diff --git a/hw/intc/arm_gicv3.c b/hw/intc/arm_gicv3.c
index 96e0d2f..171d587 100644
--- a/hw/intc/arm_gicv3.c
+++ b/hw/intc/arm_gicv3.c
@@ -21,6 +21,287 @@
 #include "hw/intc/arm_gicv3.h"
 #include "gicv3_internal.h"
 
+static bool irqbetter(GICv3CPUState *cs, int irq, uint8_t prio)
+{
+    /* Return true if this IRQ at this priority should take
+     * precedence over the current recorded highest priority
+     * pending interrupt for this CPU. We also return true if
+     * the current recorded highest priority pending interrupt
+     * is the same as this one (a property which the calling code
+     * relies on).
+     */
+    if (prio < cs->hppi.prio) {
+        return true;
+    }
+    /* If multiple pending interrupts have the same priority then it is an
+     * IMPDEF choice which of them to signal to the CPU. We choose to
+     * signal the one with the lowest interrupt number.
+     */
+    if (prio == cs->hppi.prio && irq <= cs->hppi.irq) {
+        return true;
+    }
+    return false;
+}
+
+static uint32_t gicd_int_pending(GICv3State *s, int irq)
+{
+    /* Recalculate which distributor interrupts are actually pending
+     * in the group of 32 interrupts starting at irq (which should be a multiple
+     * of 32), and return a 32-bit integer which has a bit set for each
+     * interrupt that is eligible to be signaled to the CPU interface.
+     *
+     * An interrupt is pending if:
+     *  + the PENDING latch is set OR it is level triggered and the input is 1
+     *  + its ENABLE bit is set
+     *  + the GICD enable bit for its group is set
+     * Conveniently we can bulk-calculate this with bitwise operations.
+     */
+    uint32_t pend, grpmask;
+    uint32_t pending = *gic_bmp_ptr32(s->pending, irq);
+    uint32_t edge_trigger = *gic_bmp_ptr32(s->edge_trigger, irq);
+    uint32_t level = *gic_bmp_ptr32(s->level, irq);
+    uint32_t group = *gic_bmp_ptr32(s->group, irq);
+    uint32_t grpmod = *gic_bmp_ptr32(s->grpmod, irq);
+    uint32_t enable = *gic_bmp_ptr32(s->enabled, irq);
+
+    pend = pending | (~edge_trigger & level);
+    pend &= enable;
+
+    if (s->gicd_ctlr & GICD_CTLR_DS) {
+        grpmod = 0;
+    }
+
+    grpmask = 0;
+    if (s->gicd_ctlr & GICD_CTLR_EN_GRP1NS) {
+        grpmask |= group;
+    }
+    if (s->gicd_ctlr & GICD_CTLR_EN_GRP1S) {
+        grpmask |= (~group & grpmod);
+    }
+    if (s->gicd_ctlr & GICD_CTLR_EN_GRP0) {
+        grpmask |= (~group & ~grpmod);
+    }
+    pend &= grpmask;
+
+    return pend;
+}
+
+static uint32_t gicr_int_pending(GICv3CPUState *cs)
+{
+    /* Recalculate which redistributor interrupts are actually pending,
+     * and return a 32-bit integer which has a bit set for each interrupt
+     * that is eligible to be signaled to the CPU interface.
+     *
+     * An interrupt is pending if:
+     *  + the PENDING latch is set OR it is level triggered and the input is 1
+     *  + its ENABLE bit is set
+     *  + the GICD enable bit for its group is set
+     * Conveniently we can bulk-calculate this with bitwise operations.
+     */
+    uint32_t pend, grpmask, grpmod;
+
+    pend = cs->gicr_ipendr0 | (~cs->edge_trigger & cs->level);
+    pend &= cs->gicr_ienabler0;
+
+    if (cs->gic->gicd_ctlr & GICD_CTLR_DS) {
+        grpmod = 0;
+    } else {
+        grpmod = cs->gicr_igrpmodr0;
+    }
+
+    grpmask = 0;
+    if (cs->gic->gicd_ctlr & GICD_CTLR_EN_GRP1NS) {
+        grpmask |= cs->gicr_igroupr0;
+    }
+    if (cs->gic->gicd_ctlr & GICD_CTLR_EN_GRP1S) {
+        grpmask |= (~cs->gicr_igroupr0 & grpmod);
+    }
+    if (cs->gic->gicd_ctlr & GICD_CTLR_EN_GRP0) {
+        grpmask |= (~cs->gicr_igroupr0 & ~grpmod);
+    }
+    pend &= grpmask;
+
+    return pend;
+}
+
+/* Update the interrupt status after state in a redistributor
+ * or CPU interface has changed, but don't tell the CPU i/f.
+ */
+static void gicv3_redist_update_noirqset(GICv3CPUState *cs)
+{
+    /* Find the highest priority pending interrupt among the
+     * redistributor interrupts (SGIs and PPIs).
+     */
+    bool seenbetter = false;
+    uint8_t prio;
+    int i;
+    uint32_t pend;
+
+    /* Find out which redistributor interrupts are eligible to be
+     * signaled to the CPU interface.
+     */
+    pend = gicr_int_pending(cs);
+
+    if (pend) {
+        for (i = 0; i < GIC_INTERNAL; i++) {
+            if (!(pend & (1 << i))) {
+                continue;
+            }
+            prio = cs->gicr_ipriorityr[i];
+            if (irqbetter(cs, i, prio)) {
+                cs->hppi.irq = i;
+                cs->hppi.prio = prio;
+                seenbetter = true;
+            }
+        }
+    }
+
+    if (seenbetter) {
+        cs->hppi.grp = gicv3_irq_group(cs->gic, cs, cs->hppi.irq);
+    }
+
+    /* If the best interrupt we just found would preempt whatever
+     * was the previous best interrupt before this update, then
+     * we know it's definitely the best one now.
+     * If we didn't find an interrupt that would preempt the previous
+     * best, and the previous best is outside our range (or there was no
+     * previous pending interrupt at all), then that is still valid, and
+     * we leave it as the best.
+     * Otherwise, we need to do a full update (because the previous best
+     * interrupt has reduced in priority and any other interrupt could
+     * now be the new best one).
+     */
+    if (!seenbetter && cs->hppi.prio != 0xff && cs->hppi.irq < GIC_INTERNAL) {
+        gicv3_full_update_noirqset(cs->gic);
+    }
+}
+
+/* Update the GIC status after state in a redistributor or
+ * CPU interface has changed, and inform the CPU i/f of
+ * its new highest priority pending interrupt.
+ */
+void gicv3_redist_update(GICv3CPUState *cs)
+{
+    gicv3_redist_update_noirqset(cs);
+    gicv3_cpuif_update(cs);
+}
+
+/* Update the GIC status after state in the distributor has
+ * changed affecting @len interrupts starting at @start,
+ * but don't tell the CPU i/f.
+ */
+static void gicv3_update_noirqset(GICv3State *s, int start, int len)
+{
+    int i;
+    uint8_t prio;
+    uint32_t pend = 0;
+
+    assert(start >= GIC_INTERNAL);
+    assert(len > 0);
+
+    for (i = 0; i < s->num_cpu; i++) {
+        s->cpu[i].seenbetter = false;
+    }
+
+    /* Find the highest priority pending interrupt in this range. */
+    for (i = start; i < start + len; i++) {
+        GICv3CPUState *cs;
+
+        if (i == start || (i & 0x1f) == 0) {
+            /* Calculate the next 32 bits worth of pending status */
+            pend = gicd_int_pending(s, i & ~0x1f);
+        }
+
+        if (!(pend & (1 << (i & 0x1f)))) {
+            continue;
+        }
+        cs = s->gicd_irouter_target[i];
+        if (!cs) {
+            /* Interrupts targeting no implemented CPU should remain pending
+             * and not be forwarded to any CPU.
+             */
+            continue;
+        }
+        prio = s->gicd_ipriority[i];
+        if (irqbetter(cs, i, prio)) {
+            cs->hppi.irq = i;
+            cs->hppi.prio = prio;
+            cs->seenbetter = true;
+        }
+    }
+
+    /* If the best interrupt we just found would preempt whatever
+     * was the previous best interrupt before this update, then
+     * we know it's definitely the best one now.
+     * If we didn't find an interrupt that would preempt the previous
+     * best, and the previous best is outside our range (or there was
+     * no previous pending interrupt at all), then that
+     * is still valid, and we leave it as the best.
+     * Otherwise, we need to do a full update (because the previous best
+     * interrupt has reduced in priority and any other interrupt could
+     * now be the new best one).
+     */
+    for (i = 0; i < s->num_cpu; i++) {
+        GICv3CPUState *cs = &s->cpu[i];
+
+        if (cs->seenbetter) {
+            cs->hppi.grp = gicv3_irq_group(cs->gic, cs, cs->hppi.irq);
+        }
+
+        if (!cs->seenbetter && cs->hppi.prio != 0xff &&
+            cs->hppi.irq >= start && cs->hppi.irq < start + len) {
+            gicv3_full_update_noirqset(s);
+            break;
+        }
+    }
+}
+
+void gicv3_update(GICv3State *s, int start, int len)
+{
+    int i;
+
+    gicv3_update_noirqset(s, start, len);
+    for (i = 0; i < s->num_cpu; i++) {
+        gicv3_cpuif_update(&s->cpu[i]);
+    }
+}
+
+void gicv3_full_update_noirqset(GICv3State *s)
+{
+    /* Completely recalculate the GIC status from scratch, but
+     * don't update any outbound IRQ lines.
+     */
+    int i;
+
+    for (i = 0; i < s->num_cpu; i++) {
+        s->cpu[i].hppi.prio = 0xff;
+    }
+
+    /* Note that we can guarantee that these functions will not
+     * recursively call back into gicv3_full_update(), because
+     * at each point the "previous best" is always outside the
+     * range we ask them to update.
+     */
+    gicv3_update_noirqset(s, GIC_INTERNAL, s->num_irq - GIC_INTERNAL);
+
+    for (i = 0; i < s->num_cpu; i++) {
+        gicv3_redist_update_noirqset(&s->cpu[i]);
+    }
+}
+
+void gicv3_full_update(GICv3State *s)
+{
+    /* Completely recalculate the GIC status from scratch, including
+     * updating outbound IRQ lines.
+     */
+    int i;
+
+    gicv3_full_update_noirqset(s);
+    for (i = 0; i < s->num_cpu; i++) {
+        gicv3_cpuif_update(&s->cpu[i]);
+    }
+}
+
 /* Process a change in an external IRQ input. */
 static void gicv3_set_irq(void *opaque, int irq, int level)
 {
@@ -33,6 +314,16 @@ static void gicv3_set_irq(void *opaque, int irq, int level)
     /* Do nothing for now */
 }
 
+static void arm_gicv3_post_load(GICv3State *s)
+{
+    /* Recalculate our cached idea of the current highest priority
+     * pending interrupt, but don't set IRQ or FIQ lines.
+     */
+    gicv3_full_update_noirqset(s);
+    /* Repopulate the cache of GICv3CPUState pointers for target CPUs */
+    gicv3_cache_all_target_cpustates(s);
+}
+
 static void arm_gic_realize(DeviceState *dev, Error **errp)
 {
     /* Device instance realize function for the GIC sysbus device */
@@ -52,8 +343,10 @@ static void arm_gic_realize(DeviceState *dev, Error **errp)
 static void arm_gicv3_class_init(ObjectClass *klass, void *data)
 {
     DeviceClass *dc = DEVICE_CLASS(klass);
+    ARMGICv3CommonClass *agcc = ARM_GICV3_COMMON_CLASS(klass);
     ARMGICv3Class *agc = ARM_GICV3_CLASS(klass);
 
+    agcc->post_load = arm_gicv3_post_load;
     agc->parent_realize = dc->realize;
     dc->realize = arm_gic_realize;
 }
diff --git a/hw/intc/arm_gicv3_common.c b/hw/intc/arm_gicv3_common.c
index d1714e4..0f8c4b8 100644
--- a/hw/intc/arm_gicv3_common.c
+++ b/hw/intc/arm_gicv3_common.c
@@ -246,6 +246,8 @@ static void arm_gicv3_common_reset(DeviceState *dev)
         cs->gicr_nsacr = 0;
         memset(cs->gicr_ipriorityr, 0, sizeof(cs->gicr_ipriorityr));
 
+        cs->hppi.prio = 0xff;
+
         /* State in the CPU interface must *not* be reset here, because it
          * is part of the CPU's reset domain, not the GIC device's.
          */
@@ -271,6 +273,13 @@ static void arm_gicv3_common_reset(DeviceState *dev)
     memset(s->gicd_ipriority, 0, sizeof(s->gicd_ipriority));
     memset(s->gicd_irouter, 0, sizeof(s->gicd_irouter));
     memset(s->gicd_nsacr, 0, sizeof(s->gicd_nsacr));
+    /* GICD_IROUTER are UNKNOWN at reset so in theory the guest must
+     * write these to get sane behaviour and we need not populate the
+     * pointer cache here; however having the cache be different for
+     * "happened to be 0 from reset" and "guest wrote 0" would be
+     * too confusing.
+     */
+    gicv3_cache_all_target_cpustates(s);
 
     if (s->irq_reset_nonsecure) {
         /* If we're resetting a TZ-aware GIC as if secure firmware
diff --git a/hw/intc/gicv3_internal.h b/hw/intc/gicv3_internal.h
index 97c9d75..2ee9eeb 100644
--- a/hw/intc/gicv3_internal.h
+++ b/hw/intc/gicv3_internal.h
@@ -159,6 +159,63 @@
 #define ICC_CTLR_EL3_A3V (1U << 15)
 #define ICC_CTLR_EL3_NDS (1U << 17)
 
+/* Functions internal to the emulated GICv3 */
+
+/**
+ * gicv3_redist_update:
+ * @cs: GICv3CPUState for this redistributor
+ *
+ * Recalculate the highest priority pending interrupt after a
+ * change to redistributor state, and inform the CPU accordingly.
+ */
+void gicv3_redist_update(GICv3CPUState *cs);
+
+/**
+ * gicv3_update:
+ * @s: GICv3State
+ * @start: first interrupt whose state changed
+ * @len: length of the range of interrupts whose state changed
+ *
+ * Recalculate the highest priority pending interrupts after a
+ * change to the distributor state affecting @len interrupts
+ * starting at @start, and inform the CPUs accordingly.
+ */
+void gicv3_update(GICv3State *s, int start, int len);
+
+/**
+ * gicv3_full_update_noirqset:
+ * @s: GICv3State
+ *
+ * Recalculate the cached information about highest priority
+ * pending interrupts, but don't inform the CPUs. This should be
+ * called after an incoming migration has loaded new state.
+ */
+void gicv3_full_update_noirqset(GICv3State *s);
+
+/**
+ * gicv3_full_update:
+ * @s: GICv3State
+ *
+ * Recalculate the highest priority pending interrupts after
+ * a change that could affect the status of all interrupts,
+ * and inform the CPUs accordingly.
+ */
+void gicv3_full_update(GICv3State *s);
+
+/**
+ * gicv3_cpuif_update:
+ * @cs: GICv3CPUState for the CPU to update
+ *
+ * Recalculate whether to assert the IRQ or FIQ lines after a change
+ * to the current highest priority pending interrupt, the CPU's
+ * current running priority or the CPU's current exception level or
+ * security state.
+ */
+static inline void gicv3_cpuif_update(GICv3CPUState *cs)
+{
+    /* This will be implemented in a later commit. */
+}
+
 static inline uint32_t gicv3_iidr(void)
 {
     /* Return the Implementer Identification Register value
@@ -184,6 +241,32 @@ static inline uint32_t gicv3_idreg(int regoffset)
 }
 
 /**
+ * gicv3_irq_group:
+ *
+ * Return the group which this interrupt is configured as (GICV3_G0,
+ * GICV3_G1 or GICV3_G1NS).
+ */
+static inline int gicv3_irq_group(GICv3State *s, GICv3CPUState *cs, int irq)
+{
+    bool grpbit, grpmodbit;
+
+    if (irq < GIC_INTERNAL) {
+        grpbit = extract32(cs->gicr_igroupr0, irq, 1);
+        grpmodbit = extract32(cs->gicr_igrpmodr0, irq, 1);
+    } else {
+        grpbit = gicv3_gicd_group_test(s, irq);
+        grpmodbit = gicv3_gicd_grpmod_test(s, irq);
+    }
+    if (grpbit) {
+        return GICV3_G1NS;
+    }
+    if (s->gicd_ctlr & GICD_CTLR_DS) {
+        return GICV3_G0;
+    }
+    return grpmodbit ? GICV3_G1 : GICV3_G0;
+}
+
+/**
  * gicv3_redist_affid:
  *
  * Return the 32-bit affinity ID of the CPU connected to this redistributor
@@ -193,4 +276,42 @@ static inline uint32_t gicv3_redist_affid(GICv3CPUState *cs)
     return cs->gicr_typer >> 32;
 }
 
+/**
+ * gicv3_cache_target_cpustate:
+ *
+ * Update the cached CPU state corresponding to the target for this interrupt
+ * (which is kept in s->gicd_irouter_target[]).
+ */
+static inline void gicv3_cache_target_cpustate(GICv3State *s, int irq)
+{
+    GICv3CPUState *cs = NULL;
+    int i;
+    uint32_t tgtaff = extract64(s->gicd_irouter[irq], 0, 24) |
+        extract64(s->gicd_irouter[irq], 32, 8) << 24;
+
+    for (i = 0; i < s->num_cpu; i++) {
+        if (s->cpu[i].gicr_typer >> 32 == tgtaff) {
+            cs = &s->cpu[i];
+            break;
+        }
+    }
+
+    s->gicd_irouter_target[irq] = cs;
+}
+
+/**
+ * gicv3_cache_all_target_cpustates:
+ *
+ * Populate the entire cache of CPU state pointers for interrupt targets
+ * (eg after inbound migration or CPU reset)
+ */
+static inline void gicv3_cache_all_target_cpustates(GICv3State *s)
+{
+    int irq;
+
+    for (irq = GIC_INTERNAL; irq < GICV3_MAXIRQ; irq++) {
+        gicv3_cache_target_cpustate(s, irq);
+    }
+}
+
 #endif /* !QEMU_ARM_GIC_INTERNAL_H */
diff --git a/include/hw/intc/arm_gicv3_common.h b/include/hw/intc/arm_gicv3_common.h
index cc6ac74..f72e499 100644
--- a/include/hw/intc/arm_gicv3_common.h
+++ b/include/hw/intc/arm_gicv3_common.h
@@ -131,6 +131,12 @@ typedef struct GICv3CPUState GICv3CPUState;
 #define GICV3_S 0
 #define GICV3_NS 1
 
+typedef struct {
+    int irq;
+    uint8_t prio;
+    int grp;
+} PendingIrq;
+
 struct GICv3CPUState {
     GICv3State *gic;
     CPUState *cpu;
@@ -163,6 +169,14 @@ struct GICv3CPUState {
     uint64_t icc_apr[3][4];
     uint64_t icc_igrpen[3];
     uint64_t icc_ctlr_el3;
+
+    /* Current highest priority pending interrupt for this CPU.
+     * This is cached information that can be recalculated from the
+     * real state above; it doesn't need to be migrated.
+     */
+    PendingIrq hppi;
+    /* This is temporary working state, to avoid a malloc in gicv3_update() */
+    bool seenbetter;
 };
 
 struct GICv3State {
@@ -198,6 +212,10 @@ struct GICv3State {
     GIC_DECLARE_BITMAP(edge_trigger); /* GICD_ICFGR even bits */
     uint8_t gicd_ipriority[GICV3_MAXIRQ];
     uint64_t gicd_irouter[GICV3_MAXIRQ];
+    /* Cached information: pointer to the cpu i/f for the CPUs specified
+     * in the IROUTER registers
+     */
+    GICv3CPUState *gicd_irouter_target[GICV3_MAXIRQ];
     uint32_t gicd_nsacr[DIV_ROUND_UP(GICV3_MAXIRQ, 16)];
 
     GICv3CPUState *cpu;
