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Diffstat (limited to 'sysdeps/ia64/fpu/s_atanl.S')
| -rw-r--r-- | sysdeps/ia64/fpu/s_atanl.S | 2007 |
1 files changed, 0 insertions, 2007 deletions
diff --git a/sysdeps/ia64/fpu/s_atanl.S b/sysdeps/ia64/fpu/s_atanl.S deleted file mode 100644 index 1a23611307..0000000000 --- a/sysdeps/ia64/fpu/s_atanl.S +++ /dev/null @@ -1,2007 +0,0 @@ -.file "atanl.s" - - -// Copyright (c) 2000 - 2005, Intel Corporation -// All rights reserved. -// -// Contributed 2000 by the Intel Numerics Group, Intel Corporation -// -// Redistribution and use in source and binary forms, with or without -// modification, are permitted provided that the following conditions are -// met: -// -// * Redistributions of source code must retain the above copyright -// notice, this list of conditions and the following disclaimer. -// -// * Redistributions in binary form must reproduce the above copyright -// notice, this list of conditions and the following disclaimer in the -// documentation and/or other materials provided with the distribution. -// -// * The name of Intel Corporation may not be used to endorse or promote -// products derived from this software without specific prior written -// permission. - -// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS -// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT -// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR -// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS -// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, -// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, -// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR -// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY -// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING -// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS -// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. -// -// Intel Corporation is the author of this code, and requests that all -// problem reports or change requests be submitted to it directly at -// http://www.intel.com/software/products/opensource/libraries/num.htm. -// -// -//********************************************************************* -// -// History -// 02/02/00 (hand-optimized) -// 04/04/00 Unwind support added -// 08/15/00 Bundle added after call to __libm_error_support to properly -// set [the previously overwritten] GR_Parameter_RESULT. -// 03/13/01 Fixed flags when denormal raised on intermediate result -// 01/08/02 Improved speed. -// 02/06/02 Corrected .section statement -// 05/20/02 Cleaned up namespace and sf0 syntax -// 02/10/03 Reordered header: .section, .global, .proc, .align; -// used data8 for long double table values -// 03/31/05 Reformatted delimiters between data tables -// -//********************************************************************* -// -// Function: atanl(x) = inverse tangent(x), for double extended x values -// Function: atan2l(y,x) = atan(y/x), for double extended y, x values -// -// API -// -// long double atanl (long double x) -// long double atan2l (long double y, long double x) -// -//********************************************************************* -// -// Resources Used: -// -// Floating-Point Registers: f8 (Input and Return Value) -// f9 (Input for atan2l) -// f10-f15, f32-f83 -// -// General Purpose Registers: -// r32-r51 -// r49-r52 (Arguments to error support for 0,0 case) -// -// Predicate Registers: p6-p15 -// -//********************************************************************* -// -// IEEE Special Conditions: -// -// Denormal fault raised on denormal inputs -// Underflow exceptions may occur -// Special error handling for the y=0 and x=0 case -// Inexact raised when appropriate by algorithm -// -// atanl(SNaN) = QNaN -// atanl(QNaN) = QNaN -// atanl(+/-0) = +/- 0 -// atanl(+/-Inf) = +/-pi/2 -// -// atan2l(Any NaN for x or y) = QNaN -// atan2l(+/-0,x) = +/-0 for x > 0 -// atan2l(+/-0,x) = +/-pi for x < 0 -// atan2l(+/-0,+0) = +/-0 -// atan2l(+/-0,-0) = +/-pi -// atan2l(y,+/-0) = pi/2 y > 0 -// atan2l(y,+/-0) = -pi/2 y < 0 -// atan2l(+/-y, Inf) = +/-0 for finite y > 0 -// atan2l(+/-Inf, x) = +/-pi/2 for finite x -// atan2l(+/-y, -Inf) = +/-pi for finite y > 0 -// atan2l(+/-Inf, Inf) = +/-pi/4 -// atan2l(+/-Inf, -Inf) = +/-3pi/4 -// -//********************************************************************* -// -// Mathematical Description -// --------------------------- -// -// The function ATANL( Arg_Y, Arg_X ) returns the "argument" -// or the "phase" of the complex number -// -// Arg_X + i Arg_Y -// -// or equivalently, the angle in radians from the positive -// x-axis to the line joining the origin and the point -// (Arg_X,Arg_Y) -// -// -// (Arg_X, Arg_Y) x -// \ -// \ -// \ -// \ -// \ angle between is ATANL(Arg_Y,Arg_X) - - - - -// \ -// ------------------> X-axis - -// Origin -// -// Moreover, this angle is reported in the range [-pi,pi] thus -// -// -pi <= ATANL( Arg_Y, Arg_X ) <= pi. -// -// From the geometry, it is easy to define ATANL when one of -// Arg_X or Arg_Y is +-0 or +-inf: -// -// -// \ Y | -// X \ | +0 | -0 | +inf | -inf | finite non-zero -// \ | | | | | -// ______________________________________________________ -// | | | | -// +-0 | Invalid/ | pi/2 | -pi/2 | sign(Y)*pi/2 -// | qNaN | | | -// -------------------------------------------------------- -// | | | | | -// +inf | +0 | -0 | pi/4 | -pi/4 | sign(Y)*0 -// -------------------------------------------------------- -// | | | | | -// -inf | +pi | -pi | 3pi/4 | -3pi/4 | sign(Y)*pi -// -------------------------------------------------------- -// finite | X>0? | pi/2 | -pi/2 | normal case -// non-zero| sign(Y)*0: | | | -// | sign(Y)*pi | | | -// -// -// One must take note that ATANL is NOT the arctangent of the -// value Arg_Y/Arg_X; but rather ATANL and arctan are related -// in a slightly more complicated way as follows: -// -// Let U := max(|Arg_X|, |Arg_Y|); V := min(|Arg_X|, |Arg_Y|); -// sign_X be the sign bit of Arg_X, i.e., sign_X is 0 or 1; -// s_X be the sign of Arg_X, i.e., s_X = (-1)^sign_X; -// -// sign_Y be the sign bit of Arg_Y, i.e., sign_Y is 0 or 1; -// s_Y be the sign of Arg_Y, i.e., s_Y = (-1)^sign_Y; -// -// swap be 0 if |Arg_X| >= |Arg_Y| and 1 otherwise. -// -// Then, ATANL(Arg_Y, Arg_X) = -// -// / arctan(V/U) \ sign_X = 0 & swap = 0 -// | pi/2 - arctan(V/U) | sign_X = 0 & swap = 1 -// s_Y * | | -// | pi - arctan(V/U) | sign_X = 1 & swap = 0 -// \ pi/2 + arctan(V/U) / sign_X = 1 & swap = 1 -// -// -// This relationship also suggest that the algorithm's major -// task is to calculate arctan(V/U) for 0 < V <= U; and the -// final Result is given by -// -// s_Y * { (P_hi + P_lo) + sigma * arctan(V/U) } -// -// where -// -// (P_hi,P_lo) represents M(sign_X,swap)*(pi/2) accurately -// -// M(sign_X,swap) = 0 for sign_X = 0 and swap = 0 -// 1 for swap = 1 -// 2 for sign_X = 1 and swap = 0 -// -// and -// -// sigma = { (sign_X XOR swap) : -1.0 : 1.0 } -// -// = (-1) ^ ( sign_X XOR swap ) -// -// Both (P_hi,P_lo) and sigma can be stored in a table and fetched -// using (sign_X,swap) as an index. (P_hi, P_lo) can be stored as a -// double-precision, and single-precision pair; and sigma can -// obviously be just a single-precision number. -// -// In the algorithm we propose, arctan(V/U) is calculated to high accuracy -// as A_hi + A_lo. Consequently, the Result ATANL( Arg_Y, Arg_X ) is -// given by -// -// s_Y*P_hi + s_Y*sigma*A_hi + s_Y*(sigma*A_lo + P_lo) -// -// We now discuss the calculation of arctan(V/U) for 0 < V <= U. -// -// For (V/U) < 2^(-3), we use a simple polynomial of the form -// -// z + z^3*(P_1 + z^2*(P_2 + z^2*(P_3 + ... + P_8))) -// -// where z = V/U. -// -// For the sake of accuracy, the first term "z" must approximate V/U to -// extra precision. For z^3 and higher power, a working precision -// approximation to V/U suffices. Thus, we obtain: -// -// z_hi + z_lo = V/U to extra precision and -// z = V/U to working precision -// -// The value arctan(V/U) is delivered as two pieces (A_hi, A_lo) -// -// (A_hi,A_lo) = (z_hi, z^3*(P_1 + ... + P_8) + z_lo). -// -// -// For 2^(-3) <= (V/U) <= 1, we use a table-driven approach. -// Consider -// -// (V/U) = 2^k * 1.b_1 b_2 .... b_63 b_64 b_65 .... -// -// Define -// -// z_hi = 2^k * 1.b_1 b_2 b_3 b_4 1 -// -// then -// / \ -// | (V/U) - z_hi | - -// arctan(V/U) = arctan(z_hi) + acrtan| -------------- | -// | 1 + (V/U)*z_hi | -// \ / -// -// / \ -// | V - z_hi*U | - -// = arctan(z_hi) + acrtan| -------------- | -// | U + V*z_hi | -// \ / -// -// = arctan(z_hi) + acrtan( V' / U' ) -// -// -// where -// -// V' = V - U*z_hi; U' = U + V*z_hi. -// -// Let -// -// w_hi + w_lo = V'/U' to extra precision and -// w = V'/U' to working precision -// -// then we can approximate arctan(V'/U') by -// -// arctan(V'/U') = w_hi + w_lo -// + w^3*(Q_1 + w^2*(Q_2 + w^2*(Q_3 + w^2*Q_4))) -// -// = w_hi + w_lo + poly -// -// Finally, arctan(z_hi) is calculated beforehand and stored in a table -// as Tbl_hi, Tbl_lo. Thus, -// -// (A_hi, A_lo) = (Tbl_hi, w_hi+(poly+(w_lo+Tbl_lo))) -// -// This completes the mathematical description. -// -// -// Algorithm -// ------------- -// -// Step 0. Check for unsupported format. -// -// If -// ( expo(Arg_X) not zero AND msb(Arg_X) = 0 ) OR -// ( expo(Arg_Y) not zero AND msb(Arg_Y) = 0 ) -// -// then one of the arguments is unsupported. Generate an -// invalid and return qNaN. -// -// Step 1. Initialize -// -// Normalize Arg_X and Arg_Y and set the following -// -// sign_X := sign_bit(Arg_X) -// s_Y := (sign_bit(Arg_Y)==0? 1.0 : -1.0) -// swap := (|Arg_X| >= |Arg_Y|? 0 : 1 ) -// U := max( |Arg_X|, |Arg_Y| ) -// V := min( |Arg_X|, |Arg_Y| ) -// -// execute: frcpa E, pred, V, U -// If pred is 0, go to Step 5 for special cases handling. -// -// Step 2. Decide on branch. -// -// Q := E * V -// If Q < 2^(-3) go to Step 4 for simple polynomial case. -// -// Step 3. Table-driven algorithm. -// -// Q is represented as -// -// 2^(-k) * 1.b_1 b_2 b_3 ... b_63; k = 0,-1,-2,-3 -// -// and that if k = 0, b_1 = b_2 = b_3 = b_4 = 0. -// -// Define -// -// z_hi := 2^(-k) * 1.b_1 b_2 b_3 b_4 1 -// -// (note that there are 49 possible values of z_hi). -// -// ...We now calculate V' and U'. While V' is representable -// ...as a 64-bit number because of cancellation, U' is -// ...not in general a 64-bit number. Obtaining U' accurately -// ...requires two working precision numbers -// -// U_prime_hi := U + V * z_hi ...WP approx. to U' -// U_prime_lo := ( U - U_prime_hi ) + V*z_hi ...observe order -// V_prime := V - U * z_hi ...this is exact -// -// C_hi := frcpa (1.0, U_prime_hi) ...C_hi approx 1/U'_hi -// -// loop 3 times -// C_hi := C_hi + C_hi*(1.0 - C_hi*U_prime_hi) -// -// ...at this point C_hi is (1/U_prime_hi) to roughly 64 bits -// -// w_hi := V_prime * C_hi ...w_hi is V_prime/U_prime to -// ...roughly working precision -// -// ...note that we want w_hi + w_lo to approximate -// ...V_prime/(U_prime_hi + U_prime_lo) to extra precision -// ...but for now, w_hi is good enough for the polynomial -// ...calculation. -// -// wsq := w_hi*w_hi -// poly := w_hi*wsq*(Q_1 + wsq*(Q_2 + wsq*(Q_3 + wsq*Q_4))) -// -// Fetch -// (Tbl_hi, Tbl_lo) = atan(z_hi) indexed by (k,b_1,b_2,b_3,b_4) -// ...Tbl_hi is a double-precision number -// ...Tbl_lo is a single-precision number -// -// (P_hi, P_lo) := M(sign_X,swap)*(Pi_by_2_hi, Pi_by_2_lo) -// ...as discussed previous. Again; the implementation can -// ...chose to fetch P_hi and P_lo from a table indexed by -// ...(sign_X, swap). -// ...P_hi is a double-precision number; -// ...P_lo is a single-precision number. -// -// ...calculate w_lo so that w_hi + w_lo is V'/U' accurately -// w_lo := ((V_prime - w_hi*U_prime_hi) - -// w_hi*U_prime_lo) * C_hi ...observe order -// -// -// ...Ready to deliver arctan(V'/U') as A_hi, A_lo -// A_hi := Tbl_hi -// A_lo := w_hi + (poly + (Tbl_lo + w_lo)) ...observe order -// -// ...Deliver final Result -// ...s_Y*P_hi + s_Y*sigma*A_hi + s_Y*(sigma*A_lo + P_lo) -// -// sigma := ( (sign_X XOR swap) ? -1.0 : 1.0 ) -// ...sigma can be obtained by a table lookup using -// ...(sign_X,swap) as index and stored as single precision -// ...sigma should be calculated earlier -// -// P_hi := s_Y*P_hi -// A_hi := s_Y*A_hi -// -// Res_hi := P_hi + sigma*A_hi ...this is exact because -// ...both P_hi and Tbl_hi -// ...are double-precision -// ...and |Tbl_hi| > 2^(-4) -// ...P_hi is either 0 or -// ...between (1,4) -// -// Res_lo := sigma*A_lo + P_lo -// -// Return Res_hi + s_Y*Res_lo in user-defined rounding control -// -// Step 4. Simple polynomial case. -// -// ...E and Q are inherited from Step 2. -// -// A_hi := Q ...Q is inherited from Step 2 Q approx V/U -// -// loop 3 times -// E := E + E2(1.0 - E*U1 -// ...at this point E approximates 1/U to roughly working precision -// -// z := V * E ...z approximates V/U to roughly working precision -// zsq := z * z -// z4 := zsq * zsq; z8 := z4 * z4 -// -// poly1 := P_4 + zsq*(P_5 + zsq*(P_6 + zsq*(P_7 + zsq*P_8))) -// poly2 := zsq*(P_1 + zsq*(P_2 + zsq*P_3)) -// -// poly := poly1 + z8*poly2 -// -// z_lo := (V - A_hi*U)*E -// -// A_lo := z*poly + z_lo -// ...A_hi, A_lo approximate arctan(V/U) accurately -// -// (P_hi, P_lo) := M(sign_X,swap)*(Pi_by_2_hi, Pi_by_2_lo) -// ...one can store the M(sign_X,swap) as single precision -// ...values -// -// ...Deliver final Result -// ...s_Y*P_hi + s_Y*sigma*A_hi + s_Y*(sigma*A_lo + P_lo) -// -// sigma := ( (sign_X XOR swap) ? -1.0 : 1.0 ) -// ...sigma can be obtained by a table lookup using -// ...(sign_X,swap) as index and stored as single precision -// ...sigma should be calculated earlier -// -// P_hi := s_Y*P_hi -// A_hi := s_Y*A_hi -// -// Res_hi := P_hi + sigma*A_hi ...need to compute -// ...P_hi + sigma*A_hi -// ...exactly -// -// tmp := (P_hi - Res_hi) + sigma*A_hi -// -// Res_lo := s_Y*(sigma*A_lo + P_lo) + tmp -// -// Return Res_hi + Res_lo in user-defined rounding control -// -// Step 5. Special Cases -// -// These are detected early in the function by fclass instructions. -// -// We are in one of those special cases when X or Y is 0,+-inf or NaN -// -// If one of X and Y is NaN, return X+Y (which will generate -// invalid in case one is a signaling NaN). Otherwise, -// return the Result as described in the table -// -// -// -// \ Y | -// X \ | +0 | -0 | +inf | -inf | finite non-zero -// \ | | | | | -// ______________________________________________________ -// | | | | -// +-0 | Invalid/ | pi/2 | -pi/2 | sign(Y)*pi/2 -// | qNaN | | | -// -------------------------------------------------------- -// | | | | | -// +inf | +0 | -0 | pi/4 | -pi/4 | sign(Y)*0 -// -------------------------------------------------------- -// | | | | | -// -inf | +pi | -pi | 3pi/4 | -3pi/4 | sign(Y)*pi -// -------------------------------------------------------- -// finite | X>0? | pi/2 | -pi/2 | -// non-zero| sign(Y)*0: | | | N/A -// | sign(Y)*pi | | | -// -// - -ArgY_orig = f8 -Result = f8 -FR_RESULT = f8 -ArgX_orig = f9 -ArgX = f10 -FR_X = f10 -ArgY = f11 -FR_Y = f11 -s_Y = f12 -U = f13 -V = f14 -E = f15 -Q = f32 -z_hi = f33 -U_prime_hi = f34 -U_prime_lo = f35 -V_prime = f36 -C_hi = f37 -w_hi = f38 -w_lo = f39 -wsq = f40 -poly = f41 -Tbl_hi = f42 -Tbl_lo = f43 -P_hi = f44 -P_lo = f45 -A_hi = f46 -A_lo = f47 -sigma = f48 -Res_hi = f49 -Res_lo = f50 -Z = f52 -zsq = f53 -z4 = f54 -z8 = f54 -poly1 = f55 -poly2 = f56 -z_lo = f57 -tmp = f58 -P_1 = f59 -Q_1 = f60 -P_2 = f61 -Q_2 = f62 -P_3 = f63 -Q_3 = f64 -P_4 = f65 -Q_4 = f66 -P_5 = f67 -P_6 = f68 -P_7 = f69 -P_8 = f70 -U_hold = f71 -TWO_TO_NEG3 = f72 -C_hi_hold = f73 -E_hold = f74 -M = f75 -ArgX_abs = f76 -ArgY_abs = f77 -Result_lo = f78 -A_temp = f79 -FR_temp = f80 -Xsq = f81 -Ysq = f82 -tmp_small = f83 - -GR_SAVE_PFS = r33 -GR_SAVE_B0 = r34 -GR_SAVE_GP = r35 -sign_X = r36 -sign_Y = r37 -swap = r38 -table_ptr1 = r39 -table_ptr2 = r40 -k = r41 -lookup = r42 -exp_ArgX = r43 -exp_ArgY = r44 -exponent_Q = r45 -significand_Q = r46 -special = r47 -sp_exp_Q = r48 -sp_exp_4sig_Q = r49 -table_base = r50 -int_temp = r51 - -GR_Parameter_X = r49 -GR_Parameter_Y = r50 -GR_Parameter_RESULT = r51 -GR_Parameter_TAG = r52 -GR_temp = r52 - -RODATA -.align 16 - -LOCAL_OBJECT_START(Constants_atan) -// double pi/2 -data8 0x3FF921FB54442D18 -// single lo_pi/2, two**(-3) -data4 0x248D3132, 0x3E000000 -data8 0xAAAAAAAAAAAAAAA3, 0xBFFD // P_1 -data8 0xCCCCCCCCCCCC54B2, 0x3FFC // P_2 -data8 0x9249249247E4D0C2, 0xBFFC // P_3 -data8 0xE38E38E058870889, 0x3FFB // P_4 -data8 0xBA2E895B290149F8, 0xBFFB // P_5 -data8 0x9D88E6D4250F733D, 0x3FFB // P_6 -data8 0x884E51FFFB8745A0, 0xBFFB // P_7 -data8 0xE1C7412B394396BD, 0x3FFA // P_8 -data8 0xAAAAAAAAAAAAA52F, 0xBFFD // Q_1 -data8 0xCCCCCCCCC75B60D3, 0x3FFC // Q_2 -data8 0x924923AD011F1940, 0xBFFC // Q_3 -data8 0xE36F716D2A5F89BD, 0x3FFB // Q_4 -// -// Entries Tbl_hi (double precision) -// B = 1+Index/16+1/32 Index = 0 -// Entries Tbl_lo (single precision) -// B = 1+Index/16+1/32 Index = 0 -// -data8 0x3FE9A000A935BD8E -data4 0x23ACA08F, 0x00000000 -// -// Entries Tbl_hi (double precision) Index = 0,1,...,15 -// B = 2^(-1)*(1+Index/16+1/32) -// Entries Tbl_lo (single precision) -// Index = 0,1,...,15 B = 2^(-1)*(1+Index/16+1/32) -// -data8 0x3FDE77EB7F175A34 -data4 0x238729EE, 0x00000000 -data8 0x3FE0039C73C1A40B -data4 0x249334DB, 0x00000000 -data8 0x3FE0C6145B5B43DA -data4 0x22CBA7D1, 0x00000000 -data8 0x3FE1835A88BE7C13 -data4 0x246310E7, 0x00000000 -data8 0x3FE23B71E2CC9E6A -data4 0x236210E5, 0x00000000 -data8 0x3FE2EE628406CBCA -data4 0x2462EAF5, 0x00000000 -data8 0x3FE39C391CD41719 -data4 0x24B73EF3, 0x00000000 -data8 0x3FE445065B795B55 -data4 0x24C11260, 0x00000000 -data8 0x3FE4E8DE5BB6EC04 -data4 0x242519EE, 0x00000000 -data8 0x3FE587D81F732FBA -data4 0x24D4346C, 0x00000000 -data8 0x3FE6220D115D7B8D -data4 0x24ED487B, 0x00000000 -data8 0x3FE6B798920B3D98 -data4 0x2495FF1E, 0x00000000 -data8 0x3FE748978FBA8E0F -data4 0x223D9531, 0x00000000 -data8 0x3FE7D528289FA093 -data4 0x242B0411, 0x00000000 -data8 0x3FE85D69576CC2C5 -data4 0x2335B374, 0x00000000 -data8 0x3FE8E17AA99CC05D -data4 0x24C27CFB, 0x00000000 -// -// Entries Tbl_hi (double precision) Index = 0,1,...,15 -// B = 2^(-2)*(1+Index/16+1/32) -// Entries Tbl_lo (single precision) -// Index = 0,1,...,15 B = 2^(-2)*(1+Index/16+1/32) -// -data8 0x3FD025FA510665B5 -data4 0x24263482, 0x00000000 -data8 0x3FD1151A362431C9 -data4 0x242C8DC9, 0x00000000 -data8 0x3FD2025567E47C95 -data4 0x245CF9BA, 0x00000000 -data8 0x3FD2ED987A823CFE -data4 0x235C892C, 0x00000000 -data8 0x3FD3D6D129271134 -data4 0x2389BE52, 0x00000000 -data8 0x3FD4BDEE586890E6 -data4 0x24436471, 0x00000000 -data8 0x3FD5A2E0175E0F4E -data4 0x2389DBD4, 0x00000000 -data8 0x3FD685979F5FA6FD -data4 0x2476D43F, 0x00000000 -data8 0x3FD7660752817501 -data4 0x24711774, 0x00000000 -data8 0x3FD84422B8DF95D7 -data4 0x23EBB501, 0x00000000 -data8 0x3FD91FDE7CD0C662 -data4 0x23883A0C, 0x00000000 -data8 0x3FD9F93066168001 -data4 0x240DF63F, 0x00000000 -data8 0x3FDAD00F5422058B -data4 0x23FE261A, 0x00000000 -data8 0x3FDBA473378624A5 -data4 0x23A8CD0E, 0x00000000 -data8 0x3FDC76550AAD71F8 -data4 0x2422D1D0, 0x00000000 -data8 0x3FDD45AEC9EC862B -data4 0x2344A109, 0x00000000 -// -// Entries Tbl_hi (double precision) Index = 0,1,...,15 -// B = 2^(-3)*(1+Index/16+1/32) -// Entries Tbl_lo (single precision) -// Index = 0,1,...,15 B = 2^(-3)*(1+Index/16+1/32) -// -data8 0x3FC068D584212B3D -data4 0x239874B6, 0x00000000 -data8 0x3FC1646541060850 -data4 0x2335E774, 0x00000000 -data8 0x3FC25F6E171A535C -data4 0x233E36BE, 0x00000000 -data8 0x3FC359E8EDEB99A3 -data4 0x239680A3, 0x00000000 -data8 0x3FC453CEC6092A9E -data4 0x230FB29E, 0x00000000 -data8 0x3FC54D18BA11570A -data4 0x230C1418, 0x00000000 -data8 0x3FC645BFFFB3AA73 -data4 0x23F0564A, 0x00000000 -data8 0x3FC73DBDE8A7D201 -data4 0x23D4A5E1, 0x00000000 -data8 0x3FC8350BE398EBC7 -data4 0x23D4ADDA, 0x00000000 -data8 0x3FC92BA37D050271 -data4 0x23BCB085, 0x00000000 -data8 0x3FCA217E601081A5 -data4 0x23BC841D, 0x00000000 -data8 0x3FCB1696574D780B -data4 0x23CF4A8E, 0x00000000 -data8 0x3FCC0AE54D768466 -data4 0x23BECC90, 0x00000000 -data8 0x3FCCFE654E1D5395 -data4 0x2323DCD2, 0x00000000 -data8 0x3FCDF110864C9D9D -data4 0x23F53F3A, 0x00000000 -data8 0x3FCEE2E1451D980C -data4 0x23CCB11F, 0x00000000 -// -data8 0x400921FB54442D18, 0x3CA1A62633145C07 // PI two doubles -data8 0x3FF921FB54442D18, 0x3C91A62633145C07 // PI_by_2 two dbles -data8 0x3FE921FB54442D18, 0x3C81A62633145C07 // PI_by_4 two dbles -data8 0x4002D97C7F3321D2, 0x3C9A79394C9E8A0A // 3PI_by_4 two dbles -LOCAL_OBJECT_END(Constants_atan) - - -.section .text -GLOBAL_IEEE754_ENTRY(atanl) - -// Use common code with atan2l after setting x=1.0 -{ .mfi - alloc r32 = ar.pfs, 0, 17, 4, 0 - fma.s1 Ysq = ArgY_orig, ArgY_orig, f0 // Form y*y - nop.i 999 -} -{ .mfi - addl table_ptr1 = @ltoff(Constants_atan#), gp // Address of table pointer - fma.s1 Xsq = f1, f1, f0 // Form x*x - nop.i 999 -} -;; - -{ .mfi - ld8 table_ptr1 = [table_ptr1] // Get table pointer - fnorm.s1 ArgY = ArgY_orig - nop.i 999 -} -{ .mfi - nop.m 999 - fnorm.s1 ArgX = f1 - nop.i 999 -} -;; - -{ .mfi - getf.exp sign_X = f1 // Get signexp of x - fmerge.s ArgX_abs = f0, f1 // Form |x| - nop.i 999 -} -{ .mfi - nop.m 999 - fnorm.s1 ArgX_orig = f1 - nop.i 999 -} -;; - -{ .mfi - getf.exp sign_Y = ArgY_orig // Get signexp of y - fmerge.s ArgY_abs = f0, ArgY_orig // Form |y| - mov table_base = table_ptr1 // Save base pointer to tables -} -;; - -{ .mfi - ldfd P_hi = [table_ptr1],8 // Load double precision hi part of pi - fclass.m p8,p0 = ArgY_orig, 0x1e7 // Test y natval, nan, inf, zero - nop.i 999 -} -;; - -{ .mfi - ldfps P_lo, TWO_TO_NEG3 = [table_ptr1], 8 // Load P_lo and constant 2^-3 - nop.f 999 - nop.i 999 -} -{ .mfi - nop.m 999 - fma.s1 M = f1, f1, f0 // Set M = 1.0 - nop.i 999 -} -;; - -// -// Check for everything - if false, then must be pseudo-zero -// or pseudo-nan (IA unsupporteds). -// -{ .mfb - nop.m 999 - fclass.m p0,p12 = f1, 0x1FF // Test x unsupported -(p8) br.cond.spnt ATANL_Y_SPECIAL // Branch if y natval, nan, inf, zero -} -;; - -// U = max(ArgX_abs,ArgY_abs) -// V = min(ArgX_abs,ArgY_abs) -{ .mfi - nop.m 999 - fcmp.ge.s1 p6,p7 = Xsq, Ysq // Test for |x| >= |y| using squares - nop.i 999 -} -{ .mfb - nop.m 999 - fma.s1 V = ArgX_abs, f1, f0 // Set V assuming |x| < |y| - br.cond.sptk ATANL_COMMON // Branch to common code -} -;; - -GLOBAL_IEEE754_END(atanl) - -GLOBAL_IEEE754_ENTRY(atan2l) - -{ .mfi - alloc r32 = ar.pfs, 0, 17, 4, 0 - fma.s1 Ysq = ArgY_orig, ArgY_orig, f0 // Form y*y - nop.i 999 -} -{ .mfi - addl table_ptr1 = @ltoff(Constants_atan#), gp // Address of table pointer - fma.s1 Xsq = ArgX_orig, ArgX_orig, f0 // Form x*x - nop.i 999 -} -;; - -{ .mfi - ld8 table_ptr1 = [table_ptr1] // Get table pointer - fnorm.s1 ArgY = ArgY_orig - nop.i 999 -} -{ .mfi - nop.m 999 - fnorm.s1 ArgX = ArgX_orig - nop.i 999 -} -;; - -{ .mfi - getf.exp sign_X = ArgX_orig // Get signexp of x - fmerge.s ArgX_abs = f0, ArgX_orig // Form |x| - nop.i 999 -} -;; - -{ .mfi - getf.exp sign_Y = ArgY_orig // Get signexp of y - fmerge.s ArgY_abs = f0, ArgY_orig // Form |y| - mov table_base = table_ptr1 // Save base pointer to tables -} -;; - -{ .mfi - ldfd P_hi = [table_ptr1],8 // Load double precision hi part of pi - fclass.m p8,p0 = ArgY_orig, 0x1e7 // Test y natval, nan, inf, zero - nop.i 999 -} -;; - -{ .mfi - ldfps P_lo, TWO_TO_NEG3 = [table_ptr1], 8 // Load P_lo and constant 2^-3 - fclass.m p9,p0 = ArgX_orig, 0x1e7 // Test x natval, nan, inf, zero - nop.i 999 -} -{ .mfi - nop.m 999 - fma.s1 M = f1, f1, f0 // Set M = 1.0 - nop.i 999 -} -;; - -// -// Check for everything - if false, then must be pseudo-zero -// or pseudo-nan (IA unsupporteds). -// -{ .mfb - nop.m 999 - fclass.m p0,p12 = ArgX_orig, 0x1FF // Test x unsupported -(p8) br.cond.spnt ATANL_Y_SPECIAL // Branch if y natval, nan, inf, zero -} -;; - -// U = max(ArgX_abs,ArgY_abs) -// V = min(ArgX_abs,ArgY_abs) -{ .mfi - nop.m 999 - fcmp.ge.s1 p6,p7 = Xsq, Ysq // Test for |x| >= |y| using squares - nop.i 999 -} -{ .mfb - nop.m 999 - fma.s1 V = ArgX_abs, f1, f0 // Set V assuming |x| < |y| -(p9) br.cond.spnt ATANL_X_SPECIAL // Branch if x natval, nan, inf, zero -} -;; - -// Now common code for atanl and atan2l -ATANL_COMMON: -{ .mfi - nop.m 999 - fclass.m p0,p13 = ArgY_orig, 0x1FF // Test y unsupported - shr sign_X = sign_X, 17 // Get sign bit of x -} -{ .mfi - nop.m 999 - fma.s1 U = ArgY_abs, f1, f0 // Set U assuming |x| < |y| - adds table_ptr1 = 176, table_ptr1 // Point to Q4 -} -;; - -{ .mfi -(p6) add swap = r0, r0 // Set swap=0 if |x| >= |y| -(p6) frcpa.s1 E, p0 = ArgY_abs, ArgX_abs // Compute E if |x| >= |y| - shr sign_Y = sign_Y, 17 // Get sign bit of y -} -{ .mfb - nop.m 999 -(p6) fma.s1 V = ArgY_abs, f1, f0 // Set V if |x| >= |y| -(p12) br.cond.spnt ATANL_UNSUPPORTED // Branch if x unsupported -} -;; - -// Set p8 if y >=0 -// Set p9 if y < 0 -// Set p10 if |x| >= |y| and x >=0 -// Set p11 if |x| >= |y| and x < 0 -{ .mfi - cmp.eq p8, p9 = 0, sign_Y // Test for y >= 0 -(p7) frcpa.s1 E, p0 = ArgX_abs, ArgY_abs // Compute E if |x| < |y| -(p7) add swap = 1, r0 // Set swap=1 if |x| < |y| -} -{ .mfb -(p6) cmp.eq.unc p10, p11 = 0, sign_X // If |x| >= |y|, test for x >= 0 -(p6) fma.s1 U = ArgX_abs, f1, f0 // Set U if |x| >= |y| -(p13) br.cond.spnt ATANL_UNSUPPORTED // Branch if y unsupported -} -;; - -// -// if p8, s_Y = 1.0 -// if p9, s_Y = -1.0 -// -.pred.rel "mutex",p8,p9 -{ .mfi - nop.m 999 -(p8) fadd.s1 s_Y = f0, f1 // If y >= 0 set s_Y = 1.0 - nop.i 999 -} -{ .mfi - nop.m 999 -(p9) fsub.s1 s_Y = f0, f1 // If y < 0 set s_Y = -1.0 - nop.i 999 -} -;; - -.pred.rel "mutex",p10,p11 -{ .mfi - nop.m 999 -(p10) fsub.s1 M = M, f1 // If |x| >= |y| and x >=0, set M=0 - nop.i 999 -} -{ .mfi - nop.m 999 -(p11) fadd.s1 M = M, f1 // If |x| >= |y| and x < 0, set M=2.0 - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fcmp.eq.s0 p0, p9 = ArgX_orig, ArgY_orig // Dummy to set denormal flag - nop.i 999 -} -// ************************************************* -// ********************* STEP2 ********************* -// ************************************************* -// -// Q = E * V -// -{ .mfi - nop.m 999 - fmpy.s1 Q = E, V - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fnma.s1 E_hold = E, U, f1 // E_hold = 1.0 - E*U (1) if POLY path - nop.i 999 -} -;; - -// Create a single precision representation of the signexp of Q with the -// 4 most significant bits of the significand followed by a 1 and then 18 0's -{ .mfi - nop.m 999 - fmpy.s1 P_hi = M, P_hi - dep.z special = 0x1, 18, 1 // Form 0x0000000000040000 -} -{ .mfi - nop.m 999 - fmpy.s1 P_lo = M, P_lo - add table_ptr2 = 32, table_ptr1 -} -;; - -{ .mfi - nop.m 999 - fma.s1 A_temp = Q, f1, f0 // Set A_temp if POLY path - nop.i 999 -} -{ .mfi - nop.m 999 - fma.s1 E = E, E_hold, E // E = E + E*E_hold (1) if POLY path - nop.i 999 -} -;; - -// -// Is Q < 2**(-3)? -// swap = xor(swap,sign_X) -// -{ .mfi - nop.m 999 - fcmp.lt.s1 p9, p0 = Q, TWO_TO_NEG3 // Test Q < 2^-3 - xor swap = sign_X, swap -} -;; - -// P_hi = s_Y * P_hi -{ .mmf - getf.exp exponent_Q = Q // Get signexp of Q - cmp.eq.unc p7, p6 = 0x00000, swap - fmpy.s1 P_hi = s_Y, P_hi -} -;; - -// -// if (PR_1) sigma = -1.0 -// if (PR_2) sigma = 1.0 -// -{ .mfi - getf.sig significand_Q = Q // Get significand of Q -(p6) fsub.s1 sigma = f0, f1 - nop.i 999 -} -{ .mfb -(p9) add table_ptr1 = 128, table_base // Point to P8 if POLY path -(p7) fadd.s1 sigma = f0, f1 -(p9) br.cond.spnt ATANL_POLY // Branch to POLY if 0 < Q < 2^-3 -} -;; - -// -// ************************************************* -// ******************** STEP3 ********************** -// ************************************************* -// -// lookup = b_1 b_2 b_3 B_4 -// -{ .mmi - nop.m 999 - nop.m 999 - andcm k = 0x0003, exponent_Q // k=0,1,2,3 for exp_Q=0,-1,-2,-3 -} -;; - -// -// Generate sign_exp_Q b_1 b_2 b_3 b_4 1 0 0 0 ... 0 in single precision -// representation. Note sign of Q is always 0. -// -{ .mfi - cmp.eq p8, p9 = 0x0000, k // Test k=0 - nop.f 999 - extr.u lookup = significand_Q, 59, 4 // Extract b_1 b_2 b_3 b_4 for index -} -{ .mfi - sub sp_exp_Q = 0x7f, k // Form single prec biased exp of Q - nop.f 999 - sub k = k, r0, 1 // Decrement k -} -;; - -// Form pointer to B index table -{ .mfi - ldfe Q_4 = [table_ptr1], -16 // Load Q_4 - nop.f 999 -(p9) shl k = k, 8 // k = 0, 256, or 512 -} -{ .mfi -(p9) shladd table_ptr2 = lookup, 4, table_ptr2 - nop.f 999 - shladd sp_exp_4sig_Q = sp_exp_Q, 4, lookup // Shift and add in 4 high bits -} -;; - -{ .mmi -(p8) add table_ptr2 = -16, table_ptr2 // Pointer if original k was 0 -(p9) add table_ptr2 = k, table_ptr2 // Pointer if k was 1, 2, 3 - dep special = sp_exp_4sig_Q, special, 19, 13 // Form z_hi as single prec -} -;; - -// z_hi = s exp 1.b_1 b_2 b_3 b_4 1 0 0 0 ... 0 -{ .mmi - ldfd Tbl_hi = [table_ptr2], 8 // Load Tbl_hi from index table -;; - setf.s z_hi = special // Form z_hi - nop.i 999 -} -{ .mmi - ldfs Tbl_lo = [table_ptr2], 8 // Load Tbl_lo from index table -;; - ldfe Q_3 = [table_ptr1], -16 // Load Q_3 - nop.i 999 -} -;; - -{ .mmi - ldfe Q_2 = [table_ptr1], -16 // Load Q_2 - nop.m 999 - nop.i 999 -} -;; - -{ .mmf - ldfe Q_1 = [table_ptr1], -16 // Load Q_1 - nop.m 999 - nop.f 999 -} -;; - -{ .mfi - nop.m 999 - fma.s1 U_prime_hi = V, z_hi, U // U_prime_hi = U + V * z_hi - nop.i 999 -} -{ .mfi - nop.m 999 - fnma.s1 V_prime = U, z_hi, V // V_prime = V - U * z_hi - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - mov A_hi = Tbl_hi // Start with A_hi = Tbl_hi - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fsub.s1 U_hold = U, U_prime_hi // U_hold = U - U_prime_hi - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - frcpa.s1 C_hi, p0 = f1, U_prime_hi // C_hi = frcpa(1,U_prime_hi) - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fmpy.s1 A_hi = s_Y, A_hi // A_hi = s_Y * A_hi - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fma.s1 U_prime_lo = z_hi, V, U_hold // U_prime_lo = U_hold + V * z_hi - nop.i 999 -} -;; - -// C_hi_hold = 1 - C_hi * U_prime_hi (1) -{ .mfi - nop.m 999 - fnma.s1 C_hi_hold = C_hi, U_prime_hi, f1 - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fma.s1 Res_hi = sigma, A_hi, P_hi // Res_hi = P_hi + sigma * A_hi - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fma.s1 C_hi = C_hi_hold, C_hi, C_hi // C_hi = C_hi + C_hi * C_hi_hold (1) - nop.i 999 -} -;; - -// C_hi_hold = 1 - C_hi * U_prime_hi (2) -{ .mfi - nop.m 999 - fnma.s1 C_hi_hold = C_hi, U_prime_hi, f1 - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fma.s1 C_hi = C_hi_hold, C_hi, C_hi // C_hi = C_hi + C_hi * C_hi_hold (2) - nop.i 999 -} -;; - -// C_hi_hold = 1 - C_hi * U_prime_hi (3) -{ .mfi - nop.m 999 - fnma.s1 C_hi_hold = C_hi, U_prime_hi, f1 - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fma.s1 C_hi = C_hi_hold, C_hi, C_hi // C_hi = C_hi + C_hi * C_hi_hold (3) - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fmpy.s1 w_hi = V_prime, C_hi // w_hi = V_prime * C_hi - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fmpy.s1 wsq = w_hi, w_hi // wsq = w_hi * w_hi - nop.i 999 -} -{ .mfi - nop.m 999 - fnma.s1 w_lo = w_hi, U_prime_hi, V_prime // w_lo = V_prime-w_hi*U_prime_hi - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fma.s1 poly = wsq, Q_4, Q_3 // poly = Q_3 + wsq * Q_4 - nop.i 999 -} -{ .mfi - nop.m 999 - fnma.s1 w_lo = w_hi, U_prime_lo, w_lo // w_lo = w_lo - w_hi * U_prime_lo - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fma.s1 poly = wsq, poly, Q_2 // poly = Q_2 + wsq * poly - nop.i 999 -} -{ .mfi - nop.m 999 - fmpy.s1 w_lo = C_hi, w_lo // w_lo = = w_lo * C_hi - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fma.s1 poly = wsq, poly, Q_1 // poly = Q_1 + wsq * poly - nop.i 999 -} -{ .mfi - nop.m 999 - fadd.s1 A_lo = Tbl_lo, w_lo // A_lo = Tbl_lo + w_lo - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fmpy.s0 Q_1 = Q_1, Q_1 // Dummy operation to raise inexact - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fmpy.s1 poly = wsq, poly // poly = wsq * poly - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fmpy.s1 poly = w_hi, poly // poly = w_hi * poly - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fadd.s1 A_lo = A_lo, poly // A_lo = A_lo + poly - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fadd.s1 A_lo = A_lo, w_hi // A_lo = A_lo + w_hi - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fma.s1 Res_lo = sigma, A_lo, P_lo // Res_lo = P_lo + sigma * A_lo - nop.i 999 -} -;; - -// -// Result = Res_hi + Res_lo * s_Y (User Supplied Rounding Mode) -// -{ .mfb - nop.m 999 - fma.s0 Result = Res_lo, s_Y, Res_hi - br.ret.sptk b0 // Exit table path 2^-3 <= V/U < 1 -} -;; - - -ATANL_POLY: -// Here if 0 < V/U < 2^-3 -// -// *********************************************** -// ******************** STEP4 ******************** -// *********************************************** - -// -// Following: -// Iterate 3 times E = E + E*(1.0 - E*U) -// Also load P_8, P_7, P_6, P_5, P_4 -// -{ .mfi - ldfe P_8 = [table_ptr1], -16 // Load P_8 - fnma.s1 z_lo = A_temp, U, V // z_lo = V - A_temp * U - nop.i 999 -} -{ .mfi - nop.m 999 - fnma.s1 E_hold = E, U, f1 // E_hold = 1.0 - E*U (2) - nop.i 999 -} -;; - -{ .mmi - ldfe P_7 = [table_ptr1], -16 // Load P_7 -;; - ldfe P_6 = [table_ptr1], -16 // Load P_6 - nop.i 999 -} -;; - -{ .mfi - ldfe P_5 = [table_ptr1], -16 // Load P_5 - fma.s1 E = E, E_hold, E // E = E + E_hold*E (2) - nop.i 999 -} -;; - -{ .mmi - ldfe P_4 = [table_ptr1], -16 // Load P_4 -;; - ldfe P_3 = [table_ptr1], -16 // Load P_3 - nop.i 999 -} -;; - -{ .mfi - ldfe P_2 = [table_ptr1], -16 // Load P_2 - fnma.s1 E_hold = E, U, f1 // E_hold = 1.0 - E*U (3) - nop.i 999 -} -{ .mlx - nop.m 999 - movl int_temp = 0x24005 // Signexp for small neg number -} -;; - -{ .mmf - ldfe P_1 = [table_ptr1], -16 // Load P_1 - setf.exp tmp_small = int_temp // Form small neg number - fma.s1 E = E, E_hold, E // E = E + E_hold*E (3) -} -;; - -// -// -// At this point E approximates 1/U to roughly working precision -// Z = V*E approximates V/U -// -{ .mfi - nop.m 999 - fmpy.s1 Z = V, E // Z = V * E - nop.i 999 -} -{ .mfi - nop.m 999 - fmpy.s1 z_lo = z_lo, E // z_lo = z_lo * E - nop.i 999 -} -;; - -// -// Now what we want to do is -// poly1 = P_4 + zsq*(P_5 + zsq*(P_6 + zsq*(P_7 + zsq*P_8))) -// poly2 = zsq*(P_1 + zsq*(P_2 + zsq*P_3)) -// -// -// Fixup added to force inexact later - -// A_hi = A_temp + z_lo -// z_lo = (A_temp - A_hi) + z_lo -// -{ .mfi - nop.m 999 - fmpy.s1 zsq = Z, Z // zsq = Z * Z - nop.i 999 -} -{ .mfi - nop.m 999 - fadd.s1 A_hi = A_temp, z_lo // A_hi = A_temp + z_lo - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fma.s1 poly1 = zsq, P_8, P_7 // poly1 = P_7 + zsq * P_8 - nop.i 999 -} -{ .mfi - nop.m 999 - fma.s1 poly2 = zsq, P_3, P_2 // poly2 = P_2 + zsq * P_3 - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fmpy.s1 z4 = zsq, zsq // z4 = zsq * zsq - nop.i 999 -} -{ .mfi - nop.m 999 - fsub.s1 A_temp = A_temp, A_hi // A_temp = A_temp - A_hi - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fmerge.s tmp = A_hi, A_hi // Copy tmp = A_hi - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fma.s1 poly1 = zsq, poly1, P_6 // poly1 = P_6 + zsq * poly1 - nop.i 999 -} -{ .mfi - nop.m 999 - fma.s1 poly2 = zsq, poly2, P_1 // poly2 = P_2 + zsq * poly2 - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fmpy.s1 z8 = z4, z4 // z8 = z4 * z4 - nop.i 999 -} -{ .mfi - nop.m 999 - fadd.s1 z_lo = A_temp, z_lo // z_lo = (A_temp - A_hi) + z_lo - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fma.s1 poly1 = zsq, poly1, P_5 // poly1 = P_5 + zsq * poly1 - nop.i 999 -} -{ .mfi - nop.m 999 - fmpy.s1 poly2 = poly2, zsq // poly2 = zsq * poly2 - nop.i 999 -} -;; - -// Create small GR double in case need to raise underflow -{ .mfi - nop.m 999 - fma.s1 poly1 = zsq, poly1, P_4 // poly1 = P_4 + zsq * poly1 - dep GR_temp = -1,r0,0,53 -} -;; - -// Create small double in case need to raise underflow -{ .mfi - setf.d FR_temp = GR_temp - fma.s1 poly = z8, poly1, poly2 // poly = poly2 + z8 * poly1 - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fma.s1 A_lo = Z, poly, z_lo // A_lo = z_lo + Z * poly - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fadd.s1 A_hi = tmp, A_lo // A_hi = tmp + A_lo - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fsub.s1 tmp = tmp, A_hi // tmp = tmp - A_hi - nop.i 999 -} -{ .mfi - nop.m 999 - fmpy.s1 A_hi = s_Y, A_hi // A_hi = s_Y * A_hi - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fadd.s1 A_lo = tmp, A_lo // A_lo = tmp + A_lo - nop.i 999 -} -{ .mfi - nop.m 999 - fma.s1 Res_hi = sigma, A_hi, P_hi // Res_hi = P_hi + sigma * A_hi - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fsub.s1 tmp = P_hi, Res_hi // tmp = P_hi - Res_hi - nop.i 999 -} -;; - -// -// Test if A_lo is zero -// -{ .mfi - nop.m 999 - fclass.m p6,p0 = A_lo, 0x007 // Test A_lo = 0 - nop.i 999 -} -;; - -{ .mfi - nop.m 999 -(p6) mov A_lo = tmp_small // If A_lo zero, make very small - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fma.s1 tmp = A_hi, sigma, tmp // tmp = sigma * A_hi + tmp - nop.i 999 -} -{ .mfi - nop.m 999 - fma.s1 sigma = A_lo, sigma, P_lo // sigma = A_lo * sigma + P_lo - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fma.s1 Res_lo = s_Y, sigma, tmp // Res_lo = s_Y * sigma + tmp - nop.i 999 -} -;; - -// -// Test if Res_lo is denormal -// -{ .mfi - nop.m 999 - fclass.m p14, p15 = Res_lo, 0x0b - nop.i 999 -} -;; - -// -// Compute Result = Res_lo + Res_hi. Use s3 if Res_lo is denormal. -// -{ .mfi - nop.m 999 -(p14) fadd.s3 Result = Res_lo, Res_hi // Result for Res_lo denormal - nop.i 999 -} -{ .mfi - nop.m 999 -(p15) fadd.s0 Result = Res_lo, Res_hi // Result for Res_lo normal - nop.i 999 -} -;; - -// -// If Res_lo is denormal test if Result equals zero -// -{ .mfi - nop.m 999 -(p14) fclass.m.unc p14, p0 = Result, 0x07 - nop.i 999 -} -;; - -// -// If Res_lo is denormal and Result equals zero, raise inexact, underflow -// by squaring small double -// -{ .mfb - nop.m 999 -(p14) fmpy.d.s0 FR_temp = FR_temp, FR_temp - br.ret.sptk b0 // Exit POLY path, 0 < Q < 2^-3 -} -;; - - -ATANL_UNSUPPORTED: -{ .mfb - nop.m 999 - fmpy.s0 Result = ArgX,ArgY - br.ret.sptk b0 -} -;; - -// Here if y natval, nan, inf, zero -ATANL_Y_SPECIAL: -// Here if x natval, nan, inf, zero -ATANL_X_SPECIAL: -{ .mfi - nop.m 999 - fclass.m p13,p12 = ArgY_orig, 0x0c3 // Test y nan - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fclass.m p15,p14 = ArgY_orig, 0x103 // Test y natval - nop.i 999 -} -;; - -{ .mfi - nop.m 999 -(p12) fclass.m p13,p0 = ArgX_orig, 0x0c3 // Test x nan - nop.i 999 -} -;; - -{ .mfi - nop.m 999 -(p14) fclass.m p15,p0 = ArgX_orig, 0x103 // Test x natval - nop.i 999 -} -;; - -{ .mfb - nop.m 999 -(p13) fmpy.s0 Result = ArgX_orig, ArgY_orig // Result nan if x or y nan -(p13) br.ret.spnt b0 // Exit if x or y nan -} -;; - -{ .mfb - nop.m 999 -(p15) fmpy.s0 Result = ArgX_orig, ArgY_orig // Result natval if x or y natval -(p15) br.ret.spnt b0 // Exit if x or y natval -} -;; - - -// Here if x or y inf or zero -ATANL_SPECIAL_HANDLING: -{ .mfi - nop.m 999 - fclass.m p6, p7 = ArgY_orig, 0x007 // Test y zero - mov special = 992 // Offset to table -} -;; - -{ .mfb - add table_ptr1 = table_base, special // Point to 3pi/4 - fcmp.eq.s0 p0, p9 = ArgX_orig, ArgY_orig // Dummy to set denormal flag -(p7) br.cond.spnt ATANL_ArgY_Not_ZERO // Branch if y not zero -} -;; - -// Here if y zero -{ .mmf - ldfd Result = [table_ptr1], 8 // Get pi high - nop.m 999 - fclass.m p14, p0 = ArgX, 0x035 // Test for x>=+0 -} -;; - -{ .mmf - nop.m 999 - ldfd Result_lo = [table_ptr1], -8 // Get pi lo - fclass.m p15, p0 = ArgX, 0x036 // Test for x<=-0 -} -;; - -// -// Return sign_Y * 0 when ArgX > +0 -// -{ .mfi - nop.m 999 -(p14) fmerge.s Result = ArgY, f0 // If x>=+0, y=0, hi sgn(y)*0 - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fclass.m p13, p0 = ArgX, 0x007 // Test for x=0 - nop.i 999 -} -;; - -{ .mfi - nop.m 999 -(p14) fmerge.s Result_lo = ArgY, f0 // If x>=+0, y=0, lo sgn(y)*0 - nop.i 999 -} -;; - -{ .mfi -(p13) mov GR_Parameter_TAG = 36 // Error tag for x=0, y=0 - nop.f 999 - nop.i 999 -} -;; - -// -// Return sign_Y * pi when ArgX < -0 -// -{ .mfi - nop.m 999 -(p15) fmerge.s Result = ArgY, Result // If x<0, y=0, hi=sgn(y)*pi - nop.i 999 -} -;; - -{ .mfi - nop.m 999 -(p15) fmerge.s Result_lo = ArgY, Result_lo // If x<0, y=0, lo=sgn(y)*pi - nop.i 999 -} -;; - -// -// Call error support function for atan(0,0) -// -{ .mfb - nop.m 999 - fadd.s0 Result = Result, Result_lo -(p13) br.cond.spnt __libm_error_region // Branch if atan(0,0) -} -;; - -{ .mib - nop.m 999 - nop.i 999 - br.ret.sptk b0 // Exit for y=0, x not 0 -} -;; - -// Here if y not zero -ATANL_ArgY_Not_ZERO: -{ .mfi - nop.m 999 - fclass.m p0, p10 = ArgY, 0x023 // Test y inf - nop.i 999 -} -;; - -{ .mfb - nop.m 999 - fclass.m p6, p0 = ArgX, 0x017 // Test for 0 <= |x| < inf -(p10) br.cond.spnt ATANL_ArgY_Not_INF // Branch if 0 < |y| < inf -} -;; - -// Here if y=inf -// -// Return +PI/2 when ArgY = +Inf and ArgX = +/-0 or normal -// Return -PI/2 when ArgY = -Inf and ArgX = +/-0 or normal -// Return +PI/4 when ArgY = +Inf and ArgX = +Inf -// Return -PI/4 when ArgY = -Inf and ArgX = +Inf -// Return +3PI/4 when ArgY = +Inf and ArgX = -Inf -// Return -3PI/4 when ArgY = -Inf and ArgX = -Inf -// -{ .mfi - nop.m 999 - fclass.m p7, p0 = ArgX, 0x021 // Test for x=+inf - nop.i 999 -} -;; - -{ .mfi -(p6) add table_ptr1 = 16, table_ptr1 // Point to pi/2, if x finite - fclass.m p8, p0 = ArgX, 0x022 // Test for x=-inf - nop.i 999 -} -;; - -{ .mmi -(p7) add table_ptr1 = 32, table_ptr1 // Point to pi/4 if x=+inf -;; -(p8) add table_ptr1 = 48, table_ptr1 // Point to 3pi/4 if x=-inf - - nop.i 999 -} -;; - -{ .mmi - ldfd Result = [table_ptr1], 8 // Load pi/2, pi/4, or 3pi/4 hi -;; - ldfd Result_lo = [table_ptr1], -8 // Load pi/2, pi/4, or 3pi/4 lo - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fmerge.s Result = ArgY, Result // Merge sgn(y) in hi - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fmerge.s Result_lo = ArgY, Result_lo // Merge sgn(y) in lo - nop.i 999 -} -;; - -{ .mfb - nop.m 999 - fadd.s0 Result = Result, Result_lo // Compute complete result - br.ret.sptk b0 // Exit for y=inf -} -;; - -// Here if y not INF, and x=0 or INF -ATANL_ArgY_Not_INF: -// -// Return +PI/2 when ArgY NOT Inf, ArgY > 0 and ArgX = +/-0 -// Return -PI/2 when ArgY NOT Inf, ArgY < 0 and ArgX = +/-0 -// Return +0 when ArgY NOT Inf, ArgY > 0 and ArgX = +Inf -// Return -0 when ArgY NOT Inf, ArgY > 0 and ArgX = +Inf -// Return +PI when ArgY NOT Inf, ArgY > 0 and ArgX = -Inf -// Return -PI when ArgY NOT Inf, ArgY > 0 and ArgX = -Inf -// -{ .mfi - nop.m 999 - fclass.m p7, p9 = ArgX, 0x021 // Test for x=+inf - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fclass.m p6, p0 = ArgX, 0x007 // Test for x=0 - nop.i 999 -} -;; - -{ .mfi -(p6) add table_ptr1 = 16, table_ptr1 // Point to pi/2 - fclass.m p8, p0 = ArgX, 0x022 // Test for x=-inf - nop.i 999 -} -;; - -.pred.rel "mutex",p7,p9 -{ .mfi -(p9) ldfd Result = [table_ptr1], 8 // Load pi or pi/2 hi -(p7) fmerge.s Result = ArgY, f0 // If y not inf, x=+inf, sgn(y)*0 - nop.i 999 -} -;; - -{ .mfi -(p9) ldfd Result_lo = [table_ptr1], -8 // Load pi or pi/2 lo -(p7) fnorm.s0 Result = Result // If y not inf, x=+inf normalize - nop.i 999 -} -;; - -{ .mfi - nop.m 999 -(p9) fmerge.s Result = ArgY, Result // Merge sgn(y) in hi - nop.i 999 -} -;; - -{ .mfi - nop.m 999 -(p9) fmerge.s Result_lo = ArgY, Result_lo // Merge sgn(y) in lo - nop.i 999 -} -;; - -{ .mfb - nop.m 999 -(p9) fadd.s0 Result = Result, Result_lo // Compute complete result - br.ret.spnt b0 // Exit for y not inf, x=0,inf -} -;; - -GLOBAL_IEEE754_END(atan2l) - -LOCAL_LIBM_ENTRY(__libm_error_region) -.prologue -{ .mfi - add GR_Parameter_Y=-32,sp // Parameter 2 value - nop.f 0 -.save ar.pfs,GR_SAVE_PFS - mov GR_SAVE_PFS=ar.pfs // Save ar.pfs -} -{ .mfi -.fframe 64 - add sp=-64,sp // Create new stack - nop.f 0 - mov GR_SAVE_GP=gp // Save gp -};; -{ .mmi - stfe [GR_Parameter_Y] = FR_Y,16 // Save Parameter 2 on stack - add GR_Parameter_X = 16,sp // Parameter 1 address -.save b0, GR_SAVE_B0 - mov GR_SAVE_B0=b0 // Save b0 -};; -.body -{ .mib - stfe [GR_Parameter_X] = FR_X // Store Parameter 1 on stack - add GR_Parameter_RESULT = 0,GR_Parameter_Y - nop.b 0 // Parameter 3 address -} -{ .mib - stfe [GR_Parameter_Y] = FR_RESULT // Store Parameter 3 on stack - add GR_Parameter_Y = -16,GR_Parameter_Y - br.call.sptk b0=__libm_error_support# // Call error handling function -};; -{ .mmi - nop.m 0 - nop.m 0 - add GR_Parameter_RESULT = 48,sp -};; -{ .mmi - ldfe f8 = [GR_Parameter_RESULT] // Get return result off stack -.restore sp - add sp = 64,sp // Restore stack pointer - mov b0 = GR_SAVE_B0 // Restore return address -};; -{ .mib - mov gp = GR_SAVE_GP // Restore gp - mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs - br.ret.sptk b0 // Return -};; - -LOCAL_LIBM_END(__libm_error_region#) -.type __libm_error_support#,@function -.global __libm_error_support# |