[Beignet] [Patch for Release_v0.9.x 3/6] GBE: fix bug in pow/pown.
Zhigang Gong
zhigang.gong at linux.intel.com
Tue Nov 4 21:42:46 PST 2014
The subject is incorrect, please ignore it, I already fixed it locally.
It should be fix bug in erf/erfc.
On Wed, Nov 05, 2014 at 01:14:42PM +0800, Zhigang Gong wrote:
> erf/erfc diverge (instead of converging to 1 or 0) for arguments above
> about 2.
>
> This patch is from:
> https://bugs.debian.org/cgi-bin/bugreport.cgi?msg=5;filename=Fix-pow-erf-tgamma.patch;att=3;bug=768090
>
> Signed-off-by: Zhigang Gong <zhigang.gong at intel.com>
> ---
> backend/src/ocl_stdlib.tmpl.h | 288 +++++++++++++++++++++++++++++++++++++++++-
> utests/utest_math_gen.py | 16 +--
> 2 files changed, 290 insertions(+), 14 deletions(-)
>
> diff --git a/backend/src/ocl_stdlib.tmpl.h b/backend/src/ocl_stdlib.tmpl.h
> index d6900ee..cacba85 100755
> --- a/backend/src/ocl_stdlib.tmpl.h
> +++ b/backend/src/ocl_stdlib.tmpl.h
> @@ -2501,12 +2501,6 @@ INLINE_OVERLOADABLE float __gen_ocl_internal_atan(float x) {
> INLINE_OVERLOADABLE float __gen_ocl_internal_atanpi(float x) {
> return __gen_ocl_internal_atan(x) / M_PI_F;
> }
> -INLINE_OVERLOADABLE float __gen_ocl_internal_erf(float x) {
> - return M_2_SQRTPI_F * (x - __gen_ocl_pow(x, 3) / 3 + __gen_ocl_pow(x, 5) / 10 - __gen_ocl_pow(x, 7) / 42 + __gen_ocl_pow(x, 9) / 216);
> -}
> -INLINE_OVERLOADABLE float __gen_ocl_internal_erfc(float x) {
> - return 1 - __gen_ocl_internal_erf(x);
> -}
>
> // XXX work-around PTX profile
> #define sqrt native_sqrt
> @@ -2726,6 +2720,288 @@ INLINE_OVERLOADABLE float __gen_ocl_internal_exp(float x) {
> return y*twom100;
> }
> }
> +
> +/* erf,erfc from glibc s_erff.c -- float version of s_erf.c.
> + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian at cygnus.com.
> + */
> +
> +/*
> + * ====================================================
> + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
> + *
> + * Developed at SunPro, a Sun Microsystems, Inc. business.
> + * Permission to use, copy, modify, and distribute this
> + * software is freely granted, provided that this notice
> + * is preserved.
> + * ====================================================
> + */
> +
> +INLINE_OVERLOADABLE float __gen_ocl_internal_erf(float x) {
> +/*...*/
> +const float
> +tiny = 1.0e-30,
> +half_val= 5.0000000000e-01, /* 0x3F000000 */
> +one = 1.0000000000e+00, /* 0x3F800000 */
> +two = 2.0000000000e+00, /* 0x40000000 */
> + /* c = (subfloat)0.84506291151 */
> +erx = 8.4506291151e-01, /* 0x3f58560b */
> +/*
> + * Coefficients for approximation to erf on [0,0.84375]
> + */
> +efx = 1.2837916613e-01, /* 0x3e0375d4 */
> +efx8= 1.0270333290e+00, /* 0x3f8375d4 */
> +pp0 = 1.2837916613e-01, /* 0x3e0375d4 */
> +pp1 = -3.2504209876e-01, /* 0xbea66beb */
> +pp2 = -2.8481749818e-02, /* 0xbce9528f */
> +pp3 = -5.7702702470e-03, /* 0xbbbd1489 */
> +pp4 = -2.3763017452e-05, /* 0xb7c756b1 */
> +qq1 = 3.9791721106e-01, /* 0x3ecbbbce */
> +qq2 = 6.5022252500e-02, /* 0x3d852a63 */
> +qq3 = 5.0813062117e-03, /* 0x3ba68116 */
> +qq4 = 1.3249473704e-04, /* 0x390aee49 */
> +qq5 = -3.9602282413e-06, /* 0xb684e21a */
> +/*
> + * Coefficients for approximation to erf in [0.84375,1.25]
> + */
> +pa0 = -2.3621185683e-03, /* 0xbb1acdc6 */
> +pa1 = 4.1485610604e-01, /* 0x3ed46805 */
> +pa2 = -3.7220788002e-01, /* 0xbebe9208 */
> +pa3 = 3.1834661961e-01, /* 0x3ea2fe54 */
> +pa4 = -1.1089469492e-01, /* 0xbde31cc2 */
> +pa5 = 3.5478305072e-02, /* 0x3d1151b3 */
> +pa6 = -2.1663755178e-03, /* 0xbb0df9c0 */
> +qa1 = 1.0642088205e-01, /* 0x3dd9f331 */
> +qa2 = 5.4039794207e-01, /* 0x3f0a5785 */
> +qa3 = 7.1828655899e-02, /* 0x3d931ae7 */
> +qa4 = 1.2617121637e-01, /* 0x3e013307 */
> +qa5 = 1.3637083583e-02, /* 0x3c5f6e13 */
> +qa6 = 1.1984500103e-02, /* 0x3c445aa3 */
> + /*
> + * Coefficients for approximation to erfc in [1.25,1/0.35]
> + */ra0 = -9.8649440333e-03, /* 0xbc21a093 */
> +ra1 = -6.9385856390e-01, /* 0xbf31a0b7 */
> +ra2 = -1.0558626175e+01, /* 0xc128f022 */
> +ra3 = -6.2375331879e+01, /* 0xc2798057 */
> +ra4 = -1.6239666748e+02, /* 0xc322658c */
> +ra5 = -1.8460508728e+02, /* 0xc3389ae7 */
> +ra6 = -8.1287437439e+01, /* 0xc2a2932b */
> +ra7 = -9.8143291473e+00, /* 0xc11d077e */
> +sa1 = 1.9651271820e+01, /* 0x419d35ce */
> +sa2 = 1.3765776062e+02, /* 0x4309a863 */
> +sa3 = 4.3456588745e+02, /* 0x43d9486f */
> +sa4 = 6.4538726807e+02, /* 0x442158c9 */
> +sa5 = 4.2900814819e+02, /* 0x43d6810b */
> +sa6 = 1.0863500214e+02, /* 0x42d9451f */
> +sa7 = 6.5702495575e+00, /* 0x40d23f7c */
> +sa8 = -6.0424413532e-02, /* 0xbd777f97 */
> +/*
> + * Coefficients for approximation to erfc in [1/.35,28]
> + */
> +rb0 = -9.8649431020e-03, /* 0xbc21a092 */
> +rb1 = -7.9928326607e-01, /* 0xbf4c9dd4 */
> +rb2 = -1.7757955551e+01, /* 0xc18e104b */
> +rb3 = -1.6063638306e+02, /* 0xc320a2ea */
> +rb4 = -6.3756646729e+02, /* 0xc41f6441 */
> +rb5 = -1.0250950928e+03, /* 0xc480230b */
> +rb6 = -4.8351919556e+02, /* 0xc3f1c275 */
> +sb1 = 3.0338060379e+01, /* 0x41f2b459 */
> +sb2 = 3.2579251099e+02, /* 0x43a2e571 */
> +sb3 = 1.5367296143e+03, /* 0x44c01759 */
> +sb4 = 3.1998581543e+03, /* 0x4547fdbb */
> +sb5 = 2.5530502930e+03, /* 0x451f90ce */
> +sb6 = 4.7452853394e+02, /* 0x43ed43a7 */
> +sb7 = -2.2440952301e+01; /* 0xc1b38712 */
> +
> + int hx,ix,i;
> + float R,S,P,Q,s,y,z,r;
> + GEN_OCL_GET_FLOAT_WORD(hx,x);
> + ix = hx&0x7fffffff;
> + if(ix>=0x7f800000) { /* erf(nan)=nan */
> + i = ((unsigned int)hx>>31)<<1;
> + return (float)(1-i)+one/x; /* erf(+-inf)=+-1 */
> + }
> +
> + if(ix < 0x3f580000) { /* |x|<0.84375 */
> + if(ix < 0x31800000) { /* |x|<2**-28 */
> + if (ix < 0x04000000)
> + /*avoid underflow */
> + return (float)0.125*((float)8.0*x+efx8*x);
> + return x + efx*x;
> + }
> + z = x*x;
> + r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
> + s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
> + y = r/s;
> + return x + x*y;
> + }
> + if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */
> + s = __gen_ocl_internal_fabs(x)-one;
> + P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
> + Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
> + if(hx>=0) return erx + P/Q; else return -erx - P/Q;
> + }
> + if (ix >= 0x40c00000) { /* inf>|x|>=6 */
> + if(hx>=0) return one-tiny; else return tiny-one;
> + }
> + x = __gen_ocl_internal_fabs(x);
> + s = one/(x*x);
> + if(ix< 0x4036DB6E) { /* |x| < 1/0.35 */
> + R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
> + ra5+s*(ra6+s*ra7))))));
> + S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
> + sa5+s*(sa6+s*(sa7+s*sa8)))))));
> + } else { /* |x| >= 1/0.35 */
> + R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
> + rb5+s*rb6)))));
> + S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
> + sb5+s*(sb6+s*sb7))))));
> + }
> + GEN_OCL_GET_FLOAT_WORD(ix,x);
> + GEN_OCL_SET_FLOAT_WORD(z,ix&0xfffff000);
> + r = __gen_ocl_internal_exp(-z*z-(float)0.5625)*__gen_ocl_internal_exp((z-x)*(z+x)+R/S);
> + if(hx>=0) return one-r/x; else return r/x-one;
> +}
> +INLINE_OVERLOADABLE float __gen_ocl_internal_erfc(float x) {
> +/*...*/
> +const float
> +tiny = 1.0e-30,
> +half_val= 5.0000000000e-01, /* 0x3F000000 */
> +one = 1.0000000000e+00, /* 0x3F800000 */
> +two = 2.0000000000e+00, /* 0x40000000 */
> + /* c = (subfloat)0.84506291151 */
> +erx = 8.4506291151e-01, /* 0x3f58560b */
> +/*
> + * Coefficients for approximation to erf on [0,0.84375]
> + */
> +efx = 1.2837916613e-01, /* 0x3e0375d4 */
> +efx8= 1.0270333290e+00, /* 0x3f8375d4 */
> +pp0 = 1.2837916613e-01, /* 0x3e0375d4 */
> +pp1 = -3.2504209876e-01, /* 0xbea66beb */
> +pp2 = -2.8481749818e-02, /* 0xbce9528f */
> +pp3 = -5.7702702470e-03, /* 0xbbbd1489 */
> +pp4 = -2.3763017452e-05, /* 0xb7c756b1 */
> +qq1 = 3.9791721106e-01, /* 0x3ecbbbce */
> +qq2 = 6.5022252500e-02, /* 0x3d852a63 */
> +qq3 = 5.0813062117e-03, /* 0x3ba68116 */
> +qq4 = 1.3249473704e-04, /* 0x390aee49 */
> +qq5 = -3.9602282413e-06, /* 0xb684e21a */
> +/*
> + * Coefficients for approximation to erf in [0.84375,1.25]
> + */
> +pa0 = -2.3621185683e-03, /* 0xbb1acdc6 */
> +pa1 = 4.1485610604e-01, /* 0x3ed46805 */
> +pa2 = -3.7220788002e-01, /* 0xbebe9208 */
> +pa3 = 3.1834661961e-01, /* 0x3ea2fe54 */
> +pa4 = -1.1089469492e-01, /* 0xbde31cc2 */
> +pa5 = 3.5478305072e-02, /* 0x3d1151b3 */
> +pa6 = -2.1663755178e-03, /* 0xbb0df9c0 */
> +qa1 = 1.0642088205e-01, /* 0x3dd9f331 */
> +qa2 = 5.4039794207e-01, /* 0x3f0a5785 */
> +qa3 = 7.1828655899e-02, /* 0x3d931ae7 */
> +qa4 = 1.2617121637e-01, /* 0x3e013307 */
> +qa5 = 1.3637083583e-02, /* 0x3c5f6e13 */
> +qa6 = 1.1984500103e-02, /* 0x3c445aa3 */
> + /*
> + * Coefficients for approximation to erfc in [1.25,1/0.35]
> + */ra0 = -9.8649440333e-03, /* 0xbc21a093 */
> +ra1 = -6.9385856390e-01, /* 0xbf31a0b7 */
> +ra2 = -1.0558626175e+01, /* 0xc128f022 */
> +ra3 = -6.2375331879e+01, /* 0xc2798057 */
> +ra4 = -1.6239666748e+02, /* 0xc322658c */
> +ra5 = -1.8460508728e+02, /* 0xc3389ae7 */
> +ra6 = -8.1287437439e+01, /* 0xc2a2932b */
> +ra7 = -9.8143291473e+00, /* 0xc11d077e */
> +sa1 = 1.9651271820e+01, /* 0x419d35ce */
> +sa2 = 1.3765776062e+02, /* 0x4309a863 */
> +sa3 = 4.3456588745e+02, /* 0x43d9486f */
> +sa4 = 6.4538726807e+02, /* 0x442158c9 */
> +sa5 = 4.2900814819e+02, /* 0x43d6810b */
> +sa6 = 1.0863500214e+02, /* 0x42d9451f */
> +sa7 = 6.5702495575e+00, /* 0x40d23f7c */
> +sa8 = -6.0424413532e-02, /* 0xbd777f97 */
> +/*
> + * Coefficients for approximation to erfc in [1/.35,28]
> + */
> +rb0 = -9.8649431020e-03, /* 0xbc21a092 */
> +rb1 = -7.9928326607e-01, /* 0xbf4c9dd4 */
> +rb2 = -1.7757955551e+01, /* 0xc18e104b */
> +rb3 = -1.6063638306e+02, /* 0xc320a2ea */
> +rb4 = -6.3756646729e+02, /* 0xc41f6441 */
> +rb5 = -1.0250950928e+03, /* 0xc480230b */
> +rb6 = -4.8351919556e+02, /* 0xc3f1c275 */
> +sb1 = 3.0338060379e+01, /* 0x41f2b459 */
> +sb2 = 3.2579251099e+02, /* 0x43a2e571 */
> +sb3 = 1.5367296143e+03, /* 0x44c01759 */
> +sb4 = 3.1998581543e+03, /* 0x4547fdbb */
> +sb5 = 2.5530502930e+03, /* 0x451f90ce */
> +sb6 = 4.7452853394e+02, /* 0x43ed43a7 */
> +sb7 = -2.2440952301e+01; /* 0xc1b38712 */
> + int hx,ix;
> + float R,S,P,Q,s,y,z,r;
> + GEN_OCL_GET_FLOAT_WORD(hx,x);
> + ix = hx&0x7fffffff;
> + if(ix>=0x7f800000) { /* erfc(nan)=nan */
> + /* erfc(+-inf)=0,2 */
> + return (float)(((unsigned int)hx>>31)<<1)+one/x;
> + }
> +
> + if(ix < 0x3f580000) { /* |x|<0.84375 */
> + if(ix < 0x23800000) /* |x|<2**-56 */
> + return one-x;
> + z = x*x;
> + r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
> + s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
> + y = r/s;
> + if(hx < 0x3e800000) { /* x<1/4 */
> + return one-(x+x*y);
> + } else {
> + r = x*y;
> + r += (x-half_val);
> + return half_val - r ;
> + }
> + }
> + if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */
> + s = __gen_ocl_internal_fabs(x)-one;
> + P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
> + Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
> + if(hx>=0) {
> + z = one-erx; return z - P/Q;
> + } else {
> + z = erx+P/Q; return one+z;
> + }
> + }
> + if (ix < 0x41e00000) { /* |x|<28 */
> + x = __gen_ocl_internal_fabs(x);
> + s = one/(x*x);
> + if(ix< 0x4036DB6D) { /* |x| < 1/.35 ~ 2.857143*/
> + R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
> + ra5+s*(ra6+s*ra7))))));
> + S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
> + sa5+s*(sa6+s*(sa7+s*sa8)))))));
> + } else { /* |x| >= 1/.35 ~ 2.857143 */
> + if(hx<0&&ix>=0x40c00000) return two-tiny;/* x < -6 */
> + R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
> + rb5+s*rb6)))));
> + S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
> + sb5+s*(sb6+s*sb7))))));
> + }
> + GEN_OCL_GET_FLOAT_WORD(ix,x);
> + GEN_OCL_SET_FLOAT_WORD(z,ix&0xffffe000);
> + r = __gen_ocl_internal_exp(-z*z-(float)0.5625)*
> + __gen_ocl_internal_exp((z-x)*(z+x)+R/S);
> + if(hx>0) {
> + float ret = r/x;
> + return ret;
> + } else
> + return two-r/x;
> + } else {
> + if(hx>0) {
> + return tiny*tiny;
> + } else
> + return two-tiny;
> + }
> +}
> +
> INLINE_OVERLOADABLE float __gen_ocl_internal_fmod (float x, float y) {
> //return x-y*__gen_ocl_rndz(x/y);
> float one = 1.0;
> diff --git a/utests/utest_math_gen.py b/utests/utest_math_gen.py
> index 30a9b24..69b42a1 100755
> --- a/utests/utest_math_gen.py
> +++ b/utests/utest_math_gen.py
> @@ -217,16 +217,16 @@ static float atanpi(float x){
> cospiUtests = func('cospi','cospi',[cospi_input_type],cospi_output_type,[cospi_input_values],'2 * FLT_ULP',cospi_cpu_func)
>
> # ##### gentype erf(gentype)
> -# erf_input_values = base_input_values
> -# erf_input_type = ['float','float2','float4','float8','float16']
> -# erf_output_type = ['float','float2','float4','float8','float16']
> -# erfUtests = func('erf','erf',[erf_input_type],erf_output_type,[erf_input_values],'16 * FLT_ULP')
> + erf_input_values = base_input_values
> + erf_input_type = ['float','float2','float4','float8','float16']
> + erf_output_type = ['float','float2','float4','float8','float16']
> + erfUtests = func('erf','erf',[erf_input_type],erf_output_type,[erf_input_values],'16 * FLT_ULP')
>
> # ##### gentype erfc(gentype)
> -# erfc_input_values = base_input_values
> -# erfc_input_type = ['float','float2','float4','float8','float16']
> -# erfc_output_type = ['float','float2','float4','float8','float16']
> -# erfcUtests = func('erfc','erfc',[erfc_input_type],erfc_output_type,[erfc_input_values],'16 * FLT_ULP')
> + erfc_input_values = base_input_values
> + erfc_input_type = ['float','float2','float4','float8','float16']
> + erfc_output_type = ['float','float2','float4','float8','float16']
> + erfcUtests = func('erfc','erfc',[erfc_input_type],erfc_output_type,[erfc_input_values],'16 * FLT_ULP')
>
> ##### gentype exp(gentype x)
> exp_input_values = base_input_values
> --
> 1.8.3.2
>
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