scalar_4x64_impl.h File Reference

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Macros
#define	SECP256K1_N_0   ((uint64_t)0xBFD25E8CD0364141ULL)
#define	SECP256K1_N_1   ((uint64_t)0xBAAEDCE6AF48A03BULL)
#define	SECP256K1_N_2   ((uint64_t)0xFFFFFFFFFFFFFFFEULL)
#define	SECP256K1_N_3   ((uint64_t)0xFFFFFFFFFFFFFFFFULL)
#define	SECP256K1_N_C_0   (~SECP256K1_N_0 + 1)
#define	SECP256K1_N_C_1   (~SECP256K1_N_1)
#define	SECP256K1_N_C_2   (1)
#define	SECP256K1_N_H_0   ((uint64_t)0xDFE92F46681B20A0ULL)
#define	SECP256K1_N_H_1   ((uint64_t)0x5D576E7357A4501DULL)
#define	SECP256K1_N_H_2   ((uint64_t)0xFFFFFFFFFFFFFFFFULL)
#define	SECP256K1_N_H_3   ((uint64_t)0x7FFFFFFFFFFFFFFFULL)
#define	muladd(a, b)
	Add a*b to the number defined by (c0,c1,c2). More...
#define	muladd_fast(a, b)
	Add a*b to the number defined by (c0,c1). More...
#define	muladd2(a, b)
	Add 2*a*b to the number defined by (c0,c1,c2). More...
#define	sumadd(a)
	Add a to the number defined by (c0,c1,c2). More...
#define	sumadd_fast(a)
	Add a to the number defined by (c0,c1). More...
#define	extract(n)
	Extract the lowest 64 bits of (c0,c1,c2) into n, and left shift the number 64 bits. More...
#define	extract_fast(n)
	Extract the lowest 64 bits of (c0,c1,c2) into n, and left shift the number 64 bits. More...

Functions
static SECP256K1_INLINE void	secp256k1_scalar_clear (secp256k1_scalar *r)
static SECP256K1_INLINE void	secp256k1_scalar_set_int (secp256k1_scalar *r, unsigned int v)
static SECP256K1_INLINE unsigned int	secp256k1_scalar_get_bits (const secp256k1_scalar *a, unsigned int offset, unsigned int count)
static SECP256K1_INLINE unsigned int	secp256k1_scalar_get_bits_var (const secp256k1_scalar *a, unsigned int offset, unsigned int count)
static SECP256K1_INLINE int	secp256k1_scalar_check_overflow (const secp256k1_scalar *a)
static SECP256K1_INLINE int	secp256k1_scalar_reduce (secp256k1_scalar *r, unsigned int overflow)
static int	secp256k1_scalar_add (secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b)
static void	secp256k1_scalar_cadd_bit (secp256k1_scalar *r, unsigned int bit, int flag)
static void	secp256k1_scalar_set_b32 (secp256k1_scalar *r, const unsigned char *b32, int *overflow)
static void	secp256k1_scalar_get_b32 (unsigned char *bin, const secp256k1_scalar *a)
static SECP256K1_INLINE int	secp256k1_scalar_is_zero (const secp256k1_scalar *a)
static void	secp256k1_scalar_negate (secp256k1_scalar *r, const secp256k1_scalar *a)
static SECP256K1_INLINE int	secp256k1_scalar_is_one (const secp256k1_scalar *a)
static int	secp256k1_scalar_is_high (const secp256k1_scalar *a)
static int	secp256k1_scalar_cond_negate (secp256k1_scalar *r, int flag)
static void	secp256k1_scalar_reduce_512 (secp256k1_scalar *r, const uint64_t *l)
static void	secp256k1_scalar_mul_512 (uint64_t l[8], const secp256k1_scalar *a, const secp256k1_scalar *b)
static void	secp256k1_scalar_sqr_512 (uint64_t l[8], const secp256k1_scalar *a)
static void	secp256k1_scalar_mul (secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b)
static int	secp256k1_scalar_shr_int (secp256k1_scalar *r, int n)
static void	secp256k1_scalar_sqr (secp256k1_scalar *r, const secp256k1_scalar *a)
static SECP256K1_INLINE int	secp256k1_scalar_eq (const secp256k1_scalar *a, const secp256k1_scalar *b)
static SECP256K1_INLINE void	secp256k1_scalar_mul_shift_var (secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b, unsigned int shift)

Macro Definition Documentation

extract

#define extract

(

n

)

Value:

{ \
    (n) = c0; \
    c0 = c1; \
    c1 = c2; \
    c2 = 0; \
}

Extract the lowest 64 bits of (c0,c1,c2) into n, and left shift the number 64 bits.

Definition at line 255 of file scalar_4x64_impl.h.

Referenced by secp256k1_scalar_mul_512(), secp256k1_scalar_reduce_512(), and secp256k1_scalar_sqr_512().

extract_fast

#define extract_fast

(

n

)

Value:

{ \
    (n) = c0; \
    c0 = c1; \
    c1 = 0; \
    VERIFY_CHECK(c2 == 0); \
}

Extract the lowest 64 bits of (c0,c1,c2) into n, and left shift the number 64 bits.

c2 is required to be zero.

Definition at line 263 of file scalar_4x64_impl.h.

Referenced by secp256k1_scalar_mul_512(), secp256k1_scalar_reduce_512(), and secp256k1_scalar_sqr_512().

muladd

#define muladd	(		a,
			b
	)

Value:

{ \
    uint64_t tl, th; \
    { \
        uint128_t t = (uint128_t)a * b; \
        th = t >> 64;         /* at most 0xFFFFFFFFFFFFFFFE */ \
        tl = t; \
    } \
    c0 += tl;                 /* overflow is handled on the next line */ \
    th += (c0 < tl) ? 1 : 0;  /* at most 0xFFFFFFFFFFFFFFFF */ \
    c1 += th;                 /* overflow is handled on the next line */ \
    c2 += (c1 < th) ? 1 : 0;  /* never overflows by contract (verified in the next line) */ \
    VERIFY_CHECK((c1 >= th) || (c2 != 0)); \
}

Add a*b to the number defined by (c0,c1,c2).

c2 must never overflow.

Definition at line 187 of file scalar_4x64_impl.h.

Referenced by secp256k1_scalar_mul_512(), secp256k1_scalar_reduce_512(), and secp256k1_scalar_sqr_512().

muladd2

#define muladd2	(		a,
			b
	)

Value:

{ \
    uint64_t tl, th, th2, tl2; \
    { \
        uint128_t t = (uint128_t)a * b; \
        th = t >> 64;               /* at most 0xFFFFFFFFFFFFFFFE */ \
        tl = t; \
    } \
    th2 = th + th;                  /* at most 0xFFFFFFFFFFFFFFFE (in case th was 0x7FFFFFFFFFFFFFFF) */ \
    c2 += (th2 < th) ? 1 : 0;       /* never overflows by contract (verified the next line) */ \
    VERIFY_CHECK((th2 >= th) || (c2 != 0)); \
    tl2 = tl + tl;                  /* at most 0xFFFFFFFFFFFFFFFE (in case the lowest 63 bits of tl were 0x7FFFFFFFFFFFFFFF) */ \
    th2 += (tl2 < tl) ? 1 : 0;      /* at most 0xFFFFFFFFFFFFFFFF */ \
    c0 += tl2;                      /* overflow is handled on the next line */ \
    th2 += (c0 < tl2) ? 1 : 0;      /* second overflow is handled on the next line */ \
    c2 += (c0 < tl2) & (th2 == 0);  /* never overflows by contract (verified the next line) */ \
    VERIFY_CHECK((c0 >= tl2) || (th2 != 0) || (c2 != 0)); \
    c1 += th2;                      /* overflow is handled on the next line */ \
    c2 += (c1 < th2) ? 1 : 0;       /* never overflows by contract (verified the next line) */ \
    VERIFY_CHECK((c1 >= th2) || (c2 != 0)); \
}

Add 2*a*b to the number defined by (c0,c1,c2).

c2 must never overflow.

Definition at line 216 of file scalar_4x64_impl.h.

Referenced by secp256k1_scalar_sqr_512().

muladd_fast

#define muladd_fast	(		a,
			b
	)

Value:

{ \
    uint64_t tl, th; \
    { \
        uint128_t t = (uint128_t)a * b; \
        th = t >> 64;         /* at most 0xFFFFFFFFFFFFFFFE */ \
        tl = t; \
    } \
    c0 += tl;                 /* overflow is handled on the next line */ \
    th += (c0 < tl) ? 1 : 0;  /* at most 0xFFFFFFFFFFFFFFFF */ \
    c1 += th;                 /* never overflows by contract (verified in the next line) */ \
    VERIFY_CHECK(c1 >= th); \
}

Add a*b to the number defined by (c0,c1).

c1 must never overflow.

Definition at line 202 of file scalar_4x64_impl.h.

Referenced by secp256k1_scalar_mul_512(), secp256k1_scalar_reduce_512(), and secp256k1_scalar_sqr_512().

SECP256K1_N_0

#define SECP256K1_N_0   ((uint64_t)0xBFD25E8CD0364141ULL)

Definition at line 11 of file scalar_4x64_impl.h.

Referenced by secp256k1_scalar_check_overflow(), secp256k1_scalar_cond_negate(), and secp256k1_scalar_negate().

SECP256K1_N_1

#define SECP256K1_N_1   ((uint64_t)0xBAAEDCE6AF48A03BULL)

Definition at line 12 of file scalar_4x64_impl.h.

Referenced by secp256k1_scalar_check_overflow(), secp256k1_scalar_cond_negate(), and secp256k1_scalar_negate().

SECP256K1_N_2

#define SECP256K1_N_2   ((uint64_t)0xFFFFFFFFFFFFFFFEULL)

Definition at line 13 of file scalar_4x64_impl.h.

Referenced by secp256k1_scalar_check_overflow(), secp256k1_scalar_cond_negate(), and secp256k1_scalar_negate().

SECP256K1_N_3

#define SECP256K1_N_3   ((uint64_t)0xFFFFFFFFFFFFFFFFULL)

Definition at line 14 of file scalar_4x64_impl.h.

Referenced by secp256k1_scalar_check_overflow(), secp256k1_scalar_cond_negate(), and secp256k1_scalar_negate().

SECP256K1_N_C_0

#define SECP256K1_N_C_0   (~SECP256K1_N_0 + 1)

Definition at line 17 of file scalar_4x64_impl.h.

Referenced by secp256k1_scalar_reduce(), and secp256k1_scalar_reduce_512().

SECP256K1_N_C_1

#define SECP256K1_N_C_1   (~SECP256K1_N_1)

Definition at line 18 of file scalar_4x64_impl.h.

Referenced by secp256k1_scalar_reduce(), and secp256k1_scalar_reduce_512().

SECP256K1_N_C_2

#define SECP256K1_N_C_2   (1)

Definition at line 19 of file scalar_4x64_impl.h.

Referenced by secp256k1_scalar_reduce().

SECP256K1_N_H_0

#define SECP256K1_N_H_0   ((uint64_t)0xDFE92F46681B20A0ULL)

Definition at line 22 of file scalar_4x64_impl.h.

Referenced by secp256k1_scalar_is_high().

SECP256K1_N_H_1

#define SECP256K1_N_H_1   ((uint64_t)0x5D576E7357A4501DULL)

Definition at line 23 of file scalar_4x64_impl.h.

Referenced by secp256k1_scalar_is_high().

SECP256K1_N_H_2

#define SECP256K1_N_H_2   ((uint64_t)0xFFFFFFFFFFFFFFFFULL)

Definition at line 24 of file scalar_4x64_impl.h.

Referenced by secp256k1_scalar_is_high().

SECP256K1_N_H_3

#define SECP256K1_N_H_3   ((uint64_t)0x7FFFFFFFFFFFFFFFULL)

Definition at line 25 of file scalar_4x64_impl.h.

Referenced by secp256k1_scalar_is_high().

sumadd

#define sumadd

(

a

)

Value:

{ \
    unsigned int over; \
    c0 += (a);                  /* overflow is handled on the next line */ \
    over = (c0 < (a)) ? 1 : 0; \
    c1 += over;                 /* overflow is handled on the next line */ \
    c2 += (c1 < over) ? 1 : 0;  /* never overflows by contract */ \
}

Add a to the number defined by (c0,c1,c2).

c2 must never overflow.

Definition at line 238 of file scalar_4x64_impl.h.

Referenced by secp256k1_scalar_reduce_512().

sumadd_fast

#define sumadd_fast

(

a

)

Value:

{ \
    c0 += (a);                 /* overflow is handled on the next line */ \
    c1 += (c0 < (a)) ? 1 : 0;  /* never overflows by contract (verified the next line) */ \
    VERIFY_CHECK((c1 != 0) | (c0 >= (a))); \
    VERIFY_CHECK(c2 == 0); \
}

Add a to the number defined by (c0,c1).

c1 must never overflow, c2 must be zero.

Definition at line 247 of file scalar_4x64_impl.h.

Referenced by secp256k1_scalar_reduce_512().

Function Documentation

secp256k1_scalar_add()

static int secp256k1_scalar_add ( secp256k1_scalar *  r, const secp256k1_scalar *  a, const secp256k1_scalar *  b  )

static

Definition at line 83 of file scalar_4x64_impl.h.

References secp256k1_scalar::d, secp256k1_scalar_check_overflow(), secp256k1_scalar_reduce(), and VERIFY_CHECK.

secp256k1_scalar_cadd_bit()

static void secp256k1_scalar_cadd_bit ( secp256k1_scalar *  r, unsigned int  bit, int  flag  )

static

Definition at line 99 of file scalar_4x64_impl.h.

References secp256k1_scalar::d, secp256k1_scalar_check_overflow(), and VERIFY_CHECK.

Referenced by secp256k1_scalar_mul_shift_var().

secp256k1_scalar_check_overflow()

static SECP256K1_INLINE int secp256k1_scalar_check_overflow ( const secp256k1_scalar *  a )

static

Definition at line 57 of file scalar_4x64_impl.h.

References secp256k1_scalar::d, SECP256K1_N_0, SECP256K1_N_1, SECP256K1_N_2, and SECP256K1_N_3.

Referenced by run_scalar_tests(), secp256k1_scalar_add(), secp256k1_scalar_cadd_bit(), secp256k1_scalar_reduce_512(), and secp256k1_scalar_set_b32().

secp256k1_scalar_clear()

static SECP256K1_INLINE void secp256k1_scalar_clear ( secp256k1_scalar *  r )

static

Definition at line 27 of file scalar_4x64_impl.h.

References secp256k1_scalar::d.

secp256k1_scalar_cond_negate()

static int secp256k1_scalar_cond_negate ( secp256k1_scalar *  r, int  flag  )

static

Definition at line 168 of file scalar_4x64_impl.h.

References secp256k1_scalar::d, immer::detail::hamts::mask, SECP256K1_N_0, SECP256K1_N_1, SECP256K1_N_2, SECP256K1_N_3, and secp256k1_scalar_is_zero().

secp256k1_scalar_eq()

static SECP256K1_INLINE int secp256k1_scalar_eq ( const secp256k1_scalar *  a, const secp256k1_scalar *  b  )

static

Definition at line 928 of file scalar_4x64_impl.h.

References secp256k1_scalar::d.

secp256k1_scalar_get_b32()

static void secp256k1_scalar_get_b32 ( unsigned char *  bin, const secp256k1_scalar *  a  )

static

Definition at line 129 of file scalar_4x64_impl.h.

References secp256k1_scalar::d.

secp256k1_scalar_get_bits()

static SECP256K1_INLINE unsigned int secp256k1_scalar_get_bits ( const secp256k1_scalar *  a, unsigned int  offset, unsigned int  count  )

static

Definition at line 41 of file scalar_4x64_impl.h.

References count, secp256k1_scalar::d, and VERIFY_CHECK.

Referenced by secp256k1_scalar_get_bits_var().

secp256k1_scalar_get_bits_var()

static SECP256K1_INLINE unsigned int secp256k1_scalar_get_bits_var ( const secp256k1_scalar *  a, unsigned int  offset, unsigned int  count  )

static

Definition at line 46 of file scalar_4x64_impl.h.

References count, secp256k1_scalar::d, secp256k1_scalar_get_bits(), and VERIFY_CHECK.

secp256k1_scalar_is_high()

static int secp256k1_scalar_is_high ( const secp256k1_scalar *  a )

static

Definition at line 156 of file scalar_4x64_impl.h.

References secp256k1_scalar::d, SECP256K1_N_H_0, SECP256K1_N_H_1, SECP256K1_N_H_2, and SECP256K1_N_H_3.

secp256k1_scalar_is_one()

static SECP256K1_INLINE int secp256k1_scalar_is_one ( const secp256k1_scalar *  a )

static

Definition at line 152 of file scalar_4x64_impl.h.

References secp256k1_scalar::d.

secp256k1_scalar_is_zero()

static SECP256K1_INLINE int secp256k1_scalar_is_zero ( const secp256k1_scalar *  a )

static

Definition at line 136 of file scalar_4x64_impl.h.

References secp256k1_scalar::d.

Referenced by secp256k1_scalar_cond_negate(), and secp256k1_scalar_negate().

secp256k1_scalar_mul()

static void secp256k1_scalar_mul ( secp256k1_scalar *  r, const secp256k1_scalar *  a, const secp256k1_scalar *  b  )

static

Definition at line 891 of file scalar_4x64_impl.h.

References secp256k1_scalar_mul_512(), and secp256k1_scalar_reduce_512().

secp256k1_scalar_mul_512()

static void secp256k1_scalar_mul_512 ( uint64_t  l[8], const secp256k1_scalar *  a, const secp256k1_scalar *  b  )

static

Definition at line 579 of file scalar_4x64_impl.h.

References secp256k1_scalar::d, extract, extract_fast, muladd, muladd_fast, and VERIFY_CHECK.

Referenced by secp256k1_scalar_mul(), and secp256k1_scalar_mul_shift_var().

secp256k1_scalar_mul_shift_var()

static SECP256K1_INLINE void secp256k1_scalar_mul_shift_var ( secp256k1_scalar *  r, const secp256k1_scalar *  a, const secp256k1_scalar *  b, unsigned int  shift  )

static

Definition at line 932 of file scalar_4x64_impl.h.

References secp256k1_scalar::d, secp256k1_scalar_cadd_bit(), secp256k1_scalar_mul_512(), and VERIFY_CHECK.

secp256k1_scalar_negate()

static void secp256k1_scalar_negate ( secp256k1_scalar *  r, const secp256k1_scalar *  a  )

static

Definition at line 140 of file scalar_4x64_impl.h.

References secp256k1_scalar::d, SECP256K1_N_0, SECP256K1_N_1, SECP256K1_N_2, SECP256K1_N_3, and secp256k1_scalar_is_zero().

secp256k1_scalar_reduce()

static SECP256K1_INLINE int secp256k1_scalar_reduce ( secp256k1_scalar *  r, unsigned int  overflow  )

static

Definition at line 69 of file scalar_4x64_impl.h.

References secp256k1_scalar::d, SECP256K1_N_C_0, SECP256K1_N_C_1, SECP256K1_N_C_2, and VERIFY_CHECK.

Referenced by secp256k1_scalar_add(), secp256k1_scalar_reduce_512(), and secp256k1_scalar_set_b32().

secp256k1_scalar_reduce_512()

static void secp256k1_scalar_reduce_512 ( secp256k1_scalar *  r, const uint64_t *  l  )

static

Definition at line 270 of file scalar_4x64_impl.h.

References secp256k1_scalar::d, extract, extract_fast, muladd, muladd_fast, SECP256K1_N_C_0, SECP256K1_N_C_1, secp256k1_scalar_check_overflow(), secp256k1_scalar_reduce(), sumadd, sumadd_fast, and VERIFY_CHECK.

Referenced by secp256k1_scalar_mul(), and secp256k1_scalar_sqr().

secp256k1_scalar_set_b32()

static void secp256k1_scalar_set_b32 ( secp256k1_scalar *  r, const unsigned char *  b32, int *  overflow  )

static

Definition at line 117 of file scalar_4x64_impl.h.

References secp256k1_scalar::d, secp256k1_scalar_check_overflow(), and secp256k1_scalar_reduce().

secp256k1_scalar_set_int()

static SECP256K1_INLINE void secp256k1_scalar_set_int ( secp256k1_scalar *  r, unsigned int  v  )

static

Definition at line 34 of file scalar_4x64_impl.h.

References secp256k1_scalar::d.

secp256k1_scalar_shr_int()

static int secp256k1_scalar_shr_int ( secp256k1_scalar *  r, int  n  )

static

Definition at line 897 of file scalar_4x64_impl.h.

References secp256k1_scalar::d, and VERIFY_CHECK.

secp256k1_scalar_sqr()

static void secp256k1_scalar_sqr ( secp256k1_scalar *  r, const secp256k1_scalar *  a  )

static

Definition at line 909 of file scalar_4x64_impl.h.

References secp256k1_scalar_reduce_512(), and secp256k1_scalar_sqr_512().

secp256k1_scalar_sqr_512()

static void secp256k1_scalar_sqr_512 ( uint64_t  l[8], const secp256k1_scalar *  a  )

static

Definition at line 746 of file scalar_4x64_impl.h.

References secp256k1_scalar::d, extract, extract_fast, muladd, muladd2, muladd_fast, and VERIFY_CHECK.

Referenced by secp256k1_scalar_sqr().