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Add JD_HANDLE_SMALL_SEGMENTS option (#18316)
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@ -815,6 +815,8 @@
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*/
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#if DISABLED(CLASSIC_JERK)
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#define JUNCTION_DEVIATION_MM 0.013 // (mm) Distance from real junction edge
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#define JD_HANDLE_SMALL_SEGMENTS // Use curvature estimation instead of just the junction angle
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// for small segments (< 1mm) with large junction angles (> 135°).
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#endif
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/**
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@ -2352,89 +2352,93 @@ bool Planner::_populate_block(block_t * const block, bool split_move,
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vmax_junction_sqr = junction_acceleration * junction_deviation_mm * sin_theta_d2 / (1.0f - sin_theta_d2);
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// For small moves with >135° junction (octagon) find speed for approximate arc
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if (block->millimeters < 1 && junction_cos_theta < -0.7071067812f) {
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#if ENABLED(JD_HANDLE_SMALL_SEGMENTS)
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#if ENABLED(JD_USE_MATH_ACOS)
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// For small moves with >135° junction (octagon) find speed for approximate arc
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if (block->millimeters < 1 && junction_cos_theta < -0.7071067812f) {
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#error "TODO: Inline maths with the MCU / FPU."
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#if ENABLED(JD_USE_MATH_ACOS)
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#elif ENABLED(JD_USE_LOOKUP_TABLE)
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#error "TODO: Inline maths with the MCU / FPU."
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// Fast acos approximation (max. error +-0.01 rads)
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// Based on LUT table and linear interpolation
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#elif ENABLED(JD_USE_LOOKUP_TABLE)
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/**
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* // Generate the JD Lookup Table
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* constexpr float c = 1.00751495f; // Correction factor to center error around 0
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* for (int i = 0; i < jd_lut_count - 1; ++i) {
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* const float x0 = (sq(i) - 1) / sq(i),
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* y0 = acos(x0) * (i == 0 ? 1 : c),
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* x1 = i < jd_lut_count - 1 ? 0.5 * x0 + 0.5 : 0.999999f,
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* y1 = acos(x1) * (i < jd_lut_count - 1 ? c : 1);
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* jd_lut_k[i] = (y0 - y1) / (x0 - x1);
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* jd_lut_b[i] = (y1 * x0 - y0 * x1) / (x0 - x1);
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* }
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*
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* // Compute correction factor (Set c to 1.0f first!)
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* float min = INFINITY, max = -min;
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* for (float t = 0; t <= 1; t += 0.0003f) {
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* const float e = acos(t) / approx(t);
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* if (isfinite(e)) {
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* if (e < min) min = e;
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* if (e > max) max = e;
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* }
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* }
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* fprintf(stderr, "%.9gf, ", (min + max) / 2);
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*/
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static constexpr int16_t jd_lut_count = 16;
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static constexpr uint16_t jd_lut_tll = _BV(jd_lut_count - 1);
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static constexpr int16_t jd_lut_tll0 = __builtin_clz(jd_lut_tll) + 1; // i.e., 16 - jd_lut_count + 1
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static constexpr float jd_lut_k[jd_lut_count] PROGMEM = {
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-1.03145837f, -1.30760646f, -1.75205851f, -2.41705704f,
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-3.37769222f, -4.74888992f, -6.69649887f, -9.45661736f,
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-13.3640480f, -18.8928222f, -26.7136841f, -37.7754593f,
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-53.4201813f, -75.5458374f, -106.836761f, -218.532821f };
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static constexpr float jd_lut_b[jd_lut_count] PROGMEM = {
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1.57079637f, 1.70887053f, 2.04220939f, 2.62408352f,
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3.52467871f, 4.85302639f, 6.77020454f, 9.50875854f,
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13.4009285f, 18.9188995f, 26.7321243f, 37.7885055f,
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53.4293975f, 75.5523529f, 106.841369f, 218.534011f };
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// Fast acos approximation (max. error +-0.01 rads)
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// Based on LUT table and linear interpolation
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const float neg = junction_cos_theta < 0 ? -1 : 1,
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t = neg * junction_cos_theta;
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/**
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* // Generate the JD Lookup Table
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* constexpr float c = 1.00751495f; // Correction factor to center error around 0
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* for (int i = 0; i < jd_lut_count - 1; ++i) {
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* const float x0 = (sq(i) - 1) / sq(i),
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* y0 = acos(x0) * (i == 0 ? 1 : c),
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* x1 = i < jd_lut_count - 1 ? 0.5 * x0 + 0.5 : 0.999999f,
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* y1 = acos(x1) * (i < jd_lut_count - 1 ? c : 1);
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* jd_lut_k[i] = (y0 - y1) / (x0 - x1);
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* jd_lut_b[i] = (y1 * x0 - y0 * x1) / (x0 - x1);
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* }
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*
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* // Compute correction factor (Set c to 1.0f first!)
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* float min = INFINITY, max = -min;
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* for (float t = 0; t <= 1; t += 0.0003f) {
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* const float e = acos(t) / approx(t);
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* if (isfinite(e)) {
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* if (e < min) min = e;
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* if (e > max) max = e;
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* }
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* }
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* fprintf(stderr, "%.9gf, ", (min + max) / 2);
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*/
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static constexpr int16_t jd_lut_count = 16;
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static constexpr uint16_t jd_lut_tll = _BV(jd_lut_count - 1);
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static constexpr int16_t jd_lut_tll0 = __builtin_clz(jd_lut_tll) + 1; // i.e., 16 - jd_lut_count + 1
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static constexpr float jd_lut_k[jd_lut_count] PROGMEM = {
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-1.03145837f, -1.30760646f, -1.75205851f, -2.41705704f,
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-3.37769222f, -4.74888992f, -6.69649887f, -9.45661736f,
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-13.3640480f, -18.8928222f, -26.7136841f, -37.7754593f,
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-53.4201813f, -75.5458374f, -106.836761f, -218.532821f };
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static constexpr float jd_lut_b[jd_lut_count] PROGMEM = {
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1.57079637f, 1.70887053f, 2.04220939f, 2.62408352f,
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3.52467871f, 4.85302639f, 6.77020454f, 9.50875854f,
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13.4009285f, 18.9188995f, 26.7321243f, 37.7885055f,
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53.4293975f, 75.5523529f, 106.841369f, 218.534011f };
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const int16_t idx = (t < 0.00000003f) ? 0 : __builtin_clz(uint16_t((1.0f - t) * jd_lut_tll)) - jd_lut_tll0;
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const float neg = junction_cos_theta < 0 ? -1 : 1,
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t = neg * junction_cos_theta;
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float junction_theta = t * pgm_read_float(&jd_lut_k[idx]) + pgm_read_float(&jd_lut_b[idx]);
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if (neg > 0) junction_theta = RADIANS(180) - junction_theta; // acos(-t)
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const int16_t idx = (t < 0.00000003f) ? 0 : __builtin_clz(uint16_t((1.0f - t) * jd_lut_tll)) - jd_lut_tll0;
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#else
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float junction_theta = t * pgm_read_float(&jd_lut_k[idx]) + pgm_read_float(&jd_lut_b[idx]);
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if (neg > 0) junction_theta = RADIANS(180) - junction_theta; // acos(-t)
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// Fast acos(-t) approximation (max. error +-0.033rad = 1.89°)
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// Based on MinMax polynomial published by W. Randolph Franklin, see
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// https://wrf.ecse.rpi.edu/Research/Short_Notes/arcsin/onlyelem.html
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// acos( t) = pi / 2 - asin(x)
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// acos(-t) = pi - acos(t) ... pi / 2 + asin(x)
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#else
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const float neg = junction_cos_theta < 0 ? -1 : 1,
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t = neg * junction_cos_theta,
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asinx = 0.032843707f
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+ t * (-1.451838349f
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+ t * ( 29.66153956f
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+ t * (-131.1123477f
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+ t * ( 262.8130562f
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+ t * (-242.7199627f
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+ t * ( 84.31466202f ) ))))),
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junction_theta = RADIANS(90) + neg * asinx; // acos(-t)
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// Fast acos(-t) approximation (max. error +-0.033rad = 1.89°)
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// Based on MinMax polynomial published by W. Randolph Franklin, see
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// https://wrf.ecse.rpi.edu/Research/Short_Notes/arcsin/onlyelem.html
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// acos( t) = pi / 2 - asin(x)
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// acos(-t) = pi - acos(t) ... pi / 2 + asin(x)
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// NOTE: junction_theta bottoms out at 0.033 which avoids divide by 0.
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const float neg = junction_cos_theta < 0 ? -1 : 1,
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t = neg * junction_cos_theta,
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asinx = 0.032843707f
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+ t * (-1.451838349f
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+ t * ( 29.66153956f
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+ t * (-131.1123477f
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+ t * ( 262.8130562f
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+ t * (-242.7199627f
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+ t * ( 84.31466202f ) ))))),
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junction_theta = RADIANS(90) + neg * asinx; // acos(-t)
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#endif
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// NOTE: junction_theta bottoms out at 0.033 which avoids divide by 0.
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const float limit_sqr = (block->millimeters * junction_acceleration) / junction_theta;
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NOMORE(vmax_junction_sqr, limit_sqr);
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}
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#endif
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const float limit_sqr = (block->millimeters * junction_acceleration) / junction_theta;
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NOMORE(vmax_junction_sqr, limit_sqr);
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}
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#endif // JD_HANDLE_SMALL_SEGMENTS
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}
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// Get the lowest speed
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@ -32,7 +32,7 @@
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#include "../MarlinCore.h"
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#if HAS_JUNCTION_DEVIATION
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#if ENABLED(JD_HANDLE_SMALL_SEGMENTS)
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// Enable this option for perfect accuracy but maximum
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// computation. Should be fine on ARM processors.
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//#define JD_USE_MATH_ACOS
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