fix16.c

#include "fix16.h"
#if !defined(FIXMATH_NO_64BIT)
#include "int64.h"
#endif

/* Subtraction and addition with overflow detection.
 * The versions without overflow detection are inlined in the header.
 */
#ifndef FIXMATH_NO_OVERFLOW
fix16_t fix16_add(fix16_t a, fix16_t b)
{
	// Use unsigned integers because overflow with signed integers is
	// an undefined operation (http://www.airs.com/blog/archives/120).
	uint32_t _a = a, _b = b;
	uint32_t sum = _a + _b;

	// Overflow can only happen if sign of a == sign of b, and then
	// it causes sign of sum != sign of a.
	if (!((_a ^ _b) & 0x80000000) && ((_a ^ sum) & 0x80000000))
		return fix16_overflow;
	
	return sum;
}

fix16_t fix16_sub(fix16_t a, fix16_t b)
{
	uint32_t _a = a, _b = b;
	uint32_t diff = _a - _b;

	// Overflow can only happen if sign of a != sign of b, and then
	// it causes sign of diff != sign of a.
	if (((_a ^ _b) & 0x80000000) && ((_a ^ diff) & 0x80000000))
		return fix16_overflow;
	
	return diff;
}

/* Saturating arithmetic */
fix16_t fix16_sadd(fix16_t a, fix16_t b)
{
	fix16_t result = fix16_add(a, b);

	if (result == fix16_overflow)
		return (a >= 0) ? fix16_maximum : fix16_minimum;

	return result;
}	

fix16_t fix16_ssub(fix16_t a, fix16_t b)
{
	fix16_t result = fix16_sub(a, b);

	if (result == fix16_overflow)
		return (a >= 0) ? fix16_maximum : fix16_minimum;

	return result;
}
#endif



/* 64-bit implementation for fix16_mul. Fastest version for e.g. ARM Cortex M3.
 * Performs a 32*32 -> 64bit multiplication. The middle 32 bits are the result,
 * bottom 16 bits are used for rounding, and upper 16 bits are used for overflow
 * detection.
 */
 
#if !defined(FIXMATH_NO_64BIT) && !defined(FIXMATH_OPTIMIZE_8BIT)
fix16_t fix16_mul(fix16_t inArg0, fix16_t inArg1)
{
	int64_t product = (int64_t)inArg0 * inArg1;
	
	#ifndef FIXMATH_NO_OVERFLOW
	// The upper 17 bits should all be the same (the sign).
	uint32_t upper = (product >> 47);
	#endif
	
	if (product < 0)
	{
		#ifndef FIXMATH_NO_OVERFLOW
		if (~upper)
				return fix16_overflow;
		#endif
		
		#ifndef FIXMATH_NO_ROUNDING
		// This adjustment is required in order to round -1/2 correctly
		product--;
		#endif
	}
	else
	{
		#ifndef FIXMATH_NO_OVERFLOW
		if (upper)
				return fix16_overflow;
		#endif
	}
	
	#ifdef FIXMATH_NO_ROUNDING
	return product >> 16;
	#else
	fix16_t result = product >> 16;
	result += (product & 0x8000) >> 15;
	
	return result;
	#endif
}
#endif

/* 32-bit implementation of fix16_mul. Potentially fast on 16-bit processors,
 * and this is a relatively good compromise for compilers that do not support
 * uint64_t. Uses 16*16->32bit multiplications.
 */
#if defined(FIXMATH_NO_64BIT) && !defined(FIXMATH_OPTIMIZE_8BIT)
fix16_t fix16_mul(fix16_t inArg0, fix16_t inArg1)
{
	// Each argument is divided to 16-bit parts.
	//					AB
	//			*	 CD
	// -----------
	//					BD	16 * 16 -> 32 bit products
	//				 CB
	//				 AD
	//				AC
	//			 |----| 64 bit product
	int32_t A = (inArg0 >> 16), C = (inArg1 >> 16);
	uint32_t B = (inArg0 & 0xFFFF), D = (inArg1 & 0xFFFF);
	
	int32_t AC = A*C;
	int32_t AD_CB = A*D + C*B;
	uint32_t BD = B*D;
	
	int32_t product_hi = AC + (AD_CB >> 16);
	
	// Handle carry from lower 32 bits to upper part of result.
	uint32_t ad_cb_temp = AD_CB << 16;
	uint32_t product_lo = BD + ad_cb_temp;
	if (product_lo < BD)
		product_hi++;
	
#ifndef FIXMATH_NO_OVERFLOW
	// The upper 17 bits should all be the same (the sign).
	if (product_hi >> 31 != product_hi >> 15)
		return fix16_overflow;
#endif
	
#ifdef FIXMATH_NO_ROUNDING
	return (product_hi << 16) | (product_lo >> 16);
#else
	// Subtracting 0x8000 (= 0.5) and then using signed right shift
	// achieves proper rounding to result-1, except in the corner
	// case of negative numbers and lowest word = 0x8000.
	// To handle that, we also have to subtract 1 for negative numbers.
	uint32_t product_lo_tmp = product_lo;
	product_lo -= 0x8000;
	product_lo -= (uint32_t)product_hi >> 31;
	if (product_lo > product_lo_tmp)
		product_hi--;
	
	// Discard the lowest 16 bits. Note that this is not exactly the same
	// as dividing by 0x10000. For example if product = -1, result will
	// also be -1 and not 0. This is compensated by adding +1 to the result
	// and compensating this in turn in the rounding above.
	fix16_t result = (product_hi << 16) | (product_lo >> 16);
	result += 1;
	return result;
#endif
}
#endif

/* 8-bit implementation of fix16_mul. Fastest on e.g. Atmel AVR.
 * Uses 8*8->16bit multiplications, and also skips any bytes that
 * are zero.
 */
#if defined(FIXMATH_OPTIMIZE_8BIT)
fix16_t fix16_mul(fix16_t inArg0, fix16_t inArg1)
{
	uint32_t _a = (inArg0 >= 0) ? inArg0 : (-inArg0);
	uint32_t _b = (inArg1 >= 0) ? inArg1 : (-inArg1);
	
	uint8_t va[4] = {_a, (_a >> 8), (_a >> 16), (_a >> 24)};
	uint8_t vb[4] = {_b, (_b >> 8), (_b >> 16), (_b >> 24)};
	
	uint32_t low = 0;
	uint32_t mid = 0;
	
	// Result column i depends on va[0..i] and vb[i..0]

	#ifndef FIXMATH_NO_OVERFLOW
	// i = 6
	if (va[3] && vb[3]) return fix16_overflow;
	#endif
	
	// i = 5
	if (va[2] && vb[3]) mid += (uint16_t)va[2] * vb[3];
	if (va[3] && vb[2]) mid += (uint16_t)va[3] * vb[2];
	mid <<= 8;
	
	// i = 4
	if (va[1] && vb[3]) mid += (uint16_t)va[1] * vb[3];
	if (va[2] && vb[2]) mid += (uint16_t)va[2] * vb[2];
	if (va[3] && vb[1]) mid += (uint16_t)va[3] * vb[1];
	
	#ifndef FIXMATH_NO_OVERFLOW
	if (mid & 0xFF000000) return fix16_overflow;
	#endif
	mid <<= 8;
	
	// i = 3
	if (va[0] && vb[3]) mid += (uint16_t)va[0] * vb[3];
	if (va[1] && vb[2]) mid += (uint16_t)va[1] * vb[2];
	if (va[2] && vb[1]) mid += (uint16_t)va[2] * vb[1];
	if (va[3] && vb[0]) mid += (uint16_t)va[3] * vb[0];
	
	#ifndef FIXMATH_NO_OVERFLOW
	if (mid & 0xFF000000) return fix16_overflow;
	#endif
	mid <<= 8;
	
	// i = 2
	if (va[0] && vb[2]) mid += (uint16_t)va[0] * vb[2];
	if (va[1] && vb[1]) mid += (uint16_t)va[1] * vb[1];
	if (va[2] && vb[0]) mid += (uint16_t)va[2] * vb[0];		
	
	// i = 1
	if (va[0] && vb[1]) low += (uint16_t)va[0] * vb[1];
	if (va[1] && vb[0]) low += (uint16_t)va[1] * vb[0];
	low <<= 8;
	
	// i = 0
	if (va[0] && vb[0]) low += (uint16_t)va[0] * vb[0];
	
	#ifndef FIXMATH_NO_ROUNDING
	low += 0x8000;
	#endif
	mid += (low >> 16);
	
	#ifndef FIXMATH_NO_OVERFLOW
	if (mid & 0x80000000)
		return fix16_overflow;
	#endif
	
	fix16_t result = mid;
	
	/* Figure out the sign of result */
	if ((inArg0 >= 0) != (inArg1 >= 0))
	{
		result = -result;
	}
	
	return result;
}
#endif

#ifndef FIXMATH_NO_OVERFLOW
/* Wrapper around fix16_mul to add saturating arithmetic. */
fix16_t fix16_smul(fix16_t inArg0, fix16_t inArg1)
{
	fix16_t result = fix16_mul(inArg0, inArg1);
	
	if (result == fix16_overflow)
	{
		if ((inArg0 >= 0) == (inArg1 >= 0))
			return fix16_maximum;
		else
			return fix16_minimum;
	}
	
	return result;
}
#endif

/* 32-bit implementation of fix16_div. Fastest version for e.g. ARM Cortex M3.
 * Performs 32-bit divisions repeatedly to reduce the remainder. For this to
 * be efficient, the processor has to have 32-bit hardware division.
 */
#if !defined(FIXMATH_OPTIMIZE_8BIT)
#ifdef __GNUC__
// Count leading zeros, using processor-specific instruction if available.
#define clz(x) (__builtin_clzl(x) - (8 * sizeof(long) - 32))
#else
static uint8_t clz(uint32_t x)
{
	uint8_t result = 0;
	if (x == 0) return 32;
	while (!(x & 0xF0000000)) { result += 4; x <<= 4; }
	while (!(x & 0x80000000)) { result += 1; x <<= 1; }
	return result;
}
#endif

fix16_t fix16_div(fix16_t a, fix16_t b)
{
	// This uses a hardware 32/32 bit division multiple times, until we have
	// computed all the bits in (a<<17)/b. Usually this takes 1-3 iterations.
	
	if (b == 0)
			return fix16_minimum;
	
	uint32_t remainder = (a >= 0) ? a : (-a);
	uint32_t divider = (b >= 0) ? b : (-b);
	uint32_t quotient = 0;
	int bit_pos = 17;
	
	// Kick-start the division a bit.
	// This improves speed in the worst-case scenarios where N and D are large
	// It gets a lower estimate for the result by N/(D >> 17 + 1).
	if (divider & 0xFFF00000)
	{
		uint32_t shifted_div = ((divider >> 17) + 1);
		quotient = remainder / shifted_div;
		remainder -= ((uint64_t)quotient * divider) >> 17;
	}
	
	// If the divider is divisible by 2^n, take advantage of it.
	while (!(divider & 0xF) && bit_pos >= 4)
	{
		divider >>= 4;
		bit_pos -= 4;
	}
	
	while (remainder && bit_pos >= 0)
	{
		// Shift remainder as much as we can without overflowing
		int shift = clz(remainder);
		if (shift > bit_pos) shift = bit_pos;
		remainder <<= shift;
		bit_pos -= shift;
		
		uint32_t div = remainder / divider;
		remainder = remainder % divider;
		quotient += div << bit_pos;

		#ifndef FIXMATH_NO_OVERFLOW
		if (div & ~(0xFFFFFFFF >> bit_pos))
				return fix16_overflow;
		#endif
		
		remainder <<= 1;
		bit_pos--;
	}
	
	#ifndef FIXMATH_NO_ROUNDING
	// Quotient is always positive so rounding is easy
	quotient++;
	#endif
	
	fix16_t result = quotient >> 1;
	
	// Figure out the sign of the result
	if ((a ^ b) & 0x80000000)
	{
		#ifndef FIXMATH_NO_OVERFLOW
		if (result == fix16_minimum)
				return fix16_overflow;
		#endif
		
		result = -result;
	}
	
	return result;
}
#endif

/* Alternative 32-bit implementation of fix16_div. Fastest on e.g. Atmel AVR.
 * This does the division manually, and is therefore good for processors that
 * do not have hardware division.
 */
#if defined(FIXMATH_OPTIMIZE_8BIT)
fix16_t fix16_div(fix16_t a, fix16_t b)
{
	// This uses the basic binary restoring division algorithm.
	// It appears to be faster to do the whole division manually than
	// trying to compose a 64-bit divide out of 32-bit divisions on
	// platforms without hardware divide.
	
	if (b == 0)
		return fix16_minimum;
	
	uint32_t remainder = (a >= 0) ? a : (-a);
	uint32_t divider = (b >= 0) ? b : (-b);

	uint32_t quotient = 0;
	uint32_t bit = 0x10000;
	
	/* The algorithm requires D >= R */
	while (divider < remainder)
	{
		divider <<= 1;
		bit <<= 1;
	}
	
	#ifndef FIXMATH_NO_OVERFLOW
	if (!bit)
		return fix16_overflow;
	#endif
	
	if (divider & 0x80000000)
	{
		// Perform one step manually to avoid overflows later.
		// We know that divider's bottom bit is 0 here.
		if (remainder >= divider)
		{
				quotient |= bit;
				remainder -= divider;
		}
		divider >>= 1;
		bit >>= 1;
	}
	
	/* Main division loop */
	while (bit && remainder)
	{
		if (remainder >= divider)
		{
				quotient |= bit;
				remainder -= divider;
		}
		
		remainder <<= 1;
		bit >>= 1;
	}	 
			
	#ifndef FIXMATH_NO_ROUNDING
	if (remainder >= divider)
	{
		quotient++;
	}
	#endif
	
	fix16_t result = quotient;
	
	/* Figure out the sign of result */
	if ((a ^ b) & 0x80000000)
	{
		#ifndef FIXMATH_NO_OVERFLOW
		if (result == fix16_minimum)
				return fix16_overflow;
		#endif
		
		result = -result;
	}
	
	return result;
}
#endif

#ifndef FIXMATH_NO_OVERFLOW
/* Wrapper around fix16_div to add saturating arithmetic. */
fix16_t fix16_sdiv(fix16_t inArg0, fix16_t inArg1)
{
	fix16_t result = fix16_div(inArg0, inArg1);
	
	if (result == fix16_overflow)
	{
		if ((inArg0 >= 0) == (inArg1 >= 0))
			return fix16_maximum;
		else
			return fix16_minimum;
	}
	
	return result;
}
#endif

fix16_t fix16_mod(fix16_t x, fix16_t y)
{
	#ifdef FIXMATH_OPTIMIZE_8BIT
		/* The reason we do this, rather than use a modulo operator
		 * is that if you don't have a hardware divider, this will result
		 * in faster operations when the angles are close to the bounds. 
		 */
		while(x >=  y) x -= y;
		while(x <= -y) x += y;
	#else
		/* Note that in C90, the sign of result of the modulo operation is
		 * undefined. in C99, it's the same as the dividend (aka numerator).
		 */
		x %= y;
	#endif

	return x;
}


#ifndef FIXMATH_NO_64BIT

fix16_t fix16_lerp8(fix16_t inArg0, fix16_t inArg1, uint8_t inFract)
{
	int64_t tempOut = int64_mul_i32_i32(inArg0, ((1 << 8) - inFract));
	tempOut = int64_add(tempOut, int64_mul_i32_i32(inArg1, inFract));
	tempOut = int64_shift(tempOut, -8);
	return (fix16_t)int64_lo(tempOut);
}

fix16_t fix16_lerp16(fix16_t inArg0, fix16_t inArg1, uint16_t inFract)
{
	int64_t tempOut = int64_mul_i32_i32(inArg0, (((int32_t)1 << 16) - inFract));
	tempOut = int64_add(tempOut, int64_mul_i32_i32(inArg1, inFract));
	tempOut = int64_shift(tempOut, -16);
	return (fix16_t)int64_lo(tempOut);
}

fix16_t fix16_lerp32(fix16_t inArg0, fix16_t inArg1, uint32_t inFract)
{
	int64_t tempOut;
	tempOut  = ((int64_t)inArg0 * (0 - inFract));
	tempOut	+= ((int64_t)inArg1 * inFract);
	tempOut >>= 32;
	return (fix16_t)tempOut;
}
#endif