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glibc/sysdeps/ia64/fpu/s_atan.S
Siddhesh Poyarekar 30891f35fa Remove "Contributed by" lines 
We stopped adding "Contributed by" or similar lines in sources in 2012
in favour of git logs and keeping the Contributors section of the
glibc manual up to date.  Removing these lines makes the license
header a bit more consistent across files and also removes the
possibility of error in attribution when license blocks or files are
copied across since the contributed-by lines don't actually reflect
reality in those cases.

Move all "Contributed by" and similar lines (Written by, Test by,
etc.) into a new file CONTRIBUTED-BY to retain record of these
contributions.  These contributors are also mentioned in
manual/contrib.texi, so we just maintain this additional record as a
courtesy to the earlier developers.

The following scripts were used to filter a list of files to edit in
place and to clean up the CONTRIBUTED-BY file respectively.  These
were not added to the glibc sources because they're not expected to be
of any use in future given that this is a one time task:

https://gist.github.com/siddhesh/b5ecac94eabfd72ed2916d6d8157e7dc
https://gist.github.com/siddhesh/15ea1f5e435ace9774f485030695ee02

Reviewed-by: Carlos O'Donell <carlos@redhat.com>
2021-09-03 22:06:44 +05:30

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.file "atan.s"
// Copyright (c) 2000 - 2003, Intel Corporation
// All rights reserved.
//
//
// 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
// 04/13/00 Improved speed
// 04/19/00 Removed the qualifying predicate from the fmerge.s that
// takes the absolute value.
// 06/16/00 Reassigned FP registers to eliminate stalls on loads
// 08/30/00 Saved 5 cycles in main path by rearranging large argument logic
// and delaying use of result of fcmp in load by 1 group
// 05/20/02 Cleaned up namespace and sf0 syntax
// 08/20/02 Use atan2 algorithm with x=1 for better accuracy
// 02/06/03 Reordered header: .section, .global, .proc, .align
//
// API
//==============================================================
// double atan(double Y)
//
// Overview of operation
//==============================================================
//
// The atan function returns values in the interval [-pi/2,+pi/2].
//
// The algorithm used is the atan2(Y,X) algorithm where we fix X=1.0.
//
// There are two basic paths: swap true and swap false.
// atan2(Y,X) ==> atan2(V/U) where U >= V. If Y > X, we must swap.
//
// p6 swap True |Y| > |X|
// p7 swap False |Y| <= |X|
//
//
// Simple trigonometric identities show
// Region 1
// |Y|<=1.0, V=Y, U=1.0 atan2(Y,X) = sgnY * (0 + atan(V/U))
//
// Region 2
// |Y|>1.0, V=1.0, U=Y atan2(Y,X) = sgnY * (pi/2 - atan(V/U))
//
//
// We compute atan(V/U) from the identity
// atan(z) + atan([(V/U)-z] / [1+(V/U)z])
// where z is a limited precision approximation (16 bits) to V/U
//
// z is calculated with the assistance of the frcpa instruction.
//
// atan(z) is calculated by a polynomial z + z^3 * p(w), w=z^2
// where p(w) = P0+P1*w+...+P22*w^22
//
// Let d = [(V/U)-z] / [1+(V/U)z]) = (V-U*z)/(U+V*z)
//
// Approximate atan(d) by d + P0*d^3
// Let F = 1/(U+V*z) * (1-a), where |a|< 2^-8.8.
// Compute q(a) = 1 + a + ... + a^5.
// Then F*q(a) approximates the reciprocal to more than 50 bits.
// Special values
//==============================================================
// atan(QNAN) = QNAN
// atan(SNAN) = quieted SNAN
// atan(+-inf) = +- pi/2
// atan(+-0) = +-0
// Registers used
//==============================================================
// predicate registers used:
// p6 -> p15
// floating-point registers used:
// f8, input
// f32 -> f116
// general registers used
// r14 -> r16
// Assembly macros
//==============================================================
EXP_AD_P1 = r14
EXP_AD_P2 = r15
rsig_near_one = r16
atan2_Y = f8
atan2_X = f1
atan2_u1_X = f32
atan2_u1_Y = f33
atan2_z2_X = f34
atan2_two = f36
atan2_B1sq_Y = f37
atan2_z1_X = f38
atan2_B1X = f40
atan2_B1Y = f41
atan2_wp_X = f42
atan2_B1sq_X = f43
atan2_z = f44
atan2_w = f45
atan2_P0 = f46
atan2_P1 = f47
atan2_P2 = f48
atan2_P3 = f49
atan2_P4 = f50
atan2_P5 = f51
atan2_P6 = f52
atan2_P7 = f53
atan2_P8 = f54
atan2_P9 = f55
atan2_P10 = f56
atan2_P11 = f57
atan2_P12 = f58
atan2_P13 = f59
atan2_P14 = f60
atan2_P15 = f61
atan2_P16 = f62
atan2_P17 = f63
atan2_P18 = f64
atan2_P19 = f65
atan2_P20 = f66
atan2_P21 = f67
atan2_P22 = f68
atan2_pi_by_2 = f69
atan2_sgn_pi_by_2 = f69
atan2_V13 = f70
atan2_W11 = f71
atan2_E = f72
atan2_wp_Y = f73
atan2_V11 = f74
atan2_V12 = f75
atan2_V7 = f76
atan2_V8 = f77
atan2_W7 = f78
atan2_W8 = f79
atan2_W3 = f80
atan2_W4 = f81
atan2_V3 = f82
atan2_V4 = f83
atan2_F = f84
atan2_gV = f85
atan2_V10 = f86
atan2_zcub = f87
atan2_V6 = f88
atan2_V9 = f89
atan2_W10 = f90
atan2_W6 = f91
atan2_W2 = f92
atan2_V2 = f93
atan2_alpha = f94
atan2_alpha_1 = f95
atan2_gVF = f96
atan2_V5 = f97
atan2_W12 = f98
atan2_W5 = f99
atan2_alpha_sq = f100
atan2_Cp = f101
atan2_V1 = f102
atan2_ysq = f103
atan2_W1 = f104
atan2_alpha_cub = f105
atan2_C = f106
atan2_d = f108
atan2_A_hi = f109
atan2_dsq = f110
atan2_pd = f111
atan2_A_lo = f112
atan2_A = f113
atan2_Pp = f114
atan2_sgnY = f115
atan2_sig_near_one = f116
atan2_near_one = f116
/////////////////////////////////////////////////////////////
RODATA
.align 16
LOCAL_OBJECT_START(atan2_tb1)
data8 0xA21922DC45605EA1 , 0x00003FFA // P11
data8 0xB199DD6D2675C40F , 0x0000BFFA // P10
data8 0xC2F01E5DDD100DBE , 0x00003FFA // P9
data8 0xD78F28FC2A592781 , 0x0000BFFA // P8
data8 0xF0F03ADB3FC930D3 , 0x00003FFA // P7
data8 0x88887EBB209E3543 , 0x0000BFFB // P6
data8 0x9D89D7D55C3287A5 , 0x00003FFB // P5
data8 0xBA2E8B9793955C77 , 0x0000BFFB // P4
data8 0xE38E38E320A8A098 , 0x00003FFB // P3
data8 0x9249249247E37913 , 0x0000BFFC // P2
data8 0xCCCCCCCCCCC906CD , 0x00003FFC // P1
data8 0xAAAAAAAAAAAAA8A9 , 0x0000BFFD // P0
data8 0x0000000000000000 , 0x00000000 // pad to avoid bank conflict
LOCAL_OBJECT_END(atan2_tb1)
LOCAL_OBJECT_START(atan2_tb2)
data8 0xCE585A259BD8374C , 0x00003FF0 // P21
data8 0x9F90FB984D8E39D0 , 0x0000BFF3 // P20
data8 0x9D3436AABE218776 , 0x00003FF5 // P19
data8 0xDEC343E068A6D2A8 , 0x0000BFF6 // P18
data8 0xF396268151CFB11C , 0x00003FF7 // P17
data8 0xD818B4BB43D84BF2 , 0x0000BFF8 // P16
data8 0xA2270D30A90AA220 , 0x00003FF9 // P15
data8 0xD5F4F2182E7A8725 , 0x0000BFF9 // P14
data8 0x80D601879218B53A , 0x00003FFA // P13
data8 0x9297B23CCFFB291F , 0x0000BFFA // P12
data8 0xFE7E52D2A89995B3 , 0x0000BFEC // P22
data8 0xC90FDAA22168C235 , 0x00003FFF // pi/2
LOCAL_OBJECT_END(atan2_tb2)
.section .text
GLOBAL_LIBM_ENTRY(atan)
{ .mfi
nop.m 999
frcpa.s1 atan2_u1_Y,p7 = f1,atan2_Y
nop.i 999
}
{ .mfi
addl EXP_AD_P1 = @ltoff(atan2_tb1), gp
fma.s1 atan2_two = f1,f1,f1
nop.i 999
;;
}
{ .mfi
ld8 EXP_AD_P1 = [EXP_AD_P1]
frcpa.s1 atan2_u1_X,p6 = f1,atan2_X
nop.i 999
}
{ .mfi
nop.m 999
fma.s1 atan2_ysq = atan2_Y,atan2_Y,f0
nop.i 999
}
;;
{ .mfi
add EXP_AD_P2 = 0xd0,EXP_AD_P1
fmerge.s atan2_sgnY = atan2_Y,f1
nop.i 999
}
;;
{ .mfi
ldfe atan2_P11 = [EXP_AD_P1],16
fclass.m p10,p0 = atan2_Y, 0xc3 // Test for y=nan
nop.i 999
}
{ .mfi
ldfe atan2_P21 = [EXP_AD_P2],16
nop.f 999
nop.i 999
;;
}
{ .mfi
ldfe atan2_P10 = [EXP_AD_P1],16
fnma.s1 atan2_B1Y = atan2_u1_Y, atan2_Y, atan2_two
nop.i 999
}
{ .mfi
ldfe atan2_P20 = [EXP_AD_P2],16
fma.s1 atan2_wp_Y = atan2_u1_Y, atan2_u1_Y, f0
nop.i 999
;;
}
{ .mfi
ldfe atan2_P9 = [EXP_AD_P1],16
fma.s1 atan2_z1_X = atan2_u1_X, atan2_Y, f0
nop.i 999
}
{ .mfi
ldfe atan2_P19 = [EXP_AD_P2],16
fnma.s1 atan2_B1X = atan2_u1_X, atan2_X, atan2_two
nop.i 999
}
;;
{ .mfi
ldfe atan2_P8 = [EXP_AD_P1],16
fma.s1 atan2_z2_X = atan2_u1_X, atan2_ysq, f0
nop.i 999
}
{ .mfb
ldfe atan2_P18 = [EXP_AD_P2],16
(p10) fma.d.s0 f8 = atan2_Y,atan2_X,f0 // If y=nan, result quietized y
(p10) br.ret.spnt b0 // Exit if y=nan
}
;;
// p6 true if swap, means |y| > 1.0 or ysq > 1.0
// p7 true if no swap, means 1.0 >= |y| or 1.0 >= ysq
{ .mfi
ldfe atan2_P7 = [EXP_AD_P1],16
fcmp.ge.s1 p7,p6 = f1, atan2_ysq
nop.i 999
}
{ .mmf
ldfe atan2_P17 = [EXP_AD_P2],16
nop.m 999
nop.f 999
}
;;
{ .mfi
ldfe atan2_P6 = [EXP_AD_P1],16
fma.s1 atan2_E = atan2_u1_Y, atan2_B1Y, atan2_Y
nop.i 999
}
{ .mfi
ldfe atan2_P16 = [EXP_AD_P2],16
fma.s1 atan2_B1sq_Y = atan2_B1Y, atan2_B1Y, f0
nop.i 999
;;
}
{ .mfi
ldfe atan2_P5 = [EXP_AD_P1],16
(p7) fma.s1 atan2_wp_X = atan2_z1_X, atan2_z1_X, f0
nop.i 999
}
{ .mfi
ldfe atan2_P15 = [EXP_AD_P2],16
(p7) fma.s1 atan2_B1sq_X = atan2_B1X, atan2_B1X, f0
nop.i 999
;;
}
{ .mfi
ldfe atan2_P4 = [EXP_AD_P1],16
(p6) fma.s1 atan2_z = atan2_u1_Y, atan2_B1Y, f0
nop.i 999
}
{ .mfi
ldfe atan2_P14 = [EXP_AD_P2],16
(p7) fma.s1 atan2_E = atan2_z2_X, atan2_B1X, atan2_X
nop.i 999
;;
}
{ .mfi
ldfe atan2_P3 = [EXP_AD_P1],16
fcmp.eq.s0 p14,p15=atan2_X,atan2_Y // Dummy for denorm and invalid
nop.i 999
}
{ .mmf
ldfe atan2_P13 = [EXP_AD_P2],16
nop.m 999
(p7) fma.s1 atan2_z = atan2_z1_X, atan2_B1X, f0
;;
}
{ .mfi
ldfe atan2_P2 = [EXP_AD_P1],16
(p6) fma.s1 atan2_w = atan2_wp_Y, atan2_B1sq_Y,f0
nop.i 999
}
{ .mlx
ldfe atan2_P12 = [EXP_AD_P2],16
movl rsig_near_one = 0x8000000000000001 // signif near 1.0
;;
}
{ .mfi
ldfe atan2_P1 = [EXP_AD_P1],16
fclass.m p9,p0 = atan2_Y, 0x23 // test if y inf
nop.i 999
}
{ .mfi
ldfe atan2_P22 = [EXP_AD_P2],16
(p7) fma.s1 atan2_w = atan2_wp_X, atan2_B1sq_X,f0
nop.i 999
;;
}
{ .mfi
ldfe atan2_P0 = [EXP_AD_P1],16
frcpa.s1 atan2_F,p0 = f1, atan2_E
nop.i 999
}
{ .mfi
ldfe atan2_pi_by_2 = [EXP_AD_P2],16
(p6) fnma.s1 atan2_gV = atan2_Y, atan2_z, atan2_X
nop.i 999
;;
}
{ .mfi
setf.sig atan2_sig_near_one = rsig_near_one
(p7) fnma.s1 atan2_gV = atan2_X, atan2_z, atan2_Y
nop.i 999
}
{ .mfb
nop.m 999
(p9) fma.d.s0 f8 = atan2_sgnY, atan2_pi_by_2, f0 // +-pi/2 if y inf
(p9) br.ret.spnt b0 // exit if y inf, result is +-pi/2
;;
}
{ .mfi
nop.m 999
fma.s1 atan2_V13 = atan2_w, atan2_P11, atan2_P10
nop.i 999
}
{ .mfi
nop.m 999
fma.s1 atan2_W11 = atan2_w, atan2_P21, atan2_P20
nop.i 999
;;
}
{ .mfi
nop.m 999
fma.s1 atan2_V11 = atan2_w, atan2_P9, atan2_P8
nop.i 999
}
{ .mfi
nop.m 999
fma.s1 atan2_V12 = atan2_w, atan2_w, f0
nop.i 999
;;
}
{ .mfi
nop.m 999
fma.s1 atan2_V8 = atan2_w, atan2_P7 , atan2_P6
nop.i 999
}
{ .mfi
nop.m 999
fma.s1 atan2_W8 = atan2_w, atan2_P19, atan2_P18
nop.i 999
;;
}
{ .mfi
nop.m 999
fnma.s1 atan2_alpha = atan2_E, atan2_F, f1
nop.i 999
}
{ .mfi
nop.m 999
fnma.s1 atan2_alpha_1 = atan2_E, atan2_F, atan2_two
nop.i 999
;;
}
{ .mfi
nop.m 999
fma.s1 atan2_V7 = atan2_w, atan2_P5 , atan2_P4
nop.i 999
}
{ .mfi
nop.m 999
fma.s1 atan2_W7 = atan2_w, atan2_P17, atan2_P16
nop.i 999
;;
}
{ .mfi
nop.m 999
fma.s1 atan2_V4 = atan2_w, atan2_P3 , atan2_P2
nop.i 999
}
{ .mfi
nop.m 999
fma.s1 atan2_W4 = atan2_w, atan2_P15, atan2_P14
nop.i 999
;;
}
{ .mfi
nop.m 999
fma.s1 atan2_V3 = atan2_w, atan2_P1 , atan2_P0
nop.i 999
}
{ .mfi
nop.m 999
fma.s1 atan2_W3 = atan2_w, atan2_P13, atan2_P12
nop.i 999
;;
}
{ .mfi
nop.m 999
fma.s1 atan2_V10 = atan2_V12, atan2_V13, atan2_V11
nop.i 999
}
{ .mfi
nop.m 999
fma.s1 atan2_gVF = atan2_gV, atan2_F, f0
nop.i 999
;;
}
{ .mfi
nop.m 999
fma.s1 atan2_alpha_sq = atan2_alpha, atan2_alpha, f0
nop.i 999
}
{ .mfi
nop.m 999
fma.s1 atan2_Cp = atan2_alpha, atan2_alpha_1, f1
nop.i 999
;;
}
{ .mfi
nop.m 999
fma.s1 atan2_V9 = atan2_V12, atan2_V12, f0
nop.i 999
}
{ .mfi
nop.m 999
fma.s1 atan2_W10 = atan2_V12, atan2_P22 , atan2_W11
nop.i 999
;;
}
{ .mfi
nop.m 999
fma.s1 atan2_V6 = atan2_V12, atan2_V8 , atan2_V7
nop.i 999
}
{ .mfi
nop.m 999
fma.s1 atan2_W6 = atan2_V12, atan2_W8 , atan2_W7
nop.i 999
;;
}
{ .mfi
nop.m 999
fma.s1 atan2_V2 = atan2_V12, atan2_V4 , atan2_V3
nop.i 999
}
{ .mfi
nop.m 999
fma.s1 atan2_W2 = atan2_V12, atan2_W4 , atan2_W3
nop.i 999
;;
}
{ .mfi
nop.m 999
fma.s1 atan2_alpha_cub = atan2_alpha, atan2_alpha_sq, f0
nop.i 999
}
{ .mfi
nop.m 999
fma.s1 atan2_C = atan2_gVF, atan2_Cp, f0
nop.i 999
;;
}
{ .mfi
nop.m 999
fma.s1 atan2_W12 = atan2_V9, atan2_V9, f0
nop.i 999
;;
}
{ .mfi
nop.m 999
fma.s1 atan2_V5 = atan2_V9, atan2_V10, atan2_V6
nop.i 999
}
{ .mfi
nop.m 999
fma.s1 atan2_W5 = atan2_V9, atan2_W10, atan2_W6
nop.i 999
;;
}
{ .mfi
nop.m 999
fclass.m p8,p0 = atan2_Y, 0x07 // Test for y=0
nop.i 999
}
{ .mfi
nop.m 999
fma.s1 atan2_d = atan2_alpha_cub, atan2_C, atan2_C
nop.i 999
}
;;
{ .mfi
nop.m 999
fma.s1 atan2_W12 = atan2_V9, atan2_W12, f0
nop.i 999
}
;;
{ .mfi
nop.m 999
fma.s1 atan2_V1 = atan2_V9, atan2_V5, atan2_V2
nop.i 999
}
{ .mfi
nop.m 999
fma.s1 atan2_W1 = atan2_V9, atan2_W5, atan2_W2
nop.i 999
;;
}
{ .mfi
nop.m 999
(p8) fmerge.s f8 = atan2_sgnY, f0 // +-0 if y=0
nop.i 999
}
{ .mfb
nop.m 999
fma.s1 atan2_zcub = atan2_z, atan2_w, f0
(p8) br.ret.spnt b0 // Exit if y=0
;;
}
{ .mfi
nop.m 999
fma.s1 atan2_pd = atan2_P0, atan2_d, f0
nop.i 999
}
{ .mfi
nop.m 999
fma.s1 atan2_dsq = atan2_d, atan2_d, f0
nop.i 999
;;
}
{ .mfi
nop.m 999
fmerge.se atan2_near_one = f1, atan2_sig_near_one // Const ~1.0
nop.i 999
}
{ .mfi
nop.m 999
fma.s1 atan2_Pp = atan2_W12, atan2_W1, atan2_V1
nop.i 999
;;
}
{ .mfi
nop.m 999
fma.s1 atan2_sgn_pi_by_2 = atan2_pi_by_2, atan2_sgnY, f0
nop.i 999
}
{ .mfi
nop.m 999
fma.s1 atan2_A_lo = atan2_pd, atan2_dsq, atan2_d
nop.i 999
;;
}
{ .mfi
nop.m 999
fma.s1 atan2_A_hi = atan2_zcub, atan2_Pp, atan2_z
nop.i 999
;;
}
{ .mfi
nop.m 999
(p6) fma.s1 atan2_A = atan2_A_hi, f1, atan2_A_lo
nop.i 999
}
// For |Y| <= |X| and X > 0, result is A_hi + A_lo
{ .mfi
nop.m 999
(p7) fma.d.s0 f8 = atan2_A_hi, f1, atan2_A_lo
nop.i 999
;;
}
// For |Y| > |X|, result is +- pi/2 - (A_hi + A_lo)
// We perturb A by multiplying by 1.0+1ulp as we produce the result
// in order to get symmetrically rounded results in directed rounding modes.
// If we don't do this, there are a few cases where the trailing 11 bits of
// the significand of the result, before converting to double, are zero. These
// cases do not round symmetrically in round to +infinity or round to -infinity.
{ .mfb
nop.m 999
(p6) fnma.d.s0 f8 = atan2_A, atan2_near_one, atan2_sgn_pi_by_2
br.ret.sptk b0
;;
}
GLOBAL_LIBM_END(atan)
libm_alias_double_other (atan, atan)
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