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glibc/sysdeps/ia64/fpu/libm_sincos_large.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_large.s"
// Copyright (c) 2002 - 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
//==============================================================
// 02/15/02 Initial version
// 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
// 05/15/03 Reformatted data tables
//
//
// Overview of operation
//==============================================================
//
// These functions calculate the sin and cos for inputs
// greater than 2^10
//
// __libm_sin_large#
// __libm_cos_large#
// They accept argument in f8
// and return result in f8 without final rounding
//
// __libm_sincos_large#
// It accepts argument in f8
// and returns cos in f8 and sin in f9 without final rounding
//
//
//*********************************************************************
//
// Accuracy: Within .7 ulps for 80-bit floating point values
// Very accurate for double precision values
//
//*********************************************************************
//
// Resources Used:
//
// Floating-Point Registers: f8 as Input Value, f8 and f9 as Return Values
// f32-f103
//
// General Purpose Registers:
// r32-r43
// r44-r45 (Used to pass arguments to pi_by_2 reduce routine)
//
// 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
//
// sin(SNaN) = QNaN
// sin(QNaN) = QNaN
// sin(inf) = QNaN
// sin(+/-0) = +/-0
// cos(inf) = QNaN
// cos(SNaN) = QNaN
// cos(QNaN) = QNaN
// cos(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
//
// cos( Arg ) = sin( (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
//
// sin( Arg ) = (-1)^i_0 sin( alpha ) if i_1 = 0,
// = (-1)^i_0 cos( 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, sin(r+c) and cos(r+c) can be
// computed very easily by 2 or 3 terms of the Taylor series
// expansion as follows:
//
// Case 2:
// -------
//
// sin(r + c) = r + c - r^3/6 accurately
// cos(r + c) = 1 - 2^(-67) accurately
//
// Case 4:
// -------
//
// sin(r + c) = r + c - r^3/6 + r^5/120 accurately
// cos(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
//
// sin(r + c) = sin(r) + correction, or
// cos(r + c) = cos(r) + correction.
//
// Specifically,
//
// sin(r + c) = sin(r) + c sin'(r) + O(c^2)
// = sin(r) + c cos (r) + O(c^2)
// = sin(r) + c(1 - r^2/2) accurately.
// Similarly,
//
// cos(r + c) = cos(r) - c sin(r) + O(c^2)
// = cos(r) - c(r - r^3/6) accurately.
//
// We therefore concentrate on accurately calculating sin(r) and
// cos(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 sin(r) and cos(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
//
// sin(Arg) = (-1)^i_0 * sin(r + c) if i_1 = 0
// = (-1)^i_0 * cos(r + c) if i_1 = 1
//
// can be accurately approximated by
//
// sin(Arg) = (-1)^i_0 * [sin(r) + c] if i_1 = 0
// = (-1)^i_0 * [cos(r) - c*r] if i_1 = 1
//
// because |r| is small and thus the second terms in the correction
// are unnecessary.
//
// Finally, sin(r) and cos(r) are approximated by polynomials of
// moderate lengths.
//
// sin(r) = r + S_1 r^3 + S_2 r^5 + ... + S_5 r^11
// cos(r) = 1 + C_1 r^2 + C_2 r^4 + ... + C_5 r^10
//
// We can make use of predicates to selectively calculate
// sin(r) or cos(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,
//
// sin(Arg) = (-1)^i_0 * sin(r + c) if i_1 = 0
// = (-1)^i_0 * cos(r + c) if i_1 = 1.
//
// Because |r| is now larger, we need one extra term in the
// correction. sin(Arg) can be accurately approximated by
//
// sin(Arg) = (-1)^i_0 * [sin(r) + c(1-r^2/2)] if i_1 = 0
// = (-1)^i_0 * [cos(r) - c*r*(1 - r^2/6)] i_1 = 1.
//
// Finally, sin(r) and cos(r) are approximated by polynomials of
// moderate lengths.
//
// sin(r) = r + PP_1_hi r^3 + PP_1_lo r^3 +
// PP_2 r^5 + ... + PP_8 r^17
//
// cos(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(FSINCOS_CONSTANTS)
data4 0x4B800000 // two**24
data4 0xCB800000 // -two**24
data4 0x00000000 // pad
data4 0x00000000 // pad
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
data4 0x5F000000 // two**63
data4 0xDF000000 // -two**63
data4 0x00000000 // pad
data4 0x00000000 // pad
data8 0xA397E5046EC6B45A, 0x00003FE7 // Inv_P_0
data8 0x8D848E89DBD171A1, 0x0000BFBF // d_1
data8 0xD5394C3618A66F8E, 0x0000BF7C // d_2
data8 0xC90FDAA22168C234, 0x00003FFE // pi_by_4
data8 0xC90FDAA22168C234, 0x0000BFFE // neg_pi_by_4
data4 0x3E000000 // two**-3
data4 0xBE000000 // -two**-3
data4 0x00000000 // pad
data4 0x00000000 // pad
data4 0x2F000000 // two**-33
data4 0xAF000000 // -two**-33
data4 0x9E000000 // -two**-67
data4 0x00000000 // pad
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
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
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
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 // two**-14
data4 0xB8800000 // -two**-14
LOCAL_OBJECT_END(FSINCOS_CONSTANTS)
// sin and cos registers
// FR
FR_Input_X = f8
FR_r = f8
FR_c = f9
FR_Two_to_63 = f32
FR_Two_to_24 = f33
FR_Pi_by_4 = f33
FR_Two_to_M14 = f34
FR_Two_to_M33 = f35
FR_Neg_Two_to_24 = f36
FR_Neg_Pi_by_4 = f36
FR_Neg_Two_to_M14 = 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_prelim = 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 = f81
FR_PP_7 = f82
FR_QQ_7 = f82
FR_PP_6 = f83
FR_QQ_6 = f83
FR_PP_5 = f84
FR_QQ_5 = f84
FR_PP_4 = f85
FR_QQ_4 = f85
FR_PP_3 = f86
FR_QQ_3 = f86
FR_PP_2 = f87
FR_QQ_2 = f87
FR_QQ_1 = 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_Neg_Two_to_63 = f94
FR_P_0 = f95
FR_C_lo = f96
FR_PP_1 = f97
FR_PP_1_lo = f98
FR_ArgPrime = f99
// GR
GR_Table_Base = r32
GR_Table_Base1 = r33
GR_i_0 = r34
GR_i_1 = r35
GR_N_Inc = r36
GR_Sin_or_Cos = r37
GR_SAVE_B0 = r39
GR_SAVE_GP = r40
GR_SAVE_PFS = r41
// sincos combined routine registers
// GR
GR_SINCOS_SAVE_PFS = r32
GR_SINCOS_SAVE_B0 = r33
GR_SINCOS_SAVE_GP = r34
// FR
FR_SINCOS_ARG = f100
FR_SINCOS_RES_SIN = f101
.section .text
GLOBAL_LIBM_ENTRY(__libm_sincos_large)
{ .mfi
alloc GR_SINCOS_SAVE_PFS = ar.pfs,0,3,0,0
fma.s1 FR_SINCOS_ARG = f8, f1, f0 // Save argument for sin and cos
mov GR_SINCOS_SAVE_B0 = b0
};;
{ .mfb
mov GR_SINCOS_SAVE_GP = gp
nop.f 0
br.call.sptk b0 = __libm_sin_large // Call sin
};;
{ .mfi
nop.m 0
fma.s1 FR_SINCOS_RES_SIN = f8, f1, f0 // Save sin result
nop.i 0
};;
{ .mfb
nop.m 0
fma.s1 f8 = FR_SINCOS_ARG, f1, f0 // Arg for cos
br.call.sptk b0 = __libm_cos_large // Call cos
};;
{ .mfi
mov gp = GR_SINCOS_SAVE_GP
fma.s1 f9 = FR_SINCOS_RES_SIN, f1, f0 // Out sin result
mov b0 = GR_SINCOS_SAVE_B0
};;
{ .mib
nop.m 0
mov ar.pfs = GR_SINCOS_SAVE_PFS
br.ret.sptk b0 // sincos_large exit
};;
GLOBAL_LIBM_END(__libm_sincos_large)
GLOBAL_LIBM_ENTRY(__libm_sin_large)
{ .mlx
alloc GR_Table_Base = ar.pfs,0,12,2,0
movl GR_Sin_or_Cos = 0x0 ;;
}
{ .mmi
nop.m 999
addl GR_Table_Base = @ltoff(FSINCOS_CONSTANTS#), gp
nop.i 999
}
;;
{ .mmi
ld8 GR_Table_Base = [GR_Table_Base]
nop.m 999
nop.i 999
}
;;
{ .mib
nop.m 999
nop.i 999
br.cond.sptk SINCOS_CONTINUE ;;
}
GLOBAL_LIBM_END(__libm_sin_large)
GLOBAL_LIBM_ENTRY(__libm_cos_large)
{ .mlx
alloc GR_Table_Base= ar.pfs,0,12,2,0
movl GR_Sin_or_Cos = 0x1 ;;
}
{ .mmi
nop.m 999
addl GR_Table_Base = @ltoff(FSINCOS_CONSTANTS#), gp
nop.i 999
}
;;
{ .mmi
ld8 GR_Table_Base = [GR_Table_Base]
nop.m 999
nop.i 999
}
;;
//
// Load Table Address
//
SINCOS_CONTINUE:
{ .mmi
add GR_Table_Base1 = 96, GR_Table_Base
ldfs FR_Two_to_24 = [GR_Table_Base], 4
nop.i 999
}
;;
{ .mmi
nop.m 999
//
// Load 2**24, load 2**63.
//
ldfs FR_Neg_Two_to_24 = [GR_Table_Base], 12
mov r41 = ar.pfs ;;
}
{ .mfi
ldfs FR_Two_to_63 = [GR_Table_Base1], 4
//
// Check for unnormals - unsupported operands. We do not want
// to generate denormal exception
// Check for NatVals, QNaNs, SNaNs, +/-Infs
// Check for EM unsupporteds
// Check for Zero
//
fclass.m.unc p6, p8 = FR_Input_X, 0x1E3
mov r40 = gp ;;
}
{ .mfi
nop.m 999
fclass.nm.unc p8, p0 = FR_Input_X, 0x1FF
// GR_Sin_or_Cos denotes
mov r39 = b0
}
{ .mfb
ldfs FR_Neg_Two_to_63 = [GR_Table_Base1], 12
fclass.m.unc p10, p0 = FR_Input_X, 0x007
(p6) br.cond.spnt SINCOS_SPECIAL ;;
}
{ .mib
nop.m 999
nop.i 999
(p8) br.cond.spnt SINCOS_SPECIAL ;;
}
{ .mib
nop.m 999
nop.i 999
//
// Branch if +/- NaN, Inf.
// Load -2**24, load -2**63.
//
(p10) br.cond.spnt SINCOS_ZERO ;;
}
{ .mmb
ldfe FR_Inv_pi_by_2 = [GR_Table_Base], 16
ldfe FR_Inv_P_0 = [GR_Table_Base1], 16
nop.b 999 ;;
}
{ .mmb
nop.m 999
ldfe FR_d_1 = [GR_Table_Base1], 16
nop.b 999 ;;
}
//
// Raise possible denormal operand flag with useful fcmp
// Is x <= -2**63
// Load Inv_P_0 for pre-reduction
// Load Inv_pi_by_2
//
{ .mmb
ldfe FR_P_0 = [GR_Table_Base], 16
ldfe FR_d_2 = [GR_Table_Base1], 16
nop.b 999 ;;
}
//
// Load P_0
// Load d_1
// Is x >= 2**63
// Is x <= -2**24?
//
{ .mmi
ldfe FR_P_1 = [GR_Table_Base], 16 ;;
//
// Load P_1
// Load d_2
// Is x >= 2**24?
//
ldfe FR_P_2 = [GR_Table_Base], 16
nop.i 999 ;;
}
{ .mmf
nop.m 999
ldfe FR_P_3 = [GR_Table_Base], 16
fcmp.le.unc.s1 p7, p8 = FR_Input_X, FR_Neg_Two_to_24
}
{ .mfi
nop.m 999
//
// Branch if +/- zero.
// Decide about the paths to take:
// If -2**24 < FR_Input_X < 2**24 - CASE 1 OR 2
// OTHERWISE - CASE 3 OR 4
//
fcmp.le.unc.s1 p10, p11 = FR_Input_X, FR_Neg_Two_to_63
nop.i 999 ;;
}
{ .mfi
nop.m 999
(p8) fcmp.ge.s1 p7, p0 = FR_Input_X, FR_Two_to_24
nop.i 999
}
{ .mfi
ldfe FR_Pi_by_4 = [GR_Table_Base1], 16
(p11) fcmp.ge.s1 p10, p0 = FR_Input_X, FR_Two_to_63
nop.i 999 ;;
}
{ .mmi
ldfe FR_Neg_Pi_by_4 = [GR_Table_Base1], 16 ;;
ldfs FR_Two_to_M3 = [GR_Table_Base1], 4
nop.i 999 ;;
}
{ .mib
ldfs FR_Neg_Two_to_M3 = [GR_Table_Base1], 12
nop.i 999
//
// Load P_2
// Load P_3
// Load pi_by_4
// Load neg_pi_by_4
// Load 2**(-3)
// Load -2**(-3).
//
(p10) br.cond.spnt SINCOS_ARG_TOO_LARGE ;;
}
{ .mib
nop.m 999
nop.i 999
//
// Branch out if x >= 2**63. Use Payne-Hanek Reduction
//
(p7) br.cond.spnt SINCOS_LARGER_ARG ;;
}
{ .mfi
nop.m 999
//
// Branch if Arg <= -2**24 or Arg >= 2**24 and use pre-reduction.
//
fma.s1 FR_N_float = FR_Input_X, FR_Inv_pi_by_2, f0
nop.i 999 ;;
}
{ .mfi
nop.m 999
fcmp.lt.unc.s1 p6, p7 = FR_Input_X, FR_Pi_by_4
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// Select the case when |Arg| < pi/4
// Else Select the case when |Arg| >= pi/4
//
fcvt.fx.s1 FR_N_fix = FR_N_float
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// N = Arg * 2/pi
// Check if Arg < pi/4
//
(p6) fcmp.gt.s1 p6, p7 = FR_Input_X, FR_Neg_Pi_by_4
nop.i 999 ;;
}
//
// Case 2: Convert integer N_fix back to normalized floating-point value.
// Case 1: p8 is only affected when p6 is set
//
{ .mfi
(p7) ldfs FR_Two_to_M33 = [GR_Table_Base1], 4
//
// Grab the integer part of N and call it N_fix
//
(p6) fmerge.se FR_r = FR_Input_X, FR_Input_X
// If |x| < pi/4, r = x and c = 0
// lf |x| < pi/4, is x < 2**(-3).
// r = Arg
// c = 0
(p6) mov GR_N_Inc = GR_Sin_or_Cos ;;
}
{ .mmf
nop.m 999
(p7) ldfs FR_Neg_Two_to_M33 = [GR_Table_Base1], 4
(p6) fmerge.se FR_c = f0, f0
}
{ .mfi
nop.m 999
(p6) fcmp.lt.unc.s1 p8, p9 = FR_Input_X, FR_Two_to_M3
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// 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
//
(p7) fcvt.xf FR_N_float = FR_N_fix
nop.i 999 ;;
}
{ .mmf
nop.m 999
(p7) getf.sig GR_N_Inc = FR_N_fix
(p8) fcmp.gt.s1 p8, p0 = FR_Input_X, FR_Neg_Two_to_M3 ;;
}
{ .mib
nop.m 999
nop.i 999
//
// Load 2**(-33), -2**(-33)
//
(p8) br.cond.spnt SINCOS_SMALL_R ;;
}
{ .mib
nop.m 999
nop.i 999
(p6) br.cond.sptk SINCOS_NORMAL_R ;;
}
//
// if |x| < pi/4, branch based on |x| < 2**(-3) or otherwise.
//
//
// In this branch, |x| >= pi/4.
//
{ .mfi
ldfs FR_Neg_Two_to_M67 = [GR_Table_Base1], 8
//
// Load -2**(-67)
//
fnma.s1 FR_s = FR_N_float, FR_P_1, FR_Input_X
//
// w = N * P_2
// s = -N * P_1 + Arg
//
add GR_N_Inc = GR_N_Inc, GR_Sin_or_Cos
}
{ .mfi
nop.m 999
fma.s1 FR_w = FR_N_float, FR_P_2, f0
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// Adjust N_fix by N_inc to determine whether sine or
// cosine is being calculated
//
fcmp.lt.unc.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
nop.i 999 ;;
}
{ .mfi
nop.m 999
// Remember x >= pi/4.
// Is s <= -2**(-33) or s >= 2**(-33) (p6)
// or -2**(-33) < s < 2**(-33) (p7)
(p6) fms.s1 FR_r = FR_s, f1, FR_w
nop.i 999
}
{ .mfi
nop.m 999
(p7) fma.s1 FR_w = FR_N_float, FR_P_3, f0
nop.i 999 ;;
}
{ .mfi
nop.m 999
(p7) fma.s1 FR_U_1 = FR_N_float, FR_P_2, FR_w
nop.i 999
}
{ .mfi
nop.m 999
(p6) fms.s1 FR_c = FR_s, f1, FR_r
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// For big s: r = s - w: No futher reduction is necessary
// For small s: w = N * P_3 (change sign) More reduction
//
(p6) fcmp.lt.unc.s1 p8, p9 = FR_r, FR_Two_to_M3
nop.i 999 ;;
}
{ .mfi
nop.m 999
(p8) fcmp.gt.s1 p8, p9 = FR_r, FR_Neg_Two_to_M3
nop.i 999 ;;
}
{ .mfi
nop.m 999
(p7) fms.s1 FR_r = FR_s, f1, FR_U_1
nop.i 999
}
{ .mfb
nop.m 999
//
// 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.
//
(p6) fms.s1 FR_c = FR_c, f1, FR_w
//
// For big s: c = c + w (w has not been negated.)
// For small s: r = S - U_1
//
(p8) br.cond.spnt SINCOS_SMALL_R ;;
}
{ .mib
nop.m 999
nop.i 999
(p9) br.cond.sptk SINCOS_NORMAL_R ;;
}
{ .mfi
(p7) add GR_Table_Base1 = 224, GR_Table_Base1
//
// Branch to SINCOS_SMALL_R or SINCOS_NORMAL_R
//
(p7) fms.s1 FR_U_2 = FR_N_float, FR_P_2, FR_U_1
//
// c = S - U_1
// r = S_1 * r
//
//
(p7) extr.u GR_i_1 = GR_N_Inc, 0, 1
}
{ .mmi
nop.m 999 ;;
//
// Get [i_0,i_1] - two lsb of N_fix_gr.
// Do dummy fmpy so inexact is always set.
//
(p7) cmp.eq.unc p9, p10 = 0x0, GR_i_1
(p7) extr.u GR_i_0 = GR_N_Inc, 1, 1 ;;
}
//
// For small s: U_2 = N * P_2 - U_1
// S_1 stored constant - grab the one stored with the
// coefficients.
//
{ .mfi
(p7) ldfe FR_S_1 = [GR_Table_Base1], 16
//
// Check if i_1 and i_0 != 0
//
(p10) fma.s1 FR_poly = f0, f1, FR_Neg_Two_to_M67
(p7) cmp.eq.unc p11, p12 = 0x0, GR_i_0 ;;
}
{ .mfi
nop.m 999
(p7) 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
//
(p7) fma.s1 FR_rsq = FR_r, FR_r, f0
nop.i 999 ;;
}
{ .mfi
nop.m 999
(p7) fma.s1 FR_U_2 = FR_U_2, f1, FR_w
nop.i 999
}
{ .mfi
nop.m 999
//(p7) fmerge.se FR_Input_X = FR_r, FR_r
(p7) fmerge.se FR_prelim = FR_r, FR_r
nop.i 999 ;;
}
{ .mfi
nop.m 999
//(p10) fma.s1 FR_Input_X = f0, f1, f1
(p10) fma.s1 FR_prelim = f0, f1, f1
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// FR_rsq = r * r
// Save r as the result.
//
(p7) 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_Input_X = FR_Input_X, f1, f0
(p12) fnma.s1 FR_prelim = FR_prelim, f1, f0
nop.i 999
}
{ .mfi
nop.m 999
(p7) fma.s1 FR_r = FR_S_1, FR_r, f0
nop.i 999 ;;
}
{ .mfi
nop.m 999
(p7) fma.d.s1 FR_S_1 = FR_S_1, FR_S_1, f0
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// If i_1 != 0, poly = 2**(-67)
//
(p7) 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.s1 FR_Input_X = FR_prelim, f1, FR_poly
nop.i 999 ;;
}
{ .mfb
nop.m 999
(p12) fms.s1 FR_Input_X = FR_prelim, f1, FR_poly
//
// if (i_0 == 0), Result = Result + poly
// else Result = Result - poly
//
br.ret.sptk b0 ;;
}
SINCOS_LARGER_ARG:
{ .mfi
nop.m 999
fma.s1 FR_N_0 = FR_Input_X, FR_Inv_P_0, f0
nop.i 999
}
;;
// This path for argument > 2*24
// Adjust table_ptr1 to beginning of table.
//
{ .mmi
nop.m 999
addl GR_Table_Base = @ltoff(FSINCOS_CONSTANTS#), gp
nop.i 999
}
;;
{ .mmi
ld8 GR_Table_Base = [GR_Table_Base]
nop.m 999
nop.i 999
}
;;
//
// Point to 2*-14
// N_0 = Arg * Inv_P_0
//
{ .mmi
add GR_Table_Base = 688, GR_Table_Base ;;
ldfs FR_Two_to_M14 = [GR_Table_Base], 4
nop.i 999 ;;
}
{ .mfi
ldfs FR_Neg_Two_to_M14 = [GR_Table_Base], 0
nop.f 999
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// Load values 2**(-14) and -2**(-14)
//
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
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 ;;
}
{ .mfi
nop.m 999
(p9) fms.s1 FR_U_lo = FR_N_0, FR_d_1, FR_U_hi
nop.i 999 ;;
}
{ .mfi
nop.m 999
(p9) fmerge.s FR_V_hiabs = f0, FR_V_hi
nop.i 999
}
{ .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 SINCOS_SMALL_R ;;
}
{ .mib
nop.m 999
nop.i 999
(p13) br.cond.sptk SINCOS_NORMAL_R ;;
}
{ .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.
//
(p9) fcmp.ge.unc.s1 p10, p11 = FR_U_hiabs, FR_V_hiabs
extr.u GR_i_1 = GR_N_Inc, 0, 1 ;;
}
{ .mfi
nop.m 999
//
// C_hi = S + A
//
(p9) fma.s1 FR_t = FR_U_lo, f1, FR_V_lo
extr.u GR_i_0 = GR_N_Inc, 1, 1 ;;
}
{ .mfi
nop.m 999
//
// t = U_lo + V_lo
//
//
(p10) fms.s1 FR_a = FR_U_hi, f1, FR_A
nop.i 999 ;;
}
{ .mfi
nop.m 999
(p11) fma.s1 FR_a = FR_V_hi, f1, FR_A
nop.i 999
}
;;
{ .mmi
nop.m 999
addl GR_Table_Base = @ltoff(FSINCOS_CONSTANTS#), gp
nop.i 999
}
;;
{ .mmi
ld8 GR_Table_Base = [GR_Table_Base]
nop.m 999
nop.i 999
}
;;
{ .mfi
add GR_Table_Base = 528, GR_Table_Base
//
// Is U_hiabs >= V_hiabs?
//
(p9) fma.s1 FR_C_hi = FR_s, f1, FR_A
nop.i 999 ;;
}
{ .mmi
ldfe FR_C_1 = [GR_Table_Base], 16 ;;
ldfe FR_C_2 = [GR_Table_Base], 64
nop.i 999 ;;
}
{ .mmf
nop.m 999
//
// c = c + C_lo finished.
// Load C_2
//
ldfe FR_S_1 = [GR_Table_Base], 16
//
// C_lo = S - C_hi
//
fma.s1 FR_t = FR_t, f1, FR_w ;;
}
//
// 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_Table_Base], 64
//
// t = t + w
//
(p10) fms.s1 FR_a = FR_a, f1, FR_V_hi
cmp.eq.unc p9, p10 = 0x0, GR_i_0
}
{ .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
(p11) fms.s1 FR_a = FR_U_hi, f1, FR_a
cmp.eq.unc p11, p12 = 0x0, GR_i_1
}
{ .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
// Adjust Table_Base to beginning of table
//
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
//
// Table_Base points to C_1
// 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
//
//(p11) fma.s1 FR_Input_X = f0, f1, FR_r
(p11) fma.s1 FR_prelim = f0, f1, FR_r
nop.i 999 ;;
}
{ .mfi
nop.m 999
//(p12) fma.s1 FR_Input_X = f0, f1, f1
(p12) fma.s1 FR_prelim = f0, f1, f1
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// Compute r_cube = FR_rsq * r
//
(p11) fma.s1 FR_poly = FR_rsq, FR_S_2, FR_S_1
nop.i 999 ;;
}
{ .mfi
nop.m 999
(p12) 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
//
//(p10) fms.s1 FR_Input_X = f0, f1, FR_Input_X
(p10) fms.s1 FR_prelim = f0, f1, FR_prelim
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// if i_1 ==0: Result = r
// else Result = 1.0
//
(p11) fma.s1 FR_poly = FR_r_cubed, FR_poly, FR_c
nop.i 999 ;;
}
{ .mfi
nop.m 999
(p12) fma.s1 FR_poly = FR_rsq, FR_poly, f0
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// if i_0 !=0: Result = -Result
//
(p9) fma.s1 FR_Input_X = FR_prelim, f1, FR_poly
nop.i 999 ;;
}
{ .mfb
nop.m 999
(p10) fms.s1 FR_Input_X = FR_prelim, f1, FR_poly
//
// if i_0 == 0: Result = Result + poly
// else Result = Result - poly
//
br.ret.sptk b0 ;;
}
SINCOS_SMALL_R:
{ .mii
nop.m 999
extr.u GR_i_1 = GR_N_Inc, 0, 1 ;;
//
//
// Compare both i_1 and i_0 with 0.
// if i_1 == 0, set p9.
// if i_0 == 0, set p11.
//
cmp.eq.unc p9, p10 = 0x0, GR_i_1 ;;
}
{ .mfi
nop.m 999
fma.s1 FR_rsq = FR_r, FR_r, f0
extr.u GR_i_0 = GR_N_Inc, 1, 1 ;;
}
{ .mfi
nop.m 999
//
// Z = Z * FR_rsq
//
(p10) fnma.s1 FR_c = FR_c, FR_r, f0
cmp.eq.unc p11, p12 = 0x0, GR_i_0
}
;;
// ******************************************************************
// ******************************************************************
// ******************************************************************
// r and c have been computed.
// We know whether this is the sine or cosine routine.
// Make sure ftz mode is set - should be automatic when using wre
// |r| < 2**(-3)
//
// Set table_ptr1 to beginning of constant table.
// Get [i_0,i_1] - two lsb of N_fix_gr.
//
{ .mmi
nop.m 999
addl GR_Table_Base = @ltoff(FSINCOS_CONSTANTS#), gp
nop.i 999
}
;;
{ .mmi
ld8 GR_Table_Base = [GR_Table_Base]
nop.m 999
nop.i 999
}
;;
//
// Set table_ptr1 to point to S_5.
// Set table_ptr1 to point to C_5.
// Compute FR_rsq = r * r
//
{ .mfi
(p9) add GR_Table_Base = 672, GR_Table_Base
(p10) fmerge.s FR_r = f1, f1
(p10) add GR_Table_Base = 592, GR_Table_Base ;;
}
//
// Set table_ptr1 to point to S_5.
// Set table_ptr1 to point to C_5.
//
{ .mmi
(p9) ldfe FR_S_5 = [GR_Table_Base], -16 ;;
//
// if (i_1 == 0) load S_5
// if (i_1 != 0) load C_5
//
(p9) ldfe FR_S_4 = [GR_Table_Base], -16
nop.i 999 ;;
}
{ .mmf
(p10) ldfe FR_C_5 = [GR_Table_Base], -16
//
// Z = FR_rsq * FR_rsq
//
(p9) ldfe FR_S_3 = [GR_Table_Base], -16
//
// Compute FR_rsq = r * r
// if (i_1 == 0) load S_4
// if (i_1 != 0) load C_4
//
fma.s1 FR_Z = FR_rsq, FR_rsq, f0 ;;
}
//
// if (i_1 == 0) load S_3
// if (i_1 != 0) load C_3
//
{ .mmi
(p9) ldfe FR_S_2 = [GR_Table_Base], -16 ;;
//
// if (i_1 == 0) load S_2
// if (i_1 != 0) load C_2
//
(p9) ldfe FR_S_1 = [GR_Table_Base], -16
nop.i 999
}
{ .mmi
(p10) ldfe FR_C_4 = [GR_Table_Base], -16 ;;
(p10) ldfe FR_C_3 = [GR_Table_Base], -16
nop.i 999 ;;
}
{ .mmi
(p10) ldfe FR_C_2 = [GR_Table_Base], -16 ;;
(p10) ldfe FR_C_1 = [GR_Table_Base], -16
nop.i 999
}
{ .mfi
nop.m 999
//
// if (i_1 != 0):
// poly_lo = FR_rsq * C_5 + C_4
// poly_hi = FR_rsq * C_2 + C_1
//
(p9) fma.s1 FR_Z = FR_Z, FR_r, f0
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// if (i_1 == 0) load S_1
// if (i_1 != 0) load C_1
//
(p9) fma.s1 FR_poly_lo = FR_rsq, FR_S_5, FR_S_4
nop.i 999
}
{ .mfi
nop.m 999
//
// c = -c * r
// dummy fmpy's to flag inexact.
//
(p9) fma.d.s1 FR_S_4 = FR_S_4, FR_S_4, f0
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// poly_lo = FR_rsq * poly_lo + C_3
// poly_hi = FR_rsq * poly_hi
//
fma.s1 FR_Z = FR_Z, FR_rsq, f0
nop.i 999 ;;
}
{ .mfi
nop.m 999
(p9) fma.s1 FR_poly_hi = FR_rsq, FR_S_2, FR_S_1
nop.i 999
}
{ .mfi
nop.m 999
//
// if (i_1 == 0):
// poly_lo = FR_rsq * S_5 + S_4
// poly_hi = FR_rsq * S_2 + S_1
//
(p10) fma.s1 FR_poly_lo = FR_rsq, FR_C_5, FR_C_4
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// if (i_1 == 0):
// Z = Z * r for only one of the small r cases - not there
// in original implementation notes.
//
(p9) fma.s1 FR_poly_lo = FR_rsq, FR_poly_lo, FR_S_3
nop.i 999 ;;
}
{ .mfi
nop.m 999
(p10) fma.s1 FR_poly_hi = FR_rsq, FR_C_2, FR_C_1
nop.i 999
}
{ .mfi
nop.m 999
(p10) fma.d.s1 FR_C_1 = FR_C_1, FR_C_1, f0
nop.i 999 ;;
}
{ .mfi
nop.m 999
(p9) fma.s1 FR_poly_hi = FR_poly_hi, FR_rsq, f0
nop.i 999
}
{ .mfi
nop.m 999
//
// poly_lo = FR_rsq * poly_lo + S_3
// poly_hi = FR_rsq * poly_hi
//
(p10) fma.s1 FR_poly_lo = FR_rsq, FR_poly_lo, FR_C_3
nop.i 999 ;;
}
{ .mfi
nop.m 999
(p10) fma.s1 FR_poly_hi = FR_poly_hi, FR_rsq, f0
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// if (i_1 == 0): dummy fmpy's to flag inexact
// r = 1
//
(p9) fma.s1 FR_poly_hi = FR_r, FR_poly_hi, f0
nop.i 999
}
{ .mfi
nop.m 999
//
// poly_hi = r * poly_hi
//
fma.s1 FR_poly = FR_Z, FR_poly_lo, FR_c
nop.i 999 ;;
}
{ .mfi
nop.m 999
(p12) fms.s1 FR_r = f0, f1, FR_r
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// poly_hi = Z * poly_lo + c
// if i_0 == 1: r = -r
//
fma.s1 FR_poly = FR_poly, f1, FR_poly_hi
nop.i 999 ;;
}
{ .mfi
nop.m 999
(p12) fms.s1 FR_Input_X = FR_r, f1, FR_poly
nop.i 999
}
{ .mfb
nop.m 999
//
// poly = poly + poly_hi
//
(p11) fma.s1 FR_Input_X = FR_r, f1, FR_poly
//
// if (i_0 == 0) Result = r + poly
// if (i_0 != 0) Result = r - poly
//
br.ret.sptk b0 ;;
}
SINCOS_NORMAL_R:
{ .mii
nop.m 999
extr.u GR_i_1 = GR_N_Inc, 0, 1 ;;
//
// Set table_ptr1 and table_ptr2 to base address of
// constant table.
cmp.eq.unc p9, p10 = 0x0, GR_i_1 ;;
}
{ .mfi
nop.m 999
fma.s1 FR_rsq = FR_r, FR_r, f0
extr.u GR_i_0 = GR_N_Inc, 1, 1 ;;
}
{ .mfi
nop.m 999
frcpa.s1 FR_r_hi, p6 = f1, FR_r
cmp.eq.unc p11, p12 = 0x0, GR_i_0
}
;;
// ******************************************************************
// ******************************************************************
// ******************************************************************
//
// r and c have been computed.
// We known whether this is the sine or cosine routine.
// Make sure ftz mode is set - should be automatic when using wre
// Get [i_0,i_1] - two lsb of N_fix_gr alone.
//
{ .mmi
nop.m 999
addl GR_Table_Base = @ltoff(FSINCOS_CONSTANTS#), gp
nop.i 999
}
;;
{ .mmi
ld8 GR_Table_Base = [GR_Table_Base]
nop.m 999
nop.i 999
}
;;
{ .mfi
(p10) add GR_Table_Base = 384, GR_Table_Base
//(p12) fms.s1 FR_Input_X = f0, f1, f1
(p12) fms.s1 FR_prelim = f0, f1, f1
(p9) add GR_Table_Base = 224, GR_Table_Base ;;
}
{ .mmf
nop.m 999
(p10) ldfe FR_QQ_8 = [GR_Table_Base], 16
//
// if (i_1==0) poly = poly * FR_rsq + PP_1_lo
// else poly = FR_rsq * poly
//
//(p11) fma.s1 FR_Input_X = f0, f1, f1 ;;
(p11) fma.s1 FR_prelim = f0, f1, f1 ;;
}
{ .mmf
(p10) ldfe FR_QQ_7 = [GR_Table_Base], 16
//
// Adjust table pointers based on i_0
// Compute rsq = r * r
//
(p9) ldfe FR_PP_8 = [GR_Table_Base], 16
fma.s1 FR_r_cubed = FR_r, FR_rsq, f0 ;;
}
{ .mmf
(p9) ldfe FR_PP_7 = [GR_Table_Base], 16
(p10) ldfe FR_QQ_6 = [GR_Table_Base], 16
//
// Load PP_8 and QQ_8; PP_7 and QQ_7
//
frcpa.s1 FR_r_hi, p6 = f1, FR_r_hi ;;
}
//
// if (i_1==0) poly = PP_7 + FR_rsq * PP_8.
// else poly = QQ_7 + FR_rsq * QQ_8.
//
{ .mmb
(p9) ldfe FR_PP_6 = [GR_Table_Base], 16
(p10) ldfe FR_QQ_5 = [GR_Table_Base], 16
nop.b 999 ;;
}
{ .mmb
(p9) ldfe FR_PP_5 = [GR_Table_Base], 16
(p10) ldfe FR_S_1 = [GR_Table_Base], 16
nop.b 999 ;;
}
{ .mmb
(p10) ldfe FR_QQ_1 = [GR_Table_Base], 16
(p9) ldfe FR_C_1 = [GR_Table_Base], 16
nop.b 999 ;;
}
{ .mmi
(p10) ldfe FR_QQ_4 = [GR_Table_Base], 16 ;;
(p9) ldfe FR_PP_1 = [GR_Table_Base], 16
nop.i 999 ;;
}
{ .mmf
(p10) ldfe FR_QQ_3 = [GR_Table_Base], 16
//
// if (i_1=0) corr = corr + c*c
// else corr = corr * c
//
(p9) ldfe FR_PP_4 = [GR_Table_Base], 16
(p10) fma.s1 FR_poly = FR_rsq, FR_QQ_8, FR_QQ_7 ;;
}
//
// if (i_1=0) poly = rsq * poly + PP_5
// else poly = rsq * poly + QQ_5
// Load PP_4 or QQ_4
//
{ .mmf
(p9) ldfe FR_PP_3 = [GR_Table_Base], 16
(p10) ldfe FR_QQ_2 = [GR_Table_Base], 16
//
// r_hi = frcpa(frcpa(r)).
// r_cube = r * FR_rsq.
//
(p9) fma.s1 FR_poly = FR_rsq, FR_PP_8, FR_PP_7 ;;
}
//
// Do dummy multiplies so inexact is always set.
//
{ .mfi
(p9) ldfe FR_PP_2 = [GR_Table_Base], 16
//
// r_lo = r - r_hi
//
(p9) fma.s1 FR_U_lo = FR_r_hi, FR_r_hi, f0
nop.i 999 ;;
}
{ .mmf
nop.m 999
(p9) ldfe FR_PP_1_lo = [GR_Table_Base], 16
(p10) fma.s1 FR_corr = FR_S_1, FR_r_cubed, FR_r
}
{ .mfi
nop.m 999
(p10) fma.s1 FR_poly = FR_rsq, FR_poly, FR_QQ_6
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// if (i_1=0) U_lo = r_hi * r_hi
// else U_lo = r_hi + r
//
(p9) fma.s1 FR_corr = FR_C_1, FR_rsq, f0
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// if (i_1=0) corr = C_1 * rsq
// else corr = S_1 * r_cubed + r
//
(p9) fma.s1 FR_poly = FR_rsq, FR_poly, FR_PP_6
nop.i 999
}
{ .mfi
nop.m 999
(p10) fma.s1 FR_U_lo = FR_r_hi, f1, FR_r
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// if (i_1=0) U_hi = r_hi + U_hi
// else U_hi = QQ_1 * U_hi + 1
//
(p9) fma.s1 FR_U_lo = FR_r, FR_r_hi, FR_U_lo
nop.i 999
}
{ .mfi
nop.m 999
//
// U_hi = r_hi * r_hi
//
fms.s1 FR_r_lo = FR_r, f1, FR_r_hi
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// Load PP_1, PP_6, PP_5, and C_1
// Load QQ_1, QQ_6, QQ_5, and S_1
//
fma.s1 FR_U_hi = FR_r_hi, FR_r_hi, f0
nop.i 999 ;;
}
{ .mfi
nop.m 999
(p10) fma.s1 FR_poly = FR_rsq, FR_poly, FR_QQ_5
nop.i 999
}
{ .mfi
nop.m 999
(p10) fnma.s1 FR_corr = FR_corr, FR_c, f0
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// if (i_1=0) U_lo = r * r_hi + U_lo
// else U_lo = r_lo * U_lo
//
(p9) fma.s1 FR_corr = FR_corr, FR_c, FR_c
nop.i 999 ;;
}
{ .mfi
nop.m 999
(p9) fma.s1 FR_poly = FR_rsq, FR_poly, FR_PP_5
nop.i 999
}
{ .mfi
nop.m 999
//
// if (i_1 =0) U_hi = r + U_hi
// if (i_1 =0) U_lo = r_lo * U_lo
//
//
(p9) fma.d.s1 FR_PP_5 = FR_PP_5, FR_PP_4, f0
nop.i 999 ;;
}
{ .mfi
nop.m 999
(p9) fma.s1 FR_U_lo = FR_r, FR_r, FR_U_lo
nop.i 999
}
{ .mfi
nop.m 999
(p10) fma.s1 FR_U_lo = FR_r_lo, FR_U_lo, f0
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// if (i_1=0) poly = poly * rsq + PP_6
// else poly = poly * rsq + QQ_6
//
(p9) fma.s1 FR_U_hi = FR_r_hi, FR_U_hi, f0
nop.i 999 ;;
}
{ .mfi
nop.m 999
(p10) fma.s1 FR_poly = FR_rsq, FR_poly, FR_QQ_4
nop.i 999
}
{ .mfi
nop.m 999
(p10) fma.s1 FR_U_hi = FR_QQ_1, FR_U_hi, f1
nop.i 999 ;;
}
{ .mfi
nop.m 999
(p10) fma.d.s1 FR_QQ_5 = FR_QQ_5, FR_QQ_5, f0
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// if (i_1!=0) U_hi = PP_1 * U_hi
// if (i_1!=0) U_lo = r * r + U_lo
// Load PP_3 or QQ_3
//
(p9) fma.s1 FR_poly = FR_rsq, FR_poly, FR_PP_4
nop.i 999 ;;
}
{ .mfi
nop.m 999
(p9) fma.s1 FR_U_lo = FR_r_lo, FR_U_lo, f0
nop.i 999
}
{ .mfi
nop.m 999
(p10) fma.s1 FR_U_lo = FR_QQ_1,FR_U_lo, f0
nop.i 999 ;;
}
{ .mfi
nop.m 999
(p9) fma.s1 FR_U_hi = FR_PP_1, FR_U_hi, f0
nop.i 999 ;;
}
{ .mfi
nop.m 999
(p10) fma.s1 FR_poly = FR_rsq, FR_poly, FR_QQ_3
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// Load PP_2, QQ_2
//
(p9) fma.s1 FR_poly = FR_rsq, FR_poly, FR_PP_3
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// if (i_1==0) poly = FR_rsq * poly + PP_3
// else poly = FR_rsq * poly + QQ_3
// Load PP_1_lo
//
(p9) fma.s1 FR_U_lo = FR_PP_1, FR_U_lo, f0
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// if (i_1 =0) poly = poly * rsq + pp_r4
// else poly = poly * rsq + qq_r4
//
(p9) fma.s1 FR_U_hi = FR_r, f1, FR_U_hi
nop.i 999 ;;
}
{ .mfi
nop.m 999
(p10) fma.s1 FR_poly = FR_rsq, FR_poly, FR_QQ_2
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// if (i_1==0) U_lo = PP_1_hi * U_lo
// else U_lo = QQ_1 * U_lo
//
(p9) fma.s1 FR_poly = FR_rsq, FR_poly, FR_PP_2
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// if (i_0==0) Result = 1
// else Result = -1
//
fma.s1 FR_V = FR_U_lo, f1, FR_corr
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_1==0) poly = FR_rsq * poly + PP_2
// else poly = FR_rsq * poly + QQ_2
//
(p9) fma.s1 FR_poly = FR_rsq, FR_poly, FR_PP_1_lo
nop.i 999 ;;
}
{ .mfi
nop.m 999
(p10) fma.s1 FR_poly = FR_rsq, FR_poly, f0
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// V = U_lo + corr
//
(p9) fma.s1 FR_poly = FR_r_cubed, FR_poly, f0
nop.i 999 ;;
}
{ .mfi
nop.m 999
//
// if (i_1==0) poly = r_cube * poly
// else poly = FR_rsq * poly
//
fma.s1 FR_V = FR_poly, f1, FR_V
nop.i 999 ;;
}
{ .mfi
nop.m 999
//(p12) fms.s1 FR_Input_X = FR_Input_X, FR_U_hi, FR_V
(p12) fms.s1 FR_Input_X = FR_prelim, FR_U_hi, FR_V
nop.i 999
}
{ .mfb
nop.m 999
//
// V = V + poly
//
//(p11) fma.s1 FR_Input_X = FR_Input_X, FR_U_hi, FR_V
(p11) fma.s1 FR_Input_X = FR_prelim, FR_U_hi, FR_V
//
// if (i_0==0) Result = Result * U_hi + V
// else Result = Result * U_hi - V
//
br.ret.sptk b0 ;;
}
//
// If cosine, FR_Input_X = 1
// If sine, FR_Input_X = +/-Zero (Input FR_Input_X)
// Results are exact, no exceptions
//
SINCOS_ZERO:
{ .mmb
cmp.eq.unc p6, p7 = 0x1, GR_Sin_or_Cos
nop.m 999
nop.b 999 ;;
}
{ .mfi
nop.m 999
(p7) fmerge.s FR_Input_X = FR_Input_X, FR_Input_X
nop.i 999
}
{ .mfb
nop.m 999
(p6) fmerge.s FR_Input_X = f1, f1
br.ret.sptk b0 ;;
}
SINCOS_SPECIAL:
//
// Path for Arg = +/- QNaN, SNaN, Inf
// Invalid can be raised. SNaNs
// become QNaNs
//
{ .mfb
nop.m 999
fmpy.s1 FR_Input_X = FR_Input_X, f0
br.ret.sptk b0 ;;
}
GLOBAL_LIBM_END(__libm_cos_large)
// *******************************************************************
// *******************************************************************
// *******************************************************************
//
// 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 r49-50. 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_2)
SINCOS_ARG_TOO_LARGE:
.prologue
// Readjust Table ptr
{ .mfi
adds GR_Table_Base1 = -16, GR_Table_Base1
nop.f 999
.save ar.pfs,GR_SAVE_PFS
mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
};;
{ .mmi
ldfs FR_Two_to_M3 = [GR_Table_Base1],4
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
ldfs FR_Neg_Two_to_M3 = [GR_Table_Base1],0
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 SINCOS_SMALL_R // Branch if |r| < 1/4
br.cond.sptk SINCOS_NORMAL_R ;; // Branch if 1/4 <= |r| < pi/4
}
LOCAL_LIBM_END(__libm_callout_2)
.type __libm_pi_by_2_reduce#,@function
.global __libm_pi_by_2_reduce#
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