gists/c-programming/math/opt_int_div.h

/*
 * opt_int_div.h
 *
 * "Optimized integer division"
 *
 * Author: Intel A80486DX2-66
 * License: Creative Commons Zero 1.0 Universal
 */

#include <math.h>
#include <stdint.h>

// parameters
#define OPT_INT_DIV_IS_TEST_PRECISION_LIMITED 0 /* true (1) or false (0) */
#define OPT_INT_DIV_TEST_PRECISION 8 /* only if the above parameter is 1 */

// constants
#define OPT_INT_DIV_ROUNDING                                                  \
    /* formula: 10^OPT_INT_DIV_TEST_PRECISION */                              \
    powl(10.l, (long double) OPT_INT_DIV_TEST_PRECISION)

// helper functions
#define INT_BIN_DIV(a, b) ((a) >> (uintmax_t) log2l((b)))
#define INT_DIV_NEG_RESULT_SIGN(a, b)                                         \
    /* the sign is negative only if one of the numbers is negative */         \
    (((a) < 0) != ((b) < 0)) /* 1 if sign is negative else 0 */
#define INT_ABS(x) ((x) < 0 ? -(x) : (x))
#define LOG2_DEC_PORTION(b) fmodl(log2l(INT_ABS((b))), 1.l)
#define OPT_INT_DIV_TEST(b)                                                   \
    /* check if b is a power of 2 */                                          \
    /* */                                                                     \
    /* formula: round(log_2(b) % 1, OPT_INT_DIV_TEST_PRECISION digits      */ \
    /* after point) == 0                                                   */ \
    OPT_INT_DIV_IS_TEST_PRECISION_LIMITED ?                                   \
        roundl(LOG2_DEC_PORTION((b)) * OPT_INT_DIV_ROUNDING) == 0.l           \
    :                                                                         \
        LOG2_DEC_PORTION((b)) == 0.l

// the main macro
#define OPT_INT_DIV(a, b)                                                     \
    ( /* beginning */                                                         \
        /* check for equality of a and b */                                   \
        INT_ABS((a)) == INT_ABS((b)) ?                                        \
            /* the result is +/-1 */                                          \
            (INT_DIV_NEG_RESULT_SIGN(a, b) ? -1 : 1) : (                      \
                                                                              \
        /* check if abs(a) < abs(b) */                                        \
        INT_ABS((a)) < INT_ABS((b)) ?                                         \
            0 : (                                                             \
                                                                              \
        OPT_INT_DIV_TEST((b)) ?                                               \
            (INT_DIV_NEG_RESULT_SIGN(a, b) ?                                  \
                -INT_BIN_DIV(INT_ABS((a)), INT_ABS((b)))                      \
            :                                                                 \
                INT_BIN_DIV(INT_ABS((a)), INT_ABS((b))))                      \
        :                                                                     \
            ((a) / (b)) ))                                                    \
    ) /* end */