#include #include #include #include #include #include #include extern "C" { #include } #include "layout/string_layout.h" namespace Poincare { int Decimal::exponent(const char * integralPart, int integralPartLength, const char * fractionalPart, int fractionalPartLength, const char * exponent, int exponentLength, bool exponentNegative) { int base = 10; int exp = 0; for (int i = 0; i < exponentLength; i++) { exp *= base; exp += *exponent-'0'; exponent++; } if (exponentNegative) { exp = -exp; } const char * integralPartEnd = integralPart + integralPartLength; if (integralPart != nullptr) { while (*integralPart == '0' && integralPart < integralPartEnd) { integralPart++; } } exp += integralPartEnd-integralPart-1; if (integralPart == integralPartEnd) { const char * fractionalPartEnd = fractionalPart + fractionalPartLength; if (fractionalPart != nullptr) { while (*fractionalPart == '0' && fractionalPart < fractionalPartEnd) { fractionalPart++; exp--; } } if (fractionalPart == fractionalPartEnd) { exp += fractionalPartLength+1; } } return exp; } void removeZeroAtTheEnd(Integer & i) { if (i.isZero()) { return; } Integer base = Integer(10); IntegerDivision d = Integer::Division(i, base); while (d.remainder.isZero()) { i = d.quotient; d = Integer::Division(i, base); } } Integer Decimal::mantissa(const char * integralPart, int integralPartLength, const char * fractionalPart, int fractionalPartLength, bool negative) { Integer zero = Integer(0); Integer base = Integer(10); Integer numerator = Integer(integralPart, negative); for (int i = 0; i < fractionalPartLength; i++) { numerator = Integer::Multiplication(numerator, base); numerator = Integer::Addition(numerator, Integer(*fractionalPart-'0')); fractionalPart++; } removeZeroAtTheEnd(numerator); return numerator; } Decimal::Decimal(Integer mantissa, int exponent) : m_mantissa(mantissa), m_exponent(exponent) { } Decimal::Decimal(double f) { double logBase10 = f != 0 ? std::log10(std::fabs(f)) : 0; int exponentInBase10 = std::floor(logBase10); /* Correct the exponent in base 10: sometines the exact log10 of f is 6.999999 * but is stored as 7 in hardware. We catch these cases here. */ if (f != 0 && logBase10 == (int)logBase10 && std::fabs(f) < std::pow(10, logBase10)) { exponentInBase10--; } double m = f*std::pow(10, (double)-exponentInBase10); // TODO: hangle exponentInBase10 is too big! mantissa is nan m = m * std::pow(10, (double)(k_doublePrecision-1)); int64_t integerMantissa = std::round(m); /* If m > 999999999999999.5, the mantissa stored will be 1 (as we keep only * 15 significative numbers from double. In that case, the exponent must be * increment as well. */ if (m >= k_biggestMantissaFromDouble+0.5) { exponentInBase10++; } m_mantissa = Integer(integerMantissa); removeZeroAtTheEnd(m_mantissa); m_exponent = exponentInBase10; } Expression::Type Decimal::type() const { return Type::Decimal; } Expression * Decimal::clone() const { return new Decimal(m_mantissa, m_exponent); } template Expression * Decimal::templatedApproximate(Context& context, Expression::AngleUnit angleUnit) const { T m = m_mantissa.approximate(); int numberOfDigits = numberOfDigitsInMantissaWithoutSign(); return new Complex(Complex::Float(m*std::pow((T)10.0, (T)(m_exponent-numberOfDigits+1)))); } int Decimal::writeTextInBuffer(char * buffer, int bufferSize, int numberOfSignificantDigits) const { if (bufferSize == 0) { return -1; } buffer[bufferSize-1] = 0; int currentChar = 0; if (currentChar >= bufferSize-1) { return bufferSize-1; } if (m_mantissa.isZero()) { buffer[currentChar++] = '0'; buffer[currentChar] = 0; return currentChar; } char tempBuffer[200]; int mantissaLength = m_mantissa.writeTextInBuffer(tempBuffer, 200); if (strcmp(tempBuffer, "undef") == 0) { strlcpy(buffer, tempBuffer, bufferSize); return mantissaLength; } int nbOfDigitsInMantissaWithoutSign = numberOfDigitsInMantissaWithoutSign(); int numberOfRequiredDigits = nbOfDigitsInMantissaWithoutSign > m_exponent ? nbOfDigitsInMantissaWithoutSign : m_exponent; numberOfRequiredDigits = m_exponent < 0 ? 1+nbOfDigitsInMantissaWithoutSign-m_exponent : numberOfRequiredDigits; /* Case 0: the number would be too long if we print it as a natural decimal */ if (numberOfRequiredDigits > k_maxLength) { if (nbOfDigitsInMantissaWithoutSign == 1) { currentChar += strlcpy(buffer, tempBuffer, bufferSize); } else { currentChar++; if (currentChar >= bufferSize-1) { return bufferSize-1; } currentChar += strlcpy(buffer+currentChar, tempBuffer, bufferSize-currentChar); int decimalMarkerPosition = 1; if (buffer[1] == '-') { decimalMarkerPosition++; buffer[0] = buffer[1]; } buffer[decimalMarkerPosition-1] = buffer[decimalMarkerPosition]; buffer[decimalMarkerPosition] = '.'; } if (m_exponent == 0) { return currentChar; } if (currentChar >= bufferSize-1) { return bufferSize-1; } buffer[currentChar++] = Ion::Charset::Exponent; currentChar += Integer(m_exponent).writeTextInBuffer(buffer+currentChar, bufferSize-currentChar); return currentChar; } /* Case 2: Print a natural decimal number */ int deltaCharMantissa = m_exponent < 0 ? -m_exponent+1 : 0; strlcpy(buffer+deltaCharMantissa, tempBuffer, bufferSize-deltaCharMantissa); if (m_mantissa.isNegative()) { buffer[currentChar++] = '-'; } if (m_exponent < 0) { for (int i = 0; i <= -m_exponent; i++) { if (currentChar >= bufferSize-1) { return bufferSize-1; } if (i == 1) { buffer[currentChar++] = '.'; continue; } buffer[currentChar++] = '0'; } } /* If mantissa is negative, m_mantissa.writeTextInBuffer is going to add an * unwanted '-' in place of the temp char. We store it to replace it back * after calling m_mantissa.writeTextInBuffer. */ char tempChar = 0; int tempCharPosition = 0; if (m_mantissa.isNegative()) { currentChar--; tempChar = buffer[currentChar]; tempCharPosition = currentChar; } currentChar += mantissaLength; if (m_mantissa.isNegative()) { // replace the temp char back buffer[tempCharPosition] = tempChar; } int currentExponent = m_mantissa.isNegative() ? currentChar-2 : currentChar-1; if (m_exponent >= 0 && m_exponent < currentExponent) { if (currentChar+1 >= bufferSize-1) { return bufferSize-1; } int decimalMarkerPosition = m_mantissa.isNegative() ? m_exponent +1 : m_exponent; for (int i = currentChar-1; i > decimalMarkerPosition; i--) { buffer[i+1] = buffer[i]; } buffer[decimalMarkerPosition+1] = '.'; currentChar++; } if (m_exponent >= 0 && m_exponent > currentExponent) { int decimalMarkerPosition = m_mantissa.isNegative() ? m_exponent+1 : m_exponent; for (int i = currentChar-1; i < decimalMarkerPosition; i++) { if (currentChar+1 >= bufferSize-1) { return bufferSize-1; } buffer[currentChar++] = '0'; } } buffer[currentChar] = 0; return currentChar; } bool Decimal::needParenthesisWithParent(const Expression * e) const { if (sign() == Sign::Positive) { return false; } Type types[] = {Type::Addition, Type::Subtraction, Type::Opposite, Type::Multiplication, Type::Division, Type::Power, Type::Factorial}; return e->isOfType(types, 7); } ExpressionLayout * Decimal::privateCreateLayout(FloatDisplayMode floatDisplayMode, ComplexFormat complexFormat) const { char buffer[255]; int numberOfChars = writeTextInBuffer(buffer, 255); return new StringLayout(buffer, numberOfChars); } Expression * Decimal::shallowReduce(Context& context, AngleUnit angleUnit) { Expression * e = Expression::shallowReduce(context, angleUnit); if (e != this) { return e; } // Do not reduce decimal to rational if the exponent is too big or too small. if (m_exponent > k_maxDoubleExponent || m_exponent < -k_maxDoubleExponent) { return this; // TODO: return new Infinite() ? new Rational(0) ? } int numberOfDigits = numberOfDigitsInMantissaWithoutSign(); Integer numerator = m_mantissa; Integer denominator = Integer(1); if (m_exponent >= numberOfDigits-1) { numerator = Integer::Multiplication(m_mantissa, Integer::Power(Integer(10), Integer(m_exponent-numberOfDigits+1))); } else { denominator = Integer::Power(Integer(10), Integer(numberOfDigits-1-m_exponent)); } return replaceWith(new Rational(numerator, denominator), true); } Expression * Decimal::shallowBeautify(Context & context, AngleUnit angleUnit) { if (m_mantissa.isNegative()) { m_mantissa.setNegative(false); Opposite * o = new Opposite(this, true); return replaceWith(o, true); } return this; } int Decimal::simplificationOrderSameType(const Expression * e, bool canBeInterrupted) const { assert(e->type() == Type::Decimal); const Decimal * other = static_cast(e); if (sign() == Sign::Negative && other->sign() == Sign::Positive) { return -1; } if (sign() == Sign::Positive && other->sign() == Sign::Negative) { return 1; } assert(sign() == other->sign()); int unsignedComparison = 0; if (exponent() < other->exponent()) { unsignedComparison = -1; } else if (exponent() > other->exponent()) { unsignedComparison = 1; } else { assert(exponent() == other->exponent()); unsignedComparison = Integer::NaturalOrder(mantissa(), other->mantissa()); } return ((int)sign())*unsignedComparison; } int Decimal::numberOfDigitsInMantissaWithoutSign() const { int numberOfDigits = 1; Integer mantissaCopy = m_mantissa; mantissaCopy.setNegative(false); IntegerDivision d = Integer::Division(mantissaCopy, Integer(10)); while (!d.quotient.isZero()) { mantissaCopy = d.quotient; d = Integer::Division(mantissaCopy, Integer(10)); numberOfDigits++; } return numberOfDigits; } }