1 // Copyright 2017, VIXL authors
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3 //
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26
27 #include "examples.h"
28
29 using namespace vixl;
30 using namespace vixl::aarch32;
31
32 #define __ masm->
33
GenerateMandelBrot(MacroAssembler * masm)34 void GenerateMandelBrot(MacroAssembler* masm) {
35 const QRegister kCReal = q0;
36 const QRegister kCImag = q1;
37
38 const QRegister kCRealStep = q13;
39 const QRegister kCImagStep = q14;
40
41 const QRegister kModSqLimit = q15;
42
43 // Save register values.
44 __ Push(RegisterList(r4, r5, r6));
45
46 __ Vmov(F32, kCRealStep, 0.125);
47 __ Vmov(F32, kCImagStep, 0.0625);
48
49 const Register kZero = r2;
50 __ Mov(kZero, 0);
51
52 const DRegister kStars = d6;
53 const DRegister kSpaces = d7;
54 // Output characters - packed 4 characters into 32 bits.
55 __ Vmov(I8, kStars, '*');
56 __ Vmov(I8, kSpaces, ' ');
57
58 const DRegisterLane kNegTwo = DRegisterLane(d7, 1);
59 __ Vmov(s15, -2.0);
60
61 // Imaginary part of c.
62 __ Vdup(Untyped32, kCImag, kNegTwo);
63
64 // Max modulus squared.
65 __ Vmov(F32, kModSqLimit, 4.0);
66
67 // Height of output in characters.
68 __ Mov(r4, 64);
69
70 // String length will be 129, so need 132 bytes of space.
71 const uint32_t kStringLength = 132;
72
73 // Make space for our string.
74 __ Sub(sp, sp, kStringLength);
75
76 // Set up a starting pointer for the string.
77 const Register kStringPtr = r6;
78 __ Mov(kStringPtr, sp);
79
80 // Loop over imaginary values of c from -2 to 2, taking
81 // 64 equally spaced values in the range.
82 {
83 Label c_imag_loop;
84
85 __ Bind(&c_imag_loop);
86
87 // Real part of c.
88 // Store 4 equally spaced values in q0 (kCReal) to use SIMD.
89 __ Vmov(s0, -2.0);
90 __ Vmov(s1, -1.96875);
91 __ Vmov(s2, -1.9375);
92 __ Vmov(s3, -1.90625);
93
94 // Width of output in terms of sets of 4 characters - twice that
95 // of height to compensate for ratio of character height to width.
96 __ Mov(r5, 32);
97
98 const Register kWriteCursor = r3;
99 // Set a cursor ready to write the next line.
100 __ Mov(kWriteCursor, kStringPtr);
101
102 // Loop over real values of c from -2 to 2, processing
103 // 4 different values simultaneously using SIMD.
104 {
105 const QRegister kFlags = q2;
106 const DRegister kLowerFlags = d4;
107
108 Label c_real_loop;
109 __ Bind(&c_real_loop);
110
111 // Get number of iterations.
112 __ Add(r1, r0, 1);
113
114 // Perform the iterations of z(n+1) = zn^2 + c using SIMD.
115 // If the result is that c is in the set, the element of
116 // kFlags will be 0, else ~0.
117 {
118 const QRegister kZReal = q8;
119 const QRegister kZImag = q9;
120
121 // Real part of z.
122 __ Vmov(F32, kZReal, 0.0);
123
124 // Imaginary part of z.
125 __ Vmov(F32, kZImag, 0.0);
126
127 __ Vmov(F32, kFlags, 0.0);
128
129 Label iterative_formula_start, iterative_formula_end;
130 __ Bind(&iterative_formula_start);
131 __ Subs(r1, r1, 1);
132 __ B(le, &iterative_formula_end);
133
134 // z(n+1) = zn^2 + c.
135 // re(z(n+1)) = re(c) + re(zn)^2 - im(zn)^2.
136 // im(z(n+1)) = im(c) + 2 * re(zn) * im(zn)
137
138 __ Vmul(F32, q10, kZReal, kZImag); // re(zn) * im(zn)
139
140 __ Vmul(F32, kZReal, kZReal, kZReal); // re(zn)^2
141 __ Vadd(F32, kZReal, kCReal, kZReal); // re(c) + re(zn)^2
142 __ Vmls(F32, kZReal, kZImag, kZImag); // re(c) + re(zn)^2 - im(zn)^2
143
144 __ Vmov(F32, kZImag, kCImag); // im(c)
145 __ Vmls(F32, kZImag, q10, kNegTwo); // im(c) + 2 * re(zn) * im(zn)
146
147 __ Vmul(F32, q10, kZReal, kZReal); // re(z(n+1))^2
148 __ Vmla(F32, q10, kZImag, kZImag); // re(z(n+1))^2 + im(z(n+1))^2
149 __ Vcgt(F32, q10, q10, kModSqLimit); // |z(n+1)|^2 > 4 ? ~0 : 0
150 __ Vorr(F32, kFlags, kFlags, q10); // (~0/0) | above result
151
152 __ B(&iterative_formula_start);
153 __ Bind(&iterative_formula_end);
154 }
155
156 // Narrow twice so that each mask is 8 bits, packed into
157 // a single 32 bit register s4.
158 // kLowerFlags is the lower half of kFlags, so the second narrow will
159 // be working on the results of the first to halve the size of each
160 // representation again.
161 __ Vmovn(I32, kLowerFlags, kFlags);
162 __ Vmovn(I16, kLowerFlags, kFlags);
163
164 // '*' if in set, ' ' if not.
165 __ Vbsl(Untyped32, kLowerFlags, kSpaces, kStars);
166
167 // Add this to the string.
168 __ Vst1(Untyped32,
169 NeonRegisterList(kLowerFlags, 0),
170 AlignedMemOperand(kWriteCursor, k32BitAlign, PostIndex));
171
172 // Increase real part of c.
173 __ Vadd(F32, kCReal, kCReal, kCRealStep);
174
175 __ Subs(r5, r5, 1);
176 __ B(ne, &c_real_loop);
177 }
178
179 // Put terminating character.
180 __ Strb(kZero, MemOperand(kWriteCursor));
181
182 // Print the string.
183 __ Printf("%s\n", kStringPtr);
184
185 // Increase imaginary part of c.
186 __ Vadd(F32, kCImag, kCImag, kCImagStep);
187
188 __ Subs(r4, r4, 1);
189 __ B(ne, &c_imag_loop);
190 }
191 // Restore stack pointer.
192 __ Add(sp, sp, kStringLength);
193 // Restore register values.
194 __ Pop(RegisterList(r4, r5, r6));
195 __ Bx(lr);
196 }
197
198 #ifndef TEST_EXAMPLES
main()199 int main() {
200 MacroAssembler masm;
201 // Generate the code for the example function.
202 Label mandelbrot;
203 masm.Bind(&mandelbrot);
204 GenerateMandelBrot(&masm);
205 masm.FinalizeCode();
206 #ifdef VIXL_INCLUDE_SIMULATOR_AARCH32
207 // There is no simulator defined for VIXL AArch32.
208 printf("This example cannot be simulated\n");
209 #else
210 byte* code = masm.GetBuffer()->GetStartAddress<byte*>();
211 uint32_t code_size = masm.GetSizeOfCodeGenerated();
212 ExecutableMemory memory(code, code_size);
213 // Run the example function.
214 double (*mandelbrot_func)(uint32_t) =
215 memory.GetEntryPoint<double (*)(uint32_t)>(mandelbrot,
216 masm.GetInstructionSetInUse());
217 uint32_t iterations = 1000;
218 (*mandelbrot_func)(iterations);
219 #endif
220 return 0;
221 }
222 #endif // TEST_EXAMPLES
223