[Libclc-dev] [PATCH 3/4] Implement cos builtin for float types
Tom Stellard
thomas.stellard at amd.com
Wed Jul 2 13:11:15 PDT 2014
The double version still uses @llvm.cos.
---
generic/include/clc/math/cos.h | 9 +-
generic/lib/SOURCES | 2 +
generic/lib/math/cos.cl | 66 ++++++++
generic/lib/math/sincos_helpers.cl | 308 +++++++++++++++++++++++++++++++++++++
generic/lib/math/sincos_helpers.h | 25 +++
5 files changed, 404 insertions(+), 6 deletions(-)
create mode 100644 generic/lib/math/cos.cl
create mode 100644 generic/lib/math/sincos_helpers.cl
create mode 100644 generic/lib/math/sincos_helpers.h
diff --git a/generic/include/clc/math/cos.h b/generic/include/clc/math/cos.h
index 974f9d1..3d4cf39 100644
--- a/generic/include/clc/math/cos.h
+++ b/generic/include/clc/math/cos.h
@@ -1,6 +1,3 @@
-#undef cos
-#define cos __clc_cos
-
-#define __CLC_FUNCTION __clc_cos
-#define __CLC_INTRINSIC "llvm.cos"
-#include <clc/math/unary_intrin.inc>
+#define __CLC_BODY <clc/math/cos.inc>
+#include <clc/math/gentype.inc>
+#undef __CLC_BODY
diff --git a/generic/lib/SOURCES b/generic/lib/SOURCES
index aa8b88d..4d30669 100644
--- a/generic/lib/SOURCES
+++ b/generic/lib/SOURCES
@@ -29,6 +29,7 @@ integer/sub_sat_impl.ll
integer/upsample.cl
math/atan.cl
math/atan2.cl
+math/cos.cl
math/exp.cl
math/fmax.cl
math/fmin.cl
@@ -38,6 +39,7 @@ math/mix.cl
math/clc_nextafter.cl
math/nextafter.cl
math/sincos.cl
+math/sincos_helpers.cl
relational/all.cl
relational/any.cl
relational/isequal.cl
diff --git a/generic/lib/math/cos.cl b/generic/lib/math/cos.cl
new file mode 100644
index 0000000..4fa6aee
--- /dev/null
+++ b/generic/lib/math/cos.cl
@@ -0,0 +1,66 @@
+/*
+ * Copyright (c) 2014 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 "sincos_helpers.h"
+
+_CLC_OVERLOAD _CLC_DEF float cos(float x)
+{
+ int ix = as_int(x);
+ int ax = ix & 0x7fffffff;
+ float dx = as_float(ax);
+
+ float r0, r1;
+ int regn = argReductionS(&r0, &r1, dx);
+
+ float ss = -sinf_piby4(r0, r1);
+ float cc = cosf_piby4(r0, r1);
+
+ float c = (regn & 1) != 0 ? ss : cc;
+ c = as_float(as_int(c) ^ ((regn > 1) << 31));
+
+ c = ax >= PINFBITPATT_SP32 ? as_float(QNANBITPATT_SP32) : c;
+
+ return c;
+}
+
+_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, float, cos, float);
+
+#ifdef cl_khr_fp64
+
+#pragma OPENCL EXTENSION cl_khr_fp64 : enable
+
+#define __CLC_FUNCTION __clc_cos_intrinsic
+#define __CLC_INTRINSIC "llvm.cos"
+#include <clc/math/unary_intrin.inc>
+#undef __CLC_FUNCTION
+#undef __CLC_INTRINSIC
+
+_CLC_OVERLOAD _CLC_DEF double cos(double x) {
+ return __clc_cos_intrinsic(x);
+}
+
+_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, double, cos, double);
+
+#endif
diff --git a/generic/lib/math/sincos_helpers.cl b/generic/lib/math/sincos_helpers.cl
new file mode 100644
index 0000000..1a5f10c
--- /dev/null
+++ b/generic/lib/math/sincos_helpers.cl
@@ -0,0 +1,308 @@
+/*
+ * Copyright (c) 2014 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 "sincos_helpers.h"
+
+uint bitalign(uint hi, uint lo, uint shift)
+{
+ return (hi << (32 - shift)) | (lo >> shift);
+}
+
+float sinf_piby4(float x, float y)
+{
+ // Taylor series for sin(x) is x - x^3/3! + x^5/5! - x^7/7! ...
+ // = x * (1 - x^2/3! + x^4/5! - x^6/7! ...
+ // = x * f(w)
+ // where w = x*x and f(w) = (1 - w/3! + w^2/5! - w^3/7! ...
+ // We use a minimax approximation of (f(w) - 1) / w
+ // because this produces an expansion in even powers of x.
+
+ const float c1 = -0.1666666666e0f;
+ const float c2 = 0.8333331876e-2f;
+ const float c3 = -0.198400874e-3f;
+ const float c4 = 0.272500015e-5f;
+ const float c5 = -2.5050759689e-08f; // 0xb2d72f34
+ const float c6 = 1.5896910177e-10f; // 0x2f2ec9d3
+
+ float z = x * x;
+ float v = z * x;
+ float r = mad(z, mad(z, mad(z, mad(z, c6, c5), c4), c3), c2);
+ float ret = x - mad(v, -c1, mad(z, mad(y, 0.5f, -v*r), -y));
+
+ return ret;
+}
+
+float cosf_piby4(float x, float y)
+{
+ // Taylor series for cos(x) is 1 - x^2/2! + x^4/4! - x^6/6! ...
+ // = f(w)
+ // where w = x*x and f(w) = (1 - w/2! + w^2/4! - w^3/6! ...
+ // We use a minimax approximation of (f(w) - 1 + w/2) / (w*w)
+ // because this produces an expansion in even powers of x.
+
+ const float c1 = 0.416666666e-1f;
+ const float c2 = -0.138888876e-2f;
+ const float c3 = 0.248006008e-4f;
+ const float c4 = -0.2730101334e-6f;
+ const float c5 = 2.0875723372e-09f; // 0x310f74f6
+ const float c6 = -1.1359647598e-11f; // 0xad47d74e
+
+ float z = x * x;
+ float r = z * mad(z, mad(z, mad(z, mad(z, mad(z, c6, c5), c4), c3), c2), c1);
+
+ // if |x| < 0.3
+ float qx = 0.0f;
+
+ int ix = as_int(x) & EXSIGNBIT_SP32;
+
+ // 0.78125 > |x| >= 0.3
+ float xby4 = as_float(ix - 0x01000000);
+ qx = (ix >= 0x3e99999a) & (ix <= 0x3f480000) ? xby4 : qx;
+
+ // x > 0.78125
+ qx = ix > 0x3f480000 ? 0.28125f : qx;
+
+ float hz = mad(z, 0.5f, -qx);
+ float a = 1.0f - qx;
+ float ret = a - (hz - mad(z, r, -x*y));
+ return ret;
+}
+
+void fullMulS(float *hi, float *lo, float a, float b, float bh, float bt)
+{
+ if (HAVE_HW_FMA32()) {
+ float ph = a * b;
+ *hi = ph;
+ *lo = fma(a, b, -ph);
+ } else {
+ float ah = as_float(as_uint(a) & 0xfffff000U);
+ float at = a - ah;
+ float ph = a * b;
+ float pt = mad(at, bt, mad(at, bh, mad(ah, bt, mad(ah, bh, -ph))));
+ *hi = ph;
+ *lo = pt;
+ }
+}
+
+float removePi2S(float *hi, float *lo, float x)
+{
+ // 72 bits of pi/2
+ const float fpiby2_1 = (float) 0xC90FDA / 0x1.0p+23f;
+ const float fpiby2_1_h = (float) 0xC90 / 0x1.0p+11f;
+ const float fpiby2_1_t = (float) 0xFDA / 0x1.0p+23f;
+
+ const float fpiby2_2 = (float) 0xA22168 / 0x1.0p+47f;
+ const float fpiby2_2_h = (float) 0xA22 / 0x1.0p+35f;
+ const float fpiby2_2_t = (float) 0x168 / 0x1.0p+47f;
+
+ const float fpiby2_3 = (float) 0xC234C4 / 0x1.0p+71f;
+ const float fpiby2_3_h = (float) 0xC23 / 0x1.0p+59f;
+ const float fpiby2_3_t = (float) 0x4C4 / 0x1.0p+71f;
+
+ const float twobypi = 0x1.45f306p-1f;
+
+ float fnpi2 = trunc(mad(x, twobypi, 0.5f));
+
+ // subtract n * pi/2 from x
+ float rhead, rtail;
+ fullMulS(&rhead, &rtail, fnpi2, fpiby2_1, fpiby2_1_h, fpiby2_1_t);
+ float v = x - rhead;
+ float rem = v + (((x - v) - rhead) - rtail);
+
+ float rhead2, rtail2;
+ fullMulS(&rhead2, &rtail2, fnpi2, fpiby2_2, fpiby2_2_h, fpiby2_2_t);
+ v = rem - rhead2;
+ rem = v + (((rem - v) - rhead2) - rtail2);
+
+ float rhead3, rtail3;
+ fullMulS(&rhead3, &rtail3, fnpi2, fpiby2_3, fpiby2_3_h, fpiby2_3_t);
+ v = rem - rhead3;
+
+ *hi = v + ((rem - v) - rhead3);
+ *lo = -rtail3;
+ return fnpi2;
+}
+
+int argReductionSmallS(float *r, float *rr, float x)
+{
+ float fnpi2 = removePi2S(r, rr, x);
+ return (int)fnpi2 & 0x3;
+}
+
+#define FULL_MUL(A, B, HI, LO) \
+ LO = A * B; \
+ HI = mul_hi(A, B)
+
+#define FULL_MAD(A, B, C, HI, LO) \
+ LO = ((A) * (B) + (C)); \
+ HI = mul_hi(A, B); \
+ HI += LO < C
+
+int argReductionLargeS(float *r, float *rr, float x)
+{
+ int xe = (int)(as_uint(x) >> 23) - 127;
+ uint xm = 0x00800000U | (as_uint(x) & 0x7fffffU);
+
+ // 224 bits of 2/PI: . A2F9836E 4E441529 FC2757D1 F534DDC0 DB629599 3C439041 FE5163AB
+ const uint b6 = 0xA2F9836EU;
+ const uint b5 = 0x4E441529U;
+ const uint b4 = 0xFC2757D1U;
+ const uint b3 = 0xF534DDC0U;
+ const uint b2 = 0xDB629599U;
+ const uint b1 = 0x3C439041U;
+ const uint b0 = 0xFE5163ABU;
+
+ uint p0, p1, p2, p3, p4, p5, p6, p7, c0, c1;
+
+ FULL_MUL(xm, b0, c0, p0);
+ FULL_MAD(xm, b1, c0, c1, p1);
+ FULL_MAD(xm, b2, c1, c0, p2);
+ FULL_MAD(xm, b3, c0, c1, p3);
+ FULL_MAD(xm, b4, c1, c0, p4);
+ FULL_MAD(xm, b5, c0, c1, p5);
+ FULL_MAD(xm, b6, c1, p7, p6);
+
+ uint fbits = 224 + 23 - xe;
+
+ // shift amount to get 2 lsb of integer part at top 2 bits
+ // min: 25 (xe=18) max: 134 (xe=127)
+ uint shift = 256U - 2 - fbits;
+
+ // Shift by up to 134/32 = 4 words
+ int c = shift > 31;
+ p7 = c ? p6 : p7;
+ p6 = c ? p5 : p6;
+ p5 = c ? p4 : p5;
+ p4 = c ? p3 : p4;
+ p3 = c ? p2 : p3;
+ p2 = c ? p1 : p2;
+ p1 = c ? p0 : p1;
+ shift -= (-c) & 32;
+
+ c = shift > 31;
+ p7 = c ? p6 : p7;
+ p6 = c ? p5 : p6;
+ p5 = c ? p4 : p5;
+ p4 = c ? p3 : p4;
+ p3 = c ? p2 : p3;
+ p2 = c ? p1 : p2;
+ shift -= (-c) & 32;
+
+ c = shift > 31;
+ p7 = c ? p6 : p7;
+ p6 = c ? p5 : p6;
+ p5 = c ? p4 : p5;
+ p4 = c ? p3 : p4;
+ p3 = c ? p2 : p3;
+ shift -= (-c) & 32;
+
+ c = shift > 31;
+ p7 = c ? p6 : p7;
+ p6 = c ? p5 : p6;
+ p5 = c ? p4 : p5;
+ p4 = c ? p3 : p4;
+ shift -= (-c) & 32;
+
+ // bitalign cannot handle a shift of 32
+ c = shift > 0;
+ shift = 32 - shift;
+ uint t7 = bitalign(p7, p6, shift);
+ uint t6 = bitalign(p6, p5, shift);
+ uint t5 = bitalign(p5, p4, shift);
+ p7 = c ? t7 : p7;
+ p6 = c ? t6 : p6;
+ p5 = c ? t5 : p5;
+
+ // Get 2 lsb of int part and msb of fraction
+ int i = p7 >> 29;
+
+ // Scoot up 2 more bits so only fraction remains
+ p7 = bitalign(p7, p6, 30);
+ p6 = bitalign(p6, p5, 30);
+ p5 = bitalign(p5, p4, 30);
+
+ // Subtract 1 if msb of fraction is 1, i.e. fraction >= 0.5
+ uint flip = i & 1 ? 0xffffffffU : 0U;
+ uint sign = i & 1 ? 0x80000000U : 0U;
+ p7 = p7 ^ flip;
+ p6 = p6 ^ flip;
+ p5 = p5 ^ flip;
+
+ // Find exponent and shift away leading zeroes and hidden bit
+ xe = clz(p7) + 1;
+ shift = 32 - xe;
+ p7 = bitalign(p7, p6, shift);
+ p6 = bitalign(p6, p5, shift);
+
+ // Most significant part of fraction
+ float q1 = as_float(sign | ((127 - xe) << 23) | (p7 >> 9));
+
+ // Shift out bits we captured on q1
+ p7 = bitalign(p7, p6, 32-23);
+
+ // Get 24 more bits of fraction in another float, there are not long strings of zeroes here
+ int xxe = clz(p7) + 1;
+ p7 = bitalign(p7, p6, 32-xxe);
+ float q0 = as_float(sign | ((127 - (xe + 23 + xxe)) << 23) | (p7 >> 9));
+
+ // At this point, the fraction q1 + q0 is correct to at least 48 bits
+ // Now we need to multiply the fraction by pi/2
+ // This loses us about 4 bits
+ // pi/2 = C90 FDA A22 168 C23 4C4
+
+ const float pio2h = (float)0xc90fda / 0x1.0p+23f;
+ const float pio2hh = (float)0xc90 / 0x1.0p+11f;
+ const float pio2ht = (float)0xfda / 0x1.0p+23f;
+ const float pio2t = (float)0xa22168 / 0x1.0p+47f;
+
+ float rh, rt;
+
+ if (HAVE_HW_FMA32()) {
+ rh = q1 * pio2h;
+ rt = fma(q0, pio2h, fma(q1, pio2t, fma(q1, pio2h, -rh)));
+ } else {
+ float q1h = as_float(as_uint(q1) & 0xfffff000);
+ float q1t = q1 - q1h;
+ rh = q1 * pio2h;
+ rt = mad(q1t, pio2ht, mad(q1t, pio2hh, mad(q1h, pio2ht, mad(q1h, pio2hh, -rh))));
+ rt = mad(q0, pio2h, mad(q1, pio2t, rt));
+ }
+
+ float t = rh + rt;
+ rt = rt - (t - rh);
+
+ *r = t;
+ *rr = rt;
+ return ((i >> 1) + (i & 1)) & 0x3;
+}
+
+int argReductionS(float *r, float *rr, float x)
+{
+ if (x < 0x1.0p+23f)
+ return argReductionSmallS(r, rr, x);
+ else
+ return argReductionLargeS(r, rr, x);
+}
+
diff --git a/generic/lib/math/sincos_helpers.h b/generic/lib/math/sincos_helpers.h
new file mode 100644
index 0000000..f89c19f
--- /dev/null
+++ b/generic/lib/math/sincos_helpers.h
@@ -0,0 +1,25 @@
+/*
+ * Copyright (c) 2014 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.
+ */
+
+float sinf_piby4(float x, float y);
+float cosf_piby4(float x, float y);
+int argReductionS(float *r, float *rr, float x);
--
1.8.1.5
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