improving custom formulae

libmandel/CMakeLists.txt

@@ -42,6 +42,7 @@ SET(MandelSources
     src/IterationGenerator.cpp
     src/IterationFormula.cpp
     src/IterationCompiler.cpp
+    src/IterationCompilerCl.cpp
     src/IterationIR.cpp
     src/NaiveIRGenerator.cpp
     src/FloatLog.cpp

libmandel/include/FloatLog.h

@@ -1,7 +1,23 @@
 #ifndef MANDEL_FLOATLOG_H
 #define MANDEL_FLOATLOG_H
 
+///
+/// \file FloatLog.h
+///
+/// This file exists as a workaround to the problem that when accessing functions
+/// in headers from a compilation unit which is compiled for a different
+/// instruction set (e.g. avx), the linker may take the avx-version also for
+/// calls from files compiled without avx.
+///
+
+///
+/// \brief same as \code float logf(float) \endcode
+///
 float floatLog(float x);
+
+///
+/// \brief same as \code float log2f(float) \endcode
+///
 float floatLog2(float x);
 
 #endif // MANDEL_FLOATLOG_H

libmandel/include/IterationGenerator.h

@@ -19,6 +19,7 @@ namespace mnd
     class CompiledGeneratorVec;
     class CompiledClGenerator;
     class CompiledClGeneratorDouble;
+    class CompiledClGeneratorDoubleDouble;
 
     // forward declaration
     struct ExecData;
@@ -97,6 +98,12 @@ class mnd::CompiledClGeneratorDouble : public mnd::ClGeneratorDouble
 public:
     CompiledClGeneratorDouble(MandelDevice& device, const std::string& code);
 };
+
+class mnd::CompiledClGeneratorDoubleDouble : public mnd::ClGeneratorDoubleDouble
+{
+public:
+    CompiledClGeneratorDoubleDouble(MandelDevice& device, const std::string& code);
+};
 #endif // WITH_OPENCL
 
 

libmandel/src/FloatLog.cpp

@@ -1,11 +1,13 @@
 #include "FloatLog.h"
 #include <cmath>
 
+
 float floatLog(float x)
 {
     return ::logf(x);
 }
 
+
 float floatLog2(float x)
 {
     return ::log2f(x);

libmandel/src/IterationCompiler.cpp

@@ -798,12 +798,6 @@ namespace mnd
 #endif // defined(__x86_64__) || defined(_M_X64)
 #endif // WITH_ASMJIT
 
-        //vec.push_back(std::make_unique<NaiveIRGenerator<mnd::DoubleDouble>>(irf));
-        //vec.push_back(std::make_unique<NaiveIRGenerator<mnd::QuadDouble>>(irf));
-        
-        //auto dg = std::make_unique<NaiveIRGenerator>(*irf, mnd::getPrecision<double>());
-
-        //vec.push_back(std::move(ng));
         return vec;
     }
 

libmandel/src/IterationGenerator.cpp

@@ -258,6 +258,13 @@ CompiledClGeneratorDouble::CompiledClGeneratorDouble(mnd::MandelDevice& device,
 {
 }
 
+
+CompiledClGeneratorDoubleDouble::CompiledClGeneratorDoubleDouble(mnd::MandelDevice& device, const std::string& code) :
+    ClGeneratorDoubleDouble{ device, code }
+{
+}
+
+
 #endif // WITH_OPENCL
 
 

libmandel/src/opencl/doubledouble.cl

@@ -14,18 +14,9 @@ inline double2 quickTwoSum(double a, double b) {
 }
 
 inline double2 twoProd(double a, double b) {
-//#ifdef QD_FMS
     double p = a * b;
     double e = fma(a, b, -p);
     return (double2)(p, e);
-//#else
-//  double a_hi, a_lo, b_hi, b_lo;
-//  double p = a * b;
-//  split(a, a_hi, a_lo);
-//  split(b, b_hi, b_lo);
-//  err = ((a_hi * b_hi - p) + a_hi * b_lo + a_lo * b_hi) + a_lo * b_lo;
-//  return p;
-//#endif
 }
 
 inline double2 mul(double2 a, double2 b) {
@@ -36,8 +27,8 @@ inline double2 mul(double2 a, double2 b) {
 
 inline double2 sq(double2 a) {
     double2 p = twoProd(a.s0, a.s0);
-    double e = a.s0 * a.s1;
-    p.s1 += e + e;
+    double e = 2 * a.s0 * a.s1;
+    p.s1 += e;
     return quickTwoSum(p.s0, p.s1);
 }
 

libmandel/src/opencl/doubledouble.h

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+  0x0a, 0x7d
 };
-unsigned int doubledouble_cl_len = 2964;
+unsigned int doubledouble_cl_len = 2726;

libmandel/src/opencl/hexdouble.h

@@ -429,175 +429,176 @@ unsigned char hexdouble_cl[] = {
   0x31, 0x20, 0x7d, 0x3b, 0x0d, 0x0a, 0x7d, 0x0d, 0x0a, 0x0d, 0x0a, 0x0d,
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+  0x5d, 0x20, 0x2b, 0x20, 0x62, 0x62, 0x2e, 0x78, 0x5b, 0x30, 0x5d, 0x20,
+  0x3e, 0x20, 0x31, 0x36, 0x29, 0x20, 0x62, 0x72, 0x65, 0x61, 0x6b, 0x3b,
+  0x0d, 0x0a, 0x20, 0x20, 0x20, 0x20, 0x20, 0x20, 0x20, 0x20, 0x6e, 0x2b,
+  0x2b, 0x3b, 0x0d, 0x0a, 0x20, 0x20, 0x20, 0x20, 0x7d, 0x0d, 0x0a, 0x0d,
+  0x0a, 0x20, 0x20, 0x20, 0x20, 0x2f, 0x2f, 0x20, 0x4e, 0x20, 0x2b, 0x20,
+  0x31, 0x20, 0x2d, 0x20, 0x6c, 0x6f, 0x67, 0x20, 0x28, 0x6c, 0x6f, 0x67,
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+  0x66, 0x20, 0x28, 0x6e, 0x20, 0x3e, 0x3d, 0x20, 0x6d, 0x61, 0x78, 0x20,
+  0x2d, 0x20, 0x31, 0x29, 0x0d, 0x0a, 0x20, 0x20, 0x20, 0x20, 0x20, 0x20,
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+  0x30, 0x5d, 0x20, 0x2b, 0x20, 0x62, 0x2e, 0x78, 0x5b, 0x30, 0x5d, 0x20,
+  0x2a, 0x20, 0x62, 0x2e, 0x78, 0x5b, 0x30, 0x5d, 0x29, 0x20, 0x2a, 0x20,
+  0x30, 0x2e, 0x35, 0x29, 0x3b, 0x0d, 0x0a, 0x20, 0x20, 0x20, 0x20, 0x20,
+  0x20, 0x20, 0x20, 0x65, 0x6c, 0x73, 0x65, 0x0d, 0x0a, 0x20, 0x20, 0x20,
+  0x20, 0x20, 0x20, 0x20, 0x20, 0x20, 0x20, 0x20, 0x20, 0x41, 0x5b, 0x69,
+  0x6e, 0x64, 0x65, 0x78, 0x5d, 0x20, 0x3d, 0x20, 0x28, 0x28, 0x66, 0x6c,
+  0x6f, 0x61, 0x74, 0x29, 0x6e, 0x29, 0x3b, 0x0d, 0x0a, 0x20, 0x20, 0x20,
+  0x20, 0x7d, 0x0d, 0x0a, 0x20, 0x20, 0x20, 0x20, 0x2f, 0x2f, 0x20, 0x20,
+  0x20, 0x20, 0x20, 0x20, 0x20, 0x20, 0x20, 0x20, 0x20, 0x20, 0x20, 0x20,
+  0x20, 0x41, 0x5b, 0x69, 0x6e, 0x64, 0x65, 0x78, 0x5d, 0x20, 0x3d, 0x20,
+  0x28, 0x28, 0x66, 0x6c, 0x6f, 0x61, 0x74, 0x29, 0x6e, 0x29, 0x20, 0x2b,
+  0x20, 0x31, 0x20, 0x2d, 0x20, 0x28, 0x61, 0x20, 0x2a, 0x20, 0x61, 0x20,
+  0x2b, 0x20, 0x62, 0x20, 0x2a, 0x20, 0x62, 0x20, 0x2d, 0x20, 0x31, 0x36,
+  0x29, 0x20, 0x2f, 0x20, 0x28, 0x32, 0x35, 0x36, 0x20, 0x2d, 0x20, 0x31,
+  0x36, 0x29, 0x3b, 0x0d, 0x0a, 0x20, 0x20, 0x20, 0x20, 0x2f, 0x2f, 0x20,
+  0x20, 0x20, 0x20, 0x20, 0x20, 0x20, 0x20, 0x20, 0x20, 0x20, 0x41, 0x5b,
+  0x67, 0x65, 0x74, 0x5f, 0x67, 0x6c, 0x6f, 0x62, 0x61, 0x6c, 0x5f, 0x69,
+  0x64, 0x28, 0x30, 0x29, 0x5d, 0x20, 0x3d, 0x20, 0x35, 0x3b, 0x0d, 0x0a,
+  0x7d, 0x0d, 0x0a, 0x0d, 0x0a
 };
-unsigned int hexdouble_cl_len = 7191;
+unsigned int hexdouble_cl_len = 7205;

libmandel/src/opencl_template/doubledouble.cl

@@ -0,0 +1,88 @@
+#pragma OPENCL EXTENSION cl_khr_fp64 : enable
+
+inline double2 twoSum(double a, double b) {
+    double s = a + b;
+    double bb = s - a;
+    double e = (a - (s - bb)) + (b - bb);
+    return (double2)(s, e);
+}
+
+inline double2 quickTwoSum(double a, double b) {
+    double s = a + b;
+    double e = b - (s - a);
+    return (double2)(s, e);
+}
+
+inline double2 twoProd(double a, double b) {
+    double p = a * b;
+    double e = fma(a, b, -p);
+    return (double2)(p, e);
+}
+
+inline double2 mul(double2 a, double2 b) {
+    double2 p = twoProd(a.s0, b.s0);
+    p.s1 += (a.s0 * b.s1 + a.s1 * b.s0);
+    return quickTwoSum(p.s0, p.s1);
+}
+
+inline double2 sq(double2 a) {
+    double2 p = twoProd(a.s0, a.s0);
+    double e = 2 * a.s0 * a.s1;
+    p.s1 += e;
+    return quickTwoSum(p.s0, p.s1);
+}
+
+inline double2 add(double2 a, double2 b) {
+    double2 se = twoSum(a.s0, b.s0);
+    se.s1 += a.s1 + b.s1;
+    return quickTwoSum(se.s0, se.s1);
+}
+
+inline double2 mulDouble(double2 a, double b) {
+    double2 p = twoProd(a.s0, b);
+    p.s1 += a.s1 * b;
+    return quickTwoSum(p.s0, p.s1);
+}
+
+__kernel void iterate(__global float* A, const int width,
+                      double x1, double x2, double y1, double y2,
+                      double pw1, double pw2, double ph1, double ph2, int max, int smooth,
+                      int julia, double jx1, double jx2, double jy1, double jy2) {
+    int index = get_global_id(0);
+    int px = index % width;
+    int py = index / width;
+
+    double2 xl = (double2)(x1, x2);
+    double2 yt = (double2)(y1, y2);
+    double2 pixelScaleX = (double2)(pw1, pw2);
+    double2 pixelScaleY = (double2)(ph1, ph2);
+    double2 a = add(mulDouble(pixelScaleX, (double) px), xl); // pixelScaleX * px + xl
+    double2 b = add(mulDouble(pixelScaleY, (double) py), yt); // pixelScaleY * py + yt
+    double2 ca = julia != 0 ? ((double2) (jx1, jx2)) : a;
+    double2 cb = julia != 0 ? ((double2) (jy1, jy2)) : b;
+
+
+    int n = 0;
+    while (n < max - 1) {
+        double2 aa = mul(a, a);
+        double2 bb = mul(b, b);
+        double2 ab = mul(a, b);
+        double2 minusbb = (double2)(-bb.s0, -bb.s1);
+        a = add(add(aa, minusbb), ca);
+        b = add(add(ab, ab), cb);
+        if (aa.s0 + bb.s0 > 16) break;
+        n++;
+    }
+
+    // N + 1 - log (log  |Z(N)|) / log 2
+    if (n >= max - 1)
+        A[index] = max;
+    else {
+        if (smooth != 0)
+            A[index] = ((float) n) + 1 - log(log(a.s0 * a.s0 + b.s0 * b.s0) / 2) / log(2.0f);
+        else
+            A[index] = ((float) n);
+    }
+    //               A[index] = ((float)n) + 1 - (a * a + b * b - 16) / (256 - 16);
+    //           A[get_global_id(0)] = 5;
+}

libmandel/src/opencl_template/doubledouble.h

@@ -0,0 +1,231 @@
+unsigned char doubledouble_cl[] = {
+  0x23, 0x70, 0x72, 0x61, 0x67, 0x6d, 0x61, 0x20, 0x4f, 0x50, 0x45, 0x4e,
+  0x43, 0x4c, 0x20, 0x45, 0x58, 0x54, 0x45, 0x4e, 0x53, 0x49, 0x4f, 0x4e,
+  0x20, 0x63, 0x6c, 0x5f, 0x6b, 0x68, 0x72, 0x5f, 0x66, 0x70, 0x36, 0x34,
+  0x20, 0x3a, 0x20, 0x65, 0x6e, 0x61, 0x62, 0x6c, 0x65, 0x0d, 0x0a, 0x0d,
+  0x0a, 0x69, 0x6e, 0x6c, 0x69, 0x6e, 0x65, 0x20, 0x64, 0x6f, 0x75, 0x62,
+  0x6c, 0x65, 0x32, 0x20, 0x74, 0x77, 0x6f, 0x53, 0x75, 0x6d, 0x28, 0x64,
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+  0x62, 0x6c, 0x65, 0x20, 0x62, 0x29, 0x20, 0x7b, 0x0d, 0x0a, 0x20, 0x20,
+  0x20, 0x20, 0x64, 0x6f, 0x75, 0x62, 0x6c, 0x65, 0x20, 0x73, 0x20, 0x3d,
+  0x20, 0x61, 0x20, 0x2b, 0x20, 0x62, 0x3b, 0x0d, 0x0a, 0x20, 0x20, 0x20,
+  0x20, 0x64, 0x6f, 0x75, 0x62, 0x6c, 0x65, 0x20, 0x62, 0x62, 0x20, 0x3d,
+  0x20, 0x73, 0x20, 0x2d, 0x20, 0x61, 0x3b, 0x0d, 0x0a, 0x20, 0x20, 0x20,
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+  0x29, 0x29, 0x20, 0x2b, 0x20, 0x28, 0x62, 0x20, 0x2d, 0x20, 0x62, 0x62,
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+  0x20, 0x20, 0x20, 0x20, 0x20, 0x20, 0x20, 0x20, 0x20, 0x20, 0x20, 0x41,
+  0x5b, 0x67, 0x65, 0x74, 0x5f, 0x67, 0x6c, 0x6f, 0x62, 0x61, 0x6c, 0x5f,
+  0x69, 0x64, 0x28, 0x30, 0x29, 0x5d, 0x20, 0x3d, 0x20, 0x35, 0x3b, 0x0d,
+  0x0a, 0x7d
+};
+unsigned int doubledouble_cl_len = 2726;

libmandel/src/opencl_template/makefile

@@ -0,0 +1,9 @@
+
+HEADERS := $(patsubst %.cl,%.h,$(wildcard *.cl))
+
+
+all: $(HEADERS)
+
+%.h: %.cl
+	xxd -i $< > $@
+