Atomically increment two integers with CAS

Question

Apparently, it is possible to atomically increment two integers with compare-and-swap instructions. This talk claims that such an algorithm exists but it does not detail wha

Answer 1

Make me think of a sequence lock. Not very accurate (putting this from memory) but something along the lines of:

let x,y and s be 64 bit integers.

To increment:

atomic s++ (I mean atomic increment using 64 bit CAS op)

memory barrier
atomic x++
atomic y++
atomic s++
memory barrier

To read:

do {
    S1 = load s
    X = load x
    Y = load y
    memory barrier
    S2 = load s
} while (S1 != S2)

Also see https://en.wikipedia.org/wiki/Seqlock

Answer 2

If sse2 is available, you can use paddq to add 2 64 bit integers to two other 64 bit integers in one instruction.

#include "emmintrin.h"
//initialize your values somewhere:
//const __m128i ones = _mm_set1_epi64x(1);
//volatile register __m128i vars = 
//    _mm_set_epi64x(24,7);
static inline __m128i inc_both(__m128i vars, __m128i ones){
  return _mm_add_epi64(vars,ones);
}

This should compile to

    paddq  %xmm0, %xmm1

Since it is static inline, it may use other xmm registers though. If there is significant register pressure the ones operands may become ones(℅rip)

Note: this can be used for adding values other than 1 and there are similar operations for most other math, bitwise and compare instructions, should you need them.

So you can use the lock prefix and make it into an inline asm macro

#define inc64x2(vars) asm volatile( \
    "paddq %0, %1\n":"+x"(vars):"x"(ones) \
  );

The arm neon equivalent is something like: vaddq_s64(...), but there is a great article about arm/x86 equivalents here.

Answer 3

I've got a solution I've tested. Contained herein is a soup to nuts proof of concept program.

The algorithm is a "use CAS thread id gate" as the 3rd integer. I watched the video talk twice, and I believe this qualifies. It may not be the algorithm that the presenter was thinking of, but it does work.

The X and Y values can be anywhere in memory and the program places them far enough away from each other that they are on different cache lines. It doesn't really matter.

---

A quick description of the algorithm:

Each thread has a unique id number or tid (non-zero), taken from one's favorite source: pthead_t, getpid, gettid, make one up by whatever means you want. In the program, it just assigns them sequentially starting from 1.

Each thread will call the increment function with this number.

The increment function will spin on a global gate variable using CAS with an old value of 0 and a new value of tid.

When the CAS succeeds, the thread now "owns" things. In other words, if the gate is zero, it's up for grabs. A non-zero value is the tid of the owner and the gate is locked.

Now, the owner is free to increment the X and Y values with simple x += 1 and y += 1.

After that, the increment function releases by doing a store of 0 into the gate.

---

Here is the diagnostic/proof-of-concept program with everything. The algorithm itself has no restrictions, but I coded it for my machine.

Some caveats:

• It assumes gcc/clang
• It assumes a 64 bit x86_64 arch.
• This was coded using nothing but inline asm and needs no [nor uses any] compiler atomic support for clarity, simplicity, and transparency.
• This was built under linux, but should work on any "reasonable" x86 machine/OS (e.g. BSD, OSX should be fine, cygwin probably, and mingw maybe)
• Other arches are fine if they support CAS, I just didn't code for them (e.g. arm might work if you code the CAS with ldex/stex pairs)
• There are enough abstract primitives that this would/should be easy.
• No attempt at Windows compatibility [if you want it, do your own port but send me no tears--or comments :-)].
• The makefile and program have been defaulted to best values
• Some x86 CPUs may need to use different defaults (e.g. need fence instructions). See the makefile.

Anyway, here it is:

// caslock -- prove cas lock algorithm

#include <stdio.h>
#include <stdlib.h>
#include <unistd.h>
#include <time.h>
#include <pthread.h>

#define systls              __thread

// repeat the madness only once
#ifdef __clang__
#define inline_common       inline
#else
#define inline_common       static inline
#endif
#define inline_always       inline_common __attribute__((__always_inline__))
#define inline_never        __attribute__((__noinline__))

// WARNING: inline CAS fails for gcc but works for clang!
#if _USE_CASINLINE_
#define inline_cas          inline_always
#else
#define inline_cas          inline_never
#endif

typedef unsigned int u32;
typedef unsigned long long u64;

#ifndef LOOPMAX
#define LOOPMAX             1000000
#endif

#ifndef TIDMAX
#define TIDMAX              20
#endif

#if _USE_VPTR_
typedef volatile u32 *xptr32_p;
typedef volatile u64 *xptr64_p;
#else
typedef u32 *xptr32_p;
typedef u64 *xptr64_p;
#endif

#if _USE_TID64_
typedef u64 tid_t;
#define tidload(_xptr)                  loadu64(_xptr)
#define tidcas(_xptr,_oval,_nval)       casu64(_xptr,_oval,_nval)
#define tidstore(_xptr,_nval)           storeu64(_xptr,_nval)
#else
typedef u32 tid_t;
#define tidload(_xptr)                  loadu32(_xptr)
#define tidcas(_xptr,_oval,_nval)       casu32(_xptr,_oval,_nval)
#define tidstore(_xptr,_nval)           storeu32(_xptr,_nval)
#endif
tid_t tidgate;                          // gate control
tid_t readycnt;                         // number of threads ready
tid_t donecnt;                          // number of threads complete

// ensure that the variables are nowhere near each other
u64 ary[100];
#define kickoff     ary[32]             // sync to fire threads
#define xval        ary[31]             // the X value
#define yval        ary[87]             // the Y value

int inctype;                            // increment algorithm to use
tid_t tidmax;                           // maximum number of tasks
u64 loopmax;                            // loop maximum for each task

// task control
struct tsk {
    tid_t tsk_tid;                      // task id
    u32 tsk_casmiss;                    // cas miss count
};
typedef struct tsk tsk_t;

tsk_t *tsklist;                         // task list
systls tsk_t *tskcur;                   // current task block

// show progress
#define PGR(_pgr) \
    do { \
        fputs(_pgr,stdout); \
        fflush(stdout); \
    } while (0)

// NOTE: some x86 arches need fence instructions
//   0 -- no fence instructions
//   1 -- use mfence
//   2 -- use lfence/sfence
#if _USE_BARRIER_ == 0
#define BARRIER_RELEASE             ""
#define BARRIER_ACQUIRE             ""
#define BARRIER_ALL                 ""
#elif _USE_BARRIER_ == 1
#define BARRIER_ACQUIRE             "\tmfence\n"
#define BARRIER_RELEASE             "\tmfence\n"
#define BARRIER_ALL                 "\tmfence\n"
#elif _USE_BARRIER_ == 2
#define BARRIER_ACQUIRE             "\tlfence\n"
#define BARRIER_RELEASE             "\tsfence\n"
#define BARRIER_ALL                 "\tmfence\n"
#else
#error caslock: unknown barrier type
#endif

// barrier_acquire -- acquire barrier
inline_always void
barrier_acquire(void)
{

    __asm__ __volatile__ (
        BARRIER_ACQUIRE
        :
        :
        :   "memory");
}

// barrier_release -- release barrier
inline_always void
barrier_release(void)
{

    __asm__ __volatile__ (
        BARRIER_RELEASE
        :
        :
        :   "memory");
}

// barrier -- barrier
inline_always void
barrier(void)
{

    __asm__ __volatile__ (
        BARRIER_ALL
        :
        :
        :   "memory");
}

// casu32 -- compare and exchange four bytes
// RETURNS: 1=ok, 0=fail
inline_cas int
casu32(xptr32_p xptr,u32 oldval,u32 newval)
{
    char ok;

    __asm__ __volatile__ (
        "   lock\n"
        "   cmpxchg     %[newval],%[xptr]\n"
        "   sete        %[ok]\n"
        :   [ok] "=r" (ok),
            [xptr] "=m" (*xptr)
        :   "a" (oldval),
            [newval] "r" (newval)
        :   "memory");

    return ok;
}

// casu64 -- compare and exchange eight bytes
// RETURNS: 1=ok, 0=fail
inline_cas int
casu64(xptr64_p xptr,u64 oldval,u64 newval)
{
    char ok;

    __asm__ __volatile__ (
        "   lock\n"
        "   cmpxchg     %[newval],%[xptr]\n"
        "   sete        %[ok]\n"
        :   [ok] "=r" (ok),
            [xptr] "=m" (*xptr)
        :   "a" (oldval),
            [newval] "r" (newval)
        :   "memory");

    return ok;
}

// loadu32 -- load value with barrier
// RETURNS: loaded value
inline_always u32
loadu32(const xptr32_p xptr)
{
    u32 val;

    barrier_acquire();

    val = *xptr;

    return val;
}

// loadu64 -- load value with barrier
// RETURNS: loaded value
inline_always u64
loadu64(const xptr64_p xptr)
{
    u64 val;

    barrier_acquire();

    val = *xptr;

    return val;
}

// storeu32 -- store value with barrier
inline_always void
storeu32(xptr32_p xptr,u32 val)
{

    *xptr = val;

    barrier_release();
}

// storeu64 -- store value with barrier
inline_always void
storeu64(xptr64_p xptr,u64 val)
{

    *xptr = val;

    barrier_release();
}

// qsleep -- do a quick sleep
inline_always void
qsleep(int bigflg)
{
    struct timespec ts;

    if (bigflg) {
        ts.tv_sec = 1;
        ts.tv_nsec = 0;
    }
    else {
        ts.tv_sec = 0;
        ts.tv_nsec = 1000;
    }

    nanosleep(&ts,NULL);
}

// incby_tidgate -- increment by using thread id gate
void
incby_tidgate(tid_t tid)
// tid -- unique id for accessing entity (e.g. thread id)
{
    tid_t *gptr;
    tid_t oval;

    gptr = &tidgate;

    // acquire the gate
    while (1) {
        oval = 0;

        // test mode -- just do a nop instead of CAS to prove diagnostic
#if _USE_CASOFF_
        *gptr = oval;
        break;
#else
        if (tidcas(gptr,oval,tid))
            break;
#endif

        ++tskcur->tsk_casmiss;
    }

#if _USE_INCBARRIER_
    barrier_acquire();
#endif

    // increment the values
    xval += 1;
    yval += 1;

#if _USE_INCBARRIER_
    barrier_release();
#endif

    // release the gate
    // NOTE: CAS will always provide a barrier
#if _USE_CASPOST_ && (_USE_CASOFF_ == 0)
    oval = tidcas(gptr,tid,0);
#else
    tidstore(gptr,0);
#endif
}

// tskcld -- child task
void *
tskcld(void *arg)
{
    tid_t tid;
    tid_t oval;
    u64 loopcur;

    tskcur = arg;
    tid = tskcur->tsk_tid;

    // tell master thread that we're fully ready
    while (1) {
        oval = tidload(&readycnt);
        if (tidcas(&readycnt,oval,oval + 1))
            break;
    }

    // wait until we're given the starting gun
    while (1) {
        if (loadu64(&kickoff))
            break;
        qsleep(0);
    }

    // do the increments
    for (loopcur = loopmax;  loopcur > 0;  --loopcur)
        incby_tidgate(tid);

    barrier();

    // tell master thread that we're fully complete
    while (1) {
        oval = tidload(&donecnt);
        if (tidcas(&donecnt,oval,oval + 1))
            break;
    }

    return (void *) 0;
}

// tskstart -- start a child task
void
tskstart(tid_t tid)
{
    pthread_attr_t attr;
    pthread_t thr;
    int err;
    tsk_t *tsk;

    tsk = tsklist + tid;
    tsk->tsk_tid = tid;

    pthread_attr_init(&attr);
    pthread_attr_setdetachstate(&attr,1);
    err = pthread_create(&thr,&attr,tskcld,tsk);
    pthread_attr_destroy(&attr);

    if (err)
        printf("tskstart: error -- err=%d\n",err);
}

// tskall -- run a single test
void
tskall(void)
{
    tid_t tidcur;
    tsk_t *tsk;
    u64 incmax;
    u64 val;
    int err;

    xval = 0;
    yval = 0;

    kickoff = 0;
    readycnt = 0;
    donecnt = 0;
    tidgate = 0;

    // prealloc the task blocks
    tsklist = calloc(tidmax + 1,sizeof(tsk_t));

    // start all tasks
    PGR(" St");
    for (tidcur = 1;  tidcur <= tidmax;  ++tidcur)
        tskstart(tidcur);

    // wait for all tasks to be fully ready
    PGR(" Sw");
    while (1) {
        if (tidload(&readycnt) == tidmax)
            break;
        qsleep(1);
    }

    // the starting gun -- all tasks are waiting for this
    PGR(" Ko");
    storeu64(&kickoff,1);

    // wait for all tasks to be fully done
    PGR(" Wd");
    while (1) {
        if (tidload(&donecnt) == tidmax)
            break;
        qsleep(1);
    }

    PGR(" Done\n");

    // check the final count
    incmax = loopmax * tidmax;

    // show per-task statistics
    for (tidcur = 1;  tidcur <= tidmax;  ++tidcur) {
        tsk = tsklist + tidcur;
        printf("tskall: tsk=%llu tsk_casmiss=%d (%.3f%%)\n",
            (u64) tidcur,tsk->tsk_casmiss,(double) tsk->tsk_casmiss / loopmax);
    }

    err = 0;

    // check for failure
    val = loadu64(&xval);
    if (val != incmax) {
        printf("tskall: xval fault -- xval=%lld incmax=%lld\n",val,incmax);
        err = 1;
    }

    // check for failure
    val = loadu64(&yval);
    if (val != incmax) {
        printf("tskall: yval fault -- yval=%lld incmax=%lld\n",val,incmax);
        err = 1;
    }

    if (! err)
        printf("tskall: SUCCESS\n");

    free(tsklist);
}

// main -- master control
int
main(void)
{

    loopmax = LOOPMAX;
    tidmax = TIDMAX;

    inctype = 0;
    tskall();

    return 0;
}

---

Here is the Makefile. Sorry for the extra boilerplate:

# caslock/Makefile -- make file for caslock
#
# options:
#   LOOPMAX -- maximum loops / thread
#
#   TIDMAX -- maximum number of threads
#
#   BARRIER -- generate fence/barrier instructions
#     0 -- none
#     1 -- use mfence everywhere
#     2 -- use lfence for acquire, sfence for release
#
#   CASOFF -- disable CAS to prove diagnostic works
#     0 -- normal mode
#     1 -- inhibit CAS during X/Y increment
#
#   CASINLINE -- inline the CAS functions
#     0 -- do _not_ inline
#     1 -- inline them (WARNING: this fails for gcc but works for clang!)
#
#   CASPOST -- increment gate release mode
#     0 -- use fenced store
#     1 -- use CAS store (NOTE: not really required)
#
#   INCBARRIER -- use extra barriers around increments
#     0 -- rely on CAS for barrier
#     1 -- add extra safety barriers immediately before increment of X/Y
#
#   TID64 -- use 64 bit thread "id"s
#     0 -- use 32 bit
#     1 -- use 64 bit
#
#   VPTR -- use volatile pointers in function definitions
#     0 -- use ordinary pointers
#     1 -- use volatile pointers (NOTE: not really required)

ifndef _CASLOCK_MK_
_CASLOCK_MK_ = 1

  OLIST += caslock.o

  ifndef LOOPMAX
    LOOPMAX = 1000000
  endif

  ifndef TIDMAX
    TIDMAX = 20
  endif

  ifndef BARRIER
    BARRIER = 0
  endif

  ifndef CASINLINE
    CASINLINE = 0
  endif

  ifndef CASOFF
    CASOFF = 0
  endif

  ifndef CASPOST
    CASPOST = 0
  endif

  ifndef INCBARRIER
    INCBARRIER = 0
  endif

  ifndef TID64
    TID64 = 0
  endif

  ifndef VPTR
    VPTR = 0
  endif

  CFLAGS += -DLOOPMAX=$(LOOPMAX)
  CFLAGS += -DTIDMAX=$(TIDMAX)

  CFLAGS += -D_USE_BARRIER_=$(BARRIER)
  CFLAGS += -D_USE_CASINLINE_=$(CASINLINE)
  CFLAGS += -D_USE_CASOFF_=$(CASOFF)
  CFLAGS += -D_USE_CASPOST_=$(CASPOST)
  CFLAGS += -D_USE_INCBARRIER_=$(INCBARRIER)
  CFLAGS += -D_USE_TID64_=$(TID64)
  CFLAGS += -D_USE_VPTR_=$(VPTR)

  STDLIB += -lpthread

  ALL += caslock
  CLEAN += caslock

  OVRPUB := 1

  ifndef OVRTOP
    OVRTOP := $(shell pwd)
    OVRTOP := $(dir $(OVRTOP))
  endif
endif

# ovrlib/rules.mk -- rules control
#
# options:
#   GDB -- enable debug symbols
#     0 -- normal
#     1 -- use -O0 and define _USE_GDB_=1
#
#   CLANG -- use clang instead of gcc
#     0 -- use gcc
#     1 -- use clang
#
#   BNC -- enable benchmarks
#     0 -- normal mode
#     1 -- enable benchmarks for function enter/exit pairs

ifdef OVRPUB
  ifndef SDIR
    SDIR := $(shell pwd)
    STAIL := $(notdir $(SDIR))
  endif

  ifndef GENTOP
    GENTOP := $(dir $(SDIR))
  endif

  ifndef GENDIR
    GENDIR := $(GENTOP)/$(STAIL)
  endif

  ifndef ODIR
    ODIR := $(GENDIR)
  endif

  PROTOLST := true
  PROTOGEN := @true
endif

ifndef SDIR
  $(error rules: SDIR not defined)
endif
ifndef ODIR
  $(error rules: ODIR not defined)
endif
ifndef GENDIR
  $(error rules: GENDIR not defined)
endif
ifndef GENTOP
  $(error rules: GENTOP not defined)
endif

ifndef _RULES_MK_
_RULES_MK_ = 1

  CLEAN += *.proto
  CLEAN += *.a
  CLEAN += *.o
  CLEAN += *.i
  CLEAN += *.dis
  CLEAN += *.TMP

  QPROTO := $(shell $(PROTOLST) -i -l -O$(GENTOP) $(SDIR)/*.c $(CPROTO))
  HDEP += $(QPROTO)

###VPATH += $(GENDIR)
###VPATH += $(SDIR)

  ifdef INCLUDE_MK
    -include $(INCLUDE_MK)
  endif

  ifdef GSYM
    CFLAGS += -gdwarf-2
  endif

  ifdef GDB
    CFLAGS += -gdwarf-2
    DFLAGS += -D_USE_GDB_
  else
    CFLAGS += -O2
  endif

  ifndef ZPRT
    DFLAGS += -D_USE_ZPRT_=0
  endif

  ifdef BNC
    DFLAGS += -D_USE_BNC_=1
  endif

  ifdef CLANG
    CC := clang
  endif

  DFLAGS += -I$(GENTOP)
  DFLAGS += -I$(OVRTOP)

  CFLAGS += -Wall -Werror
  CFLAGS += -Wno-unknown-pragmas
  CFLAGS += -Wempty-body
  CFLAGS += -fno-diagnostics-color

  # NOTE: we now need this to prevent inlining (enabled at -O2)
  ifndef CLANG
    CFLAGS += -fno-inline-small-functions
  endif

  # NOTE: we now need this to prevent inlining (enabled at -O3)
  CFLAGS += -fno-inline-functions

  CFLAGS += $(DFLAGS)
endif

all: $(PREP) proto $(ALL)

%.o: %.c $(HDEP)
    $(CC) $(CFLAGS) -c -o $*.o $<

%.i: %.c
    cpp $(DFLAGS) -P $*.c > $*.i

%.s: %.c
    $(CC) $(CFLAGS) -S -o $*.s $<

# build a library (type (2) build)
$(LIBNAME):: $(OLIST)
    ar rv $@ $(OLIST)

.PHONY: proto
proto::
    $(PROTOGEN) -i -v -O$(GENTOP) $(SDIR)/*.c $(CPROTO)

.PHONY: clean
clean::
    rm -f $(CLEAN)

.PHONY: help
help::
    egrep '^#' Makefile

caslock:: $(OLIST) $(LIBLIST) $(STDLIB)
    $(CC) $(CFLAGS) -o caslock $(OLIST) $(LIBLIST) $(STDLIB)

---

NOTE: I may have blown some of the asm constraints because when doing the CAS function as an inline, compiling with gcc produces incorrect results. However, clang works fine with inline. So, the default is that the CAS function is not inline. For consistency, I didn't use a different default for gcc/clang, even though I could.

Here's the disassembly of the relevant function with inline as built by gcc (this fails):

00000000004009c0 <incby_tidgate>:
  4009c0:       31 c0                   xor    %eax,%eax
  4009c2:       f0 0f b1 3d 3a 1a 20    lock cmpxchg %edi,0x201a3a(%rip)        # 602404 <tidgate>
  4009c9:       00
  4009ca:       0f 94 c2                sete   %dl
  4009cd:       84 d2                   test   %dl,%dl
  4009cf:       75 23                   jne    4009f4 <L01>
  4009d1:       0f 1f 80 00 00 00 00    nopl   0x0(%rax)
  4009d8:L00    64 48 8b 14 25 f8 ff    mov    %fs:0xfffffffffffffff8,%rdx
  4009df:       ff ff
  4009e1:       83 42 04 01             addl   $0x1,0x4(%rdx)
  4009e5:       f0 0f b1 3d 17 1a 20    lock cmpxchg %edi,0x201a17(%rip)        # 602404 <tidgate>
  4009ec:       00
  4009ed:       0f 94 c2                sete   %dl
  4009f0:       84 d2                   test   %dl,%dl
  4009f2:       74 e4                   je     4009d8 <L00>
  4009f4:L01    48 83 05 dc 17 20 00    addq   $0x1,0x2017dc(%rip)        # 6021d8 <ary+0xf8>
  4009fb:       01
  4009fc:       48 83 05 94 19 20 00    addq   $0x1,0x201994(%rip)        # 602398 <ary+0x2b8>
  400a03:       01
  400a04:       c7 05 f6 19 20 00 00    movl   $0x0,0x2019f6(%rip)        # 602404 <tidgate>
  400a0b:       00 00 00
  400a0e:       c3                      retq

Here's the disassembly of the relevant function with inline as built by clang (this succeeds):

0000000000400990 <incby_tidgate>:
  400990:       31 c0                   xor    %eax,%eax
  400992:       f0 0f b1 3d 3a 1a 20    lock cmpxchg %edi,0x201a3a(%rip)        # 6023d4 <tidgate>
  400999:       00
  40099a:       0f 94 c0                sete   %al
  40099d:       eb 1a                   jmp    4009b9 <L01>
  40099f:       90                      nop
  4009a0:L00    64 48 8b 04 25 f8 ff    mov    %fs:0xfffffffffffffff8,%rax
  4009a7:       ff ff
  4009a9:       ff 40 04                incl   0x4(%rax)
  4009ac:       31 c0                   xor    %eax,%eax
  4009ae:       f0 0f b1 3d 1e 1a 20    lock cmpxchg %edi,0x201a1e(%rip)        # 6023d4 <tidgate>
  4009b5:       00
  4009b6:       0f 94 c0                sete   %al
  4009b9:L01    84 c0                   test   %al,%al
  4009bb:       74 e3                   je     4009a0 <L00>
  4009bd:       48 ff 05 e4 17 20 00    incq   0x2017e4(%rip)        # 6021a8 <ary+0xf8>
  4009c4:       48 ff 05 9d 19 20 00    incq   0x20199d(%rip)        # 602368 <ary+0x2b8>
  4009cb:       c7 05 ff 19 20 00 00    movl   $0x0,0x2019ff(%rip)        # 6023d4 <tidgate>
  4009d2:       00 00 00
  4009d5:       c3                      retq
  4009d6:       66 2e 0f 1f 84 00 00    nopw   %cs:0x0(%rax,%rax,1)
  4009dd:       00 00 00