https://github.com/frasercrmck created https://github.com/llvm/llvm-project/pull/132918
Similar to d46a6999, this commit simultaneously moves these three functions to the CLC library and optimizes them for vector types by avoiding scalarization. >From 1fb1a82f1dff423d96e803889e831e8aced1aba1 Mon Sep 17 00:00:00 2001 From: Fraser Cormack <fra...@codeplay.com> Date: Tue, 25 Mar 2025 10:50:53 +0000 Subject: [PATCH] [libclc] Move asinpi/acospi/atanpi to the CLC library Similar to d46a6999, this commit simultaneously moves these three functions to the CLC library and optimizes them for vector types by avoiding scalarization. --- libclc/clc/include/clc/math/clc_acospi.h | 20 +++ libclc/clc/include/clc/math/clc_asinpi.h | 20 +++ libclc/clc/include/clc/math/clc_atanpi.h | 20 +++ libclc/clc/lib/generic/SOURCES | 3 + libclc/clc/lib/generic/math/clc_acospi.cl | 19 +++ libclc/clc/lib/generic/math/clc_acospi.inc | 156 +++++++++++++++++++ libclc/clc/lib/generic/math/clc_asinpi.cl | 19 +++ libclc/clc/lib/generic/math/clc_asinpi.inc | 156 +++++++++++++++++++ libclc/clc/lib/generic/math/clc_atanpi.cl | 19 +++ libclc/clc/lib/generic/math/clc_atanpi.inc | 172 +++++++++++++++++++++ libclc/generic/lib/math/acospi.cl | 158 +------------------ libclc/generic/lib/math/asinpi.cl | 149 +----------------- libclc/generic/lib/math/atanpi.cl | 169 +------------------- 13 files changed, 616 insertions(+), 464 deletions(-) create mode 100644 libclc/clc/include/clc/math/clc_acospi.h create mode 100644 libclc/clc/include/clc/math/clc_asinpi.h create mode 100644 libclc/clc/include/clc/math/clc_atanpi.h create mode 100644 libclc/clc/lib/generic/math/clc_acospi.cl create mode 100644 libclc/clc/lib/generic/math/clc_acospi.inc create mode 100644 libclc/clc/lib/generic/math/clc_asinpi.cl create mode 100644 libclc/clc/lib/generic/math/clc_asinpi.inc create mode 100644 libclc/clc/lib/generic/math/clc_atanpi.cl create mode 100644 libclc/clc/lib/generic/math/clc_atanpi.inc diff --git a/libclc/clc/include/clc/math/clc_acospi.h b/libclc/clc/include/clc/math/clc_acospi.h new file mode 100644 index 0000000000000..789078d6ccd35 --- /dev/null +++ b/libclc/clc/include/clc/math/clc_acospi.h @@ -0,0 +1,20 @@ +//===----------------------------------------------------------------------===// +// +// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. +// See https://llvm.org/LICENSE.txt for license information. +// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception +// +//===----------------------------------------------------------------------===// + +#ifndef __CLC_MATH_CLC_ACOSPI_H__ +#define __CLC_MATH_CLC_ACOSPI_H__ + +#define __CLC_BODY <clc/math/unary_decl.inc> +#define __CLC_FUNCTION __clc_acospi + +#include <clc/math/gentype.inc> + +#undef __CLC_BODY +#undef __CLC_FUNCTION + +#endif // __CLC_MATH_CLC_ACOSPI_H__ diff --git a/libclc/clc/include/clc/math/clc_asinpi.h b/libclc/clc/include/clc/math/clc_asinpi.h new file mode 100644 index 0000000000000..75b6709dd4fd3 --- /dev/null +++ b/libclc/clc/include/clc/math/clc_asinpi.h @@ -0,0 +1,20 @@ +//===----------------------------------------------------------------------===// +// +// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. +// See https://llvm.org/LICENSE.txt for license information. +// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception +// +//===----------------------------------------------------------------------===// + +#ifndef __CLC_MATH_CLC_ASINPI_H__ +#define __CLC_MATH_CLC_ASINPI_H__ + +#define __CLC_BODY <clc/math/unary_decl.inc> +#define __CLC_FUNCTION __clc_asinpi + +#include <clc/math/gentype.inc> + +#undef __CLC_BODY +#undef __CLC_FUNCTION + +#endif // __CLC_MATH_CLC_ASINPI_H__ diff --git a/libclc/clc/include/clc/math/clc_atanpi.h b/libclc/clc/include/clc/math/clc_atanpi.h new file mode 100644 index 0000000000000..d22fd9b6c7e21 --- /dev/null +++ b/libclc/clc/include/clc/math/clc_atanpi.h @@ -0,0 +1,20 @@ +//===----------------------------------------------------------------------===// +// +// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. +// See https://llvm.org/LICENSE.txt for license information. +// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception +// +//===----------------------------------------------------------------------===// + +#ifndef __CLC_MATH_CLC_ATANPI_H__ +#define __CLC_MATH_CLC_ATANPI_H__ + +#define __CLC_BODY <clc/math/unary_decl.inc> +#define __CLC_FUNCTION __clc_atanpi + +#include <clc/math/gentype.inc> + +#undef __CLC_BODY +#undef __CLC_FUNCTION + +#endif // __CLC_MATH_CLC_ATANPI_H__ diff --git a/libclc/clc/lib/generic/SOURCES b/libclc/clc/lib/generic/SOURCES index 1001287b3f483..11069e9b0b952 100644 --- a/libclc/clc/lib/generic/SOURCES +++ b/libclc/clc/lib/generic/SOURCES @@ -18,8 +18,11 @@ integer/clc_rotate.cl integer/clc_sub_sat.cl integer/clc_upsample.cl math/clc_acos.cl +math/clc_acospi.cl math/clc_asin.cl +math/clc_asinpi.cl math/clc_atan.cl +math/clc_atanpi.cl math/clc_ceil.cl math/clc_copysign.cl math/clc_fabs.cl diff --git a/libclc/clc/lib/generic/math/clc_acospi.cl b/libclc/clc/lib/generic/math/clc_acospi.cl new file mode 100644 index 0000000000000..22134d3209e60 --- /dev/null +++ b/libclc/clc/lib/generic/math/clc_acospi.cl @@ -0,0 +1,19 @@ +//===----------------------------------------------------------------------===// +// +// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. +// See https://llvm.org/LICENSE.txt for license information. +// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception +// +//===----------------------------------------------------------------------===// + +#include <clc/clc_convert.h> +#include <clc/float/definitions.h> +#include <clc/internal/clc.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/math.h> + +#define __CLC_BODY <clc_acospi.inc> +#include <clc/math/gentype.inc> diff --git a/libclc/clc/lib/generic/math/clc_acospi.inc b/libclc/clc/lib/generic/math/clc_acospi.inc new file mode 100644 index 0000000000000..82d8188ca719d --- /dev/null +++ b/libclc/clc/lib/generic/math/clc_acospi.inc @@ -0,0 +1,156 @@ +//===----------------------------------------------------------------------===// +// +// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. +// See https://llvm.org/LICENSE.txt for license information. +// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception +// +//===----------------------------------------------------------------------===// +// +// Computes arccos(x). +// +// The incoming argument is first reduced by noting that arccos(x) is invalid +// for abs(x) > 1. +// +// For denormal and small arguments arccos(x) = pi/2 to machine accuracy. +// +// Remaining argument ranges are handled as follows: +// * For abs(x) <= 0.5 use: +// arccos(x) = pi/2 - arcsin(x) = pi/2 - (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: +// arccos(x) = pi - 2 * arcsin(sqrt(1 - x)/2) +// together with the above rational approximation, and reconstruct the terms +// carefully. +// +//===----------------------------------------------------------------------===// + +#if __CLC_FPSIZE == 32 + +_CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE __clc_acospi(__CLC_GENTYPE x) { + // Some constants and split constants. + const __CLC_GENTYPE pi = __CLC_FP_LIT(3.1415926535897933e+00); + // 0x3ff921fb54442d18 + const __CLC_GENTYPE piby2_head = __CLC_FP_LIT(1.5707963267948965580e+00); + // 0x3c91a62633145c07 + const __CLC_GENTYPE piby2_tail = __CLC_FP_LIT(6.12323399573676603587e-17); + + __CLC_UINTN ux = __CLC_AS_UINTN(x); + __CLC_UINTN aux = ux & ~SIGNBIT_SP32; + __CLC_INTN xneg = ux != aux; + __CLC_INTN xexp = __CLC_AS_INTN(aux >> EXPSHIFTBITS_SP32) - EXPBIAS_SP32; + + __CLC_GENTYPE y = __CLC_AS_GENTYPE(aux); + + // transform if |x| >= 0.5 + __CLC_INTN transform = xexp >= -1; + + __CLC_GENTYPE y2 = y * y; + __CLC_GENTYPE yt = 0.5f * (1.0f - y); + __CLC_GENTYPE r = transform ? yt : y2; + + // Use a rational approximation for [0.0, 0.5] + __CLC_GENTYPE a = + __clc_mad(r, + __clc_mad(r, + __clc_mad(r, -0.00396137437848476485201154797087F, + -0.0133819288943925804214011424456F), + -0.0565298683201845211985026327361F), + 0.184161606965100694821398249421F); + __CLC_GENTYPE b = __clc_mad(r, -0.836411276854206731913362287293F, + 1.10496961524520294485512696706F); + __CLC_GENTYPE u = r * MATH_DIVIDE(a, b); + + __CLC_GENTYPE s = __clc_sqrt(r); + y = s; + __CLC_GENTYPE s1 = __CLC_AS_GENTYPE(__CLC_AS_UINTN(s) & 0xffff0000); + __CLC_GENTYPE c = MATH_DIVIDE(r - s1 * s1, s + s1); + __CLC_GENTYPE rettn = + 1.0f - MATH_DIVIDE(2.0f * (s + __clc_mad(y, u, -piby2_tail)), pi); + __CLC_GENTYPE rettp = MATH_DIVIDE(2.0f * (s1 + __clc_mad(y, u, c)), pi); + __CLC_GENTYPE rett = xneg ? rettn : rettp; + __CLC_GENTYPE ret = + MATH_DIVIDE(piby2_head - (x - __clc_mad(x, -u, piby2_tail)), pi); + + ret = transform ? rett : ret; + ret = aux > 0x3f800000U ? __CLC_GENTYPE_NAN : ret; + ret = ux == 0x3f800000U ? 0.0f : ret; + ret = ux == 0xbf800000U ? 1.0f : ret; + ret = xexp < -26 ? 0.5f : ret; + return ret; +} + +#elif __CLC_FPSIZE == 64 + +_CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE __clc_acospi(__CLC_GENTYPE x) { + const __CLC_GENTYPE pi = __CLC_FP_LIT(0x1.921fb54442d18p+1); + // 0x3c91a62633145c07 + const __CLC_GENTYPE piby2_tail = __CLC_FP_LIT(6.12323399573676603587e-17); + + __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); + + // abs(x) >= 0.5 + __CLC_LONGN transform = __CLC_CONVERT_LONGN(xexp >= -1); + + // Transform y into the range [0,0.5) + __CLC_GENTYPE r1 = 0.5 * (1.0 - y); + __CLC_GENTYPE s = __clc_sqrt(r1); + __CLC_GENTYPE r = y * y; + r = transform ? r1 : r; + y = transform ? s : y; + + // Use a rational approximation for [0.0, 0.5] + __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 ud = __clc_fma( + r, + __clc_fma(r, + __clc_fma(r, + __clc_fma(r, 0.105869422087204370341222318533, + -0.943639137032492685763471240072), + 2.76568859157270989520376345954), + -3.28431505720958658909889444194), + 1.36491501334161032038194214209); + + __CLC_GENTYPE u = r * MATH_DIVIDE(un, ud); + + // Reconstruct acos carefully in transformed region + __CLC_GENTYPE res1 = + __clc_fma(-2.0, MATH_DIVIDE(s + __clc_fma(y, u, -piby2_tail), pi), 1.0); + __CLC_GENTYPE s1 = + __CLC_AS_GENTYPE(__CLC_AS_ULONGN(s) & 0xffffffff00000000UL); + __CLC_GENTYPE c = MATH_DIVIDE(__clc_fma(-s1, s1, r), s + s1); + __CLC_GENTYPE res2 = + MATH_DIVIDE(__clc_fma(2.0, s1, __clc_fma(2.0, c, 2.0 * y * u)), pi); + res1 = xneg ? res1 : res2; + res2 = 0.5 - __clc_fma(x, u, x) / pi; + res1 = transform ? res1 : res2; + + res2 = x == 1.0 ? 0.0 : __CLC_GENTYPE_NAN; + res2 = x == -1.0 ? 1.0 : res2; + res1 = __CLC_CONVERT_LONGN(xexp >= 0) ? res2 : res1; + res1 = __CLC_CONVERT_LONGN(xexp < -56) ? 0.5 : res1; + + return res1; +} + +#elif __CLC_FPSIZE == 16 + +_CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE __clc_acospi(__CLC_GENTYPE x) { + return __CLC_CONVERT_GENTYPE(__clc_acospi(__CLC_CONVERT_FLOATN(x))); +} + +#endif diff --git a/libclc/clc/lib/generic/math/clc_asinpi.cl b/libclc/clc/lib/generic/math/clc_asinpi.cl new file mode 100644 index 0000000000000..bc680df5f9b23 --- /dev/null +++ b/libclc/clc/lib/generic/math/clc_asinpi.cl @@ -0,0 +1,19 @@ +//===----------------------------------------------------------------------===// +// +// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. +// See https://llvm.org/LICENSE.txt for license information. +// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception +// +//===----------------------------------------------------------------------===// + +#include <clc/clc_convert.h> +#include <clc/float/definitions.h> +#include <clc/internal/clc.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/math.h> + +#define __CLC_BODY <clc_asinpi.inc> +#include <clc/math/gentype.inc> diff --git a/libclc/clc/lib/generic/math/clc_asinpi.inc b/libclc/clc/lib/generic/math/clc_asinpi.inc new file mode 100644 index 0000000000000..5434b8b0f800b --- /dev/null +++ b/libclc/clc/lib/generic/math/clc_asinpi.inc @@ -0,0 +1,156 @@ +//===----------------------------------------------------------------------===// +// +// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. +// See https://llvm.org/LICENSE.txt for license information. +// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception +// +//===----------------------------------------------------------------------===// +// +// Computes arcsin(x). +// +// The incoming 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. +// +//===----------------------------------------------------------------------===// + +#if __CLC_FPSIZE == 32 + +_CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE __clc_asinpi(__CLC_GENTYPE x) { + const __CLC_GENTYPE pi = __CLC_FP_LIT(3.1415926535897933e+00); + // 0x33a22168 + const __CLC_GENTYPE piby2_tail = __CLC_FP_LIT(7.5497894159e-08); + // 0x3f490fda + const __CLC_GENTYPE hpiby2_head = __CLC_FP_LIT(7.8539812565e-01); + + __CLC_UINTN ux = __CLC_AS_UINTN(x); + __CLC_UINTN aux = ux & EXSIGNBIT_SP32; + __CLC_UINTN xs = ux ^ aux; + __CLC_GENTYPE shalf = + __CLC_AS_GENTYPE(xs | __CLC_AS_UINTN((__CLC_GENTYPE)__CLC_FP_LIT(0.5))); + + __CLC_INTN xexp = __CLC_AS_INTN(aux >> EXPSHIFTBITS_SP32) - EXPBIAS_SP32; + + __CLC_GENTYPE y = __CLC_AS_GENTYPE(aux); + + // abs(x) >= 0.5 + __CLC_INTN transform = xexp >= -1; + + __CLC_GENTYPE y2 = y * y; + __CLC_GENTYPE rt = 0.5f * (1.0f - y); + __CLC_GENTYPE r = transform ? rt : y2; + + // Use a rational approximation for [0.0, 0.5] + __CLC_GENTYPE a = + __clc_mad(r, + __clc_mad(r, + __clc_mad(r, -0.00396137437848476485201154797087F, + -0.0133819288943925804214011424456F), + -0.0565298683201845211985026327361F), + 0.184161606965100694821398249421F); + __CLC_GENTYPE b = __clc_mad(r, -0.836411276854206731913362287293F, + 1.10496961524520294485512696706F); + __CLC_GENTYPE u = r * MATH_DIVIDE(a, b); + + __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; + v = MATH_DIVIDE(v, pi); + __CLC_GENTYPE xbypi = MATH_DIVIDE(x, pi); + + __CLC_GENTYPE ret = __CLC_AS_GENTYPE(xs | __CLC_AS_UINTN(v)); + ret = aux > 0x3f800000U ? __CLC_GENTYPE_NAN : ret; + ret = aux == 0x3f800000U ? shalf : ret; + ret = xexp < -14 ? xbypi : ret; + + return ret; +} + +#elif __CLC_FPSIZE == 64 + +_CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE __clc_asinpi(__CLC_GENTYPE x) { + const __CLC_GENTYPE pi = __CLC_FP_LIT(0x1.921fb54442d18p+1); + // 0x3c91a62633145c07 + const __CLC_GENTYPE piby2_tail = __CLC_FP_LIT(6.1232339957367660e-17); + // 0x3fe921fb54442d18 + const __CLC_GENTYPE hpiby2_head = __CLC_FP_LIT(7.8539816339744831e-01); + + __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); + + // abs(x) >= 0.5 + __CLC_LONGN transform = __CLC_CONVERT_LONGN(xexp >= -1); + + __CLC_GENTYPE rt = 0.5 * (1.0 - y); + __CLC_GENTYPE y2 = y * y; + __CLC_GENTYPE r = transform ? rt : y2; + + // Use a rational approximation for [0.0, 0.5] + __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 ud = __clc_fma( + r, + __clc_fma(r, + __clc_fma(r, + __clc_fma(r, 0.105869422087204370341222318533, + -0.943639137032492685763471240072), + 2.76568859157270989520376345954), + -3.28431505720958658909889444194), + 1.36491501334161032038194214209); + + __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 = MATH_DIVIDE(v, pi); + v = __CLC_CONVERT_LONGN(xexp >= 0) ? __CLC_GENTYPE_NAN : v; + v = y == 1.0 ? 0.5 : v; + return xneg ? -v : v; +} + +#elif __CLC_FPSIZE == 16 + +_CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE __clc_asinpi(__CLC_GENTYPE x) { + return __CLC_CONVERT_GENTYPE(__clc_asinpi(__CLC_CONVERT_FLOATN(x))); +} + +#endif diff --git a/libclc/clc/lib/generic/math/clc_atanpi.cl b/libclc/clc/lib/generic/math/clc_atanpi.cl new file mode 100644 index 0000000000000..fee72aa7efb47 --- /dev/null +++ b/libclc/clc/lib/generic/math/clc_atanpi.cl @@ -0,0 +1,19 @@ +//===----------------------------------------------------------------------===// +// +// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. +// See https://llvm.org/LICENSE.txt for license information. +// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception +// +//===----------------------------------------------------------------------===// + +#include <clc/clc_convert.h> +#include <clc/float/definitions.h> +#include <clc/internal/clc.h> +#include <clc/math/clc_fabs.h> +#include <clc/math/clc_fma.h> +#include <clc/math/clc_mad.h> +#include <clc/math/math.h> +#include <clc/relational/clc_isnan.h> + +#define __CLC_BODY <clc_atanpi.inc> +#include <clc/math/gentype.inc> diff --git a/libclc/clc/lib/generic/math/clc_atanpi.inc b/libclc/clc/lib/generic/math/clc_atanpi.inc new file mode 100644 index 0000000000000..2cce212ec9a58 --- /dev/null +++ b/libclc/clc/lib/generic/math/clc_atanpi.inc @@ -0,0 +1,172 @@ +//===----------------------------------------------------------------------===// +// +// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. +// See https://llvm.org/LICENSE.txt for license information. +// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception +// +//===----------------------------------------------------------------------===// + +#if __CLC_FPSIZE == 32 + +_CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE __clc_atanpi(__CLC_GENTYPE x) { + const __CLC_GENTYPE pi = __CLC_FP_LIT(3.1415926535897932); + + __CLC_UINTN ux = __CLC_AS_UINTN(x); + __CLC_UINTN aux = ux & EXSIGNBIT_SP32; + __CLC_UINTN sx = ux ^ aux; + + __CLC_GENTYPE xbypi = MATH_DIVIDE(x, pi); + __CLC_GENTYPE shalf = + __CLC_AS_GENTYPE(sx | __CLC_AS_UINTN((__CLC_GENTYPE)__CLC_FP_LIT(0.5))); + + __CLC_GENTYPE v = __CLC_AS_GENTYPE(aux); + + // Return for NaN + __CLC_GENTYPE ret = x; + + // 2^26 <= |x| <= Inf => atan(x) is close to piby2 + ret = aux <= PINFBITPATT_SP32 ? shalf : ret; + + // Reduce arguments 2^-19 <= |x| < 2^26 + + // 39/16 <= x < 2^26 + x = -MATH_RECIP(v); + __CLC_GENTYPE c = 1.57079632679489655800f; // atan(infinity) + + // 19/16 <= x < 39/16 + __CLC_INTN l = aux < 0x401c0000; + __CLC_GENTYPE xx = MATH_DIVIDE(v - 1.5f, __clc_mad(v, 1.5f, 1.0f)); + x = l ? xx : x; + c = l ? 9.82793723247329054082e-01f : c; // atan(1.5) + + // 11/16 <= x < 19/16 + l = aux < 0x3f980000U; + xx = MATH_DIVIDE(v - 1.0f, 1.0f + v); + x = l ? xx : x; + c = l ? 7.85398163397448278999e-01f : c; // atan(1) + + // 7/16 <= x < 11/16 + l = aux < 0x3f300000; + xx = MATH_DIVIDE(__clc_mad(v, 2.0f, -1.0f), 2.0f + v); + x = l ? xx : x; + c = l ? 4.63647609000806093515e-01f : c; // atan(0.5) + + // 2^-19 <= x < 7/16 + l = aux < 0x3ee00000; + x = l ? v : x; + c = l ? 0.0f : c; + + // Core approximation: Remez(2,2) on [-7/16,7/16] + + __CLC_GENTYPE s = x * x; + __CLC_GENTYPE a = __clc_mad(s, + __clc_mad(s, 0.470677934286149214138357545549e-2f, + 0.192324546402108583211697690500f), + 0.296528598819239217902158651186f); + + __CLC_GENTYPE b = __clc_mad(s, + __clc_mad(s, 0.299309699959659728404442796915f, + 0.111072499995399550138837673349e1f), + 0.889585796862432286486651434570f); + + __CLC_GENTYPE q = x * s * MATH_DIVIDE(a, b); + + __CLC_GENTYPE z = c - (q - x); + z = MATH_DIVIDE(z, pi); + __CLC_GENTYPE zs = __CLC_AS_GENTYPE(sx | __CLC_AS_UINTN(z)); + + ret = aux < 0x4c800000 ? zs : ret; + + // |x| < 2^-19 + ret = aux < 0x36000000 ? xbypi : ret; + return ret; +} + +#elif __CLC_FPSIZE == 64 + +_CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE __clc_atanpi(__CLC_GENTYPE x) { + const __CLC_GENTYPE pi = __CLC_FP_LIT(0x1.921fb54442d18p+1); + + __CLC_GENTYPE v = __clc_fabs(x); + + // 2^56 > v > 39/16 + __CLC_GENTYPE a = -1.0; + __CLC_GENTYPE b = v; + // (chi + clo) = arctan(infinity) + __CLC_GENTYPE chi = 1.57079632679489655800e+00; + __CLC_GENTYPE clo = 6.12323399573676480327e-17; + + __CLC_GENTYPE ta = v - 1.5; + __CLC_GENTYPE tb = 1.0 + 1.5 * v; + __CLC_LONGN l = v <= 0x1.38p+1; // 39/16 > v > 19/16 + a = l ? ta : a; + b = l ? tb : b; + // (chi + clo) = arctan(1.5) + chi = l ? 9.82793723247329054082e-01 : chi; + clo = l ? 1.39033110312309953701e-17 : clo; + + ta = v - 1.0; + tb = 1.0 + v; + l = v <= 0x1.3p+0; // 19/16 > v > 11/16 + a = l ? ta : a; + b = l ? tb : b; + // (chi + clo) = arctan(1.) + chi = l ? 7.85398163397448278999e-01 : chi; + clo = l ? 3.06161699786838240164e-17 : clo; + + ta = 2.0 * v - 1.0; + tb = 2.0 + v; + l = v <= 0x1.6p-1; // 11/16 > v > 7/16 + a = l ? ta : a; + b = l ? tb : b; + // (chi + clo) = arctan(0.5) + chi = l ? 4.63647609000806093515e-01 : chi; + clo = l ? 2.26987774529616809294e-17 : clo; + + l = v <= 0x1.cp-2; // v < 7/16 + a = l ? v : a; + b = l ? 1.0 : b; + ; + chi = l ? 0.0 : chi; + clo = l ? 0.0 : clo; + + // Core approximation: Remez(4,4) on [-7/16,7/16] + __CLC_GENTYPE r = a / b; + __CLC_GENTYPE s = r * r; + __CLC_GENTYPE qn = + __clc_fma(s, + __clc_fma(s, + __clc_fma(s, + __clc_fma(s, 0.142316903342317766e-3, + 0.304455919504853031e-1), + 0.220638780716667420e0), + 0.447677206805497472e0), + 0.268297920532545909e0); + + __CLC_GENTYPE qd = + __clc_fma(s, + __clc_fma(s, + __clc_fma(s, + __clc_fma(s, 0.389525873944742195e-1, + 0.424602594203847109e0), + 0.141254259931958921e1), + 0.182596787737507063e1), + 0.804893761597637733e0); + + __CLC_GENTYPE q = r * s * qn / qd; + r = (chi - ((q - clo) - r)) / pi; + __CLC_GENTYPE vp = v / pi; + + __CLC_GENTYPE z = __clc_isnan(x) ? x : 0.5; + z = v <= 0x1.0p+56 ? r : z; + z = v < 0x1.0p-26 ? vp : z; + return x == v ? z : -z; +} + +#elif __CLC_FPSIZE == 16 + +_CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE __clc_atanpi(__CLC_GENTYPE x) { + return __CLC_CONVERT_GENTYPE(__clc_atanpi(__CLC_CONVERT_FLOATN(x))); +} + +#endif diff --git a/libclc/generic/lib/math/acospi.cl b/libclc/generic/lib/math/acospi.cl index 0b3dd62e18bca..844e0aa2f0a19 100644 --- a/libclc/generic/lib/math/acospi.cl +++ b/libclc/generic/lib/math/acospi.cl @@ -7,159 +7,9 @@ //===----------------------------------------------------------------------===// #include <clc/clc.h> -#include <clc/clcmacro.h> -#include <clc/math/math.h> +#include <clc/math/clc_acospi.h> -_CLC_OVERLOAD _CLC_DEF float acospi(float x) { - // Computes arccos(x). - // The argument is first reduced by noting that arccos(x) - // is invalid for abs(x) > 1. For denormal and small - // arguments arccos(x) = pi/2 to machine accuracy. - // Remaining argument ranges are handled as follows. - // For abs(x) <= 0.5 use - // arccos(x) = pi/2 - arcsin(x) - // = pi/2 - (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: - // arccos(x) = pi - 2*arcsin(sqrt(1-x)/2) - // together with the above rational approximation, and - // reconstruct the terms carefully. +#undef __CLC_FUNCTION +#define __CLC_FUNCTION acospi +#include <clc/math/unary_builtin.inc> - - // Some constants and split constants. - const float pi = 3.1415926535897933e+00f; - const float piby2_head = 1.5707963267948965580e+00f; /* 0x3ff921fb54442d18 */ - const float piby2_tail = 6.12323399573676603587e-17f; /* 0x3c91a62633145c07 */ - - uint ux = as_uint(x); - uint aux = ux & ~SIGNBIT_SP32; - int xneg = ux != aux; - int xexp = (int)(aux >> EXPSHIFTBITS_SP32) - EXPBIAS_SP32; - - float y = as_float(aux); - - // transform if |x| >= 0.5 - int transform = xexp >= -1; - - float y2 = y * y; - float yt = 0.5f * (1.0f - y); - float r = transform ? yt : y2; - - // Use a rational approximation for [0.0, 0.5] - float a = mad(r, mad(r, mad(r, -0.00396137437848476485201154797087F, -0.0133819288943925804214011424456F), - -0.0565298683201845211985026327361F), - 0.184161606965100694821398249421F); - float b = mad(r, -0.836411276854206731913362287293F, 1.10496961524520294485512696706F); - float u = r * MATH_DIVIDE(a, b); - - float s = MATH_SQRT(r); - y = s; - float s1 = as_float(as_uint(s) & 0xffff0000); - float c = MATH_DIVIDE(r - s1 * s1, s + s1); - // float rettn = 1.0f - MATH_DIVIDE(2.0f * (s + (y * u - piby2_tail)), pi); - float rettn = 1.0f - MATH_DIVIDE(2.0f * (s + mad(y, u, -piby2_tail)), pi); - // float rettp = MATH_DIVIDE(2.0F * s1 + (2.0F * c + 2.0F * y * u), pi); - float rettp = MATH_DIVIDE(2.0f*(s1 + mad(y, u, c)), pi); - float rett = xneg ? rettn : rettp; - // float ret = MATH_DIVIDE(piby2_head - (x - (piby2_tail - x * u)), pi); - float ret = MATH_DIVIDE(piby2_head - (x - mad(x, -u, piby2_tail)), pi); - - ret = transform ? rett : ret; - ret = aux > 0x3f800000U ? as_float(QNANBITPATT_SP32) : ret; - ret = ux == 0x3f800000U ? 0.0f : ret; - ret = ux == 0xbf800000U ? 1.0f : ret; - ret = xexp < -26 ? 0.5f : ret; - return ret; -} - -_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, float, acospi, float) - -#ifdef cl_khr_fp64 -#pragma OPENCL EXTENSION cl_khr_fp64 : enable - -_CLC_OVERLOAD _CLC_DEF double acospi(double x) { - // Computes arccos(x). - // The argument is first reduced by noting that arccos(x) - // is invalid for abs(x) > 1. For denormal and small - // arguments arccos(x) = pi/2 to machine accuracy. - // Remaining argument ranges are handled as follows. - // For abs(x) <= 0.5 use - // arccos(x) = pi/2 - arcsin(x) - // = pi/2 - (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: - // arccos(x) = pi - 2*arcsin(sqrt(1-x)/2) - // together with the above rational approximation, and - // reconstruct the terms carefully. - - const double pi = 0x1.921fb54442d18p+1; - const double piby2_tail = 6.12323399573676603587e-17; /* 0x3c91a62633145c07 */ - - double y = fabs(x); - int xneg = as_int2(x).hi < 0; - int xexp = (as_int2(y).hi >> 20) - EXPBIAS_DP64; - - // abs(x) >= 0.5 - int transform = xexp >= -1; - - // Transform y into the range [0,0.5) - double r1 = 0.5 * (1.0 - y); - double s = sqrt(r1); - double r = y * y; - r = transform ? r1 : r; - y = transform ? s : y; - - // Use a rational approximation for [0.0, 0.5] - double un = fma(r, - fma(r, - fma(r, - fma(r, - fma(r, 0.0000482901920344786991880522822991, - 0.00109242697235074662306043804220), - -0.0549989809235685841612020091328), - 0.275558175256937652532686256258), - -0.445017216867635649900123110649), - 0.227485835556935010735943483075); - - double ud = fma(r, - fma(r, - fma(r, - fma(r, 0.105869422087204370341222318533, - -0.943639137032492685763471240072), - 2.76568859157270989520376345954), - -3.28431505720958658909889444194), - 1.36491501334161032038194214209); - - double u = r * MATH_DIVIDE(un, ud); - - // Reconstruct acos carefully in transformed region - double res1 = fma(-2.0, MATH_DIVIDE(s + fma(y, u, -piby2_tail), pi), 1.0); - double s1 = as_double(as_ulong(s) & 0xffffffff00000000UL); - double c = MATH_DIVIDE(fma(-s1, s1, r), s + s1); - double res2 = MATH_DIVIDE(fma(2.0, s1, fma(2.0, c, 2.0 * y * u)), pi); - res1 = xneg ? res1 : res2; - res2 = 0.5 - fma(x, u, x) / pi; - res1 = transform ? res1 : res2; - - const double qnan = as_double(QNANBITPATT_DP64); - res2 = x == 1.0 ? 0.0 : qnan; - res2 = x == -1.0 ? 1.0 : res2; - res1 = xexp >= 0 ? res2 : res1; - res1 = xexp < -56 ? 0.5 : res1; - - return res1; -} - -_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, double, acospi, double) - -#endif - -#ifdef cl_khr_fp16 - -#pragma OPENCL EXTENSION cl_khr_fp16 : enable - -_CLC_DEFINE_UNARY_BUILTIN_FP16(acospi) - -#endif diff --git a/libclc/generic/lib/math/asinpi.cl b/libclc/generic/lib/math/asinpi.cl index 7f87a6b0c248b..7e109e8bb8dbb 100644 --- a/libclc/generic/lib/math/asinpi.cl +++ b/libclc/generic/lib/math/asinpi.cl @@ -7,149 +7,8 @@ //===----------------------------------------------------------------------===// #include <clc/clc.h> -#include <clc/clcmacro.h> -#include <clc/math/math.h> +#include <clc/math/clc_asinpi.h> -_CLC_OVERLOAD _CLC_DEF float asinpi(float 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. - - - const float pi = 3.1415926535897933e+00f; - const float piby2_tail = 7.5497894159e-08F; /* 0x33a22168 */ - const float hpiby2_head = 7.8539812565e-01F; /* 0x3f490fda */ - - uint ux = as_uint(x); - uint aux = ux & EXSIGNBIT_SP32; - uint xs = ux ^ aux; - float shalf = as_float(xs | as_uint(0.5f)); - - int xexp = (int)(aux >> EXPSHIFTBITS_SP32) - EXPBIAS_SP32; - - float y = as_float(aux); - - // abs(x) >= 0.5 - int transform = xexp >= -1; - - float y2 = y * y; - float rt = 0.5f * (1.0f - y); - float r = transform ? rt : y2; - - // Use a rational approximation for [0.0, 0.5] - float a = mad(r, - mad(r, - mad(r, -0.00396137437848476485201154797087F, -0.0133819288943925804214011424456F), - -0.0565298683201845211985026327361F), - 0.184161606965100694821398249421F); - float b = mad(r, -0.836411276854206731913362287293F, 1.10496961524520294485512696706F); - float u = r * MATH_DIVIDE(a, b); - - float s = MATH_SQRT(r); - float s1 = as_float(as_uint(s) & 0xffff0000); - float c = MATH_DIVIDE(mad(-s1, s1, r), s + s1); - float p = mad(2.0f*s, u, -mad(c, -2.0f, piby2_tail)); - float q = mad(s1, -2.0f, hpiby2_head); - float vt = hpiby2_head - (p - q); - float v = mad(y, u, y); - v = transform ? vt : v; - v = MATH_DIVIDE(v, pi); - float xbypi = MATH_DIVIDE(x, pi); - - float ret = as_float(xs | as_uint(v)); - ret = aux > 0x3f800000U ? as_float(QNANBITPATT_SP32) : ret; - ret = aux == 0x3f800000U ? shalf : ret; - ret = xexp < -14 ? xbypi : ret; - - return ret; -} - -_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, float, asinpi, float) - -#ifdef cl_khr_fp64 -#pragma OPENCL EXTENSION cl_khr_fp64 : enable - -_CLC_OVERLOAD _CLC_DEF double asinpi(double 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. - - const double pi = 0x1.921fb54442d18p+1; - const double piby2_tail = 6.1232339957367660e-17; /* 0x3c91a62633145c07 */ - const double hpiby2_head = 7.8539816339744831e-01; /* 0x3fe921fb54442d18 */ - - double y = fabs(x); - int xneg = as_int2(x).hi < 0; - int xexp = (as_int2(y).hi >> 20) - EXPBIAS_DP64; - - // abs(x) >= 0.5 - int transform = xexp >= -1; - - double rt = 0.5 * (1.0 - y); - double y2 = y * y; - double r = transform ? rt : y2; - - // Use a rational approximation for [0.0, 0.5] - double un = fma(r, - fma(r, - fma(r, - fma(r, - fma(r, 0.0000482901920344786991880522822991, - 0.00109242697235074662306043804220), - -0.0549989809235685841612020091328), - 0.275558175256937652532686256258), - -0.445017216867635649900123110649), - 0.227485835556935010735943483075); - - double ud = fma(r, - fma(r, - fma(r, - fma(r, 0.105869422087204370341222318533, - -0.943639137032492685763471240072), - 2.76568859157270989520376345954), - -3.28431505720958658909889444194), - 1.36491501334161032038194214209); - - double u = r * MATH_DIVIDE(un, ud); - - - // Reconstruct asin carefully in transformed region - double s = sqrt(r); - double sh = as_double(as_ulong(s) & 0xffffffff00000000UL); - double c = MATH_DIVIDE(fma(-sh, sh, r), s + sh); - double p = fma(2.0*s, u, -fma(-2.0, c, piby2_tail)); - double q = fma(-2.0, sh, hpiby2_head); - double vt = hpiby2_head - (p - q); - double v = fma(y, u, y); - v = transform ? vt : v; - - v = xexp < -28 ? y : v; - v = MATH_DIVIDE(v, pi); - v = xexp >= 0 ? as_double(QNANBITPATT_DP64) : v; - v = y == 1.0 ? 0.5 : v; - return xneg ? -v : v; -} - -_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, double, asinpi, double) - -#endif +#undef __CLC_FUNCTION +#define __CLC_FUNCTION asinpi +#include <clc/math/unary_builtin.inc> diff --git a/libclc/generic/lib/math/atanpi.cl b/libclc/generic/lib/math/atanpi.cl index 4aa6fe20283bf..2c67eb9592b77 100644 --- a/libclc/generic/lib/math/atanpi.cl +++ b/libclc/generic/lib/math/atanpi.cl @@ -7,169 +7,8 @@ //===----------------------------------------------------------------------===// #include <clc/clc.h> -#include <clc/clcmacro.h> -#include <clc/math/math.h> +#include <clc/math/clc_atanpi.h> -_CLC_OVERLOAD _CLC_DEF float atanpi(float x) { - const float pi = 3.1415926535897932f; - - uint ux = as_uint(x); - uint aux = ux & EXSIGNBIT_SP32; - uint sx = ux ^ aux; - - float xbypi = MATH_DIVIDE(x, pi); - float shalf = as_float(sx | as_uint(0.5f)); - - float v = as_float(aux); - - // Return for NaN - float ret = x; - - // 2^26 <= |x| <= Inf => atan(x) is close to piby2 - ret = aux <= PINFBITPATT_SP32 ? shalf : ret; - - // Reduce arguments 2^-19 <= |x| < 2^26 - - // 39/16 <= x < 2^26 - x = -MATH_RECIP(v); - float c = 1.57079632679489655800f; // atan(infinity) - - // 19/16 <= x < 39/16 - int l = aux < 0x401c0000; - float xx = MATH_DIVIDE(v - 1.5f, mad(v, 1.5f, 1.0f)); - x = l ? xx : x; - c = l ? 9.82793723247329054082e-01f : c; // atan(1.5) - - // 11/16 <= x < 19/16 - l = aux < 0x3f980000U; - xx = MATH_DIVIDE(v - 1.0f, 1.0f + v); - x = l ? xx : x; - c = l ? 7.85398163397448278999e-01f : c; // atan(1) - - // 7/16 <= x < 11/16 - l = aux < 0x3f300000; - xx = MATH_DIVIDE(mad(v, 2.0f, -1.0f), 2.0f + v); - x = l ? xx : x; - c = l ? 4.63647609000806093515e-01f : c; // atan(0.5) - - // 2^-19 <= x < 7/16 - l = aux < 0x3ee00000; - x = l ? v : x; - c = l ? 0.0f : c; - - // Core approximation: Remez(2,2) on [-7/16,7/16] - - float s = x * x; - float a = mad(s, - mad(s, 0.470677934286149214138357545549e-2f, 0.192324546402108583211697690500f), - 0.296528598819239217902158651186f); - - float b = mad(s, - mad(s, 0.299309699959659728404442796915f, 0.111072499995399550138837673349e1f), - 0.889585796862432286486651434570f); - - float q = x * s * MATH_DIVIDE(a, b); - - float z = c - (q - x); - z = MATH_DIVIDE(z, pi); - float zs = as_float(sx | as_uint(z)); - - ret = aux < 0x4c800000 ? zs : ret; - - // |x| < 2^-19 - ret = aux < 0x36000000 ? xbypi : ret; - return ret; -} - -_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, float, atanpi, float) - -#ifdef cl_khr_fp64 -#pragma OPENCL EXTENSION cl_khr_fp64 : enable - -_CLC_OVERLOAD _CLC_DEF double atanpi(double x) { - const double pi = 0x1.921fb54442d18p+1; - - double v = fabs(x); - - // 2^56 > v > 39/16 - double a = -1.0; - double b = v; - // (chi + clo) = arctan(infinity) - double chi = 1.57079632679489655800e+00; - double clo = 6.12323399573676480327e-17; - - double ta = v - 1.5; - double tb = 1.0 + 1.5 * v; - int l = v <= 0x1.38p+1; // 39/16 > v > 19/16 - a = l ? ta : a; - b = l ? tb : b; - // (chi + clo) = arctan(1.5) - chi = l ? 9.82793723247329054082e-01 : chi; - clo = l ? 1.39033110312309953701e-17 : clo; - - ta = v - 1.0; - tb = 1.0 + v; - l = v <= 0x1.3p+0; // 19/16 > v > 11/16 - a = l ? ta : a; - b = l ? tb : b; - // (chi + clo) = arctan(1.) - chi = l ? 7.85398163397448278999e-01 : chi; - clo = l ? 3.06161699786838240164e-17 : clo; - - ta = 2.0 * v - 1.0; - tb = 2.0 + v; - l = v <= 0x1.6p-1; // 11/16 > v > 7/16 - a = l ? ta : a; - b = l ? tb : b; - // (chi + clo) = arctan(0.5) - chi = l ? 4.63647609000806093515e-01 : chi; - clo = l ? 2.26987774529616809294e-17 : clo; - - l = v <= 0x1.cp-2; // v < 7/16 - a = l ? v : a; - b = l ? 1.0 : b;; - chi = l ? 0.0 : chi; - clo = l ? 0.0 : clo; - - // Core approximation: Remez(4,4) on [-7/16,7/16] - double r = a / b; - double s = r * r; - double qn = fma(s, - fma(s, - fma(s, - fma(s, 0.142316903342317766e-3, - 0.304455919504853031e-1), - 0.220638780716667420e0), - 0.447677206805497472e0), - 0.268297920532545909e0); - - double qd = fma(s, - fma(s, - fma(s, - fma(s, 0.389525873944742195e-1, - 0.424602594203847109e0), - 0.141254259931958921e1), - 0.182596787737507063e1), - 0.804893761597637733e0); - - double q = r * s * qn / qd; - r = (chi - ((q - clo) - r)) / pi; - double vp = v / pi; - - double z = isnan(x) ? x : 0.5; - z = v <= 0x1.0p+56 ? r : z; - z = v < 0x1.0p-26 ? vp : z; - return x == v ? z : -z; -} - -_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, double, atanpi, double) - -#endif - -#ifdef cl_khr_fp16 - -#pragma OPENCL EXTENSION cl_khr_fp16 : enable - -_CLC_DEFINE_UNARY_BUILTIN_FP16(atanpi) - -#endif +#undef __CLC_FUNCTION +#define __CLC_FUNCTION atanpi +#include <clc/math/unary_builtin.inc> _______________________________________________ cfe-commits mailing list cfe-commits@lists.llvm.org https://lists.llvm.org/cgi-bin/mailman/listinfo/cfe-commits
