e_atan2.s

glibc 2.9,最新版的C语言库函数

.file "atan2.s"


// Copyright (c) 2000 - 2003, 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  Initial version
// 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.
// 08/17/00  Changed predicate register macro-usage to direct predicate
//           names due to an assembler bug.
// 09/28/00  Updated to set invalid on SNaN inputs
// 01/19/01  Fixed flags for small results
// 04/13/01  Rescheduled to make all paths faster
// 05/20/02  Cleaned up namespace and sf0 syntax
// 08/20/02  Corrected inexact flag and directed rounding symmetry bugs
// 02/06/03  Reordered header: .section, .global, .proc, .align
// 04/17/03  Added missing mutex directive
// 12/23/03  atan2(NaN1,NaN2) now QNaN1, for consistency with atan2f, atan2l
//
// API
//==============================================================
// double atan2(double Y, double X)
//
// Overview of operation
//==============================================================
//
// The atan2 function returns values in the interval [-pi,+pi].
//
// There are two basic paths: swap true and swap false.
// atan2(Y,X) ==> atan2(V/U) where U >= V. If Y > X, we must swap.
//
// p6  swap True    |Y| > |X|
// p7  swap False   |Y| <= |X|
// p8  X+   (If swap=True p8=p9=0)
// p9  X-
//
// all the other predicates p10 thru p15 are false for the main path
//
// Simple trigonometric identities show
//   Region 1 (-45 to +45 degrees):
//         X>0, |Y|<=X, V=Y, U=X     atan2(Y,X) = sgnY * (0 + atan(V/U))
//
//   Region 2 (-90 to -45 degrees, and +45 to +90 degrees):
//         X>0, |Y|>X, V=X, U=Y      atan2(Y,X) = sgnY * (pi/2 - atan(V/U))
//
//   Region 3 (-135 to -90 degrees, and +90 to +135 degrees):
//         X<0, |Y|>X, V=X, U=Y      atan2(Y,X) = sgnY * (pi/2 + atan(V/U))
//
//   Region 4 (-180 to -135 degrees, and +135 to +180 degrees):
//         X<0, |Y|<=X, V=Y, U=X      atan2(Y,X) = sgnY * (pi - atan(V/U))
//
// So the result is always of the form atan2(Y,X) = P + sgnXY * atan(V/U)
//
// We compute atan(V/U) from the identity
//      atan(z) + atan([(V/U)-z] / [1+(V/U)z])
//      where z is a limited precision approximation (16 bits) to V/U
//
// z is calculated with the assistance of the frcpa instruction.
//
// atan(z) is calculated by a polynomial z + z^3 * p(w),  w=z^2
// where p(w) = P0+P1*w+...+P22*w^22
//
// Let d = [(V/U)-z] / [1+(V/U)z]) = (V-U*z)/(U+V*z)
//
// Approximate atan(d) by d + P0*d^3
// Let F = 1/(U+V*z) * (1-a), where |a|< 2^-8.8.
// Compute q(a) = 1 + a + ... + a^5.
// Then F*q(a) approximates the reciprocal to more than 50 bits.

// Special values
//==============================================================
//              Y                 x          Result
//             +number           +inf        +0
//             -number           +inf        -0
//             +number           -inf        +pi
//             -number           -inf        -pi
//
//             +inf              +number     +pi/2
//             -inf              +number     -pi/2
//             +inf              -number     +pi/2
//             -inf              -number     -pi/2
//
//             +inf              +inf        +pi/4
//             -inf              +inf        -pi/4
//             +inf              -inf        +3pi/4
//             -inf              -inf        -3pi/4
//
//             +1                +1          +pi/4
//             -1                +1          -pi/4
//             +1                -1          +3pi/4
//             -1                -1          -3pi/4
//
//             +number           +0          +pi/2
//             -number           +0          -pi/2
//             +number           -0          +pi/2
//             -number           -0          -pi/2
//
//             +0                +number     +0
//             -0                +number     -0
//             +0                -number     +pi
//             -0                -number     -pi
//
//             +0                +0          +0
//             -0                +0          -0
//             +0                -0          +pi
//             -0                -0          -pi
//
//            Nan             anything      quiet Y
//            Not NaN         NaN           quiet X

// atan2(+-0/+-0) sets double error tag to 37

// Registers used
//==============================================================

// predicate registers used:
// p6 -> p15

// floating-point registers used:
// f8, f9 input
// f32 -> f119

// general registers used
// r32 -> r41

// Assembly macros
//==============================================================

EXP_AD_P1                    = r33
EXP_AD_P2                    = r34
rsig_near_one                = r35


GR_SAVE_B0                   = r35
GR_SAVE_GP                   = r36
GR_SAVE_PFS                  = r37

GR_Parameter_X               = r38
GR_Parameter_Y               = r39
GR_Parameter_RESULT          = r40
atan2_GR_tag                 = r41

atan2_Y                      = f8
atan2_X                      = f9

atan2_u1_X                   = f32
atan2_u1_Y                   = f33
atan2_z2_X                   = f34
atan2_z2_Y                   = f35

atan2_two                    = f36
atan2_B1sq_Y                 = f37
atan2_z1_X                   = f38
atan2_z1_Y                   = f39
atan2_B1X                    = f40

atan2_B1Y                    = f41
atan2_wp_X                   = f42
atan2_B1sq_X                 = f43
atan2_z                      = f44
atan2_w                      = f45

atan2_P0                     = f46
atan2_P1                     = f47
atan2_P2                     = f48
atan2_P3                     = f49
atan2_P4                     = f50

atan2_P5                     = f51
atan2_P6                     = f52
atan2_P7                     = f53
atan2_P8                     = f54
atan2_P9                     = f55

atan2_P10                    = f56
atan2_P11                    = f57
atan2_P12                    = f58
atan2_P13                    = f59
atan2_P14                    = f60

atan2_P15                    = f61
atan2_P16                    = f62
atan2_P17                    = f63
atan2_P18                    = f64
atan2_P19                    = f65

atan2_P20                    = f66
atan2_P21                    = f67
atan2_P22                    = f68
atan2_tmp                    = f68
atan2_pi_by_2                = f69
atan2_sgn_pi_by_2            = f69
atan2_V13                    = f70

atan2_W11                    = f71
atan2_E                      = f72
atan2_wp_Y                   = f73
atan2_V11                    = f74
atan2_V12                    = f75

atan2_V7                     = f76
atan2_V8                     = f77
atan2_W7                     = f78
atan2_W8                     = f79
atan2_W3                     = f80

atan2_W4                     = f81
atan2_V3                     = f82
atan2_V4                     = f83
atan2_F                      = f84
atan2_gV                     = f85

atan2_V10                    = f86
atan2_zcub                   = f87
atan2_V6                     = f88
atan2_V9                     = f89
atan2_W10                    = f90

atan2_W6                     = f91
atan2_W2                     = f92
atan2_V2                     = f93
atan2_alpha                  = f94
atan2_alpha_1                = f95

atan2_gVF                    = f96
atan2_V5                     = f97
atan2_W12                    = f98
atan2_W5                     = f99
atan2_alpha_sq               = f100

atan2_Cp                     = f101
atan2_V1                     = f102
atan2_ysq                    = f103
atan2_W1                     = f104
atan2_alpha_cub              = f105

atan2_C                      = f106
atan2_xsq                    = f107
atan2_d                      = f108
atan2_A_hi                   = f109
atan2_dsq                    = f110

atan2_pd                     = f111
atan2_A_lo                   = f112
atan2_A                      = f113
atan2_Pp                     = f114
atan2_sgnY                   = f115

atan2_sig_near_one           = f116
atan2_near_one               = f116
atan2_pi                     = f117
atan2_sgn_pi                 = f117
atan2_3pi_by_4               = f118
atan2_pi_by_4                = f119


/////////////////////////////////////////////////////////////


RODATA

.align 16

LOCAL_OBJECT_START(atan2_tb1)
data8 0xA21922DC45605EA1 ,  0x00003FFA // P11
data8 0xB199DD6D2675C40F ,  0x0000BFFA // P10
data8 0xC2F01E5DDD100DBE ,  0x00003FFA // P9
data8 0xD78F28FC2A592781 ,  0x0000BFFA // P8
data8 0xF0F03ADB3FC930D3 ,  0x00003FFA // P7
data8 0x88887EBB209E3543 ,  0x0000BFFB // P6
data8 0x9D89D7D55C3287A5 ,  0x00003FFB // P5
data8 0xBA2E8B9793955C77 ,  0x0000BFFB // P4
data8 0xE38E38E320A8A098 ,  0x00003FFB // P3
data8 0x9249249247E37913 ,  0x0000BFFC // P2
data8 0xCCCCCCCCCCC906CD ,  0x00003FFC // P1
data8 0xAAAAAAAAAAAAA8A9 ,  0x0000BFFD // P0
data8 0xC90FDAA22168C235 ,  0x00004000 // pi
LOCAL_OBJECT_END(atan2_tb1)

LOCAL_OBJECT_START(atan2_tb2)
data8 0xCE585A259BD8374C ,  0x00003FF0 // P21
data8 0x9F90FB984D8E39D0 ,  0x0000BFF3 // P20
data8 0x9D3436AABE218776 ,  0x00003FF5 // P19
data8 0xDEC343E068A6D2A8 ,  0x0000BFF6 // P18
data8 0xF396268151CFB11C ,  0x00003FF7 // P17
data8 0xD818B4BB43D84BF2 ,  0x0000BFF8 // P16
data8 0xA2270D30A90AA220 ,  0x00003FF9 // P15
data8 0xD5F4F2182E7A8725 ,  0x0000BFF9 // P14
data8 0x80D601879218B53A ,  0x00003FFA // P13
data8 0x9297B23CCFFB291F ,  0x0000BFFA // P12
data8 0xFE7E52D2A89995B3 ,  0x0000BFEC // P22
data8 0xC90FDAA22168C235 ,  0x00003FFF // pi/2
data8 0xC90FDAA22168C235 ,  0x00003FFE // pi/4
data8 0x96cbe3f9990e91a8 ,  0x00004000 // 3pi/4
LOCAL_OBJECT_END(atan2_tb2)




.section .text
GLOBAL_IEEE754_ENTRY(atan2)

{ .mfi
           alloc        r32           = ar.pfs,1,5,4,0
           frcpa.s1     atan2_u1_X,p6 = f1,atan2_X
           nop.i 999
}
{ .mfi
           addl         EXP_AD_P1   = @ltoff(atan2_tb1), gp
           fma.s1       atan2_two  = f1,f1,f1
           nop.i 999
;;
}

{ .mfi
           ld8  EXP_AD_P1 = [EXP_AD_P1]
           frcpa.s1     atan2_u1_Y,p7 = f1,atan2_Y
           nop.i 999
}
{ .mfi
           nop.m 999
           fma.s1       atan2_xsq  = atan2_X,atan2_X,f0
           nop.i 999
;;
}

{ .mfi
           nop.m 999
           fclass.m p10,p0 = atan2_Y, 0xc3     // Test for y=nan
           nop.i 999
}
{ .mfi
           nop.m 999
           fma.s1       atan2_ysq  = atan2_Y,atan2_Y,f0
           nop.i 999
}
;;

{ .mfi
           add  EXP_AD_P2 = 0xd0,EXP_AD_P1
           fclass.m p12,p0 = atan2_X, 0xc3     // Test for x nan
           nop.i 999
}
;;


// p10 Y NAN, quiet and return
{ .mfi
           ldfe         atan2_P11  = [EXP_AD_P1],16
           fmerge.s     atan2_sgnY = atan2_Y,f1
           nop.i 999
}
{ .mfb
           ldfe         atan2_P21  = [EXP_AD_P2],16
(p10)      fma.d.s0 f8 = atan2_X,atan2_Y,f0   // If y=nan, result quietized y
(p10)      br.ret.spnt b0        // Exit if y=nan
;;
}


{ .mfi
           ldfe         atan2_P10  = [EXP_AD_P1],16
           fma.s1       atan2_z1_X = atan2_u1_X, atan2_Y, f0
           nop.i 999
}
{ .mfi
           ldfe         atan2_P20  = [EXP_AD_P2],16
           fnma.s1      atan2_B1X  = atan2_u1_X, atan2_X, atan2_two
           nop.i 999
;;
}

{ .mfi
           ldfe         atan2_P9   = [EXP_AD_P1],16
           fma.s1       atan2_z1_Y = atan2_u1_Y, atan2_X, f0
           nop.i 999
}
{ .mfi
           ldfe         atan2_P19  = [EXP_AD_P2],16
           fnma.s1      atan2_B1Y  = atan2_u1_Y, atan2_Y, atan2_two
           nop.i 999
}
;;

{ .mfi
           ldfe         atan2_P8   = [EXP_AD_P1],16
           fma.s1       atan2_z2_X = atan2_u1_X, atan2_ysq, f0
           nop.i 999
}
{ .mfi
           ldfe         atan2_P18  = [EXP_AD_P2],16
           fma.s1       atan2_z2_Y = atan2_u1_Y, atan2_xsq, f0
           nop.i 999
}
;;

// p10 ==> x  inf     y ?
// p11 ==> x !inf     y ?
{ .mfi
           ldfe         atan2_P7   = [EXP_AD_P1],16
           fclass.m p10,p11 = atan2_X, 0x23    // test for x inf
           nop.i 999
}
{ .mfb
           ldfe         atan2_P17  = [EXP_AD_P2],16
(p12)      fma.d.s0        f8 = atan2_X,atan2_Y,f0     // If x nan, result quiet x
(p12)      br.ret.spnt b0                 // Exit for x nan
;;
}

// p6 true if swap,    means |y| >  |x|    or ysq > xsq
// p7 true if no swap, means |x| >= |y|    or xsq >= ysq
{ .mmf
           ldfe         atan2_P6   = [EXP_AD_P1],16
           ldfe         atan2_P16  = [EXP_AD_P2],16
           fcmp.ge.s1 p7,p6    = atan2_xsq, atan2_ysq
;;
}

{ .mfi
           ldfe         atan2_P5   = [EXP_AD_P1],16
           fma.s1       atan2_wp_X   = atan2_z1_X, atan2_z1_X, f0
           nop.i 999
}
{ .mfi
           ldfe         atan2_P15       = [EXP_AD_P2],16
           fma.s1       atan2_B1sq_X = atan2_B1X, atan2_B1X, f0
           nop.i 999
;;
}

{ .mfi
           ldfe         atan2_P4   = [EXP_AD_P1],16
(p6)       fma.s1       atan2_wp_Y   = atan2_z1_Y, atan2_z1_Y, f0
           nop.i 999
}
{ .mfi
           ldfe         atan2_P14  = [EXP_AD_P2],16
(p6)       fma.s1       atan2_B1sq_Y = atan2_B1Y, atan2_B1Y, f0
           nop.i 999
;;
}

{ .mfi
           ldfe         atan2_P3        = [EXP_AD_P1],16
(p6)       fma.s1       atan2_E         = atan2_z2_Y, atan2_B1Y, atan2_Y
           nop.i 999
}
{ .mfi
           ldfe         atan2_P13  = [EXP_AD_P2],16
(p7)       fma.s1       atan2_E         = atan2_z2_X, atan2_B1X, atan2_X
           nop.i 999
;;
}


{ .mfi
           ldfe         atan2_P2        = [EXP_AD_P1],16
(p6)       fma.s1       atan2_z         = atan2_z1_Y, atan2_B1Y, f0
           nop.i 999
}
{ .mfi
           ldfe         atan2_P12  = [EXP_AD_P2],16
(p7)       fma.s1       atan2_z         = atan2_z1_X, atan2_B1X, f0
           nop.i 999
;;
}


{ .mfi
           ldfe         atan2_P1        = [EXP_AD_P1],16
           fcmp.eq.s0  p14,p15=atan2_X,atan2_Y  // Dummy for denorm and invalid
           nop.i 999
}
{ .mlx
           ldfe         atan2_P22       = [EXP_AD_P2],16
           movl         rsig_near_one = 0x8000000000000001 // signif near 1.0
;;
}


// p12 ==> x  inf     y inf
// p13 ==> x  inf     y !inf
{ .mmf
           ldfe         atan2_P0        = [EXP_AD_P1],16
           ldfe         atan2_pi_by_2   = [EXP_AD_P2],16
(p10)      fclass.m.unc p12,p13 = atan2_Y, 0x23  // x inf, test if y inf
;;