libclc: Update atanh (#188225)
This commit is contained in:
Matt Arsenault
GitHub
parent
8b224162fa
commit
46205ff9b4
@ -8,12 +8,13 @@
|
||||
|
||||
#include "clc/clc_convert.h"
|
||||
#include "clc/float/definitions.h"
|
||||
#include "clc/internal/clc.h"
|
||||
#include "clc/math/clc_atanh.h"
|
||||
#include "clc/math/clc_copysign.h"
|
||||
#include "clc/math/clc_ep.h"
|
||||
#include "clc/math/clc_fabs.h"
|
||||
#include "clc/math/clc_fma.h"
|
||||
#include "clc/math/clc_log1p.h"
|
||||
#include "clc/math/clc_mad.h"
|
||||
#include "clc/math/math.h"
|
||||
#include "clc/math/clc_log2_fast.h"
|
||||
#include "clc/math/clc_recip_fast.h"
|
||||
#include "clc/relational/clc_isnan.h"
|
||||
|
||||
#define __CLC_BODY "clc_atanh.inc"
|
||||
#include "clc/math/gentype.inc"
|
||||
|
||||
@ -8,98 +8,46 @@
|
||||
|
||||
#if __CLC_FPSIZE == 32
|
||||
|
||||
_CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE __clc_atanh(__CLC_GENTYPE x) {
|
||||
__CLC_UINTN ux = __CLC_AS_UINTN(x);
|
||||
__CLC_UINTN ax = ux & EXSIGNBIT_SP32;
|
||||
__CLC_UINTN xs = ux ^ ax;
|
||||
_CLC_DEF _CLC_OVERLOAD _CLC_CONST __CLC_FLOATN __clc_atanh(__CLC_FLOATN x) {
|
||||
__CLC_FLOATN y = __clc_fabs(x);
|
||||
__CLC_EP_PAIR a =
|
||||
__clc_ep_fast_div(__clc_ep_fast_add(1.0f, y), __clc_ep_fast_sub(1.0f, y));
|
||||
__CLC_FLOATN z = 0.5f * __clc_ep_ln_hi(a, 0);
|
||||
z = y < 0x1.0p-12f ? y : z;
|
||||
|
||||
// |x| > 1 or NaN
|
||||
__CLC_GENTYPE z = __CLC_GENTYPE_NAN;
|
||||
|
||||
// |x| == 1
|
||||
__CLC_GENTYPE t = __CLC_AS_GENTYPE(xs | PINFBITPATT_SP32);
|
||||
z = ax == 0x3f800000U ? t : z;
|
||||
|
||||
// 1/2 <= |x| < 1
|
||||
t = __CLC_AS_GENTYPE(ax);
|
||||
t = MATH_DIVIDE(2.0f * t, 1.0f - t);
|
||||
t = 0.5f * __clc_log1p(t);
|
||||
t = __CLC_AS_GENTYPE(xs | __CLC_AS_UINTN(t));
|
||||
z = ax < 0x3f800000U ? t : z;
|
||||
|
||||
// |x| < 1/2
|
||||
t = x * x;
|
||||
__CLC_GENTYPE a = __clc_mad(
|
||||
__clc_mad(0.92834212715e-2f, t, -0.28120347286e0f), t, 0.39453629046e0f);
|
||||
__CLC_GENTYPE b = __clc_mad(__clc_mad(0.45281890445e0f, t, -0.15537744551e1f),
|
||||
t, 0.11836088638e1f);
|
||||
__CLC_GENTYPE p = MATH_DIVIDE(a, b);
|
||||
t = __clc_mad(x * t, p, x);
|
||||
z = ax < 0x3f000000 ? t : z;
|
||||
|
||||
// |x| < 2^-13
|
||||
z = ax < 0x39000000U ? x : z;
|
||||
|
||||
return z;
|
||||
z = y > 1.0f ? FLT_NAN : z;
|
||||
z = y == 1.0f ? __CLC_GENTYPE_INF : z;
|
||||
return __clc_copysign(z, x);
|
||||
}
|
||||
|
||||
#elif __CLC_FPSIZE == 64
|
||||
|
||||
_CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE __clc_atanh(__CLC_GENTYPE x) {
|
||||
__CLC_GENTYPE absx = __clc_fabs(x);
|
||||
_CLC_DEF _CLC_OVERLOAD _CLC_CONST __CLC_DOUBLEN __clc_atanh(__CLC_DOUBLEN x) {
|
||||
__CLC_DOUBLEN y = __clc_fabs(x);
|
||||
__CLC_EP_PAIR a =
|
||||
__clc_ep_fast_div(__clc_ep_fast_add(1.0, y), __clc_ep_fast_sub(1.0, y));
|
||||
__CLC_DOUBLEN z = 0.5 * __clc_ep_ln_hi(a, 0);
|
||||
z = y < 0x1.0p-27 ? y : z;
|
||||
|
||||
__CLC_GENTYPE ret = absx == 1.0
|
||||
? __CLC_AS_GENTYPE((__CLC_ULONGN)PINFBITPATT_DP64)
|
||||
: __CLC_GENTYPE_NAN;
|
||||
z = y > 1.0 ? DBL_NAN : z;
|
||||
z = y == 1.0 ? __CLC_GENTYPE_INF : z;
|
||||
|
||||
// |x| >= 0.5
|
||||
// Note that atanh(x) = 0.5 * ln((1+x)/(1-x))
|
||||
// For greater accuracy we use
|
||||
// ln((1+x)/(1-x)) = ln(1 + 2x/(1-x)) = log1p(2x/(1-x)).
|
||||
__CLC_GENTYPE r = 0.5 * __clc_log1p(2.0 * absx / (1.0 - absx));
|
||||
ret = absx < 1.0 ? r : ret;
|
||||
|
||||
r = -ret;
|
||||
ret = x < 0.0 ? r : ret;
|
||||
|
||||
// Arguments up to 0.5 in magnitude are
|
||||
// approximated by a [5,5] minimax polynomial
|
||||
__CLC_GENTYPE t = x * x;
|
||||
|
||||
__CLC_GENTYPE pn = __clc_fma(
|
||||
t,
|
||||
__clc_fma(t,
|
||||
__clc_fma(t,
|
||||
__clc_fma(t,
|
||||
__clc_fma(t, -0.10468158892753136958e-3,
|
||||
0.28728638600548514553e-1),
|
||||
-0.28180210961780814148e0),
|
||||
0.88468142536501647470e0),
|
||||
-0.11028356797846341457e1),
|
||||
0.47482573589747356373e0);
|
||||
|
||||
__CLC_GENTYPE pd = __clc_fma(
|
||||
t,
|
||||
__clc_fma(t,
|
||||
__clc_fma(t,
|
||||
__clc_fma(t,
|
||||
__clc_fma(t, -0.35861554370169537512e-1,
|
||||
0.49561196555503101989e0),
|
||||
-0.22608883748988489342e1),
|
||||
0.45414700626084508355e1),
|
||||
-0.41631933639693546274e1),
|
||||
0.14244772076924206909e1);
|
||||
|
||||
r = __clc_fma(x * t, pn / pd, x);
|
||||
ret = absx < 0.5 ? r : ret;
|
||||
|
||||
return ret;
|
||||
return __clc_copysign(z, x);
|
||||
}
|
||||
|
||||
#elif __CLC_FPSIZE == 16
|
||||
|
||||
_CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE __clc_atanh(__CLC_GENTYPE x) {
|
||||
return __CLC_CONVERT_GENTYPE(__clc_atanh(__CLC_CONVERT_FLOATN(x)));
|
||||
_CLC_DEF _CLC_OVERLOAD _CLC_CONST __CLC_HALFN __clc_atanh(__CLC_HALFN x) {
|
||||
__CLC_HALFN absx = __clc_fabs(x);
|
||||
__CLC_FLOATN absxf = __CLC_CONVERT_FLOATN(absx);
|
||||
__CLC_FLOATN t = (1.0f + absxf) * __clc_recip_fast(1.0f - absxf);
|
||||
__CLC_HALFN ret = __CLC_CONVERT_HALFN(__clc_log2_fast(t) * 0x1.62e430p-2f);
|
||||
ret = absx < 0x1.0p-7h ? absx : ret;
|
||||
|
||||
ret = absx == 1.0h ? __CLC_GENTYPE_INF : ret;
|
||||
ret = (absx > 1.0h) || __clc_isnan(absx) ? HALF_NAN : ret;
|
||||
|
||||
return __clc_copysign(ret, x);
|
||||
}
|
||||
|
||||
#endif
|
||||
|
||||
Loading…
x
Reference in New Issue
Block a user