From 536edd67109df5e0cdb2c4ee759e9bade7976367 Mon Sep 17 00:00:00 2001 From: Eric Dumazet Date: Sat, 12 May 2012 03:32:13 +0000 Subject: [PATCH 37/41] codel: use Newton method instead of sqrt() and divides As Van pointed out, interval/sqrt(count) can be implemented using multiplies only. http://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Iterative_methods_for_reciprocal_square_roots This patch implements the Newton method and reciprocal divide. Total cost is 15 cycles instead of 120 on my Corei5 machine (64bit kernel). There is a small 'error' for count values < 5, but we don't really care. I reuse a hole in struct codel_vars : - pack the dropping boolean into one bit - use 31bit to store the reciprocal value of sqrt(count). Suggested-by: Van Jacobson Signed-off-by: Eric Dumazet Cc: Dave Taht Cc: Kathleen Nichols Cc: Tom Herbert Cc: Matt Mathis Cc: Yuchung Cheng Cc: Nandita Dukkipati Cc: Stephen Hemminger Signed-off-by: David S. Miller --- include/net/codel.h | 68 ++++++++++++++++++++++++++++----------------------- 1 file changed, 37 insertions(+), 31 deletions(-) --- a/include/net/codel.h +++ b/include/net/codel.h @@ -46,6 +46,7 @@ #include #include #include +#include /* Controlling Queue Delay (CoDel) algorithm * ========================================= @@ -123,6 +124,7 @@ struct codel_params { * entered dropping state * @lastcount: count at entry to dropping state * @dropping: set to true if in dropping state + * @rec_inv_sqrt: reciprocal value of sqrt(count) >> 1 * @first_above_time: when we went (or will go) continuously above target * for interval * @drop_next: time to drop next packet, or when we dropped last @@ -131,7 +133,8 @@ struct codel_params { struct codel_vars { u32 count; u32 lastcount; - bool dropping; + bool dropping:1; + u32 rec_inv_sqrt:31; codel_time_t first_above_time; codel_time_t drop_next; codel_time_t ldelay; @@ -158,11 +161,7 @@ static void codel_params_init(struct cod static void codel_vars_init(struct codel_vars *vars) { - vars->drop_next = 0; - vars->first_above_time = 0; - vars->dropping = false; /* exit dropping state */ - vars->count = 0; - vars->lastcount = 0; + memset(vars, 0, sizeof(*vars)); } static void codel_stats_init(struct codel_stats *stats) @@ -170,38 +169,37 @@ static void codel_stats_init(struct code stats->maxpacket = 256; } -/* return interval/sqrt(x) with good precision - * relies on int_sqrt(unsigned long x) kernel implementation +/* + * http://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Iterative_methods_for_reciprocal_square_roots + * new_invsqrt = (invsqrt / 2) * (3 - count * invsqrt^2) + * + * Here, invsqrt is a fixed point number (< 1.0), 31bit mantissa) */ -static u32 codel_inv_sqrt(u32 _interval, u32 _x) +static void codel_Newton_step(struct codel_vars *vars) { - u64 interval = _interval; - unsigned long x = _x; - - /* Scale operands for max precision */ + u32 invsqrt = vars->rec_inv_sqrt; + u32 invsqrt2 = ((u64)invsqrt * invsqrt) >> 31; + u64 val = (3LL << 31) - ((u64)vars->count * invsqrt2); -#if BITS_PER_LONG == 64 - x <<= 32; /* On 64bit arches, we can prescale x by 32bits */ - interval <<= 16; -#endif + val = (val * invsqrt) >> 32; - while (x < (1UL << (BITS_PER_LONG - 2))) { - x <<= 2; - interval <<= 1; - } - do_div(interval, int_sqrt(x)); - return (u32)interval; + vars->rec_inv_sqrt = val; } +/* + * CoDel control_law is t + interval/sqrt(count) + * We maintain in rec_inv_sqrt the reciprocal value of sqrt(count) to avoid + * both sqrt() and divide operation. + */ static codel_time_t codel_control_law(codel_time_t t, codel_time_t interval, - u32 count) + u32 rec_inv_sqrt) { - return t + codel_inv_sqrt(interval, count); + return t + reciprocal_divide(interval, rec_inv_sqrt << 1); } -static bool codel_should_drop(struct sk_buff *skb, +static bool codel_should_drop(const struct sk_buff *skb, unsigned int *backlog, struct codel_vars *vars, struct codel_params *params, @@ -274,14 +272,16 @@ static struct sk_buff *codel_dequeue(str */ while (vars->dropping && codel_time_after_eq(now, vars->drop_next)) { - if (++vars->count == 0) /* avoid zero divides */ - vars->count = ~0U; + vars->count++; /* dont care of possible wrap + * since there is no more divide + */ + codel_Newton_step(vars); if (params->ecn && INET_ECN_set_ce(skb)) { stats->ecn_mark++; vars->drop_next = codel_control_law(vars->drop_next, params->interval, - vars->count); + vars->rec_inv_sqrt); goto end; } qdisc_drop(skb, sch); @@ -296,7 +296,7 @@ static struct sk_buff *codel_dequeue(str vars->drop_next = codel_control_law(vars->drop_next, params->interval, - vars->count); + vars->rec_inv_sqrt); } } } @@ -319,12 +319,18 @@ static struct sk_buff *codel_dequeue(str if (codel_time_before(now - vars->drop_next, 16 * params->interval)) { vars->count = (vars->count - vars->lastcount) | 1; + /* we dont care if rec_inv_sqrt approximation + * is not very precise : + * Next Newton steps will correct it quadratically. + */ + codel_Newton_step(vars); } else { vars->count = 1; + vars->rec_inv_sqrt = 0x7fffffff; } vars->lastcount = vars->count; vars->drop_next = codel_control_law(now, params->interval, - vars->count); + vars->rec_inv_sqrt); } end: return skb;