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736 lines
17 KiB
736 lines
17 KiB
.file "tan.s"
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// Copyright (c) 2000, 2001, Intel Corporation
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// All rights reserved.
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//
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// Contributed 2/2/2000 by John Harrison, Ted Kubaska, Bob Norin, Shane Story,
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// and Ping Tak Peter Tang of the Computational Software Lab, Intel Corporation.
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//
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// WARRANTY DISCLAIMER
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//
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
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// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
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// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
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// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
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// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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//
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// Intel Corporation is the author of this code, and requests that all
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// problem reports or change requests be submitted to it directly at
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// http://developer.intel.com/opensource.
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//
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// History
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//==============================================================
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// 2/02/00: Initial version
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// 4/04/00 Unwind support added
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// 12/27/00 Improved speed
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// 02/21/01 Updated to call tanl
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//
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// API
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//==============================================================
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// double tan( double x);
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//
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// Overview of operation
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//==============================================================
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// If the input value in radians is |x| >= 1.xxxxx 2^10 call the
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// older slower version.
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//
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// The new algorithm is used when |x| <= 1.xxxxx 2^9.
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//
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// Represent the input X as Nfloat * pi/2 + r
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// where r can be negative and |r| <= pi/4
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//
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// tan_W = x * 2/pi
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// Nfloat = round_int(tan_W)
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//
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// tan_r = x - Nfloat * (pi/2)_hi
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// tan_r = tan_r - Nfloat * (pi/2)_lo
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//
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// We have two paths: p8, when Nfloat is even and p9. when Nfloat is odd.
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// p8: tan(X) = tan(r)
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// p9: tan(X) = -cot(r)
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//
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// Each is evaluated as a series. The p9 path requires 1/r.
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//
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// The coefficients used in the series are stored in a table as
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// are the pi constants.
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//
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// Registers used
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//==============================================================
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//
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// predicate registers used:
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// p6-10
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//
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// floating-point registers used:
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// f10-15, f32-105
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// f8, input
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//
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// general registers used
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// r14-18, r32-43
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//
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// Assembly macros
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//==============================================================
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TAN_INV_PI_BY_2_2TO64 = f10
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TAN_RSHF_2TO64 = f11
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TAN_2TOM64 = f12
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TAN_RSHF = f13
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TAN_W_2TO64_RSH = f14
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TAN_NFLOAT = f15
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tan_Inv_Pi_by_2 = f32
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tan_Pi_by_2_hi = f33
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tan_Pi_by_2_lo = f34
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tan_P0 = f35
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tan_P1 = f36
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tan_P2 = f37
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tan_P3 = f38
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tan_P4 = f39
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tan_P5 = f40
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tan_P6 = f41
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tan_P7 = f42
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tan_P8 = f43
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tan_P9 = f44
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tan_P10 = f45
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tan_P11 = f46
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tan_P12 = f47
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tan_P13 = f48
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tan_P14 = f49
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tan_P15 = f50
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tan_Q0 = f51
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tan_Q1 = f52
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tan_Q2 = f53
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tan_Q3 = f54
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tan_Q4 = f55
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tan_Q5 = f56
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tan_Q6 = f57
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tan_Q7 = f58
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tan_Q8 = f59
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tan_Q9 = f60
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tan_Q10 = f61
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tan_r = f62
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tan_rsq = f63
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tan_rcube = f64
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tan_v18 = f65
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tan_v16 = f66
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tan_v17 = f67
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tan_v12 = f68
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tan_v13 = f69
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tan_v7 = f70
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tan_v8 = f71
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tan_v4 = f72
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tan_v5 = f73
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tan_v15 = f74
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tan_v11 = f75
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tan_v14 = f76
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tan_v3 = f77
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tan_v6 = f78
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tan_v10 = f79
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tan_v2 = f80
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tan_v9 = f81
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tan_v1 = f82
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tan_int_Nfloat = f83
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tan_Nfloat = f84
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tan_NORM_f8 = f85
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tan_W = f86
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tan_y0 = f87
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tan_d = f88
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tan_y1 = f89
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tan_dsq = f90
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tan_y2 = f91
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tan_d4 = f92
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tan_inv_r = f93
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tan_z1 = f94
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tan_z2 = f95
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tan_z3 = f96
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tan_z4 = f97
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tan_z5 = f98
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tan_z6 = f99
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tan_z7 = f100
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tan_z8 = f101
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tan_z9 = f102
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tan_z10 = f103
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tan_z11 = f104
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tan_z12 = f105
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/////////////////////////////////////////////////////////////
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tan_GR_sig_inv_pi_by_2 = r14
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tan_GR_rshf_2to64 = r15
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tan_GR_exp_2tom64 = r16
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tan_GR_n = r17
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tan_GR_rshf = r18
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tan_AD = r33
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tan_GR_10009 = r34
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tan_GR_17_ones = r35
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tan_GR_N_odd_even = r36
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tan_GR_N = r37
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tan_signexp = r38
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tan_exp = r39
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tan_ADQ = r40
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GR_SAVE_PFS = r41
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GR_SAVE_B0 = r42
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GR_SAVE_GP = r43
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.data
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.align 16
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double_tan_constants:
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// data8 0xA2F9836E4E44152A, 0x00003FFE // 2/pi
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data8 0xC90FDAA22168C234, 0x00003FFF // pi/2 hi
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data8 0xBEEA54580DDEA0E1 // P14
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data8 0x3ED3021ACE749A59 // P15
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data8 0xBEF312BD91DC8DA1 // P12
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data8 0x3EFAE9AFC14C5119 // P13
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data8 0x3F2F342BF411E769 // P8
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data8 0x3F1A60FC9F3B0227 // P9
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data8 0x3EFF246E78E5E45B // P10
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data8 0x3F01D9D2E782875C // P11
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data8 0x3F8226E34C4499B6 // P4
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data8 0x3F6D6D3F12C236AC // P5
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data8 0x3F57DA1146DCFD8B // P6
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data8 0x3F43576410FE3D75 // P7
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data8 0x3FD5555555555555 // P0
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data8 0x3FC11111111111C2 // P1
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data8 0x3FABA1BA1BA0E850 // P2
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data8 0x3F9664F4886725A7 // P3
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double_Q_tan_constants:
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data8 0xC4C6628B80DC1CD1, 0x00003FBF // pi/2 lo
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data8 0x3E223A73BA576E48 // Q8
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data8 0x3DF54AD8D1F2CA43 // Q9
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data8 0x3EF66A8EE529A6AA // Q4
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data8 0x3EC2281050410EE6 // Q5
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data8 0x3E8D6BB992CC3CF5 // Q6
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data8 0x3E57F88DE34832E4 // Q7
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data8 0x3FD5555555555555 // Q0
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data8 0x3F96C16C16C16DB8 // Q1
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data8 0x3F61566ABBFFB489 // Q2
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data8 0x3F2BBD77945C1733 // Q3
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data8 0x3D927FB33E2B0E04 // Q10
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.align 32
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.global tan#
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////////////////////////////////////////////////////////
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.section .text
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.proc tan#
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.align 32
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tan:
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// The initial fnorm will take any unmasked faults and
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// normalize any single/double unorms
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{ .mlx
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alloc r32=ar.pfs,1,11,0,0
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movl tan_GR_sig_inv_pi_by_2 = 0xA2F9836E4E44152A // significand of 2/pi
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}
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{ .mlx
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addl tan_AD = @ltoff(double_tan_constants), gp
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movl tan_GR_rshf_2to64 = 0x47e8000000000000 // 1.1000 2^(63+63+1)
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}
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;;
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{ .mfi
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ld8 tan_AD = [tan_AD]
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fnorm tan_NORM_f8 = f8
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mov tan_GR_exp_2tom64 = 0xffff-64 // exponent of scaling factor 2^-64
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}
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{ .mlx
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nop.m 999
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movl tan_GR_rshf = 0x43e8000000000000 // 1.1000 2^63 for right shift
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}
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;;
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// Form two constants we need
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// 2/pi * 2^1 * 2^63, scaled by 2^64 since we just loaded the significand
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// 1.1000...000 * 2^(63+63+1) to right shift int(W) into the significand
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{ .mmi
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setf.sig TAN_INV_PI_BY_2_2TO64 = tan_GR_sig_inv_pi_by_2
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setf.d TAN_RSHF_2TO64 = tan_GR_rshf_2to64
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mov tan_GR_17_ones = 0x1ffff ;;
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}
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// Form another constant
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// 2^-64 for scaling Nfloat
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// 1.1000...000 * 2^63, the right shift constant
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{ .mmf
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setf.exp TAN_2TOM64 = tan_GR_exp_2tom64
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adds tan_ADQ = double_Q_tan_constants - double_tan_constants, tan_AD
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fclass.m.unc p6,p0 = f8, 0x07 // Test for x=0
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}
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;;
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// Form another constant
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// 2^-64 for scaling Nfloat
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// 1.1000...000 * 2^63, the right shift constant
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{ .mmf
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setf.d TAN_RSHF = tan_GR_rshf
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ldfe tan_Pi_by_2_hi = [tan_AD],16
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fclass.m.unc p7,p0 = f8, 0x23 // Test for x=inf
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}
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;;
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{ .mfb
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ldfe tan_Pi_by_2_lo = [tan_ADQ],16
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fclass.m.unc p8,p0 = f8, 0xc3 // Test for x=nan
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(p6) br.ret.spnt b0 ;; // Exit for x=0
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}
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{ .mfi
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ldfpd tan_P14,tan_P15 = [tan_AD],16
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(p7) frcpa.s0 f8,p9=f0,f0 // Set qnan indef if x=inf
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mov tan_GR_10009 = 0x10009
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}
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{ .mib
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ldfpd tan_Q8,tan_Q9 = [tan_ADQ],16
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nop.i 999
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(p7) br.ret.spnt b0 ;; // Exit for x=inf
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}
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{ .mfi
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ldfpd tan_P12,tan_P13 = [tan_AD],16
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(p8) fma.d f8=f8,f1,f8 // Set qnan if x=nan
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nop.i 999
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}
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{ .mib
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ldfpd tan_Q4,tan_Q5 = [tan_ADQ],16
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nop.i 999
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(p8) br.ret.spnt b0 ;; // Exit for x=nan
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}
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{ .mmi
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getf.exp tan_signexp = tan_NORM_f8
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ldfpd tan_P8,tan_P9 = [tan_AD],16
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nop.i 999 ;;
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}
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// Multiply x by scaled 2/pi and add large const to shift integer part of W to
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// rightmost bits of significand
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{ .mfi
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ldfpd tan_Q6,tan_Q7 = [tan_ADQ],16
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fma.s1 TAN_W_2TO64_RSH = tan_NORM_f8,TAN_INV_PI_BY_2_2TO64,TAN_RSHF_2TO64
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nop.i 999 ;;
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}
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{ .mmi
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ldfpd tan_P10,tan_P11 = [tan_AD],16
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nop.m 999
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and tan_exp = tan_GR_17_ones, tan_signexp ;;
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}
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// p7 is true if we must call DBX TAN
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// p7 is true if f8 exp is > 0x10009 (which includes all ones
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// NAN or inf)
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{ .mmi
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ldfpd tan_Q0,tan_Q1 = [tan_ADQ],16
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cmp.ge.unc p7,p0 = tan_exp,tan_GR_10009
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nop.i 999 ;;
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}
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{ .mmb
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ldfpd tan_P4,tan_P5 = [tan_AD],16
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nop.m 999
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(p7) br.cond.spnt TAN_DBX ;;
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}
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{ .mmi
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ldfpd tan_Q2,tan_Q3 = [tan_ADQ],16
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nop.m 999
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nop.i 999 ;;
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}
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// TAN_NFLOAT = Round_Int_Nearest(tan_W)
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{ .mfi
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ldfpd tan_P6,tan_P7 = [tan_AD],16
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fms.s1 TAN_NFLOAT = TAN_W_2TO64_RSH,TAN_2TOM64,TAN_RSHF
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nop.i 999 ;;
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}
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{ .mfi
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ldfd tan_Q10 = [tan_ADQ]
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nop.f 999
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nop.i 999 ;;
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}
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{ .mfi
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ldfpd tan_P0,tan_P1 = [tan_AD],16
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nop.f 999
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nop.i 999 ;;
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}
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{ .mfi
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getf.sig tan_GR_n = TAN_W_2TO64_RSH
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nop.f 999
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nop.i 999 ;;
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}
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// tan_r = -tan_Nfloat * tan_Pi_by_2_hi + x
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{ .mfi
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ldfpd tan_P2,tan_P3 = [tan_AD]
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fnma.s1 tan_r = TAN_NFLOAT, tan_Pi_by_2_hi, tan_NORM_f8
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nop.i 999 ;;
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}
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// p8 ==> even
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// p9 ==> odd
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{ .mmi
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and tan_GR_N_odd_even = 0x1, tan_GR_n ;;
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nop.m 999
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cmp.eq.unc p8,p9 = tan_GR_N_odd_even, r0 ;;
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}
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// tan_r = tan_r -tan_Nfloat * tan_Pi_by_2_lo
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{ .mfi
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nop.m 999
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fnma.s1 tan_r = TAN_NFLOAT, tan_Pi_by_2_lo, tan_r
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nop.i 999 ;;
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}
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{ .mfi
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nop.m 999
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fma.s1 tan_rsq = tan_r, tan_r, f0
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nop.i 999 ;;
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}
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{ .mfi
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nop.m 999
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(p9) frcpa.s1 tan_y0, p10 = f1,tan_r
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nop.i 999 ;;
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}
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{ .mfi
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nop.m 999
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(p8) fma.s1 tan_v18 = tan_rsq, tan_P15, tan_P14
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nop.i 999
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}
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{ .mfi
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nop.m 999
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(p8) fma.s1 tan_v4 = tan_rsq, tan_P1, tan_P0
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nop.i 999 ;;
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}
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{ .mfi
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nop.m 999
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(p8) fma.s1 tan_v16 = tan_rsq, tan_P13, tan_P12
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nop.i 999
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}
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{ .mfi
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nop.m 999
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(p8) fma.s1 tan_v17 = tan_rsq, tan_rsq, f0
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nop.i 999 ;;
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}
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{ .mfi
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nop.m 999
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(p8) fma.s1 tan_v12 = tan_rsq, tan_P9, tan_P8
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nop.i 999
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}
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{ .mfi
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nop.m 999
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(p8) fma.s1 tan_v13 = tan_rsq, tan_P11, tan_P10
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nop.i 999 ;;
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}
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{ .mfi
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nop.m 999
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(p8) fma.s1 tan_v7 = tan_rsq, tan_P5, tan_P4
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nop.i 999
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}
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{ .mfi
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nop.m 999
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(p8) fma.s1 tan_v8 = tan_rsq, tan_P7, tan_P6
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nop.i 999 ;;
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}
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{ .mfi
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nop.m 999
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(p9) fnma.s1 tan_d = tan_r, tan_y0, f1
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nop.i 999
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}
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{ .mfi
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nop.m 999
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(p8) fma.s1 tan_v5 = tan_rsq, tan_P3, tan_P2
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nop.i 999 ;;
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}
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{ .mfi
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nop.m 999
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(p9) fma.s1 tan_z11 = tan_rsq, tan_Q9, tan_Q8
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nop.i 999
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}
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{ .mfi
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nop.m 999
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(p9) fma.s1 tan_z12 = tan_rsq, tan_rsq, f0
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nop.i 999 ;;
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}
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{ .mfi
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nop.m 999
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(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#
|