[Libclc-dev] [PATCH 13/15] Use a more accurate implementation for exp

[Tom Stellard]

Using exp2(x * M_LOG2E_F) does not give us accurate enough results for
OpenCL.  If you look at the new exp implementation you'll see that
it does multiply the input by M_LOG2E_F, but it still uses the original
input in part of the calculation.

This exp implementation was ported from the AMD builtin library
and has been tested with piglit, OpenCV, and the ocl conformance tests.
---
 generic/lib/math/exp.cl  | 88 ++++++++++++++++++++++++++++++++++++++++++++++--
 generic/lib/math/exp.inc | 10 ------
 2 files changed, 85 insertions(+), 13 deletions(-)
 delete mode 100644 generic/lib/math/exp.inc

diff --git a/generic/lib/math/exp.cl b/generic/lib/math/exp.cl
index dbf4a93..37f693c 100644
--- a/generic/lib/math/exp.cl
+++ b/generic/lib/math/exp.cl
@@ -1,8 +1,90 @@
+/*
+ * Copyright (c) 2014,2015 Advanced Micro Devices, Inc.
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a copy
+ * of this software and associated documentation files (the "Software"), to deal
+ * in the Software without restriction, including without limitation the rights
+ * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+ * copies of the Software, and to permit persons to whom the Software is
+ * furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be included in
+ * all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+ * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+ * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+ * THE SOFTWARE.
+ */
+
 #include <clc/clc.h>
 
+#include "math.h"
+#include "../clcmacro.h"
+
+_CLC_OVERLOAD _CLC_DEF float exp(float x) {
+
+    // Reduce x
+    const float ln2HI = 0x1.62e300p-1f;
+    const float ln2LO = 0x1.2fefa2p-17f;
+    const float invln2 = 0x1.715476p+0f;
+
+    float fhalF = x < 0.0f ? -0.5f : 0.5f;
+    int p  = mad(x, invln2, fhalF);
+    float fp = (float)p;
+    float hi = mad(fp, -ln2HI, x); // t*ln2HI is exact here
+    float lo = -fp*ln2LO;
+
+    // Evaluate poly
+    float t = hi + lo;
+    float tt  = t*t;
+    float v = mad(tt,
+                  -mad(tt,
+                       mad(tt,
+                           mad(tt,
+                               mad(tt, 0x1.637698p-25f, -0x1.bbd41cp-20f),
+                               0x1.1566aap-14f),
+                           -0x1.6c16c2p-9f),
+                       0x1.555556p-3f),
+                  t);
+
+    float y = 1.0f - (((-lo) - MATH_DIVIDE(t * v, 2.0f - v)) - hi);
+
+    // Scale by 2^p
+    float r =  as_float(as_int(y) + (p << 23));
+
+    const float ulim =  0x1.62e430p+6f; // ln(largest_normal) = 88.72283905206835305366
+    const float llim = -0x1.5d589ep+6f; // ln(smallest_normal) = -87.33654475055310898657
+
+    r = x < llim ? 0.0f : r;
+    r = x < ulim ? r : as_float(0x7f800000);
+    return isnan(x) ? x : r;
+}
+
+_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, float, exp, float)
+
 #ifdef cl_khr_fp64
+
+#include "exp_helper.h"
+
 #pragma OPENCL EXTENSION cl_khr_fp64 : enable
-#endif
 
-#define __CLC_BODY <exp.inc>
-#include <clc/math/gentype.inc>
+_CLC_OVERLOAD _CLC_DEF double exp(double x) {
+
+    const double X_MIN = -0x1.74910d52d3051p+9; // -1075*ln(2)
+    const double X_MAX = 0x1.62e42fefa39efp+9; // 1024*ln(2)
+    const double R_64_BY_LOG2 = 0x1.71547652b82fep+6; // 64/ln(2)
+    const double R_LOG2_BY_64_LD = 0x1.62e42fefa0000p-7; // head ln(2)/64
+    const double R_LOG2_BY_64_TL = 0x1.cf79abc9e3b39p-46; // tail ln(2)/64
+
+    int n = convert_int(x * R_64_BY_LOG2);
+    double r = fma(-R_LOG2_BY_64_TL, (double)n, fma(-R_LOG2_BY_64_LD, (double)n, x));
+    return __clc_exp_helper(x, X_MIN, X_MAX, r, n);
+}
+
+_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, double, exp, double)
+
+#endif
diff --git a/generic/lib/math/exp.inc b/generic/lib/math/exp.inc
deleted file mode 100644
index 525fb59..0000000
--- a/generic/lib/math/exp.inc
+++ /dev/null
@@ -1,10 +0,0 @@
-_CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE exp(__CLC_GENTYPE val) {
-  // exp(x) = exp2(x * log2(e))
-#if __CLC_FPSIZE == 32
-  return exp2(val * M_LOG2E_F);
-#elif __CLC_FPSIZE == 64
-  return exp2(val * M_LOG2E);
-#else
-#error unknown _CLC_FPSIZE
-#endif
-}
-- 
2.0.4