diff options
Diffstat (limited to 'libc/src/math/generic/atanf.cpp')
| -rw-r--r-- | libc/src/math/generic/atanf.cpp | 110 |
1 files changed, 2 insertions, 108 deletions
diff --git a/libc/src/math/generic/atanf.cpp b/libc/src/math/generic/atanf.cpp index 22f962e..acd32f0 100644 --- a/libc/src/math/generic/atanf.cpp +++ b/libc/src/math/generic/atanf.cpp @@ -7,116 +7,10 @@ //===----------------------------------------------------------------------===// #include "src/math/atanf.h" -#include "src/__support/FPUtil/FPBits.h" -#include "src/__support/FPUtil/PolyEval.h" -#include "src/__support/FPUtil/except_value_utils.h" -#include "src/__support/FPUtil/multiply_add.h" -#include "src/__support/FPUtil/nearest_integer.h" -#include "src/__support/FPUtil/rounding_mode.h" -#include "src/__support/macros/config.h" -#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY -#include "src/__support/math/inv_trigf_utils.h" +#include "src/__support/math/atanf.h" namespace LIBC_NAMESPACE_DECL { -LLVM_LIBC_FUNCTION(float, atanf, (float x)) { - using namespace inv_trigf_utils_internal; - using FPBits = typename fputil::FPBits<float>; - - constexpr double FINAL_SIGN[2] = {1.0, -1.0}; - constexpr double SIGNED_PI_OVER_2[2] = {0x1.921fb54442d18p0, - -0x1.921fb54442d18p0}; - - FPBits x_bits(x); - Sign sign = x_bits.sign(); - x_bits.set_sign(Sign::POS); - uint32_t x_abs = x_bits.uintval(); - - // x is inf or nan, |x| < 2^-4 or |x|= > 16. - if (LIBC_UNLIKELY(x_abs <= 0x3d80'0000U || x_abs >= 0x4180'0000U)) { - double x_d = static_cast<double>(x); - double const_term = 0.0; - if (LIBC_UNLIKELY(x_abs >= 0x4180'0000)) { - // atan(+-Inf) = +-pi/2. - if (x_bits.is_inf()) { - volatile double sign_pi_over_2 = SIGNED_PI_OVER_2[sign.is_neg()]; - return static_cast<float>(sign_pi_over_2); - } - if (x_bits.is_nan()) - return x; - // x >= 16 - x_d = -1.0 / x_d; - const_term = SIGNED_PI_OVER_2[sign.is_neg()]; - } - // 0 <= x < 1/16; - if (LIBC_UNLIKELY(x_bits.is_zero())) - return x; - // x <= 2^-12; - if (LIBC_UNLIKELY(x_abs < 0x3980'0000)) { -#if defined(LIBC_TARGET_CPU_HAS_FMA_FLOAT) - return fputil::multiply_add(x, -0x1.0p-25f, x); -#else - double x_d = static_cast<double>(x); - return static_cast<float>(fputil::multiply_add(x_d, -0x1.0p-25, x_d)); -#endif // LIBC_TARGET_CPU_HAS_FMA_FLOAT - } - // Use Taylor polynomial: - // atan(x) ~ x * (1 - x^2 / 3 + x^4 / 5 - x^6 / 7 + x^8 / 9 - x^10 / 11). - constexpr double ATAN_TAYLOR[6] = { - 0x1.0000000000000p+0, -0x1.5555555555555p-2, 0x1.999999999999ap-3, - -0x1.2492492492492p-3, 0x1.c71c71c71c71cp-4, -0x1.745d1745d1746p-4, - }; - double x2 = x_d * x_d; - double x4 = x2 * x2; - double c0 = fputil::multiply_add(x2, ATAN_TAYLOR[1], ATAN_TAYLOR[0]); - double c1 = fputil::multiply_add(x2, ATAN_TAYLOR[3], ATAN_TAYLOR[2]); - double c2 = fputil::multiply_add(x2, ATAN_TAYLOR[5], ATAN_TAYLOR[4]); - double p = fputil::polyeval(x4, c0, c1, c2); - double r = fputil::multiply_add(x_d, p, const_term); - return static_cast<float>(r); - } - - // Range reduction steps: - // 1) atan(x) = sign(x) * atan(|x|) - // 2) If |x| > 1, atan(|x|) = pi/2 - atan(1/|x|) - // 3) For 1/16 < x <= 1, we find k such that: |x - k/16| <= 1/32. - // 4) Then we use polynomial approximation: - // atan(x) ~ atan((k/16) + (x - (k/16)) * Q(x - k/16) - // = P(x - k/16) - double x_d, const_term, final_sign; - int idx; - - if (x_abs > 0x3f80'0000U) { - // |x| > 1, we need to invert x, so we will perform range reduction in - // double precision. - x_d = 1.0 / static_cast<double>(x_bits.get_val()); - double k_d = fputil::nearest_integer(x_d * 0x1.0p4); - x_d = fputil::multiply_add(k_d, -0x1.0p-4, x_d); - idx = static_cast<int>(k_d); - final_sign = FINAL_SIGN[sign.is_pos()]; - // Adjust constant term of the polynomial by +- pi/2. - const_term = fputil::multiply_add(final_sign, ATAN_COEFFS[idx][0], - SIGNED_PI_OVER_2[sign.is_neg()]); - } else { - // Exceptional value: - if (LIBC_UNLIKELY(x_abs == 0x3d8d'6b23U)) { // |x| = 0x1.1ad646p-4 - return sign.is_pos() ? fputil::round_result_slightly_down(0x1.1a6386p-4f) - : fputil::round_result_slightly_up(-0x1.1a6386p-4f); - } - // Perform range reduction in single precision. - float x_f = x_bits.get_val(); - float k_f = fputil::nearest_integer(x_f * 0x1.0p4f); - x_f = fputil::multiply_add(k_f, -0x1.0p-4f, x_f); - x_d = static_cast<double>(x_f); - idx = static_cast<int>(k_f); - final_sign = FINAL_SIGN[sign.is_neg()]; - const_term = final_sign * ATAN_COEFFS[idx][0]; - } - - double p = atan_eval(x_d, idx); - double r = fputil::multiply_add(final_sign * x_d, p, const_term); - - return static_cast<float>(r); -} +LLVM_LIBC_FUNCTION(float, atanf, (float x)) { return math::atanf(x); } } // namespace LIBC_NAMESPACE_DECL |