[libclc] r213761 - Implement cos builtin for float types

Tom Stellard thomas.stellard at amd.com
Wed Jul 23 08:16:19 PDT 2014


Author: tstellar
Date: Wed Jul 23 10:16:18 2014
New Revision: 213761

URL: http://llvm.org/viewvc/llvm-project?rev=213761&view=rev
Log:
Implement cos builtin for float types

The double version still uses @llvm.cos.

Added:
    libclc/trunk/generic/include/clc/math/cos.inc
    libclc/trunk/generic/lib/math/cos.cl
    libclc/trunk/generic/lib/math/sincos_helpers.cl
    libclc/trunk/generic/lib/math/sincos_helpers.h
Modified:
    libclc/trunk/generic/include/clc/math/cos.h
    libclc/trunk/generic/lib/SOURCES

Modified: libclc/trunk/generic/include/clc/math/cos.h
URL: http://llvm.org/viewvc/llvm-project/libclc/trunk/generic/include/clc/math/cos.h?rev=213761&r1=213760&r2=213761&view=diff
==============================================================================
--- libclc/trunk/generic/include/clc/math/cos.h (original)
+++ libclc/trunk/generic/include/clc/math/cos.h Wed Jul 23 10:16:18 2014
@@ -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

Added: libclc/trunk/generic/include/clc/math/cos.inc
URL: http://llvm.org/viewvc/llvm-project/libclc/trunk/generic/include/clc/math/cos.inc?rev=213761&view=auto
==============================================================================
--- libclc/trunk/generic/include/clc/math/cos.inc (added)
+++ libclc/trunk/generic/include/clc/math/cos.inc Wed Jul 23 10:16:18 2014
@@ -0,0 +1 @@
+_CLC_OVERLOAD _CLC_DECL __CLC_GENTYPE cos(__CLC_GENTYPE a);

Modified: libclc/trunk/generic/lib/SOURCES
URL: http://llvm.org/viewvc/llvm-project/libclc/trunk/generic/lib/SOURCES?rev=213761&r1=213760&r2=213761&view=diff
==============================================================================
--- libclc/trunk/generic/lib/SOURCES (original)
+++ libclc/trunk/generic/lib/SOURCES Wed Jul 23 10:16:18 2014
@@ -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/exp10.cl
 math/fmax.cl
@@ -40,6 +41,7 @@ math/clc_nextafter.cl
 math/nextafter.cl
 math/pown.cl
 math/sincos.cl
+math/sincos_helpers.cl
 relational/all.cl
 relational/any.cl
 relational/isequal.cl

Added: libclc/trunk/generic/lib/math/cos.cl
URL: http://llvm.org/viewvc/llvm-project/libclc/trunk/generic/lib/math/cos.cl?rev=213761&view=auto
==============================================================================
--- libclc/trunk/generic/lib/math/cos.cl (added)
+++ libclc/trunk/generic/lib/math/cos.cl Wed Jul 23 10:16:18 2014
@@ -0,0 +1,67 @@
+/*
+ * 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"
+#include "../clcmacro.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

Added: libclc/trunk/generic/lib/math/sincos_helpers.cl
URL: http://llvm.org/viewvc/llvm-project/libclc/trunk/generic/lib/math/sincos_helpers.cl?rev=213761&view=auto
==============================================================================
--- libclc/trunk/generic/lib/math/sincos_helpers.cl (added)
+++ libclc/trunk/generic/lib/math/sincos_helpers.cl Wed Jul 23 10:16:18 2014
@@ -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);
+}
+

Added: libclc/trunk/generic/lib/math/sincos_helpers.h
URL: http://llvm.org/viewvc/llvm-project/libclc/trunk/generic/lib/math/sincos_helpers.h?rev=213761&view=auto
==============================================================================
--- libclc/trunk/generic/lib/math/sincos_helpers.h (added)
+++ libclc/trunk/generic/lib/math/sincos_helpers.h Wed Jul 23 10:16:18 2014
@@ -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);





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