diff options
Diffstat (limited to 'libc/src/math/generic/cbrtf.cpp')
| -rw-r--r-- | libc/src/math/generic/cbrtf.cpp | 147 |
1 files changed, 2 insertions, 145 deletions
diff --git a/libc/src/math/generic/cbrtf.cpp b/libc/src/math/generic/cbrtf.cpp index 71b23c4..0bd8f71 100644 --- a/libc/src/math/generic/cbrtf.cpp +++ b/libc/src/math/generic/cbrtf.cpp @@ -7,153 +7,10 @@ //===----------------------------------------------------------------------===// #include "src/math/cbrtf.h" -#include "hdr/fenv_macros.h" -#include "src/__support/FPUtil/FEnvImpl.h" -#include "src/__support/FPUtil/FPBits.h" -#include "src/__support/FPUtil/multiply_add.h" -#include "src/__support/common.h" -#include "src/__support/macros/config.h" -#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY +#include "src/__support/math/cbrtf.h" namespace LIBC_NAMESPACE_DECL { -namespace { - -// Look up table for 2^(i/3) for i = 0, 1, 2. -constexpr double CBRT2[3] = {1.0, 0x1.428a2f98d728bp0, 0x1.965fea53d6e3dp0}; - -// Degree-7 polynomials approximation of ((1 + x)^(1/3) - 1)/x for 0 <= x <= 1 -// generated by Sollya with: -// > for i from 0 to 15 do { -// P = fpminimax(((1 + x)^(1/3) - 1)/x, 6, [|D...|], [i/16, (i + 1)/16]); -// print("{", coeff(P, 0), ",", coeff(P, 1), ",", coeff(P, 2), ",", -// coeff(P, 3), ",", coeff(P, 4), ",", coeff(P, 5), ",", -// coeff(P, 6), "},"); -// }; -// Then (1 + x)^(1/3) ~ 1 + x * P(x). -constexpr double COEFFS[16][7] = { - {0x1.55555555554ebp-2, -0x1.c71c71c678c0cp-4, 0x1.f9add2776de81p-5, - -0x1.511e10aa964a7p-5, 0x1.ee44165937fa2p-6, -0x1.7c5c9e059345dp-6, - 0x1.047f75e0aff14p-6}, - {0x1.5555554d1149ap-2, -0x1.c71c676fcb5bp-4, 0x1.f9ab127dc57ebp-5, - -0x1.50ea8fd1d4c15p-5, 0x1.e9d68f28ced43p-6, -0x1.60e0e1e661311p-6, - 0x1.716eca1d6e3bcp-7}, - {0x1.5555546377d45p-2, -0x1.c71bc1c6d49d2p-4, 0x1.f9924cc0ed24dp-5, - -0x1.4fea3beb53b3bp-5, 0x1.de028a9a07b1bp-6, -0x1.3b090d2233524p-6, - 0x1.0aeca34893785p-7}, - {0x1.55554dce9f649p-2, -0x1.c7188b34b98f8p-4, 0x1.f93e1af34af49p-5, - -0x1.4d9a06be75c63p-5, 0x1.cb943f4f68992p-6, -0x1.139a685a5e3c4p-6, - 0x1.88410674c6a5dp-8}, - {0x1.5555347d211c3p-2, -0x1.c70f2a4b1a5fap-4, 0x1.f88420e8602c3p-5, - -0x1.49becfa4ed3ep-5, 0x1.b475cd9013162p-6, -0x1.dcfee1dd2f8efp-7, - 0x1.249bb51a1c498p-8}, - {0x1.5554f01b33dbap-2, -0x1.c6facb929dbf1p-4, 0x1.f73fb7861252ep-5, - -0x1.4459a4a0071fap-5, 0x1.9a8df2b504fc2p-6, -0x1.9a7ce3006d06ep-7, - 0x1.ba9230918fa2ep-9}, - {0x1.55545c695db5fp-2, -0x1.c6d6089f20275p-4, 0x1.f556e0ea80efp-5, - -0x1.3d91372d083f4p-5, 0x1.7f66cff331f4p-6, -0x1.606a562491737p-7, - 0x1.52e3e17c71069p-9}, - {0x1.55534a879232ap-2, -0x1.c69b836998b84p-4, 0x1.f2bb26dac0e4cp-5, - -0x1.359eed43716d7p-5, 0x1.64218cd824fbcp-6, -0x1.2e703e2e091e8p-7, - 0x1.0677d9af6aad4p-9}, - {0x1.5551836bb5494p-2, -0x1.c64658c15353bp-4, 0x1.ef68517451a6ep-5, - -0x1.2cc20a980dceep-5, 0x1.49843e0fad93ap-6, -0x1.03c59ccb68e54p-7, - 0x1.9ad325dc7adcbp-10}, - {0x1.554ecacb0d035p-2, -0x1.c5d2664026ffcp-4, 0x1.eb624796ba809p-5, - -0x1.233803d19a535p-5, 0x1.300decb1c3c28p-6, -0x1.befe18031ec3dp-8, - 0x1.449f5ee175c69p-10}, - {0x1.554ae1f5ae815p-2, -0x1.c53c6b14ff6b2p-4, 0x1.e6b2d5127bb5bp-5, - -0x1.19387336788a3p-5, 0x1.180955a6ab255p-6, -0x1.81696703ba369p-8, - 0x1.02cb36389bd79p-10}, - {0x1.55458a59f356ep-2, -0x1.c4820dd631ae9p-4, 0x1.e167af818bd15p-5, - -0x1.0ef35f6f72e52p-5, 0x1.019c33b65e4ebp-6, -0x1.4d25bdd52d3a5p-8, - 0x1.a008ae91f5936p-11}, - {0x1.553e878eafee1p-2, -0x1.c3a1d0b2a3db2p-4, 0x1.db90d8ed9f89bp-5, - -0x1.0490e20f1ae91p-5, 0x1.d9a5d1fc42fe3p-7, -0x1.20bf8227c2abfp-8, - 0x1.50f8174cdb6e9p-11}, - {0x1.5535a0dedf1b1p-2, -0x1.c29afb8bd01a1p-4, 0x1.d53f6371c1e27p-5, - -0x1.f463209b433e2p-6, 0x1.b35222a17e44p-7, -0x1.f5efbf505e133p-9, - 0x1.12e0e94e8586dp-11}, - {0x1.552aa25e57bfdp-2, -0x1.c16d811e4acadp-4, 0x1.ce8489b47aa51p-5, - -0x1.dfde7ff758ea8p-6, 0x1.901f43aac38c8p-7, -0x1.b581d07df5ad5p-9, - 0x1.c3726535f1fc6p-12}, - {0x1.551d5d9b204d3p-2, -0x1.c019e328f8db1p-4, 0x1.c7710f44fc3cep-5, - -0x1.cbbbe25ea8ba4p-6, 0x1.6fe270088623dp-7, -0x1.7e6fc79733761p-9, - 0x1.75077abf18d84p-12}, -}; - -} // anonymous namespace - -LLVM_LIBC_FUNCTION(float, cbrtf, (float x)) { - using FloatBits = typename fputil::FPBits<float>; - using DoubleBits = typename fputil::FPBits<double>; - - FloatBits x_bits(x); - - uint32_t x_abs = x_bits.uintval() & 0x7fff'ffff; - uint32_t sign_bit = (x_bits.uintval() >> 31) << DoubleBits::EXP_LEN; - - if (LIBC_UNLIKELY(x == 0.0f || x_abs >= 0x7f80'0000)) { - // x is 0, Inf, or NaN. - // Make sure it works for FTZ/DAZ modes. - return x + x; - } - - double xd = static_cast<double>(x); - DoubleBits xd_bits(xd); - - // When using biased exponent of x in double precision, - // x_e = real_exponent_of_x + 1023 - // Then: - // x_e / 3 = real_exponent_of_x / 3 + 1023/3 - // = real_exponent_of_x / 3 + 341 - // So to make it the correct biased exponent of x^(1/3), we add - // 1023 - 341 = 682 - // to the quotient x_e / 3. - unsigned x_e = static_cast<unsigned>(xd_bits.get_biased_exponent()); - unsigned out_e = (x_e / 3 + 682) | sign_bit; - unsigned shift_e = x_e % 3; - - // Set x_m = 2^(x_e % 3) * (1.mantissa) - uint64_t x_m = xd_bits.get_mantissa(); - // Use the leading 4 bits for look up table - unsigned idx = static_cast<unsigned>(x_m >> (DoubleBits::FRACTION_LEN - 4)); - - x_m |= static_cast<uint64_t>(DoubleBits::EXP_BIAS) - << DoubleBits::FRACTION_LEN; - - double x_reduced = DoubleBits(x_m).get_val(); - double dx = x_reduced - 1.0; - - double dx_sq = dx * dx; - double c0 = fputil::multiply_add(dx, COEFFS[idx][0], 1.0); - double c1 = fputil::multiply_add(dx, COEFFS[idx][2], COEFFS[idx][1]); - double c2 = fputil::multiply_add(dx, COEFFS[idx][4], COEFFS[idx][3]); - double c3 = fputil::multiply_add(dx, COEFFS[idx][6], COEFFS[idx][5]); - - double dx_4 = dx_sq * dx_sq; - double p0 = fputil::multiply_add(dx_sq, c1, c0); - double p1 = fputil::multiply_add(dx_sq, c3, c2); - - double r = fputil::multiply_add(dx_4, p1, p0) * CBRT2[shift_e]; - - uint64_t r_m = DoubleBits(r).get_mantissa(); - // Check if the output is exact. To be exact, the smallest 1-bit of the - // output has to be at least 2^-7 or higher. So we check the lowest 44 bits - // to see if they are within 2^(-52 + 3) errors from all zeros, then the - // result cube root is exact. - if (LIBC_UNLIKELY(((r_m + 8) & 0xfffffffffff) <= 16)) { - if ((r_m & 0xfffffffffff) <= 8) - r_m &= 0xffff'ffff'ffff'ffe0; - else - r_m = (r_m & 0xffff'ffff'ffff'ffe0) + 0x20; - fputil::clear_except_if_required(FE_INEXACT); - } - // Adjust exponent and sign. - uint64_t r_bits = - r_m | (static_cast<uint64_t>(out_e) << DoubleBits::FRACTION_LEN); - - return static_cast<float>(DoubleBits(r_bits).get_val()); -} +LLVM_LIBC_FUNCTION(float, cbrtf, (float x)) { return math::cbrtf(x); } } // namespace LIBC_NAMESPACE_DECL |