hotspot/src/share/vm/opto/divnode.cpp

Print this page
rev 611 : Merge

*** 1,10 **** #ifdef USE_PRAGMA_IDENT_SRC #pragma ident "@(#)divnode.cpp 1.88 07/05/05 17:06:13 JVM" #endif /* ! * Copyright 1997-2006 Sun Microsystems, Inc. All Rights Reserved. * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. * * This code is free software; you can redistribute it and/or modify it * under the terms of the GNU General Public License version 2 only, as * published by the Free Software Foundation. --- 1,10 ---- #ifdef USE_PRAGMA_IDENT_SRC #pragma ident "@(#)divnode.cpp 1.88 07/05/05 17:06:13 JVM" #endif /* ! * Copyright 1997-2009 Sun Microsystems, Inc. All Rights Reserved. * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. * * This code is free software; you can redistribute it and/or modify it * under the terms of the GNU General Public License version 2 only, as * published by the Free Software Foundation.
*** 31,153 **** #include "incls/_precompiled.incl" #include "incls/_divnode.cpp.incl" #include <math.h> ! // Implement the integer constant divide -> long multiply transform found in ! // "Division by Invariant Integers using Multiplication" ! // by Granlund and Montgomery ! static Node *transform_int_divide_to_long_multiply( PhaseGVN *phase, Node *dividend, int divisor ) { // Check for invalid divisors ! assert( divisor != 0 && divisor != min_jint && divisor != 1, "bad divisor for transforming to long multiply" ); - // Compute l = ceiling(log2(d)) - // presumes d is more likely small bool d_pos = divisor >= 0; ! int d = d_pos ? divisor : -divisor; ! unsigned ud = (unsigned)d; const int N = 32; int l = log2_intptr(d-1)+1; ! int sh_post = l; ! const uint64_t U1 = (uint64_t)1; ! // Cliff pointed out how to prevent overflow (from the paper) ! uint64_t m_low = (((U1 << l) - ud) << N) / ud + (U1 << N); ! uint64_t m_high = ((((U1 << l) - ud) << N) + (U1 << (l+1))) / ud + (U1 << N); ! ! // Reduce to lowest terms ! for ( ; sh_post > 0; sh_post-- ) { ! uint64_t m_low_1 = m_low >> 1; ! uint64_t m_high_1 = m_high >> 1; ! if ( m_low_1 >= m_high_1 ) ! break; ! m_low = m_low_1; ! m_high = m_high_1; } // Result ! Node *q; - // division by +/- 1 if (d == 1) { ! // Filtered out as identity above ! if (d_pos) ! return NULL; ! // Just negate the value ! else { ! q = new (phase->C, 3) SubINode(phase->intcon(0), dividend); ! } } // division by +/- a power of 2 - else if ( is_power_of_2(d) ) { // See if we can simply do a shift without rounding bool needs_rounding = true; const Type *dt = phase->type(dividend); ! const TypeInt *dti = dt->isa_int(); // we don't need to round a positive dividend - if (dti && dti->_lo >= 0) needs_rounding = false; ! // An AND mask of sufficient size clears the low bits and // I can avoid rounding. ! else if( dividend->Opcode() == Op_AndI ) { ! const TypeInt *andconi = phase->type( dividend->in(2) )->isa_int(); ! if( andconi && andconi->is_con(-d) ) { dividend = dividend->in(1); needs_rounding = false; } } // Add rounding to the shift to handle the sign bit ! if( needs_rounding ) { ! Node *t1 = phase->transform(new (phase->C, 3) RShiftINode(dividend, phase->intcon(l - 1))); ! Node *t2 = phase->transform(new (phase->C, 3) URShiftINode(t1, phase->intcon(N - l))); ! dividend = phase->transform(new (phase->C, 3) AddINode(dividend, t2)); } ! q = new (phase->C, 3) RShiftINode(dividend, phase->intcon(l)); ! if (!d_pos) ! q = new (phase->C, 3) SubINode(phase->intcon(0), phase->transform(q)); } ! // division by something else ! else if (m_high < (U1 << (N-1))) { ! Node *t1 = phase->transform(new (phase->C, 2) ConvI2LNode(dividend)); ! Node *t2 = phase->transform(new (phase->C, 3) MulLNode(t1, phase->longcon(m_high))); ! Node *t3 = phase->transform(new (phase->C, 3) RShiftLNode(t2, phase->intcon(sh_post+N))); ! Node *t4 = phase->transform(new (phase->C, 2) ConvL2INode(t3)); ! Node *t5 = phase->transform(new (phase->C, 3) RShiftINode(dividend, phase->intcon(N-1))); ! ! q = new (phase->C, 3) SubINode(d_pos ? t4 : t5, d_pos ? t5 : t4); ! } ! ! // This handles that case where m_high is >= 2**(N-1). In that case, ! // we subtract out 2**N from the multiply and add it in later as ! // "dividend" in the equation (t5). This case computes the same result ! // as the immediately preceeding case, save that rounding and overflow ! // are accounted for. ! else { ! Node *t1 = phase->transform(new (phase->C, 2) ConvI2LNode(dividend)); ! Node *t2 = phase->transform(new (phase->C, 3) MulLNode(t1, phase->longcon(m_high - (U1 << N)))); ! Node *t3 = phase->transform(new (phase->C, 3) RShiftLNode(t2, phase->intcon(N))); ! Node *t4 = phase->transform(new (phase->C, 2) ConvL2INode(t3)); ! Node *t5 = phase->transform(new (phase->C, 3) AddINode(dividend, t4)); ! Node *t6 = phase->transform(new (phase->C, 3) RShiftINode(t5, phase->intcon(sh_post))); ! Node *t7 = phase->transform(new (phase->C, 3) RShiftINode(dividend, phase->intcon(N-1))); ! q = new (phase->C, 3) SubINode(d_pos ? t6 : t7, d_pos ? t7 : t6); } ! return (q); } //============================================================================= //------------------------------Identity--------------------------------------- // If the divisor is 1, we are an identity on the dividend. --- 31,405 ---- #include "incls/_precompiled.incl" #include "incls/_divnode.cpp.incl" #include <math.h> ! //----------------------magic_int_divide_constants----------------------------- ! // Compute magic multiplier and shift constant for converting a 32 bit divide ! // by constant into a multiply/shift/add series. Return false if calculations ! // fail. ! // ! // Borrowed almost verbatum from Hacker's Delight by Henry S. Warren, Jr. with ! // minor type name and parameter changes. ! static bool magic_int_divide_constants(jint d, jint &M, jint &s) { ! int32_t p; ! uint32_t ad, anc, delta, q1, r1, q2, r2, t; ! const uint32_t two31 = 0x80000000L; // 2**31. ! ! ad = ABS(d); ! if (d == 0 || d == 1) return false; ! t = two31 + ((uint32_t)d >> 31); ! anc = t - 1 - t%ad; // Absolute value of nc. ! p = 31; // Init. p. ! q1 = two31/anc; // Init. q1 = 2**p/|nc|. ! r1 = two31 - q1*anc; // Init. r1 = rem(2**p, |nc|). ! q2 = two31/ad; // Init. q2 = 2**p/|d|. ! r2 = two31 - q2*ad; // Init. r2 = rem(2**p, |d|). ! do { ! p = p + 1; ! q1 = 2*q1; // Update q1 = 2**p/|nc|. ! r1 = 2*r1; // Update r1 = rem(2**p, |nc|). ! if (r1 >= anc) { // (Must be an unsigned ! q1 = q1 + 1; // comparison here). ! r1 = r1 - anc; ! } ! q2 = 2*q2; // Update q2 = 2**p/|d|. ! r2 = 2*r2; // Update r2 = rem(2**p, |d|). ! if (r2 >= ad) { // (Must be an unsigned ! q2 = q2 + 1; // comparison here). ! r2 = r2 - ad; ! } ! delta = ad - r2; ! } while (q1 < delta || (q1 == delta && r1 == 0)); ! ! M = q2 + 1; ! if (d < 0) M = -M; // Magic number and ! s = p - 32; // shift amount to return. ! ! return true; ! } ! ! //--------------------------transform_int_divide------------------------------- ! // Convert a division by constant divisor into an alternate Ideal graph. ! // Return NULL if no transformation occurs. ! static Node *transform_int_divide( PhaseGVN *phase, Node *dividend, jint divisor ) { // Check for invalid divisors ! assert( divisor != 0 && divisor != min_jint, "bad divisor for transforming to long multiply" ); bool d_pos = divisor >= 0; ! jint d = d_pos ? divisor : -divisor; const int N = 32; + + // Result + Node *q = NULL; + + if (d == 1) { + // division by +/- 1 + if (!d_pos) { + // Just negate the value + q = new (phase->C, 3) SubINode(phase->intcon(0), dividend); + } + } else if ( is_power_of_2(d) ) { + // division by +/- a power of 2 + + // See if we can simply do a shift without rounding + bool needs_rounding = true; + const Type *dt = phase->type(dividend); + const TypeInt *dti = dt->isa_int(); + if (dti && dti->_lo >= 0) { + // we don't need to round a positive dividend + needs_rounding = false; + } else if( dividend->Opcode() == Op_AndI ) { + // An AND mask of sufficient size clears the low bits and + // I can avoid rounding. + const TypeInt *andconi_t = phase->type( dividend->in(2) )->isa_int(); + if( andconi_t && andconi_t->is_con() ) { + jint andconi = andconi_t->get_con(); + if( andconi < 0 && is_power_of_2(-andconi) && (-andconi) >= d ) { + dividend = dividend->in(1); + needs_rounding = false; + } + } + } + + // Add rounding to the shift to handle the sign bit int l = log2_intptr(d-1)+1; ! if (needs_rounding) { ! // Divide-by-power-of-2 can be made into a shift, but you have to do ! // more math for the rounding. You need to add 0 for positive ! // numbers, and "i-1" for negative numbers. Example: i=4, so the ! // shift is by 2. You need to add 3 to negative dividends and 0 to ! // positive ones. So (-7+3)>>2 becomes -1, (-4+3)>>2 becomes -1, ! // (-2+3)>>2 becomes 0, etc. ! ! // Compute 0 or -1, based on sign bit ! Node *sign = phase->transform(new (phase->C, 3) RShiftINode(dividend, phase->intcon(N - 1))); ! // Mask sign bit to the low sign bits ! Node *round = phase->transform(new (phase->C, 3) URShiftINode(sign, phase->intcon(N - l))); ! // Round up before shifting ! dividend = phase->transform(new (phase->C, 3) AddINode(dividend, round)); ! } ! // Shift for division ! q = new (phase->C, 3) RShiftINode(dividend, phase->intcon(l)); ! if (!d_pos) { ! q = new (phase->C, 3) SubINode(phase->intcon(0), phase->transform(q)); ! } ! } else { ! // Attempt the jint constant divide -> multiply transform found in ! // "Division by Invariant Integers using Multiplication" ! // by Granlund and Montgomery ! // See also "Hacker's Delight", chapter 10 by Warren. ! ! jint magic_const; ! jint shift_const; ! if (magic_int_divide_constants(d, magic_const, shift_const)) { ! Node *magic = phase->longcon(magic_const); ! Node *dividend_long = phase->transform(new (phase->C, 2) ConvI2LNode(dividend)); ! ! // Compute the high half of the dividend x magic multiplication ! Node *mul_hi = phase->transform(new (phase->C, 3) MulLNode(dividend_long, magic)); ! ! if (magic_const < 0) { ! mul_hi = phase->transform(new (phase->C, 3) RShiftLNode(mul_hi, phase->intcon(N))); ! mul_hi = phase->transform(new (phase->C, 2) ConvL2INode(mul_hi)); ! ! // The magic multiplier is too large for a 32 bit constant. We've adjusted ! // it down by 2^32, but have to add 1 dividend back in after the multiplication. ! // This handles the "overflow" case described by Granlund and Montgomery. ! mul_hi = phase->transform(new (phase->C, 3) AddINode(dividend, mul_hi)); ! ! // Shift over the (adjusted) mulhi ! if (shift_const != 0) { ! mul_hi = phase->transform(new (phase->C, 3) RShiftINode(mul_hi, phase->intcon(shift_const))); } + } else { + // No add is required, we can merge the shifts together. + mul_hi = phase->transform(new (phase->C, 3) RShiftLNode(mul_hi, phase->intcon(N + shift_const))); + mul_hi = phase->transform(new (phase->C, 2) ConvL2INode(mul_hi)); + } + + // Get a 0 or -1 from the sign of the dividend. + Node *addend0 = mul_hi; + Node *addend1 = phase->transform(new (phase->C, 3) RShiftINode(dividend, phase->intcon(N-1))); + + // If the divisor is negative, swap the order of the input addends; + // this has the effect of negating the quotient. + if (!d_pos) { + Node *temp = addend0; addend0 = addend1; addend1 = temp; + } + + // Adjust the final quotient by subtracting -1 (adding 1) + // from the mul_hi. + q = new (phase->C, 3) SubINode(addend0, addend1); + } + } + + return q; + } + + //---------------------magic_long_divide_constants----------------------------- + // Compute magic multiplier and shift constant for converting a 64 bit divide + // by constant into a multiply/shift/add series. Return false if calculations + // fail. + // + // Borrowed almost verbatum from Hacker's Delight by Henry S. Warren, Jr. with + // minor type name and parameter changes. Adjusted to 64 bit word width. + static bool magic_long_divide_constants(jlong d, jlong &M, jint &s) { + int64_t p; + uint64_t ad, anc, delta, q1, r1, q2, r2, t; + const uint64_t two63 = 0x8000000000000000LL; // 2**63. + + ad = ABS(d); + if (d == 0 || d == 1) return false; + t = two63 + ((uint64_t)d >> 63); + anc = t - 1 - t%ad; // Absolute value of nc. + p = 63; // Init. p. + q1 = two63/anc; // Init. q1 = 2**p/|nc|. + r1 = two63 - q1*anc; // Init. r1 = rem(2**p, |nc|). + q2 = two63/ad; // Init. q2 = 2**p/|d|. + r2 = two63 - q2*ad; // Init. r2 = rem(2**p, |d|). + do { + p = p + 1; + q1 = 2*q1; // Update q1 = 2**p/|nc|. + r1 = 2*r1; // Update r1 = rem(2**p, |nc|). + if (r1 >= anc) { // (Must be an unsigned + q1 = q1 + 1; // comparison here). + r1 = r1 - anc; + } + q2 = 2*q2; // Update q2 = 2**p/|d|. + r2 = 2*r2; // Update r2 = rem(2**p, |d|). + if (r2 >= ad) { // (Must be an unsigned + q2 = q2 + 1; // comparison here). + r2 = r2 - ad; + } + delta = ad - r2; + } while (q1 < delta || (q1 == delta && r1 == 0)); + + M = q2 + 1; + if (d < 0) M = -M; // Magic number and + s = p - 64; // shift amount to return. + + return true; + } + + //---------------------long_by_long_mulhi-------------------------------------- + // Generate ideal node graph for upper half of a 64 bit x 64 bit multiplication + static Node *long_by_long_mulhi( PhaseGVN *phase, Node *dividend, jlong magic_const) { + // If the architecture supports a 64x64 mulhi, there is + // no need to synthesize it in ideal nodes. + if (Matcher::has_match_rule(Op_MulHiL)) { + Node *v = phase->longcon(magic_const); + return new (phase->C, 3) MulHiLNode(dividend, v); + } + + const int N = 64; + + Node *u_hi = phase->transform(new (phase->C, 3) RShiftLNode(dividend, phase->intcon(N / 2))); + Node *u_lo = phase->transform(new (phase->C, 3) AndLNode(dividend, phase->longcon(0xFFFFFFFF))); + + Node *v_hi = phase->longcon(magic_const >> N/2); + Node *v_lo = phase->longcon(magic_const & 0XFFFFFFFF); + + Node *hihi_product = phase->transform(new (phase->C, 3) MulLNode(u_hi, v_hi)); + Node *hilo_product = phase->transform(new (phase->C, 3) MulLNode(u_hi, v_lo)); + Node *lohi_product = phase->transform(new (phase->C, 3) MulLNode(u_lo, v_hi)); + Node *lolo_product = phase->transform(new (phase->C, 3) MulLNode(u_lo, v_lo)); + + Node *t1 = phase->transform(new (phase->C, 3) URShiftLNode(lolo_product, phase->intcon(N / 2))); + Node *t2 = phase->transform(new (phase->C, 3) AddLNode(hilo_product, t1)); + + // Construct both t3 and t4 before transforming so t2 doesn't go dead + // prematurely. + Node *t3 = new (phase->C, 3) RShiftLNode(t2, phase->intcon(N / 2)); + Node *t4 = new (phase->C, 3) AndLNode(t2, phase->longcon(0xFFFFFFFF)); + t3 = phase->transform(t3); + t4 = phase->transform(t4); + + Node *t5 = phase->transform(new (phase->C, 3) AddLNode(t4, lohi_product)); + Node *t6 = phase->transform(new (phase->C, 3) RShiftLNode(t5, phase->intcon(N / 2))); + Node *t7 = phase->transform(new (phase->C, 3) AddLNode(t3, hihi_product)); + + return new (phase->C, 3) AddLNode(t7, t6); + } + + + //--------------------------transform_long_divide------------------------------ + // Convert a division by constant divisor into an alternate Ideal graph. + // Return NULL if no transformation occurs. + static Node *transform_long_divide( PhaseGVN *phase, Node *dividend, jlong divisor ) { + // Check for invalid divisors + assert( divisor != 0L && divisor != min_jlong, + "bad divisor for transforming to long multiply" ); + + bool d_pos = divisor >= 0; + jlong d = d_pos ? divisor : -divisor; + const int N = 64; // Result ! Node *q = NULL; if (d == 1) { ! // division by +/- 1 ! if (!d_pos) { // Just negate the value ! q = new (phase->C, 3) SubLNode(phase->longcon(0), dividend); } + } else if ( is_power_of_2_long(d) ) { // division by +/- a power of 2 // See if we can simply do a shift without rounding bool needs_rounding = true; const Type *dt = phase->type(dividend); ! const TypeLong *dtl = dt->isa_long(); + if (dtl && dtl->_lo > 0) { // we don't need to round a positive dividend needs_rounding = false; ! } else if( dividend->Opcode() == Op_AndL ) { // An AND mask of sufficient size clears the low bits and // I can avoid rounding. ! const TypeLong *andconl_t = phase->type( dividend->in(2) )->isa_long(); ! if( andconl_t && andconl_t->is_con() ) { ! jlong andconl = andconl_t->get_con(); ! if( andconl < 0 && is_power_of_2_long(-andconl) && (-andconl) >= d ) { dividend = dividend->in(1); needs_rounding = false; } } + } // Add rounding to the shift to handle the sign bit ! int l = log2_long(d-1)+1; ! if (needs_rounding) { ! // Divide-by-power-of-2 can be made into a shift, but you have to do ! // more math for the rounding. You need to add 0 for positive ! // numbers, and "i-1" for negative numbers. Example: i=4, so the ! // shift is by 2. You need to add 3 to negative dividends and 0 to ! // positive ones. So (-7+3)>>2 becomes -1, (-4+3)>>2 becomes -1, ! // (-2+3)>>2 becomes 0, etc. ! ! // Compute 0 or -1, based on sign bit ! Node *sign = phase->transform(new (phase->C, 3) RShiftLNode(dividend, phase->intcon(N - 1))); ! // Mask sign bit to the low sign bits ! Node *round = phase->transform(new (phase->C, 3) URShiftLNode(sign, phase->intcon(N - l))); ! // Round up before shifting ! dividend = phase->transform(new (phase->C, 3) AddLNode(dividend, round)); } ! // Shift for division ! q = new (phase->C, 3) RShiftLNode(dividend, phase->intcon(l)); ! if (!d_pos) { ! q = new (phase->C, 3) SubLNode(phase->longcon(0), phase->transform(q)); } + } else { + // Attempt the jlong constant divide -> multiply transform found in + // "Division by Invariant Integers using Multiplication" + // by Granlund and Montgomery + // See also "Hacker's Delight", chapter 10 by Warren. ! jlong magic_const; ! jint shift_const; ! if (magic_long_divide_constants(d, magic_const, shift_const)) { ! // Compute the high half of the dividend x magic multiplication ! Node *mul_hi = phase->transform(long_by_long_mulhi(phase, dividend, magic_const)); ! // The high half of the 128-bit multiply is computed. ! if (magic_const < 0) { ! // The magic multiplier is too large for a 64 bit constant. We've adjusted ! // it down by 2^64, but have to add 1 dividend back in after the multiplication. ! // This handles the "overflow" case described by Granlund and Montgomery. ! mul_hi = phase->transform(new (phase->C, 3) AddLNode(dividend, mul_hi)); } ! // Shift over the (adjusted) mulhi ! if (shift_const != 0) { ! mul_hi = phase->transform(new (phase->C, 3) RShiftLNode(mul_hi, phase->intcon(shift_const))); ! } ! ! // Get a 0 or -1 from the sign of the dividend. ! Node *addend0 = mul_hi; ! Node *addend1 = phase->transform(new (phase->C, 3) RShiftLNode(dividend, phase->intcon(N-1))); ! ! // If the divisor is negative, swap the order of the input addends; ! // this has the effect of negating the quotient. ! if (!d_pos) { ! Node *temp = addend0; addend0 = addend1; addend1 = temp; ! } ! ! // Adjust the final quotient by subtracting -1 (adding 1) ! // from the mul_hi. ! q = new (phase->C, 3) SubLNode(addend0, addend1); ! } ! } ! ! return q; } //============================================================================= //------------------------------Identity--------------------------------------- // If the divisor is 1, we are an identity on the dividend.
*** 157,184 **** //------------------------------Idealize--------------------------------------- // Divides can be changed to multiplies and/or shifts Node *DivINode::Ideal(PhaseGVN *phase, bool can_reshape) { if (in(0) && remove_dead_region(phase, can_reshape)) return this; const Type *t = phase->type( in(2) ); if( t == TypeInt::ONE ) // Identity? return NULL; // Skip it const TypeInt *ti = t->isa_int(); if( !ti ) return NULL; if( !ti->is_con() ) return NULL; ! int i = ti->get_con(); // Get divisor if (i == 0) return NULL; // Dividing by zero constant does not idealize set_req(0,NULL); // Dividing by a not-zero constant; no faulting // Dividing by MININT does not optimize as a power-of-2 shift. if( i == min_jint ) return NULL; ! return transform_int_divide_to_long_multiply( phase, in(1), i ); } //------------------------------Value------------------------------------------ // A DivINode divides its inputs. The third input is a Control input, used to // prevent hoisting the divide above an unsafe test. --- 409,438 ---- //------------------------------Idealize--------------------------------------- // Divides can be changed to multiplies and/or shifts Node *DivINode::Ideal(PhaseGVN *phase, bool can_reshape) { if (in(0) && remove_dead_region(phase, can_reshape)) return this; + // Don't bother trying to transform a dead node + if( in(0) && in(0)->is_top() ) return NULL; const Type *t = phase->type( in(2) ); if( t == TypeInt::ONE ) // Identity? return NULL; // Skip it const TypeInt *ti = t->isa_int(); if( !ti ) return NULL; if( !ti->is_con() ) return NULL; ! jint i = ti->get_con(); // Get divisor if (i == 0) return NULL; // Dividing by zero constant does not idealize set_req(0,NULL); // Dividing by a not-zero constant; no faulting // Dividing by MININT does not optimize as a power-of-2 shift. if( i == min_jint ) return NULL; ! return transform_int_divide( phase, in(1), i ); } //------------------------------Value------------------------------------------ // A DivINode divides its inputs. The third input is a Control input, used to // prevent hoisting the divide above an unsafe test.
*** 254,344 **** //------------------------------Idealize--------------------------------------- // Dividing by a power of 2 is a shift. Node *DivLNode::Ideal( PhaseGVN *phase, bool can_reshape) { if (in(0) && remove_dead_region(phase, can_reshape)) return this; const Type *t = phase->type( in(2) ); if( t == TypeLong::ONE ) // Identity? return NULL; // Skip it ! const TypeLong *ti = t->isa_long(); ! if( !ti ) return NULL; ! if( !ti->is_con() ) return NULL; ! jlong i = ti->get_con(); // Get divisor ! if( i ) set_req(0, NULL); // Dividing by a not-zero constant; no faulting ! ! // Dividing by MININT does not optimize as a power-of-2 shift. ! if( i == min_jlong ) return NULL; ! ! // Check for negative power of 2 divisor, if so, negate it and set a flag ! // to indicate result needs to be negated. Note that negating the dividend ! // here does not work when it has the value MININT ! Node *dividend = in(1); ! bool negate_res = false; ! if (is_power_of_2_long(-i)) { ! i = -i; // Flip divisor ! negate_res = true; ! } ! ! // Check for power of 2 ! if (!is_power_of_2_long(i)) // Is divisor a power of 2? ! return NULL; // Not a power of 2 ! // Compute number of bits to shift ! int log_i = log2_long(i); ! // See if we can simply do a shift without rounding ! bool needs_rounding = true; ! const Type *dt = phase->type(dividend); ! const TypeLong *dtl = dt->isa_long(); ! ! if (dtl && dtl->_lo > 0) { ! // we don't need to round a positive dividend ! needs_rounding = false; ! } else if( dividend->Opcode() == Op_AndL ) { ! // An AND mask of sufficient size clears the low bits and ! // I can avoid rounding. ! const TypeLong *andconi = phase->type( dividend->in(2) )->isa_long(); ! if( andconi && ! andconi->is_con() && ! andconi->get_con() == -i ) { ! dividend = dividend->in(1); ! needs_rounding = false; ! } ! } ! ! if (!needs_rounding) { ! Node *result = new (phase->C, 3) RShiftLNode(dividend, phase->intcon(log_i)); ! if (negate_res) { ! result = phase->transform(result); ! result = new (phase->C, 3) SubLNode(phase->longcon(0), result); ! } ! return result; ! } ! ! // Divide-by-power-of-2 can be made into a shift, but you have to do ! // more math for the rounding. You need to add 0 for positive ! // numbers, and "i-1" for negative numbers. Example: i=4, so the ! // shift is by 2. You need to add 3 to negative dividends and 0 to ! // positive ones. So (-7+3)>>2 becomes -1, (-4+3)>>2 becomes -1, ! // (-2+3)>>2 becomes 0, etc. ! // Compute 0 or -1, based on sign bit ! Node *sign = phase->transform(new (phase->C, 3) RShiftLNode(dividend,phase->intcon(63))); ! // Mask sign bit to the low sign bits ! Node *round = phase->transform(new (phase->C, 3) AndLNode(sign,phase->longcon(i-1))); ! // Round up before shifting ! Node *sum = phase->transform(new (phase->C, 3) AddLNode(dividend,round)); ! // Shift for division ! Node *result = new (phase->C, 3) RShiftLNode(sum, phase->intcon(log_i)); ! if (negate_res) { ! result = phase->transform(result); ! result = new (phase->C, 3) SubLNode(phase->longcon(0), result); ! } ! return result; } //------------------------------Value------------------------------------------ // A DivLNode divides its inputs. The third input is a Control input, used to // prevent hoisting the divide above an unsafe test. --- 508,537 ---- //------------------------------Idealize--------------------------------------- // Dividing by a power of 2 is a shift. Node *DivLNode::Ideal( PhaseGVN *phase, bool can_reshape) { if (in(0) && remove_dead_region(phase, can_reshape)) return this; + // Don't bother trying to transform a dead node + if( in(0) && in(0)->is_top() ) return NULL; const Type *t = phase->type( in(2) ); if( t == TypeLong::ONE ) // Identity? return NULL; // Skip it ! const TypeLong *tl = t->isa_long(); ! if( !tl ) return NULL; ! if( !tl->is_con() ) return NULL; ! jlong l = tl->get_con(); // Get divisor ! if (l == 0) return NULL; // Dividing by zero constant does not idealize ! set_req(0,NULL); // Dividing by a not-zero constant; no faulting ! // Dividing by MININT does not optimize as a power-of-2 shift. ! if( l == min_jlong ) return NULL; ! return transform_long_divide( phase, in(1), l ); } //------------------------------Value------------------------------------------ // A DivLNode divides its inputs. The third input is a Control input, used to // prevent hoisting the divide above an unsafe test.
*** 422,432 **** (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) ) return bot; // x/x == 1, we ignore 0/0. // Note: if t1 and t2 are zero then result is NaN (JVMS page 213) ! // does not work for variables because of NaN's if( phase->eqv( in(1), in(2) ) && t1->base() == Type::FloatCon) if (!g_isnan(t1->getf()) && g_isfinite(t1->getf()) && t1->getf() != 0.0) // could be negative ZERO or NaN return TypeF::ONE; if( t2 == TypeF::ONE ) --- 615,625 ---- (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) ) return bot; // x/x == 1, we ignore 0/0. // Note: if t1 and t2 are zero then result is NaN (JVMS page 213) ! // Does not work for variables because of NaN's if( phase->eqv( in(1), in(2) ) && t1->base() == Type::FloatCon) if (!g_isnan(t1->getf()) && g_isfinite(t1->getf()) && t1->getf() != 0.0) // could be negative ZERO or NaN return TypeF::ONE; if( t2 == TypeF::ONE )
*** 458,467 **** --- 651,662 ---- //------------------------------Idealize--------------------------------------- Node *DivFNode::Ideal(PhaseGVN *phase, bool can_reshape) { if (in(0) && remove_dead_region(phase, can_reshape)) return this; + // Don't bother trying to transform a dead node + if( in(0) && in(0)->is_top() ) return NULL; const Type *t2 = phase->type( in(2) ); if( t2 == TypeF::ONE ) // Identity? return NULL; // Skip it
*** 492,502 **** } //============================================================================= //------------------------------Value------------------------------------------ // An DivDNode divides its inputs. The third input is a Control input, used to ! // prvent hoisting the divide above an unsafe test. const Type *DivDNode::Value( PhaseTransform *phase ) const { // Either input is TOP ==> the result is TOP const Type *t1 = phase->type( in(1) ); const Type *t2 = phase->type( in(2) ); if( t1 == Type::TOP ) return Type::TOP; --- 687,697 ---- } //============================================================================= //------------------------------Value------------------------------------------ // An DivDNode divides its inputs. The third input is a Control input, used to ! // prevent hoisting the divide above an unsafe test. const Type *DivDNode::Value( PhaseTransform *phase ) const { // Either input is TOP ==> the result is TOP const Type *t1 = phase->type( in(1) ); const Type *t2 = phase->type( in(2) ); if( t1 == Type::TOP ) return Type::TOP;
*** 516,530 **** --- 711,732 ---- return TypeD::ONE; if( t2 == TypeD::ONE ) return t1; + #if defined(IA32) + if (!phase->C->method()->is_strict()) + // Can't trust native compilers to properly fold strict double + // division with round-to-zero on this platform. + #endif + { // If divisor is a constant and not zero, divide them numbers if( t1->base() == Type::DoubleCon && t2->base() == Type::DoubleCon && t2->getd() != 0.0 ) // could be negative zero return TypeD::make( t1->getd()/t2->getd() ); + } // If the dividend is a constant zero // Note: if t1 and t2 are zero then result is NaN (JVMS page 213) // Test TypeF::ZERO is not sufficient as it could be negative zero if( t1 == TypeD::ZERO && !g_isnan(t2->getd()) && t2->getd() != 0.0 )
*** 543,552 **** --- 745,756 ---- } //------------------------------Idealize--------------------------------------- Node *DivDNode::Ideal(PhaseGVN *phase, bool can_reshape) { if (in(0) && remove_dead_region(phase, can_reshape)) return this; + // Don't bother trying to transform a dead node + if( in(0) && in(0)->is_top() ) return NULL; const Type *t2 = phase->type( in(2) ); if( t2 == TypeD::ONE ) // Identity? return NULL; // Skip it
*** 578,588 **** //============================================================================= //------------------------------Idealize--------------------------------------- Node *ModINode::Ideal(PhaseGVN *phase, bool can_reshape) { // Check for dead control input ! if( remove_dead_region(phase, can_reshape) ) return this; // Get the modulus const Type *t = phase->type( in(2) ); if( t == Type::TOP ) return NULL; const TypeInt *ti = t->is_int(); --- 782,794 ---- //============================================================================= //------------------------------Idealize--------------------------------------- Node *ModINode::Ideal(PhaseGVN *phase, bool can_reshape) { // Check for dead control input ! if( in(0) && remove_dead_region(phase, can_reshape) ) return this; ! // Don't bother trying to transform a dead node ! if( in(0) && in(0)->is_top() ) return NULL; // Get the modulus const Type *t = phase->type( in(2) ); if( t == Type::TOP ) return NULL; const TypeInt *ti = t->is_int();
*** 676,697 **** // Save in(1) so that it cannot be changed or deleted hook->init_req(0, in(1)); // Divide using the transform from DivI to MulL ! Node *divide = phase->transform( transform_int_divide_to_long_multiply( phase, in(1), pos_con ) ); // Re-multiply, using a shift if this is a power of two Node *mult = NULL; if( log2_con >= 0 ) mult = phase->transform( new (phase->C, 3) LShiftINode( divide, phase->intcon( log2_con ) ) ); else mult = phase->transform( new (phase->C, 3) MulINode( divide, phase->intcon( pos_con ) ) ); // Finally, subtract the multiplied divided value from the original ! Node *result = new (phase->C, 3) SubINode( in(1), mult ); // Now remove the bogus extra edges used to keep things alive if (can_reshape) { phase->is_IterGVN()->remove_dead_node(hook); } else { --- 882,906 ---- // Save in(1) so that it cannot be changed or deleted hook->init_req(0, in(1)); // Divide using the transform from DivI to MulL ! Node *result = transform_int_divide( phase, in(1), pos_con ); ! if (result != NULL) { ! Node *divide = phase->transform(result); // Re-multiply, using a shift if this is a power of two Node *mult = NULL; if( log2_con >= 0 ) mult = phase->transform( new (phase->C, 3) LShiftINode( divide, phase->intcon( log2_con ) ) ); else mult = phase->transform( new (phase->C, 3) MulINode( divide, phase->intcon( pos_con ) ) ); // Finally, subtract the multiplied divided value from the original ! result = new (phase->C, 3) SubINode( in(1), mult ); ! } // Now remove the bogus extra edges used to keep things alive if (can_reshape) { phase->is_IterGVN()->remove_dead_node(hook); } else {
*** 744,802 **** //============================================================================= //------------------------------Idealize--------------------------------------- Node *ModLNode::Ideal(PhaseGVN *phase, bool can_reshape) { // Check for dead control input ! if( remove_dead_region(phase, can_reshape) ) return this; // Get the modulus const Type *t = phase->type( in(2) ); if( t == Type::TOP ) return NULL; ! const TypeLong *ti = t->is_long(); // Check for useless control input // Check for excluding mod-zero case ! if( in(0) && (ti->_hi < 0 || ti->_lo > 0) ) { set_req(0, NULL); // Yank control input return this; } // See if we are MOD'ing by 2^k or 2^k-1. ! if( !ti->is_con() ) return NULL; ! jlong con = ti->get_con(); ! bool m1 = false; ! if( !is_power_of_2_long(con) ) { // Not 2^k ! if( !is_power_of_2_long(con+1) ) // Not 2^k-1? ! return NULL; // No interesting mod hacks ! m1 = true; // Found 2^k-1 ! con++; // Convert to 2^k form ! } ! uint k = log2_long(con); // Extract k // Expand mod ! if( !m1 ) { // Case 2^k ! } else { // Case 2^k-1 // Basic algorithm by David Detlefs. See fastmod_long.java for gory details. // Used to help a popular random number generator which does a long-mod // of 2^31-1 and shows up in SpecJBB and SciMark. 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*/}; int trip_count = 1; if( k < ARRAY_SIZE(unroll_factor)) trip_count = unroll_factor[k]; - if( trip_count > 4 ) return NULL; // Too much unrolling - if (ConditionalMoveLimit == 0) return NULL; // cmov is required Node *x = in(1); // Value being mod'd Node *divisor = in(2); // Also is mask ! Node *hook = new (phase->C, 1) Node(x); // Generate code to reduce X rapidly to nearly 2^k-1. for( int i = 0; i < trip_count; i++ ) { Node *xl = phase->transform( new (phase->C, 3) AndLNode(x,divisor) ); Node *xh = phase->transform( new (phase->C, 3) RShiftLNode(x,phase->intcon(k)) ); // Must be signed x = phase->transform( new (phase->C, 3) AddLNode(xh,xl) ); hook->set_req(0, x); // Add a use to x to prevent him from dying } // Generate sign-fixup code. Was original value positive? // long hack_res = (i >= 0) ? divisor : CONST64(1); Node *cmp1 = phase->transform( new (phase->C, 3) CmpLNode( in(1), phase->longcon(0) ) ); Node *bol1 = phase->transform( new (phase->C, 2) BoolNode( cmp1, BoolTest::ge ) ); Node *cmov1= phase->transform( new (phase->C, 4) CMoveLNode(bol1, phase->longcon(1), divisor, TypeLong::LONG) ); --- 953,1010 ---- //============================================================================= //------------------------------Idealize--------------------------------------- Node *ModLNode::Ideal(PhaseGVN *phase, bool can_reshape) { // Check for dead control input ! if( in(0) && remove_dead_region(phase, can_reshape) ) return this; ! // Don't bother trying to transform a dead node ! if( in(0) && in(0)->is_top() ) return NULL; // Get the modulus const Type *t = phase->type( in(2) ); if( t == Type::TOP ) return NULL; ! const TypeLong *tl = t->is_long(); // Check for useless control input // Check for excluding mod-zero case ! if( in(0) && (tl->_hi < 0 || tl->_lo > 0) ) { set_req(0, NULL); // Yank control input return this; } // See if we are MOD'ing by 2^k or 2^k-1. ! if( !tl->is_con() ) return NULL; ! jlong con = tl->get_con(); ! ! Node *hook = new (phase->C, 1) Node(1); // Expand mod ! if( con >= 0 && con < max_jlong && is_power_of_2_long(con+1) ) { ! uint k = exact_log2_long(con+1); // Extract k ! // Basic algorithm by David Detlefs. See fastmod_long.java for gory details. // Used to help a popular random number generator which does a long-mod // of 2^31-1 and shows up in SpecJBB and SciMark. 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*/}; int trip_count = 1; if( k < ARRAY_SIZE(unroll_factor)) trip_count = unroll_factor[k]; + // If the unroll factor is not too large, and if conditional moves are + // ok, then use this case + if( trip_count <= 5 && ConditionalMoveLimit != 0 ) { Node *x = in(1); // Value being mod'd Node *divisor = in(2); // Also is mask ! hook->init_req(0, x); // Add a use to x to prevent him from dying // Generate code to reduce X rapidly to nearly 2^k-1. for( int i = 0; i < trip_count; i++ ) { Node *xl = phase->transform( new (phase->C, 3) AndLNode(x,divisor) ); Node *xh = phase->transform( new (phase->C, 3) RShiftLNode(x,phase->intcon(k)) ); // Must be signed x = phase->transform( new (phase->C, 3) AddLNode(xh,xl) ); hook->set_req(0, x); // Add a use to x to prevent him from dying } + // Generate sign-fixup code. Was original value positive? // long hack_res = (i >= 0) ? divisor : CONST64(1); Node *cmp1 = phase->transform( new (phase->C, 3) CmpLNode( in(1), phase->longcon(0) ) ); Node *bol1 = phase->transform( new (phase->C, 2) BoolNode( cmp1, BoolTest::ge ) ); Node *cmov1= phase->transform( new (phase->C, 4) CMoveLNode(bol1, phase->longcon(1), divisor, TypeLong::LONG) );
*** 815,825 **** } else { hook->set_req(0, NULL); // Just yank bogus edge during Parse phase } return cmov2; } ! return NULL; } //------------------------------Value------------------------------------------ const Type *ModLNode::Value( PhaseTransform *phase ) const { // Either input is TOP ==> the result is TOP --- 1023,1089 ---- } else { hook->set_req(0, NULL); // Just yank bogus edge during Parse phase } return cmov2; } ! } ! ! // Fell thru, the unroll case is not appropriate. Transform the modulo ! // into a long multiply/int multiply/subtract case ! ! // Cannot handle mod 0, and min_jint isn't handled by the transform ! if( con == 0 || con == min_jlong ) return NULL; ! ! // Get the absolute value of the constant; at this point, we can use this ! jlong pos_con = (con >= 0) ? con : -con; ! ! // integer Mod 1 is always 0 ! if( pos_con == 1 ) return new (phase->C, 1) ConLNode(TypeLong::ZERO); ! ! int log2_con = -1; ! ! // If this is a power of two, they maybe we can mask it ! if( is_power_of_2_long(pos_con) ) { ! log2_con = log2_long(pos_con); ! ! const Type *dt = phase->type(in(1)); ! const TypeLong *dtl = dt->isa_long(); ! ! // See if this can be masked, if the dividend is non-negative ! if( dtl && dtl->_lo >= 0 ) ! return ( new (phase->C, 3) AndLNode( in(1), phase->longcon( pos_con-1 ) ) ); ! } ! ! // Save in(1) so that it cannot be changed or deleted ! hook->init_req(0, in(1)); ! ! // Divide using the transform from DivI to MulL ! Node *result = transform_long_divide( phase, in(1), pos_con ); ! if (result != NULL) { ! Node *divide = phase->transform(result); ! ! // Re-multiply, using a shift if this is a power of two ! Node *mult = NULL; ! ! if( log2_con >= 0 ) ! mult = phase->transform( new (phase->C, 3) LShiftLNode( divide, phase->intcon( log2_con ) ) ); ! else ! mult = phase->transform( new (phase->C, 3) MulLNode( divide, phase->longcon( pos_con ) ) ); ! ! // Finally, subtract the multiplied divided value from the original ! result = new (phase->C, 3) SubLNode( in(1), mult ); ! } ! ! // Now remove the bogus extra edges used to keep things alive ! if (can_reshape) { ! phase->is_IterGVN()->remove_dead_node(hook); ! } else { ! hook->set_req(0, NULL); // Just yank bogus edge during Parse phase ! } ! ! // return the value ! return result; } //------------------------------Value------------------------------------------ const Type *ModLNode::Value( PhaseTransform *phase ) const { // Either input is TOP ==> the result is TOP
*** 873,932 **** const Type *bot = bottom_type(); if( (t1 == bot) || (t2 == bot) || (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) ) return bot; ! // If either is a NaN, return an input NaN ! if( g_isnan(t1->getf()) ) return t1; ! if( g_isnan(t2->getf()) ) return t2; ! // It is not worth trying to constant fold this stuff! ! return Type::FLOAT; ! /* ! // If dividend is infinity or divisor is zero, or both, the result is NaN ! if( !g_isfinite(t1->getf()) || ((t2->getf() == 0.0) || (jint_cast(t2->getf()) == 0x80000000)) ) ! ! // X MOD infinity = X ! if( !g_isfinite(t2->getf()) && !g_isnan(t2->getf()) ) return t1; ! // 0 MOD finite = dividend (positive or negative zero) ! // Not valid for: NaN MOD any; any MOD nan; 0 MOD 0; or for 0 MOD NaN ! // NaNs are handled previously. ! if( !(t2->getf() == 0.0) && !((int)t2->getf() == 0x80000000)) { ! if (((t1->getf() == 0.0) || ((int)t1->getf() == 0x80000000)) && g_isfinite(t2->getf()) ) { ! return t1; ! } ! } ! // X MOD X is 0 ! // Does not work for variables because of NaN's ! if( phase->eqv( in(1), in(2) ) && t1->base() == Type::FloatCon) ! if (!g_isnan(t1->getf()) && (t1->getf() != 0.0) && ((int)t1->getf() != 0x80000000)) { ! if(t1->getf() < 0.0) { ! float result = jfloat_cast(0x80000000); ! return TypeF::make( result ); ! } ! else ! return TypeF::ZERO; ! } ! // If both numbers are not constants, we know nothing. ! if( (t1->base() != Type::FloatCon) || (t2->base() != Type::FloatCon) ) return Type::FLOAT; // We must be modulo'ing 2 float constants. // Make sure that the sign of the fmod is equal to the sign of the dividend ! float result = (float)fmod( t1->getf(), t2->getf() ); ! float dividend = t1->getf(); ! if( (dividend < 0.0) || ((int)dividend == 0x80000000) ) { ! if( result > 0.0 ) ! result = 0.0 - result; ! else if( result == 0.0 ) { ! result = jfloat_cast(0x80000000); } ! } ! return TypeF::make( result ); ! */ } //============================================================================= //------------------------------Value------------------------------------------ --- 1137,1172 ---- const Type *bot = bottom_type(); if( (t1 == bot) || (t2 == bot) || (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) ) return bot; ! // If either number is not a constant, we know nothing. ! if ((t1->base() != Type::FloatCon) || (t2->base() != Type::FloatCon)) { ! return Type::FLOAT; // note: x%x can be either NaN or 0 ! } ! float f1 = t1->getf(); ! float f2 = t2->getf(); ! jint x1 = jint_cast(f1); // note: *(int*)&f1, not just (int)f1 ! jint x2 = jint_cast(f2); ! // If either is a NaN, return an input NaN ! if (g_isnan(f1)) return t1; ! if (g_isnan(f2)) return t2; ! // If an operand is infinity or the divisor is +/- zero, punt. ! if (!g_isfinite(f1) || !g_isfinite(f2) || x2 == 0 || x2 == min_jint) return Type::FLOAT; // We must be modulo'ing 2 float constants. // Make sure that the sign of the fmod is equal to the sign of the dividend ! jint xr = jint_cast(fmod(f1, f2)); ! if ((x1 ^ xr) < 0) { ! xr ^= min_jint; } ! ! return TypeF::make(jfloat_cast(xr)); } //============================================================================= //------------------------------Value------------------------------------------
*** 941,977 **** const Type *bot = bottom_type(); if( (t1 == bot) || (t2 == bot) || (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) ) return bot; ! // If either is a NaN, return an input NaN ! if( g_isnan(t1->getd()) ) return t1; ! if( g_isnan(t2->getd()) ) return t2; ! // X MOD infinity = X ! if( !g_isfinite(t2->getd())) return t1; ! // 0 MOD finite = dividend (positive or negative zero) ! // Not valid for: NaN MOD any; any MOD nan; 0 MOD 0; or for 0 MOD NaN ! // NaNs are handled previously. ! if( !(t2->getd() == 0.0) ) { ! if( t1->getd() == 0.0 && g_isfinite(t2->getd()) ) { ! return t1; ! } } ! // X MOD X is 0 ! // does not work for variables because of NaN's ! if( phase->eqv( in(1), in(2) ) && t1->base() == Type::DoubleCon ) ! if (!g_isnan(t1->getd()) && t1->getd() != 0.0) ! return TypeD::ZERO; ! // If both numbers are not constants, we know nothing. ! if( (t1->base() != Type::DoubleCon) || (t2->base() != Type::DoubleCon) ) return Type::DOUBLE; // We must be modulo'ing 2 double constants. ! return TypeD::make( fmod( t1->getd(), t2->getd() ) ); } //============================================================================= DivModNode::DivModNode( Node *c, Node *dividend, Node *divisor ) : MultiNode(3) { --- 1181,1216 ---- const Type *bot = bottom_type(); if( (t1 == bot) || (t2 == bot) || (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) ) return bot; ! // If either number is not a constant, we know nothing. ! if ((t1->base() != Type::DoubleCon) || (t2->base() != Type::DoubleCon)) { ! return Type::DOUBLE; // note: x%x can be either NaN or 0 } ! double f1 = t1->getd(); ! double f2 = t2->getd(); ! jlong x1 = jlong_cast(f1); // note: *(long*)&f1, not just (long)f1 ! jlong x2 = jlong_cast(f2); + // If either is a NaN, return an input NaN + if (g_isnan(f1)) return t1; + if (g_isnan(f2)) return t2; ! // If an operand is infinity or the divisor is +/- zero, punt. ! if (!g_isfinite(f1) || !g_isfinite(f2) || x2 == 0 || x2 == min_jlong) return Type::DOUBLE; // We must be modulo'ing 2 double constants. ! // Make sure that the sign of the fmod is equal to the sign of the dividend ! jlong xr = jlong_cast(fmod(f1, f2)); ! if ((x1 ^ xr) < 0) { ! xr ^= min_jlong; ! } ! ! return TypeD::make(jdouble_cast(xr)); } //============================================================================= DivModNode::DivModNode( Node *c, Node *dividend, Node *divisor ) : MultiNode(3) {