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glibc/sysdeps/ia64/fpu/s_cosl.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 "sincosl.s"
// Copyright (c) 2000 - 2004, 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 (hand-optimized)
// 04/04/00 Unwind support added
// 07/30/01 Improved speed on all paths
// 08/20/01 Fixed bundling typo
// 05/13/02 Changed interface to __libm_pi_by_2_reduce
// 02/10/03 Reordered header: .section, .global, .proc, .align;
// used data8 for long double table values
// 10/13/03 Corrected final .endp name to match .proc
// 10/26/04 Avoided using r14-31 as scratch so not clobbered by dynamic loader
//
//*********************************************************************
//
// Function: Combined sinl(x) and cosl(x), where
//
// sinl(x) = sine(x), for double-extended precision x values
// cosl(x) = cosine(x), for double-extended precision x values
//
//*********************************************************************
//
// Resources Used:
//
// Floating-Point Registers: f8 (Input and Return Value)
// f32-f99
//
// General Purpose Registers:
// r32-r58
//
// Predicate Registers: p6-p13
//
//*********************************************************************
//
// IEEE Special Conditions:
//
// Denormal fault raised on denormal inputs
// Overflow exceptions do not occur
// Underflow exceptions raised when appropriate for sin
// (No specialized error handling for this routine)
// Inexact raised when appropriate by algorithm
//
// sinl(SNaN) = QNaN
// sinl(QNaN) = QNaN
// sinl(inf) = QNaN
// sinl(+/-0) = +/-0
// cosl(inf) = QNaN
// cosl(SNaN) = QNaN
// cosl(QNaN) = QNaN
// cosl(0) = 1
//
//*********************************************************************
//
// Mathematical Description
// ========================
//
// The computation of FSIN and FCOS is best handled in one piece of
// code. The main reason is that given any argument Arg, computation
// of trigonometric functions first calculate N and an approximation
// to alpha where
//
// Arg = N pi/2 + alpha, |alpha| <= pi/4.
//
// Since
//
// cosl( Arg ) = sinl( (N+1) pi/2 + alpha ),
//
// therefore, the code for computing sine will produce cosine as long
// as 1 is added to N immediately after the argument reduction
// process.
//
// Let M = N if sine
// N+1 if cosine.
//
// Now, given
//
// Arg = M pi/2 + alpha, |alpha| <= pi/4,
//
// let I = M mod 4, or I be the two lsb of M when M is represented
// as 2's complement. I = [i_0 i_1]. Then
//
// sinl( Arg ) = (-1)^i_0 sinl( alpha ) if i_1 = 0,
// = (-1)^i_0 cosl( alpha ) if i_1 = 1.
//
// For example:
// if M = -1, I = 11
// sin ((-pi/2 + alpha) = (-1) cos (alpha)
// if M = 0, I = 00
// sin (alpha) = sin (alpha)
// if M = 1, I = 01
// sin (pi/2 + alpha) = cos (alpha)
// if M = 2, I = 10
// sin (pi + alpha) = (-1) sin (alpha)
// if M = 3, I = 11
// sin ((3/2)pi + alpha) = (-1) cos (alpha)
//
// The value of alpha is obtained by argument reduction and
// represented by two working precision numbers r and c where
//
// alpha = r + c accurately.
//
// The reduction method is described in a previous write up.
// The argument reduction scheme identifies 4 cases. For Cases 2
// and 4, because |alpha| is small, sinl(r+c) and cosl(r+c) can be
// computed very easily by 2 or 3 terms of the Taylor series
// expansion as follows:
//
// Case 2:
// -------
//
// sinl(r + c) = r + c - r^3/6 accurately
// cosl(r + c) = 1 - 2^(-67) accurately
//
// Case 4:
// -------
//
// sinl(r + c) = r + c - r^3/6 + r^5/120 accurately
// cosl(r + c) = 1 - r^2/2 + r^4/24 accurately
//
// The only cases left are Cases 1 and 3 of the argument reduction
// procedure. These two cases will be merged since after the
// argument is reduced in either cases, we have the reduced argument
// represented as r + c and that the magnitude |r + c| is not small
// enough to allow the usage of a very short approximation.
//
// The required calculation is either
//
// sinl(r + c) = sinl(r) + correction, or
// cosl(r + c) = cosl(r) + correction.
//
// Specifically,
//
// sinl(r + c) = sinl(r) + c sin'(r) + O(c^2)
// = sinl(r) + c cos (r) + O(c^2)
// = sinl(r) + c(1 - r^2/2) accurately.
// Similarly,
//
// cosl(r + c) = cosl(r) - c sinl(r) + O(c^2)
// = cosl(r) - c(r - r^3/6) accurately.
//
// We therefore concentrate on accurately calculating sinl(r) and
// cosl(r) for a working-precision number r, |r| <= pi/4 to within
// 0.1% or so.
//
// The greatest challenge of this task is that the second terms of
// the Taylor series
//
// r - r^3/3! + r^r/5! - ...
//
// and
//
// 1 - r^2/2! + r^4/4! - ...
//
// are not very small when |r| is close to pi/4 and the rounding
// errors will be a concern if simple polynomial accumulation is
// used. When |r| < 2^-3, however, the second terms will be small
// enough (6 bits or so of right shift) that a normal Horner
// recurrence suffices. Hence there are two cases that we consider
// in the accurate computation of sinl(r) and cosl(r), |r| <= pi/4.
//
// Case small_r: |r| < 2^(-3)
// --------------------------
//
// Since Arg = M pi/4 + r + c accurately, and M mod 4 is [i_0 i_1],
// we have
//
// sinl(Arg) = (-1)^i_0 * sinl(r + c) if i_1 = 0
// = (-1)^i_0 * cosl(r + c) if i_1 = 1
//
// can be accurately approximated by
//
// sinl(Arg) = (-1)^i_0 * [sinl(r) + c] if i_1 = 0
// = (-1)^i_0 * [cosl(r) - c*r] if i_1 = 1
//
// because |r| is small and thus the second terms in the correction
// are unnecessary.
//
// Finally, sinl(r) and cosl(r) are approximated by polynomials of
// moderate lengths.
//
// sinl(r) = r + S_1 r^3 + S_2 r^5 + ... + S_5 r^11
// cosl(r) = 1 + C_1 r^2 + C_2 r^4 + ... + C_5 r^10
//
// We can make use of predicates to selectively calculate
// sinl(r) or cosl(r) based on i_1.
//
// Case normal_r: 2^(-3) <= |r| <= pi/4
// ------------------------------------
//
// This case is more likely than the previous one if one considers
// r to be uniformly distributed in [-pi/4 pi/4]. Again,
//
// sinl(Arg) = (-1)^i_0 * sinl(r + c) if i_1 = 0
// = (-1)^i_0 * cosl(r + c) if i_1 = 1.
//
// Because |r| is now larger, we need one extra term in the
// correction. sinl(Arg) can be accurately approximated by
//
// sinl(Arg) = (-1)^i_0 * [sinl(r) + c(1-r^2/2)] if i_1 = 0
// = (-1)^i_0 * [cosl(r) - c*r*(1 - r^2/6)] i_1 = 1.
//
// Finally, sinl(r) and cosl(r) are approximated by polynomials of
// moderate lengths.
//
// sinl(r) = r + PP_1_hi r^3 + PP_1_lo r^3 +
// PP_2 r^5 + ... + PP_8 r^17
//
// cosl(r) = 1 + QQ_1 r^2 + QQ_2 r^4 + ... + QQ_8 r^16
//
// where PP_1_hi is only about 16 bits long and QQ_1 is -1/2.
// The crux in accurate computation is to calculate
//
// r + PP_1_hi r^3 or 1 + QQ_1 r^2
//
// accurately as two pieces: U_hi and U_lo. The way to achieve this
// is to obtain r_hi as a 10 sig. bit number that approximates r to
// roughly 8 bits or so of accuracy. (One convenient way is
//
// r_hi := frcpa( frcpa( r ) ).)
//
// This way,
//
// r + PP_1_hi r^3 = r + PP_1_hi r_hi^3 +
// PP_1_hi (r^3 - r_hi^3)
// = [r + PP_1_hi r_hi^3] +
// [PP_1_hi (r - r_hi)
// (r^2 + r_hi r + r_hi^2) ]
// = U_hi + U_lo
//
// Since r_hi is only 10 bit long and PP_1_hi is only 16 bit long,
// PP_1_hi * r_hi^3 is only at most 46 bit long and thus computed
// exactly. Furthermore, r and PP_1_hi r_hi^3 are of opposite sign
// and that there is no more than 8 bit shift off between r and
// PP_1_hi * r_hi^3. Hence the sum, U_hi, is representable and thus
// calculated without any error. Finally, the fact that
//
// |U_lo| <= 2^(-8) |U_hi|
//
// says that U_hi + U_lo is approximating r + PP_1_hi r^3 to roughly
// 8 extra bits of accuracy.
//
// Similarly,
//
// 1 + QQ_1 r^2 = [1 + QQ_1 r_hi^2] +
// [QQ_1 (r - r_hi)(r + r_hi)]
// = U_hi + U_lo.
//
// Summarizing, we calculate r_hi = frcpa( frcpa( r ) ).
//
// If i_1 = 0, then
//
// U_hi := r + PP_1_hi * r_hi^3
// U_lo := PP_1_hi * (r - r_hi) * (r^2 + r*r_hi + r_hi^2)
// poly := PP_1_lo r^3 + PP_2 r^5 + ... + PP_8 r^17
// correction := c * ( 1 + C_1 r^2 )
//
// Else ...i_1 = 1
//
// U_hi := 1 + QQ_1 * r_hi * r_hi
// U_lo := QQ_1 * (r - r_hi) * (r + r_hi)
// poly := QQ_2 * r^4 + QQ_3 * r^6 + ... + QQ_8 r^16
// correction := -c * r * (1 + S_1 * r^2)
//
// End
//
// Finally,
//
// V := poly + ( U_lo + correction )
//
// / U_hi + V if i_0 = 0
// result := |
// \ (-U_hi) - V if i_0 = 1
//
// It is important that in the last step, negation of U_hi is
// performed prior to the subtraction which is to be performed in
// the user-set rounding mode.
//
//
// Algorithmic Description
// =======================
//
// The argument reduction algorithm is tightly integrated into FSIN
// and FCOS which share the same code. The following is complete and
// self-contained. The argument reduction description given
// previously is repeated below.
//
//
// Step 0. Initialization.
//
// If FSIN is invoked, set N_inc := 0; else if FCOS is invoked,
// set N_inc := 1.
//
// Step 1. Check for exceptional and special cases.
//
// * If Arg is +-0, +-inf, NaN, NaT, go to Step 10 for special
// handling.
// * If |Arg| < 2^24, go to Step 2 for reduction of moderate
// arguments. This is the most likely case.
// * If |Arg| < 2^63, go to Step 8 for pre-reduction of large
// arguments.
// * If |Arg| >= 2^63, go to Step 10 for special handling.
//
// Step 2. Reduction of moderate arguments.
//
// If |Arg| < pi/4 ...quick branch
// N_fix := N_inc (integer)
// r := Arg
// c := 0.0
// Branch to Step 4, Case_1_complete
// Else ...cf. argument reduction
// N := Arg * two_by_PI (fp)
// N_fix := fcvt.fx( N ) (int)
// N := fcvt.xf( N_fix )
// N_fix := N_fix + N_inc
// s := Arg - N * P_1 (first piece of pi/2)
// w := -N * P_2 (second piece of pi/2)
//
// If |s| >= 2^(-33)
// go to Step 3, Case_1_reduce
// Else
// go to Step 7, Case_2_reduce
// Endif
// Endif
//
// Step 3. Case_1_reduce.
//
// r := s + w
// c := (s - r) + w ...observe order
//
// Step 4. Case_1_complete
//
// ...At this point, the reduced argument alpha is
// ...accurately represented as r + c.
// If |r| < 2^(-3), go to Step 6, small_r.
//
// Step 5. Normal_r.
//
// Let [i_0 i_1] by the 2 lsb of N_fix.
// FR_rsq := r * r
// r_hi := frcpa( frcpa( r ) )
// r_lo := r - r_hi
//
// If i_1 = 0, then
// poly := r*FR_rsq*(PP_1_lo + FR_rsq*(PP_2 + ... FR_rsq*PP_8))
// U_hi := r + PP_1_hi*r_hi*r_hi*r_hi ...any order
// U_lo := PP_1_hi*r_lo*(r*r + r*r_hi + r_hi*r_hi)
// correction := c + c*C_1*FR_rsq ...any order
// Else
// poly := FR_rsq*FR_rsq*(QQ_2 + FR_rsq*(QQ_3 + ... + FR_rsq*QQ_8))
// U_hi := 1 + QQ_1 * r_hi * r_hi ...any order
// U_lo := QQ_1 * r_lo * (r + r_hi)
// correction := -c*(r + S_1*FR_rsq*r) ...any order
// Endif
//
// V := poly + (U_lo + correction) ...observe order
//
// result := (i_0 == 0? 1.0 : -1.0)
//
// Last instruction in user-set rounding mode
//
// result := (i_0 == 0? result*U_hi + V :
// result*U_hi - V)
//
// Return
//
// Step 6. Small_r.
//
// ...Use flush to zero mode without causing exception
// Let [i_0 i_1] be the two lsb of N_fix.
//
// FR_rsq := r * r
//
// If i_1 = 0 then
// z := FR_rsq*FR_rsq; z := FR_rsq*z *r
// poly_lo := S_3 + FR_rsq*(S_4 + FR_rsq*S_5)
// poly_hi := r*FR_rsq*(S_1 + FR_rsq*S_2)
// correction := c
// result := r
// Else
// z := FR_rsq*FR_rsq; z := FR_rsq*z
// poly_lo := C_3 + FR_rsq*(C_4 + FR_rsq*C_5)
// poly_hi := FR_rsq*(C_1 + FR_rsq*C_2)
// correction := -c*r
// result := 1
// Endif
//
// poly := poly_hi + (z * poly_lo + correction)
//
// If i_0 = 1, result := -result
//
// Last operation. Perform in user-set rounding mode
//
// result := (i_0 == 0? result + poly :
// result - poly )
// Return
//
// Step 7. Case_2_reduce.
//
// ...Refer to the write up for argument reduction for
// ...rationale. The reduction algorithm below is taken from
// ...argument reduction description and integrated this.
//
// w := N*P_3
// U_1 := N*P_2 + w ...FMA
// U_2 := (N*P_2 - U_1) + w ...2 FMA
// ...U_1 + U_2 is N*(P_2+P_3) accurately
//
// r := s - U_1
// c := ( (s - r) - U_1 ) - U_2
//
// ...The mathematical sum r + c approximates the reduced
// ...argument accurately. Note that although compared to
// ...Case 1, this case requires much more work to reduce
// ...the argument, the subsequent calculation needed for
// ...any of the trigonometric function is very little because
// ...|alpha| < 1.01*2^(-33) and thus two terms of the
// ...Taylor series expansion suffices.
//
// If i_1 = 0 then
// poly := c + S_1 * r * r * r ...any order
// result := r
// Else
// poly := -2^(-67)
// result := 1.0
// Endif
//
// If i_0 = 1, result := -result
//
// Last operation. Perform in user-set rounding mode
//
// result := (i_0 == 0? result + poly :
// result - poly )
//
// Return
//
//
// Step 8. Pre-reduction of large arguments.
//
// ...Again, the following reduction procedure was described
// ...in the separate write up for argument reduction, which
// ...is tightly integrated here.
// N_0 := Arg * Inv_P_0
// N_0_fix := fcvt.fx( N_0 )
// N_0 := fcvt.xf( N_0_fix)
// Arg' := Arg - N_0 * P_0
// w := N_0 * d_1
// N := Arg' * two_by_PI
// N_fix := fcvt.fx( N )
// N := fcvt.xf( N_fix )
// N_fix := N_fix + N_inc
//
// s := Arg' - N * P_1
// w := w - N * P_2
//
// If |s| >= 2^(-14)
// go to Step 3
// Else
// go to Step 9
// Endif
//
// Step 9. Case_4_reduce.
//
// ...first obtain N_0*d_1 and -N*P_2 accurately
// U_hi := N_0 * d_1 V_hi := -N*P_2
// U_lo := N_0 * d_1 - U_hi V_lo := -N*P_2 - U_hi ...FMAs
//
// ...compute the contribution from N_0*d_1 and -N*P_3
// w := -N*P_3
// w := w + N_0*d_2
// t := U_lo + V_lo + w ...any order
//
// ...at this point, the mathematical value
// ...s + U_hi + V_hi + t approximates the true reduced argument
// ...accurately. Just need to compute this accurately.
//
// ...Calculate U_hi + V_hi accurately:
// A := U_hi + V_hi
// if |U_hi| >= |V_hi| then
// a := (U_hi - A) + V_hi
// else
// a := (V_hi - A) + U_hi
// endif
// ...order in computing "a" must be observed. This branch is
// ...best implemented by predicates.
// ...A + a is U_hi + V_hi accurately. Moreover, "a" is
// ...much smaller than A: |a| <= (1/2)ulp(A).
//
// ...Just need to calculate s + A + a + t
// C_hi := s + A t := t + a
// C_lo := (s - C_hi) + A
// C_lo := C_lo + t
//
// ...Final steps for reduction
// r := C_hi + C_lo
// c := (C_hi - r) + C_lo
//
// ...At this point, we have r and c
// ...And all we need is a couple of terms of the corresponding
// ...Taylor series.
//
// If i_1 = 0
// poly := c + r*FR_rsq*(S_1 + FR_rsq*S_2)
// result := r
// Else
// poly := FR_rsq*(C_1 + FR_rsq*C_2)
// result := 1
// Endif
//
// If i_0 = 1, result := -result
//
// Last operation. Perform in user-set rounding mode
//
// result := (i_0 == 0? result + poly :
// result - poly )
// Return
//
// Large Arguments: For arguments above 2**63, a Payne-Hanek
// style argument reduction is used and pi_by_2 reduce is called.
//
RODATA
.align 16
LOCAL_OBJECT_START(FSINCOSL_CONSTANTS)
sincosl_table_p:
data8 0xA2F9836E4E44152A, 0x00003FFE // Inv_pi_by_2
data8 0xC84D32B0CE81B9F1, 0x00004016 // P_0
data8 0xC90FDAA22168C235, 0x00003FFF // P_1
data8 0xECE675D1FC8F8CBB, 0x0000BFBD // P_2
data8 0xB7ED8FBBACC19C60, 0x0000BF7C // P_3
data8 0x8D848E89DBD171A1, 0x0000BFBF // d_1
data8 0xD5394C3618A66F8E, 0x0000BF7C // d_2
LOCAL_OBJECT_END(FSINCOSL_CONSTANTS)
LOCAL_OBJECT_START(sincosl_table_d)
data8 0xC90FDAA22168C234, 0x00003FFE // pi_by_4
data8 0xA397E5046EC6B45A, 0x00003FE7 // Inv_P_0
data4 0x3E000000, 0xBE000000 // 2^-3 and -2^-3
data4 0x2F000000, 0xAF000000 // 2^-33 and -2^-33
data4 0x9E000000, 0x00000000 // -2^-67
data4 0x00000000, 0x00000000 // pad
LOCAL_OBJECT_END(sincosl_table_d)
LOCAL_OBJECT_START(sincosl_table_pp)
data8 0xCC8ABEBCA21C0BC9, 0x00003FCE // PP_8
data8 0xD7468A05720221DA, 0x0000BFD6 // PP_7
data8 0xB092382F640AD517, 0x00003FDE // PP_6
data8 0xD7322B47D1EB75A4, 0x0000BFE5 // PP_5
data8 0xFFFFFFFFFFFFFFFE, 0x0000BFFD // C_1
data8 0xAAAA000000000000, 0x0000BFFC // PP_1_hi
data8 0xB8EF1D2ABAF69EEA, 0x00003FEC // PP_4
data8 0xD00D00D00D03BB69, 0x0000BFF2 // PP_3
data8 0x8888888888888962, 0x00003FF8 // PP_2
data8 0xAAAAAAAAAAAB0000, 0x0000BFEC // PP_1_lo
LOCAL_OBJECT_END(sincosl_table_pp)
LOCAL_OBJECT_START(sincosl_table_qq)
data8 0xD56232EFC2B0FE52, 0x00003FD2 // QQ_8
data8 0xC9C99ABA2B48DCA6, 0x0000BFDA // QQ_7
data8 0x8F76C6509C716658, 0x00003FE2 // QQ_6
data8 0x93F27DBAFDA8D0FC, 0x0000BFE9 // QQ_5
data8 0xAAAAAAAAAAAAAAAA, 0x0000BFFC // S_1
data8 0x8000000000000000, 0x0000BFFE // QQ_1
data8 0xD00D00D00C6E5041, 0x00003FEF // QQ_4
data8 0xB60B60B60B607F60, 0x0000BFF5 // QQ_3
data8 0xAAAAAAAAAAAAAA9B, 0x00003FFA // QQ_2
LOCAL_OBJECT_END(sincosl_table_qq)
LOCAL_OBJECT_START(sincosl_table_c)
data8 0xFFFFFFFFFFFFFFFE, 0x0000BFFD // C_1
data8 0xAAAAAAAAAAAA719F, 0x00003FFA // C_2
data8 0xB60B60B60356F994, 0x0000BFF5 // C_3
data8 0xD00CFFD5B2385EA9, 0x00003FEF // C_4
data8 0x93E4BD18292A14CD, 0x0000BFE9 // C_5
LOCAL_OBJECT_END(sincosl_table_c)
LOCAL_OBJECT_START(sincosl_table_s)
data8 0xAAAAAAAAAAAAAAAA, 0x0000BFFC // S_1
data8 0x88888888888868DB, 0x00003FF8 // S_2
data8 0xD00D00D0055EFD4B, 0x0000BFF2 // S_3
data8 0xB8EF1C5D839730B9, 0x00003FEC // S_4
data8 0xD71EA3A4E5B3F492, 0x0000BFE5 // S_5
data4 0x38800000, 0xB8800000 // two**-14 and -two**-14
LOCAL_OBJECT_END(sincosl_table_s)
FR_Input_X = f8
FR_Result = f8
FR_r = f8
FR_c = f9
FR_norm_x = f9
FR_inv_pi_2to63 = f10
FR_rshf_2to64 = f11
FR_2tom64 = f12
FR_rshf = f13
FR_N_float_signif = f14
FR_abs_x = f15
FR_Pi_by_4 = f34
FR_Two_to_M14 = f35
FR_Neg_Two_to_M14 = f36
FR_Two_to_M33 = f37
FR_Neg_Two_to_M33 = f38
FR_Neg_Two_to_M67 = f39
FR_Inv_pi_by_2 = f40
FR_N_float = f41
FR_N_fix = f42
FR_P_1 = f43
FR_P_2 = f44
FR_P_3 = f45
FR_s = f46
FR_w = f47
FR_d_2 = f48
FR_tmp_result = f49
FR_Z = f50
FR_A = f51
FR_a = f52
FR_t = f53
FR_U_1 = f54
FR_U_2 = f55
FR_C_1 = f56
FR_C_2 = f57
FR_C_3 = f58
FR_C_4 = f59
FR_C_5 = f60
FR_S_1 = f61
FR_S_2 = f62
FR_S_3 = f63
FR_S_4 = f64
FR_S_5 = f65
FR_poly_hi = f66
FR_poly_lo = f67
FR_r_hi = f68
FR_r_lo = f69
FR_rsq = f70
FR_r_cubed = f71
FR_C_hi = f72
FR_N_0 = f73
FR_d_1 = f74
FR_V = f75
FR_V_hi = f75
FR_V_lo = f76
FR_U_hi = f77
FR_U_lo = f78
FR_U_hiabs = f79
FR_V_hiabs = f80
FR_PP_8 = f81
FR_QQ_8 = f101
FR_PP_7 = f82
FR_QQ_7 = f102
FR_PP_6 = f83
FR_QQ_6 = f103
FR_PP_5 = f84
FR_QQ_5 = f104
FR_PP_4 = f85
FR_QQ_4 = f105
FR_PP_3 = f86
FR_QQ_3 = f106
FR_PP_2 = f87
FR_QQ_2 = f107
FR_QQ_1 = f108
FR_r_hi_sq = f88
FR_N_0_fix = f89
FR_Inv_P_0 = f90
FR_corr = f91
FR_poly = f92
FR_Neg_Two_to_M3 = f93
FR_Two_to_M3 = f94
FR_P_0 = f95
FR_C_lo = f96
FR_PP_1 = f97
FR_PP_1_lo = f98
FR_ArgPrime = f99
FR_inexact = f100
GR_exp_m2_to_m3= r36
GR_N_Inc = r37
GR_Sin_or_Cos = r38
GR_signexp_x = r40
GR_exp_x = r40
GR_exp_mask = r41
GR_exp_2_to_63 = r42
GR_exp_2_to_m3 = r43
GR_exp_2_to_24 = r44
GR_sig_inv_pi = r45
GR_rshf_2to64 = r46
GR_exp_2tom64 = r47
GR_rshf = r48
GR_ad_p = r49
GR_ad_d = r50
GR_ad_pp = r51
GR_ad_qq = r52
GR_ad_c = r53
GR_ad_s = r54
GR_ad_ce = r55
GR_ad_se = r56
GR_ad_m14 = r57
GR_ad_s1 = r58
// Added for unwind support
GR_SAVE_B0 = r39
GR_SAVE_GP = r40
GR_SAVE_PFS = r41
.section .text
GLOBAL_IEEE754_ENTRY(sinl)
{ .mlx
alloc r32 = ar.pfs,0,27,2,0
movl GR_sig_inv_pi = 0xa2f9836e4e44152a // significand of 1/pi
}
{ .mlx
mov GR_Sin_or_Cos = 0x0
movl GR_rshf_2to64 = 0x47e8000000000000 // 1.1000 2^(63+64)
}
;;
{ .mfi
addl GR_ad_p = @ltoff(FSINCOSL_CONSTANTS#), gp
fclass.m p6, p0 = FR_Input_X, 0x1E3 // Test x natval, nan, inf
mov GR_exp_2_to_m3 = 0xffff - 3 // Exponent of 2^-3
}
{ .mfb
nop.m 999
fnorm.s1 FR_norm_x = FR_Input_X // Normalize x
br.cond.sptk SINCOSL_CONTINUE
}
;;
GLOBAL_IEEE754_END(sinl)
libm_alias_ldouble_other (__sin, sin)
GLOBAL_IEEE754_ENTRY(cosl)
{ .mlx
alloc r32 = ar.pfs,0,27,2,0
movl GR_sig_inv_pi = 0xa2f9836e4e44152a // significand of 1/pi
}
{ .mlx
mov GR_Sin_or_Cos = 0x1
movl GR_rshf_2to64 = 0x47e8000000000000 // 1.1000 2^(63+64)
}
;;
{ .mfi
addl GR_ad_p = @ltoff(FSINCOSL_CONSTANTS#), gp
fclass.m p6, p0 = FR_Input_X, 0x1E3 // Test x natval, nan, inf
mov GR_exp_2_to_m3 = 0xffff - 3 // Exponent of 2^-3
}
{ .mfi
nop.m 999
fnorm.s1 FR_norm_x = FR_Input_X // Normalize x
nop.i 999
}
;;
SINCOSL_CONTINUE:
{ .mfi
setf.sig FR_inv_pi_2to63 = GR_sig_inv_pi // Form 1/pi * 2^63
nop.f 999
mov GR_exp_2tom64 = 0xffff - 64 // Scaling constant to compute N
}
{ .mlx
setf.d FR_rshf_2to64 = GR_rshf_2to64 // Form const 1.1000 * 2^(63+64)
movl GR_rshf = 0x43e8000000000000 // Form const 1.1000 * 2^63
}
;;
{ .mfi
ld8 GR_ad_p = [GR_ad_p] // Point to Inv_pi_by_2
fclass.m p7, p0 = FR_Input_X, 0x0b // Test x denormal
nop.i 999
}
;;
{ .mfi
getf.exp GR_signexp_x = FR_Input_X // Get sign and exponent of x
fclass.m p10, p0 = FR_Input_X, 0x007 // Test x zero
nop.i 999
}
{ .mib
mov GR_exp_mask = 0x1ffff // Exponent mask
nop.i 999
(p6) br.cond.spnt SINCOSL_SPECIAL // Branch if x natval, nan, inf
}
;;
{ .mfi
setf.exp FR_2tom64 = GR_exp_2tom64 // Form 2^-64 for scaling N_float
nop.f 0
add GR_ad_d = 0x70, GR_ad_p // Point to constant table d
}
{ .mib
setf.d FR_rshf = GR_rshf // Form right shift const 1.1000 * 2^63
mov GR_exp_m2_to_m3 = 0x2fffc // Form -(2^-3)
(p7) br.cond.spnt SINCOSL_DENORMAL // Branch if x denormal
}
;;
SINCOSL_COMMON:
{ .mfi
and GR_exp_x = GR_exp_mask, GR_signexp_x // Get exponent of x
fclass.nm p8, p0 = FR_Input_X, 0x1FF // Test x unsupported type
mov GR_exp_2_to_63 = 0xffff + 63 // Exponent of 2^63
}
{ .mib
add GR_ad_pp = 0x40, GR_ad_d // Point to constant table pp
mov GR_exp_2_to_24 = 0xffff + 24 // Exponent of 2^24
(p10) br.cond.spnt SINCOSL_ZERO // Branch if x zero
}
;;
{ .mfi
ldfe FR_Inv_pi_by_2 = [GR_ad_p], 16 // Load 2/pi
fcmp.eq.s0 p15, p0 = FR_Input_X, f0 // Dummy to set denormal
add GR_ad_qq = 0xa0, GR_ad_pp // Point to constant table qq
}
{ .mfi
ldfe FR_Pi_by_4 = [GR_ad_d], 16 // Load pi/4 for range test
nop.f 999
cmp.ge p10,p0 = GR_exp_x, GR_exp_2_to_63 // Is |x| >= 2^63
}
;;
{ .mfi
ldfe FR_P_0 = [GR_ad_p], 16 // Load P_0 for pi/4 <= |x| < 2^63
fmerge.s FR_abs_x = f1, FR_norm_x // |x|
add GR_ad_c = 0x90, GR_ad_qq // Point to constant table c
}
{ .mfi
ldfe FR_Inv_P_0 = [GR_ad_d], 16 // Load 1/P_0 for pi/4 <= |x| < 2^63
nop.f 999
cmp.ge p7,p0 = GR_exp_x, GR_exp_2_to_24 // Is |x| >= 2^24
}
;;
{ .mfi
ldfe FR_P_1 = [GR_ad_p], 16 // Load P_1 for pi/4 <= |x| < 2^63
nop.f 999
add GR_ad_s = 0x50, GR_ad_c // Point to constant table s
}
{ .mfi
ldfe FR_PP_8 = [GR_ad_pp], 16 // Load PP_8 for 2^-3 < |r| < pi/4
nop.f 999
nop.i 999
}
;;
{ .mfi
ldfe FR_P_2 = [GR_ad_p], 16 // Load P_2 for pi/4 <= |x| < 2^63
nop.f 999
add GR_ad_ce = 0x40, GR_ad_c // Point to end of constant table c
}
{ .mfi
ldfe FR_QQ_8 = [GR_ad_qq], 16 // Load QQ_8 for 2^-3 < |r| < pi/4
nop.f 999
nop.i 999
}
;;
{ .mfi
ldfe FR_QQ_7 = [GR_ad_qq], 16 // Load QQ_7 for 2^-3 < |r| < pi/4
fma.s1 FR_N_float_signif = FR_Input_X, FR_inv_pi_2to63, FR_rshf_2to64
add GR_ad_se = 0x40, GR_ad_s // Point to end of constant table s
}
{ .mib
ldfe FR_PP_7 = [GR_ad_pp], 16 // Load PP_7 for 2^-3 < |r| < pi/4
mov GR_ad_s1 = GR_ad_s // Save pointer to S_1
(p10) br.cond.spnt SINCOSL_ARG_TOO_LARGE // Branch if |x| >= 2^63
// Use Payne-Hanek Reduction
}
;;
{ .mfi
ldfe FR_P_3 = [GR_ad_p], 16 // Load P_3 for pi/4 <= |x| < 2^63
fmerge.se FR_r = FR_norm_x, FR_norm_x // r = x, in case |x| < pi/4
add GR_ad_m14 = 0x50, GR_ad_s // Point to constant table m14
}
{ .mfb
ldfps FR_Two_to_M3, FR_Neg_Two_to_M3 = [GR_ad_d], 8
fma.s1 FR_rsq = FR_norm_x, FR_norm_x, f0 // rsq = x*x, in case |x| < pi/4
(p7) br.cond.spnt SINCOSL_LARGER_ARG // Branch if 2^24 <= |x| < 2^63
// Use pre-reduction
}
;;
{ .mmf
ldfe FR_PP_6 = [GR_ad_pp], 16 // Load PP_6 for normal path
ldfe FR_QQ_6 = [GR_ad_qq], 16 // Load QQ_6 for normal path
fmerge.se FR_c = f0, f0 // c = 0 in case |x| < pi/4
}
;;
{ .mmf
ldfe FR_PP_5 = [GR_ad_pp], 16 // Load PP_5 for normal path
ldfe FR_QQ_5 = [GR_ad_qq], 16 // Load QQ_5 for normal path
nop.f 999
}
;;
// Here if 0 < |x| < 2^24
{ .mfi
ldfe FR_S_5 = [GR_ad_se], -16 // Load S_5 if i_1=0
fcmp.lt.s1 p6, p7 = FR_abs_x, FR_Pi_by_4 // Test |x| < pi/4
nop.i 999
}
{ .mfi
ldfe FR_C_5 = [GR_ad_ce], -16 // Load C_5 if i_1=1
fms.s1 FR_N_float = FR_N_float_signif, FR_2tom64, FR_rshf
nop.i 999
}
;;
{ .mmi
ldfe FR_S_4 = [GR_ad_se], -16 // Load S_4 if i_1=0
ldfe FR_C_4 = [GR_ad_ce], -16 // Load C_4 if i_1=1
nop.i 999
}
;;
//
// N = Arg * 2/pi
// Check if Arg < pi/4
//
//
// Case 2: Convert integer N_fix back to normalized floating-point value.
// Case 1: p8 is only affected when p6 is set
//
//
// Grab the integer part of N and call it N_fix
//
{ .mfi
(p7) ldfps FR_Two_to_M33, FR_Neg_Two_to_M33 = [GR_ad_d], 8
(p6) fma.s1 FR_r_cubed = FR_r, FR_rsq, f0 // r^3 if |x| < pi/4
(p6) mov GR_N_Inc = GR_Sin_or_Cos // N_Inc if |x| < pi/4
}
;;
// If |x| < pi/4, r = x and c = 0
// lf |x| < pi/4, is x < 2**(-3).
// r = Arg
// c = 0
{ .mmi
(p7) getf.sig GR_N_Inc = FR_N_float_signif
(p6) cmp.lt.unc p8,p0 = GR_exp_x, GR_exp_2_to_m3 // Is |x| < 2^-3
(p6) tbit.z p9,p10 = GR_N_Inc, 0 // p9 if i_1=0, N mod 4 = 0,1
// p10 if i_1=1, N mod 4 = 2,3
}
;;
//
// lf |x| < pi/4, is -2**(-3)< x < 2**(-3) - set p8.
// If |x| >= pi/4,
// Create the right N for |x| < pi/4 and otherwise
// Case 2: Place integer part of N in GP register
//
{ .mbb
nop.m 999
(p8) br.cond.spnt SINCOSL_SMALL_R_0 // Branch if 0 < |x| < 2^-3
(p6) br.cond.spnt SINCOSL_NORMAL_R_0 // Branch if 2^-3 <= |x| < pi/4
}
;;
// Here if pi/4 <= |x| < 2^24
{ .mfi
ldfs FR_Neg_Two_to_M67 = [GR_ad_d], 8 // Load -2^-67
fnma.s1 FR_s = FR_N_float, FR_P_1, FR_Input_X // s = -N * P_1 + Arg
add GR_N_Inc = GR_N_Inc, GR_Sin_or_Cos // Adjust N_Inc for sin/cos
}
{ .mfi
nop.m 999
fma.s1 FR_w = FR_N_float, FR_P_2, f0 // w = N * P_2
nop.i 999
}
;;
{ .mfi
nop.m 999
fms.s1 FR_r = FR_s, f1, FR_w // r = s - w, assume |s| >= 2^-33
tbit.z p9,p10 = GR_N_Inc, 0 // p9 if i_1=0, N mod 4 = 0,1
// p10 if i_1=1, N mod 4 = 2,3
}
;;
{ .mfi
nop.m 999
fcmp.lt.s1 p7, p6 = FR_s, FR_Two_to_M33
nop.i 999
}
;;
{ .mfi
nop.m 999
(p7) fcmp.gt.s1 p7, p6 = FR_s, FR_Neg_Two_to_M33 // p6 if |s| >= 2^-33, else p7
nop.i 999
}
;;
{ .mfi
nop.m 999
fms.s1 FR_c = FR_s, f1, FR_r // c = s - r, for |s| >= 2^-33
nop.i 999
}
{ .mfi
nop.m 999
fma.s1 FR_rsq = FR_r, FR_r, f0 // rsq = r * r, for |s| >= 2^-33
nop.i 999
}
;;
{ .mfi
nop.m 999
(p7) fma.s1 FR_w = FR_N_float, FR_P_3, f0
nop.i 999
}
;;
{ .mmf
(p9) ldfe FR_C_1 = [GR_ad_pp], 16 // Load C_1 if i_1=0
(p10) ldfe FR_S_1 = [GR_ad_qq], 16 // Load S_1 if i_1=1
frcpa.s1 FR_r_hi, p15 = f1, FR_r // r_hi = frcpa(r)
}
;;
{ .mfi
nop.m 999
(p6) fcmp.lt.unc.s1 p8, p13 = FR_r, FR_Two_to_M3 // If big s, test r with 2^-3
nop.i 999
}
;;
{ .mfi
nop.m 999
(p7) fma.s1 FR_U_1 = FR_N_float, FR_P_2, FR_w
nop.i 999
}
;;
//
// For big s: r = s - w: No futher reduction is necessary
// For small s: w = N * P_3 (change sign) More reduction
//
{ .mfi
nop.m 999
(p8) fcmp.gt.s1 p8, p13 = FR_r, FR_Neg_Two_to_M3 // If big s, p8 if |r| < 2^-3
nop.i 999 ;;
}
{ .mfi
nop.m 999
(p9) fma.s1 FR_poly = FR_rsq, FR_PP_8, FR_PP_7 // poly = rsq*PP_8+PP_7 if i_1=0
nop.i 999
}
{ .mfi
nop.m 999
(p10) fma.s1 FR_poly = FR_rsq, FR_QQ_8, FR_QQ_7 // poly = rsq*QQ_8+QQ_7 if i_1=1
nop.i 999
}
;;
{ .mfi
nop.m 999
(p7) fms.s1 FR_r = FR_s, f1, FR_U_1
nop.i 999
}
;;
{ .mfi
nop.m 999
(p6) fma.s1 FR_r_cubed = FR_r, FR_rsq, f0 // rcubed = r * rsq
nop.i 999
}
;;
{ .mfi
//
// For big s: Is |r| < 2**(-3)?
// For big s: c = S - r
// For small s: U_1 = N * P_2 + w
//
// If p8 is set, prepare to branch to Small_R.
// If p9 is set, prepare to branch to Normal_R.
// For big s, r is complete here.
//
//
// For big s: c = c + w (w has not been negated.)
// For small s: r = S - U_1
//
nop.m 999
(p6) fms.s1 FR_c = FR_c, f1, FR_w
nop.i 999
}
{ .mbb
nop.m 999
(p8) br.cond.spnt SINCOSL_SMALL_R_1 // Branch if |s|>=2^-33, |r| < 2^-3,
// and pi/4 <= |x| < 2^24
(p13) br.cond.sptk SINCOSL_NORMAL_R_1 // Branch if |s|>=2^-33, |r| >= 2^-3,
// and pi/4 <= |x| < 2^24
}
;;
SINCOSL_S_TINY:
//
// Here if |s| < 2^-33, and pi/4 <= |x| < 2^24
//
{ .mfi
fms.s1 FR_U_2 = FR_N_float, FR_P_2, FR_U_1
//
// c = S - U_1
// r = S_1 * r
//
//
}
;;
{ .mmi
nop.m 999
//
// Get [i_0,i_1] - two lsb of N_fix_gr.
// Do dummy fmpy so inexact is always set.
//
tbit.z p9,p10 = GR_N_Inc, 0 // p9 if i_1=0, N mod 4 = 0,1
// p10 if i_1=1, N mod 4 = 2,3
}
;;
//
// For small s: U_2 = N * P_2 - U_1
// S_1 stored constant - grab the one stored with the
// coefficients.
//
{ .mfi
ldfe FR_S_1 = [GR_ad_s1], 16
//
// Check if i_1 and i_0 != 0
//
(p10) fma.s1 FR_poly = f0, f1, FR_Neg_Two_to_M67
tbit.z p11,p12 = GR_N_Inc, 1 // p11 if i_0=0, N mod 4 = 0,2
// p12 if i_0=1, N mod 4 = 1,3
}
;;
{ .mfi
nop.m 999
fms.s1 FR_s = FR_s, f1, FR_r
nop.i 999
}
{ .mfi
nop.m 999
//
// S = S - r
// U_2 = U_2 + w
// load S_1
//
fma.s1 FR_rsq = FR_r, FR_r, f0
nop.i 999 ;;
}
{ .mfi
nop.m 999
fma.s1 FR_U_2 = FR_U_2, f1, FR_w
nop.i 999
}
{ .mfi
nop.m 999
fmerge.se FR_tmp_result = FR_r, FR_r
nop.i 999 ;;
}
{ .mfi
nop.m 999
(p10) fma.s1 FR_tmp_result = f0, f1, f1
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// FR_rsq = r * r
// Save r as the result.
//
fms.s1 FR_c = FR_s, f1, FR_U_1
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// if ( i_1 ==0) poly = c + S_1*r*r*r
// else Result = 1
//
(p12) fnma.s1 FR_tmp_result = FR_tmp_result, f1, f0
nop.i 999
}
{ .mfi
nop.m 999
fma.s1 FR_r = FR_S_1, FR_r, f0
nop.i 999 ;;
}
{ .mfi
nop.m 999
fma.s0 FR_S_1 = FR_S_1, FR_S_1, f0
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// If i_1 != 0, poly = 2**(-67)
//
fms.s1 FR_c = FR_c, f1, FR_U_2
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// c = c - U_2
//
(p9) fma.s1 FR_poly = FR_r, FR_rsq, FR_c
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// i_0 != 0, so Result = -Result
//
(p11) fma.s0 FR_Result = FR_tmp_result, f1, FR_poly
nop.i 999 ;;
}
{ .mfb
nop.m 999
(p12) fms.s0 FR_Result = FR_tmp_result, f1, FR_poly
//
// if (i_0 == 0), Result = Result + poly
// else Result = Result - poly
//
br.ret.sptk b0 // Exit if |s| < 2^-33, and pi/4 <= |x| < 2^24
}
;;
SINCOSL_LARGER_ARG:
//
// Here if 2^24 <= |x| < 2^63
//
{ .mfi
ldfe FR_d_1 = [GR_ad_p], 16 // Load d_1 for |x| >= 2^24 path
fma.s1 FR_N_0 = FR_Input_X, FR_Inv_P_0, f0
nop.i 999
}
;;
//
// N_0 = Arg * Inv_P_0
//
// Load values 2**(-14) and -2**(-14)
{ .mmi
ldfps FR_Two_to_M14, FR_Neg_Two_to_M14 = [GR_ad_m14]
nop.i 999 ;;
}
{ .mfi
ldfe FR_d_2 = [GR_ad_p], 16 // Load d_2 for |x| >= 2^24 path
nop.f 999
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
//
fcvt.fx.s1 FR_N_0_fix = FR_N_0
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// N_0_fix = integer part of N_0
//
fcvt.xf FR_N_0 = FR_N_0_fix
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// Make N_0 the integer part
//
fnma.s1 FR_ArgPrime = FR_N_0, FR_P_0, FR_Input_X
nop.i 999
}
{ .mfi
nop.m 999
fma.s1 FR_w = FR_N_0, FR_d_1, f0
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// Arg' = -N_0 * P_0 + Arg
// w = N_0 * d_1
//
fma.s1 FR_N_float = FR_ArgPrime, FR_Inv_pi_by_2, f0
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// N = A' * 2/pi
//
fcvt.fx.s1 FR_N_fix = FR_N_float
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// N_fix is the integer part
//
fcvt.xf FR_N_float = FR_N_fix
nop.i 999 ;;
}
{ .mfi
getf.sig GR_N_Inc = FR_N_fix
nop.f 999
nop.i 999 ;;
}
{ .mii
nop.m 999
nop.i 999 ;;
add GR_N_Inc = GR_N_Inc, GR_Sin_or_Cos ;;
}
{ .mfi
nop.m 999
//
// N is the integer part of the reduced-reduced argument.
// Put the integer in a GP register
//
fnma.s1 FR_s = FR_N_float, FR_P_1, FR_ArgPrime
nop.i 999
}
{ .mfi
nop.m 999
fnma.s1 FR_w = FR_N_float, FR_P_2, FR_w
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// s = -N*P_1 + Arg'
// w = -N*P_2 + w
// N_fix_gr = N_fix_gr + N_inc
//
fcmp.lt.unc.s1 p9, p8 = FR_s, FR_Two_to_M14
nop.i 999 ;;
}
{ .mfi
nop.m 999
(p9) fcmp.gt.s1 p9, p8 = FR_s, FR_Neg_Two_to_M14 // p9 if |s| < 2^-14
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// For |s| > 2**(-14) r = S + w (r complete)
// Else U_hi = N_0 * d_1
//
(p9) fma.s1 FR_V_hi = FR_N_float, FR_P_2, f0
nop.i 999
}
{ .mfi
nop.m 999
(p9) fma.s1 FR_U_hi = FR_N_0, FR_d_1, f0
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// Either S <= -2**(-14) or S >= 2**(-14)
// or -2**(-14) < s < 2**(-14)
//
(p8) fma.s1 FR_r = FR_s, f1, FR_w
nop.i 999
}
{ .mfi
nop.m 999
(p9) fma.s1 FR_w = FR_N_float, FR_P_3, f0
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// We need abs of both U_hi and V_hi - don't
// worry about switched sign of V_hi.
//
(p9) fms.s1 FR_A = FR_U_hi, f1, FR_V_hi
nop.i 999
}
{ .mfi
nop.m 999
//
// Big s: finish up c = (S - r) + w (c complete)
// Case 4: A = U_hi + V_hi
// Note: Worry about switched sign of V_hi, so subtract instead of add.
//
(p9) fnma.s1 FR_V_lo = FR_N_float, FR_P_2, FR_V_hi
nop.i 999 ;;
}
{ .mmf
nop.m 999
nop.m 999
(p9) fms.s1 FR_U_lo = FR_N_0, FR_d_1, FR_U_hi
}
{ .mfi
nop.m 999
(p9) fmerge.s FR_V_hiabs = f0, FR_V_hi
nop.i 999 ;;
}
//{ .mfb
//(p9) fmerge.s f8= FR_V_lo,FR_V_lo
//(p9) br.ret.sptk b0
//}
//;;
{ .mfi
nop.m 999
// For big s: c = S - r
// For small s do more work: U_lo = N_0 * d_1 - U_hi
//
(p9) fmerge.s FR_U_hiabs = f0, FR_U_hi
nop.i 999
}
{ .mfi
nop.m 999
//
// For big s: Is |r| < 2**(-3)
// For big s: if p12 set, prepare to branch to Small_R.
// For big s: If p13 set, prepare to branch to Normal_R.
//
(p8) fms.s1 FR_c = FR_s, f1, FR_r
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// For small S: V_hi = N * P_2
// w = N * P_3
// Note the product does not include the (-) as in the writeup
// so (-) missing for V_hi and w.
//
(p8) fcmp.lt.unc.s1 p12, p13 = FR_r, FR_Two_to_M3
nop.i 999 ;;
}
{ .mfi
nop.m 999
(p12) fcmp.gt.s1 p12, p13 = FR_r, FR_Neg_Two_to_M3
nop.i 999 ;;
}
{ .mfi
nop.m 999
(p8) fma.s1 FR_c = FR_c, f1, FR_w
nop.i 999
}
{ .mfb
nop.m 999
(p9) fms.s1 FR_w = FR_N_0, FR_d_2, FR_w
(p12) br.cond.spnt SINCOSL_SMALL_R // Branch if |r| < 2^-3
// and 2^24 <= |x| < 2^63
}
;;
{ .mib
nop.m 999
nop.i 999
(p13) br.cond.sptk SINCOSL_NORMAL_R // Branch if |r| >= 2^-3
// and 2^24 <= |x| < 2^63
}
;;
SINCOSL_LARGER_S_TINY:
//
// Here if |s| < 2^-14, and 2^24 <= |x| < 2^63
//
{ .mfi
nop.m 999
//
// Big s: Vector off when |r| < 2**(-3). Recall that p8 will be true.
// The remaining stuff is for Case 4.
// Small s: V_lo = N * P_2 + U_hi (U_hi is in place of V_hi in writeup)
// Note: the (-) is still missing for V_lo.
// Small s: w = w + N_0 * d_2
// Note: the (-) is now incorporated in w.
//
fcmp.ge.unc.s1 p7, p8 = FR_U_hiabs, FR_V_hiabs
}
{ .mfi
nop.m 999
//
// C_hi = S + A
//
fma.s1 FR_t = FR_U_lo, f1, FR_V_lo
}
;;
{ .mfi
nop.m 999
//
// t = U_lo + V_lo
//
//
(p7) fms.s1 FR_a = FR_U_hi, f1, FR_A
nop.i 999 ;;
}
{ .mfi
nop.m 999
(p8) fma.s1 FR_a = FR_V_hi, f1, FR_A
nop.i 999
}
;;
{ .mfi
//
// Is U_hiabs >= V_hiabs?
//
nop.m 999
fma.s1 FR_C_hi = FR_s, f1, FR_A
nop.i 999 ;;
}
{ .mmi
ldfe FR_C_1 = [GR_ad_c], 16 ;;
ldfe FR_C_2 = [GR_ad_c], 64
nop.i 999 ;;
}
//
// c = c + C_lo finished.
// Load C_2
//
{ .mfi
ldfe FR_S_1 = [GR_ad_s], 16
//
// C_lo = S - C_hi
//
fma.s1 FR_t = FR_t, f1, FR_w
nop.i 999 ;;
}
//
// r and c have been computed.
// Make sure ftz mode is set - should be automatic when using wre
// |r| < 2**(-3)
// Get [i_0,i_1] - two lsb of N_fix.
// Load S_1
//
{ .mfi
ldfe FR_S_2 = [GR_ad_s], 64
//
// t = t + w
//
(p7) fms.s1 FR_a = FR_a, f1, FR_V_hi
tbit.z p9,p10 = GR_N_Inc, 0 // p9 if i_1=0, N mod 4 = 0,1
// p10 if i_1=1, N mod 4 = 2,3
}
;;
{ .mfi
nop.m 999
//
// For larger u than v: a = U_hi - A
// Else a = V_hi - A (do an add to account for missing (-) on V_hi
//
fms.s1 FR_C_lo = FR_s, f1, FR_C_hi
nop.i 999 ;;
}
{ .mfi
nop.m 999
(p8) fms.s1 FR_a = FR_U_hi, f1, FR_a
tbit.z p11,p12 = GR_N_Inc, 1 // p11 if i_0=0, N mod 4 = 0,2
// p12 if i_0=1, N mod 4 = 1,3
}
;;
{ .mfi
nop.m 999
//
// If u > v: a = (U_hi - A) + V_hi
// Else a = (V_hi - A) + U_hi
// In each case account for negative missing from V_hi.
//
fma.s1 FR_C_lo = FR_C_lo, f1, FR_A
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// C_lo = (S - C_hi) + A
//
fma.s1 FR_t = FR_t, f1, FR_a
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// t = t + a
//
fma.s1 FR_C_lo = FR_C_lo, f1, FR_t
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// C_lo = C_lo + t
//
fma.s1 FR_r = FR_C_hi, f1, FR_C_lo
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// Load S_2
//
fma.s1 FR_rsq = FR_r, FR_r, f0
nop.i 999
}
{ .mfi
nop.m 999
//
// r = C_hi + C_lo
//
fms.s1 FR_c = FR_C_hi, f1, FR_r
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// if i_1 ==0: poly = S_2 * FR_rsq + S_1
// else poly = C_2 * FR_rsq + C_1
//
(p9) fma.s1 FR_tmp_result = f0, f1, FR_r
nop.i 999 ;;
}
{ .mfi
nop.m 999
(p10) fma.s1 FR_tmp_result = f0, f1, f1
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// Compute r_cube = FR_rsq * r
//
(p9) fma.s1 FR_poly = FR_rsq, FR_S_2, FR_S_1
nop.i 999 ;;
}
{ .mfi
nop.m 999
(p10) fma.s1 FR_poly = FR_rsq, FR_C_2, FR_C_1
nop.i 999
}
{ .mfi
nop.m 999
//
// Compute FR_rsq = r * r
// Is i_1 == 0 ?
//
fma.s1 FR_r_cubed = FR_rsq, FR_r, f0
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// c = C_hi - r
// Load C_1
//
fma.s1 FR_c = FR_c, f1, FR_C_lo
nop.i 999
}
{ .mfi
nop.m 999
//
// if i_1 ==0: poly = r_cube * poly + c
// else poly = FR_rsq * poly
//
(p12) fms.s1 FR_tmp_result = f0, f1, FR_tmp_result
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// if i_1 ==0: Result = r
// else Result = 1.0
//
(p9) fma.s1 FR_poly = FR_r_cubed, FR_poly, FR_c
nop.i 999 ;;
}
{ .mfi
nop.m 999
(p10) fma.s1 FR_poly = FR_rsq, FR_poly, f0
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// if i_0 !=0: Result = -Result
//
(p11) fma.s0 FR_Result = FR_tmp_result, f1, FR_poly
nop.i 999 ;;
}
{ .mfb
nop.m 999
(p12) fms.s0 FR_Result = FR_tmp_result, f1, FR_poly
//
// if i_0 == 0: Result = Result + poly
// else Result = Result - poly
//
br.ret.sptk b0 // Exit for |s| < 2^-14, and 2^24 <= |x| < 2^63
}
;;
SINCOSL_SMALL_R:
//
// Here if |r| < 2^-3
//
// Enter with r, c, and N_Inc computed
//
// Compare both i_1 and i_0 with 0.
// if i_1 == 0, set p9.
// if i_0 == 0, set p11.
//
{ .mfi
nop.m 999
fma.s1 FR_rsq = FR_r, FR_r, f0 // rsq = r * r
tbit.z p9,p10 = GR_N_Inc, 0 // p9 if i_1=0, N mod 4 = 0,1
// p10 if i_1=1, N mod 4 = 2,3
}
;;
{ .mmi
(p9) ldfe FR_S_5 = [GR_ad_se], -16 // Load S_5 if i_1=0
(p10) ldfe FR_C_5 = [GR_ad_ce], -16 // Load C_5 if i_1=1
nop.i 999
}
;;
{ .mmi
(p9) ldfe FR_S_4 = [GR_ad_se], -16 // Load S_4 if i_1=0
(p10) ldfe FR_C_4 = [GR_ad_ce], -16 // Load C_4 if i_1=1
nop.i 999
}
;;
SINCOSL_SMALL_R_0:
// Entry point for 2^-3 < |x| < pi/4
.pred.rel "mutex",p9,p10
SINCOSL_SMALL_R_1:
// Entry point for pi/4 < |x| < 2^24 and |r| < 2^-3
.pred.rel "mutex",p9,p10
{ .mfi
(p9) ldfe FR_S_3 = [GR_ad_se], -16 // Load S_3 if i_1=0
fma.s1 FR_Z = FR_rsq, FR_rsq, f0 // Z = rsq * rsq
nop.i 999
}
{ .mfi
(p10) ldfe FR_C_3 = [GR_ad_ce], -16 // Load C_3 if i_1=1
(p10) fnma.s1 FR_c = FR_c, FR_r, f0 // c = -c * r if i_1=0
nop.i 999
}
;;
{ .mmf
(p9) ldfe FR_S_2 = [GR_ad_se], -16 // Load S_2 if i_1=0
(p10) ldfe FR_C_2 = [GR_ad_ce], -16 // Load C_2 if i_1=1
(p10) fmerge.s FR_r = f1, f1
}
;;
{ .mmi
(p9) ldfe FR_S_1 = [GR_ad_se], -16 // Load S_1 if i_1=0
(p10) ldfe FR_C_1 = [GR_ad_ce], -16 // Load C_1 if i_1=1
nop.i 999
}
;;
{ .mfi
nop.m 999
(p9) fma.s1 FR_Z = FR_Z, FR_r, f0 // Z = Z * r if i_1=0
nop.i 999
}
;;
{ .mfi
nop.m 999
(p9) fma.s1 FR_poly_lo = FR_rsq, FR_S_5, FR_S_4 // poly_lo=rsq*S_5+S_4 if i_1=0
nop.i 999
}
{ .mfi
nop.m 999
(p10) fma.s1 FR_poly_lo = FR_rsq, FR_C_5, FR_C_4 // poly_lo=rsq*C_5+C_4 if i_1=1
nop.i 999
}
;;
{ .mfi
nop.m 999
(p9) fma.s1 FR_poly_hi = FR_rsq, FR_S_2, FR_S_1 // poly_hi=rsq*S_2+S_1 if i_1=0
nop.i 999
}
{ .mfi
nop.m 999
(p10) fma.s1 FR_poly_hi = FR_rsq, FR_C_2, FR_C_1 // poly_hi=rsq*C_2+C_1 if i_1=1
nop.i 999
}
;;
{ .mfi
nop.m 999
fma.s1 FR_Z = FR_Z, FR_rsq, f0 // Z = Z * rsq
nop.i 999
}
;;
{ .mfi
nop.m 999
(p9) fma.s1 FR_poly_lo = FR_rsq, FR_poly_lo, FR_S_3 // p_lo=p_lo*rsq+S_3, i_1=0
nop.i 999
}
{ .mfi
nop.m 999
(p10) fma.s1 FR_poly_lo = FR_rsq, FR_poly_lo, FR_C_3 // p_lo=p_lo*rsq+C_3, i_1=1
nop.i 999
}
;;
{ .mfi
nop.m 999
(p9) fma.s0 FR_inexact = FR_S_4, FR_S_4, f0 // Dummy op to set inexact
tbit.z p11,p12 = GR_N_Inc, 1 // p11 if i_0=0, N mod 4 = 0,2
// p12 if i_0=1, N mod 4 = 1,3
}
{ .mfi
nop.m 999
(p10) fma.s0 FR_inexact = FR_C_1, FR_C_1, f0 // Dummy op to set inexact
nop.i 999
}
;;
{ .mfi
nop.m 999
(p9) fma.s1 FR_poly_hi = FR_poly_hi, FR_rsq, f0 // p_hi=p_hi*rsq if i_1=0
nop.i 999
}
{ .mfi
nop.m 999
(p10) fma.s1 FR_poly_hi = FR_poly_hi, FR_rsq, f0 // p_hi=p_hi*rsq if i_1=1
nop.i 999
}
;;
{ .mfi
nop.m 999
fma.s1 FR_poly = FR_Z, FR_poly_lo, FR_c // poly=Z*poly_lo+c
nop.i 999
}
;;
{ .mfi
nop.m 999
(p9) fma.s1 FR_poly_hi = FR_r, FR_poly_hi, f0 // p_hi=r*p_hi if i_1=0
nop.i 999
}
;;
{ .mfi
nop.m 999
(p12) fms.s1 FR_r = f0, f1, FR_r // r = -r if i_0=1
nop.i 999
}
;;
{ .mfi
nop.m 999
fma.s1 FR_poly = FR_poly, f1, FR_poly_hi // poly=poly+poly_hi
nop.i 999
}
;;
//
// if (i_0 == 0) Result = r + poly
// if (i_0 != 0) Result = r - poly
//
{ .mfi
nop.m 999
(p11) fma.s0 FR_Result = FR_r, f1, FR_poly
nop.i 999
}
{ .mfb
nop.m 999
(p12) fms.s0 FR_Result = FR_r, f1, FR_poly
br.ret.sptk b0 // Exit for |r| < 2^-3
}
;;
SINCOSL_NORMAL_R:
//
// Here if 2^-3 <= |r| < pi/4
// THIS IS THE MAIN PATH
//
// Enter with r, c, and N_Inc having been computed
//
{ .mfi
ldfe FR_PP_6 = [GR_ad_pp], 16 // Load PP_6
fma.s1 FR_rsq = FR_r, FR_r, f0 // rsq = r * r
tbit.z p9,p10 = GR_N_Inc, 0 // p9 if i_1=0, N mod 4 = 0,1
// p10 if i_1=1, N mod 4 = 2,3
}
{ .mfi
ldfe FR_QQ_6 = [GR_ad_qq], 16 // Load QQ_6
nop.f 999
nop.i 999
}
;;
{ .mmi
(p9) ldfe FR_PP_5 = [GR_ad_pp], 16 // Load PP_5 if i_1=0
(p10) ldfe FR_QQ_5 = [GR_ad_qq], 16 // Load QQ_5 if i_1=1
nop.i 999
}
;;
SINCOSL_NORMAL_R_0:
// Entry for 2^-3 < |x| < pi/4
.pred.rel "mutex",p9,p10
{ .mmf
(p9) ldfe FR_C_1 = [GR_ad_pp], 16 // Load C_1 if i_1=0
(p10) ldfe FR_S_1 = [GR_ad_qq], 16 // Load S_1 if i_1=1
frcpa.s1 FR_r_hi, p6 = f1, FR_r // r_hi = frcpa(r)
}
;;
{ .mfi
nop.m 999
(p9) fma.s1 FR_poly = FR_rsq, FR_PP_8, FR_PP_7 // poly = rsq*PP_8+PP_7 if i_1=0
nop.i 999
}
{ .mfi
nop.m 999
(p10) fma.s1 FR_poly = FR_rsq, FR_QQ_8, FR_QQ_7 // poly = rsq*QQ_8+QQ_7 if i_1=1
nop.i 999
}
;;
{ .mfi
nop.m 999
fma.s1 FR_r_cubed = FR_r, FR_rsq, f0 // rcubed = r * rsq
nop.i 999
}
;;
SINCOSL_NORMAL_R_1:
// Entry for pi/4 <= |x| < 2^24
.pred.rel "mutex",p9,p10
{ .mmf
(p9) ldfe FR_PP_1 = [GR_ad_pp], 16 // Load PP_1_hi if i_1=0
(p10) ldfe FR_QQ_1 = [GR_ad_qq], 16 // Load QQ_1 if i_1=1
frcpa.s1 FR_r_hi, p6 = f1, FR_r_hi // r_hi = frpca(frcpa(r))
}
;;
{ .mfi
(p9) ldfe FR_PP_4 = [GR_ad_pp], 16 // Load PP_4 if i_1=0
(p9) fma.s1 FR_poly = FR_rsq, FR_poly, FR_PP_6 // poly = rsq*poly+PP_6 if i_1=0
nop.i 999
}
{ .mfi
(p10) ldfe FR_QQ_4 = [GR_ad_qq], 16 // Load QQ_4 if i_1=1
(p10) fma.s1 FR_poly = FR_rsq, FR_poly, FR_QQ_6 // poly = rsq*poly+QQ_6 if i_1=1
nop.i 999
}
;;
{ .mfi
nop.m 999
(p9) fma.s1 FR_corr = FR_C_1, FR_rsq, f0 // corr = C_1 * rsq if i_1=0
nop.i 999
}
{ .mfi
nop.m 999
(p10) fma.s1 FR_corr = FR_S_1, FR_r_cubed, FR_r // corr = S_1 * r^3 + r if i_1=1
nop.i 999
}
;;
{ .mfi
(p9) ldfe FR_PP_3 = [GR_ad_pp], 16 // Load PP_3 if i_1=0
fma.s1 FR_r_hi_sq = FR_r_hi, FR_r_hi, f0 // r_hi_sq = r_hi * r_hi
nop.i 999
}
{ .mfi
(p10) ldfe FR_QQ_3 = [GR_ad_qq], 16 // Load QQ_3 if i_1=1
fms.s1 FR_r_lo = FR_r, f1, FR_r_hi // r_lo = r - r_hi
nop.i 999
}
;;
{ .mfi
(p9) ldfe FR_PP_2 = [GR_ad_pp], 16 // Load PP_2 if i_1=0
(p9) fma.s1 FR_poly = FR_rsq, FR_poly, FR_PP_5 // poly = rsq*poly+PP_5 if i_1=0
nop.i 999
}
{ .mfi
(p10) ldfe FR_QQ_2 = [GR_ad_qq], 16 // Load QQ_2 if i_1=1
(p10) fma.s1 FR_poly = FR_rsq, FR_poly, FR_QQ_5 // poly = rsq*poly+QQ_5 if i_1=1
nop.i 999
}
;;
{ .mfi
(p9) ldfe FR_PP_1_lo = [GR_ad_pp], 16 // Load PP_1_lo if i_1=0
(p9) fma.s1 FR_corr = FR_corr, FR_c, FR_c // corr = corr * c + c if i_1=0
nop.i 999
}
{ .mfi
nop.m 999
(p10) fnma.s1 FR_corr = FR_corr, FR_c, f0 // corr = -corr * c if i_1=1
nop.i 999
}
;;
{ .mfi
nop.m 999
(p9) fma.s1 FR_U_lo = FR_r, FR_r_hi, FR_r_hi_sq // U_lo = r*r_hi+r_hi_sq, i_1=0
nop.i 999
}
{ .mfi
nop.m 999
(p10) fma.s1 FR_U_lo = FR_r_hi, f1, FR_r // U_lo = r_hi + r if i_1=1
nop.i 999
}
;;
{ .mfi
nop.m 999
(p9) fma.s1 FR_U_hi = FR_r_hi, FR_r_hi_sq, f0 // U_hi = r_hi*r_hi_sq if i_1=0
nop.i 999
}
{ .mfi
nop.m 999
(p10) fma.s1 FR_U_hi = FR_QQ_1, FR_r_hi_sq, f1 // U_hi = QQ_1*r_hi_sq+1, i_1=1
nop.i 999
}
;;
{ .mfi
nop.m 999
(p9) fma.s1 FR_poly = FR_rsq, FR_poly, FR_PP_4 // poly = poly*rsq+PP_4 if i_1=0
nop.i 999
}
{ .mfi
nop.m 999
(p10) fma.s1 FR_poly = FR_rsq, FR_poly, FR_QQ_4 // poly = poly*rsq+QQ_4 if i_1=1
nop.i 999
}
;;
{ .mfi
nop.m 999
(p9) fma.s1 FR_U_lo = FR_r, FR_r, FR_U_lo // U_lo = r * r + U_lo if i_1=0
nop.i 999
}
{ .mfi
nop.m 999
(p10) fma.s1 FR_U_lo = FR_r_lo, FR_U_lo, f0 // U_lo = r_lo * U_lo if i_1=1
nop.i 999
}
;;
{ .mfi
nop.m 999
(p9) fma.s1 FR_U_hi = FR_PP_1, FR_U_hi, f0 // U_hi = PP_1 * U_hi if i_1=0
nop.i 999
}
;;
{ .mfi
nop.m 999
(p9) fma.s1 FR_poly = FR_rsq, FR_poly, FR_PP_3 // poly = poly*rsq+PP_3 if i_1=0
nop.i 999
}
{ .mfi
nop.m 999
(p10) fma.s1 FR_poly = FR_rsq, FR_poly, FR_QQ_3 // poly = poly*rsq+QQ_3 if i_1=1
nop.i 999
}
;;
{ .mfi
nop.m 999
(p9) fma.s1 FR_U_lo = FR_r_lo, FR_U_lo, f0 // U_lo = r_lo * U_lo if i_1=0
nop.i 999
}
{ .mfi
nop.m 999
(p10) fma.s1 FR_U_lo = FR_QQ_1,FR_U_lo, f0 // U_lo = QQ_1 * U_lo if i_1=1
nop.i 999
}
;;
{ .mfi
nop.m 999
(p9) fma.s1 FR_U_hi = FR_r, f1, FR_U_hi // U_hi = r + U_hi if i_1=0
nop.i 999
}
;;
{ .mfi
nop.m 999
(p9) fma.s1 FR_poly = FR_rsq, FR_poly, FR_PP_2 // poly = poly*rsq+PP_2 if i_1=0
nop.i 999
}
{ .mfi
nop.m 999
(p10) fma.s1 FR_poly = FR_rsq, FR_poly, FR_QQ_2 // poly = poly*rsq+QQ_2 if i_1=1
nop.i 999
}
;;
{ .mfi
nop.m 999
(p9) fma.s1 FR_U_lo = FR_PP_1, FR_U_lo, f0 // U_lo = PP_1 * U_lo if i_1=0
nop.i 999
}
;;
{ .mfi
nop.m 999
(p9) fma.s1 FR_poly = FR_rsq, FR_poly, FR_PP_1_lo // poly =poly*rsq+PP1lo i_1=0
nop.i 999
}
{ .mfi
nop.m 999
(p10) fma.s1 FR_poly = FR_rsq, FR_poly, f0 // poly = poly*rsq if i_1=1
nop.i 999
}
;;
{ .mfi
nop.m 999
fma.s1 FR_V = FR_U_lo, f1, FR_corr // V = U_lo + corr
tbit.z p11,p12 = GR_N_Inc, 1 // p11 if i_0=0, N mod 4 = 0,2
// p12 if i_0=1, N mod 4 = 1,3
}
;;
{ .mfi
nop.m 999
(p9) fma.s0 FR_inexact = FR_PP_5, FR_PP_4, f0 // Dummy op to set inexact
nop.i 999
}
{ .mfi
nop.m 999
(p10) fma.s0 FR_inexact = FR_QQ_5, FR_QQ_5, f0 // Dummy op to set inexact
nop.i 999
}
;;
{ .mfi
nop.m 999
(p9) fma.s1 FR_poly = FR_r_cubed, FR_poly, f0 // poly = poly*r^3 if i_1=0
nop.i 999
}
{ .mfi
nop.m 999
(p10) fma.s1 FR_poly = FR_rsq, FR_poly, f0 // poly = poly*rsq if i_1=1
nop.i 999
}
;;
{ .mfi
nop.m 999
(p11) fma.s1 FR_tmp_result = f0, f1, f1// tmp_result=+1.0 if i_0=0
nop.i 999
}
{ .mfi
nop.m 999
(p12) fms.s1 FR_tmp_result = f0, f1, f1// tmp_result=-1.0 if i_0=1
nop.i 999
}
;;
{ .mfi
nop.m 999
fma.s1 FR_V = FR_poly, f1, FR_V // V = poly + V
nop.i 999
}
;;
// If i_0 = 0 Result = U_hi + V
// If i_0 = 1 Result = -U_hi - V
{ .mfi
nop.m 999
(p11) fma.s0 FR_Result = FR_tmp_result, FR_U_hi, FR_V
nop.i 999
}
{ .mfb
nop.m 999
(p12) fms.s0 FR_Result = FR_tmp_result, FR_U_hi, FR_V
br.ret.sptk b0 // Exit for 2^-3 <= |r| < pi/4
}
;;
SINCOSL_ZERO:
// Here if x = 0
{ .mfi
cmp.eq.unc p6, p7 = 0x1, GR_Sin_or_Cos
nop.f 999
nop.i 999
}
;;
{ .mfi
nop.m 999
(p7) fmerge.s FR_Result = FR_Input_X, FR_Input_X // If sin, result = input
nop.i 999
}
{ .mfb
nop.m 999
(p6) fma.s0 FR_Result = f1, f1, f0 // If cos, result=1.0
br.ret.sptk b0 // Exit for x=0
}
;;
SINCOSL_DENORMAL:
{ .mmb
getf.exp GR_signexp_x = FR_norm_x // Get sign and exponent of x
nop.m 999
br.cond.sptk SINCOSL_COMMON // Return to common code
}
;;
SINCOSL_SPECIAL:
{ .mfb
nop.m 999
//
// Path for Arg = +/- QNaN, SNaN, Inf
// Invalid can be raised. SNaNs
// become QNaNs
//
fmpy.s0 FR_Result = FR_Input_X, f0
br.ret.sptk b0 ;;
}
GLOBAL_IEEE754_END(cosl)
libm_alias_ldouble_other (__cos, cos)
// *******************************************************************
// *******************************************************************
// *******************************************************************
//
// Special Code to handle very large argument case.
// Call int __libm_pi_by_2_reduce(x,r,c) for |arguments| >= 2**63
// The interface is custom:
// On input:
// (Arg or x) is in f8
// On output:
// r is in f8
// c is in f9
// N is in r8
// Be sure to allocate at least 2 GP registers as output registers for
// __libm_pi_by_2_reduce. This routine uses r59-60. These are used as
// scratch registers within the __libm_pi_by_2_reduce routine (for speed).
//
// We know also that __libm_pi_by_2_reduce preserves f10-15, f71-127. We
// use this to eliminate save/restore of key fp registers in this calling
// function.
//
// *******************************************************************
// *******************************************************************
// *******************************************************************
LOCAL_LIBM_ENTRY(__libm_callout)
SINCOSL_ARG_TOO_LARGE:
.prologue
{ .mfi
nop.f 0
.save ar.pfs,GR_SAVE_PFS
mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
};;
{ .mmi
setf.exp FR_Two_to_M3 = GR_exp_2_to_m3 // Form 2^-3
mov GR_SAVE_GP=gp // Save gp
.save b0, GR_SAVE_B0
mov GR_SAVE_B0=b0 // Save b0
};;
.body
//
// Call argument reduction with x in f8
// Returns with N in r8, r in f8, c in f9
// Assumes f71-127 are preserved across the call
//
{ .mib
setf.exp FR_Neg_Two_to_M3 = GR_exp_m2_to_m3 // Form -(2^-3)
nop.i 0
br.call.sptk b0=__libm_pi_by_2_reduce#
};;
{ .mfi
add GR_N_Inc = GR_Sin_or_Cos,r8
fcmp.lt.unc.s1 p6, p0 = FR_r, FR_Two_to_M3
mov b0 = GR_SAVE_B0 // Restore return address
};;
{ .mfi
mov gp = GR_SAVE_GP // Restore gp
(p6) fcmp.gt.unc.s1 p6, p0 = FR_r, FR_Neg_Two_to_M3
mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
};;
{ .mbb
nop.m 999
(p6) br.cond.spnt SINCOSL_SMALL_R // Branch if |r|< 2^-3 for |x| >= 2^63
br.cond.sptk SINCOSL_NORMAL_R // Branch if |r|>=2^-3 for |x| >= 2^63
};;
LOCAL_LIBM_END(__libm_callout)
.type __libm_pi_by_2_reduce#,@function
.global __libm_pi_by_2_reduce#
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