Re: [PATCH v1 1/4] KVM: stats: Support linear and logarithmic histogram statistics

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On Thu, Jul 08, 2021 at 04:40:16PM -0500, Jing Zhang wrote:
> On Thu, Jul 8, 2021 at 4:01 PM David Matlack <dmatlack@xxxxxxxxxx> wrote:
> >
> > On Tue, Jul 06, 2021 at 06:03:47PM +0000, Jing Zhang wrote:
> > > Add new types of KVM stats, linear and logarithmic histogram.
> > > Histogram are very useful for observing the value distribution
> > > of time or size related stats.
> > >
> > > Signed-off-by: Jing Zhang <jingzhangos@xxxxxxxxxx>
> > > ---
> > >  arch/arm64/kvm/guest.c    |  4 ---
> > >  arch/mips/kvm/mips.c      |  4 ---
> > >  arch/powerpc/kvm/book3s.c |  4 ---
> > >  arch/powerpc/kvm/booke.c  |  4 ---
> > >  arch/s390/kvm/kvm-s390.c  |  4 ---
> > >  arch/x86/kvm/x86.c        |  4 ---
> > >  include/linux/kvm_host.h  | 53 ++++++++++++++++++++++++++++-----------
> > >  include/linux/kvm_types.h | 16 ++++++++++++
> > >  include/uapi/linux/kvm.h  | 11 +++++---
> > >  virt/kvm/binary_stats.c   | 36 ++++++++++++++++++++++++++
> > >  10 files changed, 98 insertions(+), 42 deletions(-)
> > >
> > > diff --git a/arch/arm64/kvm/guest.c b/arch/arm64/kvm/guest.c
> > > index 1512a8007a78..cb44d8756fa7 100644
> > > --- a/arch/arm64/kvm/guest.c
> > > +++ b/arch/arm64/kvm/guest.c
> > > @@ -31,8 +31,6 @@
> > >  const struct _kvm_stats_desc kvm_vm_stats_desc[] = {
> > >       KVM_GENERIC_VM_STATS()
> > >  };
> > > -static_assert(ARRAY_SIZE(kvm_vm_stats_desc) ==
> > > -             sizeof(struct kvm_vm_stat) / sizeof(u64));
> > >
> > >  const struct kvm_stats_header kvm_vm_stats_header = {
> > >       .name_size = KVM_STATS_NAME_SIZE,
> > > @@ -52,8 +50,6 @@ const struct _kvm_stats_desc kvm_vcpu_stats_desc[] = {
> > >       STATS_DESC_COUNTER(VCPU, mmio_exit_kernel),
> > >       STATS_DESC_COUNTER(VCPU, exits)
> > >  };
> > > -static_assert(ARRAY_SIZE(kvm_vcpu_stats_desc) ==
> > > -             sizeof(struct kvm_vcpu_stat) / sizeof(u64));
> > >
> > >  const struct kvm_stats_header kvm_vcpu_stats_header = {
> > >       .name_size = KVM_STATS_NAME_SIZE,
> > > diff --git a/arch/mips/kvm/mips.c b/arch/mips/kvm/mips.c
> > > index af9dd029a4e1..75c6f264c626 100644
> > > --- a/arch/mips/kvm/mips.c
> > > +++ b/arch/mips/kvm/mips.c
> > > @@ -41,8 +41,6 @@
> > >  const struct _kvm_stats_desc kvm_vm_stats_desc[] = {
> > >       KVM_GENERIC_VM_STATS()
> > >  };
> > > -static_assert(ARRAY_SIZE(kvm_vm_stats_desc) ==
> > > -             sizeof(struct kvm_vm_stat) / sizeof(u64));
> > >
> > >  const struct kvm_stats_header kvm_vm_stats_header = {
> > >       .name_size = KVM_STATS_NAME_SIZE,
> > > @@ -85,8 +83,6 @@ const struct _kvm_stats_desc kvm_vcpu_stats_desc[] = {
> > >       STATS_DESC_COUNTER(VCPU, vz_cpucfg_exits),
> > >  #endif
> > >  };
> > > -static_assert(ARRAY_SIZE(kvm_vcpu_stats_desc) ==
> > > -             sizeof(struct kvm_vcpu_stat) / sizeof(u64));
> > >
> > >  const struct kvm_stats_header kvm_vcpu_stats_header = {
> > >       .name_size = KVM_STATS_NAME_SIZE,
> > > diff --git a/arch/powerpc/kvm/book3s.c b/arch/powerpc/kvm/book3s.c
> > > index 79833f78d1da..5cc6e90095b0 100644
> > > --- a/arch/powerpc/kvm/book3s.c
> > > +++ b/arch/powerpc/kvm/book3s.c
> > > @@ -43,8 +43,6 @@ const struct _kvm_stats_desc kvm_vm_stats_desc[] = {
> > >       STATS_DESC_ICOUNTER(VM, num_2M_pages),
> > >       STATS_DESC_ICOUNTER(VM, num_1G_pages)
> > >  };
> > > -static_assert(ARRAY_SIZE(kvm_vm_stats_desc) ==
> > > -             sizeof(struct kvm_vm_stat) / sizeof(u64));
> > >
> > >  const struct kvm_stats_header kvm_vm_stats_header = {
> > >       .name_size = KVM_STATS_NAME_SIZE,
> > > @@ -88,8 +86,6 @@ const struct _kvm_stats_desc kvm_vcpu_stats_desc[] = {
> > >       STATS_DESC_COUNTER(VCPU, pthru_host),
> > >       STATS_DESC_COUNTER(VCPU, pthru_bad_aff)
> > >  };
> > > -static_assert(ARRAY_SIZE(kvm_vcpu_stats_desc) ==
> > > -             sizeof(struct kvm_vcpu_stat) / sizeof(u64));
> > >
> > >  const struct kvm_stats_header kvm_vcpu_stats_header = {
> > >       .name_size = KVM_STATS_NAME_SIZE,
> > > diff --git a/arch/powerpc/kvm/booke.c b/arch/powerpc/kvm/booke.c
> > > index 551b30d84aee..5ed6c235e059 100644
> > > --- a/arch/powerpc/kvm/booke.c
> > > +++ b/arch/powerpc/kvm/booke.c
> > > @@ -41,8 +41,6 @@ const struct _kvm_stats_desc kvm_vm_stats_desc[] = {
> > >       STATS_DESC_ICOUNTER(VM, num_2M_pages),
> > >       STATS_DESC_ICOUNTER(VM, num_1G_pages)
> > >  };
> > > -static_assert(ARRAY_SIZE(kvm_vm_stats_desc) ==
> > > -             sizeof(struct kvm_vm_stat) / sizeof(u64));
> > >
> > >  const struct kvm_stats_header kvm_vm_stats_header = {
> > >       .name_size = KVM_STATS_NAME_SIZE,
> > > @@ -79,8 +77,6 @@ const struct _kvm_stats_desc kvm_vcpu_stats_desc[] = {
> > >       STATS_DESC_COUNTER(VCPU, pthru_host),
> > >       STATS_DESC_COUNTER(VCPU, pthru_bad_aff)
> > >  };
> > > -static_assert(ARRAY_SIZE(kvm_vcpu_stats_desc) ==
> > > -             sizeof(struct kvm_vcpu_stat) / sizeof(u64));
> > >
> > >  const struct kvm_stats_header kvm_vcpu_stats_header = {
> > >       .name_size = KVM_STATS_NAME_SIZE,
> > > diff --git a/arch/s390/kvm/kvm-s390.c b/arch/s390/kvm/kvm-s390.c
> > > index 1695f0ced5ba..7610d33d319b 100644
> > > --- a/arch/s390/kvm/kvm-s390.c
> > > +++ b/arch/s390/kvm/kvm-s390.c
> > > @@ -66,8 +66,6 @@ const struct _kvm_stats_desc kvm_vm_stats_desc[] = {
> > >       STATS_DESC_COUNTER(VM, inject_service_signal),
> > >       STATS_DESC_COUNTER(VM, inject_virtio)
> > >  };
> > > -static_assert(ARRAY_SIZE(kvm_vm_stats_desc) ==
> > > -             sizeof(struct kvm_vm_stat) / sizeof(u64));
> > >
> > >  const struct kvm_stats_header kvm_vm_stats_header = {
> > >       .name_size = KVM_STATS_NAME_SIZE,
> > > @@ -174,8 +172,6 @@ const struct _kvm_stats_desc kvm_vcpu_stats_desc[] = {
> > >       STATS_DESC_COUNTER(VCPU, diagnose_other),
> > >       STATS_DESC_COUNTER(VCPU, pfault_sync)
> > >  };
> > > -static_assert(ARRAY_SIZE(kvm_vcpu_stats_desc) ==
> > > -             sizeof(struct kvm_vcpu_stat) / sizeof(u64));
> > >
> > >  const struct kvm_stats_header kvm_vcpu_stats_header = {
> > >       .name_size = KVM_STATS_NAME_SIZE,
> > > diff --git a/arch/x86/kvm/x86.c b/arch/x86/kvm/x86.c
> > > index 8166ad113fb2..b94a80ad5b8d 100644
> > > --- a/arch/x86/kvm/x86.c
> > > +++ b/arch/x86/kvm/x86.c
> > > @@ -239,8 +239,6 @@ const struct _kvm_stats_desc kvm_vm_stats_desc[] = {
> > >       STATS_DESC_ICOUNTER(VM, nx_lpage_splits),
> > >       STATS_DESC_PCOUNTER(VM, max_mmu_page_hash_collisions)
> > >  };
> > > -static_assert(ARRAY_SIZE(kvm_vm_stats_desc) ==
> > > -             sizeof(struct kvm_vm_stat) / sizeof(u64));
> > >
> > >  const struct kvm_stats_header kvm_vm_stats_header = {
> > >       .name_size = KVM_STATS_NAME_SIZE,
> > > @@ -280,8 +278,6 @@ const struct _kvm_stats_desc kvm_vcpu_stats_desc[] = {
> > >       STATS_DESC_COUNTER(VCPU, directed_yield_successful),
> > >       STATS_DESC_ICOUNTER(VCPU, guest_mode)
> > >  };
> > > -static_assert(ARRAY_SIZE(kvm_vcpu_stats_desc) ==
> > > -             sizeof(struct kvm_vcpu_stat) / sizeof(u64));
> > >
> > >  const struct kvm_stats_header kvm_vcpu_stats_header = {
> > >       .name_size = KVM_STATS_NAME_SIZE,
> > > diff --git a/include/linux/kvm_host.h b/include/linux/kvm_host.h
> > > index ae7735b490b4..356af173114d 100644
> > > --- a/include/linux/kvm_host.h
> > > +++ b/include/linux/kvm_host.h
> > > @@ -1273,56 +1273,66 @@ struct _kvm_stats_desc {
> > >       char name[KVM_STATS_NAME_SIZE];
> > >  };
> > >
> > > -#define STATS_DESC_COMMON(type, unit, base, exp)                            \
> > > +#define STATS_DESC_COMMON(type, unit, base, exp, sz, param)                 \
> > >       .flags = type | unit | base |                                          \
> > >                BUILD_BUG_ON_ZERO(type & ~KVM_STATS_TYPE_MASK) |              \
> > >                BUILD_BUG_ON_ZERO(unit & ~KVM_STATS_UNIT_MASK) |              \
> > >                BUILD_BUG_ON_ZERO(base & ~KVM_STATS_BASE_MASK),               \
> > >       .exponent = exp,                                                       \
> > > -     .size = 1
> > > +     .size = sz,                                                            \
> > > +     .hist_param = param
> > >
> > > -#define VM_GENERIC_STATS_DESC(stat, type, unit, base, exp)                  \
> > > +#define VM_GENERIC_STATS_DESC(stat, type, unit, base, exp, sz, param)               \
> > >       {                                                                      \
> > >               {                                                              \
> > > -                     STATS_DESC_COMMON(type, unit, base, exp),              \
> > > +                     STATS_DESC_COMMON(type, unit, base, exp, sz, param),   \
> > >                       .offset = offsetof(struct kvm_vm_stat, generic.stat)   \
> > >               },                                                             \
> > >               .name = #stat,                                                 \
> > >       }
> > > -#define VCPU_GENERIC_STATS_DESC(stat, type, unit, base, exp)                \
> > > +#define VCPU_GENERIC_STATS_DESC(stat, type, unit, base, exp, sz, param)             \
> > >       {                                                                      \
> > >               {                                                              \
> > > -                     STATS_DESC_COMMON(type, unit, base, exp),              \
> > > +                     STATS_DESC_COMMON(type, unit, base, exp, sz, param),   \
> > >                       .offset = offsetof(struct kvm_vcpu_stat, generic.stat) \
> > >               },                                                             \
> > >               .name = #stat,                                                 \
> > >       }
> > > -#define VM_STATS_DESC(stat, type, unit, base, exp)                          \
> > > +#define VM_STATS_DESC(stat, type, unit, base, exp, sz, param)                       \
> > >       {                                                                      \
> > >               {                                                              \
> > > -                     STATS_DESC_COMMON(type, unit, base, exp),              \
> > > +                     STATS_DESC_COMMON(type, unit, base, exp, sz, param),   \
> > >                       .offset = offsetof(struct kvm_vm_stat, stat)           \
> > >               },                                                             \
> > >               .name = #stat,                                                 \
> > >       }
> > > -#define VCPU_STATS_DESC(stat, type, unit, base, exp)                        \
> > > +#define VCPU_STATS_DESC(stat, type, unit, base, exp, sz, param)                     \
> > >       {                                                                      \
> > >               {                                                              \
> > > -                     STATS_DESC_COMMON(type, unit, base, exp),              \
> > > +                     STATS_DESC_COMMON(type, unit, base, exp, sz, param),   \
> > >                       .offset = offsetof(struct kvm_vcpu_stat, stat)         \
> > >               },                                                             \
> > >               .name = #stat,                                                 \
> > >       }
> > >  /* SCOPE: VM, VM_GENERIC, VCPU, VCPU_GENERIC */
> > > -#define STATS_DESC(SCOPE, stat, type, unit, base, exp)                              \
> > > -     SCOPE##_STATS_DESC(stat, type, unit, base, exp)
> > > +#define STATS_DESC(SCOPE, stat, type, unit, base, exp, sz, param)           \
> > > +     SCOPE##_STATS_DESC(stat, type, unit, base, exp, sz, param)
> > >
> > >  #define STATS_DESC_CUMULATIVE(SCOPE, name, unit, base, exponent)            \
> > > -     STATS_DESC(SCOPE, name, KVM_STATS_TYPE_CUMULATIVE, unit, base, exponent)
> > > +     STATS_DESC(SCOPE, name, KVM_STATS_TYPE_CUMULATIVE,                     \
> > > +             unit, base, exponent, 1, 0)
> > >  #define STATS_DESC_INSTANT(SCOPE, name, unit, base, exponent)                       \
> > > -     STATS_DESC(SCOPE, name, KVM_STATS_TYPE_INSTANT, unit, base, exponent)
> > > +     STATS_DESC(SCOPE, name, KVM_STATS_TYPE_INSTANT,                        \
> > > +             unit, base, exponent, 1, 0)
> > >  #define STATS_DESC_PEAK(SCOPE, name, unit, base, exponent)                  \
> > > -     STATS_DESC(SCOPE, name, KVM_STATS_TYPE_PEAK, unit, base, exponent)
> > > +     STATS_DESC(SCOPE, name, KVM_STATS_TYPE_PEAK,                           \
> > > +             unit, base, exponent, 1, 0)
> > > +#define STATS_DESC_LINEAR_HIST(SCOPE, name, unit, base, exponent, sz, param)   \
> > > +     STATS_DESC(SCOPE, name, KVM_STATS_TYPE_LINEAR_HIST,                    \
> > > +             unit, base, exponent, sz, param)
> > > +#define STATS_DESC_LOG_HIST(SCOPE, name, unit, base, exponent, sz, param)      \
> > > +     STATS_DESC(SCOPE, name, KVM_STATS_TYPE_LOG_HIST,                       \
> > > +             unit, base, exponent, sz, param)
> > >
> > >  /* Cumulative counter, read/write */
> > >  #define STATS_DESC_COUNTER(SCOPE, name)                                             \
> > > @@ -1341,6 +1351,14 @@ struct _kvm_stats_desc {
> > >  #define STATS_DESC_TIME_NSEC(SCOPE, name)                                   \
> > >       STATS_DESC_CUMULATIVE(SCOPE, name, KVM_STATS_UNIT_SECONDS,             \
> > >               KVM_STATS_BASE_POW10, -9)
> > > +/* Linear histogram for time in nanosecond */
> > > +#define STATS_DESC_LINHIST_TIME_NSEC(SCOPE, name, sz, bucket_size)          \
> > > +     STATS_DESC_LINEAR_HIST(SCOPE, name, KVM_STATS_UNIT_SECONDS,            \
> > > +             KVM_STATS_BASE_POW10, -9, sz, bucket_size)
> > > +/* Logarithmic histogram for time in nanosecond */
> > > +#define STATS_DESC_LOGHIST_TIME_NSEC(SCOPE, name, sz)                               \
> > > +     STATS_DESC_LOG_HIST(SCOPE, name, KVM_STATS_UNIT_SECONDS,               \
> > > +             KVM_STATS_BASE_POW10, -9, sz, LOGHIST_BASE_2)
> > >
> > >  #define KVM_GENERIC_VM_STATS()                                                      \
> > >       STATS_DESC_COUNTER(VM_GENERIC, remote_tlb_flush)
> > > @@ -1354,10 +1372,15 @@ struct _kvm_stats_desc {
> > >       STATS_DESC_TIME_NSEC(VCPU_GENERIC, halt_poll_fail_ns)
> > >
> > >  extern struct dentry *kvm_debugfs_dir;
> > > +
> > >  ssize_t kvm_stats_read(char *id, const struct kvm_stats_header *header,
> > >                      const struct _kvm_stats_desc *desc,
> > >                      void *stats, size_t size_stats,
> > >                      char __user *user_buffer, size_t size, loff_t *offset);
> > > +void kvm_stats_linear_hist_update(u64 *data, size_t size,
> > > +                               u64 value, size_t bucket_size);
> > > +void kvm_stats_log_hist_update(u64 *data, size_t size, u64 value);
> > > +
> > >  extern const struct kvm_stats_header kvm_vm_stats_header;
> > >  extern const struct _kvm_stats_desc kvm_vm_stats_desc[];
> > >  extern const struct kvm_stats_header kvm_vcpu_stats_header;
> > > diff --git a/include/linux/kvm_types.h b/include/linux/kvm_types.h
> > > index ed6a985c5680..cc88cd676775 100644
> > > --- a/include/linux/kvm_types.h
> > > +++ b/include/linux/kvm_types.h
> > > @@ -76,6 +76,22 @@ struct kvm_mmu_memory_cache {
> > >  };
> > >  #endif
> > >
> > > +/* Constants used for histogram stats */
> > > +#define LINHIST_SIZE_SMALL           10
> > > +#define LINHIST_SIZE_MEDIUM          20
> > > +#define LINHIST_SIZE_LARGE           50
> > > +#define LINHIST_SIZE_XLARGE          100
> >
> > nit: s/SIZE/BUCKET_COUNT/
> >
> Sure, it makes more sense.
> > > +#define LINHIST_BUCKET_SIZE_SMALL    10
> > > +#define LINHIST_BUCKET_SIZE_MEDIUM   100
> > > +#define LINHIST_BUCKET_SIZE_LARGE    1000
> > > +#define LINHIST_BUCKET_SIZE_XLARGE   10000
> > > +
> > > +#define LOGHIST_SIZE_SMALL           8
> > > +#define LOGHIST_SIZE_MEDIUM          16
> > > +#define LOGHIST_SIZE_LARGE           32
> > > +#define LOGHIST_SIZE_XLARGE          64
> >
> > Ditto here.
> >
> Will do.
> > > +#define LOGHIST_BASE_2                       2
> > > +
> > >  struct kvm_vm_stat_generic {
> > >       u64 remote_tlb_flush;
> > >  };
> > > diff --git a/include/uapi/linux/kvm.h b/include/uapi/linux/kvm.h
> > > index 68c9e6d8bbda..ff34a471d9ef 100644
> > > --- a/include/uapi/linux/kvm.h
> > > +++ b/include/uapi/linux/kvm.h
> > > @@ -1963,7 +1963,9 @@ struct kvm_stats_header {
> > >  #define KVM_STATS_TYPE_CUMULATIVE    (0x0 << KVM_STATS_TYPE_SHIFT)
> > >  #define KVM_STATS_TYPE_INSTANT               (0x1 << KVM_STATS_TYPE_SHIFT)
> > >  #define KVM_STATS_TYPE_PEAK          (0x2 << KVM_STATS_TYPE_SHIFT)
> > > -#define KVM_STATS_TYPE_MAX           KVM_STATS_TYPE_PEAK
> > > +#define KVM_STATS_TYPE_LINEAR_HIST   (0x3 << KVM_STATS_TYPE_SHIFT)
> > > +#define KVM_STATS_TYPE_LOG_HIST              (0x4 << KVM_STATS_TYPE_SHIFT)
> > > +#define KVM_STATS_TYPE_MAX           KVM_STATS_TYPE_LOG_HIST
> > >
> > >  #define KVM_STATS_UNIT_SHIFT         4
> > >  #define KVM_STATS_UNIT_MASK          (0xF << KVM_STATS_UNIT_SHIFT)
> > > @@ -1987,7 +1989,10 @@ struct kvm_stats_header {
> > >   *        Every data item is of type __u64.
> > >   * @offset: The offset of the stats to the start of stat structure in
> > >   *          struture kvm or kvm_vcpu.
> > > - * @unused: Unused field for future usage. Always 0 for now.
> > > + * @hist_param: A parameter value used for histogram stats. For linear
> > > + *              histogram stats, it indicates the size of the bucket;
> > > + *              For logarithmic histogram stats, it indicates the base
> > > + *              of the logarithm. Only base of 2 is supported.
> > >   * @name: The name string for the stats. Its size is indicated by the
> > >   *        &kvm_stats_header->name_size.
> > >   */
> > > @@ -1996,7 +2001,7 @@ struct kvm_stats_desc {
> > >       __s16 exponent;
> > >       __u16 size;
> > >       __u32 offset;
> > > -     __u32 unused;
> > > +     __u32 hist_param;
> >
> > `hist_param` is vague. What about making this an anonymous union to make
> > the dual meaning explicit?
> >
> >         union {
> >                 /* Only used for KVM_STATS_TYPE_LOG_HIST. */
> >                 __u32 base;
> >                 /* Only used for KVM_STATS_TYPE_LINEAR_HIST. */
> >                 __u32 bucket_size;
> >         };
> >
> > It may make the STATS_DESC code a bit more complicated but the rest of
> > the code that uses it will be much more clear.
> >
> Since we only support base-2 log hist, maybe it is not necessary to
> have the base field.
> The reason to only support base-2 log hist is that its range is
> already large enough for
> any stats.
> Will just change hist_param to bucket_size.

Cool sounds good. We can always add a custom base in the future without
breaking userspace by adding the anonymous union and guarding it behind
the flag field.

> > >       char name[];
> > >  };
> > >
> > > diff --git a/virt/kvm/binary_stats.c b/virt/kvm/binary_stats.c
> > > index e609d428811a..6eead6979a7f 100644
> > > --- a/virt/kvm/binary_stats.c
> > > +++ b/virt/kvm/binary_stats.c
> > > @@ -144,3 +144,39 @@ ssize_t kvm_stats_read(char *id, const struct kvm_stats_header *header,
> > >       *offset = pos;
> > >       return len;
> > >  }
> > > +
> > > +/**
> > > + * kvm_stats_linear_hist_update() - Update bucket value for linear histogram
> > > + * statistics data.
> > > + *
> > > + * @data: start address of the stats data
> > > + * @size: the number of bucket of the stats data
> > > + * @value: the new value used to update the linear histogram's bucket
> > > + * @bucket_size: the size (width) of a bucket
> > > + */
> > > +void kvm_stats_linear_hist_update(u64 *data, size_t size,
> > > +                               u64 value, size_t bucket_size)
> > > +{
> > > +     size_t index = value / bucket_size;
> > > +
> > > +     if (index >= size)
> > > +             index = size - 1;
> >
> > nit: It would be simpler to use max().
> >
> >         size_t index = max(value / bucket_size, size - 1);
> >
> Will do.
> > > +     ++data[index];
> > > +}
> > > +
> > > +/**
> > > + * kvm_stats_log_hist_update() - Update bucket value for logarithmic histogram
> > > + * statistics data.
> > > + *
> > > + * @data: start address of the stats data
> > > + * @size: the number of bucket of the stats data
> > > + * @value: the new value used to update the logarithmic histogram's bucket
> > > + */
> > > +void kvm_stats_log_hist_update(u64 *data, size_t size, u64 value)
> > > +{
> > > +     size_t index = fls64(value);
> > > +
> > > +     if (index >= size)
> > > +             index = size - 1;
> >
> > Ditto here about using max().
> >
> Will do.
> > > +     ++data[index];
> > > +}
> > > --
> > > 2.32.0.93.g670b81a890-goog
> > >
> Thanks,
> Jing



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