[Libclc-dev] [PATCH] math: Implement remainder(x, y)
Matt Arsenault via Libclc-dev
libclc-dev at lists.llvm.org
Thu Jan 19 12:47:58 PST 2017
This fails conformance for me:
-------------- next part --------------
An embedded and charset-unspecified text was scrubbed...
Name: errors.txt
URL: <http://lists.llvm.org/pipermail/libclc-dev/attachments/20170119/91e6ab88/attachment-0001.txt>
-------------- next part --------------
> On Jan 18, 2017, at 20:04, Aaron Watry via Libclc-dev <libclc-dev at lists.llvm.org> wrote:
>
> Mostly ported from the amd-builtins branch.
>
> The amd-builtins branch uses __amdil_improved_fdiv_f32 and FTZ which aren't available in generic CLC.
>
> __amdil_improved_fdiv_f32 points to native_divide which does native_recip(y)*x.
>
> Since we don't have native_divide or native_recip yet, I've just stuck an actual division here.
>
> I've taken a shot at a replacement for FTZ(x), but feel free to suggest alternatives.
>
> Tested via piglit on a Radeon HD 7850 using the tests just sent to that list.
>
> v2: Use __builtin_canonicalizef(float) instead of custom flush-to-zero function
>
> Signed-off-by: Aaron Watry <awatry at gmail.com>
> CC: Tom Stellard <thomas.stellard at amd.com>
> CC: Matt Arsenault <Matthew.Arsenault at amd.com>
> ---
> generic/include/clc/clc.h | 1 +
> generic/include/clc/math/remainder.h | 2 +
> generic/include/clc/math/remainder.inc | 1 +
> generic/lib/SOURCES | 1 +
> generic/lib/math/remainder.cl | 508 +++++++++++++++++++++++++++++++++
> 5 files changed, 513 insertions(+)
> create mode 100644 generic/include/clc/math/remainder.h
> create mode 100644 generic/include/clc/math/remainder.inc
> create mode 100644 generic/lib/math/remainder.cl
>
> diff --git a/generic/include/clc/clc.h b/generic/include/clc/clc.h
> index 024bf27..2d4af4b 100644
> --- a/generic/include/clc/clc.h
> +++ b/generic/include/clc/clc.h
> @@ -82,6 +82,7 @@
> #include <clc/math/nextafter.h>
> #include <clc/math/pow.h>
> #include <clc/math/pown.h>
> +#include <clc/math/remainder.h>
> #include <clc/math/rint.h>
> #include <clc/math/round.h>
> #include <clc/math/sin.h>
> diff --git a/generic/include/clc/math/remainder.h b/generic/include/clc/math/remainder.h
> new file mode 100644
> index 0000000..97d9fad
> --- /dev/null
> +++ b/generic/include/clc/math/remainder.h
> @@ -0,0 +1,2 @@
> +#define __CLC_BODY <clc/math/remainder.inc>
> +#include <clc/math/gentype.inc>
> diff --git a/generic/include/clc/math/remainder.inc b/generic/include/clc/math/remainder.inc
> new file mode 100644
> index 0000000..00d0d69
> --- /dev/null
> +++ b/generic/include/clc/math/remainder.inc
> @@ -0,0 +1 @@
> +_CLC_OVERLOAD _CLC_DECL __CLC_GENTYPE remainder(__CLC_GENTYPE x, __CLC_GENTYPE y);
> diff --git a/generic/lib/SOURCES b/generic/lib/SOURCES
> index 517daba..39208bf 100644
> --- a/generic/lib/SOURCES
> +++ b/generic/lib/SOURCES
> @@ -113,6 +113,7 @@ math/tables.cl
> math/clc_nextafter.cl
> math/nextafter.cl
> math/pown.cl
> +math/remainder.cl
> math/sin.cl
> math/sincos.cl
> math/sincos_helpers.cl
> diff --git a/generic/lib/math/remainder.cl b/generic/lib/math/remainder.cl
> new file mode 100644
> index 0000000..df42db0
> --- /dev/null
> +++ b/generic/lib/math/remainder.cl
> @@ -0,0 +1,508 @@
> +#include <clc/clc.h>
> +
> +#include "math.h"
> +#include "config.h"
> +#include "../clcmacro.h"
> +
> +inline float _clc_remainder_scaleFullRangef32(float y, float t) {
> + float ay, ty, r = 0;
> + int k, iiy, iy, exp_iy0, exp_iy, manty, signy, miy;
> + int delta, shift, ir;
> +
> + ay = fabs(t);
> + k = ay > 1024 ? 1024 : (int) ay;
> + k = t < 0 ? -k : k;
> + t = (float) k;
> +
> + iiy = as_int(y);
> + iy = iiy & EXSIGNBIT_SP32;
> + signy = iiy & SIGNBIT_SP32;
> + ay = as_float(iy);
> +
> + exp_iy0 = iy & EXPBITS_SP32;
> + manty = iy & MANTBITS_SP32;
> +
> + //sub-normal
> + ty = exp_iy0 == 0 ? (float) manty : as_float(iy);
> + k = exp_iy0 == 0 ? k - 149 : k;
> + ay = ty;
> + iy = as_int(ay);
> + exp_iy0 = iy & EXPBITS_SP32;
> + exp_iy = (exp_iy0 >> EXPSHIFTBITS_SP32) - EXPBIAS_SP32;
> + // add k to y's exponent
> + r = as_float(iy + (k << EXPSHIFTBITS_SP32));
> + r = (exp_iy + k) > 127 ? as_float(PINFBITPATT_SP32) : r;
> + // add k to y's exponent
> + delta = -126 - (exp_iy + k);
> +
> + // sub-normal
> + miy = iy & MANTBITS_SP32;
> + miy |= IMPBIT_SP32;
> + shift = delta > 23 ? 24 : delta;
> + shift = delta < 0 ? 0 : shift;
> + miy >>= shift;
> + r = delta > 0 ? as_float(miy) : r;
> + r = t > (float) (2 * EMAX_SP32) ? as_float(PINFBITPATT_SP32) : r;
> + ir = as_int(r);
> + r = ir <= PINFBITPATT_SP32 ? as_float(as_int(r) | signy) : r;
> + return r;
> +}
> +/* Scales the float x by 2.0**n.
> +Assumes 2*EMIN <= n <= 2*EMAX, though this condition is not checked. */
> +inline float _clc_remainder_scaleFloat_2(float x, int n) {
> + float t1, t2;
> + int n1, n2;
> + n1 = n / 2;
> + n2 = n - n1;
> + /* Construct the numbers t1 = 2.0**n1 and t2 = 2.0**n2 */
> + t1 = as_float((n1 + EXPBIAS_SP32) << EXPSHIFTBITS_SP32);
> + t2 = as_float((n2 + EXPBIAS_SP32) << EXPSHIFTBITS_SP32);
> + return (x * t1) * t2;
> +}
> +/* Scales the float x by 2.0**n.
> + Assumes EMIN <= n <= EMAX, though this condition is not checked. */
> +inline float _clc_remainder_scaleFloat_1(float x, int n) {
> + float t;
> + /* Construct the number t = 2.0**n */
> + t = as_float((n + EXPBIAS_SP32) << EXPSHIFTBITS_SP32);
> + return x * t;
> +}
> +/* Computes the exact product of x and y, the result being the
> +nearly double length number (z,zz) */
> +inline void _clc_remainder_mul12f(float x, float y, float *z, float *zz) {
> + float hx, tx, hy, ty;
> + // Split x into hx (head) and tx (tail). Do the same for y.
> + uint u;
> + u = as_uint(x);
> + u &= 0xfffff000;
> + hx = as_float(u);
> + tx = x - hx;
> + u = as_uint(y);
> + u &= 0xfffff000;
> + hy = as_float(u);
> + ty = y - hy;
> + *z = x * y;
> + *zz = (((hx * hy - *z) + hx * ty) + tx * hy) + tx * ty;
> +}
> +
> +_CLC_OVERLOAD _CLC_DEF float remainder(float x, float y) {
> + if (!__clc_fp32_subnormals_supported()) {
> + const int loop_scale = 12;
> + const float fscale = 1.0f / (float) (1 << loop_scale);
> +
> + int ntimes;
> + float ret = 0;
> + int ui_x, ui_y, ui_ax, ui_ay, xexp, yexp, signx;
> + float af_x, af_y, af_ybase, fx, fxp, fxm, fy, w, scale, t, c, cc, v;
> + float yscale, scaled_w, saved_w, div, sdiv, ratio, sratio, fxexp, sub_fx;
> + int iw_scaled, wexp, it, i, ifx, ex, ey;
> + ;
> + float xr, xr0, xr_base, yr;
> + uint q;
> +
> + ui_x = as_int(x);
> + ui_y = as_int(y);
> + ui_ax = ui_x & EXSIGNBIT_SP32;
> + ui_ay = ui_y & EXSIGNBIT_SP32;
> +
> + /* special case handle */
> + if (ui_ax > PINFBITPATT_SP32)
> + return x;
> + if (ui_ax == PINFBITPATT_SP32)
> + return as_float(QNANBITPATT_SP32);
> + if (ui_ay > PINFBITPATT_SP32)
> + return y;
> + if (ui_ay == PINFBITPATT_SP32)
> + return x;
> + if (ui_ay == 0 && ui_ax == 0)
> + return as_float(QNANBITPATT_SP32);
> + if (ui_ax == 0)
> + return x;
> + if (ui_ay == 0)
> + return as_float(QNANBITPATT_SP32);
> +
> + signx = ui_x & SIGNBIT_SP32;
> + af_x = as_float(ui_ax);
> + af_ybase = af_y = as_float(ui_ay);
> + yexp = (int) ((ui_y & EXPBITS_SP32) >> EXPSHIFTBITS_SP32);
> +
> + yscale = (float) ((yexp < 48 && ui_ay != 0) ? (48 - yexp) : 0);
> + if (yscale != 0) {
> + af_y = _clc_remainder_scaleFullRangef32(af_ybase, yscale);
> + }
> +
> + ui_y = as_int(af_y);
> + yexp = (int) ((ui_y & EXPBITS_SP32) >> EXPSHIFTBITS_SP32);
> + xexp = (int) ((ui_x & EXPBITS_SP32) >> EXPSHIFTBITS_SP32);
> + fx = af_x;
> + fy = af_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 24 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. */
> + ntimes = (xexp - yexp) / loop_scale;
> + ntimes = xexp <= yexp ? 0 : ntimes;
> +
> + /* Set w = y * 2^(ntimes*loop_scale) */
> + w = _clc_remainder_scaleFloat_2(fy, ntimes * loop_scale);
> + w = ntimes == 0 ? fy : w;
> +
> + /* Set scale = 2^(-loop_scale) */
> + scale = ntimes == 0 ? 1.0f : fscale;
> +
> + // make sure recip does not overflow
> + wexp = (int) ((as_int(w) & EXPBITS_SP32) >> EXPSHIFTBITS_SP32) - EXPBIAS_SP32;
> + saved_w = w;
> + scaled_w = _clc_remainder_scaleFloat_1(w, -14);
> + iw_scaled = wexp > 105 & wexp <= 127;
> + w = (iw_scaled & ntimes) > 0 ? scaled_w : w;
> +
> + /* 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 can be performed exactly when performed
> + in double precision, and the result at each stage can
> + fit exactly in a single precision number. */
> + for (i = 0; i < ntimes; i++) {
> + /* Set fx = fx - w * t, where t is equal to trunc(dx/w). */
> + div = fx / w; //was __amdil_improved_div_f32 => native_div(x, y) => native_recip(y)*x
> + sdiv = _clc_remainder_scaleFloat_1(div, -14);
> + div = iw_scaled ? sdiv : div;
> + t = floor(div);
> + w = saved_w;
> + iw_scaled = 0;
> +
> + /* At this point, t may be one too large due to rounding of fx/w */
> +
> + /* Compute w * t in quad precision */
> + _clc_remainder_mul12f(w, t, &c, &cc);
> +
> + /* Subtract w * t from fx */
> + v = fx - c;
> + fx = v + (((fx - v) - c) - cc);
> +
> + /* If t was one too large, fx will be negative. Add back one w */
> + /* It might be possible to speed up this loop by finding
> + a way to compute correctly truncated t directly from fx and w.
> + We would then avoid the need for this check on negative fx. */
> + fxp = fx + w;
> + fxm = fx - w;
> + fx = fx < 0.0f ? fxp : fx;
> + fx = fx >= w ? fxm : fx;
> +
> + /* Scale w down by for the next iteration */
> + w *= scale;
> + saved_w = w;
> + }
> +
> + /* One more time */
> + // iw = as_int(w);
> + ifx = as_int(fx);
> + fxexp = (int) ((ifx & EXPBITS_SP32) >> EXPSHIFTBITS_SP32);
> + // wexp = (int) ((iw & EXPBITS_SP32) >> EXPSHIFTBITS_SP32);
> + sub_fx = fx;
> + // make sure recip does not overflow
> + wexp = (int) ((as_int(w) & EXPBITS_SP32) >> EXPSHIFTBITS_SP32) - EXPBIAS_SP32;
> + saved_w = w;
> + scaled_w = _clc_remainder_scaleFloat_1(w, -14);
> + iw_scaled = wexp > 105 & wexp <= 127;
> + w = iw_scaled ? scaled_w : w;
> + ratio = fx / w; //was the amdil equivalent of native_divide(x, y) => native_recip(y)*x;
> + sratio = _clc_remainder_scaleFloat_1(ratio, -14);
> + ratio = iw_scaled ? sratio : ratio;
> + t = floor(ratio);
> + it = (int) t;
> +
> + w = saved_w;
> + _clc_remainder_mul12f(w, t, &c, &cc);
> +
> + v = fx - c;
> + fx = v + (((fx - v) - c) - cc);
> +
> + if (fx < 0.0f) {
> + fx += w;
> + it--;
> + }
> +
> + if (fx >= w) {
> + fx -= w;
> + it++;
> + }
> +
> + // sub-normal fax
> + fx = fxexp == 0 ? sub_fx : fx;
> +
> + float scaleback = 0;
> +
> + // in case fx == 0 and we'got a divisor
> + it = (yscale > 30) ? 0 : ((unsigned int) it << (int) yscale);
> +
> + if (as_int(fx) != 0 && yscale != 0) {
> + xr = fx;
> + xr_base = fx;
> + yr = af_ybase;
> + q = 0;
> + ex = ilogb(fx);
> + ey = ilogb(af_ybase);
> +
> + yr = (float) _clc_remainder_scaleFullRangef32(af_ybase, (float) -ey);
> + xr = (float) _clc_remainder_scaleFullRangef32(fx, (float) -ex);
> +
> + for (i = ex - ey; i > 0; i--) {
> + q <<= 1;
> + xr0 = xr;
> + xr = (xr0 >= yr) ? xr0 - yr : xr0;
> + q = (xr0 >= yr) ? q + 1 : q;
> + xr += xr;
> + }
> + q <<= 1;
> + xr0 = xr;
> + xr = (xr0 >= yr) ? xr0 - yr : xr0;
> + q = (xr0 >= yr) ? q + 1 : q;
> + xr = _clc_remainder_scaleFullRangef32(xr, (float) ey);
> +
> + fx = (ex - ey >= 0) ? xr : xr_base;
> + q = (ex - ey >= 0) ? q : 0;
> + it += q;
> +
> + xexp = (int) ((as_int(fx) & EXPBITS_SP32) >> EXPSHIFTBITS_SP32);
> +
> + w = af_ybase;
> + if (xexp < 24) {
> + fx = _clc_remainder_scaleFullRangef32(fx, 48);
> + w = _clc_remainder_scaleFullRangef32(af_ybase, 48);
> + scaleback = -48;
> + }
> + }
> + /* At this point, dx lies in the range [0,dy) */
> + /* For the remainder function, we need to adjust dx
> + so that it lies in the range (-y/2, y/2] by carefully
> + subtracting w (== fy == y) if necessary. */
> + if (fx * 2.f > w || ((fx * 2.f == w) && (it & 1))) {
> + fx -= w;
> + it++;
> + }
> + if (scaleback != 0) {
> + fx = _clc_remainder_scaleFullRangef32(fx, scaleback);
> + }
> +
> + ret = (signx) ? as_float(as_int(fx) ^ SIGNBIT_SP32) : fx;
> +
> + return ret;
> +
> + }
> +
> + //Otherwise, Subnormals are supported
> +
> + x = __builtin_canonicalizef(x);
> + y = __builtin_canonicalizef(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;
> +
> +#define _CLC_BIT c = xr >= yr; q = (q << 1) | c; xr -= c ? yr : 0.0f; xr += xr
> +
> + while (k > 3) {
> + _CLC_BIT;
> + _CLC_BIT;
> + _CLC_BIT;
> + _CLC_BIT;
> + k -= 4;
> + }
> +
> + while (k > 0) {
> + _CLC_BIT;
> + --k;
> + }
> +
> +#undef _CLC_BIT
> +
> + 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_OVERLOAD _CLC_DEF, float, remainder, float, float);
> +
> +#ifdef cl_khr_fp64
> +
> +#pragma OPENCL EXTENSION cl_khr_fp64 : enable
> +
> +inline double
> +_clc_remainder_ldexp(double x, int n) {
> + // XXX Have to go twice here because the hardware can't handle the full range (yet)
> + int nh = n >> 1;
> + return ldexp(ldexp(x, nh), n - nh);
> +}
> +
> +_CLC_OVERLOAD _CLC_DEF double remainder(double y, double x) {
> + 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 = _clc_remainder_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_OVERLOAD _CLC_DEF, double, remainder, double, double);
> +#endif
> \ No newline at end of file
> --
> 2.9.3
>
> _______________________________________________
> Libclc-dev mailing list
> Libclc-dev at lists.llvm.org
> http://lists.llvm.org/cgi-bin/mailman/listinfo/libclc-dev
More information about the Libclc-dev
mailing list