math_test.c

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/*
 * Copyright (C) 2014 Michael Brown <mbrown@fensystems.co.uk>.
 *
 * This program is free software; you can redistribute it and/or
 * modify it under the terms of the GNU General Public License as
 * published by the Free Software Foundation; either version 2 of the
 * License, or any later version.
 *
 * This program is distributed in the hope that it will be useful, but
 * WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 * General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
 * 02110-1301, USA.
 *
 * You can also choose to distribute this program under the terms of
 * the Unmodified Binary Distribution Licence (as given in the file
 * COPYING.UBDL), provided that you have satisfied its requirements.
 */
 
FILE_LICENCE ( GPL2_OR_LATER_OR_UBDL );
 
/** @file
 *
 * Mathematical self-tests
 *
 */
 
/* Forcibly enable assertions */
#undef NDEBUG
 
#include <string.h>
#include <strings.h>
#include <assert.h>
#include <ipxe/test.h>
#include <ipxe/isqrt.h>
 
/**
 * Force a call to the non-constant implementation of ffsl()
 *
 * @v value             Value
 * @ret lsb             Least significant bit set in value (LSB=1), or zero
 */
__attribute__ (( noinline )) int ffsl_var ( long value ) {
        return ffsl ( value );
}
 
/**
 * Force a call to the non-constant implementation of ffsll()
 *
 * @v value             Value
 * @ret lsb             Least significant bit set in value (LSB=1), or zero
 */
__attribute__ (( noinline )) int ffsll_var ( long long value ) {
        return ffsll ( value );
}
 
/**
 * Force a call to the non-constant implementation of flsl()
 *
 * @v value             Value
 * @ret msb             Most significant bit set in value (LSB=1), or zero
 */
__attribute__ (( noinline )) int flsl_var ( long value ) {
        return flsl ( value );
}
 
/**
 * Force a call to the non-constant implementation of flsll()
 *
 * @v value             Value
 * @ret msb             Most significant bit set in value (LSB=1), or zero
 */
__attribute__ (( noinline )) int flsll_var ( long long value ) {
        return flsll ( value );
}
 
/**
 * Force a use of runtime 64-bit shift left
 *
 * @v value             Value
 * @v shift             Shift amount
 * @ret value           Shifted value
 */
__attribute__ (( noinline )) uint64_t lsl64_var ( uint64_t value,
                                                  unsigned int shift ) {
        return ( value << shift );
}
 
/**
 * Force a use of runtime 64-bit logical shift right
 *
 * @v value             Value
 * @v shift             Shift amount
 * @ret value           Shifted value
 */
__attribute__ (( noinline )) uint64_t lsr64_var ( uint64_t value,
                                                  unsigned int shift ) {
        return ( value >> shift );
}
 
/**
 * Force a use of runtime 64-bit arithmetic shift right
 *
 * @v value             Value
 * @v shift             Shift amount
 * @ret value           Shifted value
 */
__attribute__ (( noinline )) int64_t asr64_var ( int64_t value,
                                                 unsigned int shift ) {
        return ( value >> shift );
}
 
/**
 * Check current stack pointer
 *
 * @ret stack           A value at a fixed offset from the current stack pointer
 *
 * Used by check_divmod()
 */
static __attribute__ (( noinline )) void * stack_check ( void ) {
        int a;
        void *ret;
 
        /* Hide the fact that we are returning the address of a local
         * variable, to prevent a compiler warning.
         */
        __asm__ ( "\n" : "=g" ( ret ) : "0" ( &a ) );
 
        return ret;
}
 
/**
 * Check division/modulus operation
 *
 * One aspect of the calling convention for the implicit arithmetic
 * functions (__udivmoddi4() etc) is whether the caller or the callee
 * is expected to pop any stack-based arguments.  This distinction can
 * be masked if the compiler chooses to uses a frame pointer in the
 * caller, since the caller will then reload the stack pointer from
 * the frame pointer and so can mask an error in the value of the
 * stack pointer.
 *
 * We run the division operation in a loop, and check that the stack
 * pointer does not change value on the second iteration.  To prevent
 * the compiler from performing various optimisations which might
 * invalidate our intended test (such as unrolling the loop, or moving
 * the division operation outside the loop), we include some dummy
 * inline assembly code.
 */
#define check_divmod( dividend, divisor, OP ) ( {                       \
        uint64_t result;                                                \
        int count = 2;                                                  \
        void *check = NULL;                                             \
                                                                        \
        /* Prevent compiler from unrolling the loop */                  \
        __asm__ ( "\n" : "=g" ( count ) : "0" ( count ) );              \
                                                                        \
        do {                                                            \
                /* Check that stack pointer does not change between     \
                 * loop iterations.                                     \
                 */                                                     \
                if ( check ) {                                          \
                        assert ( check == stack_check() );              \
                } else {                                                \
                        check = stack_check();                          \
                }                                                       \
                                                                        \
                /* Perform division, preventing the compiler from       \
                 * moving the division out of the loop.                 \
                 */                                                     \
                __asm__ ( "\n" : "=g" ( dividend ), "=g" ( divisor )    \
                          : "0" ( dividend ), "1" ( divisor ) );        \
                result = ( dividend OP divisor );                       \
                __asm__ ( "\n" : "=g" ( result ) : "0" ( result ) );    \
                                                                        \
        } while ( --count );                                            \
        result; } )
 
/**
 * Force a use of runtime 64-bit unsigned integer division
 *
 * @v dividend          Dividend
 * @v divisor           Divisor
 * @ret quotient        Quotient
 */
__attribute__ (( noinline )) uint64_t u64div_var ( uint64_t dividend,
                                                   uint64_t divisor ) {
 
        return check_divmod ( dividend, divisor, / );
}
 
/**
 * Force a use of runtime 64-bit unsigned integer modulus
 *
 * @v dividend          Dividend
 * @v divisor           Divisor
 * @ret remainder       Remainder
 */
__attribute__ (( noinline )) uint64_t u64mod_var ( uint64_t dividend,
                                                   uint64_t divisor ) {
 
        return check_divmod ( dividend, divisor, % );
}
 
/**
 * Force a use of runtime 64-bit signed integer division
 *
 * @v dividend          Dividend
 * @v divisor           Divisor
 * @ret quotient        Quotient
 */
__attribute__ (( noinline )) int64_t s64div_var ( int64_t dividend,
                                                  int64_t divisor ) {
 
        return check_divmod ( dividend, divisor, / );
}
 
/**
 * Force a use of runtime 64-bit unsigned integer modulus
 *
 * @v dividend          Dividend
 * @v divisor           Divisor
 * @ret remainder       Remainder
 */
__attribute__ (( noinline )) int64_t s64mod_var ( int64_t dividend,
                                                  int64_t divisor ) {
 
        return check_divmod ( dividend, divisor, % );
}
 
/**
 * Report a ffsl() test result
 *
 * @v value             Value
 * @v lsb               Expected LSB
 * @v file              Test code file
 * @v line              Test code line
 */
static inline __attribute__ (( always_inline )) void
ffsl_okx ( long value, int lsb, const char *file, unsigned int line ) {
 
        /* Verify as a constant (requires to be inlined) */
        okx ( ffsl ( value ) == lsb, file, line );
 
        /* Verify as a non-constant */
        okx ( ffsl_var ( value ) == lsb, file, line );
}
#define ffsl_ok( value, lsb ) ffsl_okx ( value, lsb, __FILE__, __LINE__ )
 
/**
 * Report a ffsll() test result
 *
 * @v value             Value
 * @v lsb               Expected LSB
 * @v file              Test code file
 * @v line              Test code line
 */
static inline __attribute__ (( always_inline )) void
ffsll_okx ( long long value, int lsb, const char *file, unsigned int line ) {
 
        /* Verify as a constant (requires to be inlined) */
        okx ( ffsll ( value ) == lsb, file, line );
 
        /* Verify as a non-constant */
        okx ( ffsll_var ( value ) == lsb, file, line );
}
#define ffsll_ok( value, lsb ) ffsll_okx ( value, lsb, __FILE__, __LINE__ )
 
/**
 * Report a flsl() test result
 *
 * @v value             Value
 * @v msb               Expected MSB
 * @v file              Test code file
 * @v line              Test code line
 */
static inline __attribute__ (( always_inline )) void
flsl_okx ( long value, int msb, const char *file, unsigned int line ) {
 
        /* Verify as a constant (requires to be inlined) */
        okx ( flsl ( value ) == msb, file, line );
 
        /* Verify as a non-constant */
        okx ( flsl_var ( value ) == msb, file, line );
}
#define flsl_ok( value, msb ) flsl_okx ( value, msb, __FILE__, __LINE__ )
 
/**
 * Report a flsll() test result
 *
 * @v value             Value
 * @v msb               Expected MSB
 * @v file              Test code file
 * @v line              Test code line
 */
static inline __attribute__ (( always_inline )) void
flsll_okx ( long long value, int msb, const char *file, unsigned int line ) {
 
        /* Verify as a constant (requires to be inlined) */
        okx ( flsll ( value ) == msb, file, line );
 
        /* Verify as a non-constant */
        okx ( flsll_var ( value ) == msb, file, line );
}
#define flsll_ok( value, msb ) flsll_okx ( value, msb, __FILE__, __LINE__ )
 
/**
 * Report a 64-bit shift left test result
 *
 * @v value             Value
 * @v shift             Shift amount
 * @v expected          Expected value
 * @v file              Test code file
 * @v line              Test code line
 */
static inline __attribute__ (( always_inline )) void
lsl64_okx ( uint64_t value, unsigned int shift, uint64_t expected,
            const char *file, unsigned int line ) {
 
        /* Verify as a compile-time calculation */
        okx ( ( value << shift ) == expected, file, line );
 
        /* Verify as a runtime calculation */
        okx ( lsl64_var ( value, shift ) == expected, file, line );
}
#define lsl64_ok( value, shift, expected ) \
        lsl64_okx ( value, shift, expected, __FILE__, __LINE__ )
 
/**
 * Report a 64-bit logical shift right test result
 *
 * @v value             Value
 * @v shift             Shift amount
 * @v expected          Expected value
 * @v file              Test code file
 * @v line              Test code line
 */
static inline __attribute__ (( always_inline )) void
lsr64_okx ( uint64_t value, unsigned int shift, uint64_t expected,
            const char *file, unsigned int line ) {
 
        /* Verify as a compile-time calculation */
        okx ( ( value >> shift ) == expected, file, line );
 
        /* Verify as a runtime calculation */
        okx ( lsr64_var ( value, shift ) == expected, file, line );
}
#define lsr64_ok( value, shift, expected ) \
        lsr64_okx ( value, shift, expected, __FILE__, __LINE__ )
 
/**
 * Report a 64-bit arithmetic shift right test result
 *
 * @v value             Value
 * @v shift             Shift amount
 * @v expected          Expected value
 * @v file              Test code file
 * @v line              Test code line
 */
static inline __attribute__ (( always_inline )) void
asr64_okx ( int64_t value, unsigned int shift, int64_t expected,
            const char *file, unsigned int line ) {
 
        /* Verify as a compile-time calculation */
        okx ( ( value >> shift ) == expected, file, line );
 
        /* Verify as a runtime calculation */
        okx ( asr64_var ( value, shift ) == expected, file, line );
}
#define asr64_ok( value, shift, expected ) \
        asr64_okx ( value, shift, expected, __FILE__, __LINE__ )
 
/**
 * Report a 64-bit unsigned integer division test result
 *
 * @v dividend          Dividend
 * @v divisor           Divisor
 * @v quotient          Quotient
 * @v remainder         Remainder
 * @v file              Test code file
 * @v line              Test code line
 */
static void u64divmod_okx ( uint64_t dividend, uint64_t divisor,
                            uint64_t quotient, uint64_t remainder,
                            const char *file, unsigned int line ) {
 
        /* Sanity check */
        okx ( ( ( divisor * quotient ) + remainder ) == dividend, file, line );
 
        /* Check division */
        okx ( u64div_var ( dividend, divisor ) == quotient, file, line );
 
        /* Check modulus */
        okx ( u64mod_var ( dividend, divisor ) == remainder, file, line );
}
#define u64divmod_ok( dividend, divisor, quotient, remainder )  \
        u64divmod_okx ( dividend, divisor, quotient, remainder, \
                        __FILE__, __LINE__ )
 
/**
 * Report a 64-bit signed integer division test result
 *
 * @v dividend          Dividend
 * @v divisor           Divisor
 * @v quotient          Quotient
 * @v remainder         Remainder
 * @v file              Test code file
 * @v line              Test code line
 */
static void s64divmod_okx ( int64_t dividend, int64_t divisor,
                            int64_t quotient, int64_t remainder,
                            const char *file, unsigned int line ) {
 
        /* Sanity check */
        okx ( ( ( divisor * quotient ) + remainder ) == dividend, file, line );
 
        /* Check division */
        okx ( s64div_var ( dividend, divisor ) == quotient, file, line );
 
        /* Check modulus */
        okx ( s64mod_var ( dividend, divisor ) == remainder, file, line );
}
#define s64divmod_ok( dividend, divisor, quotient, remainder )  \
        s64divmod_okx ( dividend, divisor, quotient, remainder, \
                        __FILE__, __LINE__ )
 
/**
 * Perform mathematical self-tests
 *
 */
static void math_test_exec ( void ) {
 
        /* Test ffsl() */
        ffsl_ok ( 0, 0 );
        ffsl_ok ( 1, 1 );
        ffsl_ok ( 255, 1 );
        ffsl_ok ( 256, 9 );
        ffsl_ok ( 257, 1 );
        ffsl_ok ( 0x54850596, 2 );
        ffsl_ok ( 0x80000000, 32 );
 
        /* Test ffsll() */
        ffsll_ok ( 0, 0 );
        ffsll_ok ( 1, 1 );
        ffsll_ok ( 0x6d63623330ULL, 5 );
        ffsll_ok ( 0x80000000UL, 32 );
        ffsll_ok ( 0x8000000000000000ULL, 64 );
 
        /* Test flsl() */
        flsl_ok ( 0, 0 );
        flsl_ok ( 1, 1 );
        flsl_ok ( 255, 8 );
        flsl_ok ( 256, 9 );
        flsl_ok ( 257, 9 );
        flsl_ok ( 0x69505845, 31 );
        flsl_ok ( -1U, ( 8 * sizeof ( int ) ) );
        flsl_ok ( -1UL, ( 8 * sizeof ( long ) ) );
 
        /* Test flsll() */
        flsll_ok ( 0, 0 );
        flsll_ok ( 1, 1 );
        flsll_ok ( 0x6d63623330ULL, 39 );
        flsll_ok ( -1U, ( 8 * sizeof ( int ) ) );
        flsll_ok ( -1UL, ( 8 * sizeof ( long ) ) );
        flsll_ok ( -1ULL, ( 8 * sizeof ( long long ) ) );
 
        /* Test 64-bit arithmetic
         *
         * On a 64-bit machine, these tests are fairly meaningless.
         *
         * On a 32-bit machine, these tests verify the correct
         * operation of our libgcc functions __udivmoddi4()
         * etc. (including checking that the implicit calling
         * convention assumed by gcc matches our expectations).
         */
        lsl64_ok ( 0x06760c14710540c2ULL,  0, 0x06760c14710540c2ULL );
        lsr64_ok ( 0x06760c14710540c2ULL,  0, 0x06760c14710540c2ULL );
        asr64_ok ( 0x06760c14710540c2ULL,  0, 0x06760c14710540c2ULL );
        lsl64_ok ( 0xccafd1a8cb724c13ULL, 20, 0x1a8cb724c1300000ULL );
        lsr64_ok ( 0xccafd1a8cb724c13ULL, 20, 0x00000ccafd1a8cb7ULL );
        asr64_ok ( 0xccafd1a8cb724c13ULL, 20, 0xfffffccafd1a8cb7ULL );
        lsl64_ok ( 0x83567264b1234518ULL, 32, 0xb123451800000000ULL );
        lsr64_ok ( 0x83567264b1234518ULL, 32, 0x0000000083567264ULL );
        asr64_ok ( 0x83567264b1234518ULL, 32, 0xffffffff83567264ULL );
        lsl64_ok ( 0x69ee42fcbf1a4ea4ULL, 47, 0x2752000000000000ULL );
        lsr64_ok ( 0x69ee42fcbf1a4ea4ULL, 47, 0x000000000000d3dcULL );
        asr64_ok ( 0x69ee42fcbf1a4ea4ULL, 47, 0x000000000000d3dcULL );
        lsl64_ok ( 0xaa20b8caddee4269ULL, 63, 0x8000000000000000ULL );
        lsr64_ok ( 0xaa20b8caddee4269ULL, 63, 0x0000000000000001ULL );
        asr64_ok ( 0xaa20b8caddee4269ULL, 63, 0xffffffffffffffffULL );
        u64divmod_ok ( 0x2b90ddccf699f765ULL, 0xed9f5e73ULL,
                       0x2eef6ab4ULL, 0x0e12f089ULL );
        s64divmod_ok ( 0x2b90ddccf699f765ULL, 0xed9f5e73ULL,
                       0x2eef6ab4ULL, 0x0e12f089ULL );
        u64divmod_ok ( 0xc09e00dcb9e34b54ULL, 0x35968185cdc744f3ULL,
                       3, 0x1fda7c4b508d7c7bULL );
        s64divmod_ok ( -0x3f61ff23461cb4acLL, 0x35968185cdc744f3ULL,
                       -1LL, -0x9cb7d9d78556fb9LL );
        u64divmod_ok ( 0, 0x5b2f2737f4ffULL, 0, 0 );
        s64divmod_ok ( 0, 0xbb00ded72766207fULL, 0, 0 );
 
        /* Test integer square root */
        ok ( isqrt ( 0 ) == 0 );
        ok ( isqrt ( 1 ) == 1 );
        ok ( isqrt ( 255 ) == 15 );
        ok ( isqrt ( 256 ) == 16 );
        ok ( isqrt ( 257 ) == 16 );
        ok ( isqrt ( 0xa53df2adUL ) == 52652 );
        ok ( isqrt ( 0x123793c6UL ) == 17482 );
        ok ( isqrt ( -1UL ) == ( -1UL >> ( 8 * sizeof ( unsigned long ) / 2 )));
}
 
/** Mathematical self-tests */
struct self_test math_test __self_test = {
        .name = "math",
        .exec = math_test_exec,
};