Anisotropic x16 LOD (LOD)

Percentage Accurate: 75.8% → 75.8%

Time: 39.9s

Alternatives: 8

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

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

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 w) dY.u))
        (t_2 (* (floor h) dY.v))
        (t_3 (* (floor w) dX.u))
        (t_4 (fmax (+ (* t_3 t_3) (* t_0 t_0)) (+ (* t_1 t_1) (* t_2 t_2))))
        (t_5 (sqrt t_4))
        (t_6 (fabs (- (* t_3 t_2) (* t_0 t_1)))))
   (log2
    (if (> (/ t_4 t_6) (floor maxAniso))
      (/ t_5 (floor maxAniso))
      (/ t_6 t_5)))))

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(w) * dY_46_u;
	float t_2 = floorf(h) * dY_46_v;
	float t_3 = floorf(w) * dX_46_u;
	float t_4 = fmaxf(((t_3 * t_3) + (t_0 * t_0)), ((t_1 * t_1) + (t_2 * t_2)));
	float t_5 = sqrtf(t_4);
	float t_6 = fabsf(((t_3 * t_2) - (t_0 * t_1)));
	float tmp;
	if ((t_4 / t_6) > floorf(maxAniso)) {
		tmp = t_5 / floorf(maxAniso);
	} else {
		tmp = t_6 / t_5;
	}
	return log2f(tmp);
}

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(w) * dY_46_u)
	t_2 = Float32(floor(h) * dY_46_v)
	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_1 * t_1) + Float32(t_2 * t_2)) : ((Float32(Float32(t_1 * t_1) + Float32(t_2 * t_2)) != Float32(Float32(t_1 * t_1) + Float32(t_2 * t_2))) ? 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_1 * t_1) + Float32(t_2 * t_2))))
	t_5 = sqrt(t_4)
	t_6 = abs(Float32(Float32(t_3 * t_2) - Float32(t_0 * t_1)))
	tmp = Float32(0.0)
	if (Float32(t_4 / t_6) > floor(maxAniso))
		tmp = Float32(t_5 / floor(maxAniso));
	else
		tmp = Float32(t_6 / t_5);
	end
	return log2(tmp)
end

MATLAB

function tmp_2 = 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(w) * dY_46_u;
	t_2 = floor(h) * dY_46_v;
	t_3 = floor(w) * dX_46_u;
	t_4 = max(((t_3 * t_3) + (t_0 * t_0)), ((t_1 * t_1) + (t_2 * t_2)));
	t_5 = sqrt(t_4);
	t_6 = abs(((t_3 * t_2) - (t_0 * t_1)));
	tmp = single(0.0);
	if ((t_4 / t_6) > floor(maxAniso))
		tmp = t_5 / floor(maxAniso);
	else
		tmp = t_6 / t_5;
	end
	tmp_2 = log2(tmp);
end

Initial Program: 75.8% accurate, 1.0× speedup

Math

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

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 w) dY.u))
        (t_2 (* (floor h) dY.v))
        (t_3 (* (floor w) dX.u))
        (t_4 (fmax (+ (* t_3 t_3) (* t_0 t_0)) (+ (* t_1 t_1) (* t_2 t_2))))
        (t_5 (sqrt t_4))
        (t_6 (fabs (- (* t_3 t_2) (* t_0 t_1)))))
   (log2
    (if (> (/ t_4 t_6) (floor maxAniso))
      (/ t_5 (floor maxAniso))
      (/ t_6 t_5)))))

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(w) * dY_46_u;
	float t_2 = floorf(h) * dY_46_v;
	float t_3 = floorf(w) * dX_46_u;
	float t_4 = fmaxf(((t_3 * t_3) + (t_0 * t_0)), ((t_1 * t_1) + (t_2 * t_2)));
	float t_5 = sqrtf(t_4);
	float t_6 = fabsf(((t_3 * t_2) - (t_0 * t_1)));
	float tmp;
	if ((t_4 / t_6) > floorf(maxAniso)) {
		tmp = t_5 / floorf(maxAniso);
	} else {
		tmp = t_6 / t_5;
	}
	return log2f(tmp);
}

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(w) * dY_46_u)
	t_2 = Float32(floor(h) * dY_46_v)
	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_1 * t_1) + Float32(t_2 * t_2)) : ((Float32(Float32(t_1 * t_1) + Float32(t_2 * t_2)) != Float32(Float32(t_1 * t_1) + Float32(t_2 * t_2))) ? 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_1 * t_1) + Float32(t_2 * t_2))))
	t_5 = sqrt(t_4)
	t_6 = abs(Float32(Float32(t_3 * t_2) - Float32(t_0 * t_1)))
	tmp = Float32(0.0)
	if (Float32(t_4 / t_6) > floor(maxAniso))
		tmp = Float32(t_5 / floor(maxAniso));
	else
		tmp = Float32(t_6 / t_5);
	end
	return log2(tmp)
end

MATLAB

function tmp_2 = 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(w) * dY_46_u;
	t_2 = floor(h) * dY_46_v;
	t_3 = floor(w) * dX_46_u;
	t_4 = max(((t_3 * t_3) + (t_0 * t_0)), ((t_1 * t_1) + (t_2 * t_2)));
	t_5 = sqrt(t_4);
	t_6 = abs(((t_3 * t_2) - (t_0 * t_1)));
	tmp = single(0.0);
	if ((t_4 / t_6) > floor(maxAniso))
		tmp = t_5 / floor(maxAniso);
	else
		tmp = t_6 / t_5;
	end
	tmp_2 = log2(tmp);
end

Alternative 1: 75.8% accurate, 1.0× speedup

Math

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

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 w) dY.u))
        (t_2 (* (floor h) dY.v))
        (t_3 (* (floor w) dX.u))
        (t_4 (fmax (+ (* t_3 t_3) (* t_0 t_0)) (+ (* t_1 t_1) (* t_2 t_2))))
        (t_5 (sqrt t_4))
        (t_6 (fabs (- (* t_3 t_2) (* t_0 t_1)))))
   (log2
    (if (> (/ t_4 t_6) (floor maxAniso))
      (/ t_5 (floor maxAniso))
      (/ t_6 t_5)))))

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(w) * dY_46_u;
	float t_2 = floorf(h) * dY_46_v;
	float t_3 = floorf(w) * dX_46_u;
	float t_4 = fmaxf(((t_3 * t_3) + (t_0 * t_0)), ((t_1 * t_1) + (t_2 * t_2)));
	float t_5 = sqrtf(t_4);
	float t_6 = fabsf(((t_3 * t_2) - (t_0 * t_1)));
	float tmp;
	if ((t_4 / t_6) > floorf(maxAniso)) {
		tmp = t_5 / floorf(maxAniso);
	} else {
		tmp = t_6 / t_5;
	}
	return log2f(tmp);
}

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(w) * dY_46_u)
	t_2 = Float32(floor(h) * dY_46_v)
	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_1 * t_1) + Float32(t_2 * t_2)) : ((Float32(Float32(t_1 * t_1) + Float32(t_2 * t_2)) != Float32(Float32(t_1 * t_1) + Float32(t_2 * t_2))) ? 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_1 * t_1) + Float32(t_2 * t_2))))
	t_5 = sqrt(t_4)
	t_6 = abs(Float32(Float32(t_3 * t_2) - Float32(t_0 * t_1)))
	tmp = Float32(0.0)
	if (Float32(t_4 / t_6) > floor(maxAniso))
		tmp = Float32(t_5 / floor(maxAniso));
	else
		tmp = Float32(t_6 / t_5);
	end
	return log2(tmp)
end

MATLAB

function tmp_2 = 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(w) * dY_46_u;
	t_2 = floor(h) * dY_46_v;
	t_3 = floor(w) * dX_46_u;
	t_4 = max(((t_3 * t_3) + (t_0 * t_0)), ((t_1 * t_1) + (t_2 * t_2)));
	t_5 = sqrt(t_4);
	t_6 = abs(((t_3 * t_2) - (t_0 * t_1)));
	tmp = single(0.0);
	if ((t_4 / t_6) > floor(maxAniso))
		tmp = t_5 / floor(maxAniso);
	else
		tmp = t_6 / t_5;
	end
	tmp_2 = log2(tmp);
end

Derivation

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

Alternative 2: 75.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\\ t_1 := \mathsf{max}\left(\mathsf{fma}\left(dX.v \cdot t_0, dX.v, \left\lfloorw\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dX.u\right)\right)\right), \mathsf{fma}\left(dY.v \cdot t_0, dY.v, \left\lfloorw\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dY.u \cdot dY.u\right)\right)\right)\right)\\ t_2 := \sqrt{t_1}\\ t_3 := \left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.v \cdot dY.u - dX.u \cdot dY.v\right)\right)\right|\\ \log_{2} \begin{array}{l} \mathbf{if}\;\frac{t_1}{t_3} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{t_2}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_3}{t_2}\\ \end{array} \end{array} \end{array} \]

FPCore

(FPCore (w h dX.u dX.v dY.u dY.v maxAniso)
 :precision binary32
 (let* ((t_0 (* (floor h) (floor h)))
        (t_1
         (fmax
          (fma (* dX.v t_0) dX.v (* (floor w) (* (floor w) (* dX.u dX.u))))
          (fma (* dY.v t_0) dY.v (* (floor w) (* (floor w) (* dY.u dY.u))))))
        (t_2 (sqrt t_1))
        (t_3
         (fabs (* (floor h) (* (floor w) (- (* dX.v dY.u) (* dX.u dY.v)))))))
   (log2
    (if (> (/ t_1 t_3) (floor maxAniso))
      (/ t_2 (floor maxAniso))
      (/ t_3 t_2)))))

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) * floorf(h);
	float t_1 = fmaxf(fmaf((dX_46_v * t_0), dX_46_v, (floorf(w) * (floorf(w) * (dX_46_u * dX_46_u)))), fmaf((dY_46_v * t_0), dY_46_v, (floorf(w) * (floorf(w) * (dY_46_u * dY_46_u)))));
	float t_2 = sqrtf(t_1);
	float t_3 = fabsf((floorf(h) * (floorf(w) * ((dX_46_v * dY_46_u) - (dX_46_u * dY_46_v)))));
	float tmp;
	if ((t_1 / t_3) > floorf(maxAniso)) {
		tmp = t_2 / floorf(maxAniso);
	} else {
		tmp = t_3 / t_2;
	}
	return log2f(tmp);
}

Julia

function code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = Float32(floor(h) * floor(h))
	t_1 = (fma(Float32(dX_46_v * t_0), dX_46_v, Float32(floor(w) * Float32(floor(w) * Float32(dX_46_u * dX_46_u)))) != fma(Float32(dX_46_v * t_0), dX_46_v, Float32(floor(w) * Float32(floor(w) * Float32(dX_46_u * dX_46_u))))) ? fma(Float32(dY_46_v * t_0), dY_46_v, Float32(floor(w) * Float32(floor(w) * Float32(dY_46_u * dY_46_u)))) : ((fma(Float32(dY_46_v * t_0), dY_46_v, Float32(floor(w) * Float32(floor(w) * Float32(dY_46_u * dY_46_u)))) != fma(Float32(dY_46_v * t_0), dY_46_v, Float32(floor(w) * Float32(floor(w) * Float32(dY_46_u * dY_46_u))))) ? fma(Float32(dX_46_v * t_0), dX_46_v, Float32(floor(w) * Float32(floor(w) * Float32(dX_46_u * dX_46_u)))) : max(fma(Float32(dX_46_v * t_0), dX_46_v, Float32(floor(w) * Float32(floor(w) * Float32(dX_46_u * dX_46_u)))), fma(Float32(dY_46_v * t_0), dY_46_v, Float32(floor(w) * Float32(floor(w) * Float32(dY_46_u * dY_46_u))))))
	t_2 = sqrt(t_1)
	t_3 = abs(Float32(floor(h) * Float32(floor(w) * Float32(Float32(dX_46_v * dY_46_u) - Float32(dX_46_u * dY_46_v)))))
	tmp = Float32(0.0)
	if (Float32(t_1 / t_3) > floor(maxAniso))
		tmp = Float32(t_2 / floor(maxAniso));
	else
		tmp = Float32(t_3 / t_2);
	end
	return log2(tmp)
end

Derivation

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

Alternative 3: 74.3% accurate, 1.1× speedup

Math

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

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 (* (floor h) (floor h)))
        (t_2
         (fmax
          (fma (* dX.v t_1) dX.v (* (floor w) (* (floor w) (* dX.u dX.u))))
          (fma (* dY.v t_1) dY.v (* (floor w) (* (floor w) (* dY.u dY.u)))))))
   (log2
    (if (> (/ t_2 (fabs (* (floor h) (* (floor w) t_0)))) (floor maxAniso))
      (/ (sqrt t_2) (floor maxAniso))
      (*
       (floor w)
       (*
        (* (floor h) t_0)
        (/
         1.0
         (sqrt
          (fmax
           (+ (pow (* (floor w) dX.u) 2.0) (pow (* (floor h) dX.v) 2.0))
           (+
            (pow (* (floor w) dY.u) 2.0)
            (pow (* (floor h) dY.v) 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 = floorf(h) * floorf(h);
	float t_2 = fmaxf(fmaf((dX_46_v * t_1), dX_46_v, (floorf(w) * (floorf(w) * (dX_46_u * dX_46_u)))), fmaf((dY_46_v * t_1), dY_46_v, (floorf(w) * (floorf(w) * (dY_46_u * dY_46_u)))));
	float tmp;
	if ((t_2 / fabsf((floorf(h) * (floorf(w) * t_0)))) > floorf(maxAniso)) {
		tmp = sqrtf(t_2) / floorf(maxAniso);
	} else {
		tmp = floorf(w) * ((floorf(h) * t_0) * (1.0f / sqrtf(fmaxf((powf((floorf(w) * dX_46_u), 2.0f) + powf((floorf(h) * dX_46_v), 2.0f)), (powf((floorf(w) * dY_46_u), 2.0f) + powf((floorf(h) * dY_46_v), 2.0f))))));
	}
	return log2f(tmp);
}

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 = Float32(floor(h) * floor(h))
	t_2 = (fma(Float32(dX_46_v * t_1), dX_46_v, Float32(floor(w) * Float32(floor(w) * Float32(dX_46_u * dX_46_u)))) != fma(Float32(dX_46_v * t_1), dX_46_v, Float32(floor(w) * Float32(floor(w) * Float32(dX_46_u * dX_46_u))))) ? fma(Float32(dY_46_v * t_1), dY_46_v, Float32(floor(w) * Float32(floor(w) * Float32(dY_46_u * dY_46_u)))) : ((fma(Float32(dY_46_v * t_1), dY_46_v, Float32(floor(w) * Float32(floor(w) * Float32(dY_46_u * dY_46_u)))) != fma(Float32(dY_46_v * t_1), dY_46_v, Float32(floor(w) * Float32(floor(w) * Float32(dY_46_u * dY_46_u))))) ? fma(Float32(dX_46_v * t_1), dX_46_v, Float32(floor(w) * Float32(floor(w) * Float32(dX_46_u * dX_46_u)))) : max(fma(Float32(dX_46_v * t_1), dX_46_v, Float32(floor(w) * Float32(floor(w) * Float32(dX_46_u * dX_46_u)))), fma(Float32(dY_46_v * t_1), dY_46_v, Float32(floor(w) * Float32(floor(w) * Float32(dY_46_u * dY_46_u))))))
	tmp = Float32(0.0)
	if (Float32(t_2 / abs(Float32(floor(h) * Float32(floor(w) * t_0)))) > floor(maxAniso))
		tmp = Float32(sqrt(t_2) / floor(maxAniso));
	else
		tmp = Float32(floor(w) * Float32(Float32(floor(h) * t_0) * Float32(Float32(1.0) / sqrt(((Float32((Float32(floor(w) * dX_46_u) ^ Float32(2.0)) + (Float32(floor(h) * dX_46_v) ^ Float32(2.0))) != Float32((Float32(floor(w) * dX_46_u) ^ Float32(2.0)) + (Float32(floor(h) * dX_46_v) ^ Float32(2.0)))) ? Float32((Float32(floor(w) * dY_46_u) ^ Float32(2.0)) + (Float32(floor(h) * dY_46_v) ^ Float32(2.0))) : ((Float32((Float32(floor(w) * dY_46_u) ^ Float32(2.0)) + (Float32(floor(h) * dY_46_v) ^ Float32(2.0))) != Float32((Float32(floor(w) * dY_46_u) ^ Float32(2.0)) + (Float32(floor(h) * dY_46_v) ^ Float32(2.0)))) ? Float32((Float32(floor(w) * dX_46_u) ^ Float32(2.0)) + (Float32(floor(h) * dX_46_v) ^ Float32(2.0))) : max(Float32((Float32(floor(w) * dX_46_u) ^ Float32(2.0)) + (Float32(floor(h) * dX_46_v) ^ Float32(2.0))), Float32((Float32(floor(w) * dY_46_u) ^ Float32(2.0)) + (Float32(floor(h) * dY_46_v) ^ Float32(2.0))))))))));
	end
	return log2(tmp)
end

Derivation

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

Alternative 4: 42.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := dX.v \cdot dY.u - dX.u \cdot dY.v\\ t_1 := \mathsf{max}\left({\left(\left\lfloorw\right\rfloor \cdot dX.u\right)}^{2} + {\left(\left\lfloorh\right\rfloor \cdot dX.v\right)}^{2}, {\left(\left\lfloorw\right\rfloor \cdot dY.u\right)}^{2} + {\left(\left\lfloorh\right\rfloor \cdot dY.v\right)}^{2}\right)\\ t_2 := \left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\\ t_3 := \frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(dX.v \cdot t_2, dX.v, \left\lfloorw\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dX.u\right)\right)\right), \mathsf{fma}\left(dY.v \cdot t_2, dY.v, \left\lfloorw\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dY.u \cdot dY.u\right)\right)\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ t_4 := \sqrt{t_1}\\ \mathbf{if}\;dX.u \leq -3.99999992980668 \cdot 10^{-13}:\\ \;\;\;\;\log_{2} \begin{array}{l} \mathbf{if}\;\frac{t_1}{\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.v \cdot dY.u\right)\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\left\lfloorw\right\rfloor \cdot \left(\left(\left\lfloorh\right\rfloor \cdot t_0\right) \cdot \frac{1}{t_4}\right)\\ \end{array}\\ \mathbf{else}:\\ \;\;\;\;\log_{2} \begin{array}{l} \mathbf{if}\;\frac{\frac{t_1}{dX.u \cdot dY.v - dX.v \cdot dY.u}}{\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\frac{\left\lfloorh\right\rfloor}{\frac{t_4}{\left\lfloorw\right\rfloor \cdot t_0}}\\ \end{array}\\ \end{array} \end{array} \]

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
         (fmax
          (+ (pow (* (floor w) dX.u) 2.0) (pow (* (floor h) dX.v) 2.0))
          (+ (pow (* (floor w) dY.u) 2.0) (pow (* (floor h) dY.v) 2.0))))
        (t_2 (* (floor h) (floor h)))
        (t_3
         (/
          (sqrt
           (fmax
            (fma (* dX.v t_2) dX.v (* (floor w) (* (floor w) (* dX.u dX.u))))
            (fma (* dY.v t_2) dY.v (* (floor w) (* (floor w) (* dY.u dY.u))))))
          (floor maxAniso)))
        (t_4 (sqrt t_1)))
   (if (<= dX.u -3.99999992980668e-13)
     (log2
      (if (>
           (/ t_1 (* (floor h) (* (floor w) (* dX.v dY.u))))
           (floor maxAniso))
        t_3
        (* (floor w) (* (* (floor h) t_0) (/ 1.0 t_4)))))
     (log2
      (if (>
           (/ (/ t_1 (- (* dX.u dY.v) (* dX.v dY.u))) (* (floor w) (floor h)))
           (floor maxAniso))
        t_3
        (/ (floor h) (/ t_4 (* (floor w) t_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 = fmaxf((powf((floorf(w) * dX_46_u), 2.0f) + powf((floorf(h) * dX_46_v), 2.0f)), (powf((floorf(w) * dY_46_u), 2.0f) + powf((floorf(h) * dY_46_v), 2.0f)));
	float t_2 = floorf(h) * floorf(h);
	float t_3 = sqrtf(fmaxf(fmaf((dX_46_v * t_2), dX_46_v, (floorf(w) * (floorf(w) * (dX_46_u * dX_46_u)))), fmaf((dY_46_v * t_2), dY_46_v, (floorf(w) * (floorf(w) * (dY_46_u * dY_46_u)))))) / floorf(maxAniso);
	float t_4 = sqrtf(t_1);
	float tmp_1;
	if (dX_46_u <= -3.99999992980668e-13f) {
		float tmp_2;
		if ((t_1 / (floorf(h) * (floorf(w) * (dX_46_v * dY_46_u)))) > floorf(maxAniso)) {
			tmp_2 = t_3;
		} else {
			tmp_2 = floorf(w) * ((floorf(h) * t_0) * (1.0f / t_4));
		}
		tmp_1 = log2f(tmp_2);
	} else {
		float tmp_3;
		if (((t_1 / ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u))) / (floorf(w) * floorf(h))) > floorf(maxAniso)) {
			tmp_3 = t_3;
		} else {
			tmp_3 = floorf(h) / (t_4 / (floorf(w) * t_0));
		}
		tmp_1 = log2f(tmp_3);
	}
	return tmp_1;
}

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 = (Float32((Float32(floor(w) * dX_46_u) ^ Float32(2.0)) + (Float32(floor(h) * dX_46_v) ^ Float32(2.0))) != Float32((Float32(floor(w) * dX_46_u) ^ Float32(2.0)) + (Float32(floor(h) * dX_46_v) ^ Float32(2.0)))) ? Float32((Float32(floor(w) * dY_46_u) ^ Float32(2.0)) + (Float32(floor(h) * dY_46_v) ^ Float32(2.0))) : ((Float32((Float32(floor(w) * dY_46_u) ^ Float32(2.0)) + (Float32(floor(h) * dY_46_v) ^ Float32(2.0))) != Float32((Float32(floor(w) * dY_46_u) ^ Float32(2.0)) + (Float32(floor(h) * dY_46_v) ^ Float32(2.0)))) ? Float32((Float32(floor(w) * dX_46_u) ^ Float32(2.0)) + (Float32(floor(h) * dX_46_v) ^ Float32(2.0))) : max(Float32((Float32(floor(w) * dX_46_u) ^ Float32(2.0)) + (Float32(floor(h) * dX_46_v) ^ Float32(2.0))), Float32((Float32(floor(w) * dY_46_u) ^ Float32(2.0)) + (Float32(floor(h) * dY_46_v) ^ Float32(2.0)))))
	t_2 = Float32(floor(h) * floor(h))
	t_3 = Float32(sqrt(((fma(Float32(dX_46_v * t_2), dX_46_v, Float32(floor(w) * Float32(floor(w) * Float32(dX_46_u * dX_46_u)))) != fma(Float32(dX_46_v * t_2), dX_46_v, Float32(floor(w) * Float32(floor(w) * Float32(dX_46_u * dX_46_u))))) ? fma(Float32(dY_46_v * t_2), dY_46_v, Float32(floor(w) * Float32(floor(w) * Float32(dY_46_u * dY_46_u)))) : ((fma(Float32(dY_46_v * t_2), dY_46_v, Float32(floor(w) * Float32(floor(w) * Float32(dY_46_u * dY_46_u)))) != fma(Float32(dY_46_v * t_2), dY_46_v, Float32(floor(w) * Float32(floor(w) * Float32(dY_46_u * dY_46_u))))) ? fma(Float32(dX_46_v * t_2), dX_46_v, Float32(floor(w) * Float32(floor(w) * Float32(dX_46_u * dX_46_u)))) : max(fma(Float32(dX_46_v * t_2), dX_46_v, Float32(floor(w) * Float32(floor(w) * Float32(dX_46_u * dX_46_u)))), fma(Float32(dY_46_v * t_2), dY_46_v, Float32(floor(w) * Float32(floor(w) * Float32(dY_46_u * dY_46_u)))))))) / floor(maxAniso))
	t_4 = sqrt(t_1)
	tmp_1 = Float32(0.0)
	if (dX_46_u <= Float32(-3.99999992980668e-13))
		tmp_2 = Float32(0.0)
		if (Float32(t_1 / Float32(floor(h) * Float32(floor(w) * Float32(dX_46_v * dY_46_u)))) > floor(maxAniso))
			tmp_2 = t_3;
		else
			tmp_2 = Float32(floor(w) * Float32(Float32(floor(h) * t_0) * Float32(Float32(1.0) / t_4)));
		end
		tmp_1 = log2(tmp_2);
	else
		tmp_3 = Float32(0.0)
		if (Float32(Float32(t_1 / Float32(Float32(dX_46_u * dY_46_v) - Float32(dX_46_v * dY_46_u))) / Float32(floor(w) * floor(h))) > floor(maxAniso))
			tmp_3 = t_3;
		else
			tmp_3 = Float32(floor(h) / Float32(t_4 / Float32(floor(w) * t_0)));
		end
		tmp_1 = log2(tmp_3);
	end
	return tmp_1
end

Derivation

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

Alternative 5: 39.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left\lfloorh\right\rfloor \cdot dY.v\\ t_1 := \left\lfloorw\right\rfloor \cdot dX.u\\ t_2 := \left\lfloorh\right\rfloor \cdot dX.v\\ t_3 := \left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\\ t_4 := \left\lfloorw\right\rfloor \cdot dY.u\\ t_5 := \mathsf{max}\left({t_1}^{2} + {t_2}^{2}, {t_4}^{2} + {t_0}^{2}\right)\\ t_6 := \sqrt{t_5}\\ t_7 := \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right)\\ \mathbf{if}\;dY.v \leq 3.9999998989515007 \cdot 10^{-5}:\\ \;\;\;\;\log_{2} \begin{array}{l} \mathbf{if}\;\frac{-t_5}{dX.u \cdot \left(\left\lfloorw\right\rfloor \cdot t_0\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(dX.v \cdot t_3, dX.v, \left\lfloorw\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dX.u\right)\right)\right), \mathsf{fma}\left(dY.v \cdot t_3, dY.v, \left\lfloorw\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dY.u \cdot dY.u\right)\right)\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left\lfloorh\right\rfloor}{\frac{t_6}{\left\lfloorw\right\rfloor \cdot \left(dX.v \cdot dY.u - dX.u \cdot dY.v\right)}}\\ \end{array}\\ \mathbf{else}:\\ \;\;\;\;\log_{2} \begin{array}{l} \mathbf{if}\;\frac{t_5}{t_7} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(t_1 \cdot t_1 + t_2 \cdot t_2, t_4 \cdot t_4 + t_0 \cdot t_0\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_7}{t_6}\\ \end{array}\\ \end{array} \end{array} \]

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 h) dX.v))
        (t_3 (* (floor h) (floor h)))
        (t_4 (* (floor w) dY.u))
        (t_5
         (fmax
          (+ (pow t_1 2.0) (pow t_2 2.0))
          (+ (pow t_4 2.0) (pow t_0 2.0))))
        (t_6 (sqrt t_5))
        (t_7 (* (- (* dX.u dY.v) (* dX.v dY.u)) (* (floor w) (floor h)))))
   (if (<= dY.v 3.9999998989515007e-5)
     (log2
      (if (> (/ (- t_5) (* dX.u (* (floor w) t_0))) (floor maxAniso))
        (/
         (sqrt
          (fmax
           (fma (* dX.v t_3) dX.v (* (floor w) (* (floor w) (* dX.u dX.u))))
           (fma (* dY.v t_3) dY.v (* (floor w) (* (floor w) (* dY.u dY.u))))))
         (floor maxAniso))
        (/ (floor h) (/ t_6 (* (floor w) (- (* dX.v dY.u) (* dX.u dY.v)))))))
     (log2
      (if (> (/ t_5 t_7) (floor maxAniso))
        (/
         (sqrt (fmax (+ (* t_1 t_1) (* t_2 t_2)) (+ (* t_4 t_4) (* t_0 t_0))))
         (floor maxAniso))
        (/ t_7 t_6))))))

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(h) * dX_46_v;
	float t_3 = floorf(h) * floorf(h);
	float t_4 = floorf(w) * dY_46_u;
	float t_5 = fmaxf((powf(t_1, 2.0f) + powf(t_2, 2.0f)), (powf(t_4, 2.0f) + powf(t_0, 2.0f)));
	float t_6 = sqrtf(t_5);
	float t_7 = ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u)) * (floorf(w) * floorf(h));
	float tmp_1;
	if (dY_46_v <= 3.9999998989515007e-5f) {
		float tmp_2;
		if ((-t_5 / (dX_46_u * (floorf(w) * t_0))) > floorf(maxAniso)) {
			tmp_2 = sqrtf(fmaxf(fmaf((dX_46_v * t_3), dX_46_v, (floorf(w) * (floorf(w) * (dX_46_u * dX_46_u)))), fmaf((dY_46_v * t_3), dY_46_v, (floorf(w) * (floorf(w) * (dY_46_u * dY_46_u)))))) / floorf(maxAniso);
		} else {
			tmp_2 = floorf(h) / (t_6 / (floorf(w) * ((dX_46_v * dY_46_u) - (dX_46_u * dY_46_v))));
		}
		tmp_1 = log2f(tmp_2);
	} else {
		float tmp_3;
		if ((t_5 / t_7) > floorf(maxAniso)) {
			tmp_3 = sqrtf(fmaxf(((t_1 * t_1) + (t_2 * t_2)), ((t_4 * t_4) + (t_0 * t_0)))) / floorf(maxAniso);
		} else {
			tmp_3 = t_7 / t_6;
		}
		tmp_1 = log2f(tmp_3);
	}
	return tmp_1;
}

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(h) * dX_46_v)
	t_3 = Float32(floor(h) * floor(h))
	t_4 = Float32(floor(w) * dY_46_u)
	t_5 = (Float32((t_1 ^ Float32(2.0)) + (t_2 ^ Float32(2.0))) != Float32((t_1 ^ Float32(2.0)) + (t_2 ^ Float32(2.0)))) ? Float32((t_4 ^ Float32(2.0)) + (t_0 ^ Float32(2.0))) : ((Float32((t_4 ^ Float32(2.0)) + (t_0 ^ Float32(2.0))) != Float32((t_4 ^ Float32(2.0)) + (t_0 ^ Float32(2.0)))) ? Float32((t_1 ^ Float32(2.0)) + (t_2 ^ Float32(2.0))) : max(Float32((t_1 ^ Float32(2.0)) + (t_2 ^ Float32(2.0))), Float32((t_4 ^ Float32(2.0)) + (t_0 ^ Float32(2.0)))))
	t_6 = sqrt(t_5)
	t_7 = Float32(Float32(Float32(dX_46_u * dY_46_v) - Float32(dX_46_v * dY_46_u)) * Float32(floor(w) * floor(h)))
	tmp_1 = Float32(0.0)
	if (dY_46_v <= Float32(3.9999998989515007e-5))
		tmp_2 = Float32(0.0)
		if (Float32(Float32(-t_5) / Float32(dX_46_u * Float32(floor(w) * t_0))) > floor(maxAniso))
			tmp_2 = Float32(sqrt(((fma(Float32(dX_46_v * t_3), dX_46_v, Float32(floor(w) * Float32(floor(w) * Float32(dX_46_u * dX_46_u)))) != fma(Float32(dX_46_v * t_3), dX_46_v, Float32(floor(w) * Float32(floor(w) * Float32(dX_46_u * dX_46_u))))) ? fma(Float32(dY_46_v * t_3), dY_46_v, Float32(floor(w) * Float32(floor(w) * Float32(dY_46_u * dY_46_u)))) : ((fma(Float32(dY_46_v * t_3), dY_46_v, Float32(floor(w) * Float32(floor(w) * Float32(dY_46_u * dY_46_u)))) != fma(Float32(dY_46_v * t_3), dY_46_v, Float32(floor(w) * Float32(floor(w) * Float32(dY_46_u * dY_46_u))))) ? fma(Float32(dX_46_v * t_3), dX_46_v, Float32(floor(w) * Float32(floor(w) * Float32(dX_46_u * dX_46_u)))) : max(fma(Float32(dX_46_v * t_3), dX_46_v, Float32(floor(w) * Float32(floor(w) * Float32(dX_46_u * dX_46_u)))), fma(Float32(dY_46_v * t_3), dY_46_v, Float32(floor(w) * Float32(floor(w) * Float32(dY_46_u * dY_46_u)))))))) / floor(maxAniso));
		else
			tmp_2 = Float32(floor(h) / Float32(t_6 / Float32(floor(w) * Float32(Float32(dX_46_v * dY_46_u) - Float32(dX_46_u * dY_46_v)))));
		end
		tmp_1 = log2(tmp_2);
	else
		tmp_3 = Float32(0.0)
		if (Float32(t_5 / t_7) > floor(maxAniso))
			tmp_3 = Float32(sqrt(((Float32(Float32(t_1 * t_1) + Float32(t_2 * t_2)) != Float32(Float32(t_1 * t_1) + Float32(t_2 * t_2))) ? Float32(Float32(t_4 * t_4) + Float32(t_0 * t_0)) : ((Float32(Float32(t_4 * t_4) + Float32(t_0 * t_0)) != Float32(Float32(t_4 * t_4) + Float32(t_0 * t_0))) ? Float32(Float32(t_1 * t_1) + Float32(t_2 * t_2)) : max(Float32(Float32(t_1 * t_1) + Float32(t_2 * t_2)), Float32(Float32(t_4 * t_4) + Float32(t_0 * t_0)))))) / floor(maxAniso));
		else
			tmp_3 = Float32(t_7 / t_6);
		end
		tmp_1 = log2(tmp_3);
	end
	return tmp_1
end

Derivation

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

Alternative 6: 73.9% accurate, 1.2× speedup

Math

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

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 w) dY.u))
        (t_2 (* (floor h) dY.v))
        (t_3 (* (floor w) dX.u))
        (t_4
         (fmax
          (+ (pow t_3 2.0) (pow t_0 2.0))
          (+ (pow t_1 2.0) (pow t_2 2.0)))))
   (log2
    (if (>
         (/
          t_4
          (fabs (* (floor h) (* (floor w) (- (* dX.v dY.u) (* dX.u dY.v))))))
         (floor maxAniso))
      (/
       (sqrt (fmax (+ (* t_3 t_3) (* t_0 t_0)) (+ (* t_1 t_1) (* t_2 t_2))))
       (floor maxAniso))
      (/
       (* (- (* dX.u dY.v) (* dX.v dY.u)) (* (floor w) (floor h)))
       (sqrt t_4))))))

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(w) * dY_46_u;
	float t_2 = floorf(h) * dY_46_v;
	float t_3 = floorf(w) * dX_46_u;
	float t_4 = fmaxf((powf(t_3, 2.0f) + powf(t_0, 2.0f)), (powf(t_1, 2.0f) + powf(t_2, 2.0f)));
	float tmp;
	if ((t_4 / fabsf((floorf(h) * (floorf(w) * ((dX_46_v * dY_46_u) - (dX_46_u * dY_46_v)))))) > floorf(maxAniso)) {
		tmp = sqrtf(fmaxf(((t_3 * t_3) + (t_0 * t_0)), ((t_1 * t_1) + (t_2 * t_2)))) / floorf(maxAniso);
	} else {
		tmp = (((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u)) * (floorf(w) * floorf(h))) / sqrtf(t_4);
	}
	return log2f(tmp);
}

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(w) * dY_46_u)
	t_2 = Float32(floor(h) * dY_46_v)
	t_3 = Float32(floor(w) * dX_46_u)
	t_4 = (Float32((t_3 ^ Float32(2.0)) + (t_0 ^ Float32(2.0))) != Float32((t_3 ^ Float32(2.0)) + (t_0 ^ Float32(2.0)))) ? Float32((t_1 ^ Float32(2.0)) + (t_2 ^ Float32(2.0))) : ((Float32((t_1 ^ Float32(2.0)) + (t_2 ^ Float32(2.0))) != Float32((t_1 ^ Float32(2.0)) + (t_2 ^ Float32(2.0)))) ? Float32((t_3 ^ Float32(2.0)) + (t_0 ^ Float32(2.0))) : max(Float32((t_3 ^ Float32(2.0)) + (t_0 ^ Float32(2.0))), Float32((t_1 ^ Float32(2.0)) + (t_2 ^ Float32(2.0)))))
	tmp = Float32(0.0)
	if (Float32(t_4 / abs(Float32(floor(h) * Float32(floor(w) * Float32(Float32(dX_46_v * dY_46_u) - Float32(dX_46_u * dY_46_v)))))) > floor(maxAniso))
		tmp = Float32(sqrt(((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_1 * t_1) + Float32(t_2 * t_2)) : ((Float32(Float32(t_1 * t_1) + Float32(t_2 * t_2)) != Float32(Float32(t_1 * t_1) + Float32(t_2 * t_2))) ? 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_1 * t_1) + Float32(t_2 * t_2)))))) / floor(maxAniso));
	else
		tmp = Float32(Float32(Float32(Float32(dX_46_u * dY_46_v) - Float32(dX_46_v * dY_46_u)) * Float32(floor(w) * floor(h))) / sqrt(t_4));
	end
	return log2(tmp)
end

MATLAB

function tmp_2 = 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(w) * dY_46_u;
	t_2 = floor(h) * dY_46_v;
	t_3 = floor(w) * dX_46_u;
	t_4 = max(((t_3 ^ single(2.0)) + (t_0 ^ single(2.0))), ((t_1 ^ single(2.0)) + (t_2 ^ single(2.0))));
	tmp = single(0.0);
	if ((t_4 / abs((floor(h) * (floor(w) * ((dX_46_v * dY_46_u) - (dX_46_u * dY_46_v)))))) > floor(maxAniso))
		tmp = sqrt(max(((t_3 * t_3) + (t_0 * t_0)), ((t_1 * t_1) + (t_2 * t_2)))) / floor(maxAniso);
	else
		tmp = (((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u)) * (floor(w) * floor(h))) / sqrt(t_4);
	end
	tmp_2 = log2(tmp);
end

Derivation

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

Alternative 7: 39.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left\lfloorh\right\rfloor \cdot dY.v\\ t_1 := \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right)\\ t_2 := \left\lfloorw\right\rfloor \cdot dX.u\\ t_3 := \left\lfloorh\right\rfloor \cdot dX.v\\ t_4 := \left\lfloorw\right\rfloor \cdot dY.u\\ t_5 := \mathsf{max}\left({t_2}^{2} + {t_3}^{2}, {t_4}^{2} + {t_0}^{2}\right)\\ t_6 := \left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\\ t_7 := \sqrt{t_5}\\ \mathbf{if}\;dX.u \leq -3.99999992980668 \cdot 10^{-13}:\\ \;\;\;\;\log_{2} \begin{array}{l} \mathbf{if}\;\frac{t_5}{\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.v \cdot dY.u\right)\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(dX.v \cdot t_6, dX.v, \left\lfloorw\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dX.u\right)\right)\right), \mathsf{fma}\left(dY.v \cdot t_6, dY.v, \left\lfloorw\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dY.u \cdot dY.u\right)\right)\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\left\lfloorw\right\rfloor \cdot \left(\left(\left\lfloorh\right\rfloor \cdot \left(dX.v \cdot dY.u - dX.u \cdot dY.v\right)\right) \cdot \frac{1}{t_7}\right)\\ \end{array}\\ \mathbf{else}:\\ \;\;\;\;\log_{2} \begin{array}{l} \mathbf{if}\;\frac{t_5}{t_1} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(t_2 \cdot t_2 + t_3 \cdot t_3, t_4 \cdot t_4 + t_0 \cdot t_0\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{t_7}\\ \end{array}\\ \end{array} \end{array} \]

FPCore

(FPCore (w h dX.u dX.v dY.u dY.v maxAniso)
 :precision binary32
 (let* ((t_0 (* (floor h) dY.v))
        (t_1 (* (- (* dX.u dY.v) (* dX.v dY.u)) (* (floor w) (floor h))))
        (t_2 (* (floor w) dX.u))
        (t_3 (* (floor h) dX.v))
        (t_4 (* (floor w) dY.u))
        (t_5
         (fmax
          (+ (pow t_2 2.0) (pow t_3 2.0))
          (+ (pow t_4 2.0) (pow t_0 2.0))))
        (t_6 (* (floor h) (floor h)))
        (t_7 (sqrt t_5)))
   (if (<= dX.u -3.99999992980668e-13)
     (log2
      (if (>
           (/ t_5 (* (floor h) (* (floor w) (* dX.v dY.u))))
           (floor maxAniso))
        (/
         (sqrt
          (fmax
           (fma (* dX.v t_6) dX.v (* (floor w) (* (floor w) (* dX.u dX.u))))
           (fma (* dY.v t_6) dY.v (* (floor w) (* (floor w) (* dY.u dY.u))))))
         (floor maxAniso))
        (*
         (floor w)
         (* (* (floor h) (- (* dX.v dY.u) (* dX.u dY.v))) (/ 1.0 t_7)))))
     (log2
      (if (> (/ t_5 t_1) (floor maxAniso))
        (/
         (sqrt (fmax (+ (* t_2 t_2) (* t_3 t_3)) (+ (* t_4 t_4) (* t_0 t_0))))
         (floor maxAniso))
        (/ t_1 t_7))))))

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 = ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u)) * (floorf(w) * floorf(h));
	float t_2 = floorf(w) * dX_46_u;
	float t_3 = floorf(h) * dX_46_v;
	float t_4 = floorf(w) * dY_46_u;
	float t_5 = fmaxf((powf(t_2, 2.0f) + powf(t_3, 2.0f)), (powf(t_4, 2.0f) + powf(t_0, 2.0f)));
	float t_6 = floorf(h) * floorf(h);
	float t_7 = sqrtf(t_5);
	float tmp_1;
	if (dX_46_u <= -3.99999992980668e-13f) {
		float tmp_2;
		if ((t_5 / (floorf(h) * (floorf(w) * (dX_46_v * dY_46_u)))) > floorf(maxAniso)) {
			tmp_2 = sqrtf(fmaxf(fmaf((dX_46_v * t_6), dX_46_v, (floorf(w) * (floorf(w) * (dX_46_u * dX_46_u)))), fmaf((dY_46_v * t_6), dY_46_v, (floorf(w) * (floorf(w) * (dY_46_u * dY_46_u)))))) / floorf(maxAniso);
		} else {
			tmp_2 = floorf(w) * ((floorf(h) * ((dX_46_v * dY_46_u) - (dX_46_u * dY_46_v))) * (1.0f / t_7));
		}
		tmp_1 = log2f(tmp_2);
	} else {
		float tmp_3;
		if ((t_5 / t_1) > floorf(maxAniso)) {
			tmp_3 = sqrtf(fmaxf(((t_2 * t_2) + (t_3 * t_3)), ((t_4 * t_4) + (t_0 * t_0)))) / floorf(maxAniso);
		} else {
			tmp_3 = t_1 / t_7;
		}
		tmp_1 = log2f(tmp_3);
	}
	return tmp_1;
}

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(Float32(Float32(dX_46_u * dY_46_v) - Float32(dX_46_v * dY_46_u)) * Float32(floor(w) * floor(h)))
	t_2 = Float32(floor(w) * dX_46_u)
	t_3 = Float32(floor(h) * dX_46_v)
	t_4 = Float32(floor(w) * dY_46_u)
	t_5 = (Float32((t_2 ^ Float32(2.0)) + (t_3 ^ Float32(2.0))) != Float32((t_2 ^ Float32(2.0)) + (t_3 ^ Float32(2.0)))) ? Float32((t_4 ^ Float32(2.0)) + (t_0 ^ Float32(2.0))) : ((Float32((t_4 ^ Float32(2.0)) + (t_0 ^ Float32(2.0))) != Float32((t_4 ^ Float32(2.0)) + (t_0 ^ Float32(2.0)))) ? Float32((t_2 ^ Float32(2.0)) + (t_3 ^ Float32(2.0))) : max(Float32((t_2 ^ Float32(2.0)) + (t_3 ^ Float32(2.0))), Float32((t_4 ^ Float32(2.0)) + (t_0 ^ Float32(2.0)))))
	t_6 = Float32(floor(h) * floor(h))
	t_7 = sqrt(t_5)
	tmp_1 = Float32(0.0)
	if (dX_46_u <= Float32(-3.99999992980668e-13))
		tmp_2 = Float32(0.0)
		if (Float32(t_5 / Float32(floor(h) * Float32(floor(w) * Float32(dX_46_v * dY_46_u)))) > floor(maxAniso))
			tmp_2 = Float32(sqrt(((fma(Float32(dX_46_v * t_6), dX_46_v, Float32(floor(w) * Float32(floor(w) * Float32(dX_46_u * dX_46_u)))) != fma(Float32(dX_46_v * t_6), dX_46_v, Float32(floor(w) * Float32(floor(w) * Float32(dX_46_u * dX_46_u))))) ? fma(Float32(dY_46_v * t_6), dY_46_v, Float32(floor(w) * Float32(floor(w) * Float32(dY_46_u * dY_46_u)))) : ((fma(Float32(dY_46_v * t_6), dY_46_v, Float32(floor(w) * Float32(floor(w) * Float32(dY_46_u * dY_46_u)))) != fma(Float32(dY_46_v * t_6), dY_46_v, Float32(floor(w) * Float32(floor(w) * Float32(dY_46_u * dY_46_u))))) ? fma(Float32(dX_46_v * t_6), dX_46_v, Float32(floor(w) * Float32(floor(w) * Float32(dX_46_u * dX_46_u)))) : max(fma(Float32(dX_46_v * t_6), dX_46_v, Float32(floor(w) * Float32(floor(w) * Float32(dX_46_u * dX_46_u)))), fma(Float32(dY_46_v * t_6), dY_46_v, Float32(floor(w) * Float32(floor(w) * Float32(dY_46_u * dY_46_u)))))))) / floor(maxAniso));
		else
			tmp_2 = Float32(floor(w) * Float32(Float32(floor(h) * Float32(Float32(dX_46_v * dY_46_u) - Float32(dX_46_u * dY_46_v))) * Float32(Float32(1.0) / t_7)));
		end
		tmp_1 = log2(tmp_2);
	else
		tmp_3 = Float32(0.0)
		if (Float32(t_5 / t_1) > floor(maxAniso))
			tmp_3 = Float32(sqrt(((Float32(Float32(t_2 * t_2) + Float32(t_3 * t_3)) != Float32(Float32(t_2 * t_2) + Float32(t_3 * t_3))) ? Float32(Float32(t_4 * t_4) + Float32(t_0 * t_0)) : ((Float32(Float32(t_4 * t_4) + Float32(t_0 * t_0)) != Float32(Float32(t_4 * t_4) + Float32(t_0 * t_0))) ? Float32(Float32(t_2 * t_2) + Float32(t_3 * t_3)) : max(Float32(Float32(t_2 * t_2) + Float32(t_3 * t_3)), Float32(Float32(t_4 * t_4) + Float32(t_0 * t_0)))))) / floor(maxAniso));
		else
			tmp_3 = Float32(t_1 / t_7);
		end
		tmp_1 = log2(tmp_3);
	end
	return tmp_1
end

Derivation

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

Alternative 8: 38.5% accurate, 1.2× speedup

Math

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

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 w) dY.u))
        (t_2 (* (floor h) dY.v))
        (t_3 (* (floor w) dX.u))
        (t_4
         (fmax
          (+ (pow t_3 2.0) (pow t_0 2.0))
          (+ (pow t_1 2.0) (pow t_2 2.0))))
        (t_5 (* (- (* dX.u dY.v) (* dX.v dY.u)) (* (floor w) (floor h)))))
   (log2
    (if (> (/ t_4 t_5) (floor maxAniso))
      (/
       (sqrt (fmax (+ (* t_3 t_3) (* t_0 t_0)) (+ (* t_1 t_1) (* t_2 t_2))))
       (floor maxAniso))
      (/ t_5 (sqrt t_4))))))

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(w) * dY_46_u;
	float t_2 = floorf(h) * dY_46_v;
	float t_3 = floorf(w) * dX_46_u;
	float t_4 = fmaxf((powf(t_3, 2.0f) + powf(t_0, 2.0f)), (powf(t_1, 2.0f) + powf(t_2, 2.0f)));
	float t_5 = ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u)) * (floorf(w) * floorf(h));
	float tmp;
	if ((t_4 / t_5) > floorf(maxAniso)) {
		tmp = sqrtf(fmaxf(((t_3 * t_3) + (t_0 * t_0)), ((t_1 * t_1) + (t_2 * t_2)))) / floorf(maxAniso);
	} else {
		tmp = t_5 / sqrtf(t_4);
	}
	return log2f(tmp);
}

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(w) * dY_46_u)
	t_2 = Float32(floor(h) * dY_46_v)
	t_3 = Float32(floor(w) * dX_46_u)
	t_4 = (Float32((t_3 ^ Float32(2.0)) + (t_0 ^ Float32(2.0))) != Float32((t_3 ^ Float32(2.0)) + (t_0 ^ Float32(2.0)))) ? Float32((t_1 ^ Float32(2.0)) + (t_2 ^ Float32(2.0))) : ((Float32((t_1 ^ Float32(2.0)) + (t_2 ^ Float32(2.0))) != Float32((t_1 ^ Float32(2.0)) + (t_2 ^ Float32(2.0)))) ? Float32((t_3 ^ Float32(2.0)) + (t_0 ^ Float32(2.0))) : max(Float32((t_3 ^ Float32(2.0)) + (t_0 ^ Float32(2.0))), Float32((t_1 ^ Float32(2.0)) + (t_2 ^ Float32(2.0)))))
	t_5 = Float32(Float32(Float32(dX_46_u * dY_46_v) - Float32(dX_46_v * dY_46_u)) * Float32(floor(w) * floor(h)))
	tmp = Float32(0.0)
	if (Float32(t_4 / t_5) > floor(maxAniso))
		tmp = Float32(sqrt(((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_1 * t_1) + Float32(t_2 * t_2)) : ((Float32(Float32(t_1 * t_1) + Float32(t_2 * t_2)) != Float32(Float32(t_1 * t_1) + Float32(t_2 * t_2))) ? 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_1 * t_1) + Float32(t_2 * t_2)))))) / floor(maxAniso));
	else
		tmp = Float32(t_5 / sqrt(t_4));
	end
	return log2(tmp)
end

MATLAB

function tmp_2 = 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(w) * dY_46_u;
	t_2 = floor(h) * dY_46_v;
	t_3 = floor(w) * dX_46_u;
	t_4 = max(((t_3 ^ single(2.0)) + (t_0 ^ single(2.0))), ((t_1 ^ single(2.0)) + (t_2 ^ single(2.0))));
	t_5 = ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u)) * (floor(w) * floor(h));
	tmp = single(0.0);
	if ((t_4 / t_5) > floor(maxAniso))
		tmp = sqrt(max(((t_3 * t_3) + (t_0 * t_0)), ((t_1 * t_1) + (t_2 * t_2)))) / floor(maxAniso);
	else
		tmp = t_5 / sqrt(t_4);
	end
	tmp_2 = log2(tmp);
end

Derivation

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

Reproduce

herbie shell --seed 2024006 
(FPCore (w h dX.u dX.v dY.u dY.v maxAniso)
  :name "Anisotropic x16 LOD (LOD)"
  :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))
  (log2 (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)))))))))