diff options
Diffstat (limited to 'sysdeps/ia64/fpu/s_tanf.S')
| -rw-r--r-- | sysdeps/ia64/fpu/s_tanf.S | 691 |
1 files changed, 691 insertions, 0 deletions
diff --git a/sysdeps/ia64/fpu/s_tanf.S b/sysdeps/ia64/fpu/s_tanf.S new file mode 100644 index 0000000..7df762f --- /dev/null +++ b/sysdeps/ia64/fpu/s_tanf.S @@ -0,0 +1,691 @@ +.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# |