/* Compiler implementation of the D programming language * Copyright (C) 1999-2019 by The D Language Foundation, All Rights Reserved * written by KennyTM * http://www.digitalmars.com * Distributed under the Boost Software License, Version 1.0. * http://www.boost.org/LICENSE_1_0.txt * https://github.com/D-Programming-Language/dmd/blob/master/src/intrange.c */ #include "root/dsystem.h" #include "intrange.h" #include "mars.h" #include "mtype.h" #include "expression.h" // Copy the sign to the value *x*. Equivalent to `sign ? -x : x`. static uinteger_t copySign(uinteger_t x, bool sign) { // return sign ? -x : x; return (x - (uinteger_t)sign) ^ -(uinteger_t)sign; } #ifndef UINT64_MAX #define UINT64_MAX 0xFFFFFFFFFFFFFFFFULL #endif //==================== SignExtendedNumber ====================================== SignExtendedNumber SignExtendedNumber::fromInteger(uinteger_t value_) { return SignExtendedNumber(value_, value_ >> 63); } bool SignExtendedNumber::operator==(const SignExtendedNumber& a) const { return value == a.value && negative == a.negative; } bool SignExtendedNumber::operator<(const SignExtendedNumber& a) const { return (negative && !a.negative) || (negative == a.negative && value < a.value); } SignExtendedNumber SignExtendedNumber::extreme(bool minimum) { return SignExtendedNumber(minimum-1, minimum); } SignExtendedNumber SignExtendedNumber::max() { return SignExtendedNumber(UINT64_MAX, false); } SignExtendedNumber& SignExtendedNumber::operator++() { if (value != UINT64_MAX) ++value; else if (negative) { value = 0; negative = false; } return *this; } SignExtendedNumber SignExtendedNumber::operator~() const { if (~value == 0) return SignExtendedNumber(~value); else return SignExtendedNumber(~value, !negative); } SignExtendedNumber SignExtendedNumber::operator-() const { if (value == 0) return SignExtendedNumber(-negative); else return SignExtendedNumber(-value, !negative); } SignExtendedNumber SignExtendedNumber::operator&(const SignExtendedNumber& rhs) const { return SignExtendedNumber(value & rhs.value); } SignExtendedNumber SignExtendedNumber::operator|(const SignExtendedNumber& rhs) const { return SignExtendedNumber(value | rhs.value); } SignExtendedNumber SignExtendedNumber::operator^(const SignExtendedNumber& rhs) const { return SignExtendedNumber(value ^ rhs.value); } SignExtendedNumber SignExtendedNumber::operator+(const SignExtendedNumber& rhs) const { uinteger_t sum = value + rhs.value; bool carry = sum < value && sum < rhs.value; if (negative != rhs.negative) return SignExtendedNumber(sum, !carry); else if (negative) return SignExtendedNumber(carry ? sum : 0, true); else return SignExtendedNumber(carry ? UINT64_MAX : sum, false); } SignExtendedNumber SignExtendedNumber::operator-(const SignExtendedNumber& rhs) const { if (rhs.isMinimum()) return negative ? SignExtendedNumber(value, false) : max(); else return *this + (-rhs); } SignExtendedNumber SignExtendedNumber::operator*(const SignExtendedNumber& rhs) const { // perform *saturated* multiplication, otherwise we may get bogus ranges // like 0x10 * 0x10 == 0x100 == 0. /* Special handling for zeros: INT65_MIN * 0 = 0 INT65_MIN * + = INT65_MIN INT65_MIN * - = INT65_MAX 0 * anything = 0 */ if (value == 0) { if (!negative) return *this; else if (rhs.negative) return max(); else return rhs.value == 0 ? rhs : *this; } else if (rhs.value == 0) return rhs * *this; // don't duplicate the symmetric case. SignExtendedNumber rv; // these are != 0 now surely. uinteger_t tAbs = copySign(value, negative); uinteger_t aAbs = copySign(rhs.value, rhs.negative); rv.negative = negative != rhs.negative; if (UINT64_MAX / tAbs < aAbs) rv.value = rv.negative-1; else rv.value = copySign(tAbs * aAbs, rv.negative); return rv; } SignExtendedNumber SignExtendedNumber::operator/(const SignExtendedNumber& rhs) const { /* special handling for zeros: INT65_MIN / INT65_MIN = 1 anything / INT65_MIN = 0 + / 0 = INT65_MAX (eh?) - / 0 = INT65_MIN (eh?) */ if (rhs.value == 0) { if (rhs.negative) return SignExtendedNumber(value == 0 && negative); else return extreme(negative); } uinteger_t aAbs = copySign(rhs.value, rhs.negative); uinteger_t rvVal; if (!isMinimum()) rvVal = copySign(value, negative) / aAbs; // Special handling for INT65_MIN // if the denominator is not a power of 2, it is same as UINT64_MAX / x. else if (aAbs & (aAbs-1)) rvVal = UINT64_MAX / aAbs; // otherwise, it's the same as reversing the bits of x. else { if (aAbs == 1) return extreme(!rhs.negative); rvVal = 1ULL << 63; aAbs >>= 1; if (aAbs & 0xAAAAAAAAAAAAAAAAULL) rvVal >>= 1; if (aAbs & 0xCCCCCCCCCCCCCCCCULL) rvVal >>= 2; if (aAbs & 0xF0F0F0F0F0F0F0F0ULL) rvVal >>= 4; if (aAbs & 0xFF00FF00FF00FF00ULL) rvVal >>= 8; if (aAbs & 0xFFFF0000FFFF0000ULL) rvVal >>= 16; if (aAbs & 0xFFFFFFFF00000000ULL) rvVal >>= 32; } bool rvNeg = negative != rhs.negative; rvVal = copySign(rvVal, rvNeg); return SignExtendedNumber(rvVal, rvVal != 0 && rvNeg); } SignExtendedNumber SignExtendedNumber::operator%(const SignExtendedNumber& rhs) const { if (rhs.value == 0) return !rhs.negative ? rhs : isMinimum() ? SignExtendedNumber(0) : *this; uinteger_t aAbs = copySign(rhs.value, rhs.negative); uinteger_t rvVal; // a % b == sgn(a) * abs(a) % abs(b). if (!isMinimum()) rvVal = copySign(value, negative) % aAbs; // Special handling for INT65_MIN // if the denominator is not a power of 2, it is same as UINT64_MAX%x + 1. else if (aAbs & (aAbs - 1)) rvVal = UINT64_MAX % aAbs + 1; // otherwise, the modulus is trivially zero. else rvVal = 0; rvVal = copySign(rvVal, negative); return SignExtendedNumber(rvVal, rvVal != 0 && negative); } SignExtendedNumber SignExtendedNumber::operator<<(const SignExtendedNumber& rhs) const { // assume left-shift the shift-amount is always unsigned. Thus negative // shifts will give huge result. if (value == 0) return *this; else if (rhs.negative) return extreme(negative); uinteger_t v = copySign(value, negative); // compute base-2 log of 'v' to determine the maximum allowed bits to shift. // Ref: http://graphics.stanford.edu/~seander/bithacks.html#IntegerLog // Why is this a size_t? Looks like a bug. size_t r, s; r = (v > 0xFFFFFFFFULL) << 5; v >>= r; s = (v > 0xFFFFULL ) << 4; v >>= s; r |= s; s = (v > 0xFFULL ) << 3; v >>= s; r |= s; s = (v > 0xFULL ) << 2; v >>= s; r |= s; s = (v > 0x3ULL ) << 1; v >>= s; r |= s; r |= (v >> 1); uinteger_t allowableShift = 63 - r; if (rhs.value > allowableShift) return extreme(negative); else return SignExtendedNumber(value << rhs.value, negative); } SignExtendedNumber SignExtendedNumber::operator>>(const SignExtendedNumber& rhs) const { if (rhs.negative || rhs.value > 63) return negative ? SignExtendedNumber(-1, true) : SignExtendedNumber(0); else if (isMinimum()) return rhs.value == 0 ? *this : SignExtendedNumber(-1ULL << (64 - rhs.value), true); uinteger_t x = value ^ -negative; x >>= rhs.value; return SignExtendedNumber(x ^ -negative, negative); } //==================== IntRange ================================================ IntRange IntRange::widest() { return IntRange(SignExtendedNumber::min(), SignExtendedNumber::max()); } IntRange IntRange::fromType(Type *type) { return fromType(type, type->isunsigned()); } IntRange IntRange::fromType(Type *type, bool isUnsigned) { if (!type->isintegral() || type->toBasetype()->ty == Tvector) return widest(); uinteger_t mask = type->sizemask(); SignExtendedNumber lower(0), upper(mask); if (type->toBasetype()->ty == Tdchar) upper.value = 0x10FFFFULL; else if (!isUnsigned) { lower.value = ~(mask >> 1); lower.negative = true; upper.value = (mask >> 1); } return IntRange(lower, upper); } IntRange IntRange::fromNumbers2(const SignExtendedNumber numbers[2]) { if (numbers[0] < numbers[1]) return IntRange(numbers[0], numbers[1]); else return IntRange(numbers[1], numbers[0]); } IntRange IntRange::fromNumbers4(const SignExtendedNumber numbers[4]) { IntRange ab = fromNumbers2(numbers); IntRange cd = fromNumbers2(numbers + 2); if (cd.imin < ab.imin) ab.imin = cd.imin; if (cd.imax > ab.imax) ab.imax = cd.imax; return ab; } bool IntRange::contains(const IntRange& a) const { return imin <= a.imin && imax >= a.imax; } bool IntRange::containsZero() const { return (imin.negative && !imax.negative) || (!imin.negative && imin.value == 0); } IntRange& IntRange::castUnsigned(uinteger_t mask) { // .... 0x1eff ] [0x1f00 .. 0x1fff] [0 .. 0xff] [0x100 .. 0x1ff] [0x200 .... // // regular unsigned type. We just need to see if ir steps across the // boundary of validRange. If yes, ir will represent the whole validRange, // otherwise, we just take the modulus. // e.g. [0x105, 0x107] & 0xff == [5, 7] // [0x105, 0x207] & 0xff == [0, 0xff] uinteger_t minChunk = imin.value & ~mask; uinteger_t maxChunk = imax.value & ~mask; if (minChunk == maxChunk && imin.negative == imax.negative) { imin.value &= mask; imax.value &= mask; } else { imin.value = 0; imax.value = mask; } imin.negative = imax.negative = false; return *this; } IntRange& IntRange::castSigned(uinteger_t mask) { // .... 0x1e7f ] [0x1e80 .. 0x1f7f] [0x1f80 .. 0x7f] [0x80 .. 0x17f] [0x180 .... // // regular signed type. We use a technique similar to the unsigned version, // but the chunk has to be offset by 1/2 of the range. uinteger_t halfChunkMask = mask >> 1; uinteger_t minHalfChunk = imin.value & ~halfChunkMask; uinteger_t maxHalfChunk = imax.value & ~halfChunkMask; int minHalfChunkNegativity = imin.negative; // 1 = neg, 0 = nonneg, -1 = chunk containing ::max int maxHalfChunkNegativity = imax.negative; if (minHalfChunk & mask) { minHalfChunk += halfChunkMask+1; if (minHalfChunk == 0) -- minHalfChunkNegativity; } if (maxHalfChunk & mask) { maxHalfChunk += halfChunkMask+1; if (maxHalfChunk == 0) -- maxHalfChunkNegativity; } if (minHalfChunk == maxHalfChunk && minHalfChunkNegativity == maxHalfChunkNegativity) { imin.value &= mask; imax.value &= mask; // sign extend if necessary. imin.negative = imin.value & ~halfChunkMask; imax.negative = imax.value & ~halfChunkMask; halfChunkMask += 1; imin.value = (imin.value ^ halfChunkMask) - halfChunkMask; imax.value = (imax.value ^ halfChunkMask) - halfChunkMask; } else { imin = SignExtendedNumber(~halfChunkMask, true); imax = SignExtendedNumber(halfChunkMask, false); } return *this; } IntRange& IntRange::castDchar() { // special case for dchar. Casting to dchar means "I'll ignore all // invalid characters." castUnsigned(0xFFFFFFFFULL); if (imin.value > 0x10FFFFULL) // ?? imin.value = 0x10FFFFULL; // ?? if (imax.value > 0x10FFFFULL) imax.value = 0x10FFFFULL; return *this; } IntRange& IntRange::cast(Type *type) { if (!type->isintegral() || type->toBasetype()->ty == Tvector) return *this; else if (!type->isunsigned()) return castSigned(type->sizemask()); else if (type->toBasetype()->ty == Tdchar) return castDchar(); else return castUnsigned(type->sizemask()); } IntRange& IntRange::castUnsigned(Type *type) { if (!type->isintegral() || type->toBasetype()->ty == Tvector) return castUnsigned(UINT64_MAX); else if (type->toBasetype()->ty == Tdchar) return castDchar(); else return castUnsigned(type->sizemask()); } IntRange IntRange::absNeg() const { if (imax.negative) return *this; else if (!imin.negative) return IntRange(-imax, -imin); else { SignExtendedNumber imaxAbsNeg = -imax; return IntRange(imaxAbsNeg < imin ? imaxAbsNeg : imin, SignExtendedNumber(0)); } } IntRange IntRange::unionWith(const IntRange& other) const { return IntRange(imin < other.imin ? imin : other.imin, imax > other.imax ? imax : other.imax); } void IntRange::unionOrAssign(const IntRange& other, bool& union_) { if (!union_ || imin > other.imin) imin = other.imin; if (!union_ || imax < other.imax) imax = other.imax; union_ = true; } void IntRange::splitBySign(IntRange& negRange, bool& hasNegRange, IntRange& nonNegRange, bool& hasNonNegRange) const { hasNegRange = imin.negative; if (hasNegRange) { negRange.imin = imin; negRange.imax = imax.negative ? imax : SignExtendedNumber(-1, true); } hasNonNegRange = !imax.negative; if (hasNonNegRange) { nonNegRange.imin = imin.negative ? SignExtendedNumber(0) : imin; nonNegRange.imax = imax; } } IntRange IntRange::operator~() const { return IntRange(~imax, ~imin); } IntRange IntRange::operator-() const { return IntRange(-imax, -imin); } IntRange IntRange::operator&(const IntRange& rhs) const { // unsigned or identical sign bits if ((imin.negative ^ imax.negative) != 1 && (rhs.imin.negative ^ rhs.imax.negative) != 1) { return IntRange(minAnd(*this, rhs), maxAnd(*this, rhs)); } IntRange l = IntRange(*this); IntRange r = IntRange(rhs); // both intervals span [-1,0] if ((l.imin.negative ^ l.imax.negative) == 1 && (r.imin.negative ^ r.imax.negative) == 1) { // cannot be larger than either l.max or r.max, set the other one to -1 SignExtendedNumber max = l.imax.value > r.imax.value ? l.imax : r.imax; // only negative numbers for minimum l.imax.value = -1; l.imax.negative = true; r.imax.value = -1; r.imax.negative = true; return IntRange(minAnd(l, r), max); } else { // only one interval spans [-1,0] if ((l.imin.negative ^ l.imax.negative) == 1) { swap(l, r); // r spans [-1,0] } SignExtendedNumber minAndNeg = minAnd(l, IntRange(r.imin, SignExtendedNumber(-1))); SignExtendedNumber minAndPos = minAnd(l, IntRange(SignExtendedNumber(0), r.imax)); SignExtendedNumber maxAndNeg = maxAnd(l, IntRange(r.imin, SignExtendedNumber(-1))); SignExtendedNumber maxAndPos = maxAnd(l, IntRange(SignExtendedNumber(0), r.imax)); SignExtendedNumber min = minAndNeg < minAndPos ? minAndNeg : minAndPos; SignExtendedNumber max = maxAndNeg > maxAndPos ? maxAndNeg : maxAndPos; return IntRange(min, max); } } IntRange IntRange::operator|(const IntRange& rhs) const { // unsigned or identical sign bits: if ((imin.negative ^ imax.negative) == 0 && (rhs.imin.negative ^ rhs.imax.negative) == 0) { return IntRange(minOr(*this, rhs), maxOr(*this, rhs)); } IntRange l = IntRange(*this); IntRange r = IntRange(rhs); // both intervals span [-1,0] if ((l.imin.negative ^ l.imax.negative) == 1 && (r.imin.negative ^ r.imax.negative) == 1) { // cannot be smaller than either l.min or r.min, set the other one to 0 SignExtendedNumber min = l.imin.value < r.imin.value ? l.imin : r.imin; // only negative numbers for minimum l.imin.value = 0; l.imin.negative = false; r.imin.value = 0; r.imin.negative = false; return IntRange(min, maxOr(l, r)); } else { // only one interval spans [-1,0] if ((imin.negative ^ imax.negative) == 1) { swap(l, r); // r spans [-1,0] } SignExtendedNumber minOrNeg = minOr(l, IntRange(r.imin, SignExtendedNumber(-1))); SignExtendedNumber minOrPos = minOr(l, IntRange(SignExtendedNumber(0), r.imax)); SignExtendedNumber maxOrNeg = maxOr(l, IntRange(r.imin, SignExtendedNumber(-1))); SignExtendedNumber maxOrPos = maxOr(l, IntRange(SignExtendedNumber(0), r.imax)); SignExtendedNumber min = minOrNeg < minOrPos ? minOrNeg : minOrPos; SignExtendedNumber max = maxOrNeg > maxOrPos ? maxOrNeg : maxOrPos; return IntRange(min, max); } } IntRange IntRange::operator^(const IntRange& rhs) const { return (*this & (~rhs)) | (~(*this) & rhs); } IntRange IntRange::operator+(const IntRange& rhs) const { return IntRange(imin + rhs.imin, imax + rhs.imax); } IntRange IntRange::operator-(const IntRange& rhs) const { return IntRange(imin - rhs.imax, imax - rhs.imin); } IntRange IntRange::operator*(const IntRange& rhs) const { // [a,b] * [c,d] = [min (ac, ad, bc, bd), max (ac, ad, bc, bd)] SignExtendedNumber bdy[4]; bdy[0] = imin * rhs.imin; bdy[1] = imin * rhs.imax; bdy[2] = imax * rhs.imin; bdy[3] = imax * rhs.imax; return IntRange::fromNumbers4(bdy); } IntRange IntRange::operator/(const IntRange& rhs) const { // Handle divide by 0 if (rhs.imax.value == 0 && rhs.imin.value == 0) return widest(); IntRange r = IntRange(rhs); // Don't treat the whole range as divide by 0 if only one end of a range is 0. // Issue 15289 if (r.imax.value == 0) { r.imax.value--; } else if (r.imin.value == 0) { r.imin.value++; } if (!imin.negative && !imax.negative && !r.imin.negative && !r.imax.negative) { return IntRange(imin / r.imax, imax / r.imin); } else { // [a,b] / [c,d] = [min (a/c, a/d, b/c, b/d), max (a/c, a/d, b/c, b/d)] SignExtendedNumber bdy[4]; bdy[0] = imin / r.imin; bdy[1] = imin / r.imax; bdy[2] = imax / r.imin; bdy[3] = imax / r.imax; return IntRange::fromNumbers4(bdy); } } IntRange IntRange::operator%(const IntRange& rhs) const { IntRange irNum = *this; IntRange irDen = rhs.absNeg(); /* due to the rules of D (C)'s % operator, we need to consider the cases separately in different range of signs. case 1. [500, 1700] % [7, 23] (numerator is always positive) = [0, 22] case 2. [-500, 1700] % [7, 23] (numerator can be negative) = [-22, 22] case 3. [-1700, -500] % [7, 23] (numerator is always negative) = [-22, 0] the number 22 is the maximum absolute value in the denomator's range. We don't care about divide by zero. */ irDen.imin = irDen.imin + SignExtendedNumber(1); irDen.imax = -irDen.imin; if (!irNum.imin.negative) { irNum.imin.value = 0; } else if (irNum.imin < irDen.imin) { irNum.imin = irDen.imin; } if (irNum.imax.negative) { irNum.imax.negative = false; irNum.imax.value = 0; } else if (irNum.imax > irDen.imax) { irNum.imax = irDen.imax; } return irNum; } IntRange IntRange::operator<<(const IntRange& rhs) const { IntRange r = IntRange(rhs); if (r.imin.negative) { r = IntRange(SignExtendedNumber(0), SignExtendedNumber(64)); } SignExtendedNumber lower = imin << (imin.negative ? r.imax : r.imin); SignExtendedNumber upper = imax << (imax.negative ? r.imin : r.imax); return IntRange(lower, upper); } IntRange IntRange::operator>>(const IntRange& rhs) const { IntRange r = IntRange(rhs); if (r.imin.negative) { r = IntRange(SignExtendedNumber(0), SignExtendedNumber(64)); } SignExtendedNumber lower = imin >> (imin.negative ? r.imin : r.imax); SignExtendedNumber upper = imax >> (imax.negative ? r.imax : r.imin); return IntRange(lower, upper); } SignExtendedNumber IntRange::maxOr(const IntRange& lhs, const IntRange& rhs) { uinteger_t x = 0; bool sign = false; uinteger_t xorvalue = lhs.imax.value ^ rhs.imax.value; uinteger_t andvalue = lhs.imax.value & rhs.imax.value; IntRange lhsc = IntRange(lhs); IntRange rhsc = IntRange(rhs); // Sign bit not part of the .value so we need an extra iteration if (lhsc.imax.negative ^ rhsc.imax.negative) { sign = true; if (lhsc.imax.negative) { if (!lhsc.imin.negative) { lhsc.imin.value = 0; } if (!rhsc.imin.negative) { rhsc.imin.value = 0; } } } else if (lhsc.imin.negative & rhsc.imin.negative) { sign = true; } else if (lhsc.imax.negative & rhsc.imax.negative) { return SignExtendedNumber(-1, false); } for (uinteger_t d = 1ULL << (8 * sizeof(uinteger_t) - 1); d; d >>= 1) { if (xorvalue & d) { x |= d; if (lhsc.imax.value & d) { if (~lhsc.imin.value & d) { lhsc.imin.value = 0; } } else { if (~rhsc.imin.value & d) { rhsc.imin.value = 0; } } } else if (lhsc.imin.value & rhsc.imin.value & d) { x |= d; } else if (andvalue & d) { x |= (d << 1) - 1; break; } } return SignExtendedNumber(x, sign); } SignExtendedNumber IntRange::minOr(const IntRange& lhs, const IntRange& rhs) { return ~maxAnd(~lhs, ~rhs); } SignExtendedNumber IntRange::maxAnd(const IntRange& lhs, const IntRange& rhs) { uinteger_t x = 0; bool sign = false; IntRange lhsc = IntRange(lhs); IntRange rhsc = IntRange(rhs); if (lhsc.imax.negative & rhsc.imax.negative) { sign = true; } for (uinteger_t d = 1ULL << (8 * sizeof(uinteger_t) - 1); d; d >>= 1) { if (lhsc.imax.value & rhsc.imax.value & d) { x |= d; if (~lhsc.imin.value & d) { lhsc.imin.value = 0; } if (~rhsc.imin.value & d) { rhsc.imin.value = 0; } } else if (~lhsc.imin.value & d && lhsc.imax.value & d) { lhsc.imax.value |= d - 1; } else if (~rhsc.imin.value & d && rhsc.imax.value & d) { rhsc.imax.value |= d - 1; } } return SignExtendedNumber(x, sign); } SignExtendedNumber IntRange::minAnd(const IntRange& lhs, const IntRange& rhs) { return ~maxOr(~lhs, ~rhs); } void IntRange::swap(IntRange& a, IntRange& b) { IntRange aux = a; a = b; b = aux; } const IntRange& IntRange::dump(const char* funcName, Expression *e) const { printf("[(%c)%#018llx, (%c)%#018llx] @ %s ::: %s\n", imin.negative?'-':'+', (unsigned long long)imin.value, imax.negative?'-':'+', (unsigned long long)imax.value, funcName, e->toChars()); return *this; }