/*
* 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/clc_remainder.h>
#include "../clcmacro.h"
#include "config.h"
#include "math.h"
_CLC_DEF _CLC_OVERLOAD float __clc_remainder(float x, float y)
{
int ux = as_int(x);
int ax = ux & EXSIGNBIT_SP32;
float xa = as_float(ax);
int sx = ux ^ ax;
int ex = ax >> EXPSHIFTBITS_SP32;
int uy = as_int(y);
int ay = uy & EXSIGNBIT_SP32;
float ya = as_float(ay);
int ey = ay >> EXPSHIFTBITS_SP32;
float xr = as_float(0x3f800000 | (ax & 0x007fffff));
float yr = as_float(0x3f800000 | (ay & 0x007fffff));
int c;
int k = ex - ey;
uint q = 0;
while (k > 0) {
c = xr >= yr;
q = (q << 1) | c;
xr -= c ? yr : 0.0f;
xr += xr;
--k;
}
c = xr > yr;
q = (q << 1) | c;
xr -= c ? yr : 0.0f;
int lt = ex < ey;
q = lt ? 0 : q;
xr = lt ? xa : xr;
yr = lt ? ya : yr;
c = (yr < 2.0f * xr) | ((yr == 2.0f * xr) & ((q & 0x1) == 0x1));
xr -= c ? yr : 0.0f;
q += c;
float s = as_float(ey << EXPSHIFTBITS_SP32);
xr *= lt ? 1.0f : s;
c = ax == ay;
xr = c ? 0.0f : xr;
xr = as_float(sx ^ as_int(xr));
c = ax > PINFBITPATT_SP32 | ay > PINFBITPATT_SP32 | ax == PINFBITPATT_SP32 | ay == 0;
xr = c ? as_float(QNANBITPATT_SP32) : xr;
return xr;
}
_CLC_BINARY_VECTORIZE(_CLC_DEF _CLC_OVERLOAD, float, __clc_remainder, float, float);
#ifdef cl_khr_fp64
_CLC_DEF _CLC_OVERLOAD double __clc_remainder(double x, double y)
{
ulong ux = as_ulong(x);
ulong ax = ux & ~SIGNBIT_DP64;
ulong xsgn = ux ^ ax;
double dx = as_double(ax);
int xexp = convert_int(ax >> EXPSHIFTBITS_DP64);
int xexp1 = 11 - (int) clz(ax & MANTBITS_DP64);
xexp1 = xexp < 1 ? xexp1 : xexp;
ulong uy = as_ulong(y);
ulong ay = uy & ~SIGNBIT_DP64;
double dy = as_double(ay);
int yexp = convert_int(ay >> EXPSHIFTBITS_DP64);
int yexp1 = 11 - (int) clz(ay & MANTBITS_DP64);
yexp1 = yexp < 1 ? yexp1 : yexp;
int qsgn = ((ux ^ uy) & SIGNBIT_DP64) == 0UL ? 1 : -1;
// First assume |x| > |y|
// Set ntimes to the number of times we need to do a
// partial remainder. If the exponent of x is an exact multiple
// of 53 larger than the exponent of y, and the mantissa of x is
// less than the mantissa of y, ntimes will be one too large
// but it doesn't matter - it just means that we'll go round
// the loop below one extra time.
int ntimes = max(0, (xexp1 - yexp1) / 53);
double w = ldexp(dy, ntimes * 53);
w = ntimes == 0 ? dy : w;
double scale = ntimes == 0 ? 1.0 : 0x1.0p-53;
// Each time round the loop we compute a partial remainder.
// This is done by subtracting a large multiple of w
// from x each time, where w is a scaled up version of y.
// The subtraction must be performed exactly in quad
// precision, though the result at each stage can
// fit exactly in a double precision number.
int i;
double t, v, p, pp;
for (i = 0; i < ntimes; i++) {
// Compute integral multiplier
t = trunc(dx / w);
// Compute w * t in quad precision
p = w * t;
pp = fma(w, t, -p);
// Subtract w * t from dx
v = dx - p;
dx = v + (((dx - v) - p) - pp);
// If t was one too large, dx will be negative. Add back one w.
dx += dx < 0.0 ? w : 0.0;
// Scale w down by 2^(-53) for the next iteration
w *= scale;
}
// One more time
// Variable todd says whether the integer t is odd or not
t = floor(dx / w);
long lt = (long)t;
int todd = lt & 1;
p = w * t;
pp = fma(w, t, -p);
v = dx - p;
dx = v + (((dx - v) - p) - pp);
i = dx < 0.0;
todd ^= i;
dx += i ? w : 0.0;
// At this point, dx lies in the range [0,dy)
// For the fmod function, we're done apart from setting the correct sign.
//
// For the remainder function, we need to adjust dx
// so that it lies in the range (-y/2, y/2] by carefully
// subtracting w (== dy == y) if necessary. The rigmarole
// with todd is to get the correct sign of the result
// when x/y lies exactly half way between two integers,
// when we need to choose the even integer.
int al = (2.0*dx > w) | (todd & (2.0*dx == w));
double dxl = dx - (al ? w : 0.0);
int ag = (dx > 0.5*w) | (todd & (dx == 0.5*w));
double dxg = dx - (ag ? w : 0.0);
dx = dy < 0x1.0p+1022 ? dxl : dxg;
double ret = as_double(xsgn ^ as_ulong(dx));
dx = as_double(ax);
// Now handle |x| == |y|
int c = dx == dy;
t = as_double(xsgn);
ret = c ? t : ret;
// Next, handle |x| < |y|
c = dx < dy;
ret = c ? x : ret;
c &= (yexp < 1023 & 2.0*dx > dy) | (dx > 0.5*dy);
// we could use a conversion here instead since qsgn = +-1
p = qsgn == 1 ? -1.0 : 1.0;
t = fma(y, p, x);
ret = c ? t : ret;
// We don't need anything special for |x| == 0
// |y| is 0
c = dy == 0.0;
ret = c ? as_double(QNANBITPATT_DP64) : ret;
// y is +-Inf, NaN
c = yexp > BIASEDEMAX_DP64;
t = y == y ? x : y;
ret = c ? t : ret;
// x is +=Inf, NaN
c = xexp > BIASEDEMAX_DP64;
ret = c ? as_double(QNANBITPATT_DP64) : ret;
return ret;
}
_CLC_BINARY_VECTORIZE(_CLC_DEF _CLC_OVERLOAD, double, __clc_remainder, double, double);
#endif
Codebase Browser
llvm