89 //--------------------------transform_int_divide-------------------------------
90 // Convert a division by constant divisor into an alternate Ideal graph.
91 // Return NULL if no transformation occurs.
92 static Node *transform_int_divide( PhaseGVN *phase, Node *dividend, jint divisor ) {
93
94 // Check for invalid divisors
95 assert( divisor != 0 && divisor != min_jint,
96 "bad divisor for transforming to long multiply" );
97
98 bool d_pos = divisor >= 0;
99 jint d = d_pos ? divisor : -divisor;
100 const int N = 32;
101
102 // Result
103 Node *q = NULL;
104
105 if (d == 1) {
106 // division by +/- 1
107 if (!d_pos) {
108 // Just negate the value
109 q = new (phase->C) SubINode(phase->intcon(0), dividend);
110 }
111 } else if ( is_power_of_2(d) ) {
112 // division by +/- a power of 2
113
114 // See if we can simply do a shift without rounding
115 bool needs_rounding = true;
116 const Type *dt = phase->type(dividend);
117 const TypeInt *dti = dt->isa_int();
118 if (dti && dti->_lo >= 0) {
119 // we don't need to round a positive dividend
120 needs_rounding = false;
121 } else if( dividend->Opcode() == Op_AndI ) {
122 // An AND mask of sufficient size clears the low bits and
123 // I can avoid rounding.
124 const TypeInt *andconi_t = phase->type( dividend->in(2) )->isa_int();
125 if( andconi_t && andconi_t->is_con() ) {
126 jint andconi = andconi_t->get_con();
127 if( andconi < 0 && is_power_of_2(-andconi) && (-andconi) >= d ) {
128 if( (-andconi) == d ) // Remove AND if it clears bits which will be shifted
129 dividend = dividend->in(1);
130 needs_rounding = false;
131 }
132 }
133 }
134
135 // Add rounding to the shift to handle the sign bit
136 int l = log2_intptr(d-1)+1;
137 if (needs_rounding) {
138 // Divide-by-power-of-2 can be made into a shift, but you have to do
139 // more math for the rounding. You need to add 0 for positive
140 // numbers, and "i-1" for negative numbers. Example: i=4, so the
141 // shift is by 2. You need to add 3 to negative dividends and 0 to
142 // positive ones. So (-7+3)>>2 becomes -1, (-4+3)>>2 becomes -1,
143 // (-2+3)>>2 becomes 0, etc.
144
145 // Compute 0 or -1, based on sign bit
146 Node *sign = phase->transform(new (phase->C) RShiftINode(dividend, phase->intcon(N - 1)));
147 // Mask sign bit to the low sign bits
148 Node *round = phase->transform(new (phase->C) URShiftINode(sign, phase->intcon(N - l)));
149 // Round up before shifting
150 dividend = phase->transform(new (phase->C) AddINode(dividend, round));
151 }
152
153 // Shift for division
154 q = new (phase->C) RShiftINode(dividend, phase->intcon(l));
155
156 if (!d_pos) {
157 q = new (phase->C) SubINode(phase->intcon(0), phase->transform(q));
158 }
159 } else {
160 // Attempt the jint constant divide -> multiply transform found in
161 // "Division by Invariant Integers using Multiplication"
162 // by Granlund and Montgomery
163 // See also "Hacker's Delight", chapter 10 by Warren.
164
165 jint magic_const;
166 jint shift_const;
167 if (magic_int_divide_constants(d, magic_const, shift_const)) {
168 Node *magic = phase->longcon(magic_const);
169 Node *dividend_long = phase->transform(new (phase->C) ConvI2LNode(dividend));
170
171 // Compute the high half of the dividend x magic multiplication
172 Node *mul_hi = phase->transform(new (phase->C) MulLNode(dividend_long, magic));
173
174 if (magic_const < 0) {
175 mul_hi = phase->transform(new (phase->C) RShiftLNode(mul_hi, phase->intcon(N)));
176 mul_hi = phase->transform(new (phase->C) ConvL2INode(mul_hi));
177
178 // The magic multiplier is too large for a 32 bit constant. We've adjusted
179 // it down by 2^32, but have to add 1 dividend back in after the multiplication.
180 // This handles the "overflow" case described by Granlund and Montgomery.
181 mul_hi = phase->transform(new (phase->C) AddINode(dividend, mul_hi));
182
183 // Shift over the (adjusted) mulhi
184 if (shift_const != 0) {
185 mul_hi = phase->transform(new (phase->C) RShiftINode(mul_hi, phase->intcon(shift_const)));
186 }
187 } else {
188 // No add is required, we can merge the shifts together.
189 mul_hi = phase->transform(new (phase->C) RShiftLNode(mul_hi, phase->intcon(N + shift_const)));
190 mul_hi = phase->transform(new (phase->C) ConvL2INode(mul_hi));
191 }
192
193 // Get a 0 or -1 from the sign of the dividend.
194 Node *addend0 = mul_hi;
195 Node *addend1 = phase->transform(new (phase->C) RShiftINode(dividend, phase->intcon(N-1)));
196
197 // If the divisor is negative, swap the order of the input addends;
198 // this has the effect of negating the quotient.
199 if (!d_pos) {
200 Node *temp = addend0; addend0 = addend1; addend1 = temp;
201 }
202
203 // Adjust the final quotient by subtracting -1 (adding 1)
204 // from the mul_hi.
205 q = new (phase->C) SubINode(addend0, addend1);
206 }
207 }
208
209 return q;
210 }
211
212 //---------------------magic_long_divide_constants-----------------------------
213 // Compute magic multiplier and shift constant for converting a 64 bit divide
214 // by constant into a multiply/shift/add series. Return false if calculations
215 // fail.
216 //
217 // Borrowed almost verbatim from Hacker's Delight by Henry S. Warren, Jr. with
218 // minor type name and parameter changes. Adjusted to 64 bit word width.
219 static bool magic_long_divide_constants(jlong d, jlong &M, jint &s) {
220 int64_t p;
221 uint64_t ad, anc, delta, q1, r1, q2, r2, t;
222 const uint64_t two63 = 0x8000000000000000LL; // 2**63.
223
224 ad = ABS(d);
225 if (d == 0 || d == 1) return false;
244 q2 = q2 + 1; // comparison here).
245 r2 = r2 - ad;
246 }
247 delta = ad - r2;
248 } while (q1 < delta || (q1 == delta && r1 == 0));
249
250 M = q2 + 1;
251 if (d < 0) M = -M; // Magic number and
252 s = p - 64; // shift amount to return.
253
254 return true;
255 }
256
257 //---------------------long_by_long_mulhi--------------------------------------
258 // Generate ideal node graph for upper half of a 64 bit x 64 bit multiplication
259 static Node* long_by_long_mulhi(PhaseGVN* phase, Node* dividend, jlong magic_const) {
260 // If the architecture supports a 64x64 mulhi, there is
261 // no need to synthesize it in ideal nodes.
262 if (Matcher::has_match_rule(Op_MulHiL)) {
263 Node* v = phase->longcon(magic_const);
264 return new (phase->C) MulHiLNode(dividend, v);
265 }
266
267 // Taken from Hacker's Delight, Fig. 8-2. Multiply high signed.
268 // (http://www.hackersdelight.org/HDcode/mulhs.c)
269 //
270 // int mulhs(int u, int v) {
271 // unsigned u0, v0, w0;
272 // int u1, v1, w1, w2, t;
273 //
274 // u0 = u & 0xFFFF; u1 = u >> 16;
275 // v0 = v & 0xFFFF; v1 = v >> 16;
276 // w0 = u0*v0;
277 // t = u1*v0 + (w0 >> 16);
278 // w1 = t & 0xFFFF;
279 // w2 = t >> 16;
280 // w1 = u0*v1 + w1;
281 // return u1*v1 + w2 + (w1 >> 16);
282 // }
283 //
284 // Note: The version above is for 32x32 multiplications, while the
285 // following inline comments are adapted to 64x64.
286
287 const int N = 64;
288
289 // Dummy node to keep intermediate nodes alive during construction
290 Node* hook = new (phase->C) Node(4);
291
292 // u0 = u & 0xFFFFFFFF; u1 = u >> 32;
293 Node* u0 = phase->transform(new (phase->C) AndLNode(dividend, phase->longcon(0xFFFFFFFF)));
294 Node* u1 = phase->transform(new (phase->C) RShiftLNode(dividend, phase->intcon(N / 2)));
295 hook->init_req(0, u0);
296 hook->init_req(1, u1);
297
298 // v0 = v & 0xFFFFFFFF; v1 = v >> 32;
299 Node* v0 = phase->longcon(magic_const & 0xFFFFFFFF);
300 Node* v1 = phase->longcon(magic_const >> (N / 2));
301
302 // w0 = u0*v0;
303 Node* w0 = phase->transform(new (phase->C) MulLNode(u0, v0));
304
305 // t = u1*v0 + (w0 >> 32);
306 Node* u1v0 = phase->transform(new (phase->C) MulLNode(u1, v0));
307 Node* temp = phase->transform(new (phase->C) URShiftLNode(w0, phase->intcon(N / 2)));
308 Node* t = phase->transform(new (phase->C) AddLNode(u1v0, temp));
309 hook->init_req(2, t);
310
311 // w1 = t & 0xFFFFFFFF;
312 Node* w1 = phase->transform(new (phase->C) AndLNode(t, phase->longcon(0xFFFFFFFF)));
313 hook->init_req(3, w1);
314
315 // w2 = t >> 32;
316 Node* w2 = phase->transform(new (phase->C) RShiftLNode(t, phase->intcon(N / 2)));
317
318 // w1 = u0*v1 + w1;
319 Node* u0v1 = phase->transform(new (phase->C) MulLNode(u0, v1));
320 w1 = phase->transform(new (phase->C) AddLNode(u0v1, w1));
321
322 // return u1*v1 + w2 + (w1 >> 32);
323 Node* u1v1 = phase->transform(new (phase->C) MulLNode(u1, v1));
324 Node* temp1 = phase->transform(new (phase->C) AddLNode(u1v1, w2));
325 Node* temp2 = phase->transform(new (phase->C) RShiftLNode(w1, phase->intcon(N / 2)));
326
327 // Remove the bogus extra edges used to keep things alive
328 PhaseIterGVN* igvn = phase->is_IterGVN();
329 if (igvn != NULL) {
330 igvn->remove_dead_node(hook);
331 } else {
332 for (int i = 0; i < 4; i++) {
333 hook->set_req(i, NULL);
334 }
335 }
336
337 return new (phase->C) AddLNode(temp1, temp2);
338 }
339
340
341 //--------------------------transform_long_divide------------------------------
342 // Convert a division by constant divisor into an alternate Ideal graph.
343 // Return NULL if no transformation occurs.
344 static Node *transform_long_divide( PhaseGVN *phase, Node *dividend, jlong divisor ) {
345 // Check for invalid divisors
346 assert( divisor != 0L && divisor != min_jlong,
347 "bad divisor for transforming to long multiply" );
348
349 bool d_pos = divisor >= 0;
350 jlong d = d_pos ? divisor : -divisor;
351 const int N = 64;
352
353 // Result
354 Node *q = NULL;
355
356 if (d == 1) {
357 // division by +/- 1
358 if (!d_pos) {
359 // Just negate the value
360 q = new (phase->C) SubLNode(phase->longcon(0), dividend);
361 }
362 } else if ( is_power_of_2_long(d) ) {
363
364 // division by +/- a power of 2
365
366 // See if we can simply do a shift without rounding
367 bool needs_rounding = true;
368 const Type *dt = phase->type(dividend);
369 const TypeLong *dtl = dt->isa_long();
370
371 if (dtl && dtl->_lo > 0) {
372 // we don't need to round a positive dividend
373 needs_rounding = false;
374 } else if( dividend->Opcode() == Op_AndL ) {
375 // An AND mask of sufficient size clears the low bits and
376 // I can avoid rounding.
377 const TypeLong *andconl_t = phase->type( dividend->in(2) )->isa_long();
378 if( andconl_t && andconl_t->is_con() ) {
379 jlong andconl = andconl_t->get_con();
380 if( andconl < 0 && is_power_of_2_long(-andconl) && (-andconl) >= d ) {
381 if( (-andconl) == d ) // Remove AND if it clears bits which will be shifted
382 dividend = dividend->in(1);
383 needs_rounding = false;
384 }
385 }
386 }
387
388 // Add rounding to the shift to handle the sign bit
389 int l = log2_long(d-1)+1;
390 if (needs_rounding) {
391 // Divide-by-power-of-2 can be made into a shift, but you have to do
392 // more math for the rounding. You need to add 0 for positive
393 // numbers, and "i-1" for negative numbers. Example: i=4, so the
394 // shift is by 2. You need to add 3 to negative dividends and 0 to
395 // positive ones. So (-7+3)>>2 becomes -1, (-4+3)>>2 becomes -1,
396 // (-2+3)>>2 becomes 0, etc.
397
398 // Compute 0 or -1, based on sign bit
399 Node *sign = phase->transform(new (phase->C) RShiftLNode(dividend, phase->intcon(N - 1)));
400 // Mask sign bit to the low sign bits
401 Node *round = phase->transform(new (phase->C) URShiftLNode(sign, phase->intcon(N - l)));
402 // Round up before shifting
403 dividend = phase->transform(new (phase->C) AddLNode(dividend, round));
404 }
405
406 // Shift for division
407 q = new (phase->C) RShiftLNode(dividend, phase->intcon(l));
408
409 if (!d_pos) {
410 q = new (phase->C) SubLNode(phase->longcon(0), phase->transform(q));
411 }
412 } else if ( !Matcher::use_asm_for_ldiv_by_con(d) ) { // Use hardware DIV instruction when
413 // it is faster than code generated below.
414 // Attempt the jlong constant divide -> multiply transform found in
415 // "Division by Invariant Integers using Multiplication"
416 // by Granlund and Montgomery
417 // See also "Hacker's Delight", chapter 10 by Warren.
418
419 jlong magic_const;
420 jint shift_const;
421 if (magic_long_divide_constants(d, magic_const, shift_const)) {
422 // Compute the high half of the dividend x magic multiplication
423 Node *mul_hi = phase->transform(long_by_long_mulhi(phase, dividend, magic_const));
424
425 // The high half of the 128-bit multiply is computed.
426 if (magic_const < 0) {
427 // The magic multiplier is too large for a 64 bit constant. We've adjusted
428 // it down by 2^64, but have to add 1 dividend back in after the multiplication.
429 // This handles the "overflow" case described by Granlund and Montgomery.
430 mul_hi = phase->transform(new (phase->C) AddLNode(dividend, mul_hi));
431 }
432
433 // Shift over the (adjusted) mulhi
434 if (shift_const != 0) {
435 mul_hi = phase->transform(new (phase->C) RShiftLNode(mul_hi, phase->intcon(shift_const)));
436 }
437
438 // Get a 0 or -1 from the sign of the dividend.
439 Node *addend0 = mul_hi;
440 Node *addend1 = phase->transform(new (phase->C) RShiftLNode(dividend, phase->intcon(N-1)));
441
442 // If the divisor is negative, swap the order of the input addends;
443 // this has the effect of negating the quotient.
444 if (!d_pos) {
445 Node *temp = addend0; addend0 = addend1; addend1 = temp;
446 }
447
448 // Adjust the final quotient by subtracting -1 (adding 1)
449 // from the mul_hi.
450 q = new (phase->C) SubLNode(addend0, addend1);
451 }
452 }
453
454 return q;
455 }
456
457 //=============================================================================
458 //------------------------------Identity---------------------------------------
459 // If the divisor is 1, we are an identity on the dividend.
460 Node *DivINode::Identity( PhaseTransform *phase ) {
461 return (phase->type( in(2) )->higher_equal(TypeInt::ONE)) ? in(1) : this;
462 }
463
464 //------------------------------Idealize---------------------------------------
465 // Divides can be changed to multiplies and/or shifts
466 Node *DivINode::Ideal(PhaseGVN *phase, bool can_reshape) {
467 if (in(0) && remove_dead_region(phase, can_reshape)) return this;
468 // Don't bother trying to transform a dead node
469 if( in(0) && in(0)->is_top() ) return NULL;
470
720
721 // Check for out of range values
722 if( tf->is_nan() || !tf->is_finite() ) return NULL;
723
724 // Get the value
725 float f = tf->getf();
726 int exp;
727
728 // Only for special case of dividing by a power of 2
729 if( frexp((double)f, &exp) != 0.5 ) return NULL;
730
731 // Limit the range of acceptable exponents
732 if( exp < -126 || exp > 126 ) return NULL;
733
734 // Compute the reciprocal
735 float reciprocal = ((float)1.0) / f;
736
737 assert( frexp((double)reciprocal, &exp) == 0.5, "reciprocal should be power of 2" );
738
739 // return multiplication by the reciprocal
740 return (new (phase->C) MulFNode(in(1), phase->makecon(TypeF::make(reciprocal))));
741 }
742
743 //=============================================================================
744 //------------------------------Value------------------------------------------
745 // An DivDNode divides its inputs. The third input is a Control input, used to
746 // prevent hoisting the divide above an unsafe test.
747 const Type *DivDNode::Value( PhaseTransform *phase ) const {
748 // Either input is TOP ==> the result is TOP
749 const Type *t1 = phase->type( in(1) );
750 const Type *t2 = phase->type( in(2) );
751 if( t1 == Type::TOP ) return Type::TOP;
752 if( t2 == Type::TOP ) return Type::TOP;
753
754 // Either input is BOTTOM ==> the result is the local BOTTOM
755 const Type *bot = bottom_type();
756 if( (t1 == bot) || (t2 == bot) ||
757 (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) )
758 return bot;
759
760 // x/x == 1, we ignore 0/0.
814
815 // Check for out of range values
816 if( td->is_nan() || !td->is_finite() ) return NULL;
817
818 // Get the value
819 double d = td->getd();
820 int exp;
821
822 // Only for special case of dividing by a power of 2
823 if( frexp(d, &exp) != 0.5 ) return NULL;
824
825 // Limit the range of acceptable exponents
826 if( exp < -1021 || exp > 1022 ) return NULL;
827
828 // Compute the reciprocal
829 double reciprocal = 1.0 / d;
830
831 assert( frexp(reciprocal, &exp) == 0.5, "reciprocal should be power of 2" );
832
833 // return multiplication by the reciprocal
834 return (new (phase->C) MulDNode(in(1), phase->makecon(TypeD::make(reciprocal))));
835 }
836
837 //=============================================================================
838 //------------------------------Idealize---------------------------------------
839 Node *ModINode::Ideal(PhaseGVN *phase, bool can_reshape) {
840 // Check for dead control input
841 if( in(0) && remove_dead_region(phase, can_reshape) ) return this;
842 // Don't bother trying to transform a dead node
843 if( in(0) && in(0)->is_top() ) return NULL;
844
845 // Get the modulus
846 const Type *t = phase->type( in(2) );
847 if( t == Type::TOP ) return NULL;
848 const TypeInt *ti = t->is_int();
849
850 // Check for useless control input
851 // Check for excluding mod-zero case
852 if( in(0) && (ti->_hi < 0 || ti->_lo > 0) ) {
853 set_req(0, NULL); // Yank control input
854 return this;
855 }
856
857 // See if we are MOD'ing by 2^k or 2^k-1.
858 if( !ti->is_con() ) return NULL;
859 jint con = ti->get_con();
860
861 Node *hook = new (phase->C) Node(1);
862
863 // First, special check for modulo 2^k-1
864 if( con >= 0 && con < max_jint && is_power_of_2(con+1) ) {
865 uint k = exact_log2(con+1); // Extract k
866
867 // Basic algorithm by David Detlefs. See fastmod_int.java for gory details.
868 static int unroll_factor[] = { 999, 999, 29, 14, 9, 7, 5, 4, 4, 3, 3, 2, 2, 2, 2, 2, 1 /*past here we assume 1 forever*/};
869 int trip_count = 1;
870 if( k < ARRAY_SIZE(unroll_factor)) trip_count = unroll_factor[k];
871
872 // If the unroll factor is not too large, and if conditional moves are
873 // ok, then use this case
874 if( trip_count <= 5 && ConditionalMoveLimit != 0 ) {
875 Node *x = in(1); // Value being mod'd
876 Node *divisor = in(2); // Also is mask
877
878 hook->init_req(0, x); // Add a use to x to prevent him from dying
879 // Generate code to reduce X rapidly to nearly 2^k-1.
880 for( int i = 0; i < trip_count; i++ ) {
881 Node *xl = phase->transform( new (phase->C) AndINode(x,divisor) );
882 Node *xh = phase->transform( new (phase->C) RShiftINode(x,phase->intcon(k)) ); // Must be signed
883 x = phase->transform( new (phase->C) AddINode(xh,xl) );
884 hook->set_req(0, x);
885 }
886
887 // Generate sign-fixup code. Was original value positive?
888 // int hack_res = (i >= 0) ? divisor : 1;
889 Node *cmp1 = phase->transform( new (phase->C) CmpINode( in(1), phase->intcon(0) ) );
890 Node *bol1 = phase->transform( new (phase->C) BoolNode( cmp1, BoolTest::ge ) );
891 Node *cmov1= phase->transform( new (phase->C) CMoveINode(bol1, phase->intcon(1), divisor, TypeInt::POS) );
892 // if( x >= hack_res ) x -= divisor;
893 Node *sub = phase->transform( new (phase->C) SubINode( x, divisor ) );
894 Node *cmp2 = phase->transform( new (phase->C) CmpINode( x, cmov1 ) );
895 Node *bol2 = phase->transform( new (phase->C) BoolNode( cmp2, BoolTest::ge ) );
896 // Convention is to not transform the return value of an Ideal
897 // since Ideal is expected to return a modified 'this' or a new node.
898 Node *cmov2= new (phase->C) CMoveINode(bol2, x, sub, TypeInt::INT);
899 // cmov2 is now the mod
900
901 // Now remove the bogus extra edges used to keep things alive
902 if (can_reshape) {
903 phase->is_IterGVN()->remove_dead_node(hook);
904 } else {
905 hook->set_req(0, NULL); // Just yank bogus edge during Parse phase
906 }
907 return cmov2;
908 }
909 }
910
911 // Fell thru, the unroll case is not appropriate. Transform the modulo
912 // into a long multiply/int multiply/subtract case
913
914 // Cannot handle mod 0, and min_jint isn't handled by the transform
915 if( con == 0 || con == min_jint ) return NULL;
916
917 // Get the absolute value of the constant; at this point, we can use this
918 jint pos_con = (con >= 0) ? con : -con;
919
920 // integer Mod 1 is always 0
921 if( pos_con == 1 ) return new (phase->C) ConINode(TypeInt::ZERO);
922
923 int log2_con = -1;
924
925 // If this is a power of two, they maybe we can mask it
926 if( is_power_of_2(pos_con) ) {
927 log2_con = log2_intptr((intptr_t)pos_con);
928
929 const Type *dt = phase->type(in(1));
930 const TypeInt *dti = dt->isa_int();
931
932 // See if this can be masked, if the dividend is non-negative
933 if( dti && dti->_lo >= 0 )
934 return ( new (phase->C) AndINode( in(1), phase->intcon( pos_con-1 ) ) );
935 }
936
937 // Save in(1) so that it cannot be changed or deleted
938 hook->init_req(0, in(1));
939
940 // Divide using the transform from DivI to MulL
941 Node *result = transform_int_divide( phase, in(1), pos_con );
942 if (result != NULL) {
943 Node *divide = phase->transform(result);
944
945 // Re-multiply, using a shift if this is a power of two
946 Node *mult = NULL;
947
948 if( log2_con >= 0 )
949 mult = phase->transform( new (phase->C) LShiftINode( divide, phase->intcon( log2_con ) ) );
950 else
951 mult = phase->transform( new (phase->C) MulINode( divide, phase->intcon( pos_con ) ) );
952
953 // Finally, subtract the multiplied divided value from the original
954 result = new (phase->C) SubINode( in(1), mult );
955 }
956
957 // Now remove the bogus extra edges used to keep things alive
958 if (can_reshape) {
959 phase->is_IterGVN()->remove_dead_node(hook);
960 } else {
961 hook->set_req(0, NULL); // Just yank bogus edge during Parse phase
962 }
963
964 // return the value
965 return result;
966 }
967
968 //------------------------------Value------------------------------------------
969 const Type *ModINode::Value( PhaseTransform *phase ) const {
970 // Either input is TOP ==> the result is TOP
971 const Type *t1 = phase->type( in(1) );
972 const Type *t2 = phase->type( in(2) );
973 if( t1 == Type::TOP ) return Type::TOP;
974 if( t2 == Type::TOP ) return Type::TOP;
1012 if( in(0) && remove_dead_region(phase, can_reshape) ) return this;
1013 // Don't bother trying to transform a dead node
1014 if( in(0) && in(0)->is_top() ) return NULL;
1015
1016 // Get the modulus
1017 const Type *t = phase->type( in(2) );
1018 if( t == Type::TOP ) return NULL;
1019 const TypeLong *tl = t->is_long();
1020
1021 // Check for useless control input
1022 // Check for excluding mod-zero case
1023 if( in(0) && (tl->_hi < 0 || tl->_lo > 0) ) {
1024 set_req(0, NULL); // Yank control input
1025 return this;
1026 }
1027
1028 // See if we are MOD'ing by 2^k or 2^k-1.
1029 if( !tl->is_con() ) return NULL;
1030 jlong con = tl->get_con();
1031
1032 Node *hook = new (phase->C) Node(1);
1033
1034 // Expand mod
1035 if( con >= 0 && con < max_jlong && is_power_of_2_long(con+1) ) {
1036 uint k = exact_log2_long(con+1); // Extract k
1037
1038 // Basic algorithm by David Detlefs. See fastmod_long.java for gory details.
1039 // Used to help a popular random number generator which does a long-mod
1040 // of 2^31-1 and shows up in SpecJBB and SciMark.
1041 static int unroll_factor[] = { 999, 999, 61, 30, 20, 15, 12, 10, 8, 7, 6, 6, 5, 5, 4, 4, 4, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1 /*past here we assume 1 forever*/};
1042 int trip_count = 1;
1043 if( k < ARRAY_SIZE(unroll_factor)) trip_count = unroll_factor[k];
1044
1045 // If the unroll factor is not too large, and if conditional moves are
1046 // ok, then use this case
1047 if( trip_count <= 5 && ConditionalMoveLimit != 0 ) {
1048 Node *x = in(1); // Value being mod'd
1049 Node *divisor = in(2); // Also is mask
1050
1051 hook->init_req(0, x); // Add a use to x to prevent him from dying
1052 // Generate code to reduce X rapidly to nearly 2^k-1.
1053 for( int i = 0; i < trip_count; i++ ) {
1054 Node *xl = phase->transform( new (phase->C) AndLNode(x,divisor) );
1055 Node *xh = phase->transform( new (phase->C) RShiftLNode(x,phase->intcon(k)) ); // Must be signed
1056 x = phase->transform( new (phase->C) AddLNode(xh,xl) );
1057 hook->set_req(0, x); // Add a use to x to prevent him from dying
1058 }
1059
1060 // Generate sign-fixup code. Was original value positive?
1061 // long hack_res = (i >= 0) ? divisor : CONST64(1);
1062 Node *cmp1 = phase->transform( new (phase->C) CmpLNode( in(1), phase->longcon(0) ) );
1063 Node *bol1 = phase->transform( new (phase->C) BoolNode( cmp1, BoolTest::ge ) );
1064 Node *cmov1= phase->transform( new (phase->C) CMoveLNode(bol1, phase->longcon(1), divisor, TypeLong::LONG) );
1065 // if( x >= hack_res ) x -= divisor;
1066 Node *sub = phase->transform( new (phase->C) SubLNode( x, divisor ) );
1067 Node *cmp2 = phase->transform( new (phase->C) CmpLNode( x, cmov1 ) );
1068 Node *bol2 = phase->transform( new (phase->C) BoolNode( cmp2, BoolTest::ge ) );
1069 // Convention is to not transform the return value of an Ideal
1070 // since Ideal is expected to return a modified 'this' or a new node.
1071 Node *cmov2= new (phase->C) CMoveLNode(bol2, x, sub, TypeLong::LONG);
1072 // cmov2 is now the mod
1073
1074 // Now remove the bogus extra edges used to keep things alive
1075 if (can_reshape) {
1076 phase->is_IterGVN()->remove_dead_node(hook);
1077 } else {
1078 hook->set_req(0, NULL); // Just yank bogus edge during Parse phase
1079 }
1080 return cmov2;
1081 }
1082 }
1083
1084 // Fell thru, the unroll case is not appropriate. Transform the modulo
1085 // into a long multiply/int multiply/subtract case
1086
1087 // Cannot handle mod 0, and min_jlong isn't handled by the transform
1088 if( con == 0 || con == min_jlong ) return NULL;
1089
1090 // Get the absolute value of the constant; at this point, we can use this
1091 jlong pos_con = (con >= 0) ? con : -con;
1092
1093 // integer Mod 1 is always 0
1094 if( pos_con == 1 ) return new (phase->C) ConLNode(TypeLong::ZERO);
1095
1096 int log2_con = -1;
1097
1098 // If this is a power of two, then maybe we can mask it
1099 if( is_power_of_2_long(pos_con) ) {
1100 log2_con = exact_log2_long(pos_con);
1101
1102 const Type *dt = phase->type(in(1));
1103 const TypeLong *dtl = dt->isa_long();
1104
1105 // See if this can be masked, if the dividend is non-negative
1106 if( dtl && dtl->_lo >= 0 )
1107 return ( new (phase->C) AndLNode( in(1), phase->longcon( pos_con-1 ) ) );
1108 }
1109
1110 // Save in(1) so that it cannot be changed or deleted
1111 hook->init_req(0, in(1));
1112
1113 // Divide using the transform from DivL to MulL
1114 Node *result = transform_long_divide( phase, in(1), pos_con );
1115 if (result != NULL) {
1116 Node *divide = phase->transform(result);
1117
1118 // Re-multiply, using a shift if this is a power of two
1119 Node *mult = NULL;
1120
1121 if( log2_con >= 0 )
1122 mult = phase->transform( new (phase->C) LShiftLNode( divide, phase->intcon( log2_con ) ) );
1123 else
1124 mult = phase->transform( new (phase->C) MulLNode( divide, phase->longcon( pos_con ) ) );
1125
1126 // Finally, subtract the multiplied divided value from the original
1127 result = new (phase->C) SubLNode( in(1), mult );
1128 }
1129
1130 // Now remove the bogus extra edges used to keep things alive
1131 if (can_reshape) {
1132 phase->is_IterGVN()->remove_dead_node(hook);
1133 } else {
1134 hook->set_req(0, NULL); // Just yank bogus edge during Parse phase
1135 }
1136
1137 // return the value
1138 return result;
1139 }
1140
1141 //------------------------------Value------------------------------------------
1142 const Type *ModLNode::Value( PhaseTransform *phase ) const {
1143 // Either input is TOP ==> the result is TOP
1144 const Type *t1 = phase->type( in(1) );
1145 const Type *t2 = phase->type( in(2) );
1146 if( t1 == Type::TOP ) return Type::TOP;
1147 if( t2 == Type::TOP ) return Type::TOP;
1262 xr ^= min_jlong;
1263 }
1264
1265 return TypeD::make(jdouble_cast(xr));
1266 }
1267
1268 //=============================================================================
1269
1270 DivModNode::DivModNode( Node *c, Node *dividend, Node *divisor ) : MultiNode(3) {
1271 init_req(0, c);
1272 init_req(1, dividend);
1273 init_req(2, divisor);
1274 }
1275
1276 //------------------------------make------------------------------------------
1277 DivModINode* DivModINode::make(Compile* C, Node* div_or_mod) {
1278 Node* n = div_or_mod;
1279 assert(n->Opcode() == Op_DivI || n->Opcode() == Op_ModI,
1280 "only div or mod input pattern accepted");
1281
1282 DivModINode* divmod = new (C) DivModINode(n->in(0), n->in(1), n->in(2));
1283 Node* dproj = new (C) ProjNode(divmod, DivModNode::div_proj_num);
1284 Node* mproj = new (C) ProjNode(divmod, DivModNode::mod_proj_num);
1285 return divmod;
1286 }
1287
1288 //------------------------------make------------------------------------------
1289 DivModLNode* DivModLNode::make(Compile* C, Node* div_or_mod) {
1290 Node* n = div_or_mod;
1291 assert(n->Opcode() == Op_DivL || n->Opcode() == Op_ModL,
1292 "only div or mod input pattern accepted");
1293
1294 DivModLNode* divmod = new (C) DivModLNode(n->in(0), n->in(1), n->in(2));
1295 Node* dproj = new (C) ProjNode(divmod, DivModNode::div_proj_num);
1296 Node* mproj = new (C) ProjNode(divmod, DivModNode::mod_proj_num);
1297 return divmod;
1298 }
1299
1300 //------------------------------match------------------------------------------
1301 // return result(s) along with their RegMask info
1302 Node *DivModINode::match( const ProjNode *proj, const Matcher *match ) {
1303 uint ideal_reg = proj->ideal_reg();
1304 RegMask rm;
1305 if (proj->_con == div_proj_num) {
1306 rm = match->divI_proj_mask();
1307 } else {
1308 assert(proj->_con == mod_proj_num, "must be div or mod projection");
1309 rm = match->modI_proj_mask();
1310 }
1311 return new (match->C)MachProjNode(this, proj->_con, rm, ideal_reg);
1312 }
1313
1314
1315 //------------------------------match------------------------------------------
1316 // return result(s) along with their RegMask info
1317 Node *DivModLNode::match( const ProjNode *proj, const Matcher *match ) {
1318 uint ideal_reg = proj->ideal_reg();
1319 RegMask rm;
1320 if (proj->_con == div_proj_num) {
1321 rm = match->divL_proj_mask();
1322 } else {
1323 assert(proj->_con == mod_proj_num, "must be div or mod projection");
1324 rm = match->modL_proj_mask();
1325 }
1326 return new (match->C)MachProjNode(this, proj->_con, rm, ideal_reg);
1327 }
|
89 //--------------------------transform_int_divide-------------------------------
90 // Convert a division by constant divisor into an alternate Ideal graph.
91 // Return NULL if no transformation occurs.
92 static Node *transform_int_divide( PhaseGVN *phase, Node *dividend, jint divisor ) {
93
94 // Check for invalid divisors
95 assert( divisor != 0 && divisor != min_jint,
96 "bad divisor for transforming to long multiply" );
97
98 bool d_pos = divisor >= 0;
99 jint d = d_pos ? divisor : -divisor;
100 const int N = 32;
101
102 // Result
103 Node *q = NULL;
104
105 if (d == 1) {
106 // division by +/- 1
107 if (!d_pos) {
108 // Just negate the value
109 q = new SubINode(phase->intcon(0), dividend);
110 }
111 } else if ( is_power_of_2(d) ) {
112 // division by +/- a power of 2
113
114 // See if we can simply do a shift without rounding
115 bool needs_rounding = true;
116 const Type *dt = phase->type(dividend);
117 const TypeInt *dti = dt->isa_int();
118 if (dti && dti->_lo >= 0) {
119 // we don't need to round a positive dividend
120 needs_rounding = false;
121 } else if( dividend->Opcode() == Op_AndI ) {
122 // An AND mask of sufficient size clears the low bits and
123 // I can avoid rounding.
124 const TypeInt *andconi_t = phase->type( dividend->in(2) )->isa_int();
125 if( andconi_t && andconi_t->is_con() ) {
126 jint andconi = andconi_t->get_con();
127 if( andconi < 0 && is_power_of_2(-andconi) && (-andconi) >= d ) {
128 if( (-andconi) == d ) // Remove AND if it clears bits which will be shifted
129 dividend = dividend->in(1);
130 needs_rounding = false;
131 }
132 }
133 }
134
135 // Add rounding to the shift to handle the sign bit
136 int l = log2_intptr(d-1)+1;
137 if (needs_rounding) {
138 // Divide-by-power-of-2 can be made into a shift, but you have to do
139 // more math for the rounding. You need to add 0 for positive
140 // numbers, and "i-1" for negative numbers. Example: i=4, so the
141 // shift is by 2. You need to add 3 to negative dividends and 0 to
142 // positive ones. So (-7+3)>>2 becomes -1, (-4+3)>>2 becomes -1,
143 // (-2+3)>>2 becomes 0, etc.
144
145 // Compute 0 or -1, based on sign bit
146 Node *sign = phase->transform(new RShiftINode(dividend, phase->intcon(N - 1)));
147 // Mask sign bit to the low sign bits
148 Node *round = phase->transform(new URShiftINode(sign, phase->intcon(N - l)));
149 // Round up before shifting
150 dividend = phase->transform(new AddINode(dividend, round));
151 }
152
153 // Shift for division
154 q = new RShiftINode(dividend, phase->intcon(l));
155
156 if (!d_pos) {
157 q = new SubINode(phase->intcon(0), phase->transform(q));
158 }
159 } else {
160 // Attempt the jint constant divide -> multiply transform found in
161 // "Division by Invariant Integers using Multiplication"
162 // by Granlund and Montgomery
163 // See also "Hacker's Delight", chapter 10 by Warren.
164
165 jint magic_const;
166 jint shift_const;
167 if (magic_int_divide_constants(d, magic_const, shift_const)) {
168 Node *magic = phase->longcon(magic_const);
169 Node *dividend_long = phase->transform(new ConvI2LNode(dividend));
170
171 // Compute the high half of the dividend x magic multiplication
172 Node *mul_hi = phase->transform(new MulLNode(dividend_long, magic));
173
174 if (magic_const < 0) {
175 mul_hi = phase->transform(new RShiftLNode(mul_hi, phase->intcon(N)));
176 mul_hi = phase->transform(new ConvL2INode(mul_hi));
177
178 // The magic multiplier is too large for a 32 bit constant. We've adjusted
179 // it down by 2^32, but have to add 1 dividend back in after the multiplication.
180 // This handles the "overflow" case described by Granlund and Montgomery.
181 mul_hi = phase->transform(new AddINode(dividend, mul_hi));
182
183 // Shift over the (adjusted) mulhi
184 if (shift_const != 0) {
185 mul_hi = phase->transform(new RShiftINode(mul_hi, phase->intcon(shift_const)));
186 }
187 } else {
188 // No add is required, we can merge the shifts together.
189 mul_hi = phase->transform(new RShiftLNode(mul_hi, phase->intcon(N + shift_const)));
190 mul_hi = phase->transform(new ConvL2INode(mul_hi));
191 }
192
193 // Get a 0 or -1 from the sign of the dividend.
194 Node *addend0 = mul_hi;
195 Node *addend1 = phase->transform(new RShiftINode(dividend, phase->intcon(N-1)));
196
197 // If the divisor is negative, swap the order of the input addends;
198 // this has the effect of negating the quotient.
199 if (!d_pos) {
200 Node *temp = addend0; addend0 = addend1; addend1 = temp;
201 }
202
203 // Adjust the final quotient by subtracting -1 (adding 1)
204 // from the mul_hi.
205 q = new SubINode(addend0, addend1);
206 }
207 }
208
209 return q;
210 }
211
212 //---------------------magic_long_divide_constants-----------------------------
213 // Compute magic multiplier and shift constant for converting a 64 bit divide
214 // by constant into a multiply/shift/add series. Return false if calculations
215 // fail.
216 //
217 // Borrowed almost verbatim from Hacker's Delight by Henry S. Warren, Jr. with
218 // minor type name and parameter changes. Adjusted to 64 bit word width.
219 static bool magic_long_divide_constants(jlong d, jlong &M, jint &s) {
220 int64_t p;
221 uint64_t ad, anc, delta, q1, r1, q2, r2, t;
222 const uint64_t two63 = 0x8000000000000000LL; // 2**63.
223
224 ad = ABS(d);
225 if (d == 0 || d == 1) return false;
244 q2 = q2 + 1; // comparison here).
245 r2 = r2 - ad;
246 }
247 delta = ad - r2;
248 } while (q1 < delta || (q1 == delta && r1 == 0));
249
250 M = q2 + 1;
251 if (d < 0) M = -M; // Magic number and
252 s = p - 64; // shift amount to return.
253
254 return true;
255 }
256
257 //---------------------long_by_long_mulhi--------------------------------------
258 // Generate ideal node graph for upper half of a 64 bit x 64 bit multiplication
259 static Node* long_by_long_mulhi(PhaseGVN* phase, Node* dividend, jlong magic_const) {
260 // If the architecture supports a 64x64 mulhi, there is
261 // no need to synthesize it in ideal nodes.
262 if (Matcher::has_match_rule(Op_MulHiL)) {
263 Node* v = phase->longcon(magic_const);
264 return new MulHiLNode(dividend, v);
265 }
266
267 // Taken from Hacker's Delight, Fig. 8-2. Multiply high signed.
268 // (http://www.hackersdelight.org/HDcode/mulhs.c)
269 //
270 // int mulhs(int u, int v) {
271 // unsigned u0, v0, w0;
272 // int u1, v1, w1, w2, t;
273 //
274 // u0 = u & 0xFFFF; u1 = u >> 16;
275 // v0 = v & 0xFFFF; v1 = v >> 16;
276 // w0 = u0*v0;
277 // t = u1*v0 + (w0 >> 16);
278 // w1 = t & 0xFFFF;
279 // w2 = t >> 16;
280 // w1 = u0*v1 + w1;
281 // return u1*v1 + w2 + (w1 >> 16);
282 // }
283 //
284 // Note: The version above is for 32x32 multiplications, while the
285 // following inline comments are adapted to 64x64.
286
287 const int N = 64;
288
289 // Dummy node to keep intermediate nodes alive during construction
290 Node* hook = new Node(4);
291
292 // u0 = u & 0xFFFFFFFF; u1 = u >> 32;
293 Node* u0 = phase->transform(new AndLNode(dividend, phase->longcon(0xFFFFFFFF)));
294 Node* u1 = phase->transform(new RShiftLNode(dividend, phase->intcon(N / 2)));
295 hook->init_req(0, u0);
296 hook->init_req(1, u1);
297
298 // v0 = v & 0xFFFFFFFF; v1 = v >> 32;
299 Node* v0 = phase->longcon(magic_const & 0xFFFFFFFF);
300 Node* v1 = phase->longcon(magic_const >> (N / 2));
301
302 // w0 = u0*v0;
303 Node* w0 = phase->transform(new MulLNode(u0, v0));
304
305 // t = u1*v0 + (w0 >> 32);
306 Node* u1v0 = phase->transform(new MulLNode(u1, v0));
307 Node* temp = phase->transform(new URShiftLNode(w0, phase->intcon(N / 2)));
308 Node* t = phase->transform(new AddLNode(u1v0, temp));
309 hook->init_req(2, t);
310
311 // w1 = t & 0xFFFFFFFF;
312 Node* w1 = phase->transform(new AndLNode(t, phase->longcon(0xFFFFFFFF)));
313 hook->init_req(3, w1);
314
315 // w2 = t >> 32;
316 Node* w2 = phase->transform(new RShiftLNode(t, phase->intcon(N / 2)));
317
318 // w1 = u0*v1 + w1;
319 Node* u0v1 = phase->transform(new MulLNode(u0, v1));
320 w1 = phase->transform(new AddLNode(u0v1, w1));
321
322 // return u1*v1 + w2 + (w1 >> 32);
323 Node* u1v1 = phase->transform(new MulLNode(u1, v1));
324 Node* temp1 = phase->transform(new AddLNode(u1v1, w2));
325 Node* temp2 = phase->transform(new RShiftLNode(w1, phase->intcon(N / 2)));
326
327 // Remove the bogus extra edges used to keep things alive
328 PhaseIterGVN* igvn = phase->is_IterGVN();
329 if (igvn != NULL) {
330 igvn->remove_dead_node(hook);
331 } else {
332 for (int i = 0; i < 4; i++) {
333 hook->set_req(i, NULL);
334 }
335 }
336
337 return new AddLNode(temp1, temp2);
338 }
339
340
341 //--------------------------transform_long_divide------------------------------
342 // Convert a division by constant divisor into an alternate Ideal graph.
343 // Return NULL if no transformation occurs.
344 static Node *transform_long_divide( PhaseGVN *phase, Node *dividend, jlong divisor ) {
345 // Check for invalid divisors
346 assert( divisor != 0L && divisor != min_jlong,
347 "bad divisor for transforming to long multiply" );
348
349 bool d_pos = divisor >= 0;
350 jlong d = d_pos ? divisor : -divisor;
351 const int N = 64;
352
353 // Result
354 Node *q = NULL;
355
356 if (d == 1) {
357 // division by +/- 1
358 if (!d_pos) {
359 // Just negate the value
360 q = new SubLNode(phase->longcon(0), dividend);
361 }
362 } else if ( is_power_of_2_long(d) ) {
363
364 // division by +/- a power of 2
365
366 // See if we can simply do a shift without rounding
367 bool needs_rounding = true;
368 const Type *dt = phase->type(dividend);
369 const TypeLong *dtl = dt->isa_long();
370
371 if (dtl && dtl->_lo > 0) {
372 // we don't need to round a positive dividend
373 needs_rounding = false;
374 } else if( dividend->Opcode() == Op_AndL ) {
375 // An AND mask of sufficient size clears the low bits and
376 // I can avoid rounding.
377 const TypeLong *andconl_t = phase->type( dividend->in(2) )->isa_long();
378 if( andconl_t && andconl_t->is_con() ) {
379 jlong andconl = andconl_t->get_con();
380 if( andconl < 0 && is_power_of_2_long(-andconl) && (-andconl) >= d ) {
381 if( (-andconl) == d ) // Remove AND if it clears bits which will be shifted
382 dividend = dividend->in(1);
383 needs_rounding = false;
384 }
385 }
386 }
387
388 // Add rounding to the shift to handle the sign bit
389 int l = log2_long(d-1)+1;
390 if (needs_rounding) {
391 // Divide-by-power-of-2 can be made into a shift, but you have to do
392 // more math for the rounding. You need to add 0 for positive
393 // numbers, and "i-1" for negative numbers. Example: i=4, so the
394 // shift is by 2. You need to add 3 to negative dividends and 0 to
395 // positive ones. So (-7+3)>>2 becomes -1, (-4+3)>>2 becomes -1,
396 // (-2+3)>>2 becomes 0, etc.
397
398 // Compute 0 or -1, based on sign bit
399 Node *sign = phase->transform(new RShiftLNode(dividend, phase->intcon(N - 1)));
400 // Mask sign bit to the low sign bits
401 Node *round = phase->transform(new URShiftLNode(sign, phase->intcon(N - l)));
402 // Round up before shifting
403 dividend = phase->transform(new AddLNode(dividend, round));
404 }
405
406 // Shift for division
407 q = new RShiftLNode(dividend, phase->intcon(l));
408
409 if (!d_pos) {
410 q = new SubLNode(phase->longcon(0), phase->transform(q));
411 }
412 } else if ( !Matcher::use_asm_for_ldiv_by_con(d) ) { // Use hardware DIV instruction when
413 // it is faster than code generated below.
414 // Attempt the jlong constant divide -> multiply transform found in
415 // "Division by Invariant Integers using Multiplication"
416 // by Granlund and Montgomery
417 // See also "Hacker's Delight", chapter 10 by Warren.
418
419 jlong magic_const;
420 jint shift_const;
421 if (magic_long_divide_constants(d, magic_const, shift_const)) {
422 // Compute the high half of the dividend x magic multiplication
423 Node *mul_hi = phase->transform(long_by_long_mulhi(phase, dividend, magic_const));
424
425 // The high half of the 128-bit multiply is computed.
426 if (magic_const < 0) {
427 // The magic multiplier is too large for a 64 bit constant. We've adjusted
428 // it down by 2^64, but have to add 1 dividend back in after the multiplication.
429 // This handles the "overflow" case described by Granlund and Montgomery.
430 mul_hi = phase->transform(new AddLNode(dividend, mul_hi));
431 }
432
433 // Shift over the (adjusted) mulhi
434 if (shift_const != 0) {
435 mul_hi = phase->transform(new RShiftLNode(mul_hi, phase->intcon(shift_const)));
436 }
437
438 // Get a 0 or -1 from the sign of the dividend.
439 Node *addend0 = mul_hi;
440 Node *addend1 = phase->transform(new RShiftLNode(dividend, phase->intcon(N-1)));
441
442 // If the divisor is negative, swap the order of the input addends;
443 // this has the effect of negating the quotient.
444 if (!d_pos) {
445 Node *temp = addend0; addend0 = addend1; addend1 = temp;
446 }
447
448 // Adjust the final quotient by subtracting -1 (adding 1)
449 // from the mul_hi.
450 q = new SubLNode(addend0, addend1);
451 }
452 }
453
454 return q;
455 }
456
457 //=============================================================================
458 //------------------------------Identity---------------------------------------
459 // If the divisor is 1, we are an identity on the dividend.
460 Node *DivINode::Identity( PhaseTransform *phase ) {
461 return (phase->type( in(2) )->higher_equal(TypeInt::ONE)) ? in(1) : this;
462 }
463
464 //------------------------------Idealize---------------------------------------
465 // Divides can be changed to multiplies and/or shifts
466 Node *DivINode::Ideal(PhaseGVN *phase, bool can_reshape) {
467 if (in(0) && remove_dead_region(phase, can_reshape)) return this;
468 // Don't bother trying to transform a dead node
469 if( in(0) && in(0)->is_top() ) return NULL;
470
720
721 // Check for out of range values
722 if( tf->is_nan() || !tf->is_finite() ) return NULL;
723
724 // Get the value
725 float f = tf->getf();
726 int exp;
727
728 // Only for special case of dividing by a power of 2
729 if( frexp((double)f, &exp) != 0.5 ) return NULL;
730
731 // Limit the range of acceptable exponents
732 if( exp < -126 || exp > 126 ) return NULL;
733
734 // Compute the reciprocal
735 float reciprocal = ((float)1.0) / f;
736
737 assert( frexp((double)reciprocal, &exp) == 0.5, "reciprocal should be power of 2" );
738
739 // return multiplication by the reciprocal
740 return (new MulFNode(in(1), phase->makecon(TypeF::make(reciprocal))));
741 }
742
743 //=============================================================================
744 //------------------------------Value------------------------------------------
745 // An DivDNode divides its inputs. The third input is a Control input, used to
746 // prevent hoisting the divide above an unsafe test.
747 const Type *DivDNode::Value( PhaseTransform *phase ) const {
748 // Either input is TOP ==> the result is TOP
749 const Type *t1 = phase->type( in(1) );
750 const Type *t2 = phase->type( in(2) );
751 if( t1 == Type::TOP ) return Type::TOP;
752 if( t2 == Type::TOP ) return Type::TOP;
753
754 // Either input is BOTTOM ==> the result is the local BOTTOM
755 const Type *bot = bottom_type();
756 if( (t1 == bot) || (t2 == bot) ||
757 (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) )
758 return bot;
759
760 // x/x == 1, we ignore 0/0.
814
815 // Check for out of range values
816 if( td->is_nan() || !td->is_finite() ) return NULL;
817
818 // Get the value
819 double d = td->getd();
820 int exp;
821
822 // Only for special case of dividing by a power of 2
823 if( frexp(d, &exp) != 0.5 ) return NULL;
824
825 // Limit the range of acceptable exponents
826 if( exp < -1021 || exp > 1022 ) return NULL;
827
828 // Compute the reciprocal
829 double reciprocal = 1.0 / d;
830
831 assert( frexp(reciprocal, &exp) == 0.5, "reciprocal should be power of 2" );
832
833 // return multiplication by the reciprocal
834 return (new MulDNode(in(1), phase->makecon(TypeD::make(reciprocal))));
835 }
836
837 //=============================================================================
838 //------------------------------Idealize---------------------------------------
839 Node *ModINode::Ideal(PhaseGVN *phase, bool can_reshape) {
840 // Check for dead control input
841 if( in(0) && remove_dead_region(phase, can_reshape) ) return this;
842 // Don't bother trying to transform a dead node
843 if( in(0) && in(0)->is_top() ) return NULL;
844
845 // Get the modulus
846 const Type *t = phase->type( in(2) );
847 if( t == Type::TOP ) return NULL;
848 const TypeInt *ti = t->is_int();
849
850 // Check for useless control input
851 // Check for excluding mod-zero case
852 if( in(0) && (ti->_hi < 0 || ti->_lo > 0) ) {
853 set_req(0, NULL); // Yank control input
854 return this;
855 }
856
857 // See if we are MOD'ing by 2^k or 2^k-1.
858 if( !ti->is_con() ) return NULL;
859 jint con = ti->get_con();
860
861 Node *hook = new Node(1);
862
863 // First, special check for modulo 2^k-1
864 if( con >= 0 && con < max_jint && is_power_of_2(con+1) ) {
865 uint k = exact_log2(con+1); // Extract k
866
867 // Basic algorithm by David Detlefs. See fastmod_int.java for gory details.
868 static int unroll_factor[] = { 999, 999, 29, 14, 9, 7, 5, 4, 4, 3, 3, 2, 2, 2, 2, 2, 1 /*past here we assume 1 forever*/};
869 int trip_count = 1;
870 if( k < ARRAY_SIZE(unroll_factor)) trip_count = unroll_factor[k];
871
872 // If the unroll factor is not too large, and if conditional moves are
873 // ok, then use this case
874 if( trip_count <= 5 && ConditionalMoveLimit != 0 ) {
875 Node *x = in(1); // Value being mod'd
876 Node *divisor = in(2); // Also is mask
877
878 hook->init_req(0, x); // Add a use to x to prevent him from dying
879 // Generate code to reduce X rapidly to nearly 2^k-1.
880 for( int i = 0; i < trip_count; i++ ) {
881 Node *xl = phase->transform( new AndINode(x,divisor) );
882 Node *xh = phase->transform( new RShiftINode(x,phase->intcon(k)) ); // Must be signed
883 x = phase->transform( new AddINode(xh,xl) );
884 hook->set_req(0, x);
885 }
886
887 // Generate sign-fixup code. Was original value positive?
888 // int hack_res = (i >= 0) ? divisor : 1;
889 Node *cmp1 = phase->transform( new CmpINode( in(1), phase->intcon(0) ) );
890 Node *bol1 = phase->transform( new BoolNode( cmp1, BoolTest::ge ) );
891 Node *cmov1= phase->transform( new CMoveINode(bol1, phase->intcon(1), divisor, TypeInt::POS) );
892 // if( x >= hack_res ) x -= divisor;
893 Node *sub = phase->transform( new SubINode( x, divisor ) );
894 Node *cmp2 = phase->transform( new CmpINode( x, cmov1 ) );
895 Node *bol2 = phase->transform( new BoolNode( cmp2, BoolTest::ge ) );
896 // Convention is to not transform the return value of an Ideal
897 // since Ideal is expected to return a modified 'this' or a new node.
898 Node *cmov2= new CMoveINode(bol2, x, sub, TypeInt::INT);
899 // cmov2 is now the mod
900
901 // Now remove the bogus extra edges used to keep things alive
902 if (can_reshape) {
903 phase->is_IterGVN()->remove_dead_node(hook);
904 } else {
905 hook->set_req(0, NULL); // Just yank bogus edge during Parse phase
906 }
907 return cmov2;
908 }
909 }
910
911 // Fell thru, the unroll case is not appropriate. Transform the modulo
912 // into a long multiply/int multiply/subtract case
913
914 // Cannot handle mod 0, and min_jint isn't handled by the transform
915 if( con == 0 || con == min_jint ) return NULL;
916
917 // Get the absolute value of the constant; at this point, we can use this
918 jint pos_con = (con >= 0) ? con : -con;
919
920 // integer Mod 1 is always 0
921 if( pos_con == 1 ) return new ConINode(TypeInt::ZERO);
922
923 int log2_con = -1;
924
925 // If this is a power of two, they maybe we can mask it
926 if( is_power_of_2(pos_con) ) {
927 log2_con = log2_intptr((intptr_t)pos_con);
928
929 const Type *dt = phase->type(in(1));
930 const TypeInt *dti = dt->isa_int();
931
932 // See if this can be masked, if the dividend is non-negative
933 if( dti && dti->_lo >= 0 )
934 return ( new AndINode( in(1), phase->intcon( pos_con-1 ) ) );
935 }
936
937 // Save in(1) so that it cannot be changed or deleted
938 hook->init_req(0, in(1));
939
940 // Divide using the transform from DivI to MulL
941 Node *result = transform_int_divide( phase, in(1), pos_con );
942 if (result != NULL) {
943 Node *divide = phase->transform(result);
944
945 // Re-multiply, using a shift if this is a power of two
946 Node *mult = NULL;
947
948 if( log2_con >= 0 )
949 mult = phase->transform( new LShiftINode( divide, phase->intcon( log2_con ) ) );
950 else
951 mult = phase->transform( new MulINode( divide, phase->intcon( pos_con ) ) );
952
953 // Finally, subtract the multiplied divided value from the original
954 result = new SubINode( in(1), mult );
955 }
956
957 // Now remove the bogus extra edges used to keep things alive
958 if (can_reshape) {
959 phase->is_IterGVN()->remove_dead_node(hook);
960 } else {
961 hook->set_req(0, NULL); // Just yank bogus edge during Parse phase
962 }
963
964 // return the value
965 return result;
966 }
967
968 //------------------------------Value------------------------------------------
969 const Type *ModINode::Value( PhaseTransform *phase ) const {
970 // Either input is TOP ==> the result is TOP
971 const Type *t1 = phase->type( in(1) );
972 const Type *t2 = phase->type( in(2) );
973 if( t1 == Type::TOP ) return Type::TOP;
974 if( t2 == Type::TOP ) return Type::TOP;
1012 if( in(0) && remove_dead_region(phase, can_reshape) ) return this;
1013 // Don't bother trying to transform a dead node
1014 if( in(0) && in(0)->is_top() ) return NULL;
1015
1016 // Get the modulus
1017 const Type *t = phase->type( in(2) );
1018 if( t == Type::TOP ) return NULL;
1019 const TypeLong *tl = t->is_long();
1020
1021 // Check for useless control input
1022 // Check for excluding mod-zero case
1023 if( in(0) && (tl->_hi < 0 || tl->_lo > 0) ) {
1024 set_req(0, NULL); // Yank control input
1025 return this;
1026 }
1027
1028 // See if we are MOD'ing by 2^k or 2^k-1.
1029 if( !tl->is_con() ) return NULL;
1030 jlong con = tl->get_con();
1031
1032 Node *hook = new Node(1);
1033
1034 // Expand mod
1035 if( con >= 0 && con < max_jlong && is_power_of_2_long(con+1) ) {
1036 uint k = exact_log2_long(con+1); // Extract k
1037
1038 // Basic algorithm by David Detlefs. See fastmod_long.java for gory details.
1039 // Used to help a popular random number generator which does a long-mod
1040 // of 2^31-1 and shows up in SpecJBB and SciMark.
1041 static int unroll_factor[] = { 999, 999, 61, 30, 20, 15, 12, 10, 8, 7, 6, 6, 5, 5, 4, 4, 4, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1 /*past here we assume 1 forever*/};
1042 int trip_count = 1;
1043 if( k < ARRAY_SIZE(unroll_factor)) trip_count = unroll_factor[k];
1044
1045 // If the unroll factor is not too large, and if conditional moves are
1046 // ok, then use this case
1047 if( trip_count <= 5 && ConditionalMoveLimit != 0 ) {
1048 Node *x = in(1); // Value being mod'd
1049 Node *divisor = in(2); // Also is mask
1050
1051 hook->init_req(0, x); // Add a use to x to prevent him from dying
1052 // Generate code to reduce X rapidly to nearly 2^k-1.
1053 for( int i = 0; i < trip_count; i++ ) {
1054 Node *xl = phase->transform( new AndLNode(x,divisor) );
1055 Node *xh = phase->transform( new RShiftLNode(x,phase->intcon(k)) ); // Must be signed
1056 x = phase->transform( new AddLNode(xh,xl) );
1057 hook->set_req(0, x); // Add a use to x to prevent him from dying
1058 }
1059
1060 // Generate sign-fixup code. Was original value positive?
1061 // long hack_res = (i >= 0) ? divisor : CONST64(1);
1062 Node *cmp1 = phase->transform( new CmpLNode( in(1), phase->longcon(0) ) );
1063 Node *bol1 = phase->transform( new BoolNode( cmp1, BoolTest::ge ) );
1064 Node *cmov1= phase->transform( new CMoveLNode(bol1, phase->longcon(1), divisor, TypeLong::LONG) );
1065 // if( x >= hack_res ) x -= divisor;
1066 Node *sub = phase->transform( new SubLNode( x, divisor ) );
1067 Node *cmp2 = phase->transform( new CmpLNode( x, cmov1 ) );
1068 Node *bol2 = phase->transform( new BoolNode( cmp2, BoolTest::ge ) );
1069 // Convention is to not transform the return value of an Ideal
1070 // since Ideal is expected to return a modified 'this' or a new node.
1071 Node *cmov2= new CMoveLNode(bol2, x, sub, TypeLong::LONG);
1072 // cmov2 is now the mod
1073
1074 // Now remove the bogus extra edges used to keep things alive
1075 if (can_reshape) {
1076 phase->is_IterGVN()->remove_dead_node(hook);
1077 } else {
1078 hook->set_req(0, NULL); // Just yank bogus edge during Parse phase
1079 }
1080 return cmov2;
1081 }
1082 }
1083
1084 // Fell thru, the unroll case is not appropriate. Transform the modulo
1085 // into a long multiply/int multiply/subtract case
1086
1087 // Cannot handle mod 0, and min_jlong isn't handled by the transform
1088 if( con == 0 || con == min_jlong ) return NULL;
1089
1090 // Get the absolute value of the constant; at this point, we can use this
1091 jlong pos_con = (con >= 0) ? con : -con;
1092
1093 // integer Mod 1 is always 0
1094 if( pos_con == 1 ) return new ConLNode(TypeLong::ZERO);
1095
1096 int log2_con = -1;
1097
1098 // If this is a power of two, then maybe we can mask it
1099 if( is_power_of_2_long(pos_con) ) {
1100 log2_con = exact_log2_long(pos_con);
1101
1102 const Type *dt = phase->type(in(1));
1103 const TypeLong *dtl = dt->isa_long();
1104
1105 // See if this can be masked, if the dividend is non-negative
1106 if( dtl && dtl->_lo >= 0 )
1107 return ( new AndLNode( in(1), phase->longcon( pos_con-1 ) ) );
1108 }
1109
1110 // Save in(1) so that it cannot be changed or deleted
1111 hook->init_req(0, in(1));
1112
1113 // Divide using the transform from DivL to MulL
1114 Node *result = transform_long_divide( phase, in(1), pos_con );
1115 if (result != NULL) {
1116 Node *divide = phase->transform(result);
1117
1118 // Re-multiply, using a shift if this is a power of two
1119 Node *mult = NULL;
1120
1121 if( log2_con >= 0 )
1122 mult = phase->transform( new LShiftLNode( divide, phase->intcon( log2_con ) ) );
1123 else
1124 mult = phase->transform( new MulLNode( divide, phase->longcon( pos_con ) ) );
1125
1126 // Finally, subtract the multiplied divided value from the original
1127 result = new SubLNode( in(1), mult );
1128 }
1129
1130 // Now remove the bogus extra edges used to keep things alive
1131 if (can_reshape) {
1132 phase->is_IterGVN()->remove_dead_node(hook);
1133 } else {
1134 hook->set_req(0, NULL); // Just yank bogus edge during Parse phase
1135 }
1136
1137 // return the value
1138 return result;
1139 }
1140
1141 //------------------------------Value------------------------------------------
1142 const Type *ModLNode::Value( PhaseTransform *phase ) const {
1143 // Either input is TOP ==> the result is TOP
1144 const Type *t1 = phase->type( in(1) );
1145 const Type *t2 = phase->type( in(2) );
1146 if( t1 == Type::TOP ) return Type::TOP;
1147 if( t2 == Type::TOP ) return Type::TOP;
1262 xr ^= min_jlong;
1263 }
1264
1265 return TypeD::make(jdouble_cast(xr));
1266 }
1267
1268 //=============================================================================
1269
1270 DivModNode::DivModNode( Node *c, Node *dividend, Node *divisor ) : MultiNode(3) {
1271 init_req(0, c);
1272 init_req(1, dividend);
1273 init_req(2, divisor);
1274 }
1275
1276 //------------------------------make------------------------------------------
1277 DivModINode* DivModINode::make(Compile* C, Node* div_or_mod) {
1278 Node* n = div_or_mod;
1279 assert(n->Opcode() == Op_DivI || n->Opcode() == Op_ModI,
1280 "only div or mod input pattern accepted");
1281
1282 DivModINode* divmod = new DivModINode(n->in(0), n->in(1), n->in(2));
1283 Node* dproj = new ProjNode(divmod, DivModNode::div_proj_num);
1284 Node* mproj = new ProjNode(divmod, DivModNode::mod_proj_num);
1285 return divmod;
1286 }
1287
1288 //------------------------------make------------------------------------------
1289 DivModLNode* DivModLNode::make(Compile* C, Node* div_or_mod) {
1290 Node* n = div_or_mod;
1291 assert(n->Opcode() == Op_DivL || n->Opcode() == Op_ModL,
1292 "only div or mod input pattern accepted");
1293
1294 DivModLNode* divmod = new DivModLNode(n->in(0), n->in(1), n->in(2));
1295 Node* dproj = new ProjNode(divmod, DivModNode::div_proj_num);
1296 Node* mproj = new ProjNode(divmod, DivModNode::mod_proj_num);
1297 return divmod;
1298 }
1299
1300 //------------------------------match------------------------------------------
1301 // return result(s) along with their RegMask info
1302 Node *DivModINode::match( const ProjNode *proj, const Matcher *match ) {
1303 uint ideal_reg = proj->ideal_reg();
1304 RegMask rm;
1305 if (proj->_con == div_proj_num) {
1306 rm = match->divI_proj_mask();
1307 } else {
1308 assert(proj->_con == mod_proj_num, "must be div or mod projection");
1309 rm = match->modI_proj_mask();
1310 }
1311 return new MachProjNode(this, proj->_con, rm, ideal_reg);
1312 }
1313
1314
1315 //------------------------------match------------------------------------------
1316 // return result(s) along with their RegMask info
1317 Node *DivModLNode::match( const ProjNode *proj, const Matcher *match ) {
1318 uint ideal_reg = proj->ideal_reg();
1319 RegMask rm;
1320 if (proj->_con == div_proj_num) {
1321 rm = match->divL_proj_mask();
1322 } else {
1323 assert(proj->_con == mod_proj_num, "must be div or mod projection");
1324 rm = match->modL_proj_mask();
1325 }
1326 return new MachProjNode(this, proj->_con, rm, ideal_reg);
1327 }
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