@@ -32,6 +32,149 @@
#elif BITS_PER_LONG == 32
+/* macroized fls implementation to ensure proper constant propagation */
+#define __div64_fls(bits) \
+({ \
+ unsigned int __left = (bits), __nr = 0; \
+ if (__left & 0xffff0000) __nr += 16, __left >>= 16; \
+ if (__left & 0x0000ff00) __nr += 8, __left >>= 8; \
+ if (__left & 0x000000f0) __nr += 4, __left >>= 4; \
+ if (__left & 0x0000000c) __nr += 2, __left >>= 2; \
+ if (__left & 0x00000002) __nr += 1; \
+ __nr; \
+})
+
+/*
+ * If the divisor happens to be constant, we determine the appropriate
+ * inverse at compile time to turn the division into a few inline
+ * multiplications which ought to be much faster. And yet only if compiling
+ * with a sufficiently recent gcc version to perform proper 64-bit constant
+ * propagation.
+ *
+ * (It is unfortunate that gcc doesn't perform all this internally.)
+ */
+#define __div64_const32(n, ___b) \
+({ \
+ /* \
+ * Multiplication by reciprocal of b: n / b = n * (p / b) / p \
+ * \
+ * We rely on the fact that most of this code gets optimized \
+ * away at compile time due to constant propagation and only \
+ * a few multiplication instructions should remain. \
+ * Hence this monstrous macro (static inline doesn't always \
+ * do the trick for some reason). \
+ */ \
+ uint64_t ___res, ___x, ___t, ___m, ___n = (n); \
+ uint32_t ___c, ___p, ___m_lo, ___m_hi, ___n_lo, ___n_hi; \
+ \
+ /* determine number of bits to represent b */ \
+ ___p = 1 << __div64_fls(___b); \
+ \
+ /* compute m = ((p << 64) + b - 1) / b */ \
+ ___m = (~0ULL / ___b) * ___p; \
+ ___m += (((~0ULL % ___b + 1) * ___p) + ___b - 1) / ___b; \
+ \
+ /* dividend that produces one less than the highest result */ \
+ ___x = ~0ULL / ___b * ___b - 1; \
+ \
+ /* test our m with res = m * x / (p << 64) */ \
+ ___res = ((___m & 0xffffffff) * (___x & 0xffffffff)) >> 32; \
+ ___t = ___res += (___m & 0xffffffff) * (___x >> 32); \
+ ___res += (___x & 0xffffffff) * (___m >> 32); \
+ ___t = (___res < ___t) ? (1ULL << 32) : 0; \
+ ___res = (___res >> 32) + ___t; \
+ ___res += (___m >> 32) * (___x >> 32); \
+ ___res /= ___p; \
+ \
+ /* Now sanitize and optimize what we've got. */ \
+ if (~0ULL % (___b / (___b & -___b)) == 0) { \
+ /* those cases can be simplified with: */ \
+ ___n /= (___b & -___b); \
+ ___m = ~0ULL / (___b / (___b & -___b)); \
+ ___p = 1; \
+ ___c = 1; \
+ } else if (___res != ___x / ___b) { \
+ /* \
+ * We can't get away without a correction to compensate \
+ * for bit truncation errors. To avoid it we'd need an \
+ * additional bit to represent m which would overflow \
+ * our 64-bit variable. \
+ * \
+ * Instead we do m = p / b and n / b = (n * m + m) / p. \
+ */ \
+ ___c = 1; \
+ /* Compute m = (p << 64) / b */ \
+ ___m = (~0ULL / ___b) * ___p; \
+ ___m += ((~0ULL % ___b + 1) * ___p) / ___b; \
+ } else { \
+ /* \
+ * Reduce m / p, and try to clear bit 31 of m when \
+ * possible, otherwise that'll need extra overflow \
+ * handling later. \
+ */ \
+ unsigned int ___bits = -(___m & -___m); \
+ ___bits |= ___m >> 32; \
+ ___bits = (~___bits) << 1; \
+ /* \
+ * If ___bits == 0 then setting bit 31 is unavoidable. \
+ * Simply apply the maximum possible reduction in that \
+ * case. Otherwise the MSB of ___bits indicates the \
+ * best reduction we should apply. \
+ */ \
+ if (!___bits) { \
+ ___p /= (___m & -___m); \
+ ___m /= (___m & -___m); \
+ } else { \
+ ___p >>= __div64_fls(___bits); \
+ ___m >>= __div64_fls(___bits); \
+ } \
+ /* No correction needed. */ \
+ ___c = 0; \
+ } \
+ \
+ /* \
+ * Now we have a combination of 2 conditions: \
+ * \
+ * 1) whether or not we need a correction (___c), and \
+ * \
+ * 2) whether or not there might be an overflow in the cross \
+ * product determined by (___m & ((1 << 63) | (1 << 31))). \
+ * \
+ * Select the best way to do the m * n / (p << 64) operation. \
+ * From here on there will be actual runtime code generated. \
+ */ \
+ \
+ ___m_lo = ___m; \
+ ___m_hi = ___m >> 32; \
+ ___n_lo = ___n; \
+ ___n_hi = ___n >> 32; \
+ \
+ if (!___c) { \
+ ___res = ((uint64_t)___m_lo * ___n_lo) >> 32; \
+ } else if (!(___m & ((1ULL << 63) | (1ULL << 31)))) { \
+ ___res = (___m + (uint64_t)___m_lo * ___n_lo) >> 32; \
+ } else { \
+ ___res = ___m + (uint64_t)___m_lo * ___n_lo; \
+ ___t = (___res < ___m) ? (1ULL << 32) : 0; \
+ ___res = (___res >> 32) + ___t; \
+ } \
+ \
+ if (!(___m & ((1ULL << 63) | (1ULL << 31)))) { \
+ ___res += (uint64_t)___m_lo * ___n_hi; \
+ ___res += (uint64_t)___m_hi * ___n_lo; \
+ ___res >>= 32; \
+ } else { \
+ ___t = ___res += (uint64_t)___m_lo * ___n_hi; \
+ ___res += (uint64_t)___m_hi * ___n_lo; \
+ ___t = (___res < ___t) ? (1ULL << 32) : 0; \
+ ___res = (___res >> 32) + ___t; \
+ } \
+ \
+ ___res += (uint64_t)___m_hi * ___n_hi; \
+ \
+ ___res / ___p; \
+})
+
extern uint32_t __div64_32(uint64_t *dividend, uint32_t divisor);
/* The unnecessary pointer compare is there
@@ -41,7 +184,20 @@ extern uint32_t __div64_32(uint64_t *dividend, uint32_t divisor);
uint32_t __base = (base); \
uint32_t __rem; \
(void)(((typeof((n)) *)0) == ((uint64_t *)0)); \
- if (likely(((n) >> 32) == 0)) { \
+ if (__builtin_constant_p(__base) && \
+ (__base & (__base - 1)) == 0) { \
+ /* constant power of 2: gcc is fine */ \
+ __rem = (n) & (__base - 1); \
+ (n) /= __base; \
+ } else if ((__GNUC__ >= 4) && \
+ __builtin_constant_p(__base) && \
+ __base != 0) { \
+ uint32_t __res_lo, __n_lo = (n); \
+ (n) = __div64_const32(n, __base); \
+ /* the remainder can be computed with 32-bit regs */ \
+ __res_lo = (n); \
+ __rem = __n_lo - __res_lo * __base; \
+ } else if (likely(((n) >> 32) == 0)) { \
__rem = (uint32_t)(n) % __base; \
(n) = (uint32_t)(n) / __base; \
} else \