integer.cpp
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#include <poincare/integer.h>
extern "C" {
#include <stdlib.h>
#include <string.h>
#include <assert.h>
}
#include <cmath>
#include <poincare/complex.h>
#include "layout/string_layout.h"
#define MAX(a,b) ((a)>(b)?a:b)
#define NATIVE_UINT_BIT_COUNT (8*sizeof(native_uint_t))
namespace Poincare {
uint8_t log2(native_uint_t v) {
assert(NATIVE_UINT_BIT_COUNT < 256); // Otherwise uint8_t isn't OK
for (uint8_t i=0; i<NATIVE_UINT_BIT_COUNT; i++) {
if (v < ((native_uint_t)1<<i)) {
return i;
}
}
return 32;
}
static inline char char_from_digit(native_uint_t digit) {
return '0'+digit;
}
Integer::Integer(Integer&& other) {
// Pilfer other's data
m_numberOfDigits = other.m_numberOfDigits;
m_digits = other.m_digits;
m_negative = other.m_negative;
// Reset other
other.m_negative = 0;
other.m_numberOfDigits = 0;
other.m_digits = NULL;
}
Integer::Integer(native_int_t i) {
assert(sizeof(native_int_t) <= sizeof(native_uint_t));
m_negative = (i<0);
m_numberOfDigits = 1;
m_digits = new native_uint_t[1];
*m_digits = (native_uint_t)(i>0 ? i : -i);
}
/* Caution: string is NOT guaranteed to be NULL-terminated! */
Integer::Integer(const char * digits, bool negative) {
m_negative = negative;
if (digits != nullptr && digits[0] == '-') {
m_negative = true;
digits++;
}
Integer result = Integer((native_int_t)0);
if (digits != nullptr) {
Integer base = Integer(10);
while (*digits >= '0' && *digits <= '9') {
result = result.multiply_by(base);
result = result.add(Integer(*digits-'0'));
digits++;
}
}
// Pilfer v's ivars
m_numberOfDigits = result.m_numberOfDigits;
m_digits = result.m_digits;
// Zero-out v
result.m_numberOfDigits = 0;
result.m_digits = NULL;
}
Integer::~Integer() {
if (m_digits) {
delete[] m_digits;
}
}
// Private methods
Integer::Integer(native_uint_t * digits, uint16_t numberOfDigits, bool negative) :
m_digits(digits),
m_numberOfDigits(numberOfDigits),
m_negative(negative) {
}
int8_t Integer::ucmp(const Integer &other) const {
if (m_numberOfDigits < other.m_numberOfDigits) {
return -1;
} else if (other.m_numberOfDigits < m_numberOfDigits) {
return 1;
}
for (uint16_t i = 0; i < m_numberOfDigits; i++) {
// Digits are stored most-significant last
native_uint_t digit = m_digits[m_numberOfDigits-i-1];
native_uint_t otherDigit = other.m_digits[m_numberOfDigits-i-1];
if (digit < otherDigit) {
return -1;
} else if (otherDigit < digit) {
return 1;
}
}
return 0;
}
static inline int8_t sign(bool negative) {
return 1 - 2*(int8_t)negative;
}
bool Integer::operator<(const Integer &other) const {
if (m_negative != other.m_negative) {
return m_negative;
}
return (sign(m_negative)*ucmp(other) < 0);
}
bool Integer::operator==(const Integer &other) const {
if (m_negative != other.m_negative) {
return false;
}
return (ucmp(other) == 0);
}
Integer& Integer::operator=(Integer&& other) {
if (this != &other) {
// Release our ivars
m_negative = 0;
m_numberOfDigits = 0;
delete[] m_digits;
// Pilfer other's ivars
m_numberOfDigits = other.m_numberOfDigits;
m_digits = other.m_digits;
m_negative = other.m_negative;
// Reset other
other.m_negative = 0;
other.m_numberOfDigits = 0;
other.m_digits = NULL;
}
return *this;
}
Integer Integer::add(const Integer &other, bool inverse_other_negative) const {
bool other_negative = (inverse_other_negative ? !other.m_negative : other.m_negative);
if (m_negative == other_negative) {
return usum(other, false, m_negative);
} else {
/* The signs are different, this is in fact a subtraction
* s = this+other = (abs(this)-abs(other) OR abs(other)-abs(this))
* 1/abs(this)>abs(other) : s = sign*udiff(this, other)
* 2/abs(other)>abs(this) : s = sign*udiff(other, this)
* sign? sign of the greater! */
if (ucmp(other) >= 0) {
return usum(other, true, m_negative);
} else {
return other.usum(*this, true, other_negative);
}
}
}
Integer Integer::add(const Integer &other) const {
return add(other, false);
}
Integer Integer::subtract(const Integer &other) const {
return add(other, true);
}
Integer Integer::usum(const Integer &other, bool subtract, bool output_negative) const {
uint16_t size = MAX(m_numberOfDigits, other.m_numberOfDigits);
if (!subtract) {
// Addition can overflow
size += 1;
}
native_uint_t * digits = new native_uint_t [size];
bool carry = false;
for (uint16_t i = 0; i<size; i++) {
native_uint_t a = (i >= m_numberOfDigits ? 0 : m_digits[i]);
native_uint_t b = (i >= other.m_numberOfDigits ? 0 : other.m_digits[i]);
native_uint_t result = (subtract ? a - b - carry : a + b + carry);
digits[i] = result;
carry = (subtract ? (a<result) : ((a>result)||(b>result))); // There's been an underflow or overflow
}
while (digits[size-1] == 0 && size>1) {
size--;
// We could realloc digits to a smaller size. Probably not worth the trouble.
}
return Integer(digits, size, output_negative);
}
Integer Integer::multiply_by(const Integer &other) const {
assert(sizeof(double_native_uint_t) == 2*sizeof(native_uint_t));
uint16_t productSize = other.m_numberOfDigits + m_numberOfDigits;
native_uint_t * digits = new native_uint_t [productSize];
memset(digits, 0, productSize*sizeof(native_uint_t));
double_native_uint_t carry = 0;
for (uint16_t i=0; i<m_numberOfDigits; i++) {
double_native_uint_t a = m_digits[i];
carry = 0;
for (uint16_t j=0; j<other.m_numberOfDigits; j++) {
double_native_uint_t b = other.m_digits[j];
/* The fact that a and b are double_native is very important, otherwise
* the product might end up being computed on single_native size and
* then zero-padded. */
double_native_uint_t p = a*b + carry + (double_native_uint_t)(digits[i+j]); // TODO: Prove it cannot overflow double_native type
native_uint_t * l = (native_uint_t *)&p;
digits[i+j] = l[0];
carry = l[1];
}
digits[i+other.m_numberOfDigits] += carry;
}
while (digits[productSize-1] == 0 && productSize>1) {
productSize--;
/* At this point we could realloc m_digits to a smaller size. */
}
return Integer(digits, productSize, m_negative != other.m_negative);
}
Division::Division(const Integer &numerator, const Integer &denominator) :
m_quotient(Integer((native_int_t)0)),
m_remainder(Integer((native_int_t)0)) {
// FIXME: First, test if denominator is zero.
if (numerator < denominator) {
m_quotient = Integer((native_int_t)0);
m_remainder = numerator.add(Integer((native_int_t)0));
// FIXME: This is a ugly way to bypass creating a copy constructor!
return;
}
// Recursive case
*this = Division(numerator, denominator.add(denominator));
m_quotient = m_quotient.add(m_quotient);
if (!(m_remainder < denominator)) {
m_remainder = m_remainder.subtract(denominator);
m_quotient = m_quotient.add(Integer(1));
}
}
Integer Integer::divide_by(const Integer &other) const {
return Division(*this, other).m_quotient;
}
Expression * Integer::clone() const {
Integer * clone = new Integer((native_int_t)0);
clone->m_numberOfDigits = m_numberOfDigits;
clone->m_negative = m_negative;
delete[] clone->m_digits;
clone->m_digits = new native_uint_t [m_numberOfDigits];
for (unsigned int i=0;i<m_numberOfDigits; i++) {
clone->m_digits[i] = m_digits[i];
}
return clone;
}
Evaluation<float> * Integer::privateEvaluate(SinglePrecision p, Context& context, AngleUnit angleUnit) const {
union {
uint32_t uint_result;
float float_result;
};
assert(sizeof(float) == 4);
/* We're generating an IEEE 754 compliant float.
* Theses numbers are 32-bit values, stored as follow:
* sign (1 bit)
* exponent (8 bits)
* mantissa (23 bits)
*
* We can tell that:
* - the sign is going to be 0 for now, we only handle positive numbers
* - the exponent is the length of our BigInt, in bits - 1 + 127;
* - the mantissa is the beginning of our BigInt, discarding the first bit
*/
native_uint_t lastDigit = m_digits[m_numberOfDigits-1];
uint8_t numberOfBitsInLastDigit = log2(lastDigit);
bool sign = m_negative;
uint8_t exponent = 126;
/* if the exponent is bigger then 255, it cannot be stored as a uint8. Also,
* the integer whose 2-exponent is bigger than 255 cannot be stored as a
* float (IEEE 754 floating point). The approximation is thus INFINITY. */
if ((int)exponent + (m_numberOfDigits-1)*32 +numberOfBitsInLastDigit> 255) {
return new Complex<float>(Complex<float>::Float(INFINITY));
}
exponent += (m_numberOfDigits-1)*32;
exponent += numberOfBitsInLastDigit;
uint32_t mantissa = 0;
mantissa |= (lastDigit << (32-numberOfBitsInLastDigit));
if (m_numberOfDigits >= 2) {
native_uint_t beforeLastDigit = m_digits[m_numberOfDigits-2];
mantissa |= (beforeLastDigit >> numberOfBitsInLastDigit);
}
if ((m_numberOfDigits==1) && (m_digits[0]==0)) {
/* This special case for 0 is needed, because the current algorithm assumes
* that the big integer is non zero, thus puts the exponent to 126 (integer
* area), the issue is that when the mantissa is 0, a "shadow bit" is
* assumed to be there, thus 126 0x000000 is equal to 0.5 and not zero.
*/
float result = m_negative ? -0.0f : 0.0f;
return new Complex<float>(Complex<float>::Float(result));
}
uint_result = 0;
uint_result |= (sign << 31);
uint_result |= (exponent << 23);
uint_result |= (mantissa >> (32-23-1) & 0x7FFFFF);
/* If exponent is 255 and the float is undefined, we have exceed IEEE 754
* representable float. */
if (exponent == 255 && std::isnan(float_result)) {
return new Complex<float>(Complex<float>::Float(INFINITY));
}
return new Complex<float>(Complex<float>::Float(float_result));
}
Evaluation<double> * Integer::privateEvaluate(DoublePrecision p, Context& context, AngleUnit angleUnit) const {
union {
uint64_t uint_result;
double double_result;
};
assert(sizeof(double) == 8);
/* We're generating an IEEE 754 compliant double.
* Theses numbers are 64-bit values, stored as follow:
* sign (1 bit)
* exponent (11 bits)
* mantissa (52 bits)
*
* We can tell that:
* - the exponent is the length of our BigInt, in bits - 1 + 1023;
* - the mantissa is the beginning of our BigInt, discarding the first bit
*/
native_uint_t lastDigit = m_digits[m_numberOfDigits-1];
uint8_t numberOfBitsInLastDigit = log2(lastDigit);
bool sign = m_negative;
uint16_t exponent = 1022;
/* if the exponent is bigger then 2047, it cannot be stored as a uint11. Also,
* the integer whose 2-exponent is bigger than 2047 cannot be stored as a
* double (IEEE 754 double point). The approximation is thus INFINITY. */
if ((int)exponent + (m_numberOfDigits-1)*32 +numberOfBitsInLastDigit> 2047) {
return new Complex<double>(Complex<double>::Float(INFINITY));
}
exponent += (m_numberOfDigits-1)*32;
exponent += numberOfBitsInLastDigit;
uint64_t mantissa = 0;
mantissa |= ((uint64_t)lastDigit << (64-numberOfBitsInLastDigit));
int digitIndex = 2;
int numberOfBits = log2(lastDigit);
while (m_numberOfDigits >= digitIndex) {
lastDigit = m_digits[m_numberOfDigits-digitIndex];
numberOfBits += 32;
if (64 > numberOfBits) {
mantissa |= ((uint64_t)lastDigit << (64-numberOfBits));
} else {
mantissa |= ((uint64_t)lastDigit >> (numberOfBits-64));
}
digitIndex++;
}
if ((m_numberOfDigits==1) && (m_digits[0]==0)) {
/* This special case for 0 is needed, because the current algorithm assumes
* that the big integer is non zero, thus puts the exponent to 126 (integer
* area), the issue is that when the mantissa is 0, a "shadow bit" is
* assumed to be there, thus 126 0x000000 is equal to 0.5 and not zero.
*/
float result = m_negative ? -0.0f : 0.0f;
return new Complex<double>(Complex<double>::Float(result));
}
uint_result = 0;
uint_result |= ((uint64_t)sign << 63);
uint_result |= ((uint64_t)exponent << 52);
uint_result |= ((uint64_t)mantissa >> (64-52-1) & 0xFFFFFFFFFFFFF);
/* If exponent is 2047 and the double is undefined, we have exceed IEEE 754
* representable double. */
if (exponent == 2047 && std::isnan(double_result)) {
return new Complex<double>(Complex<double>::Float(INFINITY));
}
return new Complex<double>(Complex<double>::Float(double_result));
}
Expression::Type Integer::type() const {
return Type::Integer;
}
ExpressionLayout * Integer::privateCreateLayout(FloatDisplayMode floatDisplayMode, ComplexFormat complexFormat) const {
assert(floatDisplayMode != FloatDisplayMode::Default);
assert(complexFormat != ComplexFormat::Default);
/* If the integer is too long, this method may overflow the stack.
* Experimentally, we can display at most integer whose number of digits is
* around 7. However, to avoid crashing when the stack is already half full,
* we decide not to display integers whose number of digits > 5. */
if (m_numberOfDigits > 5) {
return new StringLayout("inf", 3);
}
char buffer[255];
Integer base = Integer(10);
Division d = Division(*this, base);
int size = 0;
if (*this == Integer((native_int_t)0)) {
buffer[size++] = '0';
}
while (!(d.m_remainder == Integer((native_int_t)0) &&
d.m_quotient == Integer((native_int_t)0))) {
assert(size<255); //TODO: malloc an extra buffer
char c = char_from_digit(d.m_remainder.m_digits[0]);
buffer[size++] = c;
d = Division(d.m_quotient, base);
}
buffer[size] = 0;
// Flip the string
for (int i=0, j=size-1 ; i < j ; i++, j--) {
char c = buffer[i];
buffer[i] = buffer[j];
buffer[j] = c;
}
return new StringLayout(buffer, size);
}
bool Integer::valueEquals(const Expression * e) const {
assert(e->type() == Type::Integer);
return (*this == *(Integer *)e); // FIXME: Remove operator overloading
}
}