path: root/src/lib8tion/math8.h

#ifndef __INC_LIB8TION_MATH_H
#define __INC_LIB8TION_MATH_H

#include "scale8.h"

///@ingroup lib8tion

///@defgroup Math Basic math operations
/// Fast, efficient 8-bit math functions specifically
/// designed for high-performance LED programming.
///
/// Because of the AVR(Arduino) and ARM assembly language
/// implementations provided, using these functions often
/// results in smaller and faster code than the equivalent
/// program using plain "C" arithmetic and logic.
///@{


/// add one byte to another, saturating at 0xFF
/// @param i - first byte to add
/// @param j - second byte to add
/// @returns the sum of i & j, capped at 0xFF
LIB8STATIC_ALWAYS_INLINE uint8_t qadd8( uint8_t i, uint8_t j)
{
#if QADD8_C == 1
    unsigned int t = i + j;
    if( t > 255) t = 255;
    return t;
#elif QADD8_AVRASM == 1
    asm volatile(
        /* First, add j to i, conditioning the C flag */
        "add %0, %1    \n\t"

        /* Now test the C flag.
        If C is clear, we branch around a load of 0xFF into i.
        If C is set, we go ahead and load 0xFF into i.
        */
        "brcc L_%=     \n\t"
        "ldi %0, 0xFF  \n\t"
        "L_%=: "
        : "+a" (i)
        : "a"  (j)
    );
    return i;
#elif QADD8_ARM_DSP_ASM == 1
    asm volatile( "uqadd8 %0, %0, %1" : "+r" (i) : "r" (j));
    return i;
#else
#error "No implementation for qadd8 available."
#endif
}

/// Add one byte to another, saturating at 0x7F and -0x80
/// @param i - first byte to add
/// @param j - second byte to add
/// @returns the sum of i & j, capped at 0xFF and -0x80
LIB8STATIC_ALWAYS_INLINE int8_t qadd7( int8_t i, int8_t j)
{
#if QADD7_C == 1
    int16_t t = i + j;
    if( t > 127) t = 127;
    if( t < -128) t = -128;
    return t;
#elif QADD7_AVRASM == 1
    asm volatile(
        /* First, add j to i, conditioning the V flag */
        "add %0, %1    \n\t"

        /* Now test the V flag.
        If V is clear, we are done.
        If V is set, we assume that result is positive and load 0x7F into i.
        */
        "brvc L_%=     \n\t"
        "ldi %0, 0x7F  \n\t"

        /* Now test the S flag.
        If S is clear, our assumption is right.
        If S is set, we load 0x80 into i.
        */
        "brge L_%=     \n\t"
        "ldi %0, 0x80  \n\t"
        "L_%=: "
        : "+a" (i)
        : "a"  (j)
    );
    return i;
#elif QADD7_ARM_DSP_ASM == 1
    asm volatile( "qadd8 %0, %0, %1" : "+r" (i) : "r" (j));
    return i;
#else
#error "No implementation for qadd7 available."
#endif
}

/// subtract one byte from another, saturating at 0x00
/// @returns i - j with a floor of 0
LIB8STATIC_ALWAYS_INLINE uint8_t qsub8( uint8_t i, uint8_t j)
{
#if QSUB8_C == 1
    int t = i - j;
    if( t < 0) t = 0;
    return t;
#elif QSUB8_AVRASM == 1

    asm volatile(
        /* First, subtract j from i, conditioning the C flag */
        "sub %0, %1    \n\t"

        /* Now test the C flag.
        If C is clear, we branch around a load of 0x00 into i.
        If C is set, we go ahead and load 0x00 into i.
        */
        "brcc L_%=     \n\t"
        "ldi %0, 0x00  \n\t"
        "L_%=: "
        : "+a" (i)
        : "a"  (j)
    );
    return i;
#else
#error "No implementation for qsub8 available."
#endif
}

/// add one byte to another, with one byte result
LIB8STATIC_ALWAYS_INLINE uint8_t add8( uint8_t i, uint8_t j)
{
#if ADD8_C == 1
    int t = i + j;
    return t;
#elif ADD8_AVRASM == 1
    // Add j to i, period.
    asm volatile( "add %0, %1" : "+a" (i) : "a" (j));
    return i;
#else
#error "No implementation for add8 available."
#endif
}

/// add one byte to two bytes, with two bytes result
LIB8STATIC_ALWAYS_INLINE uint16_t add8to16( uint8_t i, uint16_t j)
{
#if ADD8_C == 1
    uint16_t t = i + j;
    return t;
#elif ADD8_AVRASM == 1
    // Add i(one byte) to j(two bytes)
    asm volatile(
        "add %A[j], %[i]              \n\t"
        "adc %B[j], __zero_reg__      \n\t"
        : [j] "+a" (j)
        : [i] "a"  (i)
    );
    return i;
#else
#error "No implementation for add8to16 available."
#endif
}


/// subtract one byte from another, 8-bit result
LIB8STATIC_ALWAYS_INLINE uint8_t sub8( uint8_t i, uint8_t j)
{
#if SUB8_C == 1
    int t = i - j;
    return t;
#elif SUB8_AVRASM == 1
    // Subtract j from i, period.
    asm volatile( "sub %0, %1" : "+a" (i) : "a" (j));
    return i;
#else
#error "No implementation for sub8 available."
#endif
}

/// Calculate an integer average of two unsigned
///       8-bit integer values (uint8_t).
///       Fractional results are rounded down, e.g. avg8(20,41) = 30
LIB8STATIC_ALWAYS_INLINE uint8_t avg8( uint8_t i, uint8_t j)
{
#if AVG8_C == 1
    return (i + j) >> 1;
#elif AVG8_AVRASM == 1
    asm volatile(
        /* First, add j to i, 9th bit overflows into C flag */
        "add %0, %1    \n\t"
        /* Divide by two, moving C flag into high 8th bit */
        "ror %0        \n\t"
        : "+a" (i)
        : "a"  (j)
    );
    return i;
#else
#error "No implementation for avg8 available."
#endif
}

/// Calculate an integer average of two unsigned
///       8-bit integer values (uint8_t).
///       Fractional results are rounded up, e.g. avg8(20,41) = 31
LIB8STATIC_ALWAYS_INLINE uint8_t avg8r( uint8_t i, uint8_t j)
{
#if AVG8_C == 1
    return (i + j + 1) >> 1;
#elif AVG8_AVRASM == 1
    asm volatile(
        /* First, add j to i, 9th bit overflows into C flag */
        "add %0, %1          \n\t"
        /* Divide by two, moving C flag into high 8th bit, old 1st bit now in C */
        "ror %0              \n\t"
        /* Add C flag */
        "adc %0, __zero_reg__\n\t"
        : "+a" (i)
        : "a"  (j)
    );
    return i;
#else
#error "No implementation for avg8r available."
#endif
}

/// Calculate an integer average of two unsigned
///       16-bit integer values (uint16_t).
///       Fractional results are rounded down, e.g. avg16(20,41) = 30
LIB8STATIC_ALWAYS_INLINE uint16_t avg16( uint16_t i, uint16_t j)
{
#if AVG16_C == 1
    return (uint32_t)((uint32_t)(i) + (uint32_t)(j)) >> 1;
#elif AVG16_AVRASM == 1
    asm volatile(
        /* First, add jLo (heh) to iLo, 9th bit overflows into C flag */
        "add %A[i], %A[j]    \n\t"
        /* Now, add C + jHi to iHi, 17th bit overflows into C flag */
        "adc %B[i], %B[j]    \n\t"
        /* Divide iHi by two, moving C flag into high 16th bit, old 9th bit now in C */
        "ror %B[i]        \n\t"
        /* Divide iLo by two, moving C flag into high 8th bit */
        "ror %A[i]        \n\t"
        : [i] "+a" (i)
        : [j] "a"  (j)
    );
    return i;
#else
#error "No implementation for avg16 available."
#endif
}

/// Calculate an integer average of two unsigned
///       16-bit integer values (uint16_t).
///       Fractional results are rounded up, e.g. avg16(20,41) = 31
LIB8STATIC_ALWAYS_INLINE uint16_t avg16r( uint16_t i, uint16_t j)
{
#if AVG16_C == 1
    return (uint32_t)((uint32_t)(i) + (uint32_t)(j) + 1) >> 1;
#elif AVG16_AVRASM == 1
    asm volatile(
        /* First, add jLo (heh) to iLo, 9th bit overflows into C flag */
        "add %A[i], %A[j]    \n\t"
        /* Now, add C + jHi to iHi, 17th bit overflows into C flag */
        "adc %B[i], %B[j]    \n\t"
        /* Divide iHi by two, moving C flag into high 16th bit, old 9th bit now in C */
        "ror %B[i]        \n\t"
        /* Divide iLo by two, moving C flag into high 8th bit, old 1st bit now in C */
        "ror %A[i]        \n\t"
        /* Add C flag */
        "adc %A[i], __zero_reg__\n\t"
        "adc %B[i], __zero_reg__\n\t"
        : [i] "+a" (i)
        : [j] "a"  (j)
    );
    return i;
#else
#error "No implementation for avg16r available."
#endif
}


/// Calculate an integer average of two signed 7-bit
///       integers (int8_t)
///       If the first argument is even, result is rounded down.
///       If the first argument is odd, result is rounded up.
LIB8STATIC_ALWAYS_INLINE int8_t avg7( int8_t i, int8_t j)
{
#if AVG7_C == 1
    return (i>>1) + (j>>1) + (i & 0x1);
#elif AVG7_AVRASM == 1
    asm volatile(
        "asr %1        \n\t"
        "asr %0        \n\t"
        "adc %0, %1    \n\t"
        : "+a" (i)
        : "a"  (j)
    );
    return i;
#else
#error "No implementation for avg7 available."
#endif
}

/// Calculate an integer average of two signed 15-bit
///       integers (int16_t)
///       If the first argument is even, result is rounded down.
///       If the first argument is odd, result is rounded up.
LIB8STATIC_ALWAYS_INLINE int16_t avg15( int16_t i, int16_t j)
{
#if AVG15_C == 1
    return (i>>1) + (j>>1) + (i & 0x1);
#elif AVG15_AVRASM == 1
    asm volatile(
        /* first divide j by 2, throwing away lowest bit */
        "asr %B[j]          \n\t"
        "ror %A[j]          \n\t"
        /* now divide i by 2, with lowest bit going into C */
        "asr %B[i]          \n\t"
        "ror %A[i]          \n\t"
        /* add j + C to i */
        "adc %A[i], %A[j]   \n\t"
        "adc %B[i], %B[j]   \n\t"
        : [i] "+a" (i)
        : [j] "a"  (j)
    );
    return i;
#else
#error "No implementation for avg15 available."
#endif
}


///       Calculate the remainder of one unsigned 8-bit
///       value divided by anoter, aka A % M.
///       Implemented by repeated subtraction, which is
///       very compact, and very fast if A is 'probably'
///       less than M.  If A is a large multiple of M,
///       the loop has to execute multiple times.  However,
///       even in that case, the loop is only two
///       instructions long on AVR, i.e., quick.
LIB8STATIC_ALWAYS_INLINE uint8_t mod8( uint8_t a, uint8_t m)
{
#if defined(__AVR__)
    asm volatile (
        "L_%=:  sub %[a],%[m]    \n\t"
        "       brcc L_%=        \n\t"
        "       add %[a],%[m]    \n\t"
        : [a] "+r" (a)
        : [m] "r"  (m)
    );
#else
    while( a >= m) a -= m;
#endif
    return a;
}

///          Add two numbers, and calculate the modulo
///          of the sum and a third number, M.
///          In other words, it returns (A+B) % M.
///          It is designed as a compact mechanism for
///          incrementing a 'mode' switch and wrapping
///          around back to 'mode 0' when the switch
///          goes past the end of the available range.
///          e.g. if you have seven modes, this switches
///          to the next one and wraps around if needed:
///            mode = addmod8( mode, 1, 7);
///LIB8STATIC_ALWAYS_INLINESee 'mod8' for notes on performance.
LIB8STATIC uint8_t addmod8( uint8_t a, uint8_t b, uint8_t m)
{
#if defined(__AVR__)
    asm volatile (
        "       add %[a],%[b]    \n\t"
        "L_%=:  sub %[a],%[m]    \n\t"
        "       brcc L_%=        \n\t"
        "       add %[a],%[m]    \n\t"
        : [a] "+r" (a)
        : [b] "r"  (b), [m] "r" (m)
    );
#else
    a += b;
    while( a >= m) a -= m;
#endif
    return a;
}

///          Subtract two numbers, and calculate the modulo
///          of the difference and a third number, M.
///          In other words, it returns (A-B) % M.
///LIB8STATIC_ALWAYS_INLINESee 'mod8' for notes on performance.
LIB8STATIC uint8_t submod8( uint8_t a, uint8_t b, uint8_t m)
{
#if defined(__AVR__)
    asm volatile (
        "       sub %[a],%[b]    \n\t"
        "L_%=:  sub %[a],%[m]    \n\t"
        "       brcc L_%=        \n\t"
        "       add %[a],%[m]    \n\t"
        : [a] "+r" (a)
        : [b] "r"  (b), [m] "r" (m)
    );
#else
    a -= b;
    while( a >= m) a -= m;
#endif
    return a;
}

/// 8x8 bit multiplication, with 8 bit result
LIB8STATIC_ALWAYS_INLINE uint8_t mul8( uint8_t i, uint8_t j)
{
#if MUL8_C == 1
    return ((int)i * (int)(j) ) & 0xFF;
#elif MUL8_AVRASM == 1
    asm volatile(
        /* Multiply 8-bit i * 8-bit j, giving 16-bit r1,r0 */
        "mul %0, %1          \n\t"
        /* Extract the LOW 8-bits (r0) */
        "mov %0, r0          \n\t"
        /* Restore r1 to "0"; it's expected to always be that */
        "clr __zero_reg__    \n\t"
        : "+a" (i)
        : "a"  (j)
        : "r0", "r1"
    );
    return i;
#else
#error "No implementation for mul8 available."
#endif
}


/// saturating 8x8 bit multiplication, with 8 bit result
/// @returns the product of i * j, capping at 0xFF
LIB8STATIC_ALWAYS_INLINE uint8_t qmul8( uint8_t i, uint8_t j)
{
#if QMUL8_C == 1
    int p = ((int)i * (int)(j) );
    if( p > 255) p = 255;
    return p;
#elif QMUL8_AVRASM == 1
    asm volatile(
        /* Multiply 8-bit i * 8-bit j, giving 16-bit r1,r0 */
        "  mul %0, %1          \n\t"
        /* Extract the LOW 8-bits (r0) */
        "  mov %0, r0          \n\t"
        /* If high byte of result is zero, all is well. */
        "  tst r1              \n\t"
        "  breq Lnospill_%=    \n\t"
        /* If high byte of result > 0, saturate to 0xFF */
        "  ldi %0, 0xFF         \n\t"
        "Lnospill_%=:          \n\t"
        /* Restore r1 to "0"; it's expected to always be that */
        "  clr __zero_reg__    \n\t"
        : "+a" (i)
        : "a"  (j)
        : "r0", "r1"
    );
    return i;
#else
#error "No implementation for qmul8 available."
#endif
}


/// take abs() of a signed 8-bit uint8_t
LIB8STATIC_ALWAYS_INLINE int8_t abs8( int8_t i)
{
#if ABS8_C == 1
    if( i < 0) i = -i;
    return i;
#elif ABS8_AVRASM == 1
    asm volatile(
        /* First, check the high bit, and prepare to skip if it's clear */
        "sbrc %0, 7 \n"

        /* Negate the value */
        "neg %0     \n"

        : "+r" (i) : "r" (i)
    );
    return i;
#else
#error "No implementation for abs8 available."
#endif
}

///         square root for 16-bit integers
///         About three times faster and five times smaller
///         than Arduino's general sqrt on AVR.
LIB8STATIC uint8_t sqrt16(uint16_t x)
{
    if( x <= 1) {
        return x;
    }

    uint8_t low = 1; // lower bound
    uint8_t hi, mid;

    if( x > 7904) {
        hi = 255;
    } else {
        hi = (x >> 5) + 8; // initial estimate for upper bound
    }

    do {
        mid = (low + hi) >> 1;
        if ((uint16_t)(mid * mid) > x) {
            hi = mid - 1;
        } else {
            if( mid == 255) {
                return 255;
            }
            low = mid + 1;
        }
    } while (hi >= low);

    return low - 1;
}

/// blend a variable proproportion(0-255) of one byte to another
/// @param a - the starting byte value
/// @param b - the byte value to blend toward
/// @param amountOfB - the proportion (0-255) of b to blend
/// @returns a byte value between a and b, inclusive
#if (FASTLED_BLEND_FIXED == 1)
LIB8STATIC uint8_t blend8( uint8_t a, uint8_t b, uint8_t amountOfB)
{

    // The BLEND_FIXED formula is
    //
    //   result = (  A*(amountOfA) + B*(amountOfB)              )/ 256
    //
    // …where amountOfA = 255-amountOfB.
    //
    // This formula will never return 255, which is why the BLEND_FIXED + SCALE8_FIXED version is
    //
    //   result = (  A*(amountOfA) + A + B*(amountOfB) + B      ) / 256
    //
    // We can rearrange this formula for some great optimisations.
    //
    //   result = (  A*(amountOfA) + A + B*(amountOfB) + B      ) / 256
    //          = (  A*(255-amountOfB) + A + B*(amountOfB) + B  ) / 256
    //          = (  A*(256-amountOfB) + B*(amountOfB) + B      ) / 256
    //          = (  A*256 + B + B*(amountOfB) - A*(amountOfB)  ) / 256  // this is the version used in SCALE8_FIXED AVR below
    //          = (  A*256 + B + (B-A)*(amountOfB)              ) / 256  // this is the version used in SCALE8_FIXED C below

    uint16_t partial;
    uint8_t result;

#if BLEND8_C == 1

#   if (FASTLED_SCALE8_FIXED == 1)
    partial = (a << 8) | b; // A*256 + B

    // on many platforms this compiles to a single multiply of (B-A) * amountOfB
    partial += (b * amountOfB);
    partial -= (a * amountOfB);

#   else
    uint8_t amountOfA = 255 - amountOfB;

    // on the other hand, this compiles to two multiplies, and gives the "wrong" answer :]
    partial = (a * amountOfA);
    partial += (b * amountOfB);
#   endif
    
    result = partial >> 8;
    
    return result;

#elif BLEND8_AVRASM == 1

#   if (FASTLED_SCALE8_FIXED == 1)

    // 1 or 2 cycles depending on how the compiler optimises
    partial = (a << 8) | b;

    // 7 cycles
    asm volatile (
        "  mul %[a], %[amountOfB]        \n\t"
        "  sub %A[partial], r0           \n\t"
        "  sbc %B[partial], r1           \n\t"
        "  mul %[b], %[amountOfB]        \n\t"
        "  add %A[partial], r0           \n\t"
        "  adc %B[partial], r1           \n\t"
        "  clr __zero_reg__              \n\t"
        : [partial] "+r" (partial)
        : [amountOfB] "r" (amountOfB),
          [a] "r" (a),
          [b] "r" (b)
        : "r0", "r1"
    );

#   else

    // non-SCALE8-fixed version

    // 7 cycles
    asm volatile (
        /* partial = b * amountOfB */
        "  mul %[b], %[amountOfB]        \n\t"
        "  movw %A[partial], r0          \n\t"

        /* amountOfB (aka amountOfA) = 255 - amountOfB */
        "  com %[amountOfB]              \n\t"

        /* partial += a * amountOfB (aka amountOfA) */
        "  mul %[a], %[amountOfB]        \n\t"

        "  add %A[partial], r0           \n\t"
        "  adc %B[partial], r1           \n\t"
                  
        "  clr __zero_reg__              \n\t"
                        
        : [partial] "=r" (partial),
          [amountOfB] "+a" (amountOfB)
        : [a] "a" (a),
          [b] "a" (b)
        : "r0", "r1"
    );

#   endif
    
    result = partial >> 8;
    
    return result;
    
#else
#   error "No implementation for blend8 available."
#endif
}

#else
LIB8STATIC uint8_t blend8( uint8_t a, uint8_t b, uint8_t amountOfB)
{
    // This version loses precision in the integer math
    // and can actually return results outside of the range
    // from a to b.  Its use is not recommended.
    uint8_t result;
    uint8_t amountOfA = 255 - amountOfB;
    result = scale8_LEAVING_R1_DIRTY( a, amountOfA)
           + scale8_LEAVING_R1_DIRTY( b, amountOfB);
    cleanup_R1();
    return result;
}
#endif


///@}
#endif