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@ -117,379 +117,380 @@ int GetRoundedValue(fInt); /* Incomplete function - Usef
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*/
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fInt fExponential(fInt exponent) /*Can be used to calculate e^exponent*/
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{
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uint32_t i;
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bool bNegated = false;
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uint32_t i;
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bool bNegated = false;
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fInt fPositiveOne = ConvertToFraction(1);
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fInt fZERO = ConvertToFraction(0);
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fInt fPositiveOne = ConvertToFraction(1);
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fInt fZERO = ConvertToFraction(0);
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fInt lower_bound = Divide(78, 10000);
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fInt solution = fPositiveOne; /*Starting off with baseline of 1 */
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fInt error_term;
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fInt lower_bound = Divide(78, 10000);
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fInt solution = fPositiveOne; /*Starting off with baseline of 1 */
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fInt error_term;
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uint32_t k_array[11] = {55452, 27726, 13863, 6931, 4055, 2231, 1178, 606, 308, 155, 78};
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uint32_t expk_array[11] = {2560000, 160000, 40000, 20000, 15000, 12500, 11250, 10625, 10313, 10156, 10078};
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uint32_t k_array[11] = {55452, 27726, 13863, 6931, 4055, 2231, 1178, 606, 308, 155, 78};
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uint32_t expk_array[11] = {2560000, 160000, 40000, 20000, 15000, 12500, 11250, 10625, 10313, 10156, 10078};
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if (GreaterThan(fZERO, exponent)) {
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exponent = fNegate(exponent);
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bNegated = true;
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}
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if (GreaterThan(fZERO, exponent)) {
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exponent = fNegate(exponent);
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bNegated = true;
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}
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while (GreaterThan(exponent, lower_bound)) {
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for (i = 0; i < 11; i++) {
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if (GreaterThan(exponent, GetScaledFraction(k_array[i], 10000))) {
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exponent = fSubtract(exponent, GetScaledFraction(k_array[i], 10000));
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solution = fMultiply(solution, GetScaledFraction(expk_array[i], 10000));
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}
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}
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}
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while (GreaterThan(exponent, lower_bound)) {
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for (i = 0; i < 11; i++) {
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if (GreaterThan(exponent, GetScaledFraction(k_array[i], 10000))) {
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exponent = fSubtract(exponent, GetScaledFraction(k_array[i], 10000));
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solution = fMultiply(solution, GetScaledFraction(expk_array[i], 10000));
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}
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}
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}
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error_term = fAdd(fPositiveOne, exponent);
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error_term = fAdd(fPositiveOne, exponent);
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solution = fMultiply(solution, error_term);
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solution = fMultiply(solution, error_term);
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if (bNegated)
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solution = fDivide(fPositiveOne, solution);
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if (bNegated)
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solution = fDivide(fPositiveOne, solution);
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return solution;
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return solution;
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}
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fInt fNaturalLog(fInt value)
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{
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uint32_t i;
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fInt upper_bound = Divide(8, 1000);
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fInt fNegativeOne = ConvertToFraction(-1);
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fInt solution = ConvertToFraction(0); /*Starting off with baseline of 0 */
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fInt error_term;
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uint32_t i;
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fInt upper_bound = Divide(8, 1000);
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fInt fNegativeOne = ConvertToFraction(-1);
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fInt solution = ConvertToFraction(0); /*Starting off with baseline of 0 */
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fInt error_term;
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uint32_t k_array[10] = {160000, 40000, 20000, 15000, 12500, 11250, 10625, 10313, 10156, 10078};
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uint32_t logk_array[10] = {27726, 13863, 6931, 4055, 2231, 1178, 606, 308, 155, 78};
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uint32_t k_array[10] = {160000, 40000, 20000, 15000, 12500, 11250, 10625, 10313, 10156, 10078};
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uint32_t logk_array[10] = {27726, 13863, 6931, 4055, 2231, 1178, 606, 308, 155, 78};
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while (GreaterThan(fAdd(value, fNegativeOne), upper_bound)) {
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for (i = 0; i < 10; i++) {
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if (GreaterThan(value, GetScaledFraction(k_array[i], 10000))) {
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value = fDivide(value, GetScaledFraction(k_array[i], 10000));
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solution = fAdd(solution, GetScaledFraction(logk_array[i], 10000));
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}
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}
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}
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while (GreaterThan(fAdd(value, fNegativeOne), upper_bound)) {
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for (i = 0; i < 10; i++) {
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if (GreaterThan(value, GetScaledFraction(k_array[i], 10000))) {
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value = fDivide(value, GetScaledFraction(k_array[i], 10000));
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solution = fAdd(solution, GetScaledFraction(logk_array[i], 10000));
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}
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}
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}
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error_term = fAdd(fNegativeOne, value);
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error_term = fAdd(fNegativeOne, value);
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return (fAdd(solution, error_term));
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return (fAdd(solution, error_term));
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}
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fInt fDecodeLinearFuse(uint32_t fuse_value, fInt f_min, fInt f_range, uint32_t bitlength)
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{
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fInt f_fuse_value = Convert_ULONG_ToFraction(fuse_value);
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fInt f_bit_max_value = Convert_ULONG_ToFraction((uPow(2, bitlength)) - 1);
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fInt f_fuse_value = Convert_ULONG_ToFraction(fuse_value);
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fInt f_bit_max_value = Convert_ULONG_ToFraction((uPow(2, bitlength)) - 1);
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fInt f_decoded_value;
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fInt f_decoded_value;
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f_decoded_value = fDivide(f_fuse_value, f_bit_max_value);
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f_decoded_value = fMultiply(f_decoded_value, f_range);
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f_decoded_value = fAdd(f_decoded_value, f_min);
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f_decoded_value = fDivide(f_fuse_value, f_bit_max_value);
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f_decoded_value = fMultiply(f_decoded_value, f_range);
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f_decoded_value = fAdd(f_decoded_value, f_min);
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return f_decoded_value;
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return f_decoded_value;
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}
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fInt fDecodeLogisticFuse(uint32_t fuse_value, fInt f_average, fInt f_range, uint32_t bitlength)
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{
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fInt f_fuse_value = Convert_ULONG_ToFraction(fuse_value);
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fInt f_bit_max_value = Convert_ULONG_ToFraction((uPow(2, bitlength)) - 1);
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fInt f_fuse_value = Convert_ULONG_ToFraction(fuse_value);
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fInt f_bit_max_value = Convert_ULONG_ToFraction((uPow(2, bitlength)) - 1);
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fInt f_CONSTANT_NEG13 = ConvertToFraction(-13);
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fInt f_CONSTANT1 = ConvertToFraction(1);
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fInt f_CONSTANT_NEG13 = ConvertToFraction(-13);
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fInt f_CONSTANT1 = ConvertToFraction(1);
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fInt f_decoded_value;
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fInt f_decoded_value;
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f_decoded_value = fSubtract(fDivide(f_bit_max_value, f_fuse_value), f_CONSTANT1);
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f_decoded_value = fNaturalLog(f_decoded_value);
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f_decoded_value = fMultiply(f_decoded_value, fDivide(f_range, f_CONSTANT_NEG13));
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f_decoded_value = fAdd(f_decoded_value, f_average);
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f_decoded_value = fSubtract(fDivide(f_bit_max_value, f_fuse_value), f_CONSTANT1);
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f_decoded_value = fNaturalLog(f_decoded_value);
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f_decoded_value = fMultiply(f_decoded_value, fDivide(f_range, f_CONSTANT_NEG13));
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f_decoded_value = fAdd(f_decoded_value, f_average);
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return f_decoded_value;
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return f_decoded_value;
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}
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fInt fDecodeLeakageID (uint32_t leakageID_fuse, fInt ln_max_div_min, fInt f_min, uint32_t bitlength)
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{
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fInt fLeakage;
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fInt f_bit_max_value = Convert_ULONG_ToFraction((uPow(2, bitlength)) - 1);
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fInt fLeakage;
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fInt f_bit_max_value = Convert_ULONG_ToFraction((uPow(2, bitlength)) - 1);
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fLeakage = fMultiply(ln_max_div_min, Convert_ULONG_ToFraction(leakageID_fuse));
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fLeakage = fDivide(fLeakage, f_bit_max_value);
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fLeakage = fExponential(fLeakage);
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fLeakage = fMultiply(fLeakage, f_min);
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fLeakage = fMultiply(ln_max_div_min, Convert_ULONG_ToFraction(leakageID_fuse));
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fLeakage = fDivide(fLeakage, f_bit_max_value);
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fLeakage = fExponential(fLeakage);
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fLeakage = fMultiply(fLeakage, f_min);
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return fLeakage;
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return fLeakage;
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}
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fInt ConvertToFraction(int X) /*Add all range checking here. Is it possible to make fInt a private declaration? */
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{
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fInt temp;
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fInt temp;
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if (X <= MAX)
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temp.full = (X << SHIFT_AMOUNT);
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else
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temp.full = 0;
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if (X <= MAX)
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temp.full = (X << SHIFT_AMOUNT);
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else
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temp.full = 0;
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return temp;
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return temp;
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}
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fInt fNegate(fInt X)
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{
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fInt CONSTANT_NEGONE = ConvertToFraction(-1);
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return (fMultiply(X, CONSTANT_NEGONE));
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fInt CONSTANT_NEGONE = ConvertToFraction(-1);
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return (fMultiply(X, CONSTANT_NEGONE));
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}
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fInt Convert_ULONG_ToFraction(uint32_t X)
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{
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fInt temp;
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fInt temp;
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if (X <= MAX)
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temp.full = (X << SHIFT_AMOUNT);
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else
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temp.full = 0;
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if (X <= MAX)
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temp.full = (X << SHIFT_AMOUNT);
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else
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temp.full = 0;
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return temp;
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return temp;
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}
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fInt GetScaledFraction(int X, int factor)
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{
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int times_shifted, factor_shifted;
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bool bNEGATED;
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fInt fValue;
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int times_shifted, factor_shifted;
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bool bNEGATED;
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fInt fValue;
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times_shifted = 0;
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factor_shifted = 0;
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bNEGATED = false;
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times_shifted = 0;
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factor_shifted = 0;
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bNEGATED = false;
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if (X < 0) {
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X = -1*X;
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bNEGATED = true;
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}
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if (X < 0) {
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X = -1*X;
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bNEGATED = true;
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}
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if (factor < 0) {
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factor = -1*factor;
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if (factor < 0) {
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factor = -1*factor;
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bNEGATED = !bNEGATED; /*If bNEGATED = true due to X < 0, this will cover the case of negative cancelling negative */
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}
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bNEGATED = !bNEGATED; /*If bNEGATED = true due to X < 0, this will cover the case of negative cancelling negative */
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}
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if ((X > MAX) || factor > MAX) {
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if ((X/factor) <= MAX) {
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while (X > MAX) {
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X = X >> 1;
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times_shifted++;
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}
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if ((X > MAX) || factor > MAX) {
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if ((X/factor) <= MAX) {
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while (X > MAX) {
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X = X >> 1;
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times_shifted++;
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}
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while (factor > MAX) {
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factor = factor >> 1;
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factor_shifted++;
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}
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} else {
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fValue.full = 0;
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return fValue;
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}
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}
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while (factor > MAX) {
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factor = factor >> 1;
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factor_shifted++;
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}
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} else {
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fValue.full = 0;
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return fValue;
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}
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}
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if (factor == 1)
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return (ConvertToFraction(X));
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if (factor == 1)
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return (ConvertToFraction(X));
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fValue = fDivide(ConvertToFraction(X * uPow(-1, bNEGATED)), ConvertToFraction(factor));
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fValue = fDivide(ConvertToFraction(X * uPow(-1, bNEGATED)), ConvertToFraction(factor));
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fValue.full = fValue.full << times_shifted;
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fValue.full = fValue.full >> factor_shifted;
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fValue.full = fValue.full << times_shifted;
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fValue.full = fValue.full >> factor_shifted;
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|
|
|
|
|
|
return fValue;
|
|
|
|
|
return fValue;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
/* Addition using two fInts */
|
|
|
|
|
fInt fAdd (fInt X, fInt Y)
|
|
|
|
|
{
|
|
|
|
|
fInt Sum;
|
|
|
|
|
fInt Sum;
|
|
|
|
|
|
|
|
|
|
Sum.full = X.full + Y.full;
|
|
|
|
|
Sum.full = X.full + Y.full;
|
|
|
|
|
|
|
|
|
|
return Sum;
|
|
|
|
|
return Sum;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
/* Addition using two fInts */
|
|
|
|
|
fInt fSubtract (fInt X, fInt Y)
|
|
|
|
|
{
|
|
|
|
|
fInt Difference;
|
|
|
|
|
fInt Difference;
|
|
|
|
|
|
|
|
|
|
Difference.full = X.full - Y.full;
|
|
|
|
|
Difference.full = X.full - Y.full;
|
|
|
|
|
|
|
|
|
|
return Difference;
|
|
|
|
|
return Difference;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
bool Equal(fInt A, fInt B)
|
|
|
|
|
{
|
|
|
|
|
if (A.full == B.full)
|
|
|
|
|
return true;
|
|
|
|
|
else
|
|
|
|
|
return false;
|
|
|
|
|
if (A.full == B.full)
|
|
|
|
|
return true;
|
|
|
|
|
else
|
|
|
|
|
return false;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
bool GreaterThan(fInt A, fInt B)
|
|
|
|
|
{
|
|
|
|
|
if (A.full > B.full)
|
|
|
|
|
return true;
|
|
|
|
|
else
|
|
|
|
|
return false;
|
|
|
|
|
if (A.full > B.full)
|
|
|
|
|
return true;
|
|
|
|
|
else
|
|
|
|
|
return false;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
fInt fMultiply (fInt X, fInt Y) /* Uses 64-bit integers (int64_t) */
|
|
|
|
|
{
|
|
|
|
|
fInt Product;
|
|
|
|
|
int64_t tempProduct;
|
|
|
|
|
bool X_LessThanOne, Y_LessThanOne;
|
|
|
|
|
fInt Product;
|
|
|
|
|
int64_t tempProduct;
|
|
|
|
|
bool X_LessThanOne, Y_LessThanOne;
|
|
|
|
|
|
|
|
|
|
X_LessThanOne = (X.partial.real == 0 && X.partial.decimal != 0 && X.full >= 0);
|
|
|
|
|
Y_LessThanOne = (Y.partial.real == 0 && Y.partial.decimal != 0 && Y.full >= 0);
|
|
|
|
|
X_LessThanOne = (X.partial.real == 0 && X.partial.decimal != 0 && X.full >= 0);
|
|
|
|
|
Y_LessThanOne = (Y.partial.real == 0 && Y.partial.decimal != 0 && Y.full >= 0);
|
|
|
|
|
|
|
|
|
|
/*The following is for a very specific common case: Non-zero number with ONLY fractional portion*/
|
|
|
|
|
/* TEMPORARILY DISABLED - CAN BE USED TO IMPROVE PRECISION
|
|
|
|
|
/*The following is for a very specific common case: Non-zero number with ONLY fractional portion*/
|
|
|
|
|
/* TEMPORARILY DISABLED - CAN BE USED TO IMPROVE PRECISION
|
|
|
|
|
|
|
|
|
|
if (X_LessThanOne && Y_LessThanOne) {
|
|
|
|
|
Product.full = X.full * Y.full;
|
|
|
|
|
return Product
|
|
|
|
|
}*/
|
|
|
|
|
if (X_LessThanOne && Y_LessThanOne) {
|
|
|
|
|
Product.full = X.full * Y.full;
|
|
|
|
|
return Product
|
|
|
|
|
}*/
|
|
|
|
|
|
|
|
|
|
tempProduct = ((int64_t)X.full) * ((int64_t)Y.full); /*Q(16,16)*Q(16,16) = Q(32, 32) - Might become a negative number! */
|
|
|
|
|
tempProduct = tempProduct >> 16; /*Remove lagging 16 bits - Will lose some precision from decimal; */
|
|
|
|
|
Product.full = (int)tempProduct; /*The int64_t will lose the leading 16 bits that were part of the integer portion */
|
|
|
|
|
tempProduct = ((int64_t)X.full) * ((int64_t)Y.full); /*Q(16,16)*Q(16,16) = Q(32, 32) - Might become a negative number! */
|
|
|
|
|
tempProduct = tempProduct >> 16; /*Remove lagging 16 bits - Will lose some precision from decimal; */
|
|
|
|
|
Product.full = (int)tempProduct; /*The int64_t will lose the leading 16 bits that were part of the integer portion */
|
|
|
|
|
|
|
|
|
|
return Product;
|
|
|
|
|
return Product;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
fInt fDivide (fInt X, fInt Y)
|
|
|
|
|
{
|
|
|
|
|
fInt fZERO, fQuotient;
|
|
|
|
|
int64_t longlongX, longlongY;
|
|
|
|
|
fInt fZERO, fQuotient;
|
|
|
|
|
int64_t longlongX, longlongY;
|
|
|
|
|
|
|
|
|
|
fZERO = ConvertToFraction(0);
|
|
|
|
|
fZERO = ConvertToFraction(0);
|
|
|
|
|
|
|
|
|
|
if (Equal(Y, fZERO))
|
|
|
|
|
return fZERO;
|
|
|
|
|
if (Equal(Y, fZERO))
|
|
|
|
|
return fZERO;
|
|
|
|
|
|
|
|
|
|
longlongX = (int64_t)X.full;
|
|
|
|
|
longlongY = (int64_t)Y.full;
|
|
|
|
|
longlongX = (int64_t)X.full;
|
|
|
|
|
longlongY = (int64_t)Y.full;
|
|
|
|
|
|
|
|
|
|
longlongX = longlongX << 16; /*Q(16,16) -> Q(32,32) */
|
|
|
|
|
longlongX = longlongX << 16; /*Q(16,16) -> Q(32,32) */
|
|
|
|
|
|
|
|
|
|
div64_s64(longlongX, longlongY); /*Q(32,32) divided by Q(16,16) = Q(16,16) Back to original format */
|
|
|
|
|
div64_s64(longlongX, longlongY); /*Q(32,32) divided by Q(16,16) = Q(16,16) Back to original format */
|
|
|
|
|
|
|
|
|
|
fQuotient.full = (int)longlongX;
|
|
|
|
|
return fQuotient;
|
|
|
|
|
fQuotient.full = (int)longlongX;
|
|
|
|
|
return fQuotient;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
int ConvertBackToInteger (fInt A) /*THIS is the function that will be used to check with the Golden settings table*/
|
|
|
|
|
{
|
|
|
|
|
fInt fullNumber, scaledDecimal, scaledReal;
|
|
|
|
|
fInt fullNumber, scaledDecimal, scaledReal;
|
|
|
|
|
|
|
|
|
|
scaledReal.full = GetReal(A) * uPow(10, PRECISION-1); /* DOUBLE CHECK THISSSS!!! */
|
|
|
|
|
scaledReal.full = GetReal(A) * uPow(10, PRECISION-1); /* DOUBLE CHECK THISSSS!!! */
|
|
|
|
|
|
|
|
|
|
scaledDecimal.full = uGetScaledDecimal(A);
|
|
|
|
|
scaledDecimal.full = uGetScaledDecimal(A);
|
|
|
|
|
|
|
|
|
|
fullNumber = fAdd(scaledDecimal,scaledReal);
|
|
|
|
|
fullNumber = fAdd(scaledDecimal,scaledReal);
|
|
|
|
|
|
|
|
|
|
return fullNumber.full;
|
|
|
|
|
return fullNumber.full;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
fInt fGetSquare(fInt A)
|
|
|
|
|
{
|
|
|
|
|
return fMultiply(A,A);
|
|
|
|
|
return fMultiply(A,A);
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
/* x_new = x_old - (x_old^2 - C) / (2 * x_old) */
|
|
|
|
|
fInt fSqrt(fInt num)
|
|
|
|
|
{
|
|
|
|
|
fInt F_divide_Fprime, Fprime;
|
|
|
|
|
fInt test;
|
|
|
|
|
fInt twoShifted;
|
|
|
|
|
int seed, counter, error;
|
|
|
|
|
fInt x_new, x_old, C, y;
|
|
|
|
|
fInt F_divide_Fprime, Fprime;
|
|
|
|
|
fInt test;
|
|
|
|
|
fInt twoShifted;
|
|
|
|
|
int seed, counter, error;
|
|
|
|
|
fInt x_new, x_old, C, y;
|
|
|
|
|
|
|
|
|
|
fInt fZERO = ConvertToFraction(0);
|
|
|
|
|
/* (0 > num) is the same as (num < 0), i.e., num is negative */
|
|
|
|
|
if (GreaterThan(fZERO, num) || Equal(fZERO, num))
|
|
|
|
|
return fZERO;
|
|
|
|
|
fInt fZERO = ConvertToFraction(0);
|
|
|
|
|
|
|
|
|
|
C = num;
|
|
|
|
|
/* (0 > num) is the same as (num < 0), i.e., num is negative */
|
|
|
|
|
|
|
|
|
|
if (num.partial.real > 3000)
|
|
|
|
|
seed = 60;
|
|
|
|
|
else if (num.partial.real > 1000)
|
|
|
|
|
seed = 30;
|
|
|
|
|
else if (num.partial.real > 100)
|
|
|
|
|
seed = 10;
|
|
|
|
|
else
|
|
|
|
|
seed = 2;
|
|
|
|
|
if (GreaterThan(fZERO, num) || Equal(fZERO, num))
|
|
|
|
|
return fZERO;
|
|
|
|
|
|
|
|
|
|
counter = 0;
|
|
|
|
|
C = num;
|
|
|
|
|
|
|
|
|
|
if (Equal(num, fZERO)) /*Square Root of Zero is zero */
|
|
|
|
|
return fZERO;
|
|
|
|
|
if (num.partial.real > 3000)
|
|
|
|
|
seed = 60;
|
|
|
|
|
else if (num.partial.real > 1000)
|
|
|
|
|
seed = 30;
|
|
|
|
|
else if (num.partial.real > 100)
|
|
|
|
|
seed = 10;
|
|
|
|
|
else
|
|
|
|
|
seed = 2;
|
|
|
|
|
|
|
|
|
|
twoShifted = ConvertToFraction(2);
|
|
|
|
|
x_new = ConvertToFraction(seed);
|
|
|
|
|
counter = 0;
|
|
|
|
|
|
|
|
|
|
do {
|
|
|
|
|
counter++;
|
|
|
|
|
if (Equal(num, fZERO)) /*Square Root of Zero is zero */
|
|
|
|
|
return fZERO;
|
|
|
|
|
|
|
|
|
|
x_old.full = x_new.full;
|
|
|
|
|
twoShifted = ConvertToFraction(2);
|
|
|
|
|
x_new = ConvertToFraction(seed);
|
|
|
|
|
|
|
|
|
|
test = fGetSquare(x_old); /*1.75*1.75 is reverting back to 1 when shifted down */
|
|
|
|
|
y = fSubtract(test, C); /*y = f(x) = x^2 - C; */
|
|
|
|
|
do {
|
|
|
|
|
counter++;
|
|
|
|
|
|
|
|
|
|
Fprime = fMultiply(twoShifted, x_old);
|
|
|
|
|
F_divide_Fprime = fDivide(y, Fprime);
|
|
|
|
|
x_old.full = x_new.full;
|
|
|
|
|
|
|
|
|
|
x_new = fSubtract(x_old, F_divide_Fprime);
|
|
|
|
|
test = fGetSquare(x_old); /*1.75*1.75 is reverting back to 1 when shifted down */
|
|
|
|
|
y = fSubtract(test, C); /*y = f(x) = x^2 - C; */
|
|
|
|
|
|
|
|
|
|
error = ConvertBackToInteger(x_new) - ConvertBackToInteger(x_old);
|
|
|
|
|
Fprime = fMultiply(twoShifted, x_old);
|
|
|
|
|
F_divide_Fprime = fDivide(y, Fprime);
|
|
|
|
|
|
|
|
|
|
if (counter > 20) /*20 is already way too many iterations. If we dont have an answer by then, we never will*/
|
|
|
|
|
return x_new;
|
|
|
|
|
x_new = fSubtract(x_old, F_divide_Fprime);
|
|
|
|
|
|
|
|
|
|
} while (uAbs(error) > 0);
|
|
|
|
|
error = ConvertBackToInteger(x_new) - ConvertBackToInteger(x_old);
|
|
|
|
|
|
|
|
|
|
return (x_new);
|
|
|
|
|
if (counter > 20) /*20 is already way too many iterations. If we dont have an answer by then, we never will*/
|
|
|
|
|
return x_new;
|
|
|
|
|
|
|
|
|
|
} while (uAbs(error) > 0);
|
|
|
|
|
|
|
|
|
|
return (x_new);
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
void SolveQuadracticEqn(fInt A, fInt B, fInt C, fInt Roots[])
|
|
|
|
|
{
|
|
|
|
|
fInt* pRoots = &Roots[0];
|
|
|
|
|
fInt temp, root_first, root_second;
|
|
|
|
|
fInt f_CONSTANT10, f_CONSTANT100;
|
|
|
|
|
fInt *pRoots = &Roots[0];
|
|
|
|
|
fInt temp, root_first, root_second;
|
|
|
|
|
fInt f_CONSTANT10, f_CONSTANT100;
|
|
|
|
|
|
|
|
|
|
f_CONSTANT100 = ConvertToFraction(100);
|
|
|
|
|
f_CONSTANT10 = ConvertToFraction(10);
|
|
|
|
|
f_CONSTANT100 = ConvertToFraction(100);
|
|
|
|
|
f_CONSTANT10 = ConvertToFraction(10);
|
|
|
|
|
|
|
|
|
|
while(GreaterThan(A, f_CONSTANT100) || GreaterThan(B, f_CONSTANT100) || GreaterThan(C, f_CONSTANT100)) {
|
|
|
|
|
A = fDivide(A, f_CONSTANT10);
|
|
|
|
|
B = fDivide(B, f_CONSTANT10);
|
|
|
|
|
C = fDivide(C, f_CONSTANT10);
|
|
|
|
|
}
|
|
|
|
|
while(GreaterThan(A, f_CONSTANT100) || GreaterThan(B, f_CONSTANT100) || GreaterThan(C, f_CONSTANT100)) {
|
|
|
|
|
A = fDivide(A, f_CONSTANT10);
|
|
|
|
|
B = fDivide(B, f_CONSTANT10);
|
|
|
|
|
C = fDivide(C, f_CONSTANT10);
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
temp = fMultiply(ConvertToFraction(4), A); /* root = 4*A */
|
|
|
|
|
temp = fMultiply(temp, C); /* root = 4*A*C */
|
|
|
|
|
temp = fSubtract(fGetSquare(B), temp); /* root = b^2 - 4AC */
|
|
|
|
|
temp = fSqrt(temp); /*root = Sqrt (b^2 - 4AC); */
|
|
|
|
|
temp = fMultiply(ConvertToFraction(4), A); /* root = 4*A */
|
|
|
|
|
temp = fMultiply(temp, C); /* root = 4*A*C */
|
|
|
|
|
temp = fSubtract(fGetSquare(B), temp); /* root = b^2 - 4AC */
|
|
|
|
|
temp = fSqrt(temp); /*root = Sqrt (b^2 - 4AC); */
|
|
|
|
|
|
|
|
|
|
root_first = fSubtract(fNegate(B), temp); /* b - Sqrt(b^2 - 4AC) */
|
|
|
|
|
root_second = fAdd(fNegate(B), temp); /* b + Sqrt(b^2 - 4AC) */
|
|
|
|
|
root_first = fSubtract(fNegate(B), temp); /* b - Sqrt(b^2 - 4AC) */
|
|
|
|
|
root_second = fAdd(fNegate(B), temp); /* b + Sqrt(b^2 - 4AC) */
|
|
|
|
|
|
|
|
|
|
root_first = fDivide(root_first, ConvertToFraction(2)); /* [b +- Sqrt(b^2 - 4AC)]/[2] */
|
|
|
|
|
root_first = fDivide(root_first, A); /*[b +- Sqrt(b^2 - 4AC)]/[2*A] */
|
|
|
|
|
root_first = fDivide(root_first, ConvertToFraction(2)); /* [b +- Sqrt(b^2 - 4AC)]/[2] */
|
|
|
|
|
root_first = fDivide(root_first, A); /*[b +- Sqrt(b^2 - 4AC)]/[2*A] */
|
|
|
|
|
|
|
|
|
|
root_second = fDivide(root_second, ConvertToFraction(2)); /* [b +- Sqrt(b^2 - 4AC)]/[2] */
|
|
|
|
|
root_second = fDivide(root_second, A); /*[b +- Sqrt(b^2 - 4AC)]/[2*A] */
|
|
|
|
|
root_second = fDivide(root_second, ConvertToFraction(2)); /* [b +- Sqrt(b^2 - 4AC)]/[2] */
|
|
|
|
|
root_second = fDivide(root_second, A); /*[b +- Sqrt(b^2 - 4AC)]/[2*A] */
|
|
|
|
|
|
|
|
|
|
*(pRoots + 0) = root_first;
|
|
|
|
|
*(pRoots + 1) = root_second;
|
|
|
|
|
*(pRoots + 0) = root_first;
|
|
|
|
|
*(pRoots + 1) = root_second;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
/* -----------------------------------------------------------------------------
|
|
|
|
@ -500,61 +501,58 @@ void SolveQuadracticEqn(fInt A, fInt B, fInt C, fInt Roots[])
|
|
|
|
|
/* Addition using two normal ints - Temporary - Use only for testing purposes?. */
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fInt Add (int X, int Y)
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{
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fInt A, B, Sum;
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fInt A, B, Sum;
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A.full = (X << SHIFT_AMOUNT);
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B.full = (Y << SHIFT_AMOUNT);
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A.full = (X << SHIFT_AMOUNT);
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B.full = (Y << SHIFT_AMOUNT);
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Sum.full = A.full + B.full;
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Sum.full = A.full + B.full;
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return Sum;
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return Sum;
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}
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/* Conversion Functions */
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int GetReal (fInt A)
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{
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return (A.full >> SHIFT_AMOUNT);
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return (A.full >> SHIFT_AMOUNT);
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}
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/* Temporarily Disabled */
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int GetRoundedValue(fInt A) /*For now, round the 3rd decimal place */
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{
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/* ROUNDING TEMPORARLY DISABLED
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int temp = A.full;
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/* ROUNDING TEMPORARLY DISABLED
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int temp = A.full;
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int decimal_cutoff, decimal_mask = 0x000001FF;
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decimal_cutoff = temp & decimal_mask;
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if (decimal_cutoff > 0x147) {
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temp += 673;
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}*/
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int decimal_cutoff, decimal_mask = 0x000001FF;
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decimal_cutoff = temp & decimal_mask;
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if (decimal_cutoff > 0x147) {
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temp += 673;
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}*/
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return ConvertBackToInteger(A)/10000; /*Temporary - in case this was used somewhere else */
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return ConvertBackToInteger(A)/10000; /*Temporary - in case this was used somewhere else */
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}
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fInt Multiply (int X, int Y)
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{
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fInt A, B, Product;
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fInt A, B, Product;
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A.full = X << SHIFT_AMOUNT;
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B.full = Y << SHIFT_AMOUNT;
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A.full = X << SHIFT_AMOUNT;
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B.full = Y << SHIFT_AMOUNT;
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Product = fMultiply(A, B);
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Product = fMultiply(A, B);
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return Product;
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return Product;
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}
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fInt Divide (int X, int Y)
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{
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fInt A, B, Quotient;
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fInt A, B, Quotient;
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A.full = X << SHIFT_AMOUNT;
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B.full = Y << SHIFT_AMOUNT;
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A.full = X << SHIFT_AMOUNT;
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B.full = Y << SHIFT_AMOUNT;
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Quotient = fDivide(A, B);
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Quotient = fDivide(A, B);
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return Quotient;
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return Quotient;
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}
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int uGetScaledDecimal (fInt A) /*Converts the fractional portion to whole integers - Costly function */
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@ -563,16 +561,13 @@ int uGetScaledDecimal (fInt A) /*Converts the fractional portion to whole intege
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int i, scaledDecimal = 0, tmp = A.partial.decimal;
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|
for (i = 0; i < PRECISION; i++) {
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|
dec[i] = tmp / (1 << SHIFT_AMOUNT);
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|
dec[i] = tmp / (1 << SHIFT_AMOUNT);
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|
tmp = tmp - ((1 << SHIFT_AMOUNT)*dec[i]);
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|
tmp *= 10;
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|
scaledDecimal = scaledDecimal + dec[i]*uPow(10, PRECISION - 1 -i);
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|
|
}
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tmp = tmp - ((1 << SHIFT_AMOUNT)*dec[i]);
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|
|
tmp *= 10;
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|
|
scaledDecimal = scaledDecimal + dec[i]*uPow(10, PRECISION - 1 -i);
|
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|
|
}
|
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|
|
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|
|
return scaledDecimal;
|
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|
|
return scaledDecimal;
|
|
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|
|
}
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|
|
int uPow(int base, int power)
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|
@ -601,17 +596,17 @@ int uAbs(int X)
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|
|
fInt fRoundUpByStepSize(fInt A, fInt fStepSize, bool error_term)
|
|
|
|
|
{
|
|
|
|
|
fInt solution;
|
|
|
|
|
fInt solution;
|
|
|
|
|
|
|
|
|
|
solution = fDivide(A, fStepSize);
|
|
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|
|
solution.partial.decimal = 0; /*All fractional digits changes to 0 */
|
|
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|
|
solution = fDivide(A, fStepSize);
|
|
|
|
|
solution.partial.decimal = 0; /*All fractional digits changes to 0 */
|
|
|
|
|
|
|
|
|
|
if (error_term)
|
|
|
|
|
solution.partial.real += 1; /*Error term of 1 added */
|
|
|
|
|
if (error_term)
|
|
|
|
|
solution.partial.real += 1; /*Error term of 1 added */
|
|
|
|
|
|
|
|
|
|
solution = fMultiply(solution, fStepSize);
|
|
|
|
|
solution = fAdd(solution, fStepSize);
|
|
|
|
|
solution = fMultiply(solution, fStepSize);
|
|
|
|
|
solution = fAdd(solution, fStepSize);
|
|
|
|
|
|
|
|
|
|
return solution;
|
|
|
|
|
return solution;
|
|
|
|
|
}
|
|
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|
|
|
|
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|
|