Anisotropic x16 LOD (ratio of anisotropy)

Percentage Accurate: 97.9% → 97.9%

Time: 1.6min

Alternatives: 7

Speedup: 1.0×

Specification

\[\left(\left(\left(\left(\left(\left(1 \leq w \land w \leq 16384\right) \land \left(1 \leq h \land h \leq 16384\right)\right) \land \left(10^{-20} \leq \left|dX.u\right| \land \left|dX.u\right| \leq 10^{+20}\right)\right) \land \left(10^{-20} \leq \left|dX.v\right| \land \left|dX.v\right| \leq 10^{+20}\right)\right) \land \left(10^{-20} \leq \left|dY.u\right| \land \left|dY.u\right| \leq 10^{+20}\right)\right) \land \left(10^{-20} \leq \left|dY.v\right| \land \left|dY.v\right| \leq 10^{+20}\right)\right) \land maxAniso = 16\]

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left\lfloorh\right\rfloor \cdot dX.v\\ t_1 := \left\lfloorh\right\rfloor \cdot dY.v\\ t_2 := \left\lfloorw\right\rfloor \cdot dY.u\\ t_3 := \left\lfloorw\right\rfloor \cdot dX.u\\ t_4 := \mathsf{max}\left(t_3 \cdot t_3 + t_0 \cdot t_0, t_2 \cdot t_2 + t_1 \cdot t_1\right)\\ t_5 := \sqrt{t_4}\\ t_6 := \left|t_3 \cdot t_1 - t_0 \cdot t_2\right|\\ t_7 := \frac{t_4}{t_6}\\ t_8 := t_7 > \left\lfloormaxAniso\right\rfloor\\ t_9 := \begin{array}{l} \mathbf{if}\;t_8:\\ \;\;\;\;\frac{t_5}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_6}{t_5}\\ \end{array}\\ t_10 := \begin{array}{l} \mathbf{if}\;t_8:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;t_7\\ \end{array}\\ \mathbf{if}\;t_9 < 1:\\ \;\;\;\;\mathsf{max}\left(1, t_10 \cdot t_9\right)\\ \mathbf{else}:\\ \;\;\;\;t_10\\ \end{array} \end{array} \]

FPCore

(FPCore (w h dX.u dX.v dY.u dY.v maxAniso)
 :precision binary32
 (let* ((t_0 (* (floor h) dX.v))
        (t_1 (* (floor h) dY.v))
        (t_2 (* (floor w) dY.u))
        (t_3 (* (floor w) dX.u))
        (t_4 (fmax (+ (* t_3 t_3) (* t_0 t_0)) (+ (* t_2 t_2) (* t_1 t_1))))
        (t_5 (sqrt t_4))
        (t_6 (fabs (- (* t_3 t_1) (* t_0 t_2))))
        (t_7 (/ t_4 t_6))
        (t_8 (> t_7 (floor maxAniso)))
        (t_9 (if t_8 (/ t_5 (floor maxAniso)) (/ t_6 t_5)))
        (t_10 (if t_8 (floor maxAniso) t_7)))
   (if (< t_9 1.0) (fmax 1.0 (* t_10 t_9)) t_10)))

C

float code(float w, float h, float dX_46_u, float dX_46_v, float dY_46_u, float dY_46_v, float maxAniso) {
	float t_0 = floorf(h) * dX_46_v;
	float t_1 = floorf(h) * dY_46_v;
	float t_2 = floorf(w) * dY_46_u;
	float t_3 = floorf(w) * dX_46_u;
	float t_4 = fmaxf(((t_3 * t_3) + (t_0 * t_0)), ((t_2 * t_2) + (t_1 * t_1)));
	float t_5 = sqrtf(t_4);
	float t_6 = fabsf(((t_3 * t_1) - (t_0 * t_2)));
	float t_7 = t_4 / t_6;
	int t_8 = t_7 > floorf(maxAniso);
	float tmp;
	if (t_8) {
		tmp = t_5 / floorf(maxAniso);
	} else {
		tmp = t_6 / t_5;
	}
	float t_9 = tmp;
	float tmp_1;
	if (t_8) {
		tmp_1 = floorf(maxAniso);
	} else {
		tmp_1 = t_7;
	}
	float t_10 = tmp_1;
	float tmp_2;
	if (t_9 < 1.0f) {
		tmp_2 = fmaxf(1.0f, (t_10 * t_9));
	} else {
		tmp_2 = t_10;
	}
	return tmp_2;
}

Julia

function code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = Float32(floor(h) * dX_46_v)
	t_1 = Float32(floor(h) * dY_46_v)
	t_2 = Float32(floor(w) * dY_46_u)
	t_3 = Float32(floor(w) * dX_46_u)
	t_4 = (Float32(Float32(t_3 * t_3) + Float32(t_0 * t_0)) != Float32(Float32(t_3 * t_3) + Float32(t_0 * t_0))) ? Float32(Float32(t_2 * t_2) + Float32(t_1 * t_1)) : ((Float32(Float32(t_2 * t_2) + Float32(t_1 * t_1)) != Float32(Float32(t_2 * t_2) + Float32(t_1 * t_1))) ? Float32(Float32(t_3 * t_3) + Float32(t_0 * t_0)) : max(Float32(Float32(t_3 * t_3) + Float32(t_0 * t_0)), Float32(Float32(t_2 * t_2) + Float32(t_1 * t_1))))
	t_5 = sqrt(t_4)
	t_6 = abs(Float32(Float32(t_3 * t_1) - Float32(t_0 * t_2)))
	t_7 = Float32(t_4 / t_6)
	t_8 = t_7 > floor(maxAniso)
	tmp = Float32(0.0)
	if (t_8)
		tmp = Float32(t_5 / floor(maxAniso));
	else
		tmp = Float32(t_6 / t_5);
	end
	t_9 = tmp
	tmp_1 = Float32(0.0)
	if (t_8)
		tmp_1 = floor(maxAniso);
	else
		tmp_1 = t_7;
	end
	t_10 = tmp_1
	tmp_2 = Float32(0.0)
	if (t_9 < Float32(1.0))
		tmp_2 = (Float32(1.0) != Float32(1.0)) ? Float32(t_10 * t_9) : ((Float32(t_10 * t_9) != Float32(t_10 * t_9)) ? Float32(1.0) : max(Float32(1.0), Float32(t_10 * t_9)));
	else
		tmp_2 = t_10;
	end
	return tmp_2
end

MATLAB

function tmp_4 = code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = floor(h) * dX_46_v;
	t_1 = floor(h) * dY_46_v;
	t_2 = floor(w) * dY_46_u;
	t_3 = floor(w) * dX_46_u;
	t_4 = max(((t_3 * t_3) + (t_0 * t_0)), ((t_2 * t_2) + (t_1 * t_1)));
	t_5 = sqrt(t_4);
	t_6 = abs(((t_3 * t_1) - (t_0 * t_2)));
	t_7 = t_4 / t_6;
	t_8 = t_7 > floor(maxAniso);
	tmp = single(0.0);
	if (t_8)
		tmp = t_5 / floor(maxAniso);
	else
		tmp = t_6 / t_5;
	end
	t_9 = tmp;
	tmp_2 = single(0.0);
	if (t_8)
		tmp_2 = floor(maxAniso);
	else
		tmp_2 = t_7;
	end
	t_10 = tmp_2;
	tmp_3 = single(0.0);
	if (t_9 < single(1.0))
		tmp_3 = max(single(1.0), (t_10 * t_9));
	else
		tmp_3 = t_10;
	end
	tmp_4 = tmp_3;
end

Initial Program: 97.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left\lfloorh\right\rfloor \cdot dX.v\\ t_1 := \left\lfloorh\right\rfloor \cdot dY.v\\ t_2 := \left\lfloorw\right\rfloor \cdot dY.u\\ t_3 := \left\lfloorw\right\rfloor \cdot dX.u\\ t_4 := \mathsf{max}\left(t_3 \cdot t_3 + t_0 \cdot t_0, t_2 \cdot t_2 + t_1 \cdot t_1\right)\\ t_5 := \sqrt{t_4}\\ t_6 := \left|t_3 \cdot t_1 - t_0 \cdot t_2\right|\\ t_7 := \frac{t_4}{t_6}\\ t_8 := t_7 > \left\lfloormaxAniso\right\rfloor\\ t_9 := \begin{array}{l} \mathbf{if}\;t_8:\\ \;\;\;\;\frac{t_5}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_6}{t_5}\\ \end{array}\\ t_10 := \begin{array}{l} \mathbf{if}\;t_8:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;t_7\\ \end{array}\\ \mathbf{if}\;t_9 < 1:\\ \;\;\;\;\mathsf{max}\left(1, t_10 \cdot t_9\right)\\ \mathbf{else}:\\ \;\;\;\;t_10\\ \end{array} \end{array} \]

FPCore

(FPCore (w h dX.u dX.v dY.u dY.v maxAniso)
 :precision binary32
 (let* ((t_0 (* (floor h) dX.v))
        (t_1 (* (floor h) dY.v))
        (t_2 (* (floor w) dY.u))
        (t_3 (* (floor w) dX.u))
        (t_4 (fmax (+ (* t_3 t_3) (* t_0 t_0)) (+ (* t_2 t_2) (* t_1 t_1))))
        (t_5 (sqrt t_4))
        (t_6 (fabs (- (* t_3 t_1) (* t_0 t_2))))
        (t_7 (/ t_4 t_6))
        (t_8 (> t_7 (floor maxAniso)))
        (t_9 (if t_8 (/ t_5 (floor maxAniso)) (/ t_6 t_5)))
        (t_10 (if t_8 (floor maxAniso) t_7)))
   (if (< t_9 1.0) (fmax 1.0 (* t_10 t_9)) t_10)))

C

float code(float w, float h, float dX_46_u, float dX_46_v, float dY_46_u, float dY_46_v, float maxAniso) {
	float t_0 = floorf(h) * dX_46_v;
	float t_1 = floorf(h) * dY_46_v;
	float t_2 = floorf(w) * dY_46_u;
	float t_3 = floorf(w) * dX_46_u;
	float t_4 = fmaxf(((t_3 * t_3) + (t_0 * t_0)), ((t_2 * t_2) + (t_1 * t_1)));
	float t_5 = sqrtf(t_4);
	float t_6 = fabsf(((t_3 * t_1) - (t_0 * t_2)));
	float t_7 = t_4 / t_6;
	int t_8 = t_7 > floorf(maxAniso);
	float tmp;
	if (t_8) {
		tmp = t_5 / floorf(maxAniso);
	} else {
		tmp = t_6 / t_5;
	}
	float t_9 = tmp;
	float tmp_1;
	if (t_8) {
		tmp_1 = floorf(maxAniso);
	} else {
		tmp_1 = t_7;
	}
	float t_10 = tmp_1;
	float tmp_2;
	if (t_9 < 1.0f) {
		tmp_2 = fmaxf(1.0f, (t_10 * t_9));
	} else {
		tmp_2 = t_10;
	}
	return tmp_2;
}

Julia

function code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = Float32(floor(h) * dX_46_v)
	t_1 = Float32(floor(h) * dY_46_v)
	t_2 = Float32(floor(w) * dY_46_u)
	t_3 = Float32(floor(w) * dX_46_u)
	t_4 = (Float32(Float32(t_3 * t_3) + Float32(t_0 * t_0)) != Float32(Float32(t_3 * t_3) + Float32(t_0 * t_0))) ? Float32(Float32(t_2 * t_2) + Float32(t_1 * t_1)) : ((Float32(Float32(t_2 * t_2) + Float32(t_1 * t_1)) != Float32(Float32(t_2 * t_2) + Float32(t_1 * t_1))) ? Float32(Float32(t_3 * t_3) + Float32(t_0 * t_0)) : max(Float32(Float32(t_3 * t_3) + Float32(t_0 * t_0)), Float32(Float32(t_2 * t_2) + Float32(t_1 * t_1))))
	t_5 = sqrt(t_4)
	t_6 = abs(Float32(Float32(t_3 * t_1) - Float32(t_0 * t_2)))
	t_7 = Float32(t_4 / t_6)
	t_8 = t_7 > floor(maxAniso)
	tmp = Float32(0.0)
	if (t_8)
		tmp = Float32(t_5 / floor(maxAniso));
	else
		tmp = Float32(t_6 / t_5);
	end
	t_9 = tmp
	tmp_1 = Float32(0.0)
	if (t_8)
		tmp_1 = floor(maxAniso);
	else
		tmp_1 = t_7;
	end
	t_10 = tmp_1
	tmp_2 = Float32(0.0)
	if (t_9 < Float32(1.0))
		tmp_2 = (Float32(1.0) != Float32(1.0)) ? Float32(t_10 * t_9) : ((Float32(t_10 * t_9) != Float32(t_10 * t_9)) ? Float32(1.0) : max(Float32(1.0), Float32(t_10 * t_9)));
	else
		tmp_2 = t_10;
	end
	return tmp_2
end

MATLAB

function tmp_4 = code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = floor(h) * dX_46_v;
	t_1 = floor(h) * dY_46_v;
	t_2 = floor(w) * dY_46_u;
	t_3 = floor(w) * dX_46_u;
	t_4 = max(((t_3 * t_3) + (t_0 * t_0)), ((t_2 * t_2) + (t_1 * t_1)));
	t_5 = sqrt(t_4);
	t_6 = abs(((t_3 * t_1) - (t_0 * t_2)));
	t_7 = t_4 / t_6;
	t_8 = t_7 > floor(maxAniso);
	tmp = single(0.0);
	if (t_8)
		tmp = t_5 / floor(maxAniso);
	else
		tmp = t_6 / t_5;
	end
	t_9 = tmp;
	tmp_2 = single(0.0);
	if (t_8)
		tmp_2 = floor(maxAniso);
	else
		tmp_2 = t_7;
	end
	t_10 = tmp_2;
	tmp_3 = single(0.0);
	if (t_9 < single(1.0))
		tmp_3 = max(single(1.0), (t_10 * t_9));
	else
		tmp_3 = t_10;
	end
	tmp_4 = tmp_3;
end

Alternative 1: 97.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left\lfloorh\right\rfloor \cdot dX.v\\ t_1 := \left\lfloorh\right\rfloor \cdot dY.v\\ t_2 := \left\lfloorw\right\rfloor \cdot dY.u\\ t_3 := \left\lfloorw\right\rfloor \cdot dX.u\\ t_4 := \mathsf{max}\left(t_3 \cdot t_3 + t_0 \cdot t_0, t_2 \cdot t_2 + t_1 \cdot t_1\right)\\ t_5 := \sqrt{t_4}\\ t_6 := \left|t_3 \cdot t_1 - t_0 \cdot t_2\right|\\ t_7 := \frac{t_4}{t_6}\\ t_8 := t_7 > \left\lfloormaxAniso\right\rfloor\\ t_9 := \begin{array}{l} \mathbf{if}\;t_8:\\ \;\;\;\;\frac{t_5}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_6}{t_5}\\ \end{array}\\ t_10 := \begin{array}{l} \mathbf{if}\;t_8:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;t_7\\ \end{array}\\ \mathbf{if}\;t_9 < 1:\\ \;\;\;\;\mathsf{max}\left(1, t_9 \cdot t_10\right)\\ \mathbf{else}:\\ \;\;\;\;t_10\\ \end{array} \end{array} \]

FPCore

(FPCore (w h dX.u dX.v dY.u dY.v maxAniso)
 :precision binary32
 (let* ((t_0 (* (floor h) dX.v))
        (t_1 (* (floor h) dY.v))
        (t_2 (* (floor w) dY.u))
        (t_3 (* (floor w) dX.u))
        (t_4 (fmax (+ (* t_3 t_3) (* t_0 t_0)) (+ (* t_2 t_2) (* t_1 t_1))))
        (t_5 (sqrt t_4))
        (t_6 (fabs (- (* t_3 t_1) (* t_0 t_2))))
        (t_7 (/ t_4 t_6))
        (t_8 (> t_7 (floor maxAniso)))
        (t_9 (if t_8 (/ t_5 (floor maxAniso)) (/ t_6 t_5)))
        (t_10 (if t_8 (floor maxAniso) t_7)))
   (if (< t_9 1.0) (fmax 1.0 (* t_9 t_10)) t_10)))

C

float code(float w, float h, float dX_46_u, float dX_46_v, float dY_46_u, float dY_46_v, float maxAniso) {
	float t_0 = floorf(h) * dX_46_v;
	float t_1 = floorf(h) * dY_46_v;
	float t_2 = floorf(w) * dY_46_u;
	float t_3 = floorf(w) * dX_46_u;
	float t_4 = fmaxf(((t_3 * t_3) + (t_0 * t_0)), ((t_2 * t_2) + (t_1 * t_1)));
	float t_5 = sqrtf(t_4);
	float t_6 = fabsf(((t_3 * t_1) - (t_0 * t_2)));
	float t_7 = t_4 / t_6;
	int t_8 = t_7 > floorf(maxAniso);
	float tmp;
	if (t_8) {
		tmp = t_5 / floorf(maxAniso);
	} else {
		tmp = t_6 / t_5;
	}
	float t_9 = tmp;
	float tmp_1;
	if (t_8) {
		tmp_1 = floorf(maxAniso);
	} else {
		tmp_1 = t_7;
	}
	float t_10 = tmp_1;
	float tmp_2;
	if (t_9 < 1.0f) {
		tmp_2 = fmaxf(1.0f, (t_9 * t_10));
	} else {
		tmp_2 = t_10;
	}
	return tmp_2;
}

Julia

function code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = Float32(floor(h) * dX_46_v)
	t_1 = Float32(floor(h) * dY_46_v)
	t_2 = Float32(floor(w) * dY_46_u)
	t_3 = Float32(floor(w) * dX_46_u)
	t_4 = (Float32(Float32(t_3 * t_3) + Float32(t_0 * t_0)) != Float32(Float32(t_3 * t_3) + Float32(t_0 * t_0))) ? Float32(Float32(t_2 * t_2) + Float32(t_1 * t_1)) : ((Float32(Float32(t_2 * t_2) + Float32(t_1 * t_1)) != Float32(Float32(t_2 * t_2) + Float32(t_1 * t_1))) ? Float32(Float32(t_3 * t_3) + Float32(t_0 * t_0)) : max(Float32(Float32(t_3 * t_3) + Float32(t_0 * t_0)), Float32(Float32(t_2 * t_2) + Float32(t_1 * t_1))))
	t_5 = sqrt(t_4)
	t_6 = abs(Float32(Float32(t_3 * t_1) - Float32(t_0 * t_2)))
	t_7 = Float32(t_4 / t_6)
	t_8 = t_7 > floor(maxAniso)
	tmp = Float32(0.0)
	if (t_8)
		tmp = Float32(t_5 / floor(maxAniso));
	else
		tmp = Float32(t_6 / t_5);
	end
	t_9 = tmp
	tmp_1 = Float32(0.0)
	if (t_8)
		tmp_1 = floor(maxAniso);
	else
		tmp_1 = t_7;
	end
	t_10 = tmp_1
	tmp_2 = Float32(0.0)
	if (t_9 < Float32(1.0))
		tmp_2 = (Float32(1.0) != Float32(1.0)) ? Float32(t_9 * t_10) : ((Float32(t_9 * t_10) != Float32(t_9 * t_10)) ? Float32(1.0) : max(Float32(1.0), Float32(t_9 * t_10)));
	else
		tmp_2 = t_10;
	end
	return tmp_2
end

MATLAB

function tmp_4 = code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = floor(h) * dX_46_v;
	t_1 = floor(h) * dY_46_v;
	t_2 = floor(w) * dY_46_u;
	t_3 = floor(w) * dX_46_u;
	t_4 = max(((t_3 * t_3) + (t_0 * t_0)), ((t_2 * t_2) + (t_1 * t_1)));
	t_5 = sqrt(t_4);
	t_6 = abs(((t_3 * t_1) - (t_0 * t_2)));
	t_7 = t_4 / t_6;
	t_8 = t_7 > floor(maxAniso);
	tmp = single(0.0);
	if (t_8)
		tmp = t_5 / floor(maxAniso);
	else
		tmp = t_6 / t_5;
	end
	t_9 = tmp;
	tmp_2 = single(0.0);
	if (t_8)
		tmp_2 = floor(maxAniso);
	else
		tmp_2 = t_7;
	end
	t_10 = tmp_2;
	tmp_3 = single(0.0);
	if (t_9 < single(1.0))
		tmp_3 = max(single(1.0), (t_9 * t_10));
	else
		tmp_3 = t_10;
	end
	tmp_4 = tmp_3;
end

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 2: 97.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := dX.v \cdot dY.u - dX.u \cdot dY.v\\ t_1 := \left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot t_0\right)\right|\\ t_2 := \left\lfloorw\right\rfloor \cdot dX.u\\ t_3 := \left\lfloorh\right\rfloor \cdot dY.v\\ t_4 := \mathsf{max}\left({t_2}^{2} + {\left(\left\lfloorh\right\rfloor \cdot dX.v\right)}^{2}, {\left(\left\lfloorw\right\rfloor \cdot dY.u\right)}^{2} + {t_3}^{2}\right)\\ t_5 := \frac{t_4}{\left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot t_0}\\ t_6 := t_5 > \left\lfloormaxAniso\right\rfloor\\ t_7 := \mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, dX.u \cdot t_2, \left\lfloorh\right\rfloor \cdot \left(\left\lfloorh\right\rfloor \cdot \left(dX.v \cdot dX.v\right)\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, dY.v \cdot t_3, \left\lfloorw\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dY.u \cdot dY.u\right)\right)\right)\right)\\ t_8 := \frac{t_7}{t_1} > \left\lfloormaxAniso\right\rfloor\\ t_9 := \sqrt{t_7}\\ t_10 := \frac{t_9}{\left\lfloormaxAniso\right\rfloor}\\ t_11 := \frac{t_1}{t_9}\\ \mathbf{if}\;\begin{array}{l} \mathbf{if}\;t_8:\\ \;\;\;\;t_10\\ \mathbf{else}:\\ \;\;\;\;t_11\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;t_6:\\ \;\;\;\;t_10\\ \mathbf{else}:\\ \;\;\;\;t_11\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;t_6:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array}\right)\\ \mathbf{elif}\;t_8:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\sqrt{{\left(\frac{t_4}{\left\lfloorw\right\rfloor \cdot \left(\left\lfloorh\right\rfloor \cdot t_0\right)}\right)}^{2}}\\ \end{array} \end{array} \]

FPCore

(FPCore (w h dX.u dX.v dY.u dY.v maxAniso)
 :precision binary32
 (let* ((t_0 (- (* dX.v dY.u) (* dX.u dY.v)))
        (t_1 (fabs (* (floor h) (* (floor w) t_0))))
        (t_2 (* (floor w) dX.u))
        (t_3 (* (floor h) dY.v))
        (t_4
         (fmax
          (+ (pow t_2 2.0) (pow (* (floor h) dX.v) 2.0))
          (+ (pow (* (floor w) dY.u) 2.0) (pow t_3 2.0))))
        (t_5 (/ t_4 (* (* (floor w) (floor h)) t_0)))
        (t_6 (> t_5 (floor maxAniso)))
        (t_7
         (fmax
          (fma
           (floor w)
           (* dX.u t_2)
           (* (floor h) (* (floor h) (* dX.v dX.v))))
          (fma
           (floor h)
           (* dY.v t_3)
           (* (floor w) (* (floor w) (* dY.u dY.u))))))
        (t_8 (> (/ t_7 t_1) (floor maxAniso)))
        (t_9 (sqrt t_7))
        (t_10 (/ t_9 (floor maxAniso)))
        (t_11 (/ t_1 t_9)))
   (if (< (if t_8 t_10 t_11) 1.0)
     (fmax 1.0 (* (if t_6 t_10 t_11) (if t_6 (floor maxAniso) t_5)))
     (if t_8
       (floor maxAniso)
       (sqrt (pow (/ t_4 (* (floor w) (* (floor h) t_0))) 2.0))))))

C

float code(float w, float h, float dX_46_u, float dX_46_v, float dY_46_u, float dY_46_v, float maxAniso) {
	float t_0 = (dX_46_v * dY_46_u) - (dX_46_u * dY_46_v);
	float t_1 = fabsf((floorf(h) * (floorf(w) * t_0)));
	float t_2 = floorf(w) * dX_46_u;
	float t_3 = floorf(h) * dY_46_v;
	float t_4 = fmaxf((powf(t_2, 2.0f) + powf((floorf(h) * dX_46_v), 2.0f)), (powf((floorf(w) * dY_46_u), 2.0f) + powf(t_3, 2.0f)));
	float t_5 = t_4 / ((floorf(w) * floorf(h)) * t_0);
	int t_6 = t_5 > floorf(maxAniso);
	float t_7 = fmaxf(fmaf(floorf(w), (dX_46_u * t_2), (floorf(h) * (floorf(h) * (dX_46_v * dX_46_v)))), fmaf(floorf(h), (dY_46_v * t_3), (floorf(w) * (floorf(w) * (dY_46_u * dY_46_u)))));
	int t_8 = (t_7 / t_1) > floorf(maxAniso);
	float t_9 = sqrtf(t_7);
	float t_10 = t_9 / floorf(maxAniso);
	float t_11 = t_1 / t_9;
	float tmp;
	if (t_8) {
		tmp = t_10;
	} else {
		tmp = t_11;
	}
	float tmp_3;
	if (tmp < 1.0f) {
		float tmp_4;
		if (t_6) {
			tmp_4 = t_10;
		} else {
			tmp_4 = t_11;
		}
		float tmp_5;
		if (t_6) {
			tmp_5 = floorf(maxAniso);
		} else {
			tmp_5 = t_5;
		}
		tmp_3 = fmaxf(1.0f, (tmp_4 * tmp_5));
	} else if (t_8) {
		tmp_3 = floorf(maxAniso);
	} else {
		tmp_3 = sqrtf(powf((t_4 / (floorf(w) * (floorf(h) * t_0))), 2.0f));
	}
	return tmp_3;
}

Julia

function code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = Float32(Float32(dX_46_v * dY_46_u) - Float32(dX_46_u * dY_46_v))
	t_1 = abs(Float32(floor(h) * Float32(floor(w) * t_0)))
	t_2 = Float32(floor(w) * dX_46_u)
	t_3 = Float32(floor(h) * dY_46_v)
	t_4 = (Float32((t_2 ^ Float32(2.0)) + (Float32(floor(h) * dX_46_v) ^ Float32(2.0))) != Float32((t_2 ^ Float32(2.0)) + (Float32(floor(h) * dX_46_v) ^ Float32(2.0)))) ? Float32((Float32(floor(w) * dY_46_u) ^ Float32(2.0)) + (t_3 ^ Float32(2.0))) : ((Float32((Float32(floor(w) * dY_46_u) ^ Float32(2.0)) + (t_3 ^ Float32(2.0))) != Float32((Float32(floor(w) * dY_46_u) ^ Float32(2.0)) + (t_3 ^ Float32(2.0)))) ? Float32((t_2 ^ Float32(2.0)) + (Float32(floor(h) * dX_46_v) ^ Float32(2.0))) : max(Float32((t_2 ^ Float32(2.0)) + (Float32(floor(h) * dX_46_v) ^ Float32(2.0))), Float32((Float32(floor(w) * dY_46_u) ^ Float32(2.0)) + (t_3 ^ Float32(2.0)))))
	t_5 = Float32(t_4 / Float32(Float32(floor(w) * floor(h)) * t_0))
	t_6 = t_5 > floor(maxAniso)
	t_7 = (fma(floor(w), Float32(dX_46_u * t_2), Float32(floor(h) * Float32(floor(h) * Float32(dX_46_v * dX_46_v)))) != fma(floor(w), Float32(dX_46_u * t_2), Float32(floor(h) * Float32(floor(h) * Float32(dX_46_v * dX_46_v))))) ? fma(floor(h), Float32(dY_46_v * t_3), Float32(floor(w) * Float32(floor(w) * Float32(dY_46_u * dY_46_u)))) : ((fma(floor(h), Float32(dY_46_v * t_3), Float32(floor(w) * Float32(floor(w) * Float32(dY_46_u * dY_46_u)))) != fma(floor(h), Float32(dY_46_v * t_3), Float32(floor(w) * Float32(floor(w) * Float32(dY_46_u * dY_46_u))))) ? fma(floor(w), Float32(dX_46_u * t_2), Float32(floor(h) * Float32(floor(h) * Float32(dX_46_v * dX_46_v)))) : max(fma(floor(w), Float32(dX_46_u * t_2), Float32(floor(h) * Float32(floor(h) * Float32(dX_46_v * dX_46_v)))), fma(floor(h), Float32(dY_46_v * t_3), Float32(floor(w) * Float32(floor(w) * Float32(dY_46_u * dY_46_u))))))
	t_8 = Float32(t_7 / t_1) > floor(maxAniso)
	t_9 = sqrt(t_7)
	t_10 = Float32(t_9 / floor(maxAniso))
	t_11 = Float32(t_1 / t_9)
	tmp = Float32(0.0)
	if (t_8)
		tmp = t_10;
	else
		tmp = t_11;
	end
	tmp_3 = Float32(0.0)
	if (tmp < Float32(1.0))
		tmp_4 = Float32(0.0)
		if (t_6)
			tmp_4 = t_10;
		else
			tmp_4 = t_11;
		end
		tmp_5 = Float32(0.0)
		if (t_6)
			tmp_5 = floor(maxAniso);
		else
			tmp_5 = t_5;
		end
		tmp_3 = (Float32(1.0) != Float32(1.0)) ? Float32(tmp_4 * tmp_5) : ((Float32(tmp_4 * tmp_5) != Float32(tmp_4 * tmp_5)) ? Float32(1.0) : max(Float32(1.0), Float32(tmp_4 * tmp_5)));
	elseif (t_8)
		tmp_3 = floor(maxAniso);
	else
		tmp_3 = sqrt((Float32(t_4 / Float32(floor(w) * Float32(floor(h) * t_0))) ^ Float32(2.0)));
	end
	return tmp_3
end

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 3: 97.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left\lfloorw\right\rfloor \cdot dX.u\\ t_1 := dX.v \cdot dY.u - dX.u \cdot dY.v\\ t_2 := \left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot t_1\right)\right|\\ t_3 := \left\lfloorh\right\rfloor \cdot dY.v\\ t_4 := \frac{\mathsf{max}\left({t_0}^{2} + {\left(\left\lfloorh\right\rfloor \cdot dX.v\right)}^{2}, {\left(\left\lfloorw\right\rfloor \cdot dY.u\right)}^{2} + {t_3}^{2}\right)}{\left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot t_1}\\ t_5 := t_4 > \left\lfloormaxAniso\right\rfloor\\ t_6 := \mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, dX.u \cdot t_0, \left\lfloorh\right\rfloor \cdot \left(\left\lfloorh\right\rfloor \cdot \left(dX.v \cdot dX.v\right)\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, dY.v \cdot t_3, \left\lfloorw\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dY.u \cdot dY.u\right)\right)\right)\right)\\ t_7 := \sqrt{t_6}\\ t_8 := \frac{t_7}{\left\lfloormaxAniso\right\rfloor}\\ t_9 := \frac{t_6}{t_2}\\ t_10 := t_9 > \left\lfloormaxAniso\right\rfloor\\ t_11 := \frac{t_2}{t_7}\\ \mathbf{if}\;\begin{array}{l} \mathbf{if}\;t_10:\\ \;\;\;\;t_8\\ \mathbf{else}:\\ \;\;\;\;t_11\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;t_5:\\ \;\;\;\;t_8\\ \mathbf{else}:\\ \;\;\;\;t_11\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;t_5:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array}\right)\\ \mathbf{elif}\;t_10:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;t_9\\ \end{array} \end{array} \]

FPCore

(FPCore (w h dX.u dX.v dY.u dY.v maxAniso)
 :precision binary32
 (let* ((t_0 (* (floor w) dX.u))
        (t_1 (- (* dX.v dY.u) (* dX.u dY.v)))
        (t_2 (fabs (* (floor h) (* (floor w) t_1))))
        (t_3 (* (floor h) dY.v))
        (t_4
         (/
          (fmax
           (+ (pow t_0 2.0) (pow (* (floor h) dX.v) 2.0))
           (+ (pow (* (floor w) dY.u) 2.0) (pow t_3 2.0)))
          (* (* (floor w) (floor h)) t_1)))
        (t_5 (> t_4 (floor maxAniso)))
        (t_6
         (fmax
          (fma
           (floor w)
           (* dX.u t_0)
           (* (floor h) (* (floor h) (* dX.v dX.v))))
          (fma
           (floor h)
           (* dY.v t_3)
           (* (floor w) (* (floor w) (* dY.u dY.u))))))
        (t_7 (sqrt t_6))
        (t_8 (/ t_7 (floor maxAniso)))
        (t_9 (/ t_6 t_2))
        (t_10 (> t_9 (floor maxAniso)))
        (t_11 (/ t_2 t_7)))
   (if (< (if t_10 t_8 t_11) 1.0)
     (fmax 1.0 (* (if t_5 t_8 t_11) (if t_5 (floor maxAniso) t_4)))
     (if t_10 (floor maxAniso) t_9))))

C

float code(float w, float h, float dX_46_u, float dX_46_v, float dY_46_u, float dY_46_v, float maxAniso) {
	float t_0 = floorf(w) * dX_46_u;
	float t_1 = (dX_46_v * dY_46_u) - (dX_46_u * dY_46_v);
	float t_2 = fabsf((floorf(h) * (floorf(w) * t_1)));
	float t_3 = floorf(h) * dY_46_v;
	float t_4 = fmaxf((powf(t_0, 2.0f) + powf((floorf(h) * dX_46_v), 2.0f)), (powf((floorf(w) * dY_46_u), 2.0f) + powf(t_3, 2.0f))) / ((floorf(w) * floorf(h)) * t_1);
	int t_5 = t_4 > floorf(maxAniso);
	float t_6 = fmaxf(fmaf(floorf(w), (dX_46_u * t_0), (floorf(h) * (floorf(h) * (dX_46_v * dX_46_v)))), fmaf(floorf(h), (dY_46_v * t_3), (floorf(w) * (floorf(w) * (dY_46_u * dY_46_u)))));
	float t_7 = sqrtf(t_6);
	float t_8 = t_7 / floorf(maxAniso);
	float t_9 = t_6 / t_2;
	int t_10 = t_9 > floorf(maxAniso);
	float t_11 = t_2 / t_7;
	float tmp;
	if (t_10) {
		tmp = t_8;
	} else {
		tmp = t_11;
	}
	float tmp_3;
	if (tmp < 1.0f) {
		float tmp_4;
		if (t_5) {
			tmp_4 = t_8;
		} else {
			tmp_4 = t_11;
		}
		float tmp_5;
		if (t_5) {
			tmp_5 = floorf(maxAniso);
		} else {
			tmp_5 = t_4;
		}
		tmp_3 = fmaxf(1.0f, (tmp_4 * tmp_5));
	} else if (t_10) {
		tmp_3 = floorf(maxAniso);
	} else {
		tmp_3 = t_9;
	}
	return tmp_3;
}

Julia

function code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = Float32(floor(w) * dX_46_u)
	t_1 = Float32(Float32(dX_46_v * dY_46_u) - Float32(dX_46_u * dY_46_v))
	t_2 = abs(Float32(floor(h) * Float32(floor(w) * t_1)))
	t_3 = Float32(floor(h) * dY_46_v)
	t_4 = Float32(((Float32((t_0 ^ Float32(2.0)) + (Float32(floor(h) * dX_46_v) ^ Float32(2.0))) != Float32((t_0 ^ Float32(2.0)) + (Float32(floor(h) * dX_46_v) ^ Float32(2.0)))) ? Float32((Float32(floor(w) * dY_46_u) ^ Float32(2.0)) + (t_3 ^ Float32(2.0))) : ((Float32((Float32(floor(w) * dY_46_u) ^ Float32(2.0)) + (t_3 ^ Float32(2.0))) != Float32((Float32(floor(w) * dY_46_u) ^ Float32(2.0)) + (t_3 ^ Float32(2.0)))) ? Float32((t_0 ^ Float32(2.0)) + (Float32(floor(h) * dX_46_v) ^ Float32(2.0))) : max(Float32((t_0 ^ Float32(2.0)) + (Float32(floor(h) * dX_46_v) ^ Float32(2.0))), Float32((Float32(floor(w) * dY_46_u) ^ Float32(2.0)) + (t_3 ^ Float32(2.0)))))) / Float32(Float32(floor(w) * floor(h)) * t_1))
	t_5 = t_4 > floor(maxAniso)
	t_6 = (fma(floor(w), Float32(dX_46_u * t_0), Float32(floor(h) * Float32(floor(h) * Float32(dX_46_v * dX_46_v)))) != fma(floor(w), Float32(dX_46_u * t_0), Float32(floor(h) * Float32(floor(h) * Float32(dX_46_v * dX_46_v))))) ? fma(floor(h), Float32(dY_46_v * t_3), Float32(floor(w) * Float32(floor(w) * Float32(dY_46_u * dY_46_u)))) : ((fma(floor(h), Float32(dY_46_v * t_3), Float32(floor(w) * Float32(floor(w) * Float32(dY_46_u * dY_46_u)))) != fma(floor(h), Float32(dY_46_v * t_3), Float32(floor(w) * Float32(floor(w) * Float32(dY_46_u * dY_46_u))))) ? fma(floor(w), Float32(dX_46_u * t_0), Float32(floor(h) * Float32(floor(h) * Float32(dX_46_v * dX_46_v)))) : max(fma(floor(w), Float32(dX_46_u * t_0), Float32(floor(h) * Float32(floor(h) * Float32(dX_46_v * dX_46_v)))), fma(floor(h), Float32(dY_46_v * t_3), Float32(floor(w) * Float32(floor(w) * Float32(dY_46_u * dY_46_u))))))
	t_7 = sqrt(t_6)
	t_8 = Float32(t_7 / floor(maxAniso))
	t_9 = Float32(t_6 / t_2)
	t_10 = t_9 > floor(maxAniso)
	t_11 = Float32(t_2 / t_7)
	tmp = Float32(0.0)
	if (t_10)
		tmp = t_8;
	else
		tmp = t_11;
	end
	tmp_3 = Float32(0.0)
	if (tmp < Float32(1.0))
		tmp_4 = Float32(0.0)
		if (t_5)
			tmp_4 = t_8;
		else
			tmp_4 = t_11;
		end
		tmp_5 = Float32(0.0)
		if (t_5)
			tmp_5 = floor(maxAniso);
		else
			tmp_5 = t_4;
		end
		tmp_3 = (Float32(1.0) != Float32(1.0)) ? Float32(tmp_4 * tmp_5) : ((Float32(tmp_4 * tmp_5) != Float32(tmp_4 * tmp_5)) ? Float32(1.0) : max(Float32(1.0), Float32(tmp_4 * tmp_5)));
	elseif (t_10)
		tmp_3 = floor(maxAniso);
	else
		tmp_3 = t_9;
	end
	return tmp_3
end

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 4: 73.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left\lfloorh\right\rfloor \cdot dY.v\\ t_1 := \left\lfloorw\right\rfloor \cdot dX.u\\ t_2 := \left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\\ t_3 := dX.v \cdot dY.u - dX.u \cdot dY.v\\ t_4 := \left\lfloorh\right\rfloor \cdot dX.v\\ t_5 := \left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot t_3\right)\right|\\ t_6 := \mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, dX.u \cdot t_1, \left\lfloorh\right\rfloor \cdot \left(\left\lfloorh\right\rfloor \cdot \left(dX.v \cdot dX.v\right)\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, dY.v \cdot t_0, \left\lfloorw\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dY.u \cdot dY.u\right)\right)\right)\right)\\ t_7 := \frac{t_6}{t_5}\\ t_8 := \sqrt{t_6}\\ t_9 := \left\lfloorw\right\rfloor \cdot dY.u\\ t_10 := \left|t_1 \cdot t_0 - t_4 \cdot t_9\right|\\ t_11 := \mathsf{max}\left({t_1}^{2} + {t_4}^{2}, {t_9}^{2} + {t_0}^{2}\right)\\ t_12 := \frac{t_11}{t_2 \cdot t_3}\\ t_13 := \frac{t_11}{t_2 \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ t_14 := t_12 > \left\lfloormaxAniso\right\rfloor\\ t_15 := t_13 > \left\lfloormaxAniso\right\rfloor\\ t_16 := \mathsf{max}\left(t_1 \cdot t_1 + t_4 \cdot t_4, t_9 \cdot t_9 + t_0 \cdot t_0\right)\\ t_17 := \sqrt{t_16}\\ t_18 := \begin{array}{l} \mathbf{if}\;t_15:\\ \;\;\;\;\frac{t_17}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_10}{t_17}\\ \end{array}\\ t_19 := \frac{t_16}{t_10}\\ t_20 := \begin{array}{l} \mathbf{if}\;t_14:\\ \;\;\;\;\frac{t_8}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_5}{t_8}\\ \end{array}\\ \mathbf{if}\;\left\lfloorw\right\rfloor \leq 80:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;t_20 < 1:\\ \;\;\;\;\mathsf{max}\left(1, t_20 \cdot \begin{array}{l} \mathbf{if}\;t_14:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;t_12\\ \end{array}\right)\\ \mathbf{elif}\;t_7 > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;t_7\\ \end{array}\\ \mathbf{elif}\;t_18 < 1:\\ \;\;\;\;\mathsf{max}\left(1, t_18 \cdot \begin{array}{l} \mathbf{if}\;t_15:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;t_13\\ \end{array}\right)\\ \mathbf{elif}\;t_19 > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;t_19\\ \end{array} \end{array} \]

FPCore

(FPCore (w h dX.u dX.v dY.u dY.v maxAniso)
 :precision binary32
 (let* ((t_0 (* (floor h) dY.v))
        (t_1 (* (floor w) dX.u))
        (t_2 (* (floor w) (floor h)))
        (t_3 (- (* dX.v dY.u) (* dX.u dY.v)))
        (t_4 (* (floor h) dX.v))
        (t_5 (fabs (* (floor h) (* (floor w) t_3))))
        (t_6
         (fmax
          (fma
           (floor w)
           (* dX.u t_1)
           (* (floor h) (* (floor h) (* dX.v dX.v))))
          (fma
           (floor h)
           (* dY.v t_0)
           (* (floor w) (* (floor w) (* dY.u dY.u))))))
        (t_7 (/ t_6 t_5))
        (t_8 (sqrt t_6))
        (t_9 (* (floor w) dY.u))
        (t_10 (fabs (- (* t_1 t_0) (* t_4 t_9))))
        (t_11
         (fmax
          (+ (pow t_1 2.0) (pow t_4 2.0))
          (+ (pow t_9 2.0) (pow t_0 2.0))))
        (t_12 (/ t_11 (* t_2 t_3)))
        (t_13 (/ t_11 (* t_2 (- (* dX.u dY.v) (* dX.v dY.u)))))
        (t_14 (> t_12 (floor maxAniso)))
        (t_15 (> t_13 (floor maxAniso)))
        (t_16 (fmax (+ (* t_1 t_1) (* t_4 t_4)) (+ (* t_9 t_9) (* t_0 t_0))))
        (t_17 (sqrt t_16))
        (t_18 (if t_15 (/ t_17 (floor maxAniso)) (/ t_10 t_17)))
        (t_19 (/ t_16 t_10))
        (t_20 (if t_14 (/ t_8 (floor maxAniso)) (/ t_5 t_8))))
   (if (<= (floor w) 80.0)
     (if (< t_20 1.0)
       (fmax 1.0 (* t_20 (if t_14 (floor maxAniso) t_12)))
       (if (> t_7 (floor maxAniso)) (floor maxAniso) t_7))
     (if (< t_18 1.0)
       (fmax 1.0 (* t_18 (if t_15 (floor maxAniso) t_13)))
       (if (> t_19 (floor maxAniso)) (floor maxAniso) t_19)))))

C

float code(float w, float h, float dX_46_u, float dX_46_v, float dY_46_u, float dY_46_v, float maxAniso) {
	float t_0 = floorf(h) * dY_46_v;
	float t_1 = floorf(w) * dX_46_u;
	float t_2 = floorf(w) * floorf(h);
	float t_3 = (dX_46_v * dY_46_u) - (dX_46_u * dY_46_v);
	float t_4 = floorf(h) * dX_46_v;
	float t_5 = fabsf((floorf(h) * (floorf(w) * t_3)));
	float t_6 = fmaxf(fmaf(floorf(w), (dX_46_u * t_1), (floorf(h) * (floorf(h) * (dX_46_v * dX_46_v)))), fmaf(floorf(h), (dY_46_v * t_0), (floorf(w) * (floorf(w) * (dY_46_u * dY_46_u)))));
	float t_7 = t_6 / t_5;
	float t_8 = sqrtf(t_6);
	float t_9 = floorf(w) * dY_46_u;
	float t_10 = fabsf(((t_1 * t_0) - (t_4 * t_9)));
	float t_11 = fmaxf((powf(t_1, 2.0f) + powf(t_4, 2.0f)), (powf(t_9, 2.0f) + powf(t_0, 2.0f)));
	float t_12 = t_11 / (t_2 * t_3);
	float t_13 = t_11 / (t_2 * ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u)));
	int t_14 = t_12 > floorf(maxAniso);
	int t_15 = t_13 > floorf(maxAniso);
	float t_16 = fmaxf(((t_1 * t_1) + (t_4 * t_4)), ((t_9 * t_9) + (t_0 * t_0)));
	float t_17 = sqrtf(t_16);
	float tmp;
	if (t_15) {
		tmp = t_17 / floorf(maxAniso);
	} else {
		tmp = t_10 / t_17;
	}
	float t_18 = tmp;
	float t_19 = t_16 / t_10;
	float tmp_1;
	if (t_14) {
		tmp_1 = t_8 / floorf(maxAniso);
	} else {
		tmp_1 = t_5 / t_8;
	}
	float t_20 = tmp_1;
	float tmp_5;
	if (floorf(w) <= 80.0f) {
		float tmp_7;
		if (t_20 < 1.0f) {
			float tmp_8;
			if (t_14) {
				tmp_8 = floorf(maxAniso);
			} else {
				tmp_8 = t_12;
			}
			tmp_7 = fmaxf(1.0f, (t_20 * tmp_8));
		} else if (t_7 > floorf(maxAniso)) {
			tmp_7 = floorf(maxAniso);
		} else {
			tmp_7 = t_7;
		}
		tmp_5 = tmp_7;
	} else if (t_18 < 1.0f) {
		float tmp_9;
		if (t_15) {
			tmp_9 = floorf(maxAniso);
		} else {
			tmp_9 = t_13;
		}
		tmp_5 = fmaxf(1.0f, (t_18 * tmp_9));
	} else if (t_19 > floorf(maxAniso)) {
		tmp_5 = floorf(maxAniso);
	} else {
		tmp_5 = t_19;
	}
	return tmp_5;
}

Julia

function code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = Float32(floor(h) * dY_46_v)
	t_1 = Float32(floor(w) * dX_46_u)
	t_2 = Float32(floor(w) * floor(h))
	t_3 = Float32(Float32(dX_46_v * dY_46_u) - Float32(dX_46_u * dY_46_v))
	t_4 = Float32(floor(h) * dX_46_v)
	t_5 = abs(Float32(floor(h) * Float32(floor(w) * t_3)))
	t_6 = (fma(floor(w), Float32(dX_46_u * t_1), Float32(floor(h) * Float32(floor(h) * Float32(dX_46_v * dX_46_v)))) != fma(floor(w), Float32(dX_46_u * t_1), Float32(floor(h) * Float32(floor(h) * Float32(dX_46_v * dX_46_v))))) ? fma(floor(h), Float32(dY_46_v * t_0), Float32(floor(w) * Float32(floor(w) * Float32(dY_46_u * dY_46_u)))) : ((fma(floor(h), Float32(dY_46_v * t_0), Float32(floor(w) * Float32(floor(w) * Float32(dY_46_u * dY_46_u)))) != fma(floor(h), Float32(dY_46_v * t_0), Float32(floor(w) * Float32(floor(w) * Float32(dY_46_u * dY_46_u))))) ? fma(floor(w), Float32(dX_46_u * t_1), Float32(floor(h) * Float32(floor(h) * Float32(dX_46_v * dX_46_v)))) : max(fma(floor(w), Float32(dX_46_u * t_1), Float32(floor(h) * Float32(floor(h) * Float32(dX_46_v * dX_46_v)))), fma(floor(h), Float32(dY_46_v * t_0), Float32(floor(w) * Float32(floor(w) * Float32(dY_46_u * dY_46_u))))))
	t_7 = Float32(t_6 / t_5)
	t_8 = sqrt(t_6)
	t_9 = Float32(floor(w) * dY_46_u)
	t_10 = abs(Float32(Float32(t_1 * t_0) - Float32(t_4 * t_9)))
	t_11 = (Float32((t_1 ^ Float32(2.0)) + (t_4 ^ Float32(2.0))) != Float32((t_1 ^ Float32(2.0)) + (t_4 ^ Float32(2.0)))) ? Float32((t_9 ^ Float32(2.0)) + (t_0 ^ Float32(2.0))) : ((Float32((t_9 ^ Float32(2.0)) + (t_0 ^ Float32(2.0))) != Float32((t_9 ^ Float32(2.0)) + (t_0 ^ Float32(2.0)))) ? Float32((t_1 ^ Float32(2.0)) + (t_4 ^ Float32(2.0))) : max(Float32((t_1 ^ Float32(2.0)) + (t_4 ^ Float32(2.0))), Float32((t_9 ^ Float32(2.0)) + (t_0 ^ Float32(2.0)))))
	t_12 = Float32(t_11 / Float32(t_2 * t_3))
	t_13 = Float32(t_11 / Float32(t_2 * Float32(Float32(dX_46_u * dY_46_v) - Float32(dX_46_v * dY_46_u))))
	t_14 = t_12 > floor(maxAniso)
	t_15 = t_13 > floor(maxAniso)
	t_16 = (Float32(Float32(t_1 * t_1) + Float32(t_4 * t_4)) != Float32(Float32(t_1 * t_1) + Float32(t_4 * t_4))) ? Float32(Float32(t_9 * t_9) + Float32(t_0 * t_0)) : ((Float32(Float32(t_9 * t_9) + Float32(t_0 * t_0)) != Float32(Float32(t_9 * t_9) + Float32(t_0 * t_0))) ? Float32(Float32(t_1 * t_1) + Float32(t_4 * t_4)) : max(Float32(Float32(t_1 * t_1) + Float32(t_4 * t_4)), Float32(Float32(t_9 * t_9) + Float32(t_0 * t_0))))
	t_17 = sqrt(t_16)
	tmp = Float32(0.0)
	if (t_15)
		tmp = Float32(t_17 / floor(maxAniso));
	else
		tmp = Float32(t_10 / t_17);
	end
	t_18 = tmp
	t_19 = Float32(t_16 / t_10)
	tmp_1 = Float32(0.0)
	if (t_14)
		tmp_1 = Float32(t_8 / floor(maxAniso));
	else
		tmp_1 = Float32(t_5 / t_8);
	end
	t_20 = tmp_1
	tmp_5 = Float32(0.0)
	if (floor(w) <= Float32(80.0))
		tmp_7 = Float32(0.0)
		if (t_20 < Float32(1.0))
			tmp_8 = Float32(0.0)
			if (t_14)
				tmp_8 = floor(maxAniso);
			else
				tmp_8 = t_12;
			end
			tmp_7 = (Float32(1.0) != Float32(1.0)) ? Float32(t_20 * tmp_8) : ((Float32(t_20 * tmp_8) != Float32(t_20 * tmp_8)) ? Float32(1.0) : max(Float32(1.0), Float32(t_20 * tmp_8)));
		elseif (t_7 > floor(maxAniso))
			tmp_7 = floor(maxAniso);
		else
			tmp_7 = t_7;
		end
		tmp_5 = tmp_7;
	elseif (t_18 < Float32(1.0))
		tmp_9 = Float32(0.0)
		if (t_15)
			tmp_9 = floor(maxAniso);
		else
			tmp_9 = t_13;
		end
		tmp_5 = (Float32(1.0) != Float32(1.0)) ? Float32(t_18 * tmp_9) : ((Float32(t_18 * tmp_9) != Float32(t_18 * tmp_9)) ? Float32(1.0) : max(Float32(1.0), Float32(t_18 * tmp_9)));
	elseif (t_19 > floor(maxAniso))
		tmp_5 = floor(maxAniso);
	else
		tmp_5 = t_19;
	end
	return tmp_5
end

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 5: 96.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left\lfloorw\right\rfloor \cdot dX.u\\ t_1 := dX.v \cdot dY.u - dX.u \cdot dY.v\\ t_2 := \left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot t_1\right)\right|\\ t_3 := \left\lfloorh\right\rfloor \cdot dY.v\\ t_4 := \mathsf{max}\left({t_0}^{2} + {\left(\left\lfloorh\right\rfloor \cdot dX.v\right)}^{2}, {\left(\left\lfloorw\right\rfloor \cdot dY.u\right)}^{2} + {t_3}^{2}\right)\\ t_5 := \frac{t_4}{\left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot t_1}\\ t_6 := t_5 > \left\lfloormaxAniso\right\rfloor\\ t_7 := \mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, dX.u \cdot t_0, \left\lfloorh\right\rfloor \cdot \left(\left\lfloorh\right\rfloor \cdot \left(dX.v \cdot dX.v\right)\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, dY.v \cdot t_3, \left\lfloorw\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dY.u \cdot dY.u\right)\right)\right)\right)\\ t_8 := \frac{t_7}{t_2}\\ t_9 := t_8 > \left\lfloormaxAniso\right\rfloor\\ t_10 := \sqrt{t_7}\\ t_11 := \frac{t_10}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{if}\;\begin{array}{l} \mathbf{if}\;t_9:\\ \;\;\;\;t_11\\ \mathbf{else}:\\ \;\;\;\;\left\lfloorh\right\rfloor \cdot \left(\frac{\left\lfloorw\right\rfloor}{\sqrt{t_4}} \cdot \mathsf{fma}\left(dX.v, dY.u, dX.u \cdot \left(-dY.v\right)\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;t_6:\\ \;\;\;\;t_11\\ \mathbf{else}:\\ \;\;\;\;\frac{t_2}{t_10}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;t_6:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array}\right)\\ \mathbf{elif}\;t_9:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;t_8\\ \end{array} \end{array} \]

FPCore

(FPCore (w h dX.u dX.v dY.u dY.v maxAniso)
 :precision binary32
 (let* ((t_0 (* (floor w) dX.u))
        (t_1 (- (* dX.v dY.u) (* dX.u dY.v)))
        (t_2 (fabs (* (floor h) (* (floor w) t_1))))
        (t_3 (* (floor h) dY.v))
        (t_4
         (fmax
          (+ (pow t_0 2.0) (pow (* (floor h) dX.v) 2.0))
          (+ (pow (* (floor w) dY.u) 2.0) (pow t_3 2.0))))
        (t_5 (/ t_4 (* (* (floor w) (floor h)) t_1)))
        (t_6 (> t_5 (floor maxAniso)))
        (t_7
         (fmax
          (fma
           (floor w)
           (* dX.u t_0)
           (* (floor h) (* (floor h) (* dX.v dX.v))))
          (fma
           (floor h)
           (* dY.v t_3)
           (* (floor w) (* (floor w) (* dY.u dY.u))))))
        (t_8 (/ t_7 t_2))
        (t_9 (> t_8 (floor maxAniso)))
        (t_10 (sqrt t_7))
        (t_11 (/ t_10 (floor maxAniso))))
   (if (<
        (if t_9
          t_11
          (*
           (floor h)
           (* (/ (floor w) (sqrt t_4)) (fma dX.v dY.u (* dX.u (- dY.v))))))
        1.0)
     (fmax 1.0 (* (if t_6 t_11 (/ t_2 t_10)) (if t_6 (floor maxAniso) t_5)))
     (if t_9 (floor maxAniso) t_8))))

C

float code(float w, float h, float dX_46_u, float dX_46_v, float dY_46_u, float dY_46_v, float maxAniso) {
	float t_0 = floorf(w) * dX_46_u;
	float t_1 = (dX_46_v * dY_46_u) - (dX_46_u * dY_46_v);
	float t_2 = fabsf((floorf(h) * (floorf(w) * t_1)));
	float t_3 = floorf(h) * dY_46_v;
	float t_4 = fmaxf((powf(t_0, 2.0f) + powf((floorf(h) * dX_46_v), 2.0f)), (powf((floorf(w) * dY_46_u), 2.0f) + powf(t_3, 2.0f)));
	float t_5 = t_4 / ((floorf(w) * floorf(h)) * t_1);
	int t_6 = t_5 > floorf(maxAniso);
	float t_7 = fmaxf(fmaf(floorf(w), (dX_46_u * t_0), (floorf(h) * (floorf(h) * (dX_46_v * dX_46_v)))), fmaf(floorf(h), (dY_46_v * t_3), (floorf(w) * (floorf(w) * (dY_46_u * dY_46_u)))));
	float t_8 = t_7 / t_2;
	int t_9 = t_8 > floorf(maxAniso);
	float t_10 = sqrtf(t_7);
	float t_11 = t_10 / floorf(maxAniso);
	float tmp;
	if (t_9) {
		tmp = t_11;
	} else {
		tmp = floorf(h) * ((floorf(w) / sqrtf(t_4)) * fmaf(dX_46_v, dY_46_u, (dX_46_u * -dY_46_v)));
	}
	float tmp_3;
	if (tmp < 1.0f) {
		float tmp_4;
		if (t_6) {
			tmp_4 = t_11;
		} else {
			tmp_4 = t_2 / t_10;
		}
		float tmp_5;
		if (t_6) {
			tmp_5 = floorf(maxAniso);
		} else {
			tmp_5 = t_5;
		}
		tmp_3 = fmaxf(1.0f, (tmp_4 * tmp_5));
	} else if (t_9) {
		tmp_3 = floorf(maxAniso);
	} else {
		tmp_3 = t_8;
	}
	return tmp_3;
}

Julia

function code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = Float32(floor(w) * dX_46_u)
	t_1 = Float32(Float32(dX_46_v * dY_46_u) - Float32(dX_46_u * dY_46_v))
	t_2 = abs(Float32(floor(h) * Float32(floor(w) * t_1)))
	t_3 = Float32(floor(h) * dY_46_v)
	t_4 = (Float32((t_0 ^ Float32(2.0)) + (Float32(floor(h) * dX_46_v) ^ Float32(2.0))) != Float32((t_0 ^ Float32(2.0)) + (Float32(floor(h) * dX_46_v) ^ Float32(2.0)))) ? Float32((Float32(floor(w) * dY_46_u) ^ Float32(2.0)) + (t_3 ^ Float32(2.0))) : ((Float32((Float32(floor(w) * dY_46_u) ^ Float32(2.0)) + (t_3 ^ Float32(2.0))) != Float32((Float32(floor(w) * dY_46_u) ^ Float32(2.0)) + (t_3 ^ Float32(2.0)))) ? Float32((t_0 ^ Float32(2.0)) + (Float32(floor(h) * dX_46_v) ^ Float32(2.0))) : max(Float32((t_0 ^ Float32(2.0)) + (Float32(floor(h) * dX_46_v) ^ Float32(2.0))), Float32((Float32(floor(w) * dY_46_u) ^ Float32(2.0)) + (t_3 ^ Float32(2.0)))))
	t_5 = Float32(t_4 / Float32(Float32(floor(w) * floor(h)) * t_1))
	t_6 = t_5 > floor(maxAniso)
	t_7 = (fma(floor(w), Float32(dX_46_u * t_0), Float32(floor(h) * Float32(floor(h) * Float32(dX_46_v * dX_46_v)))) != fma(floor(w), Float32(dX_46_u * t_0), Float32(floor(h) * Float32(floor(h) * Float32(dX_46_v * dX_46_v))))) ? fma(floor(h), Float32(dY_46_v * t_3), Float32(floor(w) * Float32(floor(w) * Float32(dY_46_u * dY_46_u)))) : ((fma(floor(h), Float32(dY_46_v * t_3), Float32(floor(w) * Float32(floor(w) * Float32(dY_46_u * dY_46_u)))) != fma(floor(h), Float32(dY_46_v * t_3), Float32(floor(w) * Float32(floor(w) * Float32(dY_46_u * dY_46_u))))) ? fma(floor(w), Float32(dX_46_u * t_0), Float32(floor(h) * Float32(floor(h) * Float32(dX_46_v * dX_46_v)))) : max(fma(floor(w), Float32(dX_46_u * t_0), Float32(floor(h) * Float32(floor(h) * Float32(dX_46_v * dX_46_v)))), fma(floor(h), Float32(dY_46_v * t_3), Float32(floor(w) * Float32(floor(w) * Float32(dY_46_u * dY_46_u))))))
	t_8 = Float32(t_7 / t_2)
	t_9 = t_8 > floor(maxAniso)
	t_10 = sqrt(t_7)
	t_11 = Float32(t_10 / floor(maxAniso))
	tmp = Float32(0.0)
	if (t_9)
		tmp = t_11;
	else
		tmp = Float32(floor(h) * Float32(Float32(floor(w) / sqrt(t_4)) * fma(dX_46_v, dY_46_u, Float32(dX_46_u * Float32(-dY_46_v)))));
	end
	tmp_3 = Float32(0.0)
	if (tmp < Float32(1.0))
		tmp_4 = Float32(0.0)
		if (t_6)
			tmp_4 = t_11;
		else
			tmp_4 = Float32(t_2 / t_10);
		end
		tmp_5 = Float32(0.0)
		if (t_6)
			tmp_5 = floor(maxAniso);
		else
			tmp_5 = t_5;
		end
		tmp_3 = (Float32(1.0) != Float32(1.0)) ? Float32(tmp_4 * tmp_5) : ((Float32(tmp_4 * tmp_5) != Float32(tmp_4 * tmp_5)) ? Float32(1.0) : max(Float32(1.0), Float32(tmp_4 * tmp_5)));
	elseif (t_9)
		tmp_3 = floor(maxAniso);
	else
		tmp_3 = t_8;
	end
	return tmp_3
end

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 6: 96.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left\lfloorw\right\rfloor \cdot dX.u\\ t_1 := dX.v \cdot dY.u - dX.u \cdot dY.v\\ t_2 := \left\lfloorw\right\rfloor \cdot t_1\\ t_3 := \left|\left\lfloorh\right\rfloor \cdot t_2\right|\\ t_4 := \left\lfloorh\right\rfloor \cdot dY.v\\ t_5 := \mathsf{max}\left({t_0}^{2} + {\left(\left\lfloorh\right\rfloor \cdot dX.v\right)}^{2}, {\left(\left\lfloorw\right\rfloor \cdot dY.u\right)}^{2} + {t_4}^{2}\right)\\ t_6 := \frac{t_5}{\left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot t_1}\\ t_7 := \mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, dX.u \cdot t_0, \left\lfloorh\right\rfloor \cdot \left(\left\lfloorh\right\rfloor \cdot \left(dX.v \cdot dX.v\right)\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, dY.v \cdot t_4, \left\lfloorw\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dY.u \cdot dY.u\right)\right)\right)\right)\\ t_8 := \frac{t_7}{t_3}\\ t_9 := t_8 > \left\lfloormaxAniso\right\rfloor\\ t_10 := \sqrt{t_7}\\ t_11 := \frac{t_10}{\left\lfloormaxAniso\right\rfloor}\\ t_12 := t_6 > \left\lfloormaxAniso\right\rfloor\\ \mathbf{if}\;\begin{array}{l} \mathbf{if}\;t_9:\\ \;\;\;\;t_11\\ \mathbf{else}:\\ \;\;\;\;\frac{\left\lfloorh\right\rfloor}{\frac{\sqrt{t_5}}{t_2}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;t_12:\\ \;\;\;\;t_11\\ \mathbf{else}:\\ \;\;\;\;\frac{t_3}{t_10}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;t_12:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;t_6\\ \end{array}\right)\\ \mathbf{elif}\;t_9:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;t_8\\ \end{array} \end{array} \]

FPCore

(FPCore (w h dX.u dX.v dY.u dY.v maxAniso)
 :precision binary32
 (let* ((t_0 (* (floor w) dX.u))
        (t_1 (- (* dX.v dY.u) (* dX.u dY.v)))
        (t_2 (* (floor w) t_1))
        (t_3 (fabs (* (floor h) t_2)))
        (t_4 (* (floor h) dY.v))
        (t_5
         (fmax
          (+ (pow t_0 2.0) (pow (* (floor h) dX.v) 2.0))
          (+ (pow (* (floor w) dY.u) 2.0) (pow t_4 2.0))))
        (t_6 (/ t_5 (* (* (floor w) (floor h)) t_1)))
        (t_7
         (fmax
          (fma
           (floor w)
           (* dX.u t_0)
           (* (floor h) (* (floor h) (* dX.v dX.v))))
          (fma
           (floor h)
           (* dY.v t_4)
           (* (floor w) (* (floor w) (* dY.u dY.u))))))
        (t_8 (/ t_7 t_3))
        (t_9 (> t_8 (floor maxAniso)))
        (t_10 (sqrt t_7))
        (t_11 (/ t_10 (floor maxAniso)))
        (t_12 (> t_6 (floor maxAniso))))
   (if (< (if t_9 t_11 (/ (floor h) (/ (sqrt t_5) t_2))) 1.0)
     (fmax 1.0 (* (if t_12 t_11 (/ t_3 t_10)) (if t_12 (floor maxAniso) t_6)))
     (if t_9 (floor maxAniso) t_8))))

C

float code(float w, float h, float dX_46_u, float dX_46_v, float dY_46_u, float dY_46_v, float maxAniso) {
	float t_0 = floorf(w) * dX_46_u;
	float t_1 = (dX_46_v * dY_46_u) - (dX_46_u * dY_46_v);
	float t_2 = floorf(w) * t_1;
	float t_3 = fabsf((floorf(h) * t_2));
	float t_4 = floorf(h) * dY_46_v;
	float t_5 = fmaxf((powf(t_0, 2.0f) + powf((floorf(h) * dX_46_v), 2.0f)), (powf((floorf(w) * dY_46_u), 2.0f) + powf(t_4, 2.0f)));
	float t_6 = t_5 / ((floorf(w) * floorf(h)) * t_1);
	float t_7 = fmaxf(fmaf(floorf(w), (dX_46_u * t_0), (floorf(h) * (floorf(h) * (dX_46_v * dX_46_v)))), fmaf(floorf(h), (dY_46_v * t_4), (floorf(w) * (floorf(w) * (dY_46_u * dY_46_u)))));
	float t_8 = t_7 / t_3;
	int t_9 = t_8 > floorf(maxAniso);
	float t_10 = sqrtf(t_7);
	float t_11 = t_10 / floorf(maxAniso);
	int t_12 = t_6 > floorf(maxAniso);
	float tmp;
	if (t_9) {
		tmp = t_11;
	} else {
		tmp = floorf(h) / (sqrtf(t_5) / t_2);
	}
	float tmp_3;
	if (tmp < 1.0f) {
		float tmp_4;
		if (t_12) {
			tmp_4 = t_11;
		} else {
			tmp_4 = t_3 / t_10;
		}
		float tmp_5;
		if (t_12) {
			tmp_5 = floorf(maxAniso);
		} else {
			tmp_5 = t_6;
		}
		tmp_3 = fmaxf(1.0f, (tmp_4 * tmp_5));
	} else if (t_9) {
		tmp_3 = floorf(maxAniso);
	} else {
		tmp_3 = t_8;
	}
	return tmp_3;
}

Julia

function code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = Float32(floor(w) * dX_46_u)
	t_1 = Float32(Float32(dX_46_v * dY_46_u) - Float32(dX_46_u * dY_46_v))
	t_2 = Float32(floor(w) * t_1)
	t_3 = abs(Float32(floor(h) * t_2))
	t_4 = Float32(floor(h) * dY_46_v)
	t_5 = (Float32((t_0 ^ Float32(2.0)) + (Float32(floor(h) * dX_46_v) ^ Float32(2.0))) != Float32((t_0 ^ Float32(2.0)) + (Float32(floor(h) * dX_46_v) ^ Float32(2.0)))) ? Float32((Float32(floor(w) * dY_46_u) ^ Float32(2.0)) + (t_4 ^ Float32(2.0))) : ((Float32((Float32(floor(w) * dY_46_u) ^ Float32(2.0)) + (t_4 ^ Float32(2.0))) != Float32((Float32(floor(w) * dY_46_u) ^ Float32(2.0)) + (t_4 ^ Float32(2.0)))) ? Float32((t_0 ^ Float32(2.0)) + (Float32(floor(h) * dX_46_v) ^ Float32(2.0))) : max(Float32((t_0 ^ Float32(2.0)) + (Float32(floor(h) * dX_46_v) ^ Float32(2.0))), Float32((Float32(floor(w) * dY_46_u) ^ Float32(2.0)) + (t_4 ^ Float32(2.0)))))
	t_6 = Float32(t_5 / Float32(Float32(floor(w) * floor(h)) * t_1))
	t_7 = (fma(floor(w), Float32(dX_46_u * t_0), Float32(floor(h) * Float32(floor(h) * Float32(dX_46_v * dX_46_v)))) != fma(floor(w), Float32(dX_46_u * t_0), Float32(floor(h) * Float32(floor(h) * Float32(dX_46_v * dX_46_v))))) ? fma(floor(h), Float32(dY_46_v * t_4), Float32(floor(w) * Float32(floor(w) * Float32(dY_46_u * dY_46_u)))) : ((fma(floor(h), Float32(dY_46_v * t_4), Float32(floor(w) * Float32(floor(w) * Float32(dY_46_u * dY_46_u)))) != fma(floor(h), Float32(dY_46_v * t_4), Float32(floor(w) * Float32(floor(w) * Float32(dY_46_u * dY_46_u))))) ? fma(floor(w), Float32(dX_46_u * t_0), Float32(floor(h) * Float32(floor(h) * Float32(dX_46_v * dX_46_v)))) : max(fma(floor(w), Float32(dX_46_u * t_0), Float32(floor(h) * Float32(floor(h) * Float32(dX_46_v * dX_46_v)))), fma(floor(h), Float32(dY_46_v * t_4), Float32(floor(w) * Float32(floor(w) * Float32(dY_46_u * dY_46_u))))))
	t_8 = Float32(t_7 / t_3)
	t_9 = t_8 > floor(maxAniso)
	t_10 = sqrt(t_7)
	t_11 = Float32(t_10 / floor(maxAniso))
	t_12 = t_6 > floor(maxAniso)
	tmp = Float32(0.0)
	if (t_9)
		tmp = t_11;
	else
		tmp = Float32(floor(h) / Float32(sqrt(t_5) / t_2));
	end
	tmp_3 = Float32(0.0)
	if (tmp < Float32(1.0))
		tmp_4 = Float32(0.0)
		if (t_12)
			tmp_4 = t_11;
		else
			tmp_4 = Float32(t_3 / t_10);
		end
		tmp_5 = Float32(0.0)
		if (t_12)
			tmp_5 = floor(maxAniso);
		else
			tmp_5 = t_6;
		end
		tmp_3 = (Float32(1.0) != Float32(1.0)) ? Float32(tmp_4 * tmp_5) : ((Float32(tmp_4 * tmp_5) != Float32(tmp_4 * tmp_5)) ? Float32(1.0) : max(Float32(1.0), Float32(tmp_4 * tmp_5)));
	elseif (t_9)
		tmp_3 = floor(maxAniso);
	else
		tmp_3 = t_8;
	end
	return tmp_3
end

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 7: 73.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := dX.v \cdot dY.u - dX.u \cdot dY.v\\ t_1 := \left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot t_0\right)\right|\\ t_2 := \left\lfloorw\right\rfloor \cdot dX.u\\ t_3 := \left\lfloorh\right\rfloor \cdot dY.v\\ t_4 := \frac{\mathsf{max}\left({t_2}^{2} + {\left(\left\lfloorh\right\rfloor \cdot dX.v\right)}^{2}, {\left(\left\lfloorw\right\rfloor \cdot dY.u\right)}^{2} + {t_3}^{2}\right)}{\left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot t_0}\\ t_5 := t_4 > \left\lfloormaxAniso\right\rfloor\\ t_6 := \mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, dX.u \cdot t_2, \left\lfloorh\right\rfloor \cdot \left(\left\lfloorh\right\rfloor \cdot \left(dX.v \cdot dX.v\right)\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, dY.v \cdot t_3, \left\lfloorw\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dY.u \cdot dY.u\right)\right)\right)\right)\\ t_7 := \sqrt{t_6}\\ t_8 := \begin{array}{l} \mathbf{if}\;t_5:\\ \;\;\;\;\frac{t_7}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{t_7}\\ \end{array}\\ t_9 := \frac{t_6}{t_1}\\ \mathbf{if}\;t_8 < 1:\\ \;\;\;\;\mathsf{max}\left(1, t_8 \cdot \begin{array}{l} \mathbf{if}\;t_5:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array}\right)\\ \mathbf{elif}\;t_9 > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;t_9\\ \end{array} \end{array} \]

FPCore

(FPCore (w h dX.u dX.v dY.u dY.v maxAniso)
 :precision binary32
 (let* ((t_0 (- (* dX.v dY.u) (* dX.u dY.v)))
        (t_1 (fabs (* (floor h) (* (floor w) t_0))))
        (t_2 (* (floor w) dX.u))
        (t_3 (* (floor h) dY.v))
        (t_4
         (/
          (fmax
           (+ (pow t_2 2.0) (pow (* (floor h) dX.v) 2.0))
           (+ (pow (* (floor w) dY.u) 2.0) (pow t_3 2.0)))
          (* (* (floor w) (floor h)) t_0)))
        (t_5 (> t_4 (floor maxAniso)))
        (t_6
         (fmax
          (fma
           (floor w)
           (* dX.u t_2)
           (* (floor h) (* (floor h) (* dX.v dX.v))))
          (fma
           (floor h)
           (* dY.v t_3)
           (* (floor w) (* (floor w) (* dY.u dY.u))))))
        (t_7 (sqrt t_6))
        (t_8 (if t_5 (/ t_7 (floor maxAniso)) (/ t_1 t_7)))
        (t_9 (/ t_6 t_1)))
   (if (< t_8 1.0)
     (fmax 1.0 (* t_8 (if t_5 (floor maxAniso) t_4)))
     (if (> t_9 (floor maxAniso)) (floor maxAniso) t_9))))

C

float code(float w, float h, float dX_46_u, float dX_46_v, float dY_46_u, float dY_46_v, float maxAniso) {
	float t_0 = (dX_46_v * dY_46_u) - (dX_46_u * dY_46_v);
	float t_1 = fabsf((floorf(h) * (floorf(w) * t_0)));
	float t_2 = floorf(w) * dX_46_u;
	float t_3 = floorf(h) * dY_46_v;
	float t_4 = fmaxf((powf(t_2, 2.0f) + powf((floorf(h) * dX_46_v), 2.0f)), (powf((floorf(w) * dY_46_u), 2.0f) + powf(t_3, 2.0f))) / ((floorf(w) * floorf(h)) * t_0);
	int t_5 = t_4 > floorf(maxAniso);
	float t_6 = fmaxf(fmaf(floorf(w), (dX_46_u * t_2), (floorf(h) * (floorf(h) * (dX_46_v * dX_46_v)))), fmaf(floorf(h), (dY_46_v * t_3), (floorf(w) * (floorf(w) * (dY_46_u * dY_46_u)))));
	float t_7 = sqrtf(t_6);
	float tmp;
	if (t_5) {
		tmp = t_7 / floorf(maxAniso);
	} else {
		tmp = t_1 / t_7;
	}
	float t_8 = tmp;
	float t_9 = t_6 / t_1;
	float tmp_2;
	if (t_8 < 1.0f) {
		float tmp_3;
		if (t_5) {
			tmp_3 = floorf(maxAniso);
		} else {
			tmp_3 = t_4;
		}
		tmp_2 = fmaxf(1.0f, (t_8 * tmp_3));
	} else if (t_9 > floorf(maxAniso)) {
		tmp_2 = floorf(maxAniso);
	} else {
		tmp_2 = t_9;
	}
	return tmp_2;
}

Julia

function code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = Float32(Float32(dX_46_v * dY_46_u) - Float32(dX_46_u * dY_46_v))
	t_1 = abs(Float32(floor(h) * Float32(floor(w) * t_0)))
	t_2 = Float32(floor(w) * dX_46_u)
	t_3 = Float32(floor(h) * dY_46_v)
	t_4 = Float32(((Float32((t_2 ^ Float32(2.0)) + (Float32(floor(h) * dX_46_v) ^ Float32(2.0))) != Float32((t_2 ^ Float32(2.0)) + (Float32(floor(h) * dX_46_v) ^ Float32(2.0)))) ? Float32((Float32(floor(w) * dY_46_u) ^ Float32(2.0)) + (t_3 ^ Float32(2.0))) : ((Float32((Float32(floor(w) * dY_46_u) ^ Float32(2.0)) + (t_3 ^ Float32(2.0))) != Float32((Float32(floor(w) * dY_46_u) ^ Float32(2.0)) + (t_3 ^ Float32(2.0)))) ? Float32((t_2 ^ Float32(2.0)) + (Float32(floor(h) * dX_46_v) ^ Float32(2.0))) : max(Float32((t_2 ^ Float32(2.0)) + (Float32(floor(h) * dX_46_v) ^ Float32(2.0))), Float32((Float32(floor(w) * dY_46_u) ^ Float32(2.0)) + (t_3 ^ Float32(2.0)))))) / Float32(Float32(floor(w) * floor(h)) * t_0))
	t_5 = t_4 > floor(maxAniso)
	t_6 = (fma(floor(w), Float32(dX_46_u * t_2), Float32(floor(h) * Float32(floor(h) * Float32(dX_46_v * dX_46_v)))) != fma(floor(w), Float32(dX_46_u * t_2), Float32(floor(h) * Float32(floor(h) * Float32(dX_46_v * dX_46_v))))) ? fma(floor(h), Float32(dY_46_v * t_3), Float32(floor(w) * Float32(floor(w) * Float32(dY_46_u * dY_46_u)))) : ((fma(floor(h), Float32(dY_46_v * t_3), Float32(floor(w) * Float32(floor(w) * Float32(dY_46_u * dY_46_u)))) != fma(floor(h), Float32(dY_46_v * t_3), Float32(floor(w) * Float32(floor(w) * Float32(dY_46_u * dY_46_u))))) ? fma(floor(w), Float32(dX_46_u * t_2), Float32(floor(h) * Float32(floor(h) * Float32(dX_46_v * dX_46_v)))) : max(fma(floor(w), Float32(dX_46_u * t_2), Float32(floor(h) * Float32(floor(h) * Float32(dX_46_v * dX_46_v)))), fma(floor(h), Float32(dY_46_v * t_3), Float32(floor(w) * Float32(floor(w) * Float32(dY_46_u * dY_46_u))))))
	t_7 = sqrt(t_6)
	tmp = Float32(0.0)
	if (t_5)
		tmp = Float32(t_7 / floor(maxAniso));
	else
		tmp = Float32(t_1 / t_7);
	end
	t_8 = tmp
	t_9 = Float32(t_6 / t_1)
	tmp_2 = Float32(0.0)
	if (t_8 < Float32(1.0))
		tmp_3 = Float32(0.0)
		if (t_5)
			tmp_3 = floor(maxAniso);
		else
			tmp_3 = t_4;
		end
		tmp_2 = (Float32(1.0) != Float32(1.0)) ? Float32(t_8 * tmp_3) : ((Float32(t_8 * tmp_3) != Float32(t_8 * tmp_3)) ? Float32(1.0) : max(Float32(1.0), Float32(t_8 * tmp_3)));
	elseif (t_9 > floor(maxAniso))
		tmp_2 = floor(maxAniso);
	else
		tmp_2 = t_9;
	end
	return tmp_2
end

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Reproduce

herbie shell --seed 2024010 
(FPCore (w h dX.u dX.v dY.u dY.v maxAniso)
  :name "Anisotropic x16 LOD (ratio of anisotropy)"
  :precision binary32
  :pre (and (and (and (and (and (and (and (<= 1.0 w) (<= w 16384.0)) (and (<= 1.0 h) (<= h 16384.0))) (and (<= 1e-20 (fabs dX.u)) (<= (fabs dX.u) 1e+20))) (and (<= 1e-20 (fabs dX.v)) (<= (fabs dX.v) 1e+20))) (and (<= 1e-20 (fabs dY.u)) (<= (fabs dY.u) 1e+20))) (and (<= 1e-20 (fabs dY.v)) (<= (fabs dY.v) 1e+20))) (== maxAniso 16.0))
  (if (< (if (> (/ (fmax (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v)))) (fabs (- (* (* (floor w) dX.u) (* (floor h) dY.v)) (* (* (floor h) dX.v) (* (floor w) dY.u))))) (floor maxAniso)) (/ (sqrt (fmax (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v))))) (floor maxAniso)) (/ (fabs (- (* (* (floor w) dX.u) (* (floor h) dY.v)) (* (* (floor h) dX.v) (* (floor w) dY.u)))) (sqrt (fmax (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v))))))) 1.0) (fmax 1.0 (* (if (> (/ (fmax (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v)))) (fabs (- (* (* (floor w) dX.u) (* (floor h) dY.v)) (* (* (floor h) dX.v) (* (floor w) dY.u))))) (floor maxAniso)) (floor maxAniso) (/ (fmax (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v)))) (fabs (- (* (* (floor w) dX.u) (* (floor h) dY.v)) (* (* (floor h) dX.v) (* (floor w) dY.u)))))) (if (> (/ (fmax (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v)))) (fabs (- (* (* (floor w) dX.u) (* (floor h) dY.v)) (* (* (floor h) dX.v) (* (floor w) dY.u))))) (floor maxAniso)) (/ (sqrt (fmax (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v))))) (floor maxAniso)) (/ (fabs (- (* (* (floor w) dX.u) (* (floor h) dY.v)) (* (* (floor h) dX.v) (* (floor w) dY.u)))) (sqrt (fmax (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v))))))))) (if (> (/ (fmax (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v)))) (fabs (- (* (* (floor w) dX.u) (* (floor h) dY.v)) (* (* (floor h) dX.v) (* (floor w) dY.u))))) (floor maxAniso)) (floor maxAniso) (/ (fmax (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v)))) (fabs (- (* (* (floor w) dX.u) (* (floor h) dY.v)) (* (* (floor h) dX.v) (* (floor w) dY.u))))))))