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[libc][math] Refactor acosf16 implementation to header-only in src/__support/math folder. #148412
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[libc][math] Refactor acosf16 implementation to header-only in src/__…
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,29 @@ | ||
| //===-- Shared acosf16 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 | ||
| // | ||
| //===----------------------------------------------------------------------===// | ||
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| #ifndef LLVM_LIBC_SHARED_MATH_ACOSF16_H | ||
| #define LLVM_LIBC_SHARED_MATH_ACOSF16_H | ||
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| #include "include/llvm-libc-macros/float16-macros.h" | ||
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| #ifdef LIBC_TYPES_HAS_FLOAT16 | ||
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| #include "shared/libc_common.h" | ||
| #include "src/__support/math/acosf16.h" | ||
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| namespace LIBC_NAMESPACE_DECL { | ||
| namespace shared { | ||
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| using math::acosf16; | ||
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| } // namespace shared | ||
| } // namespace LIBC_NAMESPACE_DECL | ||
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| #endif // LIBC_TYPES_HAS_FLOAT16 | ||
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| #endif // LLVM_LIBC_SHARED_MATH_ACOSF16_H |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,163 @@ | ||
| //===-- Implementation header for acosf16 -----------------------*- 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 | ||
| // | ||
| //===----------------------------------------------------------------------===// | ||
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| #ifndef LLVM_LIBC_SRC___SUPPORT_MATH_ACOSF16_H | ||
| #define LLVM_LIBC_SRC___SUPPORT_MATH_ACOSF16_H | ||
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| #include "include/llvm-libc-macros/float16-macros.h" | ||
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| #ifdef LIBC_TYPES_HAS_FLOAT16 | ||
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| #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/except_value_utils.h" | ||
| #include "src/__support/FPUtil/multiply_add.h" | ||
| #include "src/__support/FPUtil/sqrt.h" | ||
| #include "src/__support/macros/optimization.h" | ||
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| namespace LIBC_NAMESPACE_DECL { | ||
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| namespace math { | ||
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| // Generated by Sollya using the following command: | ||
| // > round(pi/2, SG, RN); | ||
| // > round(pi, SG, RN); | ||
| static constexpr float PI_OVER_2 = 0x1.921fb6p0f; | ||
| static constexpr float PI = 0x1.921fb6p1f; | ||
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| #ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS | ||
| static constexpr size_t N_EXCEPTS = 2; | ||
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| static constexpr fputil::ExceptValues<float16, N_EXCEPTS> ACOSF16_EXCEPTS{{ | ||
| // (input, RZ output, RU offset, RD offset, RN offset) | ||
| {0xacaf, 0x3e93, 1, 0, 0}, | ||
| {0xb874, 0x4052, 1, 0, 1}, | ||
| }}; | ||
| #endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS | ||
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| static constexpr float16 acosf16(float16 x) { | ||
| using FPBits = fputil::FPBits<float16>; | ||
| FPBits xbits(x); | ||
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| uint16_t x_u = xbits.uintval(); | ||
| uint16_t x_abs = x_u & 0x7fff; | ||
| uint16_t x_sign = x_u >> 15; | ||
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| // |x| > 0x1p0, |x| > 1, or x is NaN. | ||
| if (LIBC_UNLIKELY(x_abs > 0x3c00)) { | ||
| // acosf16(NaN) = NaN | ||
| if (xbits.is_nan()) { | ||
| if (xbits.is_signaling_nan()) { | ||
| fputil::raise_except_if_required(FE_INVALID); | ||
| return FPBits::quiet_nan().get_val(); | ||
| } | ||
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| return x; | ||
| } | ||
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| // 1 < |x| <= +/-inf | ||
| fputil::raise_except_if_required(FE_INVALID); | ||
| fputil::set_errno_if_required(EDOM); | ||
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| return FPBits::quiet_nan().get_val(); | ||
| } | ||
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| float xf = x; | ||
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| #ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS | ||
| // Handle exceptional values | ||
| if (auto r = ACOSF16_EXCEPTS.lookup(x_u); LIBC_UNLIKELY(r.has_value())) | ||
| return r.value(); | ||
| #endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS | ||
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| // |x| == 0x1p0, x is 1 or -1 | ||
| // if x is (-)1, return pi, else | ||
| // if x is (+)1, return 0 | ||
| if (LIBC_UNLIKELY(x_abs == 0x3c00)) | ||
| return fputil::cast<float16>(x_sign ? PI : 0.0f); | ||
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| float xsq = xf * xf; | ||
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| // |x| <= 0x1p-1, |x| <= 0.5 | ||
| if (x_abs <= 0x3800) { | ||
| // if x is 0, return pi/2 | ||
| if (LIBC_UNLIKELY(x_abs == 0)) | ||
| return fputil::cast<float16>(PI_OVER_2); | ||
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| // Note that: acos(x) = pi/2 + asin(-x) = pi/2 - asin(x) | ||
| // Degree-6 minimax polynomial of asin(x) generated by Sollya with: | ||
| // > P = fpminimax(asin(x)/x, [|0, 2, 4, 6, 8|], [|SG...|], [0, 0.5]); | ||
| float interm = | ||
| fputil::polyeval(xsq, 0x1.000002p0f, 0x1.554c2ap-3f, 0x1.3541ccp-4f, | ||
| 0x1.43b2d6p-5f, 0x1.a0d73ep-5f); | ||
| return fputil::cast<float16>(fputil::multiply_add(-xf, interm, PI_OVER_2)); | ||
| } | ||
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| // 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)) | ||
| // | ||
| // 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) | ||
| // allows us to compute for the negative x value (lhs) | ||
| // with a positive x value instead (rhs). | ||
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| float xf_abs = (xf < 0 ? -xf : xf); | ||
| float u = fputil::multiply_add(-0.5f, xf_abs, 0.5f); | ||
| float sqrt_u = fputil::sqrt<float>(u); | ||
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| // Degree-6 minimax polynomial of asin(x) generated by Sollya with: | ||
| // > P = fpminimax(asin(x)/x, [|0, 2, 4, 6, 8|], [|SG...|], [0, 0.5]); | ||
| float asin_sqrt_u = | ||
| sqrt_u * fputil::polyeval(u, 0x1.000002p0f, 0x1.554c2ap-3f, | ||
| 0x1.3541ccp-4f, 0x1.43b2d6p-5f, 0x1.a0d73ep-5f); | ||
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| return fputil::cast<float16>( | ||
| x_sign ? fputil::multiply_add(-2.0f, asin_sqrt_u, PI) : 2 * asin_sqrt_u); | ||
| } | ||
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| } // namespace math | ||
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| } // namespace LIBC_NAMESPACE_DECL | ||
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| #endif // LIBC_TYPES_HAS_FLOAT16 | ||
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| #endif // LLVM_LIBC_SRC___SUPPORT_MATH_ACOS_H | ||
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