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Aviator on the BBC Micro

Maths: Sine16Bit

Name: Sine16Bit [Show more] Type: Subroutine Category: Maths Summary: Calculate the sine of a 16-bit number Deep dive: Trigonometry
Context: See this subroutine in context in the source code References: This subroutine is called as follows: * ProjectAxisAngle calls Sine16Bit

Sets (A Y) = sin(X W) where (X W) is a 16-bit angle, with 0 to 65535 representing a quarter circle. The sine lookup table contains 256 entries that represent a quarter circle, so we work out the result by first looking up the sine for the high byte X, and then interpolating W/256 of the way between the results for X and X + 1. It might help to think of X being an integer (0 to 255) and W being a fraction (0 to 255) and we're trying to map X.W onto the sine table by finding the entry for X and doing linear interpolation between X and X + 1 for the fractional amount. Arguments: (X W) The 16-bit angle, representing a quarter-circle in the range 0 to 255 Returns: (A Y) sin(X W) (X W) Unchanged
.Sine16Bit STX H \ Store X in H for later SEC \ Set (A I) = sin(X + 1) - sin(X) LDA sinLo+1,X \ SBC sinLo,X \ starting with the low bytes STA I LDA sinHi+1,X \ And then the high bytes SBC sinHi,X \ Let's call this dX, the difference between sin(X + 1) \ sin(X) and, so (A I) = dX LSR A \ The maximum differential value we can have is 402, so ROR I \ we halve (A I) to fit the result into one byte, like LDX I \ this: \ \ (A I) = dX / 2 \ \ and then setting X to the low byte in I, so: \ \ X = dX / 2 LDY W \ Set Y = W JSR Multiply8x8 \ Set (A V) = X * Y \ = (dX / 2) * W LDX H \ Set X to the original argument we stored above ASL V \ Set (A V) = (A V) * 2 ROL A \ = (dX / 2) * W * 2 \ = dX * W \ \ and put bit 7 of (A V) into the C flag, so in effect \ we have: \ \ (C A V) = dX * W PHP \ Store the C flag on the stack CLC \ Set (A Y) = (C A) + sin(X) ADC sinLo,X \ = (dX * W / 256) + sin(X) TAY \ \ starting with the low bytes LDA #0 \ And then adding the carry to the high byte, so now we ADC sinHi,X \ have the interim result for (0 A) + sin(X) PLP \ And finally adding C (which we retrieve from the ADC #0 \ stack) to give the final result for (C A) + sin(X) \ So at this point we have: \ \ (A Y) = sin(X) + (dX * W / 256) \ \ which is the reault we want, as it takes sin(X) and \ adds on W/256 of the difference between sin(X) and \ sin(X + 1) RTS \ Return from the subroutine