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@@ -0,0 +1,167 @@
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+/*
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+* Fixed-Point number library
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+* Contains functions for decimal numbers encoded in 16.16 format
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+*/
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+
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+#define fixed_point_t char
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+
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+// Fixed point arithmetic operations using 16.16 format
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+#define FP_FRACT_BITS 16
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+#define FP_MULTIPLY_CONST 15259
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+#define FP_FRACT_MASK 0xFFFF
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+
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+
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+// Convert a fixed-point variable to a string with a given number of decimals (truncated, not rounded)
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+void FP_FPtoString(word fixedPointValue, char* outputString, word numDecimals) {
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+ word fractMask = FP_FRACT_MASK; // Needed to enforce a load(32) instruction, as constants have limited bits in arith operations
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+ word integerPart = fixedPointValue >> FP_FRACT_BITS; // Extract the integer part
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+ word fractionalPart = fixedPointValue & fractMask; // Extract the fractional part
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+
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+ // Convert the integer part, which can be signed, to a string using itoa()
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+ if (integerPart < 0)
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+ {
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+ outputString[0] = '-';
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+ if (fractionalPart > 0)
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+ {
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+ itoa(- (integerPart + 1), &outputString[1]); // integerPart-1 to fix neg numbers
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+ }
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+ else
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+ {
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+ itoa(- integerPart, &outputString[1]);
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+ }
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+ }
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+ else
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+ {
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+ itoa(integerPart, outputString);
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+ }
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+
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+ // Find the end of the integer part string
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+ char* endOfString = outputString;
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+ while (*endOfString)
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+ {
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+ endOfString++;
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+ }
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+
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+ // Add a dot to separate the integer and fractional parts
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+ *endOfString = '.';
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+ endOfString++;
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+
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+ char* decimalPosition = endOfString;
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+
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+ char decbuf[10]; // 10 with current multiply constant, as number can be 9 decimal max
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+ // Convert the fractional part to intermediate buffer
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+ if (integerPart < 0 && fractionalPart > 0)
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+ {
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+ // Fix for neg numbers (2's complement)
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+ fractionalPart = ( (~fractionalPart) & fractMask) + 1;
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+ }
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+
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+ fractionalPart *= FP_MULTIPLY_CONST;
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+ itoa(fractionalPart, decbuf);
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+
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+ // Get length of decimal part string
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+ int declen = strlen(decbuf);
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+ // Prepend with 9-(length of decimal part) zeros before adding decimal part
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+ while (declen < 9)
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+ {
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+ *endOfString = '0';
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+ endOfString++;
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+ declen++;
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+ }
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+ // Terminate string
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+ *endOfString = 0;
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+
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+ // Convert and append the fractional part directly to the result
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+ strcat(endOfString, decbuf);
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+
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+ // Truncate at number of decimals given by placing string terminator
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+ decimalPosition[numDecimals] = 0;
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+}
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+
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+
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+// Convert a string to a fixed-point number
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+fixed_point_t FP_StringToFP(char* decimalString)
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+{
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+
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+ // Get index of the dot, also return int part if no dot
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+ char* dotp = strchr(decimalString, '.');
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+ if (dotp == 0) return strToInt(decimalString) << FP_FRACT_BITS;
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+ word dotIndex = dotp - decimalString;
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+
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+ // Copy integer part
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+ char integerPart[12];
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+ memcpy(integerPart, decimalString, dotIndex);
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+
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+ // Terminate integerPart
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+ integerPart[dotIndex] = 0;
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+
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+ // Copy decimal part
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+ char decimalPart[12];
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+ strcpy(decimalPart, decimalString + dotIndex + 1);
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+
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+ // Add integer part to result
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+ word result = strToInt(integerPart) << FP_FRACT_BITS;
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+
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+ // Get decimal part as an integer
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+ word decimalPartInt = strToInt(decimalPart);
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+
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+ // Return if no or invalid decimal part
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+ if (decimalPartInt == 0)
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+ return result;
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+
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+ // Get number of decimals of the decimal part string which we need later
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+ word lenDecimalPart = strlen(decimalPart);
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+
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+ // Alternative for 10^lenDecimalPart
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+ word divisionNumber = 1;
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+ while (lenDecimalPart > 0)
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+ {
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+ divisionNumber *= 10;
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+ lenDecimalPart--;
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+ }
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+
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+ // Calculate decimal part
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+ word decResult = decimalPartInt << FP_FRACT_BITS;
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+ decResult = MATH_div(decResult, divisionNumber);
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+
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+ // Correct for negative numbers (look at string because -0.x)
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+ if (decimalString[0] == '-')
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+ {
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+ result -= (1 << FP_FRACT_BITS);
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+ decResult = (1 << FP_FRACT_BITS) - decResult;
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+ }
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+
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+ // Add decimal part to integer part
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+ word fractMask = FP_FRACT_MASK; // Needed to enforce a load(32) instruction, as constants have limited bits in arith operations
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+ result |= (decResult & fractMask);
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+
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+ return result;
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+}
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+
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+
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+// Convert an integer to a fixed-point number
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+fixed_point_t FP_intToFP(word x)
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+{
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+ return x << FP_FRACT_BITS;
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+}
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+
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+
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+// Convert a fixed-point number to an integer (truncate)
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+word FP_FPtoInt(fixed_point_t x)
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+{
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+ return x >> FP_FRACT_BITS;
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+}
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+
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+
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+// Multiply two fixed-point numbers using special instruction
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+fixed_point_t FP_Mult(fixed_point_t a, fixed_point_t b)
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+{
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+ // r4: a, r5: b
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+ fixed_point_t retval = 0;
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+ asm(
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+ "multfp r4 r5 r2 ; r2 = a*b (FP signed)\n"
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+ "write -4 r14 r2 ; write result to stack for return\n"
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+ );
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+
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+ return retval;
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+}
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