arithmetic.c File Reference

#include <stdint.h>

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Functions
static uint32_t	divl (uint64_t n, uint32_t d)
static int	nlz (uint32_t x)
static uint64_t	udiv64 (uint64_t n, uint64_t d)
static uint32_t	umod64 (uint64_t n, uint64_t d)
static int64_t	sdiv64 (int64_t n, int64_t d)
static int32_t	smod64 (int64_t n, int64_t d)
long long	__divdi3 (long long n, long long d)
long long	__moddi3 (long long n, long long d)
unsigned long long	__udivdi3 (unsigned long long n, unsigned long long d)
unsigned long long	__umoddi3 (unsigned long long n, unsigned long long d)

Function Documentation

__divdi3()

long long __divdi3	(	long long	n,
		long long	d
	)

                                    {
    return sdiv64 (n, d);
}

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__moddi3()

long long __moddi3	(	long long	n,
		long long	d
	)

                                    {
    return smod64 (n, d);
}

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__udivdi3()

unsigned long long __udivdi3	(	unsigned long long	n,
		unsigned long long	d
	)

                                                       {
    return udiv64 (n, d);
}

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__umoddi3()

unsigned long long __umoddi3	(	unsigned long long	n,
		unsigned long long	d
	)

                                                       {
    return umod64 (n, d);
}

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divl()

static uint32_t divl ( uint64_t  n, uint32_t  d  )

inlinestatic

                              {
    uint32_t n1 = n >> 32;
    uint32_t n0 = n;
    uint32_t q, r;
 
    asm ("divl %4"
            : "=d" (r), "=a" (q)
            : "0" (n1), "1" (n0), "rm" (d));
 
    return q;
}

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nlz()

static int nlz ( uint32_t  x )

static

                 {
    /* This technique is portable, but there are better ways to do
       it on particular systems.  With sufficiently new enough GCC,
       you can use __builtin_clz() to take advantage of GCC's
       knowledge of how to do it.  Or you can use the x86 BSR
       instruction directly. */
    int n = 0;
    if (x <= 0x0000FFFF) {
        n += 16;
        x <<= 16;
    }
    if (x <= 0x00FFFFFF) {
        n += 8;
        x <<= 8;
    }
    if (x <= 0x0FFFFFFF) {
        n += 4;
        x <<= 4;
    }
    if (x <= 0x3FFFFFFF) {
        n += 2;
        x <<= 2;
    }
    if (x <= 0x7FFFFFFF)
        n++;
    return n;
}

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sdiv64()

static int64_t sdiv64 ( int64_t  n, int64_t  d  )

static

                              {
    uint64_t n_abs = n >= 0 ? (uint64_t) n : -(uint64_t) n;
    uint64_t d_abs = d >= 0 ? (uint64_t) d : -(uint64_t) d;
    uint64_t q_abs = udiv64 (n_abs, d_abs);
    return (n < 0) == (d < 0) ? (int64_t) q_abs : -(int64_t) q_abs;
}

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smod64()

static int32_t smod64 ( int64_t  n, int64_t  d  )

static

                              {
    return n - d * sdiv64 (n, d);
}

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udiv64()

static uint64_t udiv64 ( uint64_t  n, uint64_t  d  )

static

                                {
    if ((d >> 32) == 0) {
        /* Proof of correctness:
 
           Let n, d, b, n1, and n0 be defined as in this function.
           Let [x] be the "floor" of x.  Let T = b[n1/d].  Assume d
           nonzero.  Then:
           [n/d] = [n/d] - T + T
           = [n/d - T] + T                         by (1) below
           = [(b*n1 + n0)/d - T] + T               by definition of n
           = [(b*n1 + n0)/d - dT/d] + T
           = [(b(n1 - d[n1/d]) + n0)/d] + T
           = [(b[n1 % d] + n0)/d] + T,             by definition of %
           which is the expression calculated below.
 
           (1) Note that for any real x, integer i: [x] + i = [x + i].
 
           To prevent divl() from trapping, [(b[n1 % d] + n0)/d] must
           be less than b.  Assume that [n1 % d] and n0 take their
           respective maximum values of d - 1 and b - 1:
           [(b(d - 1) + (b - 1))/d] < b
           <=> [(bd - 1)/d] < b
           <=> [b - 1/d] < b
           which is a tautology.
 
           Therefore, this code is correct and will not trap. */
        uint64_t b = 1ULL << 32;
        uint32_t n1 = n >> 32;
        uint32_t n0 = n;
        uint32_t d0 = d;
 
        return divl (b * (n1 % d0) + n0, d0) + b * (n1 / d0);
    } else {
        /* Based on the algorithm and proof available from
         * http://www.hackersdelight.org/revisions.pdf. */
        if (n < d)
            return 0;
        else {
            uint32_t d1 = d >> 32;
            int s = nlz (d1);
            uint64_t q = divl (n >> 1, (d << s) >> 32) >> (31 - s);
            return n - (q - 1) * d < d ? q - 1 : q;
        }
    }
}

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umod64()

static uint32_t umod64 ( uint64_t  n, uint64_t  d  )

static

                                {
    return n - d * udiv64 (n, d);
}

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