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Diffstat (limited to 'sysdeps/ia64/fpu/s_tanf.S')
| -rw-r--r-- | sysdeps/ia64/fpu/s_tanf.S | 692 |
1 files changed, 0 insertions, 692 deletions
diff --git a/sysdeps/ia64/fpu/s_tanf.S b/sysdeps/ia64/fpu/s_tanf.S deleted file mode 100644 index 193d7568a5..0000000000 --- a/sysdeps/ia64/fpu/s_tanf.S +++ /dev/null @@ -1,692 +0,0 @@ -.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# - |