bigint.h

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#ifndef _BITS_BIGINT_H
#define _BITS_BIGINT_H

/** @file
 *
 * Big integer support
 */

FILE_LICENCE ( GPL2_OR_LATER_OR_UBDL );
FILE_SECBOOT ( PERMITTED );

#include <stdint.h>
#include <string.h>

/** Element of a big integer */
typedef uint32_t bigint_element_t;

/**
 * Initialise big integer
 *
 * @v value0            Element 0 of big integer to initialise
 * @v size              Number of elements
 * @v data              Raw data
 * @v len               Length of raw data
 */
static inline __attribute__ (( always_inline )) void
bigint_init_raw ( uint32_t *value0, unsigned int size,
                  const void *data, size_t len ) {
        bigint_t ( size ) __attribute__ (( may_alias )) *value =
                ( ( void * ) value0 );
        long pad_len = ( sizeof ( *value ) - len );
        void *discard_D;
        long discard_c;

        /* Copy raw data in reverse order, padding with zeros */
        __asm__ __volatile__ ( "jecxz 2f\n\t"
                               "\n1:\n\t"
                               "movb -1(%3,%1), %%al\n\t"
                               "stosb\n\t"
                               "loop 1b\n\t"
                               "\n2:\n\t"
                               "xorl %%eax, %%eax\n\t"
                               "mov %4, %1\n\t"
                               "rep stosb\n\t"
                               : "=&D" ( discard_D ), "=&c" ( discard_c ),
                                 "+m" ( *value )
                               : "r" ( data ), "g" ( pad_len ), "0" ( value0 ),
                                 "1" ( len )
                               : "eax" );
}

/**
 * Add big integers
 *
 * @v addend0           Element 0 of big integer to add
 * @v value0            Element 0 of big integer to be added to
 * @v size              Number of elements
 * @ret carry           Carry flag
 */
static inline __attribute__ (( always_inline )) int
bigint_add_raw ( const uint32_t *addend0, uint32_t *value0,
                 unsigned int size ) {
        bigint_t ( size ) __attribute__ (( may_alias )) *value =
                ( ( void * ) value0 );
        long index;
        void *discard_S;
        long discard_c;
        int carry;

        __asm__ __volatile__ ( "xor %0, %0\n\t" /* Zero %0 and clear CF */
                               "\n1:\n\t"
                               "lodsl\n\t"
                               "adcl %%eax, (%5,%0,4)\n\t"
                               "inc %0\n\t" /* Does not affect CF */
                               "loop 1b\n\t"
                               : "=&r" ( index ), "=&S" ( discard_S ),
                                 "=&c" ( discard_c ), "=@ccc" ( carry ),
                                 "+m" ( *value )
                               : "r" ( value0 ), "1" ( addend0 ), "2" ( size )
                               : "eax" );
        return carry;
}

/**
 * Subtract big integers
 *
 * @v subtrahend0       Element 0 of big integer to subtract
 * @v value0            Element 0 of big integer to be subtracted from
 * @v size              Number of elements
 * @ret borrow          Borrow flag
 */
static inline __attribute__ (( always_inline )) int
bigint_subtract_raw ( const uint32_t *subtrahend0, uint32_t *value0,
                      unsigned int size ) {
        bigint_t ( size ) __attribute__ (( may_alias )) *value =
                ( ( void * ) value0 );
        long index;
        void *discard_S;
        long discard_c;
        int borrow;

        __asm__ __volatile__ ( "xor %0, %0\n\t" /* Zero %0 and clear CF */
                               "\n1:\n\t"
                               "lodsl\n\t"
                               "sbbl %%eax, (%5,%0,4)\n\t"
                               "inc %0\n\t" /* Does not affect CF */
                               "loop 1b\n\t"
                               : "=&r" ( index ), "=&S" ( discard_S ),
                                 "=&c" ( discard_c ), "=@ccc" ( borrow ),
                                 "+m" ( *value )
                               : "r" ( value0 ), "1" ( subtrahend0 ),
                                 "2" ( size )
                               : "eax" );
        return borrow;
}

/**
 * Shift big integer left
 *
 * @v value0            Element 0 of big integer
 * @v size              Number of elements
 * @ret out             Bit shifted out
 */
static inline __attribute__ (( always_inline )) int
bigint_shl_raw ( uint32_t *value0, unsigned int size ) {
        bigint_t ( size ) __attribute__ (( may_alias )) *value =
                ( ( void * ) value0 );
        long index;
        long discard_c;
        int out;

        __asm__ __volatile__ ( "xor %0, %0\n\t" /* Zero %0 and clear CF */
                               "\n1:\n\t"
                               "rcll $1, (%4,%0,4)\n\t"
                               "inc %0\n\t" /* Does not affect CF */
                               "loop 1b\n\t"
                               : "=&r" ( index ), "=&c" ( discard_c ),
                                 "=@ccc" ( out ), "+m" ( *value )
                               : "r" ( value0 ), "1" ( size ) );
        return out;
}

/**
 * Shift big integer right
 *
 * @v value0            Element 0 of big integer
 * @v size              Number of elements
 * @ret out             Bit shifted out
 */
static inline __attribute__ (( always_inline )) int
bigint_shr_raw ( uint32_t *value0, unsigned int size ) {
        bigint_t ( size ) __attribute__ (( may_alias )) *value =
                ( ( void * ) value0 );
        long discard_c;
        int out;

        __asm__ __volatile__ ( "clc\n\t"
                               "\n1:\n\t"
                               "rcrl $1, -4(%3,%0,4)\n\t"
                               "loop 1b\n\t"
                               : "=&c" ( discard_c ), "=@ccc" ( out ),
                                 "+m" ( *value )
                               : "r" ( value0 ), "0" ( size ) );
        return out;
}

/**
 * Test if big integer is equal to zero
 *
 * @v value0            Element 0 of big integer
 * @v size              Number of elements
 * @ret is_zero         Big integer is equal to zero
 */
static inline __attribute__ (( always_inline, pure )) int
bigint_is_zero_raw ( const uint32_t *value0, unsigned int size ) {
        void *discard_D;
        long discard_c;
        int result;

        __asm__ __volatile__ ( "xor %0, %0\n\t" /* Set ZF */
                               "repe scasl\n\t"
                               "sete %b0\n\t"
                               : "=&a" ( result ), "=&D" ( discard_D ),
                                 "=&c" ( discard_c )
                               : "1" ( value0 ), "2" ( size ) );
        return result;
}

/**
 * Compare big integers
 *
 * @v value0            Element 0 of big integer
 * @v reference0        Element 0 of reference big integer
 * @v size              Number of elements
 * @ret geq             Big integer is greater than or equal to the reference
 */
static inline __attribute__ (( always_inline, pure )) int
bigint_is_geq_raw ( const uint32_t *value0, const uint32_t *reference0,
                    unsigned int size ) {
        long discard_c;
        long discard_tmp;
        int result;

        __asm__ __volatile__ ( "\n1:\n\t"
                               "movl -4(%3, %1, 4), %k2\n\t"
                               "cmpl -4(%4, %1, 4), %k2\n\t"
                               "loope 1b\n\t"
                               "setae %b0\n\t"
                               : "=q" ( result ), "=&c" ( discard_c ),
                                 "=&r" ( discard_tmp )
                               : "r" ( value0 ), "r" ( reference0 ),
                                 "0" ( 0 ), "1" ( size ) );
        return result;
}

/**
 * Find highest bit set in big integer
 *
 * @v value0            Element 0 of big integer
 * @v size              Number of elements
 * @ret max_bit         Highest bit set + 1 (or 0 if no bits set)
 */
static inline __attribute__ (( always_inline )) int
bigint_max_set_bit_raw ( const uint32_t *value0, unsigned int size ) {
        long discard_c;
        int result;

        __asm__ __volatile__ ( "\n1:\n\t"
                               "bsrl -4(%2,%1,4), %0\n\t"
                               "loopz 1b\n\t"
                               "rol %1\n\t" /* Does not affect ZF */
                               "rol %1\n\t"
                               "leal 1(%k0,%k1,8), %k0\n\t"
                               "jnz 2f\n\t"
                               "xor %0, %0\n\t"
                               "\n2:\n\t"
                               : "=&r" ( result ), "=&c" ( discard_c )
                               : "r" ( value0 ), "1" ( size ) );
        return result;
}

/**
 * Grow big integer
 *
 * @v source0           Element 0 of source big integer
 * @v source_size       Number of elements in source big integer
 * @v dest0             Element 0 of destination big integer
 * @v dest_size         Number of elements in destination big integer
 */
static inline __attribute__ (( always_inline )) void
bigint_grow_raw ( const uint32_t *source0, unsigned int source_size,
                  uint32_t *dest0, unsigned int dest_size ) {
        bigint_t ( dest_size ) __attribute__ (( may_alias )) *dest =
                ( ( void * ) dest0 );
        long pad_size = ( dest_size - source_size );
        void *discard_D;
        void *discard_S;
        long discard_c;

        __asm__ __volatile__ ( "rep movsl\n\t"
                               "xorl %%eax, %%eax\n\t"
                               "mov %4, %2\n\t"
                               "rep stosl\n\t"
                               : "=&D" ( discard_D ), "=&S" ( discard_S ),
                                 "=&c" ( discard_c ), "+m" ( *dest )
                               : "g" ( pad_size ), "0" ( dest0 ),
                                 "1" ( source0 ), "2" ( source_size )
                               : "eax" );
}

/**
 * Shrink big integer
 *
 * @v source0           Element 0 of source big integer
 * @v source_size       Number of elements in source big integer
 * @v dest0             Element 0 of destination big integer
 * @v dest_size         Number of elements in destination big integer
 */
static inline __attribute__ (( always_inline )) void
bigint_shrink_raw ( const uint32_t *source0, unsigned int source_size __unused,
                    uint32_t *dest0, unsigned int dest_size ) {
        bigint_t ( dest_size ) __attribute__ (( may_alias )) *dest =
                ( ( void * ) dest0 );
        void *discard_D;
        void *discard_S;
        long discard_c;

        __asm__ __volatile__ ( "rep movsl\n\t"
                               : "=&D" ( discard_D ), "=&S" ( discard_S ),
                                 "=&c" ( discard_c ), "+m" ( *dest )
                               : "0" ( dest0 ), "1" ( source0 ),
                                 "2" ( dest_size )
                               : "eax" );
}

/**
 * Finalise big integer
 *
 * @v value0            Element 0 of big integer to finalise
 * @v size              Number of elements
 * @v out               Output buffer
 * @v len               Length of output buffer
 */
static inline __attribute__ (( always_inline )) void
bigint_done_raw ( const uint32_t *value0, unsigned int size __unused,
                  void *out, size_t len ) {
        struct {
                uint8_t bytes[len];
        } __attribute__ (( may_alias )) *out_bytes = out;
        void *discard_D;
        long discard_c;

        /* Copy raw data in reverse order */
        __asm__ __volatile__ ( "jecxz 2f\n\t"
                               "\n1:\n\t"
                               "movb -1(%3,%1), %%al\n\t"
                               "stosb\n\t"
                               "loop 1b\n\t"
                               "\n2:\n\t"
                               : "=&D" ( discard_D ), "=&c" ( discard_c ),
                                 "+m" ( *out_bytes )
                               : "r" ( value0 ), "0" ( out ), "1" ( len )
                               : "eax" );
}

/**
 * Multiply big integer elements
 *
 * @v multiplicand      Multiplicand element
 * @v multiplier        Multiplier element
 * @v result            Result element
 * @v carry             Carry element
 */
static inline __attribute__ (( always_inline )) void
bigint_multiply_one ( const uint32_t multiplicand, const uint32_t multiplier,
                      uint32_t *result, uint32_t *carry ) {
        uint32_t discard_a;

        __asm__ __volatile__ ( /* Perform multiplication */
                               "mull %3\n\t"
                               /* Accumulate carry */
                               "addl %5, %0\n\t"
                               "adcl $0, %1\n\t"
                               /* Accumulate result */
                               "addl %0, %2\n\t"
                               "adcl $0, %1\n\t"
                               : "=&a" ( discard_a ),
                                 "=&d" ( *carry ),
                                 "+m" ( *result )
                               : "g" ( multiplicand ),
                                 "0" ( multiplier ),
                                 "r" ( *carry ) );
}

#endif /* _BITS_BIGINT_H */