* @date 28.9.2004
* @author Sebastian Hack, Michael Beck
* @version $Id$
+ *
+ * Implements "Strenght Reduction of Multiplications by Integer Constants" by Youfeng Wu.
+ * Implements Division and Modulo by Consts from "Hackers Delight",
*/
#ifdef HAVE_CONFIG_H
# include "config.h"
return (mode_is_signed(mode) && params->allow_mulhs) || (!mode_is_signed(mode) && params->allow_mulhu);
}
-/* Replace Muls with Shifts and Add/Subs. */
-ir_node *arch_dep_replace_mul_with_shifts(ir_node *irn) {
- ir_node *res = irn;
- ir_mode *mode = get_irn_mode(irn);
+/**
+ * An instruction,
+ */
+typedef struct instruction instruction;
+struct instruction {
+ insn_kind kind; /**< the instruction kind */
+ instruction *in[2]; /**< the ins */
+ int shift_count; /**< shift count for LEA and SHIFT */
+ ir_node *irn; /**< the generated node for this instruction if any. */
+ int costs; /**< the costs for this instruction */
+};
- /* If the architecture dependent optimizations were not initialized
- or this optimization was not enabled. */
- if (params == NULL || (opts & arch_dep_mul_to_shift) == 0)
- return irn;
+/**
+ * The environment for the strength reduction of multiplications.
+ */
+typedef struct _mul_env {
+ struct obstack obst; /**< an obstack for local space. */
+ ir_mode *mode; /**< the mode of the multiplication constant */
+ int bits; /**< number of bits in the mode */
+ unsigned max_S; /**< the maximum LEA shift value. */
+ instruction *root; /**< the root of the instruction tree */
+ ir_node *op; /**< the operand that is multiplied */
+ ir_node *blk; /**< the block where the new graph is built */
+ dbg_info *dbg; /**< the debug info for the new graph. */
+ ir_mode *shf_mode; /**< the (unsigned) mode for the shift constants */
+ int fail; /**< set to 1 if the instruction sequence fails the constraints */
+ int n_shift; /**< maximum number of allowed shift instructions */
+
+ evaluate_costs_func evaluate; /**< the evaluate callback */
+} mul_env;
- if (is_Mul(irn) && mode_is_int(mode)) {
- ir_node *block = get_nodes_block(irn);
- ir_node *left = get_binop_left(irn);
- ir_node *right = get_binop_right(irn);
- tarval *tv = NULL;
- ir_node *operand = NULL;
+/**
+ * Some kind of default evaluator.
+ */
+static int default_evaluate(insn_kind kind, tarval *tv) {
+ if (kind == MUL)
+ return 13;
+ return 1;
+}
- /* Look, if one operand is a constant. */
- if (is_Const(left)) {
- tv = get_Const_tarval(left);
- operand = right;
- } else if (is_Const(right)) {
- tv = get_Const_tarval(right);
- operand = left;
- }
+/**
+ * emit a LEA (or an Add) instruction
+ */
+static instruction *emit_LEA(mul_env *env, instruction *a, instruction *b, int shift) {
+ instruction *res = obstack_alloc(&env->obst, sizeof(*res));
+ res->kind = shift > 0 ? LEA : ADD;
+ res->in[0] = a;
+ res->in[1] = b;
+ res->shift_count = shift;
+ res->irn = NULL;
+ res->costs = -1;
+ return res;
+}
- if (tv != NULL) {
- int maximum_shifts = params->maximum_shifts;
- int also_use_subs = params->also_use_subs;
- int highest_shift_amount = params->highest_shift_amount;
-
- char *bitstr = get_tarval_bitpattern(tv);
- char *p;
- int i, last = 0;
- int counter = 0;
- int curr_bit;
- int compr_len = 0;
- char compr[MAX_BITSTR];
-
- int singleton;
- int end_of_group;
- int shift_with_sub[MAX_BITSTR] = { 0 };
- int shift_without_sub[MAX_BITSTR] = { 0 };
- int shift_with_sub_pos = 0;
- int shift_without_sub_pos = 0;
-
-#if DEB
- {
- long val = get_tarval_long(tv);
- fprintf(stderr, "Found mul with %ld(%lx) = ", val, val);
- for(p = bitstr; *p != '\0'; p++)
- printf("%c", *p);
- printf("\n");
- }
-#endif
+/**
+ * emit a SHIFT (or an Add) instruction
+ */
+static instruction *emit_SHIFT(mul_env *env, instruction *a, int shift) {
+ instruction *res = obstack_alloc(&env->obst, sizeof(*res));
+ if (shift != 1) {
+ res->kind = SHIFT;
+ res->in[0] = a;
+ res->in[1] = NULL;
+ res->shift_count = shift;
+ } else {
+ res->kind = ADD;
+ res->in[0] = a;
+ res->in[1] = a;
+ res->shift_count = 0;
+ }
+ res->irn = NULL;
+ res->costs = -1;
+ return res;
+}
- for (p = bitstr; *p != '\0'; p++) {
- int bit = *p != '0';
+/**
+ * emit a SUB instruction
+ */
+static instruction *emit_SUB(mul_env *env, instruction *a, instruction *b) {
+ instruction *res = obstack_alloc(&env->obst, sizeof(*res));
+ res->kind = SUB;
+ res->in[0] = a;
+ res->in[1] = b;
+ res->shift_count = 0;
+ res->irn = NULL;
+ res->costs = -1;
+ return res;
+}
- if (bit != last) {
- /* The last was 1 we are now at 0 OR
- * The last was 0 and we are now at 1 */
- compr[compr_len++] = counter;
- counter = 1;
- } else
- counter++;
+/**
+ * emit the ROOT instruction
+ */
+static instruction *emit_ROOT(mul_env *env, ir_node *root_op) {
+ instruction *res = obstack_alloc(&env->obst, sizeof(*res));
+ res->kind = ROOT;
+ res->in[0] = NULL;
+ res->in[1] = NULL;
+ res->shift_count = 0;
+ res->irn = root_op;
+ res->costs = 0;
+ return res;
+}
- last = bit;
- }
- compr[compr_len++] = counter;
-
-#ifdef DEB
- {
- const char *prefix = "";
- for(i = 0; i < compr_len; i++, prefix = ",")
- fprintf(stderr, "%s%d", prefix, compr[i]);
- fprintf("\n");
- }
-#endif
- /* Go over all recorded one groups. */
- curr_bit = compr[0];
+/**
+ * Returns the condensed representation of the tarval tv
+ */
+static unsigned char *value_to_condensed(mul_env *env, tarval *tv, int *pr) {
+ ir_mode *mode = get_tarval_mode(tv);
+ int bits = get_mode_size_bits(mode);
+ char *bitstr = get_tarval_bitpattern(tv);
+ int i, l, r;
+ unsigned char *R = obstack_alloc(&env->obst, bits);
+
+ l = r = 0;
+ for (i = 0; bitstr[i] != '\0'; ++i) {
+ if (bitstr[i] == '1') {
+ R[r] = i - l;
+ l = i;
+ ++r;
+ }
+ }
+ free(bitstr);
- for(i = 1; i < compr_len; i = end_of_group + 2) {
- int j, zeros_in_group, ones_in_group;
+ *pr = r;
+ return R;
+}
- ones_in_group = compr[i];
- zeros_in_group = 0;
+/**
+ * Calculate the gain when using the generalized complementary technique
+ */
+static int calculate_gain(unsigned char *R, int r) {
+ int max_gain = -1;
+ int idx, i;
+ int gain;
+
+ /* the gain for r == 1 */
+ gain = 2 - 3 - R[0];
+ for (i = 2; i < r; ++i) {
+ /* calculate the gain for r from the gain for r-1 */
+ gain += 2 - R[i - 1];
+
+ if (gain > max_gain) {
+ max_gain = gain;
+ idx = i;
+ }
+ }
+ if (max_gain > 0)
+ return idx;
+ return -1;
+}
- /* Scan for singular 0s in a sequence. */
- for(j = i + 1; j < compr_len && compr[j] == 1; j += 2) {
- zeros_in_group += 1;
- ones_in_group += (j + 1 < compr_len ? compr[j + 1] : 0);
- }
- end_of_group = j - 1;
+/**
+ * Calculates the condensed complement of a given (R,r) tuple
+ */
+static unsigned char *complement_condensed(mul_env *env, unsigned char *R, int r, int gain, int *prs) {
+ unsigned char *value = obstack_alloc(&env->obst, env->bits);
+ int i, l, j;
+ unsigned char c;
- if(zeros_in_group >= ones_in_group - 1)
- end_of_group = i;
+ memset(value, 0, env->bits);
-#ifdef DEB
- fprintf(stderr, " i:%d, eg:%d\n", i, end_of_group);
-#endif
+ j = 0;
+ for (i = 0; i < gain; ++i) {
+ j += R[i];
+ value[j] = 1;
+ }
- singleton = compr[i] == 1 && i == end_of_group;
- for(j = i; j <= end_of_group; j += 2) {
- int curr_ones = compr[j];
- int biased_curr_bit = curr_bit + 1;
- int k;
+ /* negate and propagate 1 */
+ c = 1;
+ for (i = 0; i <= j; ++i) {
+ unsigned char v = !value[i];
-#ifdef DEB
- fprintf(stderr, " j:%d, ones:%d\n", j, curr_ones);
-#endif
+ value[i] = v ^ c;
+ c = v & c;
+ }
- /* If this ones group is a singleton group (it has no
- singleton zeros inside. */
- if(singleton)
- shift_with_sub[shift_with_sub_pos++] = biased_curr_bit;
- else if(j == i)
- shift_with_sub[shift_with_sub_pos++] = -biased_curr_bit;
+ /* condense it again */
+ l = r = 0;
+ R = value;
+ for (i = 0; i <= j; ++i) {
+ if (value[i] == 1) {
+ R[r] = i - l;
+ l = i;
+ ++r;
+ }
+ }
- for(k = 0; k < curr_ones; k++)
- shift_without_sub[shift_without_sub_pos++] = biased_curr_bit + k;
+ *prs = r;
+ return R;
+}
- curr_bit += curr_ones;
- biased_curr_bit = curr_bit + 1;
+/**
+ * creates a tarval from a condensed representation.
+ */
+static tarval *condensed_to_value(mul_env *env, unsigned char *R, int r) {
+ tarval *res, *tv;
+ int i, j;
+
+ j = 0;
+ tv = get_mode_one(env->mode);
+ res = NULL;
+ for (i = 0; i < r; ++i) {
+ j = R[i];
+ if (j) {
+ tarval *t = new_tarval_from_long(j, mode_Iu);
+ tv = tarval_shl(tv, t);
+ }
+ res = res ? tarval_add(res, tv) : tv;
+ }
+ return res;
+}
- if(!singleton && j == end_of_group)
- shift_with_sub[shift_with_sub_pos++] = biased_curr_bit;
- else if(j != end_of_group)
- shift_with_sub[shift_with_sub_pos++] = -biased_curr_bit;
+/* forward */
+static instruction *basic_decompose_mul(mul_env *env, unsigned char *R, int r, tarval *N);
- curr_bit += compr[j + 1];
- }
- }
+/*
+ * handle simple cases with up-to 2 bits set
+ */
+static instruction *decompose_simple_cases(mul_env *env, unsigned char *R, int r, tarval *N) {
+ instruction *ins, *ins2;
- {
- int *shifts = shift_with_sub;
- int n = shift_with_sub_pos;
- int highest_shift_wide = 0;
- int highest_shift_seq = 0;
- int last_shift = 0;
-
- /* If we may not use subs, or we can achieve the same with adds,
- prefer adds. */
- if(!also_use_subs || shift_with_sub_pos >= shift_without_sub_pos) {
- shifts = shift_without_sub;
- n = shift_without_sub_pos;
- }
+ if (r == 1) {
+ return emit_SHIFT(env, env->root, R[0]);
+ } else {
+ assert(r == 2);
- /* If the number of needed shifts exceeds the given maximum,
- use the Mul and exit. */
- if(n > maximum_shifts) {
-#ifdef DEB
- fprintf(stderr, "Only allowed %d shifts, but %d are needed\n",
- maximum_shifts, n);
-#endif
- goto end;
- }
+ ins = env->root;
+ if (R[0] != 0) {
+ ins = emit_SHIFT(env, ins, R[0]);
+ }
+ if (R[1] <= env->max_S)
+ return emit_LEA(env, ins, ins, R[1]);
- /* Compute the highest shift needed for both, the
- sequential and wide representations. */
- for(i = 0; i < n; i++) {
- int curr = abs(shifts[i]);
- int curr_seq = curr - last;
+ ins2 = emit_SHIFT(env, env->root, R[0] + R[1]);
+ return emit_LEA(env, ins, ins2, 0);
+ }
+}
- highest_shift_wide = curr > highest_shift_wide ? curr : highest_shift_wide;
- highest_shift_seq = curr_seq > highest_shift_seq ? curr_seq : highest_shift_seq;
+/**
+ * Main decompose driver.
+ */
+static instruction *decompose_mul(mul_env *env, unsigned char *R, int r, tarval *N) {
+ unsigned i;
+ int gain;
+
+ if (r <= 2)
+ return decompose_simple_cases(env, R, r, N);
+
+ if (params->also_use_subs) {
+ gain = calculate_gain(R, r);
+ if (gain > 0) {
+ instruction *instr1, *instr2;
+ unsigned char *R1, *R2;
+ int r1, r2, i, k;
+
+ R1 = complement_condensed(env, R, r, gain, &r1);
+ r2 = r - gain + 1;
+ R2 = obstack_alloc(&env->obst, r2);
+
+ k = 1;
+ for (i = 0; i < gain; ++i) {
+ k += R[i];
+ }
+ R2[0] = k;
+ R2[1] = R[gain] - 1;
+ for (i = gain; i < r; ++i) {
+ R2[i] = R[i];
+ }
- last_shift = curr;
- }
+ instr1 = decompose_mul(env, R1, r1, NULL);
+ instr2 = decompose_mul(env, R2, r2, NULL);
+ return emit_SUB(env, instr2, instr1);
+ }
+ }
- /* If the highest shift amount is greater than the given limit,
- give back the Mul */
- if(highest_shift_seq > highest_shift_amount) {
-#ifdef DEB
- fprintf(stderr, "Shift argument %d exceeds maximum %d\n",
- highest_shift_seq, highest_shift_amount);
-#endif
- goto end;
- }
+ if (N == NULL)
+ N = condensed_to_value(env, R, r);
- /* If we have subs, we cannot do sequential. */
- if(1 /* also_use_subs */) {
- if(n > 0) {
- ir_node *curr = NULL;
+ for (i = env->max_S; i > 0; --i) {
+ tarval *div_res, *mod_res;
+ tarval *tv = new_tarval_from_long((1 << i) + 1, env->mode);
- i = n - 1;
+ div_res = tarval_divmod(N, tv, &mod_res);
+ if (mod_res == get_mode_null(env->mode)) {
+ unsigned char *Rs;
+ int rs;
- do {
- int curr_shift = shifts[i];
- int sub = curr_shift < 0;
- int amount = abs(curr_shift) - 1;
- ir_node *aux = operand;
+ Rs = value_to_condensed(env, div_res, &rs);
+ if (rs < r) {
+ instruction *N1 = decompose_mul(env, Rs, rs, div_res);
+ return emit_LEA(env, N1, N1, i);
+ }
+ }
+ }
+ return basic_decompose_mul(env, R, r, N);
+}
- assert(amount >= 0 && "What is a negative shift??");
+/**
+ * basic decomposition routine
+ */
+static instruction *basic_decompose_mul(mul_env *env, unsigned char *R, int r, tarval *N) {
+ instruction *Ns;
+ unsigned t;
+
+ if (R[0] == 0) { /* Case 1 */
+ t = R[1] > max(env->max_S, R[1]);
+ R[1] -= t;
+ Ns = decompose_mul(env, &R[1], r - 1, N);
+ return emit_LEA(env, env->root, Ns, t);
+ } else if (R[0] <= env->max_S) { /* Case 2 */
+ t = R[0];
+ R[1] += t;
+ Ns = decompose_mul(env, &R[1], r - 1, N);
+ return emit_LEA(env, Ns, env->root, t);
+ } else {
+ t = R[0];
+ R[0] = 0;
+ Ns = decompose_mul(env, R, r, N);
+ return emit_SHIFT(env, Ns, t);
+ }
+}
- if (amount != 0) {
- ir_node *cnst = new_r_Const_long(current_ir_graph, block, mode_Iu, amount);
- aux = new_r_Shl(current_ir_graph, block, operand, cnst, mode);
- }
+/**
+ * recursive build the graph form the instructions.
+ *
+ * @param env the environment
+ * @param inst the instruction
+ */
+static ir_node *build_graph(mul_env *env, instruction *inst) {
+ ir_node *l, *r, *c;
+
+ if (inst->irn)
+ return inst->irn;
+
+ switch (inst->kind) {
+ case LEA:
+ l = build_graph(env, inst->in[0]);
+ r = build_graph(env, inst->in[1]);
+ c = new_r_Const(current_ir_graph, env->blk, env->shf_mode, new_tarval_from_long(inst->shift_count, env->shf_mode));
+ r = new_rd_Shl(env->dbg, current_ir_graph, env->blk, r, c, env->mode);
+ return inst->irn = new_rd_Add(env->dbg, current_ir_graph, env->blk, l, r, env->mode);
+ case SHIFT:
+ l = build_graph(env, inst->in[0]);
+ c = new_r_Const(current_ir_graph, env->blk, env->shf_mode, new_tarval_from_long(inst->shift_count, env->shf_mode));
+ return inst->irn = new_rd_Shl(env->dbg, current_ir_graph, env->blk, l, c, env->mode);
+ case SUB:
+ l = build_graph(env, inst->in[0]);
+ r = build_graph(env, inst->in[1]);
+ return inst->irn = new_rd_Sub(env->dbg, current_ir_graph, env->blk, l, r, env->mode);
+ case ADD:
+ l = build_graph(env, inst->in[0]);
+ r = build_graph(env, inst->in[1]);
+ return inst->irn = new_rd_Add(env->dbg, current_ir_graph, env->blk, l, r, env->mode);
+ default:
+ assert(0);
+ return NULL;
+ }
+}
- if (curr) {
- if (sub)
- curr = new_r_Sub(current_ir_graph, block, curr, aux, mode);
- else
- curr = new_r_Add(current_ir_graph, block, curr, aux, mode);
- } else
- curr = aux;
+/**
+ * Calculate the costs for the given instruction sequence.
+ * Note that additional costs due to higher register pressure are NOT evaluated yet
+ */
+static int evaluate_insn(mul_env *env, instruction *inst) {
+ int costs;
- } while(--i >= 0);
+ if (inst->costs >= 0) {
+ /* was already evaluated */
+ return 0;
+ }
- res = curr;
- }
- }
+ switch (inst->kind) {
+ case LEA:
+ case SUB:
+ case ADD:
+ costs = evaluate_insn(env, inst->in[0]);
+ costs += evaluate_insn(env, inst->in[1]);
+ costs += env->evaluate(inst->kind, NULL);
+ inst->costs = costs;
+ return costs;
+ case SHIFT:
+ if (inst->shift_count > params->highest_shift_amount)
+ env->fail = 1;
+ if (env->n_shift <= 0)
+ env->fail = 1;
+ else
+ --env->n_shift;
+ costs = evaluate_insn(env, inst->in[0]);
+ costs += env->evaluate(inst->kind, NULL);
+ inst->costs = costs;
+ return costs;
+ default:
+ assert(0);
+ return 0;
+ }
+}
-#ifdef DEB
- {
- const char *prefix = "";
- for (i = 0; i < n; ++i) {
- fprintf(stderr, "%s%d", prefix, shifts[i]);
- prefix = ", ";
- }
- fprintf(stderr, "\n");
- }
-#endif
+/**
+ * Evaluate the replacement instructions and build a new graph
+ * if faster than the Mul.
+ * returns the root of the new graph then or irn otherwise.
+ *
+ * @param irn the Mul operation
+ * @param operand the multiplication operand
+ * @param tv the multiplication constant
+ *
+ * @return the new graph
+ */
+static ir_node *do_decomposition(ir_node *irn, ir_node *operand, tarval *tv) {
+ mul_env env;
+ instruction *inst;
+ unsigned char *R;
+ int r;
+ ir_node *res = irn;
+ int mul_costs;
+
+ obstack_init(&env.obst);
+ env.mode = get_tarval_mode(tv);
+ env.bits = get_mode_size_bits(env.mode);
+ env.max_S = 3;
+ env.root = emit_ROOT(&env, operand);
+ env.fail = 0;
+ env.n_shift = params->maximum_shifts;
+ env.evaluate = params->evaluate != NULL ? params->evaluate : default_evaluate;
+
+ R = value_to_condensed(&env, tv, &r);
+ inst = decompose_mul(&env, R, r, tv);
+
+ /* the paper suggests 70% here */
+ mul_costs = (env.evaluate(MUL, tv) * 7) / 10;
+ if (evaluate_insn(&env, inst) <= mul_costs && !env.fail) {
+ env.op = operand;
+ env.blk = get_nodes_block(irn);
+ env.dbg = get_irn_dbg_info(irn);
+ env.shf_mode = find_unsigned_mode(env.mode);
+ if (env.shf_mode == NULL)
+ env.shf_mode = mode_Iu;
+
+ res = build_graph(&env, inst);
+ }
+ obstack_free(&env.obst, NULL);
+ return res;
+}
- }
+/* Replace Muls with Shifts and Add/Subs. */
+ir_node *arch_dep_replace_mul_with_shifts(ir_node *irn) {
+ ir_node *res = irn;
+ ir_mode *mode = get_irn_mode(irn);
+
+ /* If the architecture dependent optimizations were not initialized
+ or this optimization was not enabled. */
+ if (params == NULL || (opts & arch_dep_mul_to_shift) == 0)
+ return irn;
-end:
- if(bitstr)
- free(bitstr);
+ if (is_Mul(irn) && mode_is_int(mode)) {
+ ir_node *block = get_nodes_block(irn);
+ ir_node *left = get_binop_left(irn);
+ ir_node *right = get_binop_right(irn);
+ tarval *tv = NULL;
+ ir_node *operand = NULL;
+
+ /* Look, if one operand is a constant. */
+ if (is_Const(left)) {
+ tv = get_Const_tarval(left);
+ operand = right;
+ } else if (is_Const(right)) {
+ tv = get_Const_tarval(right);
+ operand = left;
}
- }
+ if (tv != NULL) {
+ res = do_decomposition(irn, operand, tv);
- if (res != irn)
- hook_arch_dep_replace_mul_with_shifts(irn);
+ if (res != irn) {
+ hook_arch_dep_replace_mul_with_shifts(irn);
+ exchange(irn, res);
+ }
+ }
+ }
return res;
}