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Diffstat (limited to 'ports/sysdeps/ia64/fpu/libm_sincosl.S')
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1 files changed, 0 insertions, 2528 deletions
diff --git a/ports/sysdeps/ia64/fpu/libm_sincosl.S b/ports/sysdeps/ia64/fpu/libm_sincosl.S deleted file mode 100644 index 1d89ff4bd1..0000000000 --- a/ports/sysdeps/ia64/fpu/libm_sincosl.S +++ /dev/null @@ -1,2528 +0,0 @@ -.file "libm_sincosl.s" - - -// Copyright (c) 2000 - 2004, Intel Corporation -// All rights reserved. -// -// 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 -// 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: -// 05/13/02 Initial version of sincosl (based on libm's sinl and cosl) -// 02/10/03 Reordered header: .section, .global, .proc, .align; -// used data8 for long double table values -// 10/13/03 Corrected .file name -// 02/11/04 cisl is moved to the separate file. -// 10/26/04 Avoided using r14-31 as scratch so not clobbered by dynamic loader -// -//********************************************************************* -// -// Function: Combined sincosl routine with 3 different API's -// -// API's -//============================================================== -// 1) void sincosl(long double, long double*s, long double*c) -// 2) __libm_sincosl - internal LIBM function, that accepts -// argument in f8 and returns cosine through f8, sine through f9 -// -// -//********************************************************************* -// -// Resources Used: -// -// Floating-Point Registers: f8 (Input x and cosl return value), -// f9 (sinl returned) -// f32-f121 -// -// General Purpose Registers: -// r32-r61 -// -// Predicate Registers: p6-p15 -// -//********************************************************************* -// -// IEEE Special Conditions: -// -// Denormal fault raised on denormal inputs -// Overflow exceptions do not occur -// Underflow exceptions raised when appropriate for sincosl -// (No specialized error handling for this routine) -// Inexact raised when appropriate by algorithm -// -// sincosl(SNaN) = QNaN, QNaN -// sincosl(QNaN) = QNaN, QNaN -// sincosl(inf) = QNaN, QNaN -// sincosl(+/-0) = +/-0, 1 -// -//********************************************************************* -// -// Mathematical Description -// ======================== -// -// The computation of FSIN and FCOS performed in parallel. -// -// Arg = N pi/2 + alpha, |alpha| <= pi/4. -// -// cosl( Arg ) = sinl( (N+1) pi/2 + alpha ), -// -// therefore, the code for computing sine will produce cosine as long -// as 1 is added to N immediately after the argument reduction -// process. -// -// Let M = N if sine -// N+1 if cosine. -// -// Now, given -// -// Arg = M pi/2 + alpha, |alpha| <= pi/4, -// -// let I = M mod 4, or I be the two lsb of M when M is represented -// as 2's complement. I = [i_0 i_1]. Then -// -// sinl( Arg ) = (-1)^i_0 sinl( alpha ) if i_1 = 0, -// = (-1)^i_0 cosl( alpha ) if i_1 = 1. -// -// For example: -// if M = -1, I = 11 -// sin ((-pi/2 + alpha) = (-1) cos (alpha) -// if M = 0, I = 00 -// sin (alpha) = sin (alpha) -// if M = 1, I = 01 -// sin (pi/2 + alpha) = cos (alpha) -// if M = 2, I = 10 -// sin (pi + alpha) = (-1) sin (alpha) -// if M = 3, I = 11 -// sin ((3/2)pi + alpha) = (-1) cos (alpha) -// -// The value of alpha is obtained by argument reduction and -// represented by two working precision numbers r and c where -// -// alpha = r + c accurately. -// -// The reduction method is described in a previous write up. -// The argument reduction scheme identifies 4 cases. For Cases 2 -// and 4, because |alpha| is small, sinl(r+c) and cosl(r+c) can be -// computed very easily by 2 or 3 terms of the Taylor series -// expansion as follows: -// -// Case 2: -// ------- -// -// sinl(r + c) = r + c - r^3/6 accurately -// cosl(r + c) = 1 - 2^(-67) accurately -// -// Case 4: -// ------- -// -// sinl(r + c) = r + c - r^3/6 + r^5/120 accurately -// cosl(r + c) = 1 - r^2/2 + r^4/24 accurately -// -// The only cases left are Cases 1 and 3 of the argument reduction -// procedure. These two cases will be merged since after the -// argument is reduced in either cases, we have the reduced argument -// represented as r + c and that the magnitude |r + c| is not small -// enough to allow the usage of a very short approximation. -// -// The required calculation is either -// -// sinl(r + c) = sinl(r) + correction, or -// cosl(r + c) = cosl(r) + correction. -// -// Specifically, -// -// sinl(r + c) = sinl(r) + c sin'(r) + O(c^2) -// = sinl(r) + c cos (r) + O(c^2) -// = sinl(r) + c(1 - r^2/2) accurately. -// Similarly, -// -// cosl(r + c) = cosl(r) - c sinl(r) + O(c^2) -// = cosl(r) - c(r - r^3/6) accurately. -// -// We therefore concentrate on accurately calculating sinl(r) and -// cosl(r) for a working-precision number r, |r| <= pi/4 to within -// 0.1% or so. -// -// The greatest challenge of this task is that the second terms of -// the Taylor series -// -// r - r^3/3! + r^r/5! - ... -// -// and -// -// 1 - r^2/2! + r^4/4! - ... -// -// are not very small when |r| is close to pi/4 and the rounding -// errors will be a concern if simple polynomial accumulation is -// used. When |r| < 2^-3, however, the second terms will be small -// enough (6 bits or so of right shift) that a normal Horner -// recurrence suffices. Hence there are two cases that we consider -// in the accurate computation of sinl(r) and cosl(r), |r| <= pi/4. -// -// Case small_r: |r| < 2^(-3) -// -------------------------- -// -// Since Arg = M pi/4 + r + c accurately, and M mod 4 is [i_0 i_1], -// we have -// -// sinl(Arg) = (-1)^i_0 * sinl(r + c) if i_1 = 0 -// = (-1)^i_0 * cosl(r + c) if i_1 = 1 -// -// can be accurately approximated by -// -// sinl(Arg) = (-1)^i_0 * [sinl(r) + c] if i_1 = 0 -// = (-1)^i_0 * [cosl(r) - c*r] if i_1 = 1 -// -// because |r| is small and thus the second terms in the correction -// are unneccessary. -// -// Finally, sinl(r) and cosl(r) are approximated by polynomials of -// moderate lengths. -// -// sinl(r) = r + S_1 r^3 + S_2 r^5 + ... + S_5 r^11 -// cosl(r) = 1 + C_1 r^2 + C_2 r^4 + ... + C_5 r^10 -// -// We can make use of predicates to selectively calculate -// sinl(r) or cosl(r) based on i_1. -// -// Case normal_r: 2^(-3) <= |r| <= pi/4 -// ------------------------------------ -// -// This case is more likely than the previous one if one considers -// r to be uniformly distributed in [-pi/4 pi/4]. Again, -// -// sinl(Arg) = (-1)^i_0 * sinl(r + c) if i_1 = 0 -// = (-1)^i_0 * cosl(r + c) if i_1 = 1. -// -// Because |r| is now larger, we need one extra term in the -// correction. sinl(Arg) can be accurately approximated by -// -// sinl(Arg) = (-1)^i_0 * [sinl(r) + c(1-r^2/2)] if i_1 = 0 -// = (-1)^i_0 * [cosl(r) - c*r*(1 - r^2/6)] i_1 = 1. -// -// Finally, sinl(r) and cosl(r) are approximated by polynomials of -// moderate lengths. -// -// sinl(r) = r + PP_1_hi r^3 + PP_1_lo r^3 + -// PP_2 r^5 + ... + PP_8 r^17 -// -// cosl(r) = 1 + QQ_1 r^2 + QQ_2 r^4 + ... + QQ_8 r^16 -// -// where PP_1_hi is only about 16 bits long and QQ_1 is -1/2. -// The crux in accurate computation is to calculate -// -// r + PP_1_hi r^3 or 1 + QQ_1 r^2 -// -// accurately as two pieces: U_hi and U_lo. The way to achieve this -// is to obtain r_hi as a 10 sig. bit number that approximates r to -// roughly 8 bits or so of accuracy. (One convenient way is -// -// r_hi := frcpa( frcpa( r ) ).) -// -// This way, -// -// r + PP_1_hi r^3 = r + PP_1_hi r_hi^3 + -// PP_1_hi (r^3 - r_hi^3) -// = [r + PP_1_hi r_hi^3] + -// [PP_1_hi (r - r_hi) -// (r^2 + r_hi r + r_hi^2) ] -// = U_hi + U_lo -// -// Since r_hi is only 10 bit long and PP_1_hi is only 16 bit long, -// PP_1_hi * r_hi^3 is only at most 46 bit long and thus computed -// exactly. Furthermore, r and PP_1_hi r_hi^3 are of opposite sign -// and that there is no more than 8 bit shift off between r and -// PP_1_hi * r_hi^3. Hence the sum, U_hi, is representable and thus -// calculated without any error. Finally, the fact that -// -// |U_lo| <= 2^(-8) |U_hi| -// -// says that U_hi + U_lo is approximating r + PP_1_hi r^3 to roughly -// 8 extra bits of accuracy. -// -// Similarly, -// -// 1 + QQ_1 r^2 = [1 + QQ_1 r_hi^2] + -// [QQ_1 (r - r_hi)(r + r_hi)] -// = U_hi + U_lo. -// -// Summarizing, we calculate r_hi = frcpa( frcpa( r ) ). -// -// If i_1 = 0, then -// -// U_hi := r + PP_1_hi * r_hi^3 -// U_lo := PP_1_hi * (r - r_hi) * (r^2 + r*r_hi + r_hi^2) -// poly := PP_1_lo r^3 + PP_2 r^5 + ... + PP_8 r^17 -// correction := c * ( 1 + C_1 r^2 ) -// -// Else ...i_1 = 1 -// -// U_hi := 1 + QQ_1 * r_hi * r_hi -// U_lo := QQ_1 * (r - r_hi) * (r + r_hi) -// poly := QQ_2 * r^4 + QQ_3 * r^6 + ... + QQ_8 r^16 -// correction := -c * r * (1 + S_1 * r^2) -// -// End -// -// Finally, -// -// V := poly + ( U_lo + correction ) -// -// / U_hi + V if i_0 = 0 -// result := | -// \ (-U_hi) - V if i_0 = 1 -// -// It is important that in the last step, negation of U_hi is -// performed prior to the subtraction which is to be performed in -// the user-set rounding mode. -// -// -// Algorithmic Description -// ======================= -// -// The argument reduction algorithm shares the same code between FSIN and FCOS. -// The argument reduction description given -// previously is repeated below. -// -// -// Step 0. Initialization. -// -// 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 64 - -LOCAL_OBJECT_START(FSINCOSL_CONSTANTS) - -sincosl_table_p: -//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 0xDBD171A1, 0x8D848E89, 0x0000BFBF,0x00000000 // d_1 -//data4 0x18A66F8E, 0xD5394C36, 0x0000BF7C,0x00000000 // d_2 -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) -//data4 0x2168C234, 0xC90FDAA2, 0x00003FFE,0x00000000 // pi_by_4 -//data4 0x6EC6B45A, 0xA397E504, 0x00003FE7,0x00000000 // Inv_P_0 -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) -//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 -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) -//data4 0xC2B0FE52, 0xD56232EF, 0x00003FD2 // QQ_8 -//data4 0x2B48DCA6, 0xC9C99ABA, 0x0000BFDA // QQ_7 -//data4 0x9C716658, 0x8F76C650, 0x00003FE2 // QQ_6 -//data4 0xFDA8D0FC, 0x93F27DBA, 0x0000BFE9 // QQ_5 -//data4 0xAAAAAAAA, 0xAAAAAAAA, 0x0000BFFC // 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 -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) -//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 -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) -//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 -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_ResultS = f9 -FR_ResultC = 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_r6 = f32 -FR_r7 = f33 -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_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_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_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_d_2 = f93 -FR_P_0 = f95 -FR_C_lo = f96 -FR_PP_1 = f97 -FR_PP_1_lo = f98 -FR_ArgPrime = f99 -FR_inexact = f100 - -FR_Neg_Two_to_M3 = f109 -FR_Two_to_M3 = f110 - -FR_poly_hiS = f66 -FR_poly_hiC = f112 - -FR_poly_loS = f67 -FR_poly_loC = f113 - -FR_polyS = f92 -FR_polyC = f114 - -FR_cS = FR_c -FR_cC = f115 - -FR_corrS = f91 -FR_corrC = f116 - -FR_U_hiC = f117 -FR_U_loC = f118 - -FR_VS = f75 -FR_VC = f119 - -FR_FirstS = f120 -FR_FirstC = f121 - -FR_U_hiS = FR_U_hi -FR_U_loS = FR_U_lo - -FR_Tmp = f94 - - - - -sincos_pResSin = r34 -sincos_pResCos = r35 - -GR_exp_m2_to_m3= r36 -GR_N_Inc = r37 -GR_Cis = 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_N_SignS = r45 -GR_N_SignC = r46 -GR_N_SinCos = r47 - -GR_sig_inv_pi = r48 -GR_rshf_2to64 = r49 -GR_exp_2tom64 = r50 -GR_rshf = r51 -GR_ad_p = r52 -GR_ad_d = r53 -GR_ad_pp = r54 -GR_ad_qq = r55 -GR_ad_c = r56 -GR_ad_s = r57 -GR_ad_ce = r58 -GR_ad_se = r59 -GR_ad_m14 = r60 -GR_ad_s1 = r61 - -// For unwind support -GR_SAVE_B0 = r39 -GR_SAVE_GP = r40 -GR_SAVE_PFS = r41 - - -.section .text - -GLOBAL_IEEE754_ENTRY(sincosl) -{ .mlx ///////////////////////////// 1 ///////////////// - alloc r32 = ar.pfs,3,27,2,0 - movl GR_sig_inv_pi = 0xa2f9836e4e44152a // significand of 1/pi -} -{ .mlx - mov GR_N_Inc = 0x0 - movl GR_rshf_2to64 = 0x47e8000000000000 // 1.1000 2^(63+64) -};; - -{ .mfi ///////////////////////////// 2 ///////////////// - 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 - mov GR_Cis = 0x0 - fnorm.s1 FR_norm_x = FR_Input_X // Normalize x - br.cond.sptk _COMMON_SINCOSL -};; -GLOBAL_IEEE754_END(sincosl) - -GLOBAL_LIBM_ENTRY(__libm_sincosl) -{ .mlx ///////////////////////////// 1 ///////////////// - alloc r32 = ar.pfs,3,27,2,0 - movl GR_sig_inv_pi = 0xa2f9836e4e44152a // significand of 1/pi -} -{ .mlx - mov GR_N_Inc = 0x0 - movl GR_rshf_2to64 = 0x47e8000000000000 // 1.1000 2^(63+64) -};; - -{ .mfi ///////////////////////////// 2 ///////////////// - 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 - mov GR_Cis = 0x1 - fnorm.s1 FR_norm_x = FR_Input_X // Normalize x - nop.b 0 -};; - -_COMMON_SINCOSL: -{ .mfi ///////////////////////////// 3 ///////////////// - setf.sig FR_inv_pi_2to63 = GR_sig_inv_pi // Form 1/pi * 2^63 - nop.f 0 - 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 ///////////////////////////// 4 ///////////////// - 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 0 -};; - -{ .mfi ///////////////////////////// 5 ///////////////// - 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 0 -} -{ .mib - mov GR_exp_mask = 0x1ffff // Exponent mask - nop.i 0 -(p6) br.cond.spnt SINCOSL_SPECIAL // Branch if x natval, nan, inf -};; - -{ .mfi ///////////////////////////// 6 ///////////////// - setf.exp FR_2tom64 = GR_exp_2tom64 // Form 2^-64 for scaling N_float - nop.f 0 - add GR_ad_d = 0x70, GR_ad_p // Point to constant table d -} -{ .mib - setf.d FR_rshf = GR_rshf // Form right shift const 1.1000 * 2^63 - mov GR_exp_m2_to_m3 = 0x2fffc // Form -(2^-3) -(p7) br.cond.spnt SINCOSL_DENORMAL // Branch if x denormal -};; - -SINCOSL_COMMON2: -{ .mfi ///////////////////////////// 7 ///////////////// - and GR_exp_x = GR_exp_mask, GR_signexp_x // Get exponent of x - fclass.nm p8, p0 = FR_Input_X, 0x1FF // Test x unsupported type - mov GR_exp_2_to_63 = 0xffff + 63 // Exponent of 2^63 -} -{ .mib - add GR_ad_pp = 0x40, GR_ad_d // Point to constant table pp - mov GR_exp_2_to_24 = 0xffff + 24 // Exponent of 2^24 -(p10) br.cond.spnt SINCOSL_ZERO // Branch if x zero -};; - -{ .mfi ///////////////////////////// 8 ///////////////// - ldfe FR_Inv_pi_by_2 = [GR_ad_p], 16 // Load 2/pi - fcmp.eq.s0 p15, p0 = FR_Input_X, f0 // Dummy to set denormal - add GR_ad_qq = 0xa0, GR_ad_pp // Point to constant table qq -} -{ .mfi - ldfe FR_Pi_by_4 = [GR_ad_d], 16 // Load pi/4 for range test - nop.f 0 - cmp.ge p10,p0 = GR_exp_x, GR_exp_2_to_63 // Is |x| >= 2^63 -};; - -{ .mfi ///////////////////////////// 9 ///////////////// - ldfe FR_P_0 = [GR_ad_p], 16 // Load P_0 for pi/4 <= |x| < 2^63 - fmerge.s FR_abs_x = f1, FR_norm_x // |x| - add GR_ad_c = 0x90, GR_ad_qq // Point to constant table c -} -{ .mfi - ldfe FR_Inv_P_0 = [GR_ad_d], 16 // Load 1/P_0 for pi/4 <= |x| < 2^63 - nop.f 0 - cmp.ge p7,p0 = GR_exp_x, GR_exp_2_to_24 // Is |x| >= 2^24 -};; - -{ .mfi ///////////////////////////// 10 ///////////////// - ldfe FR_P_1 = [GR_ad_p], 16 // Load P_1 for pi/4 <= |x| < 2^63 - nop.f 0 - add GR_ad_s = 0x50, GR_ad_c // Point to constant table s -} -{ .mfi - ldfe FR_PP_8 = [GR_ad_pp], 16 // Load PP_8 for 2^-3 < |r| < pi/4 - nop.f 0 - nop.i 0 -};; - -{ .mfi ///////////////////////////// 11 ///////////////// - ldfe FR_P_2 = [GR_ad_p], 16 // Load P_2 for pi/4 <= |x| < 2^63 - nop.f 0 - add GR_ad_ce = 0x40, GR_ad_c // Point to end of constant table c -} -{ .mfi - ldfe FR_QQ_8 = [GR_ad_qq], 16 // Load QQ_8 for 2^-3 < |r| < pi/4 - nop.f 0 - nop.i 0 -};; - -{ .mfi ///////////////////////////// 12 ///////////////// - ldfe FR_QQ_7 = [GR_ad_qq], 16 // Load QQ_7 for 2^-3 < |r| < pi/4 - fma.s1 FR_N_float_signif = FR_Input_X, FR_inv_pi_2to63, FR_rshf_2to64 - add GR_ad_se = 0x40, GR_ad_s // Point to end of constant table s -} -{ .mib - ldfe FR_PP_7 = [GR_ad_pp], 16 // Load PP_7 for 2^-3 < |r| < pi/4 - mov GR_ad_s1 = GR_ad_s // Save pointer to S_1 -(p10) br.cond.spnt SINCOSL_ARG_TOO_LARGE // Branch if |x| >= 2^63 - // Use Payne-Hanek Reduction -};; - -{ .mfi ///////////////////////////// 13 ///////////////// - ldfe FR_P_3 = [GR_ad_p], 16 // Load P_3 for pi/4 <= |x| < 2^63 - fmerge.se FR_r = FR_norm_x, FR_norm_x // r = x, in case |x| < pi/4 - add GR_ad_m14 = 0x50, GR_ad_s // Point to constant table m14 -} -{ .mfb - ldfps FR_Two_to_M3, FR_Neg_Two_to_M3 = [GR_ad_d], 8 - fma.s1 FR_rsq = FR_norm_x, FR_norm_x, f0 // rsq = x*x, in case |x| < pi/4 -(p7) br.cond.spnt SINCOSL_LARGER_ARG // Branch if 2^24 <= |x| < 2^63 - // Use pre-reduction -};; - -{ .mmf ///////////////////////////// 14 ///////////////// - 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 ///////////////////////////// 15 ///////////////// - 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 0 -};; - -// Here if 0 < |x| < 2^24 -{ .mfi ///////////////////////////// 17 ///////////////// - 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 0 -} -{ .mfi - ldfe FR_C_5 = [GR_ad_ce], -16 // Load C_5 if i_1=1 - fms.s1 FR_N_float = FR_N_float_signif, FR_2tom64, FR_rshf - nop.i 0 -};; - -{ .mmi ///////////////////////////// 18 ///////////////// - 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 0 -};; - -// -// N = Arg * 2/pi -// Check if Arg < pi/4 -// -// -// Case 2: Convert integer N_fix back to normalized floating-point value. -// Case 1: p8 is only affected when p6 is set -// -// -// Grab the integer part of N and call it N_fix -// -{ .mfi ///////////////////////////// 19 ///////////////// -(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 = 0x0 // N_IncS if |x| < pi/4 -};; - -// If |x| < pi/4, r = x and c = 0 -// lf |x| < pi/4, is x < 2**(-3). -// r = Arg -// c = 0 -{ .mmi ///////////////////////////// 20 ///////////////// -(p7) getf.sig GR_N_Inc = FR_N_float_signif - nop.m 0 -(p6) cmp.lt.unc p8,p0 = GR_exp_x, GR_exp_2_to_m3 // Is |x| < 2^-3 -};; - -// -// lf |x| < pi/4, is -2**(-3)< x < 2**(-3) - set p8. -// If |x| >= pi/4, -// Create the right N for |x| < pi/4 and otherwise -// Case 2: Place integer part of N in GP register -// - -{ .mbb ///////////////////////////// 21 ///////////////// - nop.m 0 -(p8) br.cond.spnt SINCOSL_SMALL_R_0 // Branch if 0 < |x| < 2^-3 -(p6) br.cond.spnt SINCOSL_NORMAL_R_0 // Branch if 2^-3 <= |x| < pi/4 -};; - -// Here if pi/4 <= |x| < 2^24 -{ .mfi - ldfs FR_Neg_Two_to_M67 = [GR_ad_d], 8 // Load -2^-67 - fnma.s1 FR_s = FR_N_float, FR_P_1, FR_Input_X // s = -N * P_1 + Arg - nop.i 0 -} -{ .mfi - nop.m 0 - fma.s1 FR_w = FR_N_float, FR_P_2, f0 // w = N * P_2 - nop.i 0 -};; - -{ .mfi - nop.m 0 - fms.s1 FR_r = FR_s, f1, FR_w // r = s - w, assume |s| >= 2^-33 - nop.i 0 -};; - -{ .mfi - nop.m 0 - fcmp.lt.s1 p7, p6 = FR_s, FR_Two_to_M33 - nop.i 0 -};; - -{ .mfi - nop.m 0 -(p7) fcmp.gt.s1 p7, p6 = FR_s, FR_Neg_Two_to_M33 // p6 if |s| >= 2^-33, else p7 - nop.i 0 -};; - -{ .mfi - nop.m 0 - fms.s1 FR_c = FR_s, f1, FR_r // c = s - r, for |s| >= 2^-33 - nop.i 0 -} -{ .mfi - nop.m 0 - fma.s1 FR_rsq = FR_r, FR_r, f0 // rsq = r * r, for |s| >= 2^-33 - nop.i 0 -};; - -{ .mfi - nop.m 0 -(p7) fma.s1 FR_w = FR_N_float, FR_P_3, f0 - nop.i 0 -};; - -{ .mmf - ldfe FR_C_1 = [GR_ad_pp], 16 // Load C_1 if i_1=0 - 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 0 -(p6) fcmp.lt.unc.s1 p8, p13 = FR_r, FR_Two_to_M3 // If big s, test r with 2^-3 - nop.i 0 -};; - -{ .mfi - nop.m 0 -(p7) fma.s1 FR_U_1 = FR_N_float, FR_P_2, FR_w - nop.i 0 -};; - -// -// For big s: r = s - w: No futher reduction is necessary -// For small s: w = N * P_3 (change sign) More reduction -// -{ .mfi - nop.m 0 -(p8) fcmp.gt.s1 p8, p13 = FR_r, FR_Neg_Two_to_M3 // If big s, p8 if |r| < 2^-3 - nop.i 0 -};; - -{ .mfi - nop.m 0 - fma.s1 FR_polyS = FR_rsq, FR_PP_8, FR_PP_7 // poly = rsq*PP_8+PP_7 - nop.i 0 -} -{ .mfi - nop.m 0 - fma.s1 FR_polyC = FR_rsq, FR_QQ_8, FR_QQ_7 // poly = rsq*QQ_8+QQ_7 - nop.i 0 -};; - -{ .mfi - nop.m 0 -(p7) fms.s1 FR_r = FR_s, f1, FR_U_1 - nop.i 0 -};; - -{ .mfi - nop.m 0 -(p6) fma.s1 FR_r_cubed = FR_r, FR_rsq, f0 // rcubed = r * rsq - nop.i 0 -};; - -{ .mfi -// -// For big s: Is |r| < 2**(-3)? -// For big s: c = S - r -// For small s: U_1 = N * P_2 + w -// -// If p8 is set, prepare to branch to Small_R. -// If p9 is set, prepare to branch to Normal_R. -// For big s, r is complete here. -// -// -// For big s: c = c + w (w has not been negated.) -// For small s: r = S - U_1 -// - nop.m 0 -(p6) fms.s1 FR_c = FR_c, f1, FR_w - nop.i 0 -} -{ .mbb - nop.m 0 -(p8) br.cond.spnt SINCOSL_SMALL_R_1 // Branch if |s|>=2^-33, |r| < 2^-3, - // and pi/4 <= |x| < 2^24 -(p13) br.cond.sptk SINCOSL_NORMAL_R_1 // Branch if |s|>=2^-33, |r| >= 2^-3, - // and pi/4 <= |x| < 2^24 -};; - -SINCOSL_S_TINY: -// -// Here if |s| < 2^-33, and pi/4 <= |x| < 2^24 -// -{ .mfi - and GR_N_SinCos = 0x1, GR_N_Inc - fms.s1 FR_U_2 = FR_N_float, FR_P_2, FR_U_1 - tbit.z p8,p12 = GR_N_Inc, 0 -};; - - -// -// For small s: U_2 = N * P_2 - U_1 -// S_1 stored constant - grab the one stored with the -// coefficients. -// -{ .mfi - ldfe FR_S_1 = [GR_ad_s1], 16 - fma.s1 FR_polyC = f0, f1, FR_Neg_Two_to_M67 - sub GR_N_SignS = GR_N_Inc, GR_N_SinCos -} -{ .mfi - add GR_N_SignC = GR_N_Inc, GR_N_SinCos - nop.f 0 - nop.i 0 -};; - -{ .mfi - nop.m 0 - fms.s1 FR_s = FR_s, f1, FR_r -(p8) tbit.z.unc p10,p11 = GR_N_SignC, 1 -} -{ .mfi - nop.m 0 - fma.s1 FR_rsq = FR_r, FR_r, f0 - nop.i 0 -};; - -{ .mfi - nop.m 0 - fma.s1 FR_U_2 = FR_U_2, f1, FR_w -(p8) tbit.z.unc p8,p9 = GR_N_SignS, 1 -};; - -{ .mfi - nop.m 0 - fmerge.se FR_FirstS = FR_r, FR_r -(p12) tbit.z.unc p14,p15 = GR_N_SignC, 1 -} -{ .mfi - nop.m 0 - fma.s1 FR_FirstC = f0, f1, f1 - nop.i 0 -};; - -{ .mfi - nop.m 0 - fms.s1 FR_c = FR_s, f1, FR_U_1 -(p12) tbit.z.unc p12,p13 = GR_N_SignS, 1 -};; - -{ .mfi - nop.m 0 - fma.s1 FR_r = FR_S_1, FR_r, f0 - nop.i 0 -};; - -{ .mfi - nop.m 0 - fma.s0 FR_S_1 = FR_S_1, FR_S_1, f0 - nop.i 0 -};; - -{ .mfi - nop.m 0 - fms.s1 FR_c = FR_c, f1, FR_U_2 - nop.i 0 -};; - -.pred.rel "mutex",p9,p15 -{ .mfi - nop.m 0 -(p9) fms.s0 FR_FirstS = f1, f0, FR_FirstS - nop.i 0 -} -{ .mfi - nop.m 0 -(p15) fms.s0 FR_FirstS = f1, f0, FR_FirstS - nop.i 0 -};; - -.pred.rel "mutex",p11,p13 -{ .mfi - nop.m 0 -(p11) fms.s0 FR_FirstC = f1, f0, FR_FirstC - nop.i 0 -} -{ .mfi - nop.m 0 -(p13) fms.s0 FR_FirstC = f1, f0, FR_FirstC - nop.i 0 -};; - -{ .mfi - nop.m 0 - fma.s1 FR_polyS = FR_r, FR_rsq, FR_c - nop.i 0 -};; - - -.pred.rel "mutex",p8,p9 -{ .mfi - nop.m 0 -(p8) fma.s0 FR_ResultS = FR_FirstS, f1, FR_polyS - nop.i 0 -} -{ .mfi - nop.m 0 -(p9) fms.s0 FR_ResultS = FR_FirstS, f1, FR_polyS - nop.i 0 -};; - -.pred.rel "mutex",p10,p11 -{ .mfi - nop.m 0 -(p10) fma.s0 FR_ResultC = FR_FirstC, f1, FR_polyC - nop.i 0 -} -{ .mfi - nop.m 0 -(p11) fms.s0 FR_ResultC = FR_FirstC, f1, FR_polyC - nop.i 0 -};; - - - -.pred.rel "mutex",p12,p13 -{ .mfi - nop.m 0 -(p12) fma.s0 FR_ResultS = FR_FirstC, f1, FR_polyC - nop.i 0 -} -{ .mfi - nop.m 0 -(p13) fms.s0 FR_ResultS = FR_FirstC, f1, FR_polyC - nop.i 0 -};; - -.pred.rel "mutex",p14,p15 -{ .mfi - nop.m 0 -(p14) fma.s0 FR_ResultC = FR_FirstS, f1, FR_polyS - nop.i 0 -} -{ .mfb - cmp.eq p10, p0 = 0x1, GR_Cis -(p15) fms.s0 FR_ResultC = FR_FirstS, f1, FR_polyS -(p10) br.ret.sptk b0 -};; - -{ .mmb // exit for sincosl - stfe [sincos_pResSin] = FR_ResultS - stfe [sincos_pResCos] = FR_ResultC - br.ret.sptk b0 -};; - - - - - - -SINCOSL_LARGER_ARG: -// -// Here if 2^24 <= |x| < 2^63 -// -{ .mfi - ldfe FR_d_1 = [GR_ad_p], 16 // Load d_1 for |x| >= 2^24 path - fma.s1 FR_N_0 = FR_Input_X, FR_Inv_P_0, f0 // N_0 = Arg * Inv_P_0 - nop.i 0 -};; - -{ .mmi - ldfps FR_Two_to_M14, FR_Neg_Two_to_M14 = [GR_ad_m14] - nop.m 0 - nop.i 0 -};; - -{ .mfi - ldfe FR_d_2 = [GR_ad_p], 16 // Load d_2 for |x| >= 2^24 path - nop.f 0 - nop.i 0 -};; - -{ .mfi - nop.m 0 - fcvt.fx.s1 FR_N_0_fix = FR_N_0 // N_0_fix = integer part of N_0 - nop.i 0 -};; - -{ .mfi - nop.m 0 - fcvt.xf FR_N_0 = FR_N_0_fix // Make N_0 the integer part - nop.i 0 -};; - -{ .mfi - nop.m 0 - fnma.s1 FR_ArgPrime = FR_N_0, FR_P_0, FR_Input_X // Arg'=-N_0*P_0+Arg - nop.i 0 -} -{ .mfi - nop.m 0 - fma.s1 FR_w = FR_N_0, FR_d_1, f0 // w = N_0 * d_1 - nop.i 0 -};; - - -{ .mfi - nop.m 0 - fma.s1 FR_N_float = FR_ArgPrime, FR_Inv_pi_by_2, f0 // N = A' * 2/pi - nop.i 0 -};; - -{ .mfi - nop.m 0 - fcvt.fx.s1 FR_N_fix = FR_N_float // N_fix is the integer part - nop.i 0 -};; - -{ .mfi - nop.m 0 - fcvt.xf FR_N_float = FR_N_fix - nop.i 0 -};; - -{ .mfi - getf.sig GR_N_Inc = FR_N_fix // N is the integer part of - // the reduced-reduced argument - nop.f 0 - nop.i 0 -};; - -{ .mfi - nop.m 0 - fnma.s1 FR_s = FR_N_float, FR_P_1, FR_ArgPrime // s = -N*P_1 + Arg' - nop.i 0 -} -{ .mfi - nop.m 0 - fnma.s1 FR_w = FR_N_float, FR_P_2, FR_w // w = -N*P_2 + w - nop.i 0 -};; - -// -// For |s| > 2**(-14) r = S + w (r complete) -// Else U_hi = N_0 * d_1 -// -{ .mfi - nop.m 0 - fcmp.lt.unc.s1 p9, p8 = FR_s, FR_Two_to_M14 - nop.i 0 -};; - -{ .mfi - nop.m 0 -(p9) fcmp.gt.s1 p9, p8 = FR_s, FR_Neg_Two_to_M14 // p9 if |s| < 2^-14 - nop.i 0 -};; - -// -// Either S <= -2**(-14) or S >= 2**(-14) -// or -2**(-14) < s < 2**(-14) -// -{ .mfi - nop.m 0 -(p9) fma.s1 FR_V_hi = FR_N_float, FR_P_2, f0 - nop.i 0 -} -{ .mfi - nop.m 0 -(p9) fma.s1 FR_U_hi = FR_N_0, FR_d_1, f0 - nop.i 0 -};; - -{ .mfi - nop.m 0 -(p8) fma.s1 FR_r = FR_s, f1, FR_w - nop.i 0 -} -{ .mfi - nop.m 0 -(p9) fma.s1 FR_w = FR_N_float, FR_P_3, f0 - nop.i 0 -};; - -// -// We need abs of both U_hi and V_hi - don't -// worry about switched sign of V_hi. -// -// 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. -// -{ .mfi - nop.m 0 -(p9) fms.s1 FR_A = FR_U_hi, f1, FR_V_hi - nop.i 0 -} -{ .mfi - nop.m 0 -(p9) fnma.s1 FR_V_lo = FR_N_float, FR_P_2, FR_V_hi - nop.i 0 -};; - -{ .mfi - nop.m 0 -(p9) fmerge.s FR_V_hiabs = f0, FR_V_hi - nop.i 0 -} -{ .mfi - nop.m 0 -(p9) fms.s1 FR_U_lo = FR_N_0, FR_d_1, FR_U_hi // For small s: U_lo=N_0*d_1-U_hi - nop.i 0 -};; - -// -// 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. -// -{ .mfi - nop.m 0 -(p9) fmerge.s FR_U_hiabs = f0, FR_U_hi - nop.i 0 -} -{ .mfi - nop.m 0 -(p8) fms.s1 FR_c = FR_s, f1, FR_r // For big s: c = S - r - nop.i 0 -};; - -// -// 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. -// -{ .mfi - nop.m 0 -(p8) fcmp.lt.unc.s1 p12, p13 = FR_r, FR_Two_to_M3 - nop.i 0 -};; - -{ .mfi - nop.m 0 -(p12) fcmp.gt.s1 p12, p13 = FR_r, FR_Neg_Two_to_M3 - nop.i 0 -};; - -{ .mfi - nop.m 0 -(p8) fma.s1 FR_c = FR_c, f1, FR_w - nop.i 0 -} -{ .mfb - nop.m 0 -(p9) fms.s1 FR_w = FR_N_0, FR_d_2, FR_w -(p12) br.cond.spnt SINCOSL_SMALL_R // Branch if |r| < 2^-3 - // and 2^24 <= |x| < 2^63 -};; - -{ .mib - nop.m 0 - nop.i 0 -(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 -// -// 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. -// -{ .mfi - and GR_N_SinCos = 0x1, GR_N_Inc - fcmp.ge.unc.s1 p6, p7 = FR_U_hiabs, FR_V_hiabs - tbit.z p8,p12 = GR_N_Inc, 0 -} -{ .mfi - nop.m 0 - fma.s1 FR_t = FR_U_lo, f1, FR_V_lo // C_hi = S + A - nop.i 0 -};; - -{ .mfi - sub GR_N_SignS = GR_N_Inc, GR_N_SinCos -(p6) fms.s1 FR_a = FR_U_hi, f1, FR_A - add GR_N_SignC = GR_N_Inc, GR_N_SinCos -} -{ .mfi - nop.m 0 -(p7) fma.s1 FR_a = FR_V_hi, f1, FR_A - nop.i 0 -};; - -{ .mmf - ldfe FR_C_1 = [GR_ad_c], 16 - ldfe FR_S_1 = [GR_ad_s], 16 - fma.s1 FR_C_hi = FR_s, f1, FR_A -};; - -{ .mmi - ldfe FR_C_2 = [GR_ad_c], 64 - ldfe FR_S_2 = [GR_ad_s], 64 -(p8) tbit.z.unc p10,p11 = GR_N_SignC, 1 -};; - -// -// 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. -// -// For larger u than v: a = U_hi - A -// Else a = V_hi - A (do an add to account for missing (-) on V_hi -// -{ .mfi - nop.m 0 - fma.s1 FR_t = FR_t, f1, FR_w // t = t + w -(p8) tbit.z.unc p8,p9 = GR_N_SignS, 1 -} -{ .mfi - nop.m 0 -(p6) fms.s1 FR_a = FR_a, f1, FR_V_hi - nop.i 0 -};; - -// -// 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. -// -{ .mfi - nop.m 0 - fms.s1 FR_C_lo = FR_s, f1, FR_C_hi -(p12) tbit.z.unc p14,p15 = GR_N_SignC, 1 -} -{ .mfi - nop.m 0 -(p7) fms.s1 FR_a = FR_U_hi, f1, FR_a - nop.i 0 -};; - -{ .mfi - nop.m 0 - fma.s1 FR_C_lo = FR_C_lo, f1, FR_A // C_lo = (S - C_hi) + A -(p12) tbit.z.unc p12,p13 = GR_N_SignS, 1 -} -{ .mfi - nop.m 0 - fma.s1 FR_t = FR_t, f1, FR_a // t = t + a - nop.i 0 -};; - -{ .mfi - nop.m 0 - fma.s1 FR_r = FR_C_hi, f1, FR_C_lo - nop.i 0 -};; - -{ .mfi - nop.m 0 - fma.s1 FR_C_lo = FR_C_lo, f1, FR_t // C_lo = C_lo + t - nop.i 0 -};; - - -{ .mfi - nop.m 0 - fma.s1 FR_rsq = FR_r, FR_r, f0 - nop.i 0 -} -{ .mfi - nop.m 0 - fms.s1 FR_c = FR_C_hi, f1, FR_r - nop.i 0 -};; - -{ .mfi - nop.m 0 - fma.s1 FR_FirstS = f0, f1, FR_r - nop.i 0 -} -{ .mfi - nop.m 0 - fma.s1 FR_FirstC = f0, f1, f1 - nop.i 0 -};; - -{ .mfi - nop.m 0 - fma.s1 FR_polyS = FR_rsq, FR_S_2, FR_S_1 - nop.i 0 -} -{ .mfi - nop.m 0 - fma.s1 FR_polyC = FR_rsq, FR_C_2, FR_C_1 - nop.i 0 -};; - -{ .mfi - nop.m 0 - fma.s1 FR_r_cubed = FR_rsq, FR_r, f0 - nop.i 0 -} -{ .mfi - nop.m 0 - fma.s1 FR_c = FR_c, f1, FR_C_lo - nop.i 0 -};; - -.pred.rel "mutex",p9,p15 -{ .mfi - nop.m 0 -(p9) fms.s0 FR_FirstS = f1, f0, FR_FirstS - nop.i 0 -} -{ .mfi - nop.m 0 -(p15) fms.s0 FR_FirstS = f1, f0, FR_FirstS - nop.i 0 -};; - -.pred.rel "mutex",p11,p13 -{ .mfi - nop.m 0 -(p11) fms.s0 FR_FirstC = f1, f0, FR_FirstC - nop.i 0 -} -{ .mfi - nop.m 0 -(p13) fms.s0 FR_FirstC = f1, f0, FR_FirstC - nop.i 0 -};; - - -{ .mfi - nop.m 0 - fma.s1 FR_polyS = FR_r_cubed, FR_polyS, FR_c - nop.i 0 -} -{ .mfi - nop.m 0 - fma.s1 FR_polyC = FR_rsq, FR_polyC, f0 - nop.i 0 -};; - - - -.pred.rel "mutex",p8,p9 -{ .mfi - nop.m 0 -(p8) fma.s0 FR_ResultS = FR_FirstS, f1, FR_polyS - nop.i 0 -} -{ .mfi - nop.m 0 -(p9) fms.s0 FR_ResultS = FR_FirstS, f1, FR_polyS - nop.i 0 -};; - -.pred.rel "mutex",p10,p11 -{ .mfi - nop.m 0 -(p10) fma.s0 FR_ResultC = FR_FirstC, f1, FR_polyC - nop.i 0 -} -{ .mfi - nop.m 0 -(p11) fms.s0 FR_ResultC = FR_FirstC, f1, FR_polyC - nop.i 0 -};; - - - -.pred.rel "mutex",p12,p13 -{ .mfi - nop.m 0 -(p12) fma.s0 FR_ResultS = FR_FirstC, f1, FR_polyC - nop.i 0 -} -{ .mfi - nop.m 0 -(p13) fms.s0 FR_ResultS = FR_FirstC, f1, FR_polyC - nop.i 0 -};; - -.pred.rel "mutex",p14,p15 -{ .mfi - nop.m 0 -(p14) fma.s0 FR_ResultC = FR_FirstS, f1, FR_polyS - nop.i 0 -} -{ .mfb - cmp.eq p10, p0 = 0x1, GR_Cis -(p15) fms.s0 FR_ResultC = FR_FirstS, f1, FR_polyS -(p10) br.ret.sptk b0 -};; - - -{ .mmb // exit for sincosl - stfe [sincos_pResSin] = FR_ResultS - stfe [sincos_pResCos] = FR_ResultC - br.ret.sptk b0 -};; - - - -SINCOSL_SMALL_R: -// -// Here if |r| < 2^-3 -// -// Enter with r, c, and N_Inc computed -// -{ .mfi - nop.m 0 - fma.s1 FR_rsq = FR_r, FR_r, f0 // rsq = r * r - nop.i 0 -};; - -{ .mmi - ldfe FR_S_5 = [GR_ad_se], -16 // Load S_5 - ldfe FR_C_5 = [GR_ad_ce], -16 // Load C_5 - nop.i 0 -};; - -{ .mmi - ldfe FR_S_4 = [GR_ad_se], -16 // Load S_4 - ldfe FR_C_4 = [GR_ad_ce], -16 // Load C_4 - nop.i 0 -};; - -SINCOSL_SMALL_R_0: -// Entry point for 2^-3 < |x| < pi/4 -SINCOSL_SMALL_R_1: -// Entry point for pi/4 < |x| < 2^24 and |r| < 2^-3 -{ .mfi - ldfe FR_S_3 = [GR_ad_se], -16 // Load S_3 - fma.s1 FR_r6 = FR_rsq, FR_rsq, f0 // Z = rsq * rsq - tbit.z p7,p11 = GR_N_Inc, 0 -} -{ .mfi - ldfe FR_C_3 = [GR_ad_ce], -16 // Load C_3 - nop.f 0 - and GR_N_SinCos = 0x1, GR_N_Inc -};; - -{ .mfi - ldfe FR_S_2 = [GR_ad_se], -16 // Load S_2 - fnma.s1 FR_cC = FR_c, FR_r, f0 // c = -c * r - sub GR_N_SignS = GR_N_Inc, GR_N_SinCos -} -{ .mfi - ldfe FR_C_2 = [GR_ad_ce], -16 // Load C_2 - nop.f 0 - add GR_N_SignC = GR_N_Inc, GR_N_SinCos -};; - -{ .mmi - ldfe FR_S_1 = [GR_ad_se], -16 // Load S_1 - ldfe FR_C_1 = [GR_ad_ce], -16 // Load C_1 -(p7) tbit.z.unc p9,p10 = GR_N_SignC, 1 -};; - -{ .mfi - nop.m 0 - fma.s1 FR_r7 = FR_r6, FR_r, f0 // Z = Z * r -(p7) tbit.z.unc p7,p8 = GR_N_SignS, 1 -};; - -{ .mfi - nop.m 0 - fma.s1 FR_poly_loS = FR_rsq, FR_S_5, FR_S_4 // poly_lo=rsq*S_5+S_4 -(p11) tbit.z.unc p13,p14 = GR_N_SignC, 1 -} -{ .mfi - nop.m 0 - fma.s1 FR_poly_loC = FR_rsq, FR_C_5, FR_C_4 // poly_lo=rsq*C_5+C_4 - nop.i 0 -};; - -{ .mfi - nop.m 0 - fma.s1 FR_poly_hiS = FR_rsq, FR_S_2, FR_S_1 // poly_hi=rsq*S_2+S_1 -(p11) tbit.z.unc p11,p12 = GR_N_SignS, 1 -} -{ .mfi - nop.m 0 - fma.s1 FR_poly_hiC = FR_rsq, FR_C_2, FR_C_1 // poly_hi=rsq*C_2+C_1 - nop.i 0 -};; - -{ .mfi - nop.m 0 - fma.s0 FR_FirstS = FR_r, f1, f0 - nop.i 0 -} -{ .mfi - nop.m 0 - fma.s0 FR_FirstC = f1, f1, f0 - nop.i 0 -};; - - -{ .mfi - nop.m 0 - fma.s1 FR_r6 = FR_r6, FR_rsq, f0 - nop.i 0 -} -{ .mfi - nop.m 0 - fma.s1 FR_r7 = FR_r7, FR_rsq, f0 - nop.i 0 -};; - -{ .mfi - nop.m 0 - fma.s1 FR_poly_loS = FR_rsq, FR_poly_loS, FR_S_3 // p_lo=p_lo*rsq+S_3 - nop.i 0 -} -{ .mfi - nop.m 0 - fma.s1 FR_poly_loC = FR_rsq, FR_poly_loC, FR_C_3 // p_lo=p_lo*rsq+C_3 - nop.i 0 -};; - -{ .mfi - nop.m 0 - fma.s0 FR_inexact = FR_S_4, FR_S_4, f0 // Dummy op to set inexact - nop.i 0 -};; - -{ .mfi - nop.m 0 - fma.s1 FR_poly_hiS = FR_poly_hiS, FR_rsq, f0 // p_hi=p_hi*rsq - nop.i 0 -} -{ .mfi - nop.m 0 - fma.s1 FR_poly_hiC = FR_poly_hiC, FR_rsq, f0 // p_hi=p_hi*rsq - nop.i 0 -};; - -.pred.rel "mutex",p8,p14 -{ .mfi - nop.m 0 -(p8) fms.s0 FR_FirstS = f1, f0, FR_FirstS - nop.i 0 -} -{ .mfi - nop.m 0 -(p14) fms.s0 FR_FirstS = f1, f0, FR_FirstS - nop.i 0 -};; - -.pred.rel "mutex",p10,p12 -{ .mfi - nop.m 0 -(p10) fms.s0 FR_FirstC = f1, f0, FR_FirstC - nop.i 0 -} -{ .mfi - nop.m 0 -(p12) fms.s0 FR_FirstC = f1, f0, FR_FirstC - nop.i 0 -};; - -{ .mfi - nop.m 0 - fma.s1 FR_polyS = FR_r7, FR_poly_loS, FR_cS // poly=Z*poly_lo+c - nop.i 0 -} -{ .mfi - nop.m 0 - fma.s1 FR_polyC = FR_r6, FR_poly_loC, FR_cC // poly=Z*poly_lo+c - nop.i 0 -};; - -{ .mfi - nop.m 0 - fma.s1 FR_poly_hiS = FR_r, FR_poly_hiS, f0 // p_hi=r*p_hi - nop.i 0 -};; - - -{ .mfi - nop.m 0 - fma.s1 FR_polyS = FR_polyS, f1, FR_poly_hiS - nop.i 0 -} -{ .mfi - nop.m 0 - fma.s1 FR_polyC = FR_polyC, f1, FR_poly_hiC - nop.i 0 -};; - -.pred.rel "mutex",p7,p8 -{ .mfi - nop.m 0 -(p7) fma.s0 FR_ResultS = FR_FirstS, f1, FR_polyS - nop.i 0 -} -{ .mfi - nop.m 0 -(p8) fms.s0 FR_ResultS = FR_FirstS, f1, FR_polyS - nop.i 0 -};; - -.pred.rel "mutex",p9,p10 -{ .mfi - nop.m 0 -(p9) fma.s0 FR_ResultC = FR_FirstC, f1, FR_polyC - nop.i 0 -} -{ .mfi - nop.m 0 -(p10) fms.s0 FR_ResultC = FR_FirstC, f1, FR_polyC - nop.i 0 -};; - -.pred.rel "mutex",p11,p12 -{ .mfi - nop.m 0 -(p11) fma.s0 FR_ResultS = FR_FirstC, f1, FR_polyC - nop.i 0 -} -{ .mfi - nop.m 0 -(p12) fms.s0 FR_ResultS = FR_FirstC, f1, FR_polyC - nop.i 0 -};; - -.pred.rel "mutex",p13,p14 -{ .mfi - nop.m 0 -(p13) fma.s0 FR_ResultC = FR_FirstS, f1, FR_polyS - nop.i 0 -} -{ .mfb - cmp.eq p15, p0 = 0x1, GR_Cis -(p14) fms.s0 FR_ResultC = FR_FirstS, f1, FR_polyS -(p15) br.ret.sptk b0 -};; - - -{ .mmb // exit for sincosl - stfe [sincos_pResSin] = FR_ResultS - stfe [sincos_pResCos] = FR_ResultC - br.ret.sptk b0 -};; - - - - - - -SINCOSL_NORMAL_R: -// -// Here if 2^-3 <= |r| < pi/4 -// THIS IS THE MAIN PATH -// -// Enter with r, c, and N_Inc having been computed -// -{ .mfi - ldfe FR_PP_6 = [GR_ad_pp], 16 // Load PP_6 - fma.s1 FR_rsq = FR_r, FR_r, f0 // rsq = r * r - nop.i 0 -} -{ .mfi - ldfe FR_QQ_6 = [GR_ad_qq], 16 // Load QQ_6 - nop.f 0 - nop.i 0 -};; - -{ .mmi - ldfe FR_PP_5 = [GR_ad_pp], 16 // Load PP_5 - ldfe FR_QQ_5 = [GR_ad_qq], 16 // Load QQ_5 - nop.i 0 -};; - - - -SINCOSL_NORMAL_R_0: -// Entry for 2^-3 < |x| < pi/4 -.pred.rel "mutex",p9,p10 -{ .mmf - ldfe FR_C_1 = [GR_ad_pp], 16 // Load C_1 - ldfe FR_S_1 = [GR_ad_qq], 16 // Load S_1 - frcpa.s1 FR_r_hi, p6 = f1, FR_r // r_hi = frcpa(r) -};; - -{ .mfi - nop.m 0 - fma.s1 FR_polyS = FR_rsq, FR_PP_8, FR_PP_7 // poly = rsq*PP_8+PP_7 - nop.i 0 -} -{ .mfi - nop.m 0 - fma.s1 FR_polyC = FR_rsq, FR_QQ_8, FR_QQ_7 // poly = rsq*QQ_8+QQ_7 - nop.i 0 -};; - -{ .mfi - nop.m 0 - fma.s1 FR_r_cubed = FR_r, FR_rsq, f0 // rcubed = r * rsq - nop.i 0 -};; - - -SINCOSL_NORMAL_R_1: -// Entry for pi/4 <= |x| < 2^24 -.pred.rel "mutex",p9,p10 -{ .mmf - ldfe FR_PP_1 = [GR_ad_pp], 16 // Load PP_1_hi - ldfe FR_QQ_1 = [GR_ad_qq], 16 // Load QQ_1 - frcpa.s1 FR_r_hi, p6 = f1, FR_r_hi // r_hi = frpca(frcpa(r)) -};; - -{ .mfi - ldfe FR_PP_4 = [GR_ad_pp], 16 // Load PP_4 - fma.s1 FR_polyS = FR_rsq, FR_polyS, FR_PP_6 // poly = rsq*poly+PP_6 - and GR_N_SinCos = 0x1, GR_N_Inc -} -{ .mfi - ldfe FR_QQ_4 = [GR_ad_qq], 16 // Load QQ_4 - fma.s1 FR_polyC = FR_rsq, FR_polyC, FR_QQ_6 // poly = rsq*poly+QQ_6 - nop.i 0 -};; - -{ .mfi - nop.m 0 - fma.s1 FR_corrS = FR_C_1, FR_rsq, f0 // corr = C_1 * rsq - sub GR_N_SignS = GR_N_Inc, GR_N_SinCos -} -{ .mfi - nop.m 0 - fma.s1 FR_corrC = FR_S_1, FR_r_cubed, FR_r // corr = S_1 * r^3 + r - add GR_N_SignC = GR_N_Inc, GR_N_SinCos -};; - -{ .mfi - ldfe FR_PP_3 = [GR_ad_pp], 16 // Load PP_3 - fma.s1 FR_r_hi_sq = FR_r_hi, FR_r_hi, f0 // r_hi_sq = r_hi * r_hi - tbit.z p7,p11 = GR_N_Inc, 0 -} -{ .mfi - ldfe FR_QQ_3 = [GR_ad_qq], 16 // Load QQ_3 - fms.s1 FR_r_lo = FR_r, f1, FR_r_hi // r_lo = r - r_hi - nop.i 0 -};; - -{ .mfi - ldfe FR_PP_2 = [GR_ad_pp], 16 // Load PP_2 - fma.s1 FR_polyS = FR_rsq, FR_polyS, FR_PP_5 // poly = rsq*poly+PP_5 -(p7) tbit.z.unc p9,p10 = GR_N_SignC, 1 -} -{ .mfi - ldfe FR_QQ_2 = [GR_ad_qq], 16 // Load QQ_2 - fma.s1 FR_polyC = FR_rsq, FR_polyC, FR_QQ_5 // poly = rsq*poly+QQ_5 - nop.i 0 -};; - -{ .mfi - ldfe FR_PP_1_lo = [GR_ad_pp], 16 // Load PP_1_lo - fma.s1 FR_corrS = FR_corrS, FR_c, FR_c // corr = corr * c + c -(p7) tbit.z.unc p7,p8 = GR_N_SignS, 1 -} -{ .mfi - nop.m 0 - fnma.s1 FR_corrC = FR_corrC, FR_c, f0 // corr = -corr * c - nop.i 0 -};; - -{ .mfi - nop.m 0 - fma.s1 FR_U_loS = FR_r, FR_r_hi, FR_r_hi_sq // U_lo = r*r_hi+r_hi_sq -(p11) tbit.z.unc p13,p14 = GR_N_SignC, 1 -} -{ .mfi - nop.m 0 - fma.s1 FR_U_loC = FR_r_hi, f1, FR_r // U_lo = r_hi + r - nop.i 0 -};; - -{ .mfi - nop.m 0 - fma.s1 FR_U_hiS = FR_r_hi, FR_r_hi_sq, f0 // U_hi = r_hi*r_hi_sq -(p11) tbit.z.unc p11,p12 = GR_N_SignS, 1 -} -{ .mfi - nop.m 0 - fma.s1 FR_U_hiC = FR_QQ_1, FR_r_hi_sq, f1 // U_hi = QQ_1*r_hi_sq+1 - nop.i 0 -};; - -{ .mfi - nop.m 0 - fma.s1 FR_polyS = FR_rsq, FR_polyS, FR_PP_4 // poly = poly*rsq+PP_4 - nop.i 0 -} -{ .mfi - nop.m 0 - fma.s1 FR_polyC = FR_rsq, FR_polyC, FR_QQ_4 // poly = poly*rsq+QQ_4 - nop.i 0 -};; - -{ .mfi - nop.m 0 - fma.s1 FR_U_loS = FR_r, FR_r, FR_U_loS // U_lo = r * r + U_lo - nop.i 0 -} -{ .mfi - nop.m 0 - fma.s1 FR_U_loC = FR_r_lo, FR_U_loC, f0 // U_lo = r_lo * U_lo - nop.i 0 -};; - -{ .mfi - nop.m 0 - fma.s1 FR_U_hiS = FR_PP_1, FR_U_hiS, f0 // U_hi = PP_1 * U_hi - nop.i 0 -};; - -{ .mfi - nop.m 0 - fma.s1 FR_polyS = FR_rsq, FR_polyS, FR_PP_3 // poly = poly*rsq+PP_3 - nop.i 0 -} -{ .mfi - nop.m 0 - fma.s1 FR_polyC = FR_rsq, FR_polyC, FR_QQ_3 // poly = poly*rsq+QQ_3 - nop.i 0 -};; - -{ .mfi - nop.m 0 - fma.s1 FR_U_loS = FR_r_lo, FR_U_loS, f0 // U_lo = r_lo * U_lo - nop.i 0 -} -{ .mfi - nop.m 0 - fma.s1 FR_U_loC = FR_QQ_1,FR_U_loC, f0 // U_lo = QQ_1 * U_lo - nop.i 0 -};; - -{ .mfi - nop.m 0 - fma.s1 FR_U_hiS = FR_r, f1, FR_U_hiS // U_hi = r + U_hi - nop.i 0 -};; - -{ .mfi - nop.m 0 - fma.s1 FR_polyS = FR_rsq, FR_polyS, FR_PP_2 // poly = poly*rsq+PP_2 - nop.i 0 -} -{ .mfi - nop.m 0 - fma.s1 FR_polyC = FR_rsq, FR_polyC, FR_QQ_2 // poly = poly*rsq+QQ_2 - nop.i 0 -};; - -{ .mfi - nop.m 0 - fma.s1 FR_U_loS = FR_PP_1, FR_U_loS, f0 // U_lo = PP_1 * U_lo - nop.i 0 -};; - -{ .mfi - nop.m 0 - fma.s1 FR_polyS = FR_rsq, FR_polyS, FR_PP_1_lo // poly =poly*rsq+PP1lo - nop.i 0 -} -{ .mfi - nop.m 0 - fma.s1 FR_polyC = FR_rsq, FR_polyC, f0 // poly = poly*rsq - nop.i 0 -};; - - -.pred.rel "mutex",p8,p14 -{ .mfi - nop.m 0 -(p8) fms.s0 FR_U_hiS = f1, f0, FR_U_hiS - nop.i 0 -} -{ .mfi - nop.m 0 -(p14) fms.s0 FR_U_hiS = f1, f0, FR_U_hiS - nop.i 0 -};; - -.pred.rel "mutex",p10,p12 -{ .mfi - nop.m 0 -(p10) fms.s0 FR_U_hiC = f1, f0, FR_U_hiC - nop.i 0 -} -{ .mfi - nop.m 0 -(p12) fms.s0 FR_U_hiC = f1, f0, FR_U_hiC - nop.i 0 -};; - - -{ .mfi - nop.m 0 - fma.s1 FR_VS = FR_U_loS, f1, FR_corrS // V = U_lo + corr - nop.i 0 -} -{ .mfi - nop.m 0 - fma.s1 FR_VC = FR_U_loC, f1, FR_corrC // V = U_lo + corr - nop.i 0 -};; - -{ .mfi - nop.m 0 - fma.s0 FR_inexact = FR_PP_5, FR_PP_4, f0 // Dummy op to set inexact - nop.i 0 -};; - - -{ .mfi - nop.m 0 - fma.s1 FR_polyS = FR_r_cubed, FR_polyS, f0 // poly = poly*r^3 - nop.i 0 -} -{ .mfi - nop.m 0 - fma.s1 FR_polyC = FR_rsq, FR_polyC, f0 // poly = poly*rsq - nop.i 0 -};; - - -{ .mfi - nop.m 0 - fma.s1 FR_VS = FR_polyS, f1, FR_VS // V = poly + V - nop.i 0 -} -{ .mfi - nop.m 0 - fma.s1 FR_VC = FR_polyC, f1, FR_VC // V = poly + V - nop.i 0 -};; - - - -.pred.rel "mutex",p7,p8 -{ .mfi - nop.m 0 -(p7) fma.s0 FR_ResultS = FR_U_hiS, f1, FR_VS - nop.i 0 -} -{ .mfi - nop.m 0 -(p8) fms.s0 FR_ResultS = FR_U_hiS, f1, FR_VS - nop.i 0 -};; - -.pred.rel "mutex",p9,p10 -{ .mfi - nop.m 0 -(p9) fma.s0 FR_ResultC = FR_U_hiC, f1, FR_VC - nop.i 0 -} -{ .mfi - nop.m 0 -(p10) fms.s0 FR_ResultC = FR_U_hiC, f1, FR_VC - nop.i 0 -};; - - - -.pred.rel "mutex",p11,p12 -{ .mfi - nop.m 0 -(p11) fma.s0 FR_ResultS = FR_U_hiC, f1, FR_VC - nop.i 0 -} -{ .mfi - nop.m 0 -(p12) fms.s0 FR_ResultS = FR_U_hiC, f1, FR_VC - nop.i 0 -};; - -.pred.rel "mutex",p13,p14 -{ .mfi - nop.m 0 -(p13) fma.s0 FR_ResultC = FR_U_hiS, f1, FR_VS - nop.i 0 -} -{ .mfb - cmp.eq p15, p0 = 0x1, GR_Cis -(p14) fms.s0 FR_ResultC = FR_U_hiS, f1, FR_VS -(p15) br.ret.sptk b0 -};; - -{ .mmb // exit for sincosl - stfe [sincos_pResSin] = FR_ResultS - stfe [sincos_pResCos] = FR_ResultC - br.ret.sptk b0 -};; - - - - - -SINCOSL_ZERO: - -{ .mfi - nop.m 0 - fmerge.s FR_ResultS = FR_Input_X, FR_Input_X // If sin, result = input - nop.i 0 -} -{ .mfb - cmp.eq p15, p0 = 0x1, GR_Cis - fma.s0 FR_ResultC = f1, f1, f0 // If cos, result=1.0 -(p15) br.ret.sptk b0 -};; - -{ .mmb // exit for sincosl - stfe [sincos_pResSin] = FR_ResultS - stfe [sincos_pResCos] = FR_ResultC - br.ret.sptk b0 -};; - - -SINCOSL_DENORMAL: -{ .mmb - getf.exp GR_signexp_x = FR_norm_x // Get sign and exponent of x - nop.m 999 - br.cond.sptk SINCOSL_COMMON2 // Return to common code -} -;; - - -SINCOSL_SPECIAL: -// -// Path for Arg = +/- QNaN, SNaN, Inf -// Invalid can be raised. SNaNs -// become QNaNs -// -{ .mfi - cmp.eq p15, p0 = 0x1, GR_Cis - fmpy.s0 FR_ResultS = FR_Input_X, f0 - nop.i 0 -} -{ .mfb - nop.m 0 - fmpy.s0 FR_ResultC = FR_Input_X, f0 -(p15) br.ret.sptk b0 -};; - -{ .mmb // exit for sincosl - stfe [sincos_pResSin] = FR_ResultS - stfe [sincos_pResCos] = FR_ResultC - br.ret.sptk b0 -};; - -GLOBAL_LIBM_END(__libm_sincosl) - - -// ******************************************************************* -// ******************************************************************* -// ******************************************************************* -// -// 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 r62-63. These are used as -// scratch registers within the __libm_pi_by_2_reduce routine (for speed). -// -// We know also that __libm_pi_by_2_reduce preserves f10-15, f71-127. We -// use this to eliminate save/restore of key fp registers in this calling -// function. -// -// ******************************************************************* -// ******************************************************************* -// ******************************************************************* - -LOCAL_LIBM_ENTRY(__libm_callout) -SINCOSL_ARG_TOO_LARGE: -.prologue -{ .mfi - nop.f 0 -.save ar.pfs,GR_SAVE_PFS - mov GR_SAVE_PFS=ar.pfs // Save ar.pfs -};; - -{ .mmi - setf.exp FR_Two_to_M3 = GR_exp_2_to_m3 // Form 2^-3 - mov GR_SAVE_GP=gp // Save gp -.save b0, GR_SAVE_B0 - mov GR_SAVE_B0=b0 // Save b0 -};; - -.body -// -// Call argument reduction with x in f8 -// Returns with N in r8, r in f8, c in f9 -// Assumes f71-127 are preserved across the call -// -{ .mib - setf.exp FR_Neg_Two_to_M3 = GR_exp_m2_to_m3 // Form -(2^-3) - nop.i 0 - br.call.sptk b0=__libm_pi_by_2_reduce# -};; - -{ .mfi - mov GR_N_Inc = 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 0 -(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# - - - |