diff --git a/libc/shared/math.h b/libc/shared/math.h index e3c674c27ffaf..135099a6b728e 100644 --- a/libc/shared/math.h +++ b/libc/shared/math.h @@ -16,6 +16,7 @@ #include "math/acosf16.h" #include "math/acoshf.h" #include "math/acoshf16.h" +#include "math/acospif16.h" #include "math/erff.h" #include "math/exp.h" #include "math/exp10.h" diff --git a/libc/shared/math/acospif16.h b/libc/shared/math/acospif16.h new file mode 100644 index 0000000000000..38225f2a0f288 --- /dev/null +++ b/libc/shared/math/acospif16.h @@ -0,0 +1,29 @@ +//===-- Shared acospif16 function -------------------------------*- C++ -*-===// +// +// 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 LLVM_LIBC_SHARED_MATH_ACOSPIF16_H +#define LLVM_LIBC_SHARED_MATH_ACOSPIF16_H + +#include "include/llvm-libc-macros/float16-macros.h" + +#ifdef LIBC_TYPES_HAS_FLOAT16 + +#include "shared/libc_common.h" +#include "src/__support/math/acospif16.h" + +namespace LIBC_NAMESPACE_DECL { +namespace shared { + +using math::acospif16; + +} // namespace shared +} // namespace LIBC_NAMESPACE_DECL + +#endif // LIBC_TYPES_HAS_FLOAT16 + +#endif // LLVM_LIBC_SHARED_MATH_ACOSPIF16_H diff --git a/libc/src/__support/math/CMakeLists.txt b/libc/src/__support/math/CMakeLists.txt index e6e2d95ace6ec..b951c91d83fb5 100644 --- a/libc/src/__support/math/CMakeLists.txt +++ b/libc/src/__support/math/CMakeLists.txt @@ -95,6 +95,21 @@ add_header_library( libc.src.__support.macros.optimization ) +add_header_library( + acospif16 + HDRS + acospif16.h + DEPENDS + libc.src.__support.FPUtil.cast + libc.src.__support.FPUtil.fenv_impl + libc.src.__support.FPUtil.fp_bits + libc.src.__support.FPUtil.multiply_add + libc.src.__support.FPUtil.polyeval + libc.src.__support.FPUtil.sqrt + libc.src.__support.macros.optimization + libc.src.__support.macros.properties.types +) + add_header_library( asin_utils HDRS diff --git a/libc/src/__support/math/acospif16.h b/libc/src/__support/math/acospif16.h new file mode 100644 index 0000000000000..5829aed2ca94a --- /dev/null +++ b/libc/src/__support/math/acospif16.h @@ -0,0 +1,147 @@ +//===-- Implementation header for acospif16 ---------------------*- C++ -*-===// +// +// 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 LLVM_LIBC_SRC___SUPPORT_MATH_ACOSPIF16_H +#define LLVM_LIBC_SRC___SUPPORT_MATH_ACOSPIF16_H + +#include "include/llvm-libc-macros/float16-macros.h" + +#ifdef LIBC_TYPES_HAS_FLOAT16 + +#include "src/__support/FPUtil/FEnvImpl.h" +#include "src/__support/FPUtil/FPBits.h" +#include "src/__support/FPUtil/PolyEval.h" +#include "src/__support/FPUtil/cast.h" +#include "src/__support/FPUtil/multiply_add.h" +#include "src/__support/FPUtil/sqrt.h" +#include "src/__support/macros/optimization.h" + +namespace LIBC_NAMESPACE_DECL { + +namespace math { + +static constexpr float16 acospif16(float16 x) { + using FPBits = fputil::FPBits; + FPBits xbits(x); + + uint16_t x_u = xbits.uintval(); + uint16_t x_abs = x_u & 0x7fff; + uint16_t x_sign = x_u >> 15; + + // |x| > 0x1p0, |x| > 1, or x is NaN. + if (LIBC_UNLIKELY(x_abs > 0x3c00)) { + // acospif16(NaN) = NaN + if (xbits.is_nan()) { + if (xbits.is_signaling_nan()) { + fputil::raise_except_if_required(FE_INVALID); + return FPBits::quiet_nan().get_val(); + } + + return x; + } + + // 1 < |x| <= +inf + fputil::raise_except_if_required(FE_INVALID); + fputil::set_errno_if_required(EDOM); + + return FPBits::quiet_nan().get_val(); + } + + // |x| == 0x1p0, x is 1 or -1 + // if x is (-)1, return 1 + // if x is (+)1, return 0 + if (LIBC_UNLIKELY(x_abs == 0x3c00)) + return fputil::cast(x_sign ? 1.0f : 0.0f); + + float xf = x; + float xsq = xf * xf; + + // Degree-6 minimax polynomial coefficients of asin(x) generated by Sollya + // with: > P = fpminimax(asin(x)/(pi * x), [|0, 2, 4, 6, 8|], [|SG...|], [0, + // 0.5]); + constexpr float POLY_COEFFS[5] = {0x1.45f308p-2f, 0x1.b2900cp-5f, + 0x1.897e36p-6f, 0x1.9efafcp-7f, + 0x1.06d884p-6f}; + // |x| <= 0x1p-1, |x| <= 0.5 + if (x_abs <= 0x3800) { + // if x is 0, return 0.5 + if (LIBC_UNLIKELY(x_abs == 0)) + return fputil::cast(0.5f); + + // Note that: acos(x) = pi/2 + asin(-x) = pi/2 - asin(x), then + // acospi(x) = 0.5 - asin(x)/pi + float interm = + fputil::polyeval(xsq, POLY_COEFFS[0], POLY_COEFFS[1], POLY_COEFFS[2], + POLY_COEFFS[3], POLY_COEFFS[4]); + + return fputil::cast(fputil::multiply_add(-xf, interm, 0.5f)); + } + + // When |x| > 0.5, assume that 0.5 < |x| <= 1 + // + // Step-by-step range-reduction proof: + // 1: Let y = asin(x), such that, x = sin(y) + // 2: From complimentary angle identity: + // x = sin(y) = cos(pi/2 - y) + // 3: Let z = pi/2 - y, such that x = cos(z) + // 4: From double angle formula; cos(2A) = 1 - 2 * sin^2(A): + // z = 2A, z/2 = A + // cos(z) = 1 - 2 * sin^2(z/2) + // 5: Make sin(z/2) subject of the formula: + // sin(z/2) = sqrt((1 - cos(z))/2) + // 6: Recall [3]; x = cos(z). Therefore: + // sin(z/2) = sqrt((1 - x)/2) + // 7: Let u = (1 - x)/2 + // 8: Therefore: + // asin(sqrt(u)) = z/2 + // 2 * asin(sqrt(u)) = z + // 9: Recall [3]; z = pi/2 - y. Therefore: + // y = pi/2 - z + // y = pi/2 - 2 * asin(sqrt(u)) + // 10: Recall [1], y = asin(x). Therefore: + // asin(x) = pi/2 - 2 * asin(sqrt(u)) + // 11: Recall that: acos(x) = pi/2 + asin(-x) = pi/2 - asin(x) + // Therefore: + // acos(x) = pi/2 - (pi/2 - 2 * asin(sqrt(u))) + // acos(x) = 2 * asin(sqrt(u)) + // acospi(x) = 2 * (asin(sqrt(u)) / pi) + // + // THE RANGE REDUCTION, HOW? + // 12: Recall [7], u = (1 - x)/2 + // 13: Since 0.5 < x <= 1, therefore: + // 0 <= u <= 0.25 and 0 <= sqrt(u) <= 0.5 + // + // Hence, we can reuse the same [0, 0.5] domain polynomial approximation for + // Step [11] as `sqrt(u)` is in range. + // When -1 < x <= -0.5, the identity: + // acos(x) = pi - acos(-x) + // acospi(x) = 1 - acos(-x)/pi + // allows us to compute for the negative x value (lhs) + // with a positive x value instead (rhs). + + float xf_abs = (xf < 0 ? -xf : xf); + float u = fputil::multiply_add(-0.5f, xf_abs, 0.5f); + float sqrt_u = fputil::sqrt(u); + + float asin_sqrt_u = + sqrt_u * fputil::polyeval(u, POLY_COEFFS[0], POLY_COEFFS[1], + POLY_COEFFS[2], POLY_COEFFS[3], POLY_COEFFS[4]); + + // Same as acos(x), but devided the expression with pi + return fputil::cast( + x_sign ? fputil::multiply_add(-2.0f, asin_sqrt_u, 1.0f) + : 2.0f * asin_sqrt_u); +} + +} // namespace math + +} // namespace LIBC_NAMESPACE_DECL + +#endif // LIBC_TYPES_HAS_FLOAT16 + +#endif // LLVM_LIBC_SRC___SUPPORT_MATH_ACOSPIF16_H diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt index a001d99e032d6..4ceef99140b3c 100644 --- a/libc/src/math/generic/CMakeLists.txt +++ b/libc/src/math/generic/CMakeLists.txt @@ -4043,16 +4043,8 @@ add_entrypoint_object( HDRS ../acospif16.h DEPENDS - libc.hdr.errno_macros - libc.hdr.fenv_macros - libc.src.__support.FPUtil.cast - libc.src.__support.FPUtil.fenv_impl - libc.src.__support.FPUtil.fp_bits - libc.src.__support.FPUtil.multiply_add - libc.src.__support.FPUtil.polyeval - libc.src.__support.FPUtil.sqrt - libc.src.__support.macros.optimization - libc.src.__support.macros.properties.types + libc.src.__support.math.acospif16 + libc.src.errno.errno ) add_header_library( diff --git a/libc/src/math/generic/acospif16.cpp b/libc/src/math/generic/acospif16.cpp index bfdf1694e3ba6..09cbd9984d4fa 100644 --- a/libc/src/math/generic/acospif16.cpp +++ b/libc/src/math/generic/acospif16.cpp @@ -7,128 +7,12 @@ //===----------------------------------------------------------------------===// #include "src/math/acospif16.h" -#include "hdr/errno_macros.h" -#include "hdr/fenv_macros.h" -#include "src/__support/FPUtil/FEnvImpl.h" -#include "src/__support/FPUtil/FPBits.h" -#include "src/__support/FPUtil/PolyEval.h" -#include "src/__support/FPUtil/cast.h" -#include "src/__support/FPUtil/multiply_add.h" -#include "src/__support/FPUtil/sqrt.h" -#include "src/__support/macros/optimization.h" +#include "src/__support/math/acospif16.h" namespace LIBC_NAMESPACE_DECL { LLVM_LIBC_FUNCTION(float16, acospif16, (float16 x)) { - using FPBits = fputil::FPBits; - FPBits xbits(x); - - uint16_t x_u = xbits.uintval(); - uint16_t x_abs = x_u & 0x7fff; - uint16_t x_sign = x_u >> 15; - - // |x| > 0x1p0, |x| > 1, or x is NaN. - if (LIBC_UNLIKELY(x_abs > 0x3c00)) { - // acospif16(NaN) = NaN - if (xbits.is_nan()) { - if (xbits.is_signaling_nan()) { - fputil::raise_except_if_required(FE_INVALID); - return FPBits::quiet_nan().get_val(); - } - - return x; - } - - // 1 < |x| <= +inf - fputil::raise_except_if_required(FE_INVALID); - fputil::set_errno_if_required(EDOM); - - return FPBits::quiet_nan().get_val(); - } - - // |x| == 0x1p0, x is 1 or -1 - // if x is (-)1, return 1 - // if x is (+)1, return 0 - if (LIBC_UNLIKELY(x_abs == 0x3c00)) - return fputil::cast(x_sign ? 1.0f : 0.0f); - - float xf = x; - float xsq = xf * xf; - - // Degree-6 minimax polynomial coefficients of asin(x) generated by Sollya - // with: > P = fpminimax(asin(x)/(pi * x), [|0, 2, 4, 6, 8|], [|SG...|], [0, - // 0.5]); - constexpr float POLY_COEFFS[5] = {0x1.45f308p-2f, 0x1.b2900cp-5f, - 0x1.897e36p-6f, 0x1.9efafcp-7f, - 0x1.06d884p-6f}; - // |x| <= 0x1p-1, |x| <= 0.5 - if (x_abs <= 0x3800) { - // if x is 0, return 0.5 - if (LIBC_UNLIKELY(x_abs == 0)) - return fputil::cast(0.5f); - - // Note that: acos(x) = pi/2 + asin(-x) = pi/2 - asin(x), then - // acospi(x) = 0.5 - asin(x)/pi - float interm = - fputil::polyeval(xsq, POLY_COEFFS[0], POLY_COEFFS[1], POLY_COEFFS[2], - POLY_COEFFS[3], POLY_COEFFS[4]); - - return fputil::cast(fputil::multiply_add(-xf, interm, 0.5f)); - } - - // When |x| > 0.5, assume that 0.5 < |x| <= 1 - // - // Step-by-step range-reduction proof: - // 1: Let y = asin(x), such that, x = sin(y) - // 2: From complimentary angle identity: - // x = sin(y) = cos(pi/2 - y) - // 3: Let z = pi/2 - y, such that x = cos(z) - // 4: From double angle formula; cos(2A) = 1 - 2 * sin^2(A): - // z = 2A, z/2 = A - // cos(z) = 1 - 2 * sin^2(z/2) - // 5: Make sin(z/2) subject of the formula: - // sin(z/2) = sqrt((1 - cos(z))/2) - // 6: Recall [3]; x = cos(z). Therefore: - // sin(z/2) = sqrt((1 - x)/2) - // 7: Let u = (1 - x)/2 - // 8: Therefore: - // asin(sqrt(u)) = z/2 - // 2 * asin(sqrt(u)) = z - // 9: Recall [3]; z = pi/2 - y. Therefore: - // y = pi/2 - z - // y = pi/2 - 2 * asin(sqrt(u)) - // 10: Recall [1], y = asin(x). Therefore: - // asin(x) = pi/2 - 2 * asin(sqrt(u)) - // 11: Recall that: acos(x) = pi/2 + asin(-x) = pi/2 - asin(x) - // Therefore: - // acos(x) = pi/2 - (pi/2 - 2 * asin(sqrt(u))) - // acos(x) = 2 * asin(sqrt(u)) - // acospi(x) = 2 * (asin(sqrt(u)) / pi) - // - // THE RANGE REDUCTION, HOW? - // 12: Recall [7], u = (1 - x)/2 - // 13: Since 0.5 < x <= 1, therefore: - // 0 <= u <= 0.25 and 0 <= sqrt(u) <= 0.5 - // - // Hence, we can reuse the same [0, 0.5] domain polynomial approximation for - // Step [11] as `sqrt(u)` is in range. - // When -1 < x <= -0.5, the identity: - // acos(x) = pi - acos(-x) - // acospi(x) = 1 - acos(-x)/pi - // allows us to compute for the negative x value (lhs) - // with a positive x value instead (rhs). - - float xf_abs = (xf < 0 ? -xf : xf); - float u = fputil::multiply_add(-0.5f, xf_abs, 0.5f); - float sqrt_u = fputil::sqrt(u); - - float asin_sqrt_u = - sqrt_u * fputil::polyeval(u, POLY_COEFFS[0], POLY_COEFFS[1], - POLY_COEFFS[2], POLY_COEFFS[3], POLY_COEFFS[4]); - - // Same as acos(x), but devided the expression with pi - return fputil::cast( - x_sign ? fputil::multiply_add(-2.0f, asin_sqrt_u, 1.0f) - : 2.0f * asin_sqrt_u); + return math::acospif16(x); } + } // namespace LIBC_NAMESPACE_DECL diff --git a/libc/test/shared/CMakeLists.txt b/libc/test/shared/CMakeLists.txt index 89b607d7e5cc3..680da9147b27c 100644 --- a/libc/test/shared/CMakeLists.txt +++ b/libc/test/shared/CMakeLists.txt @@ -12,6 +12,7 @@ add_fp_unittest( libc.src.__support.math.acosf16 libc.src.__support.math.acoshf libc.src.__support.math.acoshf16 + libc.src.__support.math.acospif16 libc.src.__support.math.erff libc.src.__support.math.exp libc.src.__support.math.exp10 diff --git a/libc/test/shared/shared_math_test.cpp b/libc/test/shared/shared_math_test.cpp index 44e90e4d0e8b7..354fa0d55e4ef 100644 --- a/libc/test/shared/shared_math_test.cpp +++ b/libc/test/shared/shared_math_test.cpp @@ -8,6 +8,7 @@ #include "shared/math.h" #include "test/UnitTest/FPMatcher.h" +#include "test/UnitTest/Test.h" #ifdef LIBC_TYPES_HAS_FLOAT16 @@ -15,6 +16,7 @@ TEST(LlvmLibcSharedMathTest, AllFloat16) { int exponent; EXPECT_FP_EQ(0x0p+0f16, LIBC_NAMESPACE::shared::acoshf16(1.0f16)); + EXPECT_FP_EQ(0x0p+0f16, LIBC_NAMESPACE::shared::acospif16(1.0f16)); EXPECT_FP_EQ(0x1p+0f16, LIBC_NAMESPACE::shared::exp10f16(0.0f16)); diff --git a/utils/bazel/llvm-project-overlay/libc/BUILD.bazel b/utils/bazel/llvm-project-overlay/libc/BUILD.bazel index 7eaa45396be71..aed7e4cbbbbf9 100644 --- a/utils/bazel/llvm-project-overlay/libc/BUILD.bazel +++ b/utils/bazel/llvm-project-overlay/libc/BUILD.bazel @@ -2184,6 +2184,21 @@ libc_support_library( ], ) +libc_support_library( + name = "__support_math_acospif16", + hdrs = ["src/__support/math/acospif16.h"], + deps = [ + ":__support_fputil_cast", + ":__support_fputil_fenv_impl", + ":__support_fputil_fp_bits", + ":__support_fputil_multiply_add", + ":__support_fputil_polyeval", + ":__support_fputil_sqrt", + ":__support_macros_optimization", + ":__support_macros_properties_types", + ], +) + libc_support_library( name = "__support_math_asin_utils", hdrs = ["src/__support/math/asin_utils.h"], @@ -2735,6 +2750,14 @@ libc_math_function( ], ) +libc_math_function( + name = "acospif16", + additional_deps = [ + ":__support_math_acospif16", + ":errno", + ], +) + libc_math_function( name = "asinf", additional_deps = [