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.file "tan.s"
// Copyright (c) 2000, 2001, Intel Corporation// All rights reserved.// // Contributed 2/2/2000 by John Harrison, Ted Kubaska, Bob Norin, Shane Story,// and Ping Tak Peter Tang of the Computational Software Lab, Intel Corporation.// // WARRANTY DISCLAIMER// // 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://developer.intel.com/opensource.//// History//==============================================================// 2/02/00: Initial version// 4/04/00 Unwind support added// 12/27/00 Improved speed// 02/21/01 Updated to call tanl//// API//==============================================================// double tan( double x);
//// Overview of operation//==============================================================// If the input value in radians is |x| >= 1.xxxxx 2^10 call the// older slower version.//// The new algorithm is used when |x| <= 1.xxxxx 2^9.//// Represent the input X as Nfloat * pi/2 + r// where r can be negative and |r| <= pi/4//// tan_W = x * 2/pi// Nfloat = round_int(tan_W)//// tan_r = x - Nfloat * (pi/2)_hi// tan_r = tan_r - Nfloat * (pi/2)_lo//// We have two paths: p8, when Nfloat is even and p9. when Nfloat is odd.// p8: tan(X) = tan(r)// p9: tan(X) = -cot(r)//// Each is evaluated as a series. The p9 path requires 1/r.//// The coefficients used in the series are stored in a table as// are the pi constants.//// Registers used//==============================================================//// predicate registers used: // p6-10//// floating-point registers used: // f10-15, f32-105// f8, input//// general registers used// r14-18, r32-43//// Assembly macros//==============================================================TAN_INV_PI_BY_2_2TO64 = f10TAN_RSHF_2TO64 = f11TAN_2TOM64 = f12TAN_RSHF = f13TAN_W_2TO64_RSH = f14TAN_NFLOAT = f15
tan_Inv_Pi_by_2 = f32tan_Pi_by_2_hi = f33tan_Pi_by_2_lo = f34
tan_P0 = f35tan_P1 = f36tan_P2 = f37tan_P3 = f38 tan_P4 = f39 tan_P5 = f40 tan_P6 = f41tan_P7 = f42tan_P8 = f43 tan_P9 = f44 tan_P10 = f45 tan_P11 = f46tan_P12 = f47 tan_P13 = f48tan_P14 = f49tan_P15 = f50
tan_Q0 = f51 tan_Q1 = f52 tan_Q2 = f53 tan_Q3 = f54 tan_Q4 = f55 tan_Q5 = f56 tan_Q6 = f57 tan_Q7 = f58 tan_Q8 = f59tan_Q9 = f60tan_Q10 = f61
tan_r = f62tan_rsq = f63tan_rcube = f64
tan_v18 = f65tan_v16 = f66tan_v17 = f67tan_v12 = f68tan_v13 = f69tan_v7 = f70tan_v8 = f71tan_v4 = f72tan_v5 = f73tan_v15 = f74tan_v11 = f75tan_v14 = f76tan_v3 = f77tan_v6 = f78tan_v10 = f79tan_v2 = f80tan_v9 = f81tan_v1 = f82tan_int_Nfloat = f83 tan_Nfloat = f84
tan_NORM_f8 = f85 tan_W = f86
tan_y0 = f87tan_d = f88 tan_y1 = f89 tan_dsq = f90 tan_y2 = f91 tan_d4 = f92 tan_inv_r = f93
tan_z1 = f94tan_z2 = f95tan_z3 = f96tan_z4 = f97tan_z5 = f98tan_z6 = f99tan_z7 = f100tan_z8 = f101tan_z9 = f102tan_z10 = f103tan_z11 = f104tan_z12 = f105
/////////////////////////////////////////////////////////////
tan_GR_sig_inv_pi_by_2 = r14tan_GR_rshf_2to64 = r15tan_GR_exp_2tom64 = r16tan_GR_n = r17tan_GR_rshf = r18
tan_AD = r33tan_GR_10009 = r34 tan_GR_17_ones = r35 tan_GR_N_odd_even = r36 tan_GR_N = r37 tan_signexp = r38tan_exp = r39tan_ADQ = r40
GR_SAVE_PFS = r41 GR_SAVE_B0 = r42 GR_SAVE_GP = r43
.data
.align 16
double_tan_constants:// data8 0xA2F9836E4E44152A, 0x00003FFE // 2/pi data8 0xC90FDAA22168C234, 0x00003FFF // pi/2 hi
data8 0xBEEA54580DDEA0E1 // P14 data8 0x3ED3021ACE749A59 // P15 data8 0xBEF312BD91DC8DA1 // P12 data8 0x3EFAE9AFC14C5119 // P13 data8 0x3F2F342BF411E769 // P8 data8 0x3F1A60FC9F3B0227 // P9 data8 0x3EFF246E78E5E45B // P10 data8 0x3F01D9D2E782875C // P11 data8 0x3F8226E34C4499B6 // P4 data8 0x3F6D6D3F12C236AC // P5 data8 0x3F57DA1146DCFD8B // P6 data8 0x3F43576410FE3D75 // P7 data8 0x3FD5555555555555 // P0 data8 0x3FC11111111111C2 // P1 data8 0x3FABA1BA1BA0E850 // P2 data8 0x3F9664F4886725A7 // P3
double_Q_tan_constants: data8 0xC4C6628B80DC1CD1, 0x00003FBF // pi/2 lo data8 0x3E223A73BA576E48 // Q8 data8 0x3DF54AD8D1F2CA43 // Q9 data8 0x3EF66A8EE529A6AA // Q4 data8 0x3EC2281050410EE6 // Q5 data8 0x3E8D6BB992CC3CF5 // Q6 data8 0x3E57F88DE34832E4 // Q7 data8 0x3FD5555555555555 // Q0 data8 0x3F96C16C16C16DB8 // Q1 data8 0x3F61566ABBFFB489 // Q2 data8 0x3F2BBD77945C1733 // Q3 data8 0x3D927FB33E2B0E04 // Q10
.align 32.global tan#
////////////////////////////////////////////////////////
.section .text.proc tan#
.align 32tan: // The initial fnorm will take any unmasked faults and// normalize any single/double unorms
{ .mlx alloc r32=ar.pfs,1,11,0,0 movl tan_GR_sig_inv_pi_by_2 = 0xA2F9836E4E44152A // significand of 2/pi}{ .mlx addl tan_AD = @ltoff(double_tan_constants), gp movl tan_GR_rshf_2to64 = 0x47e8000000000000 // 1.1000 2^(63+63+1)};;
{ .mfi ld8 tan_AD = [tan_AD] fnorm tan_NORM_f8 = f8 mov tan_GR_exp_2tom64 = 0xffff-64 // exponent of scaling factor 2^-64}{ .mlx nop.m 999 movl tan_GR_rshf = 0x43e8000000000000 // 1.1000 2^63 for right shift};;
// Form two constants we need// 2/pi * 2^1 * 2^63, scaled by 2^64 since we just loaded the significand// 1.1000...000 * 2^(63+63+1) to right shift int(W) into the significand{ .mmi setf.sig TAN_INV_PI_BY_2_2TO64 = tan_GR_sig_inv_pi_by_2 setf.d TAN_RSHF_2TO64 = tan_GR_rshf_2to64 mov tan_GR_17_ones = 0x1ffff ;;
}
// Form another constant// 2^-64 for scaling Nfloat// 1.1000...000 * 2^63, the right shift constant{ .mmf setf.exp TAN_2TOM64 = tan_GR_exp_2tom64 adds tan_ADQ = double_Q_tan_constants - double_tan_constants, tan_AD fclass.m.unc p6,p0 = f8, 0x07 // Test for x=0};;
// Form another constant// 2^-64 for scaling Nfloat// 1.1000...000 * 2^63, the right shift constant{ .mmf setf.d TAN_RSHF = tan_GR_rshf ldfe tan_Pi_by_2_hi = [tan_AD],16 fclass.m.unc p7,p0 = f8, 0x23 // Test for x=inf};;
{ .mfb ldfe tan_Pi_by_2_lo = [tan_ADQ],16 fclass.m.unc p8,p0 = f8, 0xc3 // Test for x=nan(p6) br.ret.spnt b0 ;; // Exit for x=0
}
{ .mfi ldfpd tan_P14,tan_P15 = [tan_AD],16 (p7) frcpa.s0 f8,p9=f0,f0 // Set qnan indef if x=inf mov tan_GR_10009 = 0x10009}{ .mib ldfpd tan_Q8,tan_Q9 = [tan_ADQ],16 nop.i 999(p7) br.ret.spnt b0 ;; // Exit for x=inf
}
{ .mfi ldfpd tan_P12,tan_P13 = [tan_AD],16 (p8) fma.d f8=f8,f1,f8 // Set qnan if x=nan nop.i 999}{ .mib ldfpd tan_Q4,tan_Q5 = [tan_ADQ],16 nop.i 999(p8) br.ret.spnt b0 ;; // Exit for x=nan
}
{ .mmi getf.exp tan_signexp = tan_NORM_f8 ldfpd tan_P8,tan_P9 = [tan_AD],16 nop.i 999 ;;
}
// Multiply x by scaled 2/pi and add large const to shift integer part of W to // rightmost bits of significand{ .mfi ldfpd tan_Q6,tan_Q7 = [tan_ADQ],16 fma.s1 TAN_W_2TO64_RSH = tan_NORM_f8,TAN_INV_PI_BY_2_2TO64,TAN_RSHF_2TO64 nop.i 999 ;;
}
{ .mmi ldfpd tan_P10,tan_P11 = [tan_AD],16 nop.m 999 and tan_exp = tan_GR_17_ones, tan_signexp ;;
}
// p7 is true if we must call DBX TAN// p7 is true if f8 exp is > 0x10009 (which includes all ones// NAN or inf){ .mmi ldfpd tan_Q0,tan_Q1 = [tan_ADQ],16 cmp.ge.unc p7,p0 = tan_exp,tan_GR_10009 nop.i 999 ;;
}
{ .mmb ldfpd tan_P4,tan_P5 = [tan_AD],16 nop.m 999(p7) br.cond.spnt TAN_DBX ;;
}
{ .mmi ldfpd tan_Q2,tan_Q3 = [tan_ADQ],16 nop.m 999 nop.i 999 ;;
}
// TAN_NFLOAT = Round_Int_Nearest(tan_W){ .mfi ldfpd tan_P6,tan_P7 = [tan_AD],16 fms.s1 TAN_NFLOAT = TAN_W_2TO64_RSH,TAN_2TOM64,TAN_RSHF nop.i 999 ;;
}
{ .mfi ldfd tan_Q10 = [tan_ADQ] nop.f 999 nop.i 999 ;;
}
{ .mfi ldfpd tan_P0,tan_P1 = [tan_AD],16 nop.f 999 nop.i 999 ;;
}
{ .mfi getf.sig tan_GR_n = TAN_W_2TO64_RSH nop.f 999 nop.i 999 ;;
}
// tan_r = -tan_Nfloat * tan_Pi_by_2_hi + x{ .mfi ldfpd tan_P2,tan_P3 = [tan_AD] fnma.s1 tan_r = TAN_NFLOAT, tan_Pi_by_2_hi, tan_NORM_f8 nop.i 999 ;;
}
// p8 ==> even// p9 ==> odd{ .mmi and tan_GR_N_odd_even = 0x1, tan_GR_n ;;
nop.m 999 cmp.eq.unc p8,p9 = tan_GR_N_odd_even, r0 ;;
}
// tan_r = tan_r -tan_Nfloat * tan_Pi_by_2_lo { .mfi nop.m 999 fnma.s1 tan_r = TAN_NFLOAT, tan_Pi_by_2_lo, tan_r nop.i 999 ;;
}
{ .mfi nop.m 999 fma.s1 tan_rsq = tan_r, tan_r, f0 nop.i 999 ;;
}
{ .mfi nop.m 999(p9) frcpa.s1 tan_y0, p10 = f1,tan_r nop.i 999 ;;
}
{ .mfi nop.m 999(p8) fma.s1 tan_v18 = tan_rsq, tan_P15, tan_P14 nop.i 999}{ .mfi nop.m 999(p8) fma.s1 tan_v4 = tan_rsq, tan_P1, tan_P0 nop.i 999 ;;
}
{ .mfi nop.m 999(p8) fma.s1 tan_v16 = tan_rsq, tan_P13, tan_P12 nop.i 999 }{ .mfi nop.m 999(p8) fma.s1 tan_v17 = tan_rsq, tan_rsq, f0 nop.i 999 ;;
}
{ .mfi nop.m 999(p8) fma.s1 tan_v12 = tan_rsq, tan_P9, tan_P8 nop.i 999 }{ .mfi nop.m 999(p8) fma.s1 tan_v13 = tan_rsq, tan_P11, tan_P10 nop.i 999 ;;
}
{ .mfi nop.m 999(p8) fma.s1 tan_v7 = tan_rsq, tan_P5, tan_P4 nop.i 999 }{ .mfi nop.m 999(p8) fma.s1 tan_v8 = tan_rsq, tan_P7, tan_P6 nop.i 999 ;;
}
{ .mfi nop.m 999(p9) fnma.s1 tan_d = tan_r, tan_y0, f1 nop.i 999 }{ .mfi nop.m 999(p8) fma.s1 tan_v5 = tan_rsq, tan_P3, tan_P2 nop.i 999 ;;
}
{ .mfi nop.m 999(p9) fma.s1 tan_z11 = tan_rsq, tan_Q9, tan_Q8 nop.i 999}{ .mfi nop.m 999(p9) fma.s1 tan_z12 = tan_rsq, tan_rsq, f0 nop.i 999 ;;
}
{ .mfi nop.m 999(p8) fma.s1 tan_v15 = tan_v17, tan_v18, tan_v16 nop.i 999 }{ .mfi nop.m 999(p9) fma.s1 tan_z7 = tan_rsq, tan_Q5, tan_Q4 nop.i 999 ;;
}
{ .mfi nop.m 999(p8) fma.s1 tan_v11 = tan_v17, tan_v13, tan_v12 nop.i 999}{ .mfi nop.m 999(p9) fma.s1 tan_z8 = tan_rsq, tan_Q7, tan_Q6 nop.i 999 ;;
}
{ .mfi nop.m 999(p8) fma.s1 tan_v14 = tan_v17, tan_v17, f0 nop.i 999 }{ .mfi nop.m 999(p9) fma.s1 tan_z3 = tan_rsq, tan_Q1, tan_Q0 nop.i 999 ;;
}
{ .mfi nop.m 999(p8) fma.s1 tan_v3 = tan_v17, tan_v5, tan_v4 nop.i 999}{ .mfi nop.m 999(p8) fma.s1 tan_v6 = tan_v17, tan_v8, tan_v7 nop.i 999 ;;
}
{ .mfi nop.m 999(p9) fma.s1 tan_y1 = tan_y0, tan_d, tan_y0 nop.i 999 }{ .mfi nop.m 999(p9) fma.s1 tan_dsq = tan_d, tan_d, f0 nop.i 999 ;;
}
{ .mfi nop.m 999(p9) fma.s1 tan_z10 = tan_z12, tan_Q10, tan_z11 nop.i 999 }{ .mfi nop.m 999(p9) fma.s1 tan_z9 = tan_z12, tan_z12,f0 nop.i 999 ;;
}
{ .mfi nop.m 999(p9) fma.s1 tan_z4 = tan_rsq, tan_Q3, tan_Q2 nop.i 999 }{ .mfi nop.m 999(p9) fma.s1 tan_z6 = tan_z12, tan_z8, tan_z7 nop.i 999 ;;
}
{ .mfi nop.m 999(p8) fma.s1 tan_v10 = tan_v14, tan_v15, tan_v11 nop.i 999 ;;
}
{ .mfi nop.m 999(p9) fma.s1 tan_y2 = tan_y1, tan_d, tan_y0 nop.i 999 }{ .mfi nop.m 999(p9) fma.s1 tan_d4 = tan_dsq, tan_dsq, tan_d nop.i 999 ;;
}
{ .mfi nop.m 999(p8) fma.s1 tan_v2 = tan_v14, tan_v6, tan_v3 nop.i 999}{ .mfi nop.m 999(p8) fma.s1 tan_v9 = tan_v14, tan_v14, f0 nop.i 999 ;;
}
{ .mfi nop.m 999(p9) fma.s1 tan_z2 = tan_z12, tan_z4, tan_z3 nop.i 999 }{ .mfi nop.m 999(p9) fma.s1 tan_z5 = tan_z9, tan_z10, tan_z6 nop.i 999 ;;
}
{ .mfi nop.m 999(p9) fma.s1 tan_inv_r = tan_d4, tan_y2, tan_y0 nop.i 999 }{ .mfi nop.m 999(p8) fma.s1 tan_rcube = tan_rsq, tan_r, f0 nop.i 999 ;;
}
{ .mfi nop.m 999(p8) fma.s1 tan_v1 = tan_v9, tan_v10, tan_v2 nop.i 999 }{ .mfi nop.m 999(p9) fma.s1 tan_z1 = tan_z9, tan_z5, tan_z2 nop.i 999 ;;
}
{ .mfi nop.m 999(p8) fma.d.s0 f8 = tan_v1, tan_rcube, tan_r nop.i 999 }{ .mfb nop.m 999(p9) fms.d.s0 f8 = tan_r, tan_z1, tan_inv_r br.ret.sptk b0 ;;
}.endp tan#
.proc __libm_callout__libm_callout:TAN_DBX: .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{ .mfb nop.m 999 nop.f 999(p0) br.call.sptk.many b0=__libm_tan# ;;
}
{ .mfi mov gp = GR_SAVE_GP fnorm.d f8 = f8 mov b0 = GR_SAVE_B0 };;
{ .mib nop.m 999 mov ar.pfs = GR_SAVE_PFS br.ret.sptk b0;;
}
.endp __libm_callout
.type __libm_tan#,@function
.global __libm_tan#
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