e_atan2.s

Glibc 2.3.2源代码(解压后有100多M)

.file "atan2.s"

// Copyright (C) 2000, 2001, Intel Corporation
// All rights reserved.
// 
// Contributed 2/2/2000 by John Harrison, Ted Kubaska, Bob Norin, Shane Story,
// and Ping Tak Peter Tang of the Computational Software Lab, 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://developer.intel.com/opensource.
//
// History
//==============================================================
// 2/02/00  Initial version
// 4/04/00  Unwind support added
// 8/15/00  Bundle added after call to __libm_error_support to properly
//          set [the previously overwritten] GR_Parameter_RESULT.
// 8/17/00  Changed predicate register macro-usage to direct predicate
//          names due to an assembler bug.
// 9/28/00  Updated to set invalid on SNaN inputs
// 1/19/01  Fixed flags for small results
//
// API
//==============================================================
// double atan2(double Y, double X)
//
// Overview of operation
//==============================================================
//
// 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
//            anything        NaN           quiet X

// atan2(+-0/+-0) sets double error tag to 37
// atan2(+-0/+-0) sets single error tag to 38

#include "libm_support.h"

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

EXP_AD_P1                    = r33
EXP_AD_P2                    = r34
atan2_GR_sml_exp             = 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_X                      = f9
atan2_Y                      = f8

atan2_u1_X                   = f32
atan2_u1_Y                   = f33
atan2_Umax                   = f34
atan2_Vmin                   = f35
atan2_two                    = f36
atan2_absX                   = f37
atan2_z1_X                   = f38
atan2_z1_Y                   = f39
atan2_B1X                    = f40
atan2_B1Y                    = f41
atan2_wp                     = f42
atan2_B1sq                   = 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_Pi_by_2                = f69

atan2_V13                    = f70
atan2_W11                    = f71
atan2_E                      = f72
atan2_gamma                  = 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_sml_norm               = f103
atan2_FR_tmp                 = f103

atan2_W1                     = f104
atan2_alpha_cub              = f105
atan2_C                      = f106
atan2_P                      = 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                   = f116
atan2_pi                     = f117
atan2_sgnX                   = f118
atan2_sgnXY                  = f119

atan2_3pi_by_4               = f120
atan2_pi_by_4                = f121

//atan2_sF                     = p7
//atan2_sT                     = p6

// These coefficients are for atan2. 
// You can also use this set to substitute those used in the |X| <= 1 case for atan; 
// BUT NOT vice versa.

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


#ifdef _LIBC
.rodata
#else
.data
#endif

.align 16

atan2_tb1:
ASM_TYPE_DIRECTIVE(atan2_tb1,@object)
data8 0xB199DD6D2675C40F ,  0x0000BFFA // P10
data8 0xA21922DC45605EA1 ,  0x00003FFA // P11
data8 0xD78F28FC2A592781 ,  0x0000BFFA // P8
data8 0xC2F01E5DDD100DBE ,  0x00003FFA // P9
data8 0x9D89D7D55C3287A5 ,  0x00003FFB // P5
data8 0xF0F03ADB3FC930D3 ,  0x00003FFA // P7
data8 0xF396268151CFB11C ,  0x00003FF7 // P17 
data8 0x9D3436AABE218776 ,  0x00003FF5 // P19
data8 0x80D601879218B53A ,  0x00003FFA // P13
data8 0xA2270D30A90AA220 ,  0x00003FF9 // P15
data8 0xCCCCCCCCCCC906CD ,  0x00003FFC // P1
data8 0xE38E38E320A8A098 ,  0x00003FFB // P3
data8 0xFE7E52D2A89995B3 ,  0x0000BFEC // P22
data8 0xC90FDAA22168C235 ,  0x00003FFE // pi/4
ASM_SIZE_DIRECTIVE(atan2_tb1)

atan2_tb2:
ASM_TYPE_DIRECTIVE(atan2_tb2,@object)
data8 0x9F90FB984D8E39D0 ,  0x0000BFF3 // P20
data8 0xCE585A259BD8374C ,  0x00003FF0 // P21
data8 0xBA2E8B9793955C77 ,  0x0000BFFB // P4
data8 0x88887EBB209E3543 ,  0x0000BFFB // P6
data8 0xD818B4BB43D84BF2 ,  0x0000BFF8 // P16
data8 0xDEC343E068A6D2A8 ,  0x0000BFF6 // P18
data8 0x9297B23CCFFB291F ,  0x0000BFFA // P12
data8 0xD5F4F2182E7A8725 ,  0x0000BFF9 // P14
data8 0xAAAAAAAAAAAAA8A9 ,  0x0000BFFD // P0
data8 0x9249249247E37913 ,  0x0000BFFC // P2
data8 0xC90FDAA22168C235 ,  0x00003FFF // pi/2
data8 0xC90FDAA22168C235 ,  0x00004000 // pi
data8 0x96cbe3f9990e91a8 ,  0x00004000 // 3pi/4
ASM_SIZE_DIRECTIVE(atan2_tb2)




.align 32
.global atan2#
#ifdef _LIBC
.global __atan2#
.global __ieee754_atan2#
#endif

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

.section .text
.align 32

.proc  atan2#
atan2:
#ifdef _LIBC
.proc  __atan2#
__atan2:
.proc  __ieee754_atan2#
__ieee754_atan2:
#endif
// qnan snan inf norm     unorm 0 -+
// 0    0    1   0        0     0 11


//         Y NAN?     p10 p11
// p10 ==> quiet Y and return
// p11     X NAN?     p12, p13 
// p12 ==> quiet X and return

{ .mfi
           alloc        r32           = ar.pfs,1,5,4,0
           frcpa.s1     atan2_u1_X,p6 = f1,atan2_X
           addl         EXP_AD_P2   = @ltoff(atan2_tb2), gp
}
{ .mfi
           addl         EXP_AD_P1   = @ltoff(atan2_tb1), gp
           fclass.m.unc p10,p11 = f8, 0xc3
           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_two  = f1,f1,f1 
           nop.i 999
;;
}


{ .mfi
           ld8 EXP_AD_P2 = [ EXP_AD_P2]
           famax.s1     atan2_Umax =  f8,f9
           nop.i 999
}
;;

{ .mfi
           nop.m 999
           fmerge.s     atan2_absX = f0,atan2_X
           nop.i 999
}
;;

// p10 Y NAN, quiet and return
{ .mfi
           ldfe         atan2_P10  = [EXP_AD_P1],16
           fmerge.s     atan2_sgnY = atan2_Y,f1
           nop.i 999
}
{ .mfb
           nop.m 999
(p10)      fma.d f8 = f8,f9,f0 
(p10)      br.ret.spnt b0
;;
}


{ .mmf
           ldfe         atan2_P11  = [EXP_AD_P1],16
           ldfe         atan2_P20  = [EXP_AD_P2],16
           fmerge.s     atan2_sgnX = atan2_X,f1
;;
}


{ .mfi 
           ldfe         atan2_P8   = [EXP_AD_P1],16
           fma.s1       atan2_z1_X = atan2_u1_X, atan2_Y, f0
           nop.i 999
}
{ .mfi 

           ldfe         atan2_P21  = [EXP_AD_P2],16
           fma.s1       atan2_z1_Y = atan2_u1_Y, atan2_X, f0
           nop.i 999
;;
}

{ .mfi 
           ldfe         atan2_P9   = [EXP_AD_P1],16
           fnma.s1      atan2_B1X  = atan2_u1_X, atan2_X, atan2_two
           nop.i 999
}
{ .mfi 

           ldfe         atan2_P4   = [EXP_AD_P2],16
           fnma.s1      atan2_B1Y  = atan2_u1_Y, atan2_Y, atan2_two
           nop.i 999
;;
}

// p6 (atan2_sT) true if swap
// p7 (atan2_sF) true if no swap
// p11 ==> Y !NAN;  X NAN?

{ .mfi
           ldfe         atan2_P5   = [EXP_AD_P1],16
//           fcmp.eq.unc.s1 atan2_sF,atan2_sT    = atan2_Umax, atan2_X
           fcmp.eq.unc.s1 p7,p6    = atan2_Umax, atan2_X
           nop.i 999
}
{ .mfi
           ldfe         atan2_P6   = [EXP_AD_P2],16
(p11)      fclass.m.unc p12,p13    = f9, 0xc3
           nop.i 999
;;
}

{ .mmf
           ldfe         atan2_P7   = [EXP_AD_P1],16
           ldfe         atan2_P16  = [EXP_AD_P2],16
           famin.s1     atan2_Vmin =  f8,f9
;;
}

// p8 true if X positive
// p9 true if X negative
// both are false is swap is true
{ .mfi
           ldfe         atan2_P17  = [EXP_AD_P1],16
//(atan2_sF) fcmp.eq.unc.s1 p8,p9    = atan2_sgnX,f1
(p7) fcmp.eq.unc.s1 p8,p9    = atan2_sgnX,f1
           nop.i 999
}
{ .mfi
           ldfe         atan2_P18  = [EXP_AD_P2],16
           fma.s1       atan2_sgnXY     = atan2_sgnX, atan2_sgnY, f0 
           nop.i 999
;;
}


{ .mfi
           ldfe         atan2_P19  = [EXP_AD_P1],16
//(atan2_sF) fma.s1       atan2_wp   = atan2_z1_X, atan2_z1_X, f0
(p7) fma.s1       atan2_wp   = atan2_z1_X, atan2_z1_X, f0
           nop.i 999
}
{ .mfi
           ldfe         atan2_P12  = [EXP_AD_P2],16
//(atan2_sT) fma.s1       atan2_wp   = atan2_z1_Y, atan2_z1_Y, f0
(p6) fma.s1       atan2_wp   = atan2_z1_Y, atan2_z1_Y, f0
           nop.i 999
;;
}


{ .mfi
           ldfe         atan2_P13  = [EXP_AD_P1],16
//(atan2_sF) fma.s1       atan2_z         = atan2_z1_X, atan2_B1X, f0
(p7) fma.s1       atan2_z         = atan2_z1_X, atan2_B1X, f0
           nop.i 999
}
{ .mfi
           ldfe         atan2_P14  = [EXP_AD_P2],16
//(atan2_sT) fma.s1       atan2_z         = atan2_z1_Y, atan2_B1Y, f0
(p6) fma.s1       atan2_z         = atan2_z1_Y, atan2_B1Y, f0
           nop.i 999
;;
}


{ .mfi
           ldfe         atan2_P15       = [EXP_AD_P1],16
//(atan2_sF) fma.s1       atan2_B1sq = atan2_B1X, atan2_B1X, f0
(p7) fma.s1       atan2_B1sq = atan2_B1X, atan2_B1X, f0
           nop.i 999
}
{ .mfi
           ldfe         atan2_P0        = [EXP_AD_P2],16
//(atan2_sT) fma.s1       atan2_B1sq = atan2_B1Y, atan2_B1Y, f0
(p6) fma.s1       atan2_B1sq = atan2_B1Y, atan2_B1Y, f0
           nop.i 999
;;
}


// p12 ==> X NAN, quiet and return
{ .mfi
           ldfe         atan2_P1        = [EXP_AD_P1],16
           fmerge.s     atan2_Umax      = f0,atan2_Umax
           nop.i 999
}
{ .mfb
           ldfe         atan2_P2        = [EXP_AD_P2],16
(p12)      fma.d        f8 = f9,f8,f0
(p12)      br.ret.spnt b0
;;
}


// p10 ==> x  inf     y ?
// p11 ==> x !inf     y ?
{ .mfi
           ldfe         atan2_P3        = [EXP_AD_P1],16
           fmerge.s     atan2_Vmin      = f0,atan2_Vmin
           nop.i 999
}
{ .mfi
           ldfe         atan2_Pi_by_2   = [EXP_AD_P2],16
           fclass.m.unc p10,p11 = f9, 0x23
           nop.i 999
;;
}


{ .mmf
           ldfe         atan2_P22       = [EXP_AD_P1],16
           ldfe         atan2_pi        = [EXP_AD_P2],16
           nop.f 999
;;
}

{ .mfi
           nop.m 999 
           fcmp.eq.s0  p12,p13=f9,f8   // Dummy to catch denormal and invalid
           nop.i 999
;;
}


{ .mfi
           ldfe         atan2_pi_by_4       = [EXP_AD_P1],16
//(atan2_sT) fmerge.ns    atan2_sgnXY     = atan2_sgnXY, atan2_sgnXY