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Diffstat (limited to 'libc/src/math/generic/acosf16.cpp')
-rw-r--r--libc/src/math/generic/acosf16.cpp138
1 files changed, 2 insertions, 136 deletions
diff --git a/libc/src/math/generic/acosf16.cpp b/libc/src/math/generic/acosf16.cpp
index 202a950..0bf85f8 100644
--- a/libc/src/math/generic/acosf16.cpp
+++ b/libc/src/math/generic/acosf16.cpp
@@ -8,144 +8,10 @@
//===----------------------------------------------------------------------===//
#include "src/math/acosf16.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/except_value_utils.h"
-#include "src/__support/FPUtil/multiply_add.h"
-#include "src/__support/FPUtil/sqrt.h"
-#include "src/__support/macros/optimization.h"
+#include "src/__support/math/acosf16.h"
namespace LIBC_NAMESPACE_DECL {
-// 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;
+LLVM_LIBC_FUNCTION(float16, acosf16, (float16 x)) { return math::acosf16(x); }
-#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
-static constexpr size_t N_EXCEPTS = 2;
-
-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
-
-LLVM_LIBC_FUNCTION(float16, acosf16, (float16 x)) {
- using FPBits = fputil::FPBits<float16>;
- 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)) {
- // 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();
- }
-
- return x;
- }
-
- // 1 < |x| <= +/-inf
- fputil::raise_except_if_required(FE_INVALID);
- fputil::set_errno_if_required(EDOM);
-
- return FPBits::quiet_nan().get_val();
- }
-
- float xf = x;
-
-#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
-
- // |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);
-
- float xsq = xf * xf;
-
- // |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);
-
- // 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));
- }
-
- // 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).
-
- 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);
-
- // 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);
-
- return fputil::cast<float16>(
- x_sign ? fputil::multiply_add(-2.0f, asin_sqrt_u, PI) : 2 * asin_sqrt_u);
-}
} // namespace LIBC_NAMESPACE_DECL