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libclc: Update asin (#188094)

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This was originally ported from rocm device libs in
64a8e1b83e14836f97dab4d28dae498e897804e6. Update for more
recent changes.
This commit is contained in:
Matt Arsenault 2026-03-24 08:11:24 +01:00 committed by GitHub
parent f7fb46701a
commit ff68154480
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GPG Key ID: B5690EEEBB952194
2 changed files with 111 additions and 100 deletions
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3
libclc/clc/lib/generic/math/clc_asin.cl
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@ -9,10 +9,13 @@
#include "clc/clc_convert.h"
#include "clc/float/definitions.h"
#include "clc/internal/clc.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_mad.h"
#include "clc/math/clc_sqrt.h"
#include "clc/math/clc_sqrt_fast.h"
#include "clc/math/math.h"
#define __CLC_BODY "clc_asin.inc"

208
libclc/clc/lib/generic/math/clc_asin.inc
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@ -26,129 +26,137 @@
#if __CLC_FPSIZE == 32
_CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE __clc_asin(__CLC_GENTYPE x) {
// 0x33a22168
const __CLC_GENTYPE piby2_tail = __CLC_FP_LIT(7.5497894159e-08);
// 0x3f490fda
const __CLC_GENTYPE hpiby2_head = __CLC_FP_LIT(7.8539812565e-01);
// 0x3fc90fdb
const __CLC_GENTYPE piby2 = __CLC_FP_LIT(1.5707963705e+00);
_CLC_DEF _CLC_OVERLOAD _CLC_CONST __CLC_GENTYPE __clc_asin(__CLC_GENTYPE x) {
// Computes arcsin(x).
// The argument is first reduced by noting that arcsin(x)
// is invalid for abs(x) > 1 and arcsin(-x) = -arcsin(x).
// For denormal and small arguments arcsin(x) = x to machine
// accuracy. Remaining argument ranges are handled as follows.
// For abs(x) <= 0.5 use
// arcsin(x) = x + x^3*R(x^2)
// where R(x^2) is a polynomial minimax approximation to
// (arcsin(x) - x)/x^3.
// For abs(x) > 0.5 exploit the identity:
// arcsin(x) = pi/2 - 2*arcsin(sqrt(1-x)/2)
// together with the above polynomial approximation, and
// reconstruct the terms carefully.
__CLC_UINTN ux = __CLC_AS_UINTN(x);
__CLC_UINTN aux = ux & EXSIGNBIT_SP32;
__CLC_UINTN xs = ux ^ aux;
__CLC_GENTYPE spiby2 = __CLC_AS_GENTYPE(xs | __CLC_AS_UINTN(piby2));
__CLC_INTN xexp = __CLC_AS_INTN(aux >> EXPSHIFTBITS_SP32) - EXPBIAS_SP32;
__CLC_GENTYPE y = __CLC_AS_GENTYPE(aux);
__CLC_GENTYPE ax = __clc_fabs(x);
__CLC_GENTYPE tx = __clc_mad(ax, -0.5f, 0.5f);
__CLC_GENTYPE x2 = x * x;
__CLC_GENTYPE r = ax >= 0.5f ? tx : x2;
// abs(x) >= 0.5
__CLC_INTN transform = xexp >= -1;
__CLC_GENTYPE y2 = y * y;
__CLC_GENTYPE rt = __CLC_FP_LIT(0.5) * (__CLC_FP_LIT(1.0) - y);
__CLC_GENTYPE r = transform ? rt : y2;
// Use a rational approximation for [0.0, 0.5]
__CLC_GENTYPE a =
__clc_mad(r,
__CLC_GENTYPE u = r * __clc_mad(r, __clc_mad(r, __clc_mad(r, __clc_mad(r,
__clc_mad(r,
__clc_mad(r, -0.00396137437848476485201154797087F,
-0.0133819288943925804214011424456F),
-0.0565298683201845211985026327361F),
0.184161606965100694821398249421F);
0x1.38434ep-5f, 0x1.bf8bb4p-7f), 0x1.069878p-5f), 0x1.6c8362p-5f),
0x1.33379p-4f), 0x1.555558p-3f);
__CLC_GENTYPE b = __clc_mad(r, -0.836411276854206731913362287293F,
1.10496961524520294485512696706F);
__CLC_GENTYPE u = r * MATH_DIVIDE(a, b);
__CLC_GENTYPE s = __clc_sqrt_fast(r);
__CLC_GENTYPE ret =
__clc_mad(0x1.ddcb02p-1f, 0x1.aee9d6p+0f, -2.0f * __clc_mad(s, u, s));
__CLC_GENTYPE s = __clc_sqrt(r);
__CLC_GENTYPE s1 = __CLC_AS_GENTYPE(__CLC_AS_UINTN(s) & 0xffff0000);
__CLC_GENTYPE c = MATH_DIVIDE(__clc_mad(-s1, s1, r), s + s1);
__CLC_GENTYPE p = __clc_mad(2.0f * s, u, -__clc_mad(c, -2.0f, piby2_tail));
__CLC_GENTYPE q = __clc_mad(s1, -2.0f, hpiby2_head);
__CLC_GENTYPE vt = hpiby2_head - (p - q);
__CLC_GENTYPE v = __clc_mad(y, u, y);
v = transform ? vt : v;
__CLC_GENTYPE xux = __clc_mad(ax, u, ax);
ret = ax < 0.5f ? xux : ret;
__CLC_GENTYPE ret = __CLC_AS_GENTYPE(xs | __CLC_AS_UINTN(v));
ret = aux > 0x3f800000U ? __CLC_GENTYPE_NAN : ret;
ret = aux == 0x3f800000U ? spiby2 : ret;
ret = xexp < -14 ? x : ret;
return ret;
return __clc_copysign(ret, x);
}
#elif __CLC_FPSIZE == 64
_CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE __clc_asin(__CLC_GENTYPE x) {
// 0x3c91a62633145c07
const __CLC_GENTYPE piby2_tail = __CLC_FP_LIT(6.1232339957367660e-17);
// 0x3fe921fb54442d18
const __CLC_GENTYPE hpiby2_head = 7.8539816339744831e-01;
// 0x3ff921fb54442d18
const __CLC_GENTYPE piby2 = 1.5707963267948965e+00;
static _CLC_OVERLOAD _CLC_CONST __CLC_GENTYPE __clc_asin_identity_reduction(__CLC_GENTYPE x, __CLC_GENTYPE r,
__CLC_GENTYPE u, __CLC_GENTYPE v) {
__CLC_GENTYPE y = __clc_fabs(x);
__CLC_EP_PAIR s = __clc_ep_sqrt(r);
__CLC_EP_PAIR ve = __clc_ep_fast_sub(
__clc_ep_make_pair(__CLC_FP_LIT(0x1.921fb54442d18p-1), __CLC_FP_LIT(0x1.1a62633145c07p-55)),
__clc_ep_fast_add(s, __clc_ep_mul(s, u)));
v = ve.hi + ve.hi;
return y == 1.0 ? 0x1.921fb54442d18p+0 : v;
}
_CLC_DEF _CLC_OVERLOAD _CLC_CONST __CLC_GENTYPE __clc_asin(__CLC_GENTYPE x) {
// Computes arcsin(x).
// The argument is first reduced by noting that arcsin(x)
// is invalid for abs(x) > 1 and arcsin(-x) = -arcsin(x).
// For denormal and small arguments arcsin(x) = x to machine
// accuracy. Remaining argument ranges are handled as follows.
// For abs(x) <= 0.5 use
// arcsin(x) = x + x^3*R(x^2)
// where R(x^2) is a rational minimax approximation to
// (arcsin(x) - x)/x^3.
// For abs(x) > 0.5 exploit the identity:
// arcsin(x) = pi/2 - 2*arcsin(sqrt(1-x)/2)
// together with the above rational approximation, and
// reconstruct the terms carefully.
__CLC_GENTYPE y = __clc_fabs(x);
__CLC_LONGN xneg = x < __CLC_FP_LIT(0.0);
__CLC_INTN xexp = __CLC_CONVERT_INTN(
(__CLC_AS_ULONGN(y) >> EXPSHIFTBITS_DP64) - EXPBIAS_DP64);
__CLC_S_GENTYPE transform = y >= 0.5;
// abs(x) >= 0.5
__CLC_LONGN transform = __CLC_CONVERT_LONGN(xexp >= -1);
__CLC_GENTYPE rt = __CLC_FP_LIT(0.5) * (__CLC_FP_LIT(1.0) - y);
__CLC_GENTYPE rt = __clc_mad(y, -0.5, 0.5);
__CLC_GENTYPE y2 = y * y;
__CLC_GENTYPE r = transform ? rt : y2;
// Use a rational approximation for [0.0, 0.5]
__CLC_GENTYPE u = r * __clc_mad(r, __clc_mad(r, __clc_mad(r, __clc_mad(r,
__clc_mad(r, __clc_mad(r, __clc_mad(r, __clc_mad(r,
__clc_mad(r, __clc_mad(r, __clc_mad(r,
0x1.059859fea6a70p-5, -0x1.0a5a378a05eafp-6), 0x1.4052137024d6ap-6), 0x1.ab3a098a70509p-8),
0x1.8ed60a300c8d2p-7), 0x1.c6fa84b77012bp-7), 0x1.1c6c111dccb70p-6), 0x1.6e89f0a0adacfp-6),
0x1.f1c72c668963fp-6), 0x1.6db6db41ce4bdp-5), 0x1.333333336fd5bp-4), 0x1.5555555555380p-3);
__CLC_GENTYPE un = __clc_fma(
r,
__clc_fma(
r,
__clc_fma(r,
__clc_fma(r,
__clc_fma(r, 0.0000482901920344786991880522822991,
0.00109242697235074662306043804220),
-0.0549989809235685841612020091328),
0.275558175256937652532686256258),
-0.445017216867635649900123110649),
0.227485835556935010735943483075);
__CLC_GENTYPE v = __clc_mad(y, u, y);
__CLC_GENTYPE ud = __clc_fma(
r,
__clc_fma(r,
__clc_fma(r,
__clc_fma(r, 0.105869422087204370341222318533,
-0.943639137032492685763471240072),
2.76568859157270989520376345954),
-3.28431505720958658909889444194),
1.36491501334161032038194214209);
#ifdef __CLC_SCALAR
if (transform) {
v = __clc_asin_identity_reduction(x, r, u, v);
}
#else
__CLC_GENTYPE identity = __clc_asin_identity_reduction(x, r, u, v);
v = transform ? identity : v;
#endif
__CLC_GENTYPE u = r * MATH_DIVIDE(un, ud);
// Reconstruct asin carefully in transformed region
__CLC_GENTYPE s = __clc_sqrt(r);
__CLC_GENTYPE sh =
__CLC_AS_GENTYPE(__CLC_AS_ULONGN(s) & 0xffffffff00000000UL);
__CLC_GENTYPE c = MATH_DIVIDE(__clc_fma(-sh, sh, r), s + sh);
__CLC_GENTYPE p = __clc_fma(2.0 * s, u, -__clc_fma(-2.0, c, piby2_tail));
__CLC_GENTYPE q = __clc_fma(-2.0, sh, hpiby2_head);
__CLC_GENTYPE vt = hpiby2_head - (p - q);
__CLC_GENTYPE v = __clc_fma(y, u, y);
v = transform ? vt : v;
v = __CLC_CONVERT_LONGN(xexp < -28) ? y : v;
v = __CLC_CONVERT_LONGN(xexp >= 0) ? __CLC_GENTYPE_NAN : v;
v = y == 1.0 ? piby2 : v;
return xneg ? -v : v;
return __clc_copysign(v, x);
}
#elif __CLC_FPSIZE == 16
_CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE __clc_asin(__CLC_GENTYPE x) {
return __CLC_CONVERT_GENTYPE(__clc_asin(__CLC_CONVERT_FLOATN(x)));
static _CLC_OVERLOAD _CLC_CONST __CLC_GENTYPE
__clc_asin_small_case(__CLC_GENTYPE x) {
__CLC_HALFN ax = __clc_fabs(x);
__CLC_HALFN s = x * x;
__CLC_HALFN p = s * __clc_mad(s, 0x1.828p-4h, 0x1.52p-3h);
return __clc_mad(ax, p, ax);
}
static _CLC_OVERLOAD _CLC_CONST __CLC_GENTYPE
__clc_asin_large_case(__CLC_GENTYPE x) {
__CLC_HALFN ax = __clc_fabs(x);
__CLC_FLOATN s = __clc_mad(__CLC_CONVERT_FLOATN(ax), (__CLC_FLOATN)-0.5f,
(__CLC_FLOATN)0.5f);
__CLC_FLOATN t = __clc_sqrt_fast(s);
__CLC_FLOATN p = __clc_mad(t, __clc_mad(s, -0x1.82675ap-2f, -0x1.ff9f6p+0f),
0x1.921fb6p+0f);
return __CLC_CONVERT_HALFN(p);
}
_CLC_DEF _CLC_OVERLOAD _CLC_CONST __CLC_GENTYPE __clc_asin(__CLC_GENTYPE x) {
// Computes arcsin(x).
// The argument is first reduced by noting that arcsin(x)
// is invalid for abs(x) > 1 and arcsin(-x) = -arcsin(x).
// For denormal and small arguments arcsin(x) = x to machine
// accuracy. Remaining argument ranges are handled as follows.
// For abs(x) <= 0.5 use
// arcsin(x) = x + x^3*R(x^2)
// where R(x^2) is a polynomial minimax approximation to
// (arcsin(x) - x)/x^3.
// For abs(x) > 0.5 exploit the identity:
// arcsin(x) = pi/2 - 2*arcsin(sqrt(1-x)/2)
// together with the above polynomial approximation, and
// reconstruct the terms carefully.
__CLC_HALFN ax = __clc_fabs(x);
__CLC_HALFN r =
ax <= 0.5h ? __clc_asin_small_case(x) : __clc_asin_large_case(x);
return __clc_copysign(r, x);
}
#endif