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The Need for Block Operations In system programming and game development, you constantly need to move large chunks of data—transferring level data, shifting arrays, or buffering screen regions. Writing a loop for this is slow; the Z80 provides dedicated instructions for speed. Routine 1: Block Move (memcpy) `memcpy′ (Memory Copy) copies a block of bytes from a source address to a destination address. This is the fastest way to achieve the operation. ...

The Need for 16-bit Comparison The Z80 has a dedicated CP R&prime; (Compare) instruction, but it only works on 8-bit values. When dealing with addresses, large scores, or multi-byte numbers, you need a robust routine to compare two 16-bit pairs, such as HL′ against `DE′. Goal: Compare HL with DE and set the flags (Zero, Carry) to indicate if HL &equals; DE&prime;, HL < DE′, or `HL > DE′. The Comparison Strategy: Subtraction The fastest way to compare two numbers is to subtract one from the other. ...

The Need for Data Integrity When data is transferred over an unreliable medium (like a cassette tape or a network connection), or when code is loaded from disk, electrical noise or corruption can change the data bytes. A Checksum or CRC provides a simple way to verify that the data received is exactly what was sent. Method 1: The Simple Checksum (The Fast Way) A simple checksum is the fastest method. It involves adding up every byte in the data block. ...

The Need for a Fast Block Fill In game development and system programming, you frequently need to clear large areas of RAM—such as setting the entire screen buffer to a black background or zeroing out a data structure. Doing this one byte at a time with a simple loop is slow. Goal: Write a routine that fills a specified memory range (START_ADDR&prime; to END_ADDR′) with a single constant byte (`FILL_BYTE′) as quickly as possible. ...

The Challenge of Displaying Numbers Once the Z80 has calculated a final value (e.g., a score of 4296 decimal), this number is stored as a 16-bit binary value (1000010000000000B). To display it on the screen, we need to convert it into a sequence of decimal digits (4&prime;, 2′, 9&prime;, 6′) that can be looked up in the font table. Goal: Convert a 16-bit binary number into a 16-bit BCD value (four decimal digits). ...

The Challenge of User Input When a user types a number (e.g., 4296), it is stored as a series of ASCII characters (or often converted immediately into Binary-Coded Decimal (BCD)). The Z80 needs this number in a single 16-bit binary value for fast calculation. Goal: Convert a 16-bit BCD value (representing a number from 0 to 9999) into a 16-bit binary value. The BCD Structure A 16-bit BCD value typically uses the entire word (two bytes) to store four decimal digits (0-9). ...

The Need for Fixed-Point Math As established (Part 30), Z80 floating-point math is extremely slow. Fixed-point arithmetic is the solution: it allows the Z80 to perform calculations involving fractions using only fast integer operations. The Principle: A fixed-point number is an integer where the position of the decimal point is implied and fixed by the programmer. The Q-Format (Standard Fixed-Point) We represent a fractional number (like 3.14) by scaling it up to make it an integer. This is often called a Q-format (e.g., Q16, Q8). ...

The Optimization: Exploiting the Format In standard integer math, multiplying by a power of two is done with a fast left shift (`SLA′). In floating-point math (Part 30), a multiplication or division by a power of two (like $2^N$ or $2^{-N}$) is even faster: it requires no change to the Mantissa (precision) and only a simple addition or subtraction to the Exponent. The Rule: Multiplication by $2^N$: Add $N$ to the Exponent. Division by $2^N$: Subtract $N$ from the Exponent. The Exponent Field Recall that the exponent is usually stored as a biased 8-bit integer (e.g., a bias of 127 is added to the true exponent). Adjusting the number simply means adjusting this byte. ...

The Challenge: Precision and Speed Calculating the square root of a floating-point number (Part 30) is required for precise calculations like distance, physics, or graphics shading. This requires an iterative algorithm that works across the multi-byte structure of the float. Method: The Newton-Raphson Method is the preferred algorithm for floating-point square roots because it is computationally fast (it converges quadratically). The Newton-Raphson Formula The goal is to iteratively refine a guess ($x_{n+1}$) using the previous guess ($x_n$) until the guesses stop changing (convergence). ...

The Challenge of Square Roots The Z80 cannot natively calculate a square root. This complex operation must be achieved using an iterative algorithm that repeatedly guesses the answer and refines the guess until it is accurate enough. Goal: To find the largest integer $R$ such that $R^2 \le N$, where $N$ is the input number. Method 1: Integer Binary Search (The Reliable Method) The Binary Search method is the safest and most reliable way to find the integer square root on an 8-bit processor. It works by checking the midpoint of a search range. ...