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David Gwilliam
2026-02-12 00:45:31 -08:00
commit 5f168f370b
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libraries/FastLED/src/fl/ease.cpp Normal file
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#ifndef FASTLED_INTERNAL
#define FASTLED_INTERNAL
#endif
#include "FastLED.h"
#include "fl/ease.h"
#include "lib8tion.h" // This is the problematic header that's hard to include
#include "fl/map_range.h"
#include "lib8tion/intmap.h"
#include "fl/sin32.h"
#include "fl/int.h"
namespace fl {
// Gamma 2.8 lookup table for 8-bit to 16-bit gamma correction
// This table converts linear 8-bit values to gamma-corrected 16-bit values
// using a gamma curve of 2.8 (commonly used for LED brightness correction)
const u16 gamma_2_8[256] FL_PROGMEM = {
0, 0, 0, 1, 1, 2, 4, 6, 8, 11,
14, 18, 23, 29, 35, 41, 49, 57, 67, 77,
88, 99, 112, 126, 141, 156, 173, 191, 210, 230,
251, 274, 297, 322, 348, 375, 404, 433, 464, 497,
531, 566, 602, 640, 680, 721, 763, 807, 853, 899,
948, 998, 1050, 1103, 1158, 1215, 1273, 1333, 1394, 1458,
1523, 1590, 1658, 1729, 1801, 1875, 1951, 2029, 2109, 2190,
2274, 2359, 2446, 2536, 2627, 2720, 2816, 2913, 3012, 3114,
3217, 3323, 3431, 3541, 3653, 3767, 3883, 4001, 4122, 4245,
4370, 4498, 4627, 4759, 4893, 5030, 5169, 5310, 5453, 5599,
5747, 5898, 6051, 6206, 6364, 6525, 6688, 6853, 7021, 7191,
7364, 7539, 7717, 7897, 8080, 8266, 8454, 8645, 8838, 9034,
9233, 9434, 9638, 9845, 10055, 10267, 10482, 10699, 10920, 11143,
11369, 11598, 11829, 12064, 12301, 12541, 12784, 13030, 13279, 13530,
13785, 14042, 14303, 14566, 14832, 15102, 15374, 15649, 15928, 16209,
16493, 16781, 17071, 17365, 17661, 17961, 18264, 18570, 18879, 19191,
19507, 19825, 20147, 20472, 20800, 21131, 21466, 21804, 22145, 22489,
22837, 23188, 23542, 23899, 24260, 24625, 24992, 25363, 25737, 26115,
26496, 26880, 27268, 27659, 28054, 28452, 28854, 29259, 29667, 30079,
30495, 30914, 31337, 31763, 32192, 32626, 33062, 33503, 33947, 34394,
34846, 35300, 35759, 36221, 36687, 37156, 37629, 38106, 38586, 39071,
39558, 40050, 40545, 41045, 41547, 42054, 42565, 43079, 43597, 44119,
44644, 45174, 45707, 46245, 46786, 47331, 47880, 48432, 48989, 49550,
50114, 50683, 51255, 51832, 52412, 52996, 53585, 54177, 54773, 55374,
55978, 56587, 57199, 57816, 58436, 59061, 59690, 60323, 60960, 61601,
62246, 62896, 63549, 64207, 64869, 65535};
// 8-bit easing functions
u8 easeInQuad8(u8 i) {
// Simple quadratic ease-in: i^2 scaled to 8-bit range
// Using scale8(i, i) which computes (i * i) / 255
return scale8(i, i);
}
u8 easeInOutQuad8(u8 i) {
constexpr u16 MAX = 0xFF; // 255
constexpr u16 HALF = (MAX + 1) >> 1; // 128
constexpr u16 DENOM = MAX; // divisor for scaling
constexpr u16 ROUND = DENOM >> 1; // for rounding
if (i < HALF) {
// first half: y = 2·(i/MAX)² → y_i = 2·i² / MAX
u32 t = i;
u32 num = 2 * t * t + ROUND; // 2*i², +half for rounding
return u8(num / DENOM);
} else {
// second half: y = 1 − 2·(1−i/MAX)²
// → y_i = MAX − (2·(MAX−i)² / MAX)
u32 d = MAX - i;
u32 num = 2 * d * d + ROUND; // 2*(MAX−i)², +half for rounding
return u8(MAX - (num / DENOM));
}
}
u8 easeInOutCubic8(u8 i) {
constexpr u16 MAX = 0xFF; // 255
constexpr u16 HALF = (MAX + 1) >> 1; // 128
constexpr u32 DENOM = (u32)MAX * MAX; // 255*255 = 65025
constexpr u32 ROUND = DENOM >> 1; // for rounding
if (i < HALF) {
// first half: y = 4·(i/MAX)³ → y_i = 4·i³ / MAX²
u32 ii = i;
u32 cube = ii * ii * ii; // i³
u32 num = 4 * cube + ROUND; // 4·i³, +half denom for rounding
return u8(num / DENOM);
} else {
// second half: y = 1 − ((−2·t+2)³)/2
// where t = i/MAX; equivalently:
// y_i = MAX − (4·(MAX−i)³ / MAX²)
u32 d = MAX - i;
u32 cube = d * d * d; // (MAX−i)³
u32 num = 4 * cube + ROUND;
return u8(MAX - (num / DENOM));
}
}
u8 easeOutQuad8(u8 i) {
// ease-out is the inverse of ease-in: 1 - (1-t)²
// For 8-bit: y = MAX - (MAX-i)² / MAX
constexpr u16 MAX = 0xFF;
u32 d = MAX - i; // (MAX - i)
u32 num = d * d + (MAX >> 1); // (MAX-i)² + rounding
return u8(MAX - (num / MAX));
}
u8 easeInCubic8(u8 i) {
// Simple cubic ease-in: i³ scaled to 8-bit range
// y = i³ / MAX²
constexpr u16 MAX = 0xFF;
constexpr u32 DENOM = (u32)MAX * MAX;
constexpr u32 ROUND = DENOM >> 1;
u32 ii = i;
u32 cube = ii * ii * ii; // i³
u32 num = cube + ROUND;
return u8(num / DENOM);
}
u8 easeOutCubic8(u8 i) {
// ease-out cubic: 1 - (1-t)³
// For 8-bit: y = MAX - (MAX-i)³ / MAX²
constexpr u16 MAX = 0xFF;
constexpr u32 DENOM = (u32)MAX * MAX;
constexpr u32 ROUND = DENOM >> 1;
u32 d = MAX - i; // (MAX - i)
u32 cube = d * d * d; // (MAX-i)³
u32 num = cube + ROUND;
return u8(MAX - (num / DENOM));
}
u8 easeInSine8(u8 i) {
static const u8 easeInSineTable[256] = {
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1,
1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4,
4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8,
8, 9, 9, 10, 10, 11, 11, 12, 12, 12, 13, 13, 14, 14,
15, 16, 16, 17, 17, 18, 18, 19, 20, 20, 21, 21, 22, 23,
23, 24, 25, 25, 26, 27, 27, 28, 29, 30, 30, 31, 32, 33,
33, 34, 35, 36, 37, 37, 38, 39, 40, 41, 42, 42, 43, 44,
45, 46, 47, 48, 49, 50, 51, 52, 52, 53, 54, 55, 56, 57,
58, 59, 60, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 72,
73, 74, 75, 76, 77, 79, 80, 81, 82, 83, 84, 86, 87, 88,
89, 90, 91, 93, 94, 95, 96, 98, 99, 100, 101, 103, 104, 105,
106, 108, 109, 110, 112, 113, 114, 115, 117, 118, 119, 121, 122, 123,
125, 126, 127, 129, 130, 132, 133, 134, 136, 137, 139, 140, 141, 143,
144, 146, 147, 148, 150, 151, 153, 154, 156, 157, 159, 160, 161, 163,
164, 166, 167, 169, 170, 172, 173, 175, 176, 178, 179, 181, 182, 184,
185, 187, 188, 190, 191, 193, 194, 196, 197, 199, 200, 202, 204, 205,
207, 208, 210, 211, 213, 214, 216, 217, 219, 221, 222, 224, 225, 227,
228, 230, 231, 233, 235, 236, 238, 239, 241, 242, 244, 246, 247, 249,
250, 252, 253, 255};
// ease-in sine: 1 - cos(t * π/2)
// Handle boundary conditions explicitly
return easeInSineTable[i];
}
u8 easeOutSine8(u8 i) {
// ease-out sine: sin(t * π/2)
// Delegate to 16-bit version for consistency and accuracy
// Scale 8-bit input to 16-bit range, call 16-bit function, scale result back
u16 input16 = map8_to_16(i);
u16 result16 = easeOutSine16(input16);
return map16_to_8(result16);
}
u8 easeInOutSine8(u8 i) {
// ease-in-out sine: -(cos(π*t) - 1) / 2
// Delegate to 16-bit version for consistency and accuracy
// Scale 8-bit input to 16-bit range, call 16-bit function, scale result back
u16 input16 = map8_to_16(i);
u16 result16 = easeInOutSine16(input16);
return map16_to_8(result16);
}
// 16-bit easing functions
u16 easeInQuad16(u16 i) {
// Simple quadratic ease-in: i^2 scaled to 16-bit range
// Using scale16(i, i) which computes (i * i) / 65535
return scale16(i, i);
}
u16 easeInOutQuad16(u16 x) {
// 16-bit quadratic ease-in / ease-out function
constexpr u32 MAX = 0xFFFF; // 65535
constexpr u32 HALF = (MAX + 1) >> 1; // 32768
constexpr u32 DENOM = MAX; // divisor
constexpr u32 ROUND = DENOM >> 1; // for rounding
if (x < HALF) {
// first half: y = 2·(x/MAX)² → y_i = 2·x² / MAX
fl::u64 xi = x;
fl::u64 num = 2 * xi * xi + ROUND; // 2*x², +half for rounding
return u16(num / DENOM);
} else {
// second half: y = 1 − 2·(1−x/MAX)² → y_i = MAX − (2·(MAX−x)² / MAX)
fl::u64 d = MAX - x;
fl::u64 num = 2 * d * d + ROUND; // 2*(MAX−x)², +half for rounding
return u16(MAX - (num / DENOM));
}
}
u16 easeInOutCubic16(u16 x) {
const u32 MAX = 0xFFFF; // 65535
const u32 HALF = (MAX + 1) >> 1; // 32768
const fl::u64 M2 = (fl::u64)MAX * MAX; // 65535² = 4 294 836 225
if (x < HALF) {
// first half: y = 4·(x/MAX)³ → y_i = 4·x³ / MAX²
fl::u64 xi = x;
fl::u64 cube = xi * xi * xi; // x³
// add M2/2 for rounding
fl::u64 num = 4 * cube + (M2 >> 1);
return (u16)(num / M2);
} else {
// second half: y = 1 − ((2·(1−x/MAX))³)/2
// → y_i = MAX − (4·(MAX−x)³ / MAX²)
fl::u64 d = MAX - x;
fl::u64 cube = d * d * d; // (MAX−x)³
fl::u64 num = 4 * cube + (M2 >> 1);
return (u16)(MAX - (num / M2));
}
}
u16 easeOutQuad16(u16 i) {
// ease-out quadratic: 1 - (1-t)²
// For 16-bit: y = MAX - (MAX-i)² / MAX
constexpr u32 MAX = 0xFFFF; // 65535
constexpr u32 ROUND = MAX >> 1; // for rounding
fl::u64 d = MAX - i; // (MAX - i)
fl::u64 num = d * d + ROUND; // (MAX-i)² + rounding
return u16(MAX - (num / MAX));
}
u16 easeInCubic16(u16 i) {
// Simple cubic ease-in: i³ scaled to 16-bit range
// y = i³ / MAX²
constexpr u32 MAX = 0xFFFF; // 65535
constexpr fl::u64 DENOM = (fl::u64)MAX * MAX; // 65535²
constexpr fl::u64 ROUND = DENOM >> 1; // for rounding
fl::u64 ii = i;
fl::u64 cube = ii * ii * ii; // i³
fl::u64 num = cube + ROUND;
return u16(num / DENOM);
}
u16 easeOutCubic16(u16 i) {
// ease-out cubic: 1 - (1-t)³
// For 16-bit: y = MAX - (MAX-i)³ / MAX²
constexpr u32 MAX = 0xFFFF; // 65535
constexpr fl::u64 DENOM = (fl::u64)MAX * MAX; // 65535²
constexpr fl::u64 ROUND = DENOM >> 1; // for rounding
fl::u64 d = MAX - i; // (MAX - i)
fl::u64 cube = d * d * d; // (MAX-i)³
fl::u64 num = cube + ROUND;
return u16(MAX - (num / DENOM));
}
u16 easeInSine16(u16 i) {
// ease-in sine: 1 - cos(t * π/2)
// Handle boundary conditions explicitly
if (i == 0)
return 0;
// Remove the hard-coded boundary for 65535 and let math handle it
// For 16-bit: use cos32 for efficiency and accuracy
// Map i from [0,65535] to [0,4194304] in cos32 space (zero to quarter wave)
// Formula: 1 - cos(t * π/2) where t goes from 0 to 1
// sin32/cos32 quarter cycle is 16777216/4 = 4194304
u32 angle = ((fl::u64)i * 4194304ULL) / 65535ULL;
i32 cos_result = fl::cos32(angle);
// Convert cos32 output and apply easing formula: 1 - cos(t * π/2)
// cos32 output range is [-2147418112, 2147418112]
// At t=0: cos(0) = 2147418112, result should be 0
// At t=1: cos(π/2) = 0, result should be 65535
const fl::i64 MAX_COS32 = 2147418112LL;
// Calculate: (MAX_COS32 - cos_result) and scale to [0, 65535]
fl::i64 adjusted = MAX_COS32 - (fl::i64)cos_result;
// Scale from [0, 2147418112] to [0, 65535]
fl::u64 result = (fl::u64)adjusted * 65535ULL + (MAX_COS32 >> 1); // Add half for rounding
u16 final_result = (u16)(result / (fl::u64)MAX_COS32);
return final_result;
}
u16 easeOutSine16(u16 i) {
// ease-out sine: sin(t * π/2)
// Handle boundary conditions explicitly
if (i == 0)
return 0;
if (i == 65535)
return 65535;
// For 16-bit: use sin32 for efficiency and accuracy
// Map i from [0,65535] to [0,4194304] in sin32 space (zero to quarter wave)
// Formula: sin(t * π/2) where t goes from 0 to 1
// sin32 quarter cycle is 16777216/4 = 4194304
u32 angle = ((fl::u64)i * 4194304ULL) / 65535ULL;
i32 sin_result = fl::sin32(angle);
// Convert sin32 output range [-2147418112, 2147418112] to [0, 65535]
// sin32 output is in range -32767*65536 to +32767*65536
// For ease-out sine, we only use positive portion [0, 2147418112] -> [0, 65535]
return (u16)((fl::u64)sin_result * 65535ULL / 2147418112ULL);
}
u16 easeInOutSine16(u16 i) {
// ease-in-out sine: -(cos(π*t) - 1) / 2
// Handle boundary conditions explicitly
if (i == 0)
return 0;
if (i == 65535)
return 65535;
// For 16-bit: use cos32 for efficiency and accuracy
// Map i from [0,65535] to [0,8388608] in cos32 space (0 to half wave)
// Formula: (1 - cos(π*t)) / 2 where t goes from 0 to 1
// sin32/cos32 half cycle is 16777216/2 = 8388608
u32 angle = ((fl::u64)i * 8388608ULL) / 65535ULL;
i32 cos_result = fl::cos32(angle);
// Convert cos32 output and apply easing formula: (1 - cos(π*t)) / 2
// cos32 output range is [-2147418112, 2147418112]
// We want: (2147418112 - cos_result) / 2, then scale to [0, 65535]
fl::i64 adjusted = (2147418112LL - (fl::i64)cos_result) / 2;
return (u16)((fl::u64)adjusted * 65535ULL / 2147418112ULL);
}
} // namespace fl