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219 lines
6.4 KiB
219 lines
6.4 KiB
/*
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* Copyright (c) 2014 Advanced Micro Devices, Inc.
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*
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* Permission is hereby granted, free of charge, to any person obtaining a copy
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* of this software and associated documentation files (the "Software"), to deal
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* in the Software without restriction, including without limitation the rights
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* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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* copies of the Software, and to permit persons to whom the Software is
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* furnished to do so, subject to the following conditions:
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*
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* The above copyright notice and this permission notice shall be included in
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* all copies or substantial portions of the Software.
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*
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* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
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* THE SOFTWARE.
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*/
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#include <clc/clc.h>
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#include <math/clc_remainder.h>
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#include "../clcmacro.h"
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#include "config.h"
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#include "math.h"
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_CLC_DEF _CLC_OVERLOAD float __clc_remainder(float x, float y)
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{
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int ux = as_int(x);
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int ax = ux & EXSIGNBIT_SP32;
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float xa = as_float(ax);
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int sx = ux ^ ax;
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int ex = ax >> EXPSHIFTBITS_SP32;
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int uy = as_int(y);
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int ay = uy & EXSIGNBIT_SP32;
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float ya = as_float(ay);
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int ey = ay >> EXPSHIFTBITS_SP32;
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float xr = as_float(0x3f800000 | (ax & 0x007fffff));
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float yr = as_float(0x3f800000 | (ay & 0x007fffff));
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int c;
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int k = ex - ey;
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uint q = 0;
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while (k > 0) {
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c = xr >= yr;
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q = (q << 1) | c;
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xr -= c ? yr : 0.0f;
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xr += xr;
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--k;
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}
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c = xr > yr;
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q = (q << 1) | c;
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xr -= c ? yr : 0.0f;
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int lt = ex < ey;
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q = lt ? 0 : q;
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xr = lt ? xa : xr;
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yr = lt ? ya : yr;
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c = (yr < 2.0f * xr) | ((yr == 2.0f * xr) & ((q & 0x1) == 0x1));
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xr -= c ? yr : 0.0f;
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q += c;
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float s = as_float(ey << EXPSHIFTBITS_SP32);
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xr *= lt ? 1.0f : s;
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c = ax == ay;
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xr = c ? 0.0f : xr;
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xr = as_float(sx ^ as_int(xr));
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c = ax > PINFBITPATT_SP32 | ay > PINFBITPATT_SP32 | ax == PINFBITPATT_SP32 | ay == 0;
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xr = c ? as_float(QNANBITPATT_SP32) : xr;
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return xr;
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}
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_CLC_BINARY_VECTORIZE(_CLC_DEF _CLC_OVERLOAD, float, __clc_remainder, float, float);
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#ifdef cl_khr_fp64
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_CLC_DEF _CLC_OVERLOAD double __clc_remainder(double x, double y)
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{
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ulong ux = as_ulong(x);
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ulong ax = ux & ~SIGNBIT_DP64;
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ulong xsgn = ux ^ ax;
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double dx = as_double(ax);
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int xexp = convert_int(ax >> EXPSHIFTBITS_DP64);
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int xexp1 = 11 - (int) clz(ax & MANTBITS_DP64);
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xexp1 = xexp < 1 ? xexp1 : xexp;
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ulong uy = as_ulong(y);
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ulong ay = uy & ~SIGNBIT_DP64;
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double dy = as_double(ay);
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int yexp = convert_int(ay >> EXPSHIFTBITS_DP64);
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int yexp1 = 11 - (int) clz(ay & MANTBITS_DP64);
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yexp1 = yexp < 1 ? yexp1 : yexp;
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int qsgn = ((ux ^ uy) & SIGNBIT_DP64) == 0UL ? 1 : -1;
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// First assume |x| > |y|
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// Set ntimes to the number of times we need to do a
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// partial remainder. If the exponent of x is an exact multiple
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// of 53 larger than the exponent of y, and the mantissa of x is
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// less than the mantissa of y, ntimes will be one too large
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// but it doesn't matter - it just means that we'll go round
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// the loop below one extra time.
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int ntimes = max(0, (xexp1 - yexp1) / 53);
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double w = ldexp(dy, ntimes * 53);
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w = ntimes == 0 ? dy : w;
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double scale = ntimes == 0 ? 1.0 : 0x1.0p-53;
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// Each time round the loop we compute a partial remainder.
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// This is done by subtracting a large multiple of w
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// from x each time, where w is a scaled up version of y.
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// The subtraction must be performed exactly in quad
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// precision, though the result at each stage can
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// fit exactly in a double precision number.
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int i;
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double t, v, p, pp;
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for (i = 0; i < ntimes; i++) {
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// Compute integral multiplier
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t = trunc(dx / w);
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// Compute w * t in quad precision
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p = w * t;
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pp = fma(w, t, -p);
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// Subtract w * t from dx
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v = dx - p;
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dx = v + (((dx - v) - p) - pp);
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// If t was one too large, dx will be negative. Add back one w.
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dx += dx < 0.0 ? w : 0.0;
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// Scale w down by 2^(-53) for the next iteration
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w *= scale;
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}
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// One more time
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// Variable todd says whether the integer t is odd or not
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t = floor(dx / w);
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long lt = (long)t;
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int todd = lt & 1;
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p = w * t;
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pp = fma(w, t, -p);
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v = dx - p;
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dx = v + (((dx - v) - p) - pp);
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i = dx < 0.0;
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todd ^= i;
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dx += i ? w : 0.0;
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// At this point, dx lies in the range [0,dy)
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// For the fmod function, we're done apart from setting the correct sign.
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//
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// For the remainder function, we need to adjust dx
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// so that it lies in the range (-y/2, y/2] by carefully
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// subtracting w (== dy == y) if necessary. The rigmarole
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// with todd is to get the correct sign of the result
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// when x/y lies exactly half way between two integers,
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// when we need to choose the even integer.
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int al = (2.0*dx > w) | (todd & (2.0*dx == w));
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double dxl = dx - (al ? w : 0.0);
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int ag = (dx > 0.5*w) | (todd & (dx == 0.5*w));
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double dxg = dx - (ag ? w : 0.0);
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dx = dy < 0x1.0p+1022 ? dxl : dxg;
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double ret = as_double(xsgn ^ as_ulong(dx));
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dx = as_double(ax);
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// Now handle |x| == |y|
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int c = dx == dy;
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t = as_double(xsgn);
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ret = c ? t : ret;
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// Next, handle |x| < |y|
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c = dx < dy;
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ret = c ? x : ret;
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c &= (yexp < 1023 & 2.0*dx > dy) | (dx > 0.5*dy);
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// we could use a conversion here instead since qsgn = +-1
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p = qsgn == 1 ? -1.0 : 1.0;
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t = fma(y, p, x);
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ret = c ? t : ret;
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// We don't need anything special for |x| == 0
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// |y| is 0
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c = dy == 0.0;
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ret = c ? as_double(QNANBITPATT_DP64) : ret;
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// y is +-Inf, NaN
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c = yexp > BIASEDEMAX_DP64;
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t = y == y ? x : y;
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ret = c ? t : ret;
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// x is +=Inf, NaN
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c = xexp > BIASEDEMAX_DP64;
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ret = c ? as_double(QNANBITPATT_DP64) : ret;
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return ret;
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}
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_CLC_BINARY_VECTORIZE(_CLC_DEF _CLC_OVERLOAD, double, __clc_remainder, double, double);
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#endif
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