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glibc/sysdeps/ia64/fpu/libm_sincos.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 "libm_sincos.s"
// Copyright (c) 2002 - 2005, 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
//==============================================================
// 02/01/02 Initial version
// 02/18/02 Large arguments processing routine is excluded.
// External interface entry points are added
// 03/13/02 Corrected restore of predicate registers
// 03/19/02 Added stack unwind around call to __libm_cis_large
// 09/05/02 Work range is widened by reduction strengthen (3 parts of Pi/16)
// 02/10/03 Reordered header: .section, .global, .proc, .align
// 08/08/03 Improved performance
// 02/11/04 cis is moved to the separate file.
// 03/31/05 Reformatted delimiters between data tables
//
// API
//==============================================================
// 1) void sincos(double, double*s, double*c)
// 2) __libm_sincos - internal LIBM function, that accepts
// argument in f8 and returns cosine through f8, sine through f9
//
// Overview of operation
//==============================================================
//
// Step 1
// ======
// Reduce x to region -1/2*pi/2^k ===== 0 ===== +1/2*pi/2^k where k=4
// divide x by pi/2^k.
// Multiply by 2^k/pi.
// nfloat = Round result to integer (round-to-nearest)
//
// r = x - nfloat * pi/2^k
// Do this as ((((x - nfloat * HIGH(pi/2^k))) -
// nfloat * LOW(pi/2^k)) -
// nfloat * LOWEST(pi/2^k) for increased accuracy.
// pi/2^k is stored as two numbers that when added make pi/2^k.
// pi/2^k = HIGH(pi/2^k) + LOW(pi/2^k)
// HIGH and LOW parts are rounded to zero values,
// and LOWEST is rounded to nearest one.
//
// x = (nfloat * pi/2^k) + r
// r is small enough that we can use a polynomial approximation
// and is referred to as the reduced argument.
//
// Step 3
// ======
// Take the unreduced part and remove the multiples of 2pi.
// So nfloat = nfloat (with lower k+1 bits cleared) + lower k+1 bits
//
// nfloat (with lower k+1 bits cleared) is a multiple of 2^(k+1)
// N * 2^(k+1)
// nfloat * pi/2^k = N * 2^(k+1) * pi/2^k + (lower k+1 bits) * pi/2^k
// nfloat * pi/2^k = N * 2 * pi + (lower k+1 bits) * pi/2^k
// nfloat * pi/2^k = N2pi + M * pi/2^k
//
//
// Sin(x) = Sin((nfloat * pi/2^k) + r)
// = Sin(nfloat * pi/2^k) * Cos(r) + Cos(nfloat * pi/2^k) * Sin(r)
//
// Sin(nfloat * pi/2^k) = Sin(N2pi + Mpi/2^k)
// = Sin(N2pi)Cos(Mpi/2^k) + Cos(N2pi)Sin(Mpi/2^k)
// = Sin(Mpi/2^k)
//
// Cos(nfloat * pi/2^k) = Cos(N2pi + Mpi/2^k)
// = Cos(N2pi)Cos(Mpi/2^k) + Sin(N2pi)Sin(Mpi/2^k)
// = Cos(Mpi/2^k)
//
// Sin(x) = Sin(Mpi/2^k) Cos(r) + Cos(Mpi/2^k) Sin(r)
//
//
// Step 4
// ======
// 0 <= M < 2^(k+1)
// There are 2^(k+1) Sin entries in a table.
// There are 2^(k+1) Cos entries in a table.
//
// Get Sin(Mpi/2^k) and Cos(Mpi/2^k) by table lookup.
//
//
// Step 5
// ======
// Calculate Cos(r) and Sin(r) by polynomial approximation.
//
// Cos(r) = 1 + r^2 q1 + r^4 q2 + r^6 q3 + ... = Series for Cos
// Sin(r) = r + r^3 p1 + r^5 p2 + r^7 p3 + ... = Series for Sin
//
// and the coefficients q1, q2, ... and p1, p2, ... are stored in a table
//
//
// Calculate
// Sin(x) = Sin(Mpi/2^k) Cos(r) + Cos(Mpi/2^k) Sin(r)
//
// as follows
//
// S[m] = Sin(Mpi/2^k) and C[m] = Cos(Mpi/2^k)
// rsq = r*r
//
//
// P = p1 + r^2p2 + r^4p3 + r^6p4
// Q = q1 + r^2q2 + r^4q3 + r^6q4
//
// rcub = r * rsq
// Sin(r) = r + rcub * P
// = r + r^3p1 + r^5p2 + r^7p3 + r^9p4 + ... = Sin(r)
//
// The coefficients are not exactly these values, but almost.
//
// p1 = -1/6 = -1/3!
// p2 = 1/120 = 1/5!
// p3 = -1/5040 = -1/7!
// p4 = 1/362889 = 1/9!
//
// P = r + rcub * P
//
// Answer = S[m] Cos(r) + C[m] P
//
// Cos(r) = 1 + rsq Q
// Cos(r) = 1 + r^2 Q
// Cos(r) = 1 + r^2 (q1 + r^2q2 + r^4q3 + r^6q4)
// Cos(r) = 1 + r^2q1 + r^4q2 + r^6q3 + r^8q4 + ...
//
// S[m] Cos(r) = S[m](1 + rsq Q)
// S[m] Cos(r) = S[m] + S[m] rsq Q
// S[m] Cos(r) = S[m] + s_rsq Q
// Q = S[m] + s_rsq Q
//
// Then,
//
// Answer = Q + C[m] P
// Registers used
//==============================================================
// general input registers:
// r14 -> r39
// predicate registers used:
// p6 -> p14
//
// floating-point registers used
// f9 -> f15
// f32 -> f67
// Assembly macros
//==============================================================
cis_Arg = f8
cis_Sin_res = f9
cis_Cos_res = f8
cis_NORM_f8 = f10
cis_W = f11
cis_int_Nfloat = f12
cis_Nfloat = f13
cis_r = f14
cis_rsq = f15
cis_rcub = f32
cis_Inv_Pi_by_16 = f33
cis_Pi_by_16_hi = f34
cis_Pi_by_16_lo = f35
cis_Inv_Pi_by_64 = f36
cis_Pi_by_16_lowest = f37
cis_r_exact = f38
cis_P1 = f39
cis_Q1 = f40
cis_P2 = f41
cis_Q2 = f42
cis_P3 = f43
cis_Q3 = f44
cis_P4 = f45
cis_Q4 = f46
cis_P_temp1 = f47
cis_P_temp2 = f48
cis_Q_temp1 = f49
cis_Q_temp2 = f50
cis_P = f51
cis_SIG_INV_PI_BY_16_2TO61 = f52
cis_RSHF_2TO61 = f53
cis_RSHF = f54
cis_2TOM61 = f55
cis_NFLOAT = f56
cis_W_2TO61_RSH = f57
cis_tmp = f58
cis_Sm_sin = f59
cis_Cm_sin = f60
cis_Sm_cos = f61
cis_Cm_cos = f62
cis_srsq_sin = f63
cis_srsq_cos = f64
cis_Q_sin = f65
cis_Q_cos = f66
cis_Q = f67
/////////////////////////////////////////////////////////////
cis_pResSin = r33
cis_pResCos = r34
cis_GR_sig_inv_pi_by_16 = r14
cis_GR_rshf_2to61 = r15
cis_GR_rshf = r16
cis_GR_exp_2tom61 = r17
cis_GR_n = r18
cis_GR_n_sin = r19
cis_exp_limit = r20
cis_r_signexp = r21
cis_AD_1 = r22
cis_r_sincos = r23
cis_r_exp = r24
cis_r_17_ones = r25
cis_GR_m_sin = r26
cis_GR_32m_sin = r26
cis_GR_n_cos = r27
cis_GR_m_cos = r28
cis_GR_32m_cos = r28
cis_AD_2_sin = r29
cis_AD_2_cos = r30
cis_gr_tmp = r31
GR_SAVE_B0 = r35
GR_SAVE_GP = r36
rB0_SAVED = r37
GR_SAVE_PFS = r38
GR_SAVE_PR = r39
RODATA
.align 16
// Pi/16 parts
LOCAL_OBJECT_START(double_cis_pi)
data8 0xC90FDAA22168C234, 0x00003FFC // pi/16 1st part
data8 0xC4C6628B80DC1CD1, 0x00003FBC // pi/16 2nd part
data8 0xA4093822299F31D0, 0x00003F7A // pi/16 3rd part
LOCAL_OBJECT_END(double_cis_pi)
// Coefficients for polynomials
LOCAL_OBJECT_START(double_cis_pq_k4)
data8 0x3EC71C963717C63A // P4
data8 0x3EF9FFBA8F191AE6 // Q4
data8 0xBF2A01A00F4E11A8 // P3
data8 0xBF56C16C05AC77BF // Q3
data8 0x3F8111111110F167 // P2
data8 0x3FA555555554DD45 // Q2
data8 0xBFC5555555555555 // P1
data8 0xBFDFFFFFFFFFFFFC // Q1
LOCAL_OBJECT_END(double_cis_pq_k4)
// Sincos table (S[m], C[m])
LOCAL_OBJECT_START(double_sin_cos_beta_k4)
data8 0x0000000000000000 , 0x00000000 // sin( 0 pi/16) S0
data8 0x8000000000000000 , 0x00003fff // cos( 0 pi/16) C0
//
data8 0xc7c5c1e34d3055b3 , 0x00003ffc // sin( 1 pi/16) S1
data8 0xfb14be7fbae58157 , 0x00003ffe // cos( 1 pi/16) C1
//
data8 0xc3ef1535754b168e , 0x00003ffd // sin( 2 pi/16) S2
data8 0xec835e79946a3146 , 0x00003ffe // cos( 2 pi/16) C2
//
data8 0x8e39d9cd73464364 , 0x00003ffe // sin( 3 pi/16) S3
data8 0xd4db3148750d181a , 0x00003ffe // cos( 3 pi/16) C3
//
data8 0xb504f333f9de6484 , 0x00003ffe // sin( 4 pi/16) S4
data8 0xb504f333f9de6484 , 0x00003ffe // cos( 4 pi/16) C4
//
data8 0xd4db3148750d181a , 0x00003ffe // sin( 5 pi/16) C3
data8 0x8e39d9cd73464364 , 0x00003ffe // cos( 5 pi/16) S3
//
data8 0xec835e79946a3146 , 0x00003ffe // sin( 6 pi/16) C2
data8 0xc3ef1535754b168e , 0x00003ffd // cos( 6 pi/16) S2
//
data8 0xfb14be7fbae58157 , 0x00003ffe // sin( 7 pi/16) C1
data8 0xc7c5c1e34d3055b3 , 0x00003ffc // cos( 7 pi/16) S1
//
data8 0x8000000000000000 , 0x00003fff // sin( 8 pi/16) C0
data8 0x0000000000000000 , 0x00000000 // cos( 8 pi/16) S0
//
data8 0xfb14be7fbae58157 , 0x00003ffe // sin( 9 pi/16) C1
data8 0xc7c5c1e34d3055b3 , 0x0000bffc // cos( 9 pi/16) -S1
//
data8 0xec835e79946a3146 , 0x00003ffe // sin(10 pi/16) C2
data8 0xc3ef1535754b168e , 0x0000bffd // cos(10 pi/16) -S2
//
data8 0xd4db3148750d181a , 0x00003ffe // sin(11 pi/16) C3
data8 0x8e39d9cd73464364 , 0x0000bffe // cos(11 pi/16) -S3
//
data8 0xb504f333f9de6484 , 0x00003ffe // sin(12 pi/16) S4
data8 0xb504f333f9de6484 , 0x0000bffe // cos(12 pi/16) -S4
//
data8 0x8e39d9cd73464364 , 0x00003ffe // sin(13 pi/16) S3
data8 0xd4db3148750d181a , 0x0000bffe // cos(13 pi/16) -C3
//
data8 0xc3ef1535754b168e , 0x00003ffd // sin(14 pi/16) S2
data8 0xec835e79946a3146 , 0x0000bffe // cos(14 pi/16) -C2
//
data8 0xc7c5c1e34d3055b3 , 0x00003ffc // sin(15 pi/16) S1
data8 0xfb14be7fbae58157 , 0x0000bffe // cos(15 pi/16) -C1
//
data8 0x0000000000000000 , 0x00000000 // sin(16 pi/16) S0
data8 0x8000000000000000 , 0x0000bfff // cos(16 pi/16) -C0
//
data8 0xc7c5c1e34d3055b3 , 0x0000bffc // sin(17 pi/16) -S1
data8 0xfb14be7fbae58157 , 0x0000bffe // cos(17 pi/16) -C1
//
data8 0xc3ef1535754b168e , 0x0000bffd // sin(18 pi/16) -S2
data8 0xec835e79946a3146 , 0x0000bffe // cos(18 pi/16) -C2
//
data8 0x8e39d9cd73464364 , 0x0000bffe // sin(19 pi/16) -S3
data8 0xd4db3148750d181a , 0x0000bffe // cos(19 pi/16) -C3
//
data8 0xb504f333f9de6484 , 0x0000bffe // sin(20 pi/16) -S4
data8 0xb504f333f9de6484 , 0x0000bffe // cos(20 pi/16) -S4
//
data8 0xd4db3148750d181a , 0x0000bffe // sin(21 pi/16) -C3
data8 0x8e39d9cd73464364 , 0x0000bffe // cos(21 pi/16) -S3
//
data8 0xec835e79946a3146 , 0x0000bffe // sin(22 pi/16) -C2
data8 0xc3ef1535754b168e , 0x0000bffd // cos(22 pi/16) -S2
//
data8 0xfb14be7fbae58157 , 0x0000bffe // sin(23 pi/16) -C1
data8 0xc7c5c1e34d3055b3 , 0x0000bffc // cos(23 pi/16) -S1
//
data8 0x8000000000000000 , 0x0000bfff // sin(24 pi/16) -C0
data8 0x0000000000000000 , 0x00000000 // cos(24 pi/16) S0
//
data8 0xfb14be7fbae58157 , 0x0000bffe // sin(25 pi/16) -C1
data8 0xc7c5c1e34d3055b3 , 0x00003ffc // cos(25 pi/16) S1
//
data8 0xec835e79946a3146 , 0x0000bffe // sin(26 pi/16) -C2
data8 0xc3ef1535754b168e , 0x00003ffd // cos(26 pi/16) S2
//
data8 0xd4db3148750d181a , 0x0000bffe // sin(27 pi/16) -C3
data8 0x8e39d9cd73464364 , 0x00003ffe // cos(27 pi/16) S3
//
data8 0xb504f333f9de6484 , 0x0000bffe // sin(28 pi/16) -S4
data8 0xb504f333f9de6484 , 0x00003ffe // cos(28 pi/16) S4
//
data8 0x8e39d9cd73464364 , 0x0000bffe // sin(29 pi/16) -S3
data8 0xd4db3148750d181a , 0x00003ffe // cos(29 pi/16) C3
//
data8 0xc3ef1535754b168e , 0x0000bffd // sin(30 pi/16) -S2
data8 0xec835e79946a3146 , 0x00003ffe // cos(30 pi/16) C2
//
data8 0xc7c5c1e34d3055b3 , 0x0000bffc // sin(31 pi/16) -S1
data8 0xfb14be7fbae58157 , 0x00003ffe // cos(31 pi/16) C1
//
data8 0x0000000000000000 , 0x00000000 // sin(32 pi/16) S0
data8 0x8000000000000000 , 0x00003fff // cos(32 pi/16) C0
LOCAL_OBJECT_END(double_sin_cos_beta_k4)
.section .text
GLOBAL_IEEE754_ENTRY(sincos)
// cis_GR_sig_inv_pi_by_16 = significand of 16/pi
{ .mlx
getf.exp cis_r_signexp = cis_Arg
movl cis_GR_sig_inv_pi_by_16 = 0xA2F9836E4E44152A
}
// cis_GR_rshf_2to61 = 1.1000 2^(63+63-2)
{ .mlx
addl cis_AD_1 = @ltoff(double_cis_pi), gp
movl cis_GR_rshf_2to61 = 0x47b8000000000000
};;
{ .mfi
ld8 cis_AD_1 = [cis_AD_1]
fnorm.s1 cis_NORM_f8 = cis_Arg
cmp.eq p13, p14 = r0, r0 // p13 set for sincos
}
// cis_GR_exp_2tom61 = exponent of scaling factor 2^-61
{ .mib
mov cis_GR_exp_2tom61 = 0xffff-61
nop.i 0
br.cond.sptk _CIS_COMMON
};;
GLOBAL_IEEE754_END(sincos)
libm_alias_double_other (__sincos, sincos)
GLOBAL_LIBM_ENTRY(__libm_sincos)
// cis_GR_sig_inv_pi_by_16 = significand of 16/pi
{ .mlx
getf.exp cis_r_signexp = cis_Arg
movl cis_GR_sig_inv_pi_by_16 = 0xA2F9836E4E44152A
}
// cis_GR_rshf_2to61 = 1.1000 2^(63+63-2)
{ .mlx
addl cis_AD_1 = @ltoff(double_cis_pi), gp
movl cis_GR_rshf_2to61 = 0x47b8000000000000
};;
// p14 set for __libm_sincos and cis
{ .mfi
ld8 cis_AD_1 = [cis_AD_1]
fnorm.s1 cis_NORM_f8 = cis_Arg
cmp.eq p14, p13 = r0, r0
}
// cis_GR_exp_2tom61 = exponent of scaling factor 2^-61
{ .mib
mov cis_GR_exp_2tom61 = 0xffff-61
nop.i 0
nop.b 0
};;
_CIS_COMMON:
// Form two constants we need
// 16/pi * 2^-2 * 2^63, scaled by 2^61 since we just loaded the significand
// 1.1000...000 * 2^(63+63-2) to right shift int(W) into the low significand
// fcmp used to set denormal, and invalid on snans
{ .mfi
setf.sig cis_SIG_INV_PI_BY_16_2TO61 = cis_GR_sig_inv_pi_by_16
fclass.m p6,p0 = cis_Arg, 0xe7 // if x=0,inf,nan
addl cis_gr_tmp = -1, r0
}
// 1.1000 2^63 for right shift
{ .mlx
setf.d cis_RSHF_2TO61 = cis_GR_rshf_2to61
movl cis_GR_rshf = 0x43e8000000000000
};;
// Form another constant
// 2^-61 for scaling Nfloat
// 0x1001a is register_bias + 27.
// So if f8 >= 2^27, go to large arguments routine
{ .mfi
alloc GR_SAVE_PFS = ar.pfs, 3, 5, 0, 0
fclass.m p11,p0 = cis_Arg, 0x0b // Test for x=unorm
mov cis_exp_limit = 0x1001a
}
{ .mib
setf.exp cis_2TOM61 = cis_GR_exp_2tom61
nop.i 0
(p6) br.cond.spnt _CIS_SPECIAL_ARGS
};;
// Load the two pieces of pi/16
// Form another constant
// 1.1000...000 * 2^63, the right shift constant
{ .mmb
ldfe cis_Pi_by_16_hi = [cis_AD_1],16
setf.d cis_RSHF = cis_GR_rshf
(p11) br.cond.spnt _CIS_UNORM // Branch if x=unorm
};;
_CIS_COMMON2:
// Return here if x=unorm
// Create constant inexact set
{ .mmi
ldfe cis_Pi_by_16_lo = [cis_AD_1],16
setf.sig cis_tmp = cis_gr_tmp
nop.i 0
};;
// Select exponent (17 lsb)
{ .mfi
ldfe cis_Pi_by_16_lowest = [cis_AD_1],16
nop.f 0
dep.z cis_r_exp = cis_r_signexp, 0, 17
};;
// Start loading P, Q coefficients
// p10 is true if we must call routines to handle larger arguments
// p10 is true if f8 exp is > 0x1001a
{ .mmb
ldfpd cis_P4,cis_Q4 = [cis_AD_1],16
cmp.ge p10, p0 = cis_r_exp, cis_exp_limit
(p10) br.cond.spnt _CIS_LARGE_ARGS // go to |x| >= 2^27 path
};;
// cis_W = x * cis_Inv_Pi_by_16
// Multiply x by scaled 16/pi and add large const to shift integer part of W to
// rightmost bits of significand
{ .mfi
ldfpd cis_P3,cis_Q3 = [cis_AD_1],16
fma.s1 cis_W_2TO61_RSH = cis_NORM_f8,cis_SIG_INV_PI_BY_16_2TO61,cis_RSHF_2TO61
nop.i 0
};;
// get N = (int)cis_int_Nfloat
// cis_NFLOAT = Round_Int_Nearest(cis_W)
{ .mmf
getf.sig cis_GR_n = cis_W_2TO61_RSH
ldfpd cis_P2,cis_Q2 = [cis_AD_1],16
fms.s1 cis_NFLOAT = cis_W_2TO61_RSH,cis_2TOM61,cis_RSHF
};;
// cis_r = -cis_Nfloat * cis_Pi_by_16_hi + x
{ .mfi
ldfpd cis_P1,cis_Q1 = [cis_AD_1], 16
fnma.s1 cis_r = cis_NFLOAT,cis_Pi_by_16_hi,cis_NORM_f8
nop.i 0
};;
// Add 2^(k-1) (which is in cis_r_sincos) to N
{ .mmi
add cis_GR_n_cos = 0x8, cis_GR_n
;;
//Get M (least k+1 bits of N)
and cis_GR_m_sin = 0x1f,cis_GR_n
and cis_GR_m_cos = 0x1f,cis_GR_n_cos
};;
{ .mmi
nop.m 0
nop.m 0
shl cis_GR_32m_sin = cis_GR_m_sin,5
};;
// Add 32*M to address of sin_cos_beta table
// cis_r = cis_r -cis_Nfloat * cis_Pi_by_16_lo
{ .mfi
add cis_AD_2_sin = cis_GR_32m_sin, cis_AD_1
fnma.s1 cis_r = cis_NFLOAT, cis_Pi_by_16_lo, cis_r
shl cis_GR_32m_cos = cis_GR_m_cos,5
};;
// Add 32*M to address of sin_cos_beta table
{ .mmf
ldfe cis_Sm_sin = [cis_AD_2_sin],16
add cis_AD_2_cos = cis_GR_32m_cos, cis_AD_1
fclass.m.unc p10,p0 = cis_Arg,0x0b // den. input - uflow
};;
{ .mfi
ldfe cis_Sm_cos = [cis_AD_2_cos], 16
nop.i 0
};;
{ .mfi
ldfe cis_Cm_sin = [cis_AD_2_sin]
fma.s1 cis_rsq = cis_r, cis_r, f0 // get r^2
nop.i 0
}
// fmpy forces inexact flag
{ .mfi
nop.m 0
fmpy.s0 cis_tmp = cis_tmp,cis_tmp
nop.i 0
};;
{ .mfi
nop.m 0
fnma.s1 cis_r_exact = cis_NFLOAT, cis_Pi_by_16_lowest, cis_r
nop.i 0
};;
{ .mfi
ldfe cis_Cm_cos = [cis_AD_2_cos]
fma.s1 cis_P_temp1 = cis_rsq, cis_P4, cis_P3
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 cis_Q_temp1 = cis_rsq, cis_Q4, cis_Q3
nop.i 0
};;
{ .mfi
nop.m 0
fmpy.s1 cis_srsq_sin = cis_Sm_sin, cis_rsq
nop.i 0
}
{ .mfi
nop.m 0
fmpy.s1 cis_srsq_cos = cis_Sm_cos,cis_rsq
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 cis_Q_temp2 = cis_rsq, cis_Q_temp1, cis_Q2
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 cis_P_temp2 = cis_rsq, cis_P_temp1, cis_P2
nop.i 0
};;
{ .mfi
nop.m 0
fmpy.s1 cis_rcub = cis_r_exact, cis_rsq // get r^3
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 cis_Q = cis_rsq, cis_Q_temp2, cis_Q1
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 cis_P = cis_rsq, cis_P_temp2, cis_P1
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 cis_Q_sin = cis_srsq_sin,cis_Q, cis_Sm_sin
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 cis_Q_cos = cis_srsq_cos,cis_Q, cis_Sm_cos
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 cis_P = cis_rcub,cis_P, cis_r_exact // final P
nop.i 0
};;
// If den. arg, force underflow to be set
{ .mfi
nop.m 0
(p10) fmpy.d.s0 cis_tmp = cis_Arg,cis_Arg
nop.i 0
};;
{ .mfi
nop.m 0
fma.d.s0 cis_Sin_res = cis_Cm_sin,cis_P,cis_Q_sin//Final sin
nop.i 0
}
{ .mfb
nop.m 0
fma.d.s0 cis_Cos_res = cis_Cm_cos,cis_P,cis_Q_cos//Final cos
(p14) br.ret.sptk b0 // common exit for __libm_sincos and cis main path
};;
{ .mmb
stfd [cis_pResSin] = cis_Sin_res
stfd [cis_pResCos] = cis_Cos_res
br.ret.sptk b0 // common exit for sincos main path
};;
_CIS_SPECIAL_ARGS:
// sin(+/-0) = +/-0
// sin(Inf) = NaN
// sin(NaN) = NaN
{ .mfi
nop.m 999
fma.d.s0 cis_Sin_res = cis_Arg, f0, f0 // sinf(+/-0,NaN,Inf)
nop.i 999
};;
// cos(+/-0) = 1.0
// cos(Inf) = NaN
// cos(NaN) = NaN
{ .mfb
nop.m 999
fma.d.s0 cis_Cos_res = cis_Arg, f0, f1 // cosf(+/-0,NaN,Inf)
(p14) br.ret.sptk b0 //spec exit for __libm_sincos and cis main path
};;
{ .mmb
stfd [cis_pResSin] = cis_Sin_res
stfd [cis_pResCos] = cis_Cos_res
br.ret.sptk b0 // common exit for sincos main path
};;
_CIS_UNORM:
// Here if x=unorm
{ .mfb
getf.exp cis_r_signexp = cis_NORM_f8 // Get signexp of x
fcmp.eq.s0 p11,p0 = cis_Arg, f0 // Dummy op to set denorm
br.cond.sptk _CIS_COMMON2 // Return to main path
};;
GLOBAL_LIBM_END(__libm_sincos)
//// |x| > 2^27 path ///////
.proc _CIS_LARGE_ARGS
_CIS_LARGE_ARGS:
.prologue
{ .mfi
nop.m 0
nop.f 0
.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
// Call of huge arguments sincos
{ .mib
nop.m 0
mov GR_SAVE_PR = pr
br.call.sptk b0 = __libm_sincos_large
};;
{ .mfi
mov gp = GR_SAVE_GP
nop.f 0
mov pr = GR_SAVE_PR, 0x1fffe
}
;;
{ .mfi
nop.m 0
nop.f 0
mov b0 = GR_SAVE_B0
}
;;
{ .mfi
nop.m 0
fma.d.s0 cis_Cos_res = cis_Cos_res, f1, f0
mov ar.pfs = GR_SAVE_PFS
}
{ .mfb
nop.m 0
fma.d.s0 cis_Sin_res = cis_Sin_res, f1, f0
(p14) br.ret.sptk b0 // exit for |x| > 2^27 path (__libm_sincos and cis)
};;
{ .mmb
stfd [cis_pResSin] = cis_Sin_res
stfd [cis_pResCos] = cis_Cos_res
br.ret.sptk b0 // exit for sincos |x| > 2^27 path
};;
.endp _CIS_LARGE_ARGS
.type __libm_sincos_large#,@function
.global __libm_sincos_large#
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