.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

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// 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)

libm_alias_ldouble_other (__atan, atan)

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).