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_TEST_PRECISION 8

// 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))

// 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 : (                                                             \
                                                                              \
        /* check if b is a power of 2 */                                      \
        /* */                                                                 \
        /* formula: round(log_2(b) % 1, OPT_INT_DIV_TEST_PRECISION digits */  \
        /* after point) == 0                                              */  \
        (roundl(fmodl(log2l(INT_ABS((b))), 1.l) * OPT_INT_DIV_ROUNDING)       \
         == 0.l) ? (                                                          \
            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 */