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-rw-r--r--sysdeps/ia64/fpu/s_cosl.S2760
1 files changed, 1303 insertions, 1457 deletions
diff --git a/sysdeps/ia64/fpu/s_cosl.S b/sysdeps/ia64/fpu/s_cosl.S
index 2755580c0d..8d71e50c1a 100644
--- a/sysdeps/ia64/fpu/s_cosl.S
+++ b/sysdeps/ia64/fpu/s_cosl.S
@@ -1,10 +1,10 @@
.file "sincosl.s"
-// Copyright (C) 2000, 2001, Intel Corporation
+
+// Copyright (c) 2000 - 2004, Intel Corporation
// All rights reserved.
-//
-// Contributed 2/2/2000 by John Harrison, Ted Kubaska, Bob Norin, Shane Story,
-// and Ping Tak Peter Tang of the Computational Software Lab, Intel Corporation.
+//
+// Contributed 2000 by the Intel Numerics Group, Intel Corporation
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are
@@ -20,76 +20,82 @@
// * 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
+
+// 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
+// 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
+// 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.
-//
+// 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://developer.intel.com/opensource.
+// problem reports or change requests be submitted to it directly at
+// http://www.intel.com/software/products/opensource/libraries/num.htm.
//
-// *********************************************************************
+//*********************************************************************
//
-// History:
-// 2/02/2000 (hand-optimized)
-// 4/04/00 Unwind support added
+// 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)
+// Floating-Point Registers: f8 (Input and Return Value)
// f32-f99
//
// General Purpose Registers:
-// r32-r43
-// r44-r45 (Used to pass arguments to pi_by_2 reduce routine)
+// 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
+// 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(inf) = QNaN
// sinl(+/-0) = +/-0
-// cosl(inf) = QNaN
+// 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
+// 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.
@@ -98,62 +104,62 @@
//
// 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
+// 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.
+// 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
+// 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,
+// 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
+// if M = -1, I = 11
// sin ((-pi/2 + alpha) = (-1) cos (alpha)
-// if M = 0, I = 00
+// if M = 0, I = 00
// sin (alpha) = sin (alpha)
-// if M = 1, I = 01
+// if M = 1, I = 01
// sin (pi/2 + alpha) = cos (alpha)
-// if M = 2, I = 10
+// if M = 2, I = 10
// sin (pi + alpha) = (-1) sin (alpha)
-// if M = 3, I = 11
+// if M = 3, I = 11
// sin ((3/2)pi + alpha) = (-1) cos (alpha)
//
-// The value of alpha is obtained by argument reduction and
+// 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
+// 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
+// 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
+// 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
+// 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
@@ -163,32 +169,32 @@
//
// 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.
+// 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.
+// 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
+// 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 greatest challenge of this task is that the second terms of
// the Taylor series
-//
-// r - r^3/3! + r^r/5! - ...
+//
+// r - r^3/3! + r^r/5! - ...
//
// and
//
-// 1 - r^2/2! + r^4/4! - ...
+// 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
+// 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)
@@ -197,88 +203,88 @@
// 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
+// 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
+// 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
+// because |r| is small and thus the second terms in the correction
// are unneccessary.
//
-// Finally, sinl(r) and cosl(r) are approximated by polynomials of
+// 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.
+// 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
+// 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
+// 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
+// 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
+// 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
+// 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
+// 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
+// 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
+// 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|
+// |U_lo| <= 2^(-8) |U_hi|
//
-// says that U_hi + U_lo is approximating r + PP_1_hi r^3 to roughly
+// 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 ) ).
+// 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
//
@@ -297,35 +303,35 @@
// End
//
// Finally,
-//
-// V := poly + ( U_lo + correction )
+//
+// V := poly + ( U_lo + correction )
//
// / U_hi + V if i_0 = 0
-// result := |
+// 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.
+// 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
+// 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.
+// 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
+// * 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.
@@ -335,18 +341,18 @@
//
// Step 2. Reduction of moderate arguments.
//
-// If |Arg| < pi/4 ...quick branch
-// N_fix := N_inc (integer)
+// 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)
+// 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)
+// 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
@@ -358,8 +364,8 @@
// Step 3. Case_1_reduce.
//
// r := s + w
-// c := (s - r) + w ...observe order
-//
+// c := (s - r) + w ...observe order
+//
// Step 4. Case_1_complete
//
// ...At this point, the reduced argument alpha is
@@ -375,17 +381,17 @@
//
// 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_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
+// 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_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
+// correction := -c*(r + S_1*FR_rsq*r) ...any order
// Endif
//
-// V := poly + (U_lo + correction) ...observe order
+// V := poly + (U_lo + correction) ...observe order
//
// result := (i_0 == 0? 1.0 : -1.0)
//
@@ -397,7 +403,7 @@
// 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.
//
@@ -412,7 +418,7 @@
// 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)
+// poly_hi := FR_rsq*(C_1 + FR_rsq*C_2)
// correction := -c*r
// result := 1
// Endif
@@ -429,15 +435,15 @@
//
// Step 7. Case_2_reduce.
//
-// ...Refer to the write up for argument reduction for
+// ...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 := 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
//
@@ -446,29 +452,29 @@
// ...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
+// ...|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
+// 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.
@@ -476,13 +482,13 @@
// 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
+// N_fix := N_fix + N_inc
//
// s := Arg' - N * P_1
// w := w - N * P_2
@@ -494,15 +500,15 @@
// 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
+// 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
+// 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
@@ -517,12 +523,12 @@
// 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
+// ...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_hi := s + A t := t + a
+// C_lo := (s - C_hi) + A
// C_lo := C_lo + t
//
// ...Final steps for reduction
@@ -548,156 +554,192 @@
// 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.
//
-#include "libm_support.h"
-
-#ifdef _LIBC
-.rodata
-#else
-.data
-#endif
-.align 64
-
-FSINCOSL_CONSTANTS:
-ASM_TYPE_DIRECTIVE(FSINCOSL_CONSTANTS,@object)
-data4 0x4B800000, 0xCB800000, 0x00000000,0x00000000 // two**24, -two**24
-data4 0x4E44152A, 0xA2F9836E, 0x00003FFE,0x00000000 // Inv_pi_by_2
-data4 0xCE81B9F1, 0xC84D32B0, 0x00004016,0x00000000 // P_0
-data4 0x2168C235, 0xC90FDAA2, 0x00003FFF,0x00000000 // P_1
-data4 0xFC8F8CBB, 0xECE675D1, 0x0000BFBD,0x00000000 // P_2
-data4 0xACC19C60, 0xB7ED8FBB, 0x0000BF7C,0x00000000 // P_3
-data4 0x5F000000, 0xDF000000, 0x00000000,0x00000000 // two_to_63, -two_to_63
-data4 0x6EC6B45A, 0xA397E504, 0x00003FE7,0x00000000 // Inv_P_0
-data4 0xDBD171A1, 0x8D848E89, 0x0000BFBF,0x00000000 // d_1
-data4 0x18A66F8E, 0xD5394C36, 0x0000BF7C,0x00000000 // d_2
-data4 0x2168C234, 0xC90FDAA2, 0x00003FFE,0x00000000 // pi_by_4
-data4 0x2168C234, 0xC90FDAA2, 0x0000BFFE,0x00000000 // neg_pi_by_4
-data4 0x3E000000, 0xBE000000, 0x00000000,0x00000000 // two**-3, -two**-3
-data4 0x2F000000, 0xAF000000, 0x9E000000,0x00000000 // two**-33, -two**-33, -two**-67
-data4 0xA21C0BC9, 0xCC8ABEBC, 0x00003FCE,0x00000000 // PP_8
-data4 0x720221DA, 0xD7468A05, 0x0000BFD6,0x00000000 // PP_7
-data4 0x640AD517, 0xB092382F, 0x00003FDE,0x00000000 // PP_6
-data4 0xD1EB75A4, 0xD7322B47, 0x0000BFE5,0x00000000 // PP_5
-data4 0xFFFFFFFE, 0xFFFFFFFF, 0x0000BFFD,0x00000000 // C_1
-data4 0x00000000, 0xAAAA0000, 0x0000BFFC,0x00000000 // PP_1_hi
-data4 0xBAF69EEA, 0xB8EF1D2A, 0x00003FEC,0x00000000 // PP_4
-data4 0x0D03BB69, 0xD00D00D0, 0x0000BFF2,0x00000000 // PP_3
-data4 0x88888962, 0x88888888, 0x00003FF8,0x00000000 // PP_2
-data4 0xAAAB0000, 0xAAAAAAAA, 0x0000BFEC,0x00000000 // PP_1_lo
-data4 0xC2B0FE52, 0xD56232EF, 0x00003FD2,0x00000000 // QQ_8
-data4 0x2B48DCA6, 0xC9C99ABA, 0x0000BFDA,0x00000000 // QQ_7
-data4 0x9C716658, 0x8F76C650, 0x00003FE2,0x00000000 // QQ_6
-data4 0xFDA8D0FC, 0x93F27DBA, 0x0000BFE9,0x00000000 // QQ_5
-data4 0xAAAAAAAA, 0xAAAAAAAA, 0x0000BFFC,0x00000000 // S_1
-data4 0x00000000, 0x80000000, 0x0000BFFE,0x00000000 // QQ_1
-data4 0x0C6E5041, 0xD00D00D0, 0x00003FEF,0x00000000 // QQ_4
-data4 0x0B607F60, 0xB60B60B6, 0x0000BFF5,0x00000000 // QQ_3
-data4 0xAAAAAA9B, 0xAAAAAAAA, 0x00003FFA,0x00000000 // QQ_2
-data4 0xFFFFFFFE, 0xFFFFFFFF, 0x0000BFFD,0x00000000 // C_1
-data4 0xAAAA719F, 0xAAAAAAAA, 0x00003FFA,0x00000000 // C_2
-data4 0x0356F994, 0xB60B60B6, 0x0000BFF5,0x00000000 // C_3
-data4 0xB2385EA9, 0xD00CFFD5, 0x00003FEF,0x00000000 // C_4
-data4 0x292A14CD, 0x93E4BD18, 0x0000BFE9,0x00000000 // C_5
-data4 0xAAAAAAAA, 0xAAAAAAAA, 0x0000BFFC,0x00000000 // S_1
-data4 0x888868DB, 0x88888888, 0x00003FF8,0x00000000 // S_2
-data4 0x055EFD4B, 0xD00D00D0, 0x0000BFF2,0x00000000 // S_3
-data4 0x839730B9, 0xB8EF1C5D, 0x00003FEC,0x00000000 // S_4
-data4 0xE5B3F492, 0xD71EA3A4, 0x0000BFE5,0x00000000 // S_5
-data4 0x38800000, 0xB8800000, 0x00000000 // two**-14, -two**-14
-ASM_SIZE_DIRECTIVE(FSINCOSL_CONSTANTS)
-
-FR_Input_X = f8
-FR_Neg_Two_to_M3 = f32
-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_c = f48
-FR_r = 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_d_2 = 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_Table_Base = r32
-GR_Table_Base1 = r33
-GR_i_0 = r34
-GR_i_1 = r35
-GR_N_Inc = r36
-GR_Sin_or_Cos = r37
+
+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
@@ -706,386 +748,377 @@ GR_SAVE_GP = r40
GR_SAVE_PFS = r41
-.global sinl#
-.global cosl#
-#ifdef _LIBC
-.global __sinl#
-.global __cosl#
-#endif
-
.section .text
-.proc sinl#
-#ifdef _LIBC
-.proc __sinl#
-#endif
-.align 64
-sinl:
-#ifdef _LIBC
-__sinl:
-#endif
+
+GLOBAL_IEEE754_ENTRY(sinl)
{ .mlx
-alloc GR_Table_Base = ar.pfs,0,12,2,0
-(p0) movl GR_Sin_or_Cos = 0x0 ;;
+ alloc r32 = ar.pfs,0,27,2,0
+ movl GR_sig_inv_pi = 0xa2f9836e4e44152a // significand of 1/pi
}
-
-{ .mmi
- nop.m 999
-(p0) addl GR_Table_Base = @ltoff(FSINCOSL_CONSTANTS#), gp
- nop.i 999
+{ .mlx
+ mov GR_Sin_or_Cos = 0x0
+ movl GR_rshf_2to64 = 0x47e8000000000000 // 1.1000 2^(63+64)
}
;;
-{ .mmb
- ld8 GR_Table_Base = [GR_Table_Base]
+{ .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
-(p0) br.cond.sptk L(SINCOSL_CONTINUE) ;;
+ fnorm.s1 FR_norm_x = FR_Input_X // Normalize x
+ br.cond.sptk SINCOSL_CONTINUE
}
;;
+GLOBAL_IEEE754_END(sinl)
-.endp sinl#
-ASM_SIZE_DIRECTIVE(sinl#)
-
-.section .text
-.proc cosl#
-cosl:
-#ifdef _LIBC
-.proc __cosl#
-__cosl:
-#endif
+GLOBAL_IEEE754_ENTRY(cosl)
+{ .mlx
+ alloc r32 = ar.pfs,0,27,2,0
+ movl GR_sig_inv_pi = 0xa2f9836e4e44152a // significand of 1/pi
+}
{ .mlx
-alloc GR_Table_Base= ar.pfs,0,12,2,0
-(p0) movl GR_Sin_or_Cos = 0x1 ;;
+ mov GR_Sin_or_Cos = 0x1
+ movl GR_rshf_2to64 = 0x47e8000000000000 // 1.1000 2^(63+64)
}
;;
-{ .mmi
+{ .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
-(p0) addl GR_Table_Base = @ltoff(FSINCOSL_CONSTANTS#), gp
+ fnorm.s1 FR_norm_x = FR_Input_X // Normalize x
nop.i 999
}
;;
-{ .mmb
- ld8 GR_Table_Base = [GR_Table_Base]
- nop.m 999
- nop.b 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
+}
+;;
-
-//
-// Load Table Address
-//
-
-L(SINCOSL_CONTINUE):
-{ .mmi
-(p0) add GR_Table_Base1 = 96, GR_Table_Base
-(p0) ldfs FR_Two_to_24 = [GR_Table_Base], 4
-// GR_Sin_or_Cos denotes
-(p0) mov r39 = b0 ;;
+{ .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
}
-{ .mmi
- nop.m 0
-//
-// Load 2**24, load 2**63.
-//
-(p0) ldfs FR_Neg_Two_to_24 = [GR_Table_Base], 12
- nop.i 0
+{ .mib
+ mov GR_exp_mask = 0x1ffff // Exponent mask
+ nop.i 999
+(p6) br.cond.spnt SINCOSL_SPECIAL // Branch if x natval, nan, inf
}
+;;
+
{ .mfi
-(p0) 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
-//
-(p0) fclass.m.unc p6, p0 = FR_Input_X, 0x1E3
- nop.i 0
-};;
-{ .mmf
- nop.m 999
-(p0) ldfs FR_Neg_Two_to_63 = [GR_Table_Base1], 12
-(p0) fclass.nm.unc p8, p0 = FR_Input_X, 0x1FF
-}
-{ .mfb
- nop.m 999
-(p0) fclass.m.unc p10, p0 = FR_Input_X, 0x007
-(p6) br.cond.spnt L(SINCOSL_SPECIAL) ;;
+ 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
- nop.m 999
- nop.i 999
-(p8) br.cond.spnt L(SINCOSL_SPECIAL) ;;
+ 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
}
-{ .mib
- nop.m 999
- nop.i 999
-//
-// Branch if +/- NaN, Inf.
-// Load -2**24, load -2**63.
-//
-(p10) br.cond.spnt L(SINCOSL_ZERO) ;;
+;;
+
+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
}
-{ .mmb
-(p0) ldfe FR_Inv_pi_by_2 = [GR_Table_Base], 16
-(p0) ldfe FR_Inv_P_0 = [GR_Table_Base1], 16
- nop.b 999 ;;
+{ .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
}
-{ .mmb
-(p0) ldfe FR_d_1 = [GR_Table_Base1], 16
-//
-// Raise possible denormal operand flag with useful fcmp
-// Is x <= -2**63
-// Load Inv_P_0 for pre-reduction
-// Load Inv_pi_by_2
-//
-(p0) ldfe FR_P_0 = [GR_Table_Base], 16
- nop.b 999 ;;
+;;
+
+{ .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
}
-{ .mmb
-(p0) ldfe FR_d_2 = [GR_Table_Base1], 16
-//
-// Load P_0
-// Load d_1
-// Is x >= 2**63
-// Is x <= -2**24?
-//
-(p0) ldfe FR_P_1 = [GR_Table_Base], 16
- nop.b 999 ;;
+{ .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
}
-//
-// Load P_1
-// Load d_2
-// Is x >= 2**24?
-//
+;;
+
{ .mfi
-(p0) ldfe FR_P_2 = [GR_Table_Base], 16
-(p0) fcmp.le.unc.s1 p7, p8 = FR_Input_X, FR_Neg_Two_to_24
- nop.i 999 ;;
+ 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
}
-{ .mbb
-(p0) ldfe FR_P_3 = [GR_Table_Base], 16
- nop.b 999
- nop.b 999 ;;
+{ .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
- nop.m 999
-(p8) fcmp.ge.s1 p7, p0 = FR_Input_X, FR_Two_to_24
- nop.i 999
+ 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
-(p0) ldfe FR_Pi_by_4 = [GR_Table_Base1], 16
-//
-// 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
-//
-(p0) fcmp.le.unc.s0 p10, p11 = FR_Input_X, FR_Neg_Two_to_63
- nop.i 999 ;;
+ ldfe FR_PP_8 = [GR_ad_pp], 16 // Load PP_8 for 2^-3 < |r| < pi/4
+ nop.f 999
+ nop.i 999
}
-{ .mmi
-(p0) ldfe FR_Neg_Pi_by_4 = [GR_Table_Base1], 16 ;;
-(p0) ldfs FR_Two_to_M3 = [GR_Table_Base1], 4
- 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
- nop.m 999
-(p11) fcmp.ge.s1 p10, p0 = FR_Input_X, FR_Two_to_63
- nop.i 999 ;;
+ ldfe FR_QQ_8 = [GR_ad_qq], 16 // Load QQ_8 for 2^-3 < |r| < pi/4
+ nop.f 999
+ nop.i 999
}
-{ .mib
-(p0) 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 L(SINCOSL_ARG_TOO_LARGE) ;;
+;;
+
+{ .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
- nop.m 999
- nop.i 999
-//
-// Branch out if x >= 2**63. Use Payne-Hanek Reduction
-//
-(p7) br.cond.spnt L(SINCOSL_LARGER_ARG) ;;
+ 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
- nop.m 999
-//
-// Branch if Arg <= -2**24 or Arg >= 2**24 and use pre-reduction.
-//
-(p0) fma.s1 FR_N_float = FR_Input_X, FR_Inv_pi_by_2, f0
- nop.i 999 ;;
+ 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
}
-{ .mfi
- nop.m 999
-(p0) fcmp.lt.unc.s1 p6, p7 = FR_Input_X, FR_Pi_by_4
- nop.i 999 ;;
+{ .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
- nop.m 999
-//
-// Select the case when |Arg| < pi/4
-// Else Select the case when |Arg| >= pi/4
-//
-(p0) fcvt.fx.s1 FR_N_fix = FR_N_float
- nop.i 999 ;;
+ 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
- nop.m 999
+ 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
//
-(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
+{ .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
+// 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 ;;
+{ .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
}
-{ .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
+// 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 L(SINCOSL_SMALL_R) ;;
+
+
+{ .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
}
-{ .mib
- nop.m 999
- nop.i 999
-(p6) br.cond.sptk L(SINCOSL_NORMAL_R) ;;
+;;
+
+// 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
}
-//
-// if |x| < pi/4, branch based on |x| < 2**(-3) or otherwise.
-//
-//
-// In this branch, |x| >= pi/4.
-//
{ .mfi
-(p0) ldfs FR_Neg_Two_to_M67 = [GR_Table_Base1], 8
-//
-// Load -2**(-67)
-//
-(p0) fnma.s1 FR_s = FR_N_float, FR_P_1, FR_Input_X
-//
-// w = N * P_2
-// s = -N * P_1 + Arg
-//
-(p0) add GR_N_Inc = GR_N_Inc, GR_Sin_or_Cos
+ 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
-(p0) fma.s1 FR_w = FR_N_float, FR_P_2, f0
- nop.i 999 ;;
+ 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
-//
-// Adjust N_fix by N_inc to determine whether sine or
-// cosine is being calculated
-//
-(p0) fcmp.lt.unc.s1 p7, p6 = FR_s, FR_Two_to_M33
- nop.i 999 ;;
+ 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
- nop.i 999 ;;
+ 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
-// 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
+ 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
-(p7) fma.s1 FR_w = FR_N_float, FR_P_3, f0
- nop.i 999 ;;
+ 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_U_1 = FR_N_float, FR_P_2, FR_w
- nop.i 999
+ 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) fms.s1 FR_c = FR_s, f1, FR_r
- nop.i 999 ;;
+ 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
-//
-// For big s: r = s - w: No futher reduction is necessary
+ 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
//
-(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, p13 = FR_r, FR_Neg_Two_to_M3 // If big s, p8 if |r| < 2^-3
+ nop.i 999 ;;
}
+
{ .mfi
- nop.m 999
-(p8) fcmp.gt.s1 p8, p9 = FR_r, FR_Neg_Two_to_M3
- nop.i 999 ;;
+ 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
+ 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
+ nop.i 999
}
-{ .mfb
- nop.m 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
@@ -1095,355 +1128,356 @@ L(SINCOSL_CONTINUE):
// 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 L(SINCOSL_SMALL_R) ;;
+ nop.m 999
+(p6) fms.s1 FR_c = FR_c, f1, FR_w
+ nop.i 999
}
-{ .mib
- nop.m 999
- nop.i 999
-(p9) br.cond.sptk L(SINCOSL_NORMAL_R) ;;
+{ .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
}
-{ .mfi
-(p7) add GR_Table_Base1 = 224, GR_Table_Base1
+;;
+
+SINCOSL_S_TINY:
//
-// Branch to SINCOSL_SMALL_R or SINCOSL_NORMAL_R
+// 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
//
-(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
+ 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 ;;
+ 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
-(p7) ldfe FR_S_1 = [GR_Table_Base1], 16
+ 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
-(p7) cmp.eq.unc p11, p12 = 0x0, GR_i_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
-(p7) fms.s1 FR_s = FR_s, f1, FR_r
- nop.i 999
+ nop.m 999
+ fms.s1 FR_s = FR_s, f1, FR_r
+ nop.i 999
}
{ .mfi
- nop.m 999
-//
+ 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 ;;
+ 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
+ nop.m 999
+ 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
- nop.i 999 ;;
+ nop.m 999
+ fmerge.se FR_tmp_result = FR_r, FR_r
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
-(p10) fma.s1 FR_Input_X = f0, f1, f1
- nop.i 999 ;;
+ nop.m 999
+(p10) fma.s1 FR_tmp_result = f0, f1, f1
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
-//
+ 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 ;;
+ fms.s1 FR_c = FR_s, f1, FR_U_1
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
-//
+ 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
- nop.i 999
+(p12) fnma.s1 FR_tmp_result = FR_tmp_result, f1, f0
+ nop.i 999
}
{ .mfi
- nop.m 999
-(p7) fma.s1 FR_r = FR_S_1, FR_r, f0
- nop.i 999 ;;
+ nop.m 999
+ fma.s1 FR_r = FR_S_1, FR_r, f0
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
-(p7) fma.s0 FR_S_1 = FR_S_1, FR_S_1, f0
- nop.i 999 ;;
+ nop.m 999
+ fma.s0 FR_S_1 = FR_S_1, FR_S_1, f0
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// If i_1 != 0, poly = 2**(-67)
//
-(p7) fms.s1 FR_c = FR_c, f1, FR_U_2
- nop.i 999 ;;
+ fms.s1 FR_c = FR_c, f1, FR_U_2
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
-//
+ nop.m 999
+//
// c = c - U_2
-//
+//
(p9) fma.s1 FR_poly = FR_r, FR_rsq, FR_c
- nop.i 999 ;;
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// i_0 != 0, so Result = -Result
//
-(p11) fma.s0 FR_Input_X = FR_Input_X, f1, FR_poly
- nop.i 999 ;;
+(p11) fma.s0 FR_Result = FR_tmp_result, f1, FR_poly
+ nop.i 999 ;;
}
{ .mfb
- nop.m 999
-(p12) fms.s0 FR_Input_X = FR_Input_X, f1, FR_poly
+ 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
//
-(p0) br.ret.sptk b0 ;;
-}
-L(SINCOSL_LARGER_ARG):
-{ .mfi
- nop.m 999
-(p0) fma.s1 FR_N_0 = FR_Input_X, FR_Inv_P_0, f0
- nop.i 999
+ br.ret.sptk b0 // Exit if |s| < 2^-33, and pi/4 <= |x| < 2^24
}
;;
-// This path for argument > 2*24
-// Adjust table_ptr1 to beginning of table.
+SINCOSL_LARGER_ARG:
//
-
-{ .mmi
- nop.m 999
-(p0) addl GR_Table_Base = @ltoff(FSINCOSL_CONSTANTS#), gp
- nop.i 999
-}
-;;
-
-{ .mmi
- ld8 GR_Table_Base = [GR_Table_Base]
- nop.m 999
- nop.i 999
+// 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
}
;;
-
-//
-// Point to 2*-14
+//
// N_0 = Arg * Inv_P_0
//
+// Load values 2**(-14) and -2**(-14)
{ .mmi
-(p0) add GR_Table_Base = 688, GR_Table_Base ;;
-(p0) ldfs FR_Two_to_M14 = [GR_Table_Base], 4
- nop.i 999 ;;
+ ldfps FR_Two_to_M14, FR_Neg_Two_to_M14 = [GR_ad_m14]
+ nop.i 999 ;;
}
{ .mfi
-(p0) ldfs FR_Neg_Two_to_M14 = [GR_Table_Base], 0
- nop.f 999
- nop.i 999 ;;
+ 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
+ nop.m 999
//
-// Load values 2**(-14) and -2**(-14)
//
-(p0) fcvt.fx.s1 FR_N_0_fix = FR_N_0
- nop.i 999 ;;
+ fcvt.fx.s1 FR_N_0_fix = FR_N_0
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// N_0_fix = integer part of N_0
//
-(p0) fcvt.xf FR_N_0 = FR_N_0_fix
- nop.i 999 ;;
+ fcvt.xf FR_N_0 = FR_N_0_fix
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// Make N_0 the integer part
//
-(p0) fnma.s1 FR_ArgPrime = FR_N_0, FR_P_0, FR_Input_X
- nop.i 999
+ fnma.s1 FR_ArgPrime = FR_N_0, FR_P_0, FR_Input_X
+ nop.i 999
}
{ .mfi
- nop.m 999
-(p0) fma.s1 FR_w = FR_N_0, FR_d_1, f0
- nop.i 999 ;;
+ nop.m 999
+ fma.s1 FR_w = FR_N_0, FR_d_1, f0
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// Arg' = -N_0 * P_0 + Arg
// w = N_0 * d_1
//
-(p0) fma.s1 FR_N_float = FR_ArgPrime, FR_Inv_pi_by_2, f0
- nop.i 999 ;;
+ fma.s1 FR_N_float = FR_ArgPrime, FR_Inv_pi_by_2, f0
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
-// N = A' * 2/pi
+// N = A' * 2/pi
//
-(p0) fcvt.fx.s1 FR_N_fix = FR_N_float
- nop.i 999 ;;
+ fcvt.fx.s1 FR_N_fix = FR_N_float
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
-// N_fix is the integer part
+// N_fix is the integer part
//
-(p0) fcvt.xf FR_N_float = FR_N_fix
- nop.i 999 ;;
+ fcvt.xf FR_N_float = FR_N_fix
+ nop.i 999 ;;
}
{ .mfi
-(p0) getf.sig GR_N_Inc = FR_N_fix
- nop.f 999
- nop.i 999 ;;
+ getf.sig GR_N_Inc = FR_N_fix
+ nop.f 999
+ nop.i 999 ;;
}
{ .mii
- nop.m 999
- nop.i 999 ;;
-(p0) add GR_N_Inc = GR_N_Inc, GR_Sin_or_Cos ;;
+ nop.m 999
+ nop.i 999 ;;
+ add GR_N_Inc = GR_N_Inc, GR_Sin_or_Cos ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// N is the integer part of the reduced-reduced argument.
// Put the integer in a GP register
//
-(p0) fnma.s1 FR_s = FR_N_float, FR_P_1, FR_ArgPrime
- nop.i 999
+ fnma.s1 FR_s = FR_N_float, FR_P_1, FR_ArgPrime
+ nop.i 999
}
{ .mfi
- nop.m 999
-(p0) fnma.s1 FR_w = FR_N_float, FR_P_2, FR_w
- nop.i 999 ;;
+ nop.m 999
+ fnma.s1 FR_w = FR_N_float, FR_P_2, FR_w
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// s = -N*P_1 + Arg'
// w = -N*P_2 + w
// N_fix_gr = N_fix_gr + N_inc
//
-(p0) fcmp.lt.unc.s1 p9, p8 = FR_s, FR_Two_to_M14
- nop.i 999 ;;
+ 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 ;;
+ 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
+ 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
+ nop.i 999
}
{ .mfi
- nop.m 999
+ nop.m 999
(p9) fma.s1 FR_U_hi = FR_N_0, FR_d_1, f0
- nop.i 999 ;;
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ 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
+ nop.i 999
}
{ .mfi
- nop.m 999
+ nop.m 999
(p9) fma.s1 FR_w = FR_N_float, FR_P_3, f0
- nop.i 999 ;;
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ 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
+ nop.i 999
}
{ .mfi
- nop.m 999
+ nop.m 999
//
-// Big s: finish up c = (S - r) + w (c complete)
+// 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 ;;
+ nop.i 999 ;;
}
{ .mmf
- nop.m 999
- nop.m 999
+ 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
+ nop.m 999
(p9) fmerge.s FR_V_hiabs = f0, FR_V_hi
- nop.i 999 ;;
+ nop.i 999 ;;
}
+//{ .mfb
+//(p9) fmerge.s f8= FR_V_lo,FR_V_lo
+//(p9) br.ret.sptk b0
+//}
+//;;
{ .mfi
- nop.m 999
+ 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
+ nop.i 999
}
{ .mfi
- nop.m 999
+ nop.m 999
//
-// For big s: Is |r| < 2**(-3)
+// 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 ;;
+(p8) fms.s1 FR_c = FR_s, f1, FR_r
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// For small S: V_hi = N * P_2
// w = N * P_3
@@ -1451,104 +1485,99 @@ L(SINCOSL_LARGER_ARG):
// so (-) missing for V_hi and w.
//
(p8) fcmp.lt.unc.s1 p12, p13 = FR_r, FR_Two_to_M3
- nop.i 999 ;;
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
(p12) fcmp.gt.s1 p12, p13 = FR_r, FR_Neg_Two_to_M3
- nop.i 999 ;;
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
(p8) fma.s1 FR_c = FR_c, f1, FR_w
- nop.i 999
+ nop.i 999
}
{ .mfb
- nop.m 999
+ nop.m 999
(p9) fms.s1 FR_w = FR_N_0, FR_d_2, FR_w
-(p12) br.cond.spnt L(SINCOSL_SMALL_R) ;;
+(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 L(SINCOSL_NORMAL_R) ;;
+ 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.
+ 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
-(p0) extr.u GR_i_1 = GR_N_Inc, 0, 1
+ fcmp.ge.unc.s1 p7, p8 = FR_U_hiabs, FR_V_hiabs
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// C_hi = S + A
//
-(p9) fma.s1 FR_t = FR_U_lo, f1, FR_V_lo
-(p0) extr.u GR_i_0 = GR_N_Inc, 1, 1 ;;
+ fma.s1 FR_t = FR_U_lo, f1, FR_V_lo
}
+;;
+
{ .mfi
- nop.m 999
+ nop.m 999
//
-// t = U_lo + V_lo
+// t = U_lo + V_lo
//
//
-(p10) fms.s1 FR_a = FR_U_hi, f1, FR_A
- nop.i 999 ;;
+(p7) 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
-(p0) addl GR_Table_Base = @ltoff(FSINCOSL_CONSTANTS#), gp
- nop.i 999
-}
-;;
-
-{ .mmi
- ld8 GR_Table_Base = [GR_Table_Base]
- nop.m 999
- nop.i 999
+ nop.m 999
+(p8) fma.s1 FR_a = FR_V_hi, f1, FR_A
+ nop.i 999
}
;;
-
{ .mfi
-(p0) 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 ;;
+ nop.m 999
+ fma.s1 FR_C_hi = FR_s, f1, FR_A
+ nop.i 999 ;;
}
{ .mmi
-(p0) ldfe FR_C_1 = [GR_Table_Base], 16 ;;
-(p0) ldfe FR_C_2 = [GR_Table_Base], 64
- nop.i 999 ;;
+ 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
-(p0) ldfe FR_S_1 = [GR_Table_Base], 16
+ ldfe FR_S_1 = [GR_ad_s], 16
//
-// C_lo = S - C_hi
+// C_lo = S - C_hi
//
-(p0) fma.s1 FR_t = FR_t, f1, FR_w
- nop.i 999 ;;
+ fma.s1 FR_t = FR_t, f1, FR_w
+ nop.i 999 ;;
}
//
// r and c have been computed.
@@ -1558,855 +1587,695 @@ L(SINCOSL_LARGER_ARG):
// Load S_1
//
{ .mfi
-(p0) ldfe FR_S_2 = [GR_Table_Base], 64
+ ldfe FR_S_2 = [GR_ad_s], 64
//
-// t = t + w
+// t = t + w
//
-(p10) fms.s1 FR_a = FR_a, f1, FR_V_hi
-(p0) cmp.eq.unc p9, p10 = 0x0, GR_i_0 ;;
+(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
+ 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
//
-(p0) fms.s1 FR_C_lo = FR_s, f1, FR_C_hi
- nop.i 999 ;;
+ 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
-(p0) cmp.eq.unc p11, p12 = 0x0, GR_i_1 ;;
+ 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
+ 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.
//
-(p0) fma.s1 FR_C_lo = FR_C_lo, f1, FR_A
- nop.i 999 ;;
+ fma.s1 FR_C_lo = FR_C_lo, f1, FR_A
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
-// C_lo = (S - C_hi) + A
+// C_lo = (S - C_hi) + A
//
-(p0) fma.s1 FR_t = FR_t, f1, FR_a
- nop.i 999 ;;
+ fma.s1 FR_t = FR_t, f1, FR_a
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
-// t = t + a
+// t = t + a
//
-(p0) fma.s1 FR_C_lo = FR_C_lo, f1, FR_t
- nop.i 999 ;;
+ fma.s1 FR_C_lo = FR_C_lo, f1, FR_t
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// C_lo = C_lo + t
-// Adjust Table_Base to beginning of table
//
-(p0) fma.s1 FR_r = FR_C_hi, f1, FR_C_lo
- nop.i 999 ;;
+ fma.s1 FR_r = FR_C_hi, f1, FR_C_lo
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// Load S_2
//
-(p0) fma.s1 FR_rsq = FR_r, FR_r, f0
- nop.i 999
+ fma.s1 FR_rsq = FR_r, FR_r, f0
+ nop.i 999
}
{ .mfi
- nop.m 999
+ nop.m 999
//
-// Table_Base points to C_1
// r = C_hi + C_lo
//
-(p0) fms.s1 FR_c = FR_C_hi, f1, FR_r
- nop.i 999 ;;
+ fms.s1 FR_c = FR_C_hi, f1, FR_r
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ 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
- nop.i 999 ;;
+(p9) fma.s1 FR_tmp_result = f0, f1, FR_r
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
-(p12) fma.s1 FR_Input_X = f0, f1, f1
- nop.i 999 ;;
+ nop.m 999
+(p10) fma.s1 FR_tmp_result = f0, f1, f1
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
-// Compute r_cube = FR_rsq * r
+// Compute r_cube = FR_rsq * r
//
-(p11) fma.s1 FR_poly = FR_rsq, FR_S_2, FR_S_1
- nop.i 999 ;;
+(p9) 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
+ nop.m 999
+(p10) fma.s1 FR_poly = FR_rsq, FR_C_2, FR_C_1
+ nop.i 999
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// Compute FR_rsq = r * r
// Is i_1 == 0 ?
//
-(p0) fma.s1 FR_r_cubed = FR_rsq, FR_r, f0
- nop.i 999 ;;
+ fma.s1 FR_r_cubed = FR_rsq, FR_r, f0
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// c = C_hi - r
// Load C_1
//
-(p0) fma.s1 FR_c = FR_c, f1, FR_C_lo
- nop.i 999
+ fma.s1 FR_c = FR_c, f1, FR_C_lo
+ nop.i 999
}
{ .mfi
- nop.m 999
+ 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
- nop.i 999 ;;
+(p12) fms.s1 FR_tmp_result = f0, f1, FR_tmp_result
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ 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 ;;
+(p9) 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 ;;
+ nop.m 999
+(p10) fma.s1 FR_poly = FR_rsq, FR_poly, f0
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
-// if i_0 !=0: Result = -Result
+// if i_0 !=0: Result = -Result
//
-(p9) fma.s0 FR_Input_X = FR_Input_X, f1, FR_poly
- nop.i 999 ;;
+(p11) fma.s0 FR_Result = FR_tmp_result, f1, FR_poly
+ nop.i 999 ;;
}
{ .mfb
- nop.m 999
-(p10) fms.s0 FR_Input_X = FR_Input_X, f1, FR_poly
+ 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
//
-(p0) br.ret.sptk b0 ;;
+ br.ret.sptk b0 // Exit for |s| < 2^-14, and 2^24 <= |x| < 2^63
}
-L(SINCOSL_SMALL_R):
-{ .mii
- nop.m 999
-(p0) extr.u GR_i_1 = GR_N_Inc, 0, 1 ;;
+;;
+
+
+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.
//
-(p0) cmp.eq.unc p9, p10 = 0x0, GR_i_1 ;;
-}
-{ .mfi
- nop.m 999
-(p0) fma.s1 FR_rsq = FR_r, FR_r, f0
-(p0) 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
-(p0) cmp.eq.unc p11, p12 = 0x0, GR_i_0
+ 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
}
;;
-// ******************************************************************
-// ******************************************************************
-// ******************************************************************
-// 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
-(p0) addl GR_Table_Base = @ltoff(FSINCOSL_CONSTANTS#), gp
+(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
- ld8 GR_Table_Base = [GR_Table_Base]
- nop.m 999
+(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
}
;;
-
-//
-// 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 ;;
+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
}
-//
-// 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 ;;
+{ .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
-(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
-//
-(p0) 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 ;;
+(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
-(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 ;;
+(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
-//
-// 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
+ 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
-//
-// c = -c * r
-// dummy fmpy's to flag inexact.
-//
-(p9) fma.s0 FR_S_4 = FR_S_4, FR_S_4, f0
- nop.i 999 ;;
+ 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
-//
-// poly_lo = FR_rsq * poly_lo + C_3
-// poly_hi = FR_rsq * poly_hi
-//
-(p0) fma.s1 FR_Z = FR_Z, FR_rsq, f0
- nop.i 999 ;;
+ 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
- nop.i 999
+ 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
-//
-// 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 ;;
+ 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
-//
-// 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 ;;
+ nop.m 999
+ fma.s1 FR_Z = FR_Z, FR_rsq, f0 // Z = Z * rsq
+ nop.i 999
}
+;;
+
{ .mfi
- nop.m 999
-(p10) fma.s1 FR_poly_hi = FR_rsq, FR_C_2, FR_C_1
- nop.i 999
+ 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.s0 FR_C_1 = FR_C_1, FR_C_1, f0
- nop.i 999 ;;
+ 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.s1 FR_poly_hi = FR_poly_hi, FR_rsq, f0
- nop.i 999
+ 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
-//
-// 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 ;;
+ 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
-(p10) fma.s1 FR_poly_hi = FR_poly_hi, FR_rsq, f0
- nop.i 999 ;;
+ 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
-//
-// 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
+ 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
-//
-// poly_hi = r * poly_hi
-//
-(p0) fma.s1 FR_poly = FR_Z, FR_poly_lo, FR_c
- nop.i 999 ;;
+ 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
-(p12) fms.s1 FR_r = f0, f1, FR_r
- nop.i 999 ;;
+ 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
-//
-// poly_hi = Z * poly_lo + c
-// if i_0 == 1: r = -r
-//
-(p0) fma.s1 FR_poly = FR_poly, f1, FR_poly_hi
- nop.i 999 ;;
+ 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
-(p12) fms.s0 FR_Input_X = FR_r, f1, FR_poly
- nop.i 999
+ nop.m 999
+ fma.s1 FR_poly = FR_poly, f1, FR_poly_hi // poly=poly+poly_hi
+ nop.i 999
}
-{ .mfb
- nop.m 999
-//
-// poly = poly + poly_hi
-//
-(p11) fma.s0 FR_Input_X = FR_r, f1, FR_poly
+;;
+
//
// if (i_0 == 0) Result = r + poly
// if (i_0 != 0) Result = r - poly
//
-(p0) br.ret.sptk b0 ;;
-}
-L(SINCOSL_NORMAL_R):
-{ .mii
- nop.m 999
-(p0) extr.u GR_i_1 = GR_N_Inc, 0, 1 ;;
-//
-// Set table_ptr1 and table_ptr2 to base address of
-// constant table.
-(p0) cmp.eq.unc p9, p10 = 0x0, GR_i_1 ;;
-}
{ .mfi
- nop.m 999
-(p0) fma.s1 FR_rsq = FR_r, FR_r, f0
-(p0) extr.u GR_i_0 = GR_N_Inc, 1, 1 ;;
+ nop.m 999
+(p11) fma.s0 FR_Result = FR_r, f1, FR_poly
+ nop.i 999
}
-{ .mfi
- nop.m 999
-(p0) frcpa.s1 FR_r_hi, p6 = f1, FR_r
-(p0) cmp.eq.unc p11, p12 = 0x0, GR_i_0
+{ .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:
//
-// 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.
+// Here if 2^-3 <= |r| < pi/4
+// THIS IS THE MAIN PATH
//
-
-{ .mmi
- nop.m 999
-(p0) addl GR_Table_Base = @ltoff(FSINCOSL_CONSTANTS#), gp
+// 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
- ld8 GR_Table_Base = [GR_Table_Base]
- nop.m 999
+(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
-(p10) add GR_Table_Base = 384, GR_Table_Base
-(p12) fms.s1 FR_Input_X = f0, f1, f1
-(p9) add GR_Table_Base = 224, GR_Table_Base ;;
+ 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
-(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
- nop.i 999 ;;
-}
-{ .mmb
-(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
- nop.b 999 ;;
+ 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
-(p0) fma.s1 FR_r_cubed = FR_r, FR_rsq, f0
- nop.i 999 ;;
+ 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_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
-//
-(p0) 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 ;;
-}
-{ .mmb
-(p10) ldfe FR_QQ_4 = [GR_Table_Base], 16
-(p9) ldfe FR_PP_1 = [GR_Table_Base], 16
- nop.b 999 ;;
-}
-{ .mmb
-(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
- nop.b 999 ;;
-}
-{ .mfi
- nop.m 999
-(p10) fma.s1 FR_poly = FR_rsq, FR_QQ_8, FR_QQ_7
- nop.i 999 ;;
-}
-//
-// if (i_1=0) poly = rsq * poly + PP_5
-// else poly = rsq * poly + QQ_5
-// Load PP_4 or QQ_4
-//
-{ .mmi
-(p9) ldfe FR_PP_3 = [GR_Table_Base], 16 ;;
-(p10) ldfe FR_QQ_2 = [GR_Table_Base], 16
- nop.i 999
+(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
- nop.m 999
-//
-// r_hi = frcpa(frcpa(r)).
-// r_cube = r * FR_rsq.
-//
-(p9) fma.s1 FR_poly = FR_rsq, FR_PP_8, FR_PP_7
- nop.i 999 ;;
+(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
}
-//
-// 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 ;;
-}
-{ .mbb
-(p9) ldfe FR_PP_1_lo = [GR_Table_Base], 16
- nop.b 999
- nop.b 999 ;;
+(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
-(p10) fma.s1 FR_corr = FR_S_1, FR_r_cubed, FR_r
- nop.i 999
+ 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_poly = FR_rsq, FR_poly, FR_QQ_6
- nop.i 999 ;;
+ 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
- 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 ;;
+(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
- 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 ;;
+(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
- nop.m 999
-(p10) fma.s1 FR_U_lo = FR_r_hi, f1, FR_r
- nop.i 999
+(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
- 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 ;;
+(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
- nop.m 999
-//
-// U_hi = r_hi * r_hi
-//
-(p0) fms.s1 FR_r_lo = FR_r, f1, FR_r_hi
- nop.i 999
+(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
-//
-// Load PP_1, PP_6, PP_5, and C_1
-// Load QQ_1, QQ_6, QQ_5, and S_1
-//
-(p0) fma.s1 FR_U_hi = FR_r_hi, FR_r_hi, f0
- nop.i 999 ;;
+ 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
-(p10) fma.s1 FR_poly = FR_rsq, FR_poly, FR_QQ_5
- nop.i 999
+ 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) fnma.s1 FR_corr = FR_corr, FR_c, f0
- nop.i 999 ;;
+ 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
-//
-// 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 ;;
+ 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
-(p9) fma.s1 FR_poly = FR_rsq, FR_poly, FR_PP_5
- nop.i 999
+ 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
-//
-// if (i_1 =0) U_hi = r + U_hi
-// if (i_1 =0) U_lo = r_lo * U_lo
-//
-//
-(p9) fma.s0 FR_PP_5 = FR_PP_5, FR_PP_4, f0
- nop.i 999 ;;
+ 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
-(p9) fma.s1 FR_U_lo = FR_r, FR_r, FR_U_lo
- nop.i 999 ;;
+ 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
-(p10) fma.s1 FR_U_lo = FR_r_lo, FR_U_lo, f0
- nop.i 999 ;;
+ 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
-//
-// 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
+ 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
-(p10) fma.s1 FR_poly = FR_rsq, FR_poly, FR_QQ_4
- nop.i 999 ;;
+ 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
-(p10) fma.s1 FR_U_hi = FR_QQ_1, FR_U_hi, f1
- nop.i 999
+ 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.s0 FR_QQ_5 = FR_QQ_5, FR_QQ_5, f0
- nop.i 999 ;;
+ 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
-//
-// 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 ;;
+ 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
-(p9) fma.s1 FR_U_lo = FR_r_lo, FR_U_lo, f0
- nop.i 999 ;;
+ 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
-(p10) fma.s1 FR_U_lo = FR_QQ_1,FR_U_lo, f0
- nop.i 999 ;;
+ 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_U_hi = FR_PP_1, FR_U_hi, f0
- nop.i 999
+ 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_3
- nop.i 999 ;;
+ 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
-//
-// Load PP_2, QQ_2
-//
-(p9) fma.s1 FR_poly = FR_rsq, FR_poly, FR_PP_3
- nop.i 999 ;;
+ 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
-//
-// 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 ;;
+ 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
-//
-// 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
+ 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
-(p10) fma.s1 FR_poly = FR_rsq, FR_poly, FR_QQ_2
- nop.i 999 ;;
+ 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
-//
-// 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 ;;
+ 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
-//
-// if (i_0==0) Result = 1
-// else Result = -1
-//
-(p0) fma.s1 FR_V = FR_U_lo, f1, FR_corr
- nop.i 999 ;;
+ 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
-(p10) fma.s1 FR_poly = FR_rsq, FR_poly, f0
- nop.i 999 ;;
+ 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
-//
-// 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 ;;
+ 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
-(p10) fma.s1 FR_poly = FR_rsq, FR_poly, f0
- nop.i 999 ;;
+ 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
-//
-// V = U_lo + corr
-//
-(p9) fma.s1 FR_poly = FR_r_cubed, FR_poly, f0
- nop.i 999 ;;
+ 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
-//
-// if (i_1==0) poly = r_cube * poly
-// else poly = FR_rsq * poly
-//
-(p0) fma.s1 FR_V = FR_poly, f1, FR_V
- nop.i 999 ;;
+ 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
-(p12) fms.s0 FR_Input_X = FR_Input_X, FR_U_hi, FR_V
- nop.i 999
+ nop.m 999
+(p11) fma.s0 FR_Result = FR_tmp_result, FR_U_hi, FR_V
+ nop.i 999
}
{ .mfb
- nop.m 999
-//
-// V = V + poly
-//
-(p11) fma.s0 FR_Input_X = FR_Input_X, FR_U_hi, FR_V
-//
-// if (i_0==0) Result = Result * U_hi + V
-// else Result = Result * U_hi - V
-//
-(p0) 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
-//
+ 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
+}
+;;
-L(SINCOSL_ZERO):
-{ .mbb
-(p0) cmp.eq.unc p6, p7 = 0x1, GR_Sin_or_Cos
- nop.b 999
- nop.b 999 ;;
+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_Input_X = FR_Input_X, FR_Input_X
- nop.i 999
+ 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) fmerge.s FR_Input_X = f1, f1
-(p0) br.ret.sptk b0 ;;
+ 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
}
-L(SINCOSL_SPECIAL):
+;;
+
+SINCOSL_SPECIAL:
{ .mfb
nop.m 999
//
@@ -2414,106 +2283,83 @@ L(SINCOSL_SPECIAL):
// Invalid can be raised. SNaNs
// become QNaNs
//
-(p0) fmpy.s0 FR_Input_X = FR_Input_X, f0
-(p0) br.ret.sptk b0 ;;
+ fmpy.s0 FR_Result = FR_Input_X, f0
+ br.ret.sptk b0 ;;
}
-.endp cosl#
-ASM_SIZE_DIRECTIVE(cosl#)
-// Call int pi_by_2_reduce(double* x, double *y)
-// for |arguments| >= 2**63
-// Address to save r and c as double
-//
-// sp+32 -> f0
-// r45 sp+16 -> f0
-// r44 -> sp -> InputX
-//
+GLOBAL_IEEE754_END(cosl)
-.proc __libm_callout
-__libm_callout:
-L(SINCOSL_ARG_TOO_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 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
- add r45=-32,sp // Parameter: r address
nop.f 0
.save ar.pfs,GR_SAVE_PFS
mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
-}
-{ .mfi
-.fframe 64
- add sp=-64,sp // Create new stack
- nop.f 0
- mov GR_SAVE_GP=gp // Save gp
};;
+
{ .mmi
- stfe [r45] = f0,16 // Clear Parameter r on stack
- add r44 = 16,sp // Parameter x address
+ 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
- stfe [r45] = f0,-16 // Clear Parameter c on stack
- nop.i 0
- nop.b 0
-}
-{ .mib
- stfe [r44] = FR_Input_X // Store Parameter x on stack
+ setf.exp FR_Neg_Two_to_M3 = GR_exp_m2_to_m3 // Form -(2^-3)
nop.i 0
-(p0) br.call.sptk b0=__libm_pi_by_2_reduce# ;;
+ br.call.sptk b0=__libm_pi_by_2_reduce#
};;
-{ .mii
-(p0) ldfe FR_Input_X =[r44],16
-//
-// Get r and c off stack
-//
-(p0) adds GR_Table_Base1 = -16, GR_Table_Base1
-//
-// Get r and c off stack
-//
-(p0) add GR_N_Inc = GR_Sin_or_Cos,r8 ;;
-}
-{ .mmb
-(p0) ldfe FR_r =[r45],16
-//
-// Get X off the stack
-// Readjust Table ptr
-//
-(p0) ldfs FR_Two_to_M3 = [GR_Table_Base1],4
- nop.b 999 ;;
-}
-{ .mmb
-(p0) ldfs FR_Neg_Two_to_M3 = [GR_Table_Base1],0
-(p0) ldfe FR_c =[r45]
- nop.b 999 ;;
-}
+
{ .mfi
-.restore sp
- add sp = 64,sp // Restore stack pointer
-(p0) fcmp.lt.unc.s1 p6, p0 = FR_r, FR_Two_to_M3
+ 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
};;
-{ .mib
+
+{ .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
- nop.b 0
};;
-{ .mfi
- nop.m 999
-(p6) fcmp.gt.unc.s1 p6, p0 = FR_r, FR_Neg_Two_to_M3
- nop.i 999 ;;
-}
-{ .mib
- nop.m 999
- nop.i 999
-(p6) br.cond.spnt L(SINCOSL_SMALL_R) ;;
-}
-{ .mib
- nop.m 999
- nop.i 999
-(p0) br.cond.sptk L(SINCOSL_NORMAL_R) ;;
-}
-.endp __libm_callout
-ASM_SIZE_DIRECTIVE(__libm_callout)
+
+{ .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#