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-.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|<Pi/4
-// 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|<Pi/4
-// 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|<Pi/4
-// 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|<Pi/4
-// 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)
-
-
-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#
-
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