raze/source/build/src/fix16.cpp

#include "fix16.h"
#include "fix16_int64.h"

/* 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_MAX : FIX16_MIN;

	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_MAX : FIX16_MIN;

	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.
 */

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
}

#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_MAX;
		else
			return FIX16_MIN;
	}

	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.
 */
#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_MIN;

	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_MIN)
				return FIX16_OVERFLOW;
		#endif

		result = -result;
	}

	return result;
}

#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_MAX;
		else
			return FIX16_MIN;
	}

	return result;
}
#endif

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;
}