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glibc/sysdeps/ia64/fpu/s_tan.S

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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.
//
// 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://developer.intel.com/opensource.
//
// History
//==============================================================
// 2/02/00: Initial version
// 4/04/00 Unwind support added
// 12/27/00 Improved speed
//
// 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
//
#include "libm_support.h"
// Assembly macros
//==============================================================
TAN_INV_PI_BY_2_2TO64 = f10
TAN_RSHF_2TO64 = f11
TAN_2TOM64 = f12
TAN_RSHF = f13
TAN_W_2TO64_RSH = f14
TAN_NFLOAT = f15
tan_Inv_Pi_by_2 = f32
tan_Pi_by_2_hi = f33
tan_Pi_by_2_lo = f34
tan_P0 = f35
tan_P1 = f36
tan_P2 = f37
tan_P3 = f38
tan_P4 = f39
tan_P5 = f40
tan_P6 = f41
tan_P7 = f42
tan_P8 = f43
tan_P9 = f44
tan_P10 = f45
tan_P11 = f46
tan_P12 = f47
tan_P13 = f48
tan_P14 = f49
tan_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 = f59
tan_Q9 = f60
tan_Q10 = f61
tan_r = f62
tan_rsq = f63
tan_rcube = f64
tan_v18 = f65
tan_v16 = f66
tan_v17 = f67
tan_v12 = f68
tan_v13 = f69
tan_v7 = f70
tan_v8 = f71
tan_v4 = f72
tan_v5 = f73
tan_v15 = f74
tan_v11 = f75
tan_v14 = f76
tan_v3 = f77
tan_v6 = f78
tan_v10 = f79
tan_v2 = f80
tan_v9 = f81
tan_v1 = f82
tan_int_Nfloat = f83
tan_Nfloat = f84
tan_NORM_f8 = f85
tan_W = f86
tan_y0 = f87
tan_d = f88
tan_y1 = f89
tan_dsq = f90
tan_y2 = f91
tan_d4 = f92
tan_inv_r = f93
tan_z1 = f94
tan_z2 = f95
tan_z3 = f96
tan_z4 = f97
tan_z5 = f98
tan_z6 = f99
tan_z7 = f100
tan_z8 = f101
tan_z9 = f102
tan_z10 = f103
tan_z11 = f104
tan_z12 = f105
/////////////////////////////////////////////////////////////
tan_GR_sig_inv_pi_by_2 = r14
tan_GR_rshf_2to64 = r15
tan_GR_exp_2tom64 = r16
tan_GR_n = r17
tan_GR_rshf = r18
tan_AD = r33
tan_GR_10009 = r34
tan_GR_17_ones = r35
tan_GR_N_odd_even = r36
tan_GR_N = r37
tan_signexp = r38
tan_exp = r39
tan_ADQ = r40
GR_SAVE_PFS = r41
GR_SAVE_B0 = r42
GR_SAVE_GP = r43
#ifdef _LIBC
.rodata
#else
.data
#endif
.align 16
double_tan_constants:
ASM_TYPE_DIRECTIVE(double_tan_constants,@object)
// 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
ASM_SIZE_DIRECTIVE(double_tan_constants)
double_Q_tan_constants:
ASM_TYPE_DIRECTIVE(double_Q_tan_constants,@object)
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
ASM_SIZE_DIRECTIVE(double_Q_tan_constants)
.align 32
.global tan#
#ifdef _LIBC
.global __tan#
#endif
////////////////////////////////////////////////////////
.section .text
.proc tan#
#ifdef _LIBC
.proc __tan#
#endif
.align 32
tan:
#ifdef _LIBC
__tan:
#endif
// 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 L(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#
ASM_SIZE_DIRECTIVE(tan)
.proc __libm_callout
__libm_callout:
L(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
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
ASM_SIZE_DIRECTIVE(__libm_callout)
.type __libm_tan#,@function
.global __libm_tan#
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