[Libclc-dev] [PATCH 1/2] Implement accurate log2 function
Tom Stellard
thomas.stellard at amd.com
Fri Jul 10 10:39:51 PDT 2015
Use the implementation was ported from the AMD builtin library rather
than LLVM Intrinsics.
This has been tested with piglit, OpenCV, and the ocl conformance tests.
---
generic/include/clc/math/log.h | 2 +-
generic/include/clc/math/log2.h | 28 +++-
generic/include/clc/math/log2.inc | 23 +++
generic/lib/SOURCES | 1 +
generic/lib/math/log2.cl | 37 +++++
generic/lib/math/log_base.h | 299 ++++++++++++++++++++++++++++++++++++++
generic/lib/math/tables.cl | 132 +++++++++++++++++
generic/lib/math/tables.h | 1 +
8 files changed, 517 insertions(+), 6 deletions(-)
create mode 100644 generic/include/clc/math/log2.inc
create mode 100644 generic/lib/math/log2.cl
create mode 100644 generic/lib/math/log_base.h
diff --git a/generic/include/clc/math/log.h b/generic/include/clc/math/log.h
index 644f857..ee272eb 100644
--- a/generic/include/clc/math/log.h
+++ b/generic/include/clc/math/log.h
@@ -1,4 +1,4 @@
#undef log
// log(x) = log2(x) * (1/log2(e))
-#define log(val) (__clc_log2(val) * 0.693147181f)
+#define log(val) (log2(val) * 0.693147181f)
diff --git a/generic/include/clc/math/log2.h b/generic/include/clc/math/log2.h
index 8801240..7bd813f 100644
--- a/generic/include/clc/math/log2.h
+++ b/generic/include/clc/math/log2.h
@@ -1,6 +1,24 @@
-#undef log2
-#define log2 __clc_log2
+/*
+ * Copyright (c) 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.
+ */
-#define __CLC_FUNCTION __clc_log2
-#define __CLC_INTRINSIC "llvm.log2"
-#include <clc/math/unary_intrin.inc>
+#define __CLC_BODY <clc/math/log2.inc>
+#include <clc/math/gentype.inc>
diff --git a/generic/include/clc/math/log2.inc b/generic/include/clc/math/log2.inc
new file mode 100644
index 0000000..1d27c8a
--- /dev/null
+++ b/generic/include/clc/math/log2.inc
@@ -0,0 +1,23 @@
+/*
+ * Copyright (c) 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.
+ */
+
+_CLC_OVERLOAD _CLC_DECL __CLC_GENTYPE log2(__CLC_GENTYPE a);
diff --git a/generic/lib/SOURCES b/generic/lib/SOURCES
index ec06807..bab678e 100644
--- a/generic/lib/SOURCES
+++ b/generic/lib/SOURCES
@@ -95,6 +95,7 @@ math/clc_ldexp.cl
math/ldexp.cl
math/log10.cl
math/log1p.cl
+math/log2.cl
math/mad.cl
math/tables.cl
math/clc_nextafter.cl
diff --git a/generic/lib/math/log2.cl b/generic/lib/math/log2.cl
new file mode 100644
index 0000000..df6eeb2
--- /dev/null
+++ b/generic/lib/math/log2.cl
@@ -0,0 +1,37 @@
+/*
+ * Copyright (c) 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 "../clcmacro.h"
+#include "tables.h"
+
+#ifdef cl_khr_fp64
+#pragma OPENCL EXTENSION cl_khr_fp64 : enable
+#endif // cl_khr_fp64
+
+#define COMPILING_LOG2
+#include "log_base.h"
+#undef COMPILING_LOG2
+
+_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, float, log2, float);
+
+_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, double, log2, double);
diff --git a/generic/lib/math/log_base.h b/generic/lib/math/log_base.h
new file mode 100644
index 0000000..bf2f82b
--- /dev/null
+++ b/generic/lib/math/log_base.h
@@ -0,0 +1,299 @@
+/*
+ * 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 "math.h"
+
+/*
+ Algorithm:
+
+ Based on:
+ Ping-Tak Peter Tang
+ "Table-driven implementation of the logarithm function in IEEE
+ floating-point arithmetic"
+ ACM Transactions on Mathematical Software (TOMS)
+ Volume 16, Issue 4 (December 1990)
+
+
+ x very close to 1.0 is handled differently, for x everywhere else
+ a brief explanation is given below
+
+ x = (2^m)*A
+ x = (2^m)*(G+g) with (1 <= G < 2) and (g <= 2^(-8))
+ x = (2^m)*2*(G/2+g/2)
+ x = (2^m)*2*(F+f) with (0.5 <= F < 1) and (f <= 2^(-9))
+
+ Y = (2^(-1))*(2^(-m))*(2^m)*A
+ Now, range of Y is: 0.5 <= Y < 1
+
+ F = 0x80 + (first 7 mantissa bits) + (8th mantissa bit)
+ Now, range of F is: 128 <= F <= 256
+ F = F / 256
+ Now, range of F is: 0.5 <= F <= 1
+
+ f = -(Y-F), with (f <= 2^(-9))
+
+ log(x) = m*log(2) + log(2) + log(F-f)
+ log(x) = m*log(2) + log(2) + log(F) + log(1-(f/F))
+ log(x) = m*log(2) + log(2*F) + log(1-r)
+
+ r = (f/F), with (r <= 2^(-8))
+ r = f*(1/F) with (1/F) precomputed to avoid division
+
+ log(x) = m*log(2) + log(G) - poly
+
+ log(G) is precomputed
+ poly = (r + (r^2)/2 + (r^3)/3 + (r^4)/4) + (r^5)/5))
+
+ log(2) and log(G) need to be maintained in extra precision
+ to avoid losing precision in the calculations
+
+
+ For x close to 1.0, we employ the following technique to
+ ensure faster convergence.
+
+ log(x) = log((1+s)/(1-s)) = 2*s + (2/3)*s^3 + (2/5)*s^5 + (2/7)*s^7
+ x = ((1+s)/(1-s))
+ x = 1 + r
+ s = r/(2+r)
+
+*/
+
+_CLC_OVERLOAD _CLC_DEF float
+#if defined(COMPILING_LOG2)
+log2(float x)
+#elif defined(COMPILING_LOG10)
+log10(float x)
+#else
+log(float x)
+#endif
+{
+
+#if defined(COMPILING_LOG2)
+ const float LOG2E = 0x1.715476p+0f; // 1.4426950408889634
+ const float LOG2E_HEAD = 0x1.700000p+0f; // 1.4375
+ const float LOG2E_TAIL = 0x1.547652p-8f; // 0.00519504072
+#elif defined(COMPILING_LOG10)
+ USE_TABLE(float2, p_log, LOG10_TBL);
+ const float LOG10E = 0x1.bcb7b2p-2f; // 0.43429448190325182
+ const float LOG10E_HEAD = 0x1.bc0000p-2f; // 0.43359375
+ const float LOG10E_TAIL = 0x1.6f62a4p-11f; // 0.0007007319
+ const float LOG10_2_HEAD = 0x1.340000p-2f; // 0.30078125
+ const float LOG10_2_TAIL = 0x1.04d426p-12f; // 0.000248745637
+#else
+ USE_TABLE(float2, p_log, LOGE_TBL);
+ const float LOG2_HEAD = 0x1.62e000p-1f; // 0.693115234
+ const float LOG2_TAIL = 0x1.0bfbe8p-15f; // 0.0000319461833
+#endif
+
+ uint xi = as_uint(x);
+ uint ax = xi & EXSIGNBIT_SP32;
+
+ // Calculations for |x-1| < 2^-4
+ float r = x - 1.0f;
+ int near1 = fabs(r) < 0x1.0p-4f;
+ float u2 = MATH_DIVIDE(r, 2.0f + r);
+ float corr = u2 * r;
+ float u = u2 + u2;
+ float v = u * u;
+ float znear1, z1, z2;
+
+ // 2/(5 * 2^5), 2/(3 * 2^3)
+ z2 = mad(u, mad(v, 0x1.99999ap-7f, 0x1.555556p-4f)*v, -corr);
+
+#if defined(COMPILING_LOG2)
+ z1 = as_float(as_int(r) & 0xffff0000);
+ z2 = z2 + (r - z1);
+ znear1 = mad(z1, LOG2E_HEAD, mad(z2, LOG2E_HEAD, mad(z1, LOG2E_TAIL, z2*LOG2E_TAIL)));
+#elif defined(COMPILING_LOG10)
+ z1 = as_float(as_int(r) & 0xffff0000);
+ z2 = z2 + (r - z1);
+ znear1 = mad(z1, LOG10E_HEAD, mad(z2, LOG10E_HEAD, mad(z1, LOG10E_TAIL, z2*LOG10E_TAIL)));
+#else
+ znear1 = z2 + r;
+#endif
+
+ // Calculations for x not near 1
+ int m = (int)(xi >> EXPSHIFTBITS_SP32) - EXPBIAS_SP32;
+
+ // Normalize subnormal
+ uint xis = as_uint(as_float(xi | 0x3f800000) - 1.0f);
+ int ms = (int)(xis >> EXPSHIFTBITS_SP32) - 253;
+ int c = m == -127;
+ m = c ? ms : m;
+ uint xin = c ? xis : xi;
+
+ float mf = (float)m;
+ uint indx = (xin & 0x007f0000) + ((xin & 0x00008000) << 1);
+
+ // F - Y
+ float f = as_float(0x3f000000 | indx) - as_float(0x3f000000 | (xin & MANTBITS_SP32));
+
+ indx = indx >> 16;
+ r = f * USE_TABLE(log_inv_tbl, indx);
+
+ // 1/3, 1/2
+ float poly = mad(mad(r, 0x1.555556p-2f, 0.5f), r*r, r);
+
+#if defined(COMPILING_LOG2)
+ float2 tv = USE_TABLE(log2_tbl, indx);
+ z1 = tv.s0 + mf;
+ z2 = mad(poly, -LOG2E, tv.s1);
+#elif defined(COMPILING_LOG10)
+ float2 tv = p_log[indx];
+ z1 = mad(mf, LOG10_2_HEAD, tv.s0);
+ z2 = mad(poly, -LOG10E, mf*LOG10_2_TAIL) + tv.s1;
+#else
+ float2 tv = p_log[indx];
+ z1 = mad(mf, LOG2_HEAD, tv.s0);
+ z2 = mad(mf, LOG2_TAIL, -poly) + tv.s1;
+#endif
+
+ float z = z1 + z2;
+ z = near1 ? znear1 : z;
+
+ // Corner cases
+ z = ax >= PINFBITPATT_SP32 ? x : z;
+ z = xi != ax ? as_float(QNANBITPATT_SP32) : z;
+ z = ax == 0 ? as_float(NINFBITPATT_SP32) : z;
+
+ return z;
+}
+
+#ifdef cl_khr_fp64
+
+_CLC_OVERLOAD _CLC_DEF double
+#if defined(COMPILING_LOG2)
+log2(double x)
+#elif defined(COMPILING_LOG10)
+log10(double x)
+#else
+log(double x)
+#endif
+{
+
+#ifndef COMPILING_LOG2
+ // log2_lead and log2_tail sum to an extra-precise version of ln(2)
+ const double log2_lead = 6.93147122859954833984e-01; /* 0x3fe62e42e0000000 */
+ const double log2_tail = 5.76999904754328540596e-08; /* 0x3e6efa39ef35793c */
+#endif
+
+#if defined(COMPILING_LOG10)
+ // log10e_lead and log10e_tail sum to an extra-precision version of log10(e) (19 bits in lead)
+ const double log10e_lead = 4.34293746948242187500e-01; /* 0x3fdbcb7800000000 */
+ const double log10e_tail = 7.3495500964015109100644e-7; /* 0x3ea8a93728719535 */
+#elif defined(COMPILING_LOG2)
+ // log2e_lead and log2e_tail sum to an extra-precision version of log2(e) (19 bits in lead)
+ const double log2e_lead = 1.44269180297851562500E+00; /* 0x3FF7154400000000 */
+ const double log2e_tail = 3.23791044778235969970E-06; /* 0x3ECB295C17F0BBBE */
+#endif
+
+ // log_thresh1 = 9.39412117004394531250e-1 = 0x3fee0faa00000000
+ // log_thresh2 = 1.06449508666992187500 = 0x3ff1082c00000000
+ const double log_thresh1 = 0x1.e0faap-1;
+ const double log_thresh2 = 0x1.1082cp+0;
+
+ int is_near = x >= log_thresh1 & x <= log_thresh2;
+
+ // Near 1 code
+ double r = x - 1.0;
+ double u = r / (2.0 + r);
+ double correction = r * u;
+ u = u + u;
+ double v = u * u;
+ double r1 = r;
+
+ const double ca_1 = 8.33333333333317923934e-02; /* 0x3fb55555555554e6 */
+ const double ca_2 = 1.25000000037717509602e-02; /* 0x3f89999999bac6d4 */
+ const double ca_3 = 2.23213998791944806202e-03; /* 0x3f62492307f1519f */
+ const double ca_4 = 4.34887777707614552256e-04; /* 0x3f3c8034c85dfff0 */
+
+ double r2 = fma(u*v, fma(v, fma(v, fma(v, ca_4, ca_3), ca_2), ca_1), -correction);
+
+#if defined(COMPILING_LOG10)
+ r = r1;
+ r1 = as_double(as_ulong(r1) & 0xffffffff00000000);
+ r2 = r2 + (r - r1);
+ double ret_near = fma(log10e_lead, r1, fma(log10e_lead, r2, fma(log10e_tail, r1, log10e_tail * r2)));
+#elif defined(COMPILING_LOG2)
+ r = r1;
+ r1 = as_double(as_ulong(r1) & 0xffffffff00000000);
+ r2 = r2 + (r - r1);
+ double ret_near = fma(log2e_lead, r1, fma(log2e_lead, r2, fma(log2e_tail, r1, log2e_tail*r2)));
+#else
+ double ret_near = r1 + r2;
+#endif
+
+ // This is the far from 1 code
+
+ // Deal with subnormal
+ ulong ux = as_ulong(x);
+ ulong uxs = as_ulong(as_double(0x03d0000000000000UL | ux) - 0x1.0p-962);
+ int c = ux < IMPBIT_DP64;
+ ux = c ? uxs : ux;
+ int expadjust = c ? 60 : 0;
+
+ int xexp = ((as_int2(ux).hi >> 20) & 0x7ff) - EXPBIAS_DP64 - expadjust;
+ double f = as_double(HALFEXPBITS_DP64 | (ux & MANTBITS_DP64));
+ int index = as_int2(ux).hi >> 13;
+ index = ((0x80 | (index & 0x7e)) >> 1) + (index & 0x1);
+
+ double2 tv = USE_TABLE(ln_tbl, index - 64);
+ double z1 = tv.s0;
+ double q = tv.s1;
+
+ double f1 = index * 0x1.0p-7;
+ double f2 = f - f1;
+ u = f2 / fma(f2, 0.5, f1);
+ v = u * u;
+
+ const double cb_1 = 8.33333333333333593622e-02; /* 0x3fb5555555555557 */
+ const double cb_2 = 1.24999999978138668903e-02; /* 0x3f89999999865ede */
+ const double cb_3 = 2.23219810758559851206e-03; /* 0x3f6249423bd94741 */
+
+ double poly = v * fma(v, fma(v, cb_3, cb_2), cb_1);
+ double z2 = q + fma(u, poly, u);
+
+ double dxexp = (double)xexp;
+#if defined (COMPILING_LOG10)
+ // Add xexp * log(2) to z1,z2 to get log(x)
+ r1 = fma(dxexp, log2_lead, z1);
+ r2 = fma(dxexp, log2_tail, z2);
+ double ret_far = fma(log10e_lead, r1, fma(log10e_lead, r2, fma(log10e_tail, r1, log10e_tail*r2)));
+#elif defined(COMPILING_LOG2)
+ r1 = fma(log2e_lead, z1, dxexp);
+ r2 = fma(log2e_lead, z2, fma(log2e_tail, z1, log2e_tail*z2));
+ double ret_far = r1 + r2;
+#else
+ r1 = fma(dxexp, log2_lead, z1);
+ r2 = fma(dxexp, log2_tail, z2);
+ double ret_far = r1 + r2;
+#endif
+
+ double ret = is_near ? ret_near : ret_far;
+
+ ret = isinf(x) ? as_double(PINFBITPATT_DP64) : ret;
+ ret = isnan(x) | (x < 0.0) ? as_double(QNANBITPATT_DP64) : ret;
+ ret = x == 0.0 ? as_double(NINFBITPATT_DP64) : ret;
+ return ret;
+}
+
+#endif // cl_khr_fp64
diff --git a/generic/lib/math/tables.cl b/generic/lib/math/tables.cl
index afb63c0..c1dd85c 100644
--- a/generic/lib/math/tables.cl
+++ b/generic/lib/math/tables.cl
@@ -288,6 +288,137 @@ DECLARE_TABLE(float, LOG_INV_TBL, 129) = {
0x1.000000p+0f,
};
+DECLARE_TABLE(float2, LOG2_TBL, 129) = {
+ (float2)(0x0.000000p+0f, 0x0.000000p+0f),
+ (float2)(0x1.6f8000p-7f, 0x1.942dbap-17f),
+ (float2)(0x1.6e0000p-6f, 0x1.e5a170p-16f),
+ (float2)(0x1.118000p-5f, 0x1.347544p-15f),
+ (float2)(0x1.6b8000p-5f, 0x1.69bac6p-16f),
+ (float2)(0x1.c48000p-5f, 0x1.7eae42p-15f),
+ (float2)(0x1.0e8000p-4f, 0x1.9c4fd0p-15f),
+ (float2)(0x1.3a8000p-4f, 0x1.17ee92p-15f),
+ (float2)(0x1.660000p-4f, 0x1.fb7d64p-15f),
+ (float2)(0x1.918000p-4f, 0x1.42dc8cp-17f),
+ (float2)(0x1.bc8000p-4f, 0x1.0902b6p-18f),
+ (float2)(0x1.e70000p-4f, 0x1.7608bep-15f),
+ (float2)(0x1.088000p-3f, 0x1.162336p-13f),
+ (float2)(0x1.1d8000p-3f, 0x1.3465d4p-13f),
+ (float2)(0x1.328000p-3f, 0x1.74f13cp-14f),
+ (float2)(0x1.470000p-3f, 0x1.aa7e60p-13f),
+ (float2)(0x1.5c0000p-3f, 0x1.a39fbcp-19f),
+ (float2)(0x1.700000p-3f, 0x1.d0b53ap-13f),
+ (float2)(0x1.848000p-3f, 0x1.0af40ap-13f),
+ (float2)(0x1.988000p-3f, 0x1.b741dep-13f),
+ (float2)(0x1.ac8000p-3f, 0x1.d78b6cp-13f),
+ (float2)(0x1.c08000p-3f, 0x1.6db376p-13f),
+ (float2)(0x1.d48000p-3f, 0x1.ee4c32p-15f),
+ (float2)(0x1.e80000p-3f, 0x1.02f9d2p-13f),
+ (float2)(0x1.fb8000p-3f, 0x1.05ae40p-13f),
+ (float2)(0x1.078000p-2f, 0x1.0adbb0p-14f),
+ (float2)(0x1.110000p-2f, 0x1.83ed68p-13f),
+ (float2)(0x1.1a8000p-2f, 0x1.016ca4p-12f),
+ (float2)(0x1.240000p-2f, 0x1.01eac2p-12f),
+ (float2)(0x1.2d8000p-2f, 0x1.887e26p-13f),
+ (float2)(0x1.370000p-2f, 0x1.24cea4p-14f),
+ (float2)(0x1.400000p-2f, 0x1.918ec6p-12f),
+ (float2)(0x1.498000p-2f, 0x1.3c25e6p-13f),
+ (float2)(0x1.528000p-2f, 0x1.6f7f12p-12f),
+ (float2)(0x1.5c0000p-2f, 0x1.a39fbcp-18f),
+ (float2)(0x1.650000p-2f, 0x1.8fe466p-14f),
+ (float2)(0x1.6e0000p-2f, 0x1.10e6cep-13f),
+ (float2)(0x1.770000p-2f, 0x1.d2ba7ep-14f),
+ (float2)(0x1.800000p-2f, 0x1.4ac62cp-15f),
+ (float2)(0x1.888000p-2f, 0x1.a71cb8p-12f),
+ (float2)(0x1.918000p-2f, 0x1.dd448ep-13f),
+ (float2)(0x1.9a8000p-2f, 0x1.1c8f10p-21f),
+ (float2)(0x1.a30000p-2f, 0x1.bb053ep-13f),
+ (float2)(0x1.ab8000p-2f, 0x1.861e5ep-12f),
+ (float2)(0x1.b40000p-2f, 0x1.fafdcep-12f),
+ (float2)(0x1.bd0000p-2f, 0x1.e5d3cep-15f),
+ (float2)(0x1.c58000p-2f, 0x1.2fad28p-14f),
+ (float2)(0x1.ce0000p-2f, 0x1.492474p-15f),
+ (float2)(0x1.d60000p-2f, 0x1.d4f80cp-12f),
+ (float2)(0x1.de8000p-2f, 0x1.4ff510p-12f),
+ (float2)(0x1.e70000p-2f, 0x1.3550f2p-13f),
+ (float2)(0x1.ef0000p-2f, 0x1.b59ccap-12f),
+ (float2)(0x1.f78000p-2f, 0x1.42b464p-13f),
+ (float2)(0x1.ff8000p-2f, 0x1.5e66a0p-12f),
+ (float2)(0x1.038000p-1f, 0x1.f6a2e4p-11f),
+ (float2)(0x1.080000p-1f, 0x1.39e4fep-14f),
+ (float2)(0x1.0c0000p-1f, 0x1.0500d6p-13f),
+ (float2)(0x1.100000p-1f, 0x1.13b152p-13f),
+ (float2)(0x1.140000p-1f, 0x1.93f542p-14f),
+ (float2)(0x1.180000p-1f, 0x1.467b94p-16f),
+ (float2)(0x1.1b8000p-1f, 0x1.cc47a4p-11f),
+ (float2)(0x1.1f8000p-1f, 0x1.78f4c2p-11f),
+ (float2)(0x1.238000p-1f, 0x1.107508p-11f),
+ (float2)(0x1.278000p-1f, 0x1.2602c2p-12f),
+ (float2)(0x1.2b8000p-1f, 0x1.a39fbcp-20f),
+ (float2)(0x1.2f0000p-1f, 0x1.5a1d7ap-11f),
+ (float2)(0x1.330000p-1f, 0x1.3e355ap-12f),
+ (float2)(0x1.368000p-1f, 0x1.cffedap-11f),
+ (float2)(0x1.3a8000p-1f, 0x1.d9fd50p-12f),
+ (float2)(0x1.3e0000p-1f, 0x1.f64de6p-11f),
+ (float2)(0x1.420000p-1f, 0x1.d83f4cp-12f),
+ (float2)(0x1.458000p-1f, 0x1.cea628p-11f),
+ (float2)(0x1.498000p-1f, 0x1.3c25e6p-12f),
+ (float2)(0x1.4d0000p-1f, 0x1.5a96ccp-11f),
+ (float2)(0x1.510000p-1f, 0x1.18708ap-17f),
+ (float2)(0x1.548000p-1f, 0x1.374652p-12f),
+ (float2)(0x1.580000p-1f, 0x1.2089a6p-11f),
+ (float2)(0x1.5b8000p-1f, 0x1.93432cp-11f),
+ (float2)(0x1.5f0000p-1f, 0x1.f3fd06p-11f),
+ (float2)(0x1.630000p-1f, 0x1.0b8f54p-13f),
+ (float2)(0x1.668000p-1f, 0x1.004722p-12f),
+ (float2)(0x1.6a0000p-1f, 0x1.57cf2cp-12f),
+ (float2)(0x1.6d8000p-1f, 0x1.8cb53ap-12f),
+ (float2)(0x1.710000p-1f, 0x1.9f4d8ap-12f),
+ (float2)(0x1.748000p-1f, 0x1.8feb26p-12f),
+ (float2)(0x1.780000p-1f, 0x1.5edfeep-12f),
+ (float2)(0x1.7b8000p-1f, 0x1.0c7c9ap-12f),
+ (float2)(0x1.7f0000p-1f, 0x1.322182p-13f),
+ (float2)(0x1.828000p-1f, 0x1.3ab7cep-18f),
+ (float2)(0x1.858000p-1f, 0x1.a82c2cp-11f),
+ (float2)(0x1.890000p-1f, 0x1.3dd2c0p-11f),
+ (float2)(0x1.8c8000p-1f, 0x1.871da4p-12f),
+ (float2)(0x1.900000p-1f, 0x1.cc2c00p-14f),
+ (float2)(0x1.930000p-1f, 0x1.9fdb68p-11f),
+ (float2)(0x1.968000p-1f, 0x1.ed6956p-12f),
+ (float2)(0x1.9a0000p-1f, 0x1.f1a760p-14f),
+ (float2)(0x1.9d0000p-1f, 0x1.767f54p-11f),
+ (float2)(0x1.a08000p-1f, 0x1.3f6d26p-12f),
+ (float2)(0x1.a38000p-1f, 0x1.b9fce2p-11f),
+ (float2)(0x1.a70000p-1f, 0x1.8ae816p-12f),
+ (float2)(0x1.aa0000p-1f, 0x1.c23d60p-11f),
+ (float2)(0x1.ad8000p-1f, 0x1.60f388p-12f),
+ (float2)(0x1.b08000p-1f, 0x1.9049aep-11f),
+ (float2)(0x1.b40000p-1f, 0x1.8734a8p-13f),
+ (float2)(0x1.b70000p-1f, 0x1.2523d4p-11f),
+ (float2)(0x1.ba0000p-1f, 0x1.da6ce6p-11f),
+ (float2)(0x1.bd8000p-1f, 0x1.038e62p-12f),
+ (float2)(0x1.c08000p-1f, 0x1.1b511ep-11f),
+ (float2)(0x1.c38000p-1f, 0x1.a728b8p-11f),
+ (float2)(0x1.c70000p-1f, 0x1.2b5d22p-14f),
+ (float2)(0x1.ca0000p-1f, 0x1.2c6e54p-12f),
+ (float2)(0x1.cd0000p-1f, 0x1.f35064p-12f),
+ (float2)(0x1.d00000p-1f, 0x1.4fdb48p-11f),
+ (float2)(0x1.d30000p-1f, 0x1.98ec9ep-11f),
+ (float2)(0x1.d60000p-1f, 0x1.d4f80cp-11f),
+ (float2)(0x1.d98000p-1f, 0x1.0643d6p-17f),
+ (float2)(0x1.dc8000p-1f, 0x1.33567ep-14f),
+ (float2)(0x1.df8000p-1f, 0x1.e0410cp-14f),
+ (float2)(0x1.e28000p-1f, 0x1.142e0ep-13f),
+ (float2)(0x1.e58000p-1f, 0x1.063c88p-13f),
+ (float2)(0x1.e88000p-1f, 0x1.8d66c4p-14f),
+ (float2)(0x1.eb8000p-1f, 0x1.57e32ap-15f),
+ (float2)(0x1.ee0000p-1f, 0x1.ed1c6cp-11f),
+ (float2)(0x1.f10000p-1f, 0x1.b8a076p-11f),
+ (float2)(0x1.f40000p-1f, 0x1.7822f2p-11f),
+ (float2)(0x1.f70000p-1f, 0x1.2bbc3ap-11f),
+ (float2)(0x1.fa0000p-1f, 0x1.a708bap-12f),
+ (float2)(0x1.fd0000p-1f, 0x1.be4c7ep-13f),
+ (float2)(0x1.000000p+0f, 0x0.000000p+0f)
+};
DECLARE_TABLE(uchar, PIBITS_TBL, ) = {
224, 241, 27, 193, 12, 88, 33, 116, 53, 126, 196, 126, 237, 175,
@@ -479,6 +610,7 @@ DECLARE_TABLE(float2, CBRT_TBL, 129) = {
TABLE_FUNCTION(float2, LOGE_TBL, loge_tbl);
TABLE_FUNCTION(float, LOG_INV_TBL, log_inv_tbl);
+TABLE_FUNCTION(float2, LOG2_TBL, log2_tbl);
uint4 TABLE_MANGLE(pibits_tbl)(size_t idx) {
return *(__constant uint4 *)(PIBITS_TBL + idx);
diff --git a/generic/lib/math/tables.h b/generic/lib/math/tables.h
index 7fd16a0..c0b0ab1 100644
--- a/generic/lib/math/tables.h
+++ b/generic/lib/math/tables.h
@@ -40,6 +40,7 @@
TABLE_FUNCTION_DECL(float2, loge_tbl);
TABLE_FUNCTION_DECL(float, log_inv_tbl);
+TABLE_FUNCTION_DECL(float2, log2_tbl);
TABLE_FUNCTION_DECL(uint4, pibits_tbl);
TABLE_FUNCTION_DECL(float2, sinhcosh_tbl);
TABLE_FUNCTION_DECL(float2, cbrt_tbl);
--
2.0.4
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