[0] = 1, z1[1] = z1[2] = z1[3] = 0;
z2[0] = 1, z2[1] = z2[2] = z2[3] = 0;
memcpy(x2, p_minus_s, sizeof(p_minus_s));
j = 3;
for (i = 0; i < 4; ++i) {
while (j < (const int[]){ 64, 64, 64, 63 }[i]) {
u64 bit = (key[i] >> j) & 1;
k = (64 * i + j - 3);
swap = swap ^ bit;
cswap2(swap, xz1, xz2);
swap = bit;
fsub(b, x1, z1);
fadd(a, x1, z1);
fmul(c, &table_ladder[4 * k], b, ef);
fsub(b, a, c);
fadd(a, a, c);
fsqr2(ab, ab, efgh);
fmul2(xz1, xz2, ab, efgh);
++j;
}
j = 0;
}
point_double(xz1, abcd, efgh);
point_double(xz1, abcd, efgh);
point_double(xz1, abcd, efgh);
encode_point(out, xz1);
memzero_explicit(tmp, sizeof(tmp));
}