553 lines
15 KiB
C
553 lines
15 KiB
C
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#ifndef __INC_LIB8TION_MATH_H
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#define __INC_LIB8TION_MATH_H
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#include "scale8.h"
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///@ingroup lib8tion
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///@defgroup Math Basic math operations
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/// Fast, efficient 8-bit math functions specifically
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/// designed for high-performance LED programming.
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///
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/// Because of the AVR(Arduino) and ARM assembly language
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/// implementations provided, using these functions often
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/// results in smaller and faster code than the equivalent
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/// program using plain "C" arithmetic and logic.
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///@{
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/// add one byte to another, saturating at 0xFF
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/// @param i - first byte to add
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/// @param j - second byte to add
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/// @returns the sum of i & j, capped at 0xFF
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LIB8STATIC_ALWAYS_INLINE uint8_t qadd8( uint8_t i, uint8_t j)
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{
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#if QADD8_C == 1
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uint16_t t = i + j;
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if (t > 255) t = 255;
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return t;
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#elif QADD8_AVRASM == 1
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asm volatile(
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/* First, add j to i, conditioning the C flag */
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"add %0, %1 \n\t"
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/* Now test the C flag.
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If C is clear, we branch around a load of 0xFF into i.
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If C is set, we go ahead and load 0xFF into i.
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*/
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"brcc L_%= \n\t"
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"ldi %0, 0xFF \n\t"
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"L_%=: "
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: "+a" (i)
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: "a" (j) );
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return i;
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#elif QADD8_ARM_DSP_ASM == 1
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asm volatile( "uqadd8 %0, %0, %1" : "+r" (i) : "r" (j));
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return i;
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#else
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#error "No implementation for qadd8 available."
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#endif
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}
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/// Add one byte to another, saturating at 0x7F
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/// @param i - first byte to add
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/// @param j - second byte to add
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/// @returns the sum of i & j, capped at 0xFF
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LIB8STATIC_ALWAYS_INLINE int8_t qadd7( int8_t i, int8_t j)
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{
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#if QADD7_C == 1
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int16_t t = i + j;
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if (t > 127) t = 127;
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return t;
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#elif QADD7_AVRASM == 1
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asm volatile(
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/* First, add j to i, conditioning the V flag */
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"add %0, %1 \n\t"
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/* Now test the V flag.
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If V is clear, we branch around a load of 0x7F into i.
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If V is set, we go ahead and load 0x7F into i.
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*/
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"brvc L_%= \n\t"
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"ldi %0, 0x7F \n\t"
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"L_%=: "
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: "+a" (i)
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: "a" (j) );
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return i;
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#elif QADD7_ARM_DSP_ASM == 1
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asm volatile( "qadd8 %0, %0, %1" : "+r" (i) : "r" (j));
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return i;
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#else
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#error "No implementation for qadd7 available."
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#endif
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}
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/// subtract one byte from another, saturating at 0x00
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/// @returns i - j with a floor of 0
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LIB8STATIC_ALWAYS_INLINE uint8_t qsub8( uint8_t i, uint8_t j)
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{
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#if QSUB8_C == 1
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int16_t t = i - j;
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if (t < 0) t = 0;
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return t;
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#elif QSUB8_AVRASM == 1
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asm volatile(
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/* First, subtract j from i, conditioning the C flag */
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"sub %0, %1 \n\t"
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/* Now test the C flag.
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If C is clear, we branch around a load of 0x00 into i.
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If C is set, we go ahead and load 0x00 into i.
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*/
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"brcc L_%= \n\t"
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"ldi %0, 0x00 \n\t"
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"L_%=: "
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: "+a" (i)
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: "a" (j) );
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return i;
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#else
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#error "No implementation for qsub8 available."
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#endif
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}
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/// add one byte to another, with one byte result
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LIB8STATIC_ALWAYS_INLINE uint8_t add8( uint8_t i, uint8_t j)
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{
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#if ADD8_C == 1
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uint16_t t = i + j;
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return t;
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#elif ADD8_AVRASM == 1
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// Add j to i, period.
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asm volatile( "add %0, %1" : "+a" (i) : "a" (j));
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return i;
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#else
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#error "No implementation for add8 available."
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#endif
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}
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/// add one byte to another, with one byte result
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LIB8STATIC_ALWAYS_INLINE uint16_t add8to16( uint8_t i, uint16_t j)
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{
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#if ADD8_C == 1
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uint16_t t = i + j;
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return t;
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#elif ADD8_AVRASM == 1
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// Add i(one byte) to j(two bytes)
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asm volatile( "add %A[j], %[i] \n\t"
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"adc %B[j], __zero_reg__ \n\t"
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: [j] "+a" (j)
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: [i] "a" (i)
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);
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return i;
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#else
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#error "No implementation for add8to16 available."
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#endif
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}
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/// subtract one byte from another, 8-bit result
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LIB8STATIC_ALWAYS_INLINE uint8_t sub8( uint8_t i, uint8_t j)
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{
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#if SUB8_C == 1
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int16_t t = i - j;
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return t;
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#elif SUB8_AVRASM == 1
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// Subtract j from i, period.
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asm volatile( "sub %0, %1" : "+a" (i) : "a" (j));
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return i;
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#else
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#error "No implementation for sub8 available."
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#endif
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}
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/// Calculate an integer average of two unsigned
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/// 8-bit integer values (uint8_t).
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/// Fractional results are rounded down, e.g. avg8(20,41) = 30
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LIB8STATIC_ALWAYS_INLINE uint8_t avg8( uint8_t i, uint8_t j)
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{
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#if AVG8_C == 1
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return (i + j) >> 1;
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#elif AVG8_AVRASM == 1
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asm volatile(
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/* First, add j to i, 9th bit overflows into C flag */
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"add %0, %1 \n\t"
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/* Divide by two, moving C flag into high 8th bit */
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"ror %0 \n\t"
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: "+a" (i)
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: "a" (j) );
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return i;
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#else
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#error "No implementation for avg8 available."
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#endif
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}
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/// Calculate an integer average of two unsigned
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/// 16-bit integer values (uint16_t).
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/// Fractional results are rounded down, e.g. avg16(20,41) = 30
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LIB8STATIC_ALWAYS_INLINE uint16_t avg16( uint16_t i, uint16_t j)
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{
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#if AVG16_C == 1
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return (uint32_t)((uint32_t)(i) + (uint32_t)(j)) >> 1;
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#elif AVG16_AVRASM == 1
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asm volatile(
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/* First, add jLo (heh) to iLo, 9th bit overflows into C flag */
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"add %A[i], %A[j] \n\t"
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/* Now, add C + jHi to iHi, 17th bit overflows into C flag */
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"adc %B[i], %B[j] \n\t"
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/* Divide iHi by two, moving C flag into high 16th bit, old 9th bit now in C */
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"ror %B[i] \n\t"
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/* Divide iLo by two, moving C flag into high 8th bit */
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"ror %A[i] \n\t"
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: [i] "+a" (i)
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: [j] "a" (j) );
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return i;
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#else
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#error "No implementation for avg16 available."
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#endif
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}
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/// Calculate an integer average of two signed 7-bit
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/// integers (int8_t)
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/// If the first argument is even, result is rounded down.
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/// If the first argument is odd, result is result up.
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LIB8STATIC_ALWAYS_INLINE int8_t avg7( int8_t i, int8_t j)
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{
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#if AVG7_C == 1
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return ((i + j) >> 1) + (i & 0x1);
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#elif AVG7_AVRASM == 1
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asm volatile(
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"asr %1 \n\t"
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"asr %0 \n\t"
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"adc %0, %1 \n\t"
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: "+a" (i)
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: "a" (j) );
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return i;
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#else
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#error "No implementation for avg7 available."
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#endif
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}
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/// Calculate an integer average of two signed 15-bit
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/// integers (int16_t)
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/// If the first argument is even, result is rounded down.
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/// If the first argument is odd, result is result up.
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LIB8STATIC_ALWAYS_INLINE int16_t avg15( int16_t i, int16_t j)
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{
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#if AVG15_C == 1
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return ((int32_t)((int32_t)(i) + (int32_t)(j)) >> 1) + (i & 0x1);
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#elif AVG15_AVRASM == 1
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asm volatile(
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/* first divide j by 2, throwing away lowest bit */
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"asr %B[j] \n\t"
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"ror %A[j] \n\t"
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/* now divide i by 2, with lowest bit going into C */
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"asr %B[i] \n\t"
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"ror %A[i] \n\t"
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/* add j + C to i */
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"adc %A[i], %A[j] \n\t"
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"adc %B[i], %B[j] \n\t"
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: [i] "+a" (i)
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: [j] "a" (j) );
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return i;
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#else
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#error "No implementation for avg15 available."
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#endif
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}
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/// Calculate the remainder of one unsigned 8-bit
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/// value divided by anoter, aka A % M.
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/// Implemented by repeated subtraction, which is
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/// very compact, and very fast if A is 'probably'
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/// less than M. If A is a large multiple of M,
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/// the loop has to execute multiple times. However,
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/// even in that case, the loop is only two
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/// instructions long on AVR, i.e., quick.
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LIB8STATIC_ALWAYS_INLINE uint8_t mod8( uint8_t a, uint8_t m)
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{
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#if defined(__AVR__)
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asm volatile (
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"L_%=: sub %[a],%[m] \n\t"
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" brcc L_%= \n\t"
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" add %[a],%[m] \n\t"
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: [a] "+r" (a)
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: [m] "r" (m)
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);
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#else
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while( a >= m) a -= m;
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#endif
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return a;
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}
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/// Add two numbers, and calculate the modulo
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/// of the sum and a third number, M.
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/// In other words, it returns (A+B) % M.
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/// It is designed as a compact mechanism for
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/// incrementing a 'mode' switch and wrapping
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/// around back to 'mode 0' when the switch
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/// goes past the end of the available range.
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/// e.g. if you have seven modes, this switches
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/// to the next one and wraps around if needed:
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/// mode = addmod8( mode, 1, 7);
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///LIB8STATIC_ALWAYS_INLINESee 'mod8' for notes on performance.
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LIB8STATIC uint8_t addmod8( uint8_t a, uint8_t b, uint8_t m)
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{
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#if defined(__AVR__)
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asm volatile (
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" add %[a],%[b] \n\t"
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"L_%=: sub %[a],%[m] \n\t"
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" brcc L_%= \n\t"
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" add %[a],%[m] \n\t"
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: [a] "+r" (a)
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: [b] "r" (b), [m] "r" (m)
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);
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#else
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a += b;
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while( a >= m) a -= m;
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#endif
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return a;
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}
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/// Subtract two numbers, and calculate the modulo
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/// of the difference and a third number, M.
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/// In other words, it returns (A-B) % M.
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/// It is designed as a compact mechanism for
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/// incrementing a 'mode' switch and wrapping
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/// around back to 'mode 0' when the switch
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/// goes past the end of the available range.
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/// e.g. if you have seven modes, this switches
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/// to the next one and wraps around if needed:
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/// mode = addmod8( mode, 1, 7);
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///LIB8STATIC_ALWAYS_INLINESee 'mod8' for notes on performance.
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LIB8STATIC uint8_t submod8( uint8_t a, uint8_t b, uint8_t m)
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{
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#if defined(__AVR__)
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asm volatile (
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" sub %[a],%[b] \n\t"
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"L_%=: sub %[a],%[m] \n\t"
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" brcc L_%= \n\t"
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" add %[a],%[m] \n\t"
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: [a] "+r" (a)
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: [b] "r" (b), [m] "r" (m)
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);
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#else
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a -= b;
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while( a >= m) a -= m;
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#endif
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return a;
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}
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/// 8x8 bit multiplication, with 8 bit result
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LIB8STATIC_ALWAYS_INLINE uint8_t mul8( uint8_t i, uint8_t j)
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{
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#if MUL8_C == 1
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return ((uint16_t)i * (uint16_t)(j) ) & 0xFF;
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#elif MUL8_AVRASM == 1
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asm volatile(
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/* Multiply 8-bit i * 8-bit j, giving 16-bit r1,r0 */
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"mul %0, %1 \n\t"
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/* Extract the LOW 8-bits (r0) */
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"mov %0, r0 \n\t"
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/* 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 = ((uint16_t)i * (uint16_t)(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"
|
||
|
|
/* 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 low byte to 0xFF */
|
||
|
|
" ldi %0,0xFF \n\t"
|
||
|
|
" rjmp Ldone_%= \n\t"
|
||
|
|
"Lnospill_%=: \n\t"
|
||
|
|
/* Extract the LOW 8-bits (r0) */
|
||
|
|
" mov %0, r0 \n\t"
|
||
|
|
"Ldone_%=: \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)
|
||
|
|
{
|
||
|
|
#if BLEND8_C == 1
|
||
|
|
uint16_t partial;
|
||
|
|
uint8_t result;
|
||
|
|
|
||
|
|
uint8_t amountOfA = 255 - amountOfB;
|
||
|
|
|
||
|
|
partial = (a * amountOfA);
|
||
|
|
#if (FASTLED_SCALE8_FIXED == 1)
|
||
|
|
partial += a;
|
||
|
|
//partial = add8to16( a, partial);
|
||
|
|
#endif
|
||
|
|
|
||
|
|
partial += (b * amountOfB);
|
||
|
|
#if (FASTLED_SCALE8_FIXED == 1)
|
||
|
|
partial += b;
|
||
|
|
//partial = add8to16( b, partial);
|
||
|
|
#endif
|
||
|
|
|
||
|
|
result = partial >> 8;
|
||
|
|
|
||
|
|
return result;
|
||
|
|
|
||
|
|
#elif BLEND8_AVRASM == 1
|
||
|
|
uint16_t partial;
|
||
|
|
uint8_t result;
|
||
|
|
|
||
|
|
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"
|
||
|
|
|
||
|
|
#if (FASTLED_SCALE8_FIXED == 1)
|
||
|
|
/* partial += a */
|
||
|
|
" add %A[partial], %[a] \n\t"
|
||
|
|
" adc %B[partial], __zero_reg__ \n\t"
|
||
|
|
|
||
|
|
// partial += b
|
||
|
|
" add %A[partial], %[b] \n\t"
|
||
|
|
" adc %B[partial], __zero_reg__ \n\t"
|
||
|
|
#endif
|
||
|
|
|
||
|
|
: [partial] "=r" (partial),
|
||
|
|
[amountOfB] "+a" (amountOfB)
|
||
|
|
: [a] "a" (a),
|
||
|
|
[b] "a" (b)
|
||
|
|
: "r0", "r1"
|
||
|
|
);
|
||
|
|
|
||
|
|
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
|