.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)
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#