diff options
Diffstat (limited to 'sysdeps/ia64/fpu/s_atanl.S')
| -rw-r--r-- | sysdeps/ia64/fpu/s_atanl.S | 2007 |
1 files changed, 2007 insertions, 0 deletions
diff --git a/sysdeps/ia64/fpu/s_atanl.S b/sysdeps/ia64/fpu/s_atanl.S new file mode 100644 index 0000000000..fea68abfde --- /dev/null +++ b/sysdeps/ia64/fpu/s_atanl.S @@ -0,0 +1,2007 @@ +.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# |