.file "tancotf.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 Initial version

// 04/04/00 Unwind support added

// 12/27/00 Improved speed

// 02/21/01 Updated to call tanl

// 05/30/02 Improved speed, added cotf.

// 11/25/02 Added explicit completer on fnorm

// 02/10/03 Reordered header: .section, .global, .proc, .align

// 04/17/03 Eliminated redundant stop bits

// 03/31/05 Reformatted delimiters between data tables

//

// APIs

//==============================================================

// float tanf(float)

// float cotf(float)

//

// Algorithm Description for tanf

//==============================================================

// The tanf function computes the principle value of the tangent of x,

// where x is radian argument.

//

// There are 5 paths:

// 1. x = +/-0.0

//    Return tanf(x) = +/-0.0

//

// 2. x = [S,Q]NaN

//    Return tanf(x) = QNaN

//

// 3. x = +/-Inf

//    Return tanf(x) = QNaN

//

// 4. x = r + (Pi/2)*N, N = RoundInt(x*(2/Pi)), N is even, |r|

//    Return tanf(x) = P19(r) = A1*r + A3*r^3 + A5*r^5 + ... + A19*r^19 =

//    = r*(A1 + A3*t + A5*t^2 + ... + A19*t^9) = r*P9(t), where t = r^2

//

// 5. x = r + (Pi/2)*N, N = RoundInt(x*(2/Pi)), N is odd, |r|

//    Return tanf(x) = -1/r + P11(r) = -1/r + B1*r + B3*r^3 + ... + B11*r^11 =

//    = -1/r + r*(B1 + B3*t + B5*t^2 + ... + B11*t^5) = -1/r + r*P11(t),

//    where t = r^2

//

// Algorithm Description for cotf

//==============================================================

// The cotf function computes the principle value of the cotangent of x,

// where x is radian argument.

//

// There are 5 paths:

// 1. x = +/-0.0

//    Return cotf(x) = +/-Inf and error handling is called

//

// 2. x = [S,Q]NaN

//    Return cotf(x) = QNaN

//

// 3. x = +/-Inf

//    Return cotf(x) = QNaN

//

// 4. x = r + (Pi/2)*N, N = RoundInt(x*(2/Pi)), N is odd, |r|

//    Return cotf(x) = P19(-r) = A1*(-r) + A3*(-r^3) + ... + A19*(-r^19) =

//    = -r*(A1 + A3*t + A5*t^2 + ... + A19*t^9) = -r*P9(t), where t = r^2

//

// 5. x = r + (Pi/2)*N, N = RoundInt(x*(2/Pi)), N is even, |r|

//    Return cotf(x) = 1/r + P11(-r) = 1/r + B1*(-r) + ... + B11*(-r^11) =

//    = 1/r - r*(B1 + B3*t + B5*t^2 + ... + B11*t^5) = 1/r - r*P11(t),

//    where t = r^2

//

//    We set p10 and clear p11 if computing tanf, vice versa for cotf.

//

//

// Registers used

//==============================================================

// Floating Point registers used:

// f8, input

// f32 -> f80

//

// General registers used:

// r14 -> r23, r32 -> r39

//

// Predicate registers used:

// p6 -> p13

//

// Assembly macros

//==============================================================

// integer registers

rExp                        = r14

rSignMask                   = r15

rRshf                       = r16

rScFctrExp                  = r17

rIntN                       = r18

rSigRcpPiby2                = r19

rScRshf                     = r20

rCoeffA                     = r21

rCoeffB                     = r22

rExpCut                     = r23

GR_SAVE_B0                  = r33

GR_SAVE_PFS                 = r34

GR_SAVE_GP                  = r35

GR_Parameter_X              = r36

GR_Parameter_Y              = r37

GR_Parameter_RESULT         = r38

GR_Parameter_Tag            = r39

//==============================================================

// floating point registers

fScRcpPiby2                 = f32

fScRshf                     = f33

fNormArg                    = f34

fScFctr                     = f35

fRshf                       = f36

fShiftedN                   = f37

fN                          = f38

fR                          = f39

fA01                        = f40

fA03                        = f41

fA05                        = f42

fA07                        = f43

fA09                        = f44

fA11                        = f45

fA13                        = f46

fA15                        = f47

fA17                        = f48

fA19                        = f49

fB01                        = f50

fB03                        = f51

fB05                        = f52

fB07                        = f53

fB09                        = f54

fB11                        = f55

fA03_01                     = f56

fA07_05                     = f57

fA11_09                     = f58

fA15_13                     = f59

fA19_17                     = f60

fA11_05                     = f61

fA19_13                     = f62

fA19_05                     = f63

fRbyA03_01                  = f64

fB03_01                     = f65

fB07_05                     = f66

fB11_09                     = f67

fB11_05                     = f68

fRbyB03_01                  = f69

fRbyB11_01                  = f70

fRp2                        = f71

fRp4                        = f72

fRp8                        = f73

fRp5                        = f74

fY0                         = f75

fY1                         = f76

fD                          = f77

fDp2                        = f78

fInvR                       = f79

fPiby2                      = f80

//==============================================================

RODATA

.align 16

LOCAL_OBJECT_START(coeff_A)

data8 0x3FF0000000000000 // A1  = 1.00000000000000000000e+00

data8 0x3FD5555556BCE758 // A3  = 3.33333334641442641606e-01

data8 0x3FC111105C2DAE48 // A5  = 1.33333249100689099175e-01

data8 0x3FABA1F876341060 // A7  = 5.39701122561673229739e-02

data8 0x3F965FB86D12A38D // A9  = 2.18495194027670719750e-02

data8 0x3F8265F62415F9D6 // A11 = 8.98353860497717439465e-03

data8 0x3F69E3AE64CCF58D // A13 = 3.16032468108912746342e-03

data8 0x3F63920D09D0E6F6 // A15 = 2.38897844840557235331e-03

LOCAL_OBJECT_END(coeff_A)

LOCAL_OBJECT_START(coeff_B)

data8 0xC90FDAA22168C235, 0x3FFF // pi/2

data8 0x3FD55555555358DB // B1  = 3.33333333326107426583e-01

data8 0x3F96C16C252F643F // B3  = 2.22222230621336129239e-02

data8 0x3F61566243AB3C60 // B5  = 2.11638633968606896785e-03

data8 0x3F2BC1169BD4438B // B7  = 2.11748132564551094391e-04

data8 0x3EF611B4CEA056A1 // B9  = 2.10467959860990200942e-05

data8 0x3EC600F9E32194BF // B11 = 2.62305891234274186608e-06

data8 0xBF42BA7BCC177616 // A17 =-5.71546981685324877205e-04

data8 0x3F4F2614BC6D3BB8 // A19 = 9.50584530849832782542e-04

LOCAL_OBJECT_END(coeff_B)

.section .text

LOCAL_LIBM_ENTRY(cotf)

{ .mlx

      getf.exp  rExp        = f8                    // ***** Get 2ˆ17 * s + E

      movl      rSigRcpPiby2= 0xA2F9836E4E44152A    // significand of 2/Pi

}

{ .mlx

      addl      rCoeffA     = @ltoff(coeff_A), gp

      movl      rScRshf     = 0x47e8000000000000    // 1.5*2^(63+63+1)

}

;;

{ .mfi

      alloc     r32         = ar.pfs, 0, 4, 4, 0

      fclass.m  p9, p0      = f8, 0xc3              // Test for x=nan

      cmp.eq    p11, p10    = r0, r0                // if p11=1 we compute cotf

}

{ .mib

      ld8       rCoeffA     = [rCoeffA]

      mov       rExpCut     = 0x10009               // cutoff for exponent

      br.cond.sptk Common_Path

}

;;

LOCAL_LIBM_END(cotf)

GLOBAL_IEEE754_ENTRY(tanf)

{ .mlx

      getf.exp  rExp        = f8                    // ***** Get 2ˆ17 * s + E

      movl      rSigRcpPiby2= 0xA2F9836E4E44152A    // significand of 2/Pi

}

{ .mlx

      addl      rCoeffA     = @ltoff(coeff_A), gp

      movl      rScRshf     = 0x47e8000000000000    // 1.5*2^(63+63+1)

}

;;

{ .mfi

      alloc     r32         = ar.pfs, 0, 4, 4, 0

      fclass.m  p9, p0      = f8, 0xc3              // Test for x=nan

      cmp.eq    p10, p11    = r0, r0                // if p10=1 we compute tandf

}

{ .mib

      ld8       rCoeffA     = [rCoeffA]

      mov       rExpCut     = 0x10009               // cutoff for exponent

      nop.b     0

}

;;

// Below is common path for both tandf and cotdf

Common_Path:

{ .mfi

      setf.sig  fScRcpPiby2 = rSigRcpPiby2          // 2^(63+1)*(2/Pi)

      fclass.m  p8, p0      = f8, 0x23              // Test for x=inf

      mov       rSignMask   = 0x1ffff               // mask for sign bit

}

{ .mlx

      setf.d    fScRshf     = rScRshf               // 1.5*2^(63+63+1)

      movl      rRshf       = 0x43e8000000000000    // 1.5 2^63 for right shift

}

;;

{ .mfi

      and       rSignMask   = rSignMask, rExp       // clear sign bit

(p10) fclass.m.unc p7, p0   = f8, 0x07              // Test for x=0 (for tanf)

      mov       rScFctrExp  = 0xffff-64             // exp of scaling factor

}

{ .mfb

      adds      rCoeffB     = coeff_B - coeff_A, rCoeffA

(p9)  fma.s.s0  f8          = f8, f1, f8            // Set qnan if x=nan

(p9)  br.ret.spnt b0                                // Exit for x=nan

}

;;

{ .mfi

      cmp.ge    p6, p0      = rSignMask, rExpCut    // p6 = (E => 0x10009)

(p8)  frcpa.s0  f8, p0      = f0, f0                // Set qnan indef if x=inf

      mov GR_Parameter_Tag  = 227                   // (cotf)

}

{ .mbb

      ldfe      fPiby2      = [rCoeffB], 16

(p8)  br.ret.spnt b0                                // Exit for x=inf

(p6)  br.cond.spnt Huge_Argument                    // Branch if |x|>=2^10

}

;;

{ .mfi

      nop.m     0

(p11) fclass.m.unc p6, p0   = f8, 0x07              // Test for x=0 (for cotf)

      nop.i     0

}

{ .mfb

      nop.m     0

      fnorm.s0  fNormArg    = f8

(p7)  br.ret.spnt b0                                // Exit for x=0 (for tanf)

}

;;

{ .mmf

      ldfpd     fA01, fA03  = [rCoeffA], 16

      ldfpd     fB01, fB03  = [rCoeffB], 16

      fmerge.s  f10         = f8, f8                // Save input for error call

}

;;

{ .mmf

      setf.exp  fScFctr     = rScFctrExp            // get as real

      setf.d    fRshf       = rRshf                 // get right shifter as real

(p6)  frcpa.s0  f8, p0      = f1, f8                // cotf(+-0) = +-Inf

}

;;

{ .mmb

      ldfpd     fA05, fA07  = [rCoeffA], 16

      ldfpd     fB05, fB07  = [rCoeffB], 16

(p6)  br.cond.spnt __libm_error_region    // call error support if cotf(+-0)

}

;;

{ .mmi

      ldfpd     fA09, fA11  = [rCoeffA], 16

      ldfpd     fB09, fB11  = [rCoeffB], 16

      nop.i     0

}

;;

{ .mfi

      nop.m     0

      fma.s1    fShiftedN = fNormArg,fScRcpPiby2,fScRshf // x*2^70*(2/Pi)+ScRshf

      nop.i     0

}

;;

{ .mfi

      nop.m     0

      fms.s1    fN          = fShiftedN, fScFctr, fRshf // N = Y*2^(-70) - Rshf

      nop.i     0

}

;;

.pred.rel "mutex", p10, p11

{ .mfi

      getf.sig  rIntN       = fShiftedN             // get N as integer

(p10) fnma.s1   fR          = fN, fPiby2, fNormArg  // R = x - (Pi/2)*N (tanf)

      nop.i     0

}

{ .mfi

      nop.m     0

(p11) fms.s1    fR          = fN, fPiby2, fNormArg  // R = (Pi/2)*N - x (cotf)

      nop.i     0

}

;;

{ .mmi

      ldfpd     fA13, fA15  = [rCoeffA], 16

      ldfpd     fA17, fA19  = [rCoeffB], 16

      nop.i     0

}

;;

Return_From_Huges:

{ .mfi

      nop.m     0

      fma.s1    fRp2        = fR, fR, f0            // R^2

(p11) add       rIntN       = 0x1, rIntN            // N = N + 1 (cotf)

}

;;

{ .mfi

      nop.m     0

      frcpa.s1  fY0, p0     = f1, fR                // Y0 ~ 1/R

      tbit.z    p8, p9      = rIntN, 0              // p8=1 if N is even

}

;;

// Below are mixed polynomial calculations (mixed for even and odd N)

{ .mfi

      nop.m     0

(p9)  fma.s1    fB03_01     = fRp2, fB03, fB01      // R^2*B3 + B1

      nop.i     0

}

{ .mfi

      nop.m     0

      fma.s1    fRp4        = fRp2, fRp2, f0        // R^4

      nop.i     0

}

;;

{ .mfi

      nop.m     0

(p8)  fma.s1    fA15_13     = fRp2, fA15, fA13      // R^2*A15 + A13

      nop.i     0

}

{ .mfi

      nop.m     0

(p8)  fma.s1    fA19_17     = fRp2, fA19, fA17      // R^2*A19 + A17

      nop.i     0

}

;;

{ .mfi

      nop.m     0

(p8)  fma.s1    fA07_05     = fRp2, fA07, fA05      // R^2*A7 + A5

      nop.i     0

}

{ .mfi

      nop.m     0

(p8)  fma.s1    fA11_09     = fRp2, fA11, fA09      // R^2*A11 + A9

      nop.i     0

}

;;

{ .mfi

      nop.m     0

(p9)  fma.s1    fB07_05     = fRp2, fB07, fB05      // R^2*B7 + B5

      nop.i     0

}

{ .mfi

      nop.m     0

(p9)  fma.s1    fB11_09     = fRp2, fB11, fB09      // R^2*B11 + B9

      nop.i     0

}

;;

{ .mfi

      nop.m     0

(p9)  fnma.s1   fD          = fR, fY0, f1           // D = 1 - R*Y0

      nop.i     0

}

{ .mfi

      nop.m     0

(p8)  fma.s1    fA03_01     = fRp2, fA03, fA01      // R^2*A3 + A1

      nop.i     0

}

;;

{ .mfi

      nop.m     0

      fma.s1    fRp8        = fRp4, fRp4, f0        // R^8

      nop.i     0

}

{ .mfi

      nop.m     0

      fma.s1    fRp5        = fR, fRp4, f0          // R^5

      nop.i     0

}

;;

{ .mfi

      nop.m     0

(p8)  fma.s1    fA11_05     = fRp4, fA11_09, fA07_05 // R^4*(R^2*A11 + A9) + ...

      nop.i     0

}

{ .mfi

      nop.m     0

(p8)  fma.s1    fA19_13     = fRp4, fA19_17, fA15_13 // R^4*(R^2*A19 + A17) + ..

      nop.i     0

}

;;

{ .mfi

      nop.m     0

(p9)  fma.s1    fB11_05     = fRp4, fB11_09, fB07_05 // R^4*(R^2*B11 + B9) + ...

      nop.i     0

}

{ .mfi

      nop.m     0

(p9)  fma.s1    fRbyB03_01  = fR, fB03_01, f0       // R*(R^2*B3 + B1)

      nop.i     0

}

;;

{ .mfi

      nop.m     0

(p9)  fma.s1    fY1         = fY0, fD, fY0          // Y1 = Y0*D + Y0

      nop.i     0

}

{ .mfi

      nop.m     0

(p9)  fma.s1    fDp2        = fD, fD, f0            // D^2

      nop.i     0

}

;;

{ .mfi

      nop.m     0

   // R^8*(R^6*A19 + R^4*A17 + R^2*A15 + A13) + R^6*A11 + R^4*A9 + R^2*A7 + A5

(p8)  fma.d.s1  fA19_05     = fRp8, fA19_13, fA11_05

      nop.i     0

}

{ .mfi

      nop.m     0

(p8)  fma.d.s1  fRbyA03_01  = fR, fA03_01, f0       // R*(R^2*A3 + A1)

      nop.i     0

}

;;

{ .mfi

      nop.m     0

(p9)  fma.d.s1  fInvR       = fY1, fDp2, fY1        // 1/R = Y1*D^2 + Y1

      nop.i     0

}

{ .mfi

      nop.m     0

   // R^5*(R^6*B11 + R^4*B9 + R^2*B7 + B5) + R^3*B3 + R*B1

(p9)  fma.d.s1  fRbyB11_01  = fRp5, fB11_05, fRbyB03_01

      nop.i     0

}

;;

.pred.rel "mutex", p8, p9

{ .mfi

      nop.m     0

   // Result = R^5*(R^14*A19 + R^12*A17 + R^10*A15 + ...) + R^3*A3 + R*A1

(p8)  fma.s.s0  f8          = fRp5, fA19_05, fRbyA03_01

      nop.i 0

}

{ .mfb

      nop.m     0

   // Result = -1/R + R^11*B11 + R^9*B9 + R^7*B7 + R^5*B5 + R^3*B3 + R*B1

(p9)  fnma.s.s0 f8          = f1, fInvR, fRbyB11_01

      br.ret.sptk b0                                // exit for main path

}

;;

GLOBAL_IEEE754_END(tanf)

libm_alias_float_other (__tan, tan)

LOCAL_LIBM_ENTRY(__libm_callout)

Huge_Argument:

.prologue

{ .mfi

      nop.m 0

      fmerge.s f9 = f0,f0

.save ar.pfs,GR_SAVE_PFS

      mov  GR_SAVE_PFS=ar.pfs

}

;;

{ .mfi

      mov GR_SAVE_GP=gp

      nop.f 0

.save b0, GR_SAVE_B0

      mov GR_SAVE_B0=b0

}

.body

{ .mmb

      nop.m 999

      nop.m 999

(p10) br.cond.sptk.many  call_tanl ;;

}

// Here if we should call cotl (p10=0, p11=1)

{ .mmb

      nop.m 999

      nop.m 999

      br.call.sptk.many  b0=__libm_cotl# ;;

}

{ .mfi

      mov gp        = GR_SAVE_GP

      fnorm.s.s0 f8 = f8

      mov b0        = GR_SAVE_B0

}

;;

{ .mib

      nop.m 999

      mov ar.pfs    = GR_SAVE_PFS

      br.ret.sptk     b0

;;

}

// Here if we should call tanl (p10=1, p11=0)

call_tanl:

{ .mmb

      nop.m 999

      nop.m 999

      br.call.sptk.many  b0=__libm_tanl# ;;

}

{ .mfi

      mov gp        = GR_SAVE_GP

      fnorm.s.s0 f8 = f8

      mov b0        = GR_SAVE_B0

}

;;

{ .mib

      nop.m 999

      mov ar.pfs    = GR_SAVE_PFS

      br.ret.sptk     b0

;;

}

LOCAL_LIBM_END(__libm_callout)

.type __libm_tanl#,@function

.global __libm_tanl#

.type __libm_cotl#,@function

.global __libm_cotl#

LOCAL_LIBM_ENTRY(__libm_error_region)

.prologue

// (1)

{ .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

};;

// (2)

{ .mmi

      stfs [GR_Parameter_Y] = f1,16              // STORE 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

// (3)

{ .mib

      stfs [GR_Parameter_X] = f10                // STORE Parameter 1 on stack

      add   GR_Parameter_RESULT = 0,GR_Parameter_Y  // Parameter 3 address

      nop.b 0

}

{ .mib

      stfs [GR_Parameter_Y] = f8                 // 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

};;

// (4)

{ .mmi

      ldfs  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#