//===----------------------------------------------------------------------===// // // 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 // //===----------------------------------------------------------------------===// #if __CLC_FPSIZE == 32 _CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE __clc_atan2pi(__CLC_GENTYPE y, __CLC_GENTYPE x) { const __CLC_GENTYPE pi = 0x1.921fb6p+1f; __CLC_GENTYPE ax = __clc_fabs(x); __CLC_GENTYPE ay = __clc_fabs(y); __CLC_GENTYPE v = __clc_min(ax, ay); __CLC_GENTYPE u = __clc_max(ax, ay); // Scale since u could be large, as in "regular" divide __CLC_GENTYPE s = u > 0x1.0p+96f ? 0x1.0p-32f : 1.0f; __CLC_GENTYPE vbyu = s * MATH_DIVIDE(v, s * u); __CLC_GENTYPE vbyu2 = vbyu * vbyu; __CLC_GENTYPE p = __clc_mad(vbyu2, __clc_mad(vbyu2, -0x1.7e1f78p-9f, -0x1.7d1b98p-3f), -0x1.5554d0p-2f) * vbyu2 * vbyu; __CLC_GENTYPE q = __clc_mad(vbyu2, __clc_mad(vbyu2, 0x1.1a714cp-2f, 0x1.287c56p+0f), 1.0f); // Octant 0 result __CLC_GENTYPE a = MATH_DIVIDE(__clc_mad(p, MATH_RECIP(q), vbyu), pi); // Fix up 3 other octants __CLC_GENTYPE at = 0.5f - a; a = ay > ax ? at : a; at = 1.0f - a; a = x < 0.0F ? at : a; // y == 0 => 0 for x >= 0, pi for x < 0 at = __CLC_AS_INTN(x) < 0 ? 1.0f : 0.0f; a = y == 0.0f ? at : a; // x and y are +- Inf at = x > 0.0f ? 0.25f : 0.75f; a = __clc_select(a, at, __clc_isinf(x) && __clc_isinf(y)); // x or y is NaN a = __clc_select(a, __CLC_GENTYPE_NAN, __clc_isnan(x) || __clc_isnan(y)); // Fixup sign and return return __clc_copysign(a, y); } #elif __CLC_FPSIZE == 64 _CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE __clc_atan2pi(__CLC_GENTYPE y, __CLC_GENTYPE x) { const __CLC_GENTYPE pi = 3.1415926535897932e+00; /* 0x400921fb54442d18 */ const __CLC_GENTYPE pi_head = 3.1415926218032836e+00; /* 0x400921fb50000000 */ const __CLC_GENTYPE pi_tail = 3.1786509547056392e-08; /* 0x3e6110b4611a6263 */ // 0x3ff921fb54442d18 const __CLC_GENTYPE piby2_head = 1.5707963267948965e+00; // 0x3c91a62633145c07 const __CLC_GENTYPE piby2_tail = 6.1232339957367660e-17; __CLC_GENTYPE x2 = x; __CLC_LONGN xneg = __CLC_AS_LONGN(x) < 0; __CLC_INTN xexp = __CLC_CONVERT_INTN(__CLC_AS_ULONGN(x) >> EXPSHIFTBITS_DP64) & 0x7ff; __CLC_GENTYPE y2 = y; __CLC_LONGN yneg = __CLC_AS_LONGN(y) < 0; __CLC_INTN yexp = __CLC_CONVERT_INTN(__CLC_AS_ULONGN(y) >> EXPSHIFTBITS_DP64) & 0x7ff; __CLC_LONGN cond2 = __CLC_CONVERT_LONGN(xexp < 1021 & yexp < 1021); __CLC_LONGN diffexp = __CLC_CONVERT_LONGN(yexp - xexp); // Scale up both x and y if they are both below 1/4 __CLC_GENTYPE x1 = __clc_ldexp(x, 1024); __CLC_INTN xexp1 = __CLC_CONVERT_INTN(__CLC_AS_ULONGN(x1) >> EXPSHIFTBITS_DP64) & 0x7ff; __CLC_GENTYPE y1 = __clc_ldexp(y, 1024); __CLC_INTN yexp1 = __CLC_CONVERT_INTN(__CLC_AS_ULONGN(y1) >> EXPSHIFTBITS_DP64) & 0x7ff; __CLC_LONGN diffexp1 = __CLC_CONVERT_LONGN(yexp1 - xexp1); diffexp = __clc_select(diffexp, diffexp1, cond2); x = cond2 ? x1 : x; y = cond2 ? y1 : y; // General case: take absolute values of arguments __CLC_GENTYPE u = __clc_fabs(x); __CLC_GENTYPE v = __clc_fabs(y); // Swap u and v if necessary to obtain 0 < v < u. Compute v/u. __CLC_LONGN swap_vu = u < v; __CLC_GENTYPE uu = u; u = swap_vu ? v : u; v = swap_vu ? uu : v; __CLC_GENTYPE vbyu = v / u; __CLC_GENTYPE q1, q2; // General values of v/u. Use a look-up table and series expansion. { __CLC_GENTYPE val = vbyu > 0.0625 ? vbyu : 0.063; __CLC_INTN index = __CLC_CONVERT_INTN(__clc_fma(256.0, val, 0.5)); q1 = __CLC_USE_TABLE(atan_jby256_tbl_head, (index - 16)); q2 = __CLC_USE_TABLE(atan_jby256_tbl_tail, (index - 16)); __CLC_GENTYPE c = __CLC_CONVERT_GENTYPE(index) * 0x1.0p-8; // We're going to scale u and v by 2^(-u_exponent) to bring them close to 1 // u_exponent could be EMAX so we have to do it in 2 steps __CLC_INTN m = -(__CLC_CONVERT_INTN(__CLC_AS_ULONGN(u) >> EXPSHIFTBITS_DP64) - EXPBIAS_DP64); __CLC_GENTYPE um = __clc_ldexp(u, m); __CLC_GENTYPE vm = __clc_ldexp(v, m); // 26 leading bits of u __CLC_GENTYPE u1 = __CLC_AS_GENTYPE(__CLC_AS_ULONGN(um) & 0xfffffffff8000000UL); __CLC_GENTYPE u2 = um - u1; __CLC_GENTYPE r = MATH_DIVIDE(__clc_fma(-c, u2, __clc_fma(-c, u1, vm)), __clc_fma(c, vm, um)); // Polynomial approximation to atan(r) __CLC_GENTYPE s = r * r; q2 = q2 + __clc_fma((s * __clc_fma(-s, 0.19999918038989143496, 0.33333333333224095522)), -r, r); } __CLC_GENTYPE q3, q4; { q3 = 0.0; q4 = vbyu; } __CLC_GENTYPE q5, q6; { __CLC_GENTYPE u1 = __CLC_AS_GENTYPE(__CLC_AS_ULONGN(u) & 0xffffffff00000000UL); __CLC_GENTYPE u2 = u - u1; __CLC_GENTYPE vu1 = __CLC_AS_GENTYPE(__CLC_AS_ULONGN(vbyu) & 0xffffffff00000000UL); __CLC_GENTYPE vu2 = vbyu - vu1; q5 = 0.0; __CLC_GENTYPE s = vbyu * vbyu; q6 = vbyu + __clc_fma( -vbyu * s, __clc_fma( -s, __clc_fma(-s, __clc_fma(-s, __clc_fma(-s, 0.90029810285449784439E-01, 0.11110736283514525407), 0.14285713561807169030), 0.19999999999393223405), 0.33333333333333170500), MATH_DIVIDE(__clc_fma(-u, vu2, __clc_fma(-u2, vu1, __clc_fma(-u1, vu1, v))), u)); } q3 = vbyu < 0x1.d12ed0af1a27fp-27 ? q3 : q5; q4 = vbyu < 0x1.d12ed0af1a27fp-27 ? q4 : q6; q1 = vbyu > 0.0625 ? q1 : q3; q2 = vbyu > 0.0625 ? q2 : q4; // Tidy-up according to which quadrant the arguments lie in __CLC_GENTYPE res1, res2, res3, res4; q1 = swap_vu ? piby2_head - q1 : q1; q2 = swap_vu ? piby2_tail - q2 : q2; q1 = xneg ? pi_head - q1 : q1; q2 = xneg ? pi_tail - q2 : q2; q1 = MATH_DIVIDE(q1 + q2, pi); res4 = yneg ? -q1 : q1; res1 = yneg ? -0.75 : 0.75; res2 = yneg ? -0.25 : 0.25; res3 = xneg ? res1 : res2; res3 = __clc_select(res4, res3, __CLC_CONVERT_LONGN(__clc_isinf(y2) & __clc_isinf(x2))); res1 = yneg ? -1.0 : 1.0; // abs(x)/abs(y) > 2^56 and x < 0 res3 = diffexp < -56 && xneg ? res1 : res3; res4 = MATH_DIVIDE(MATH_DIVIDE(y, x), pi); // x positive and dominant over y by a factor of 2^28 res3 = diffexp < -28 && xneg == 0 ? res4 : res3; // abs(y)/abs(x) > 2^56 res4 = yneg ? -0.5 : 0.5; // atan(y/x) is insignificant compared to piby2 res3 = diffexp > 56 ? res4 : res3; res3 = x2 == 0.0 ? res4 : res3; // Zero x gives +- pi/2 depending on sign of y res4 = xneg ? res1 : y2; // Zero y gives +-0 for positive x and +-pi for negative x res3 = y2 == 0.0 ? res4 : res3; res3 = __clc_isnan(y2) ? y2 : res3; res3 = __clc_isnan(x2) ? x2 : res3; return res3; } #elif __CLC_FPSIZE == 16 _CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE __clc_atan2pi(__CLC_GENTYPE x, __CLC_GENTYPE y) { return __CLC_CONVERT_GENTYPE( __clc_atan2pi(__CLC_CONVERT_FLOATN(x), __CLC_CONVERT_FLOATN(y))); } #endif