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diff --git a/sysdeps/ia64/fpu/libm_sincos_large.S b/sysdeps/ia64/fpu/libm_sincos_large.S new file mode 100644 index 0000000000..b09d3693a6 --- /dev/null +++ b/sysdeps/ia64/fpu/libm_sincos_large.S @@ -0,0 +1,2757 @@ +.file "libm_sincos_large.s" + + +// Copyright (c) 2002 - 2003, Intel Corporation +// All rights reserved. +// +// Contributed 2002 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 +//============================================================== +// 02/15/02 Initial version +// 05/13/02 Changed interface to __libm_pi_by_2_reduce +// 02/10/03 Reordered header: .section, .global, .proc, .align; +// used data8 for long double table values +// 05/15/03 Reformatted data tables +// +// +// Overview of operation +//============================================================== +// +// These functions calculate the sin and cos for inputs +// greater than 2^10 +// +// __libm_sin_large# +// __libm_cos_large# +// They accept argument in f8 +// and return result in f8 without final rounding +// +// __libm_sincos_large# +// It accepts argument in f8 +// and returns cos in f8 and sin in f9 without final rounding +// +// +//********************************************************************* +// +// Accuracy: Within .7 ulps for 80-bit floating point values +// Very accurate for double precision values +// +//********************************************************************* +// +// Resources Used: +// +// Floating-Point Registers: f8 as Input Value, f8 and f9 as Return Values +// f32-f103 +// +// General Purpose Registers: +// r32-r43 +// r44-r45 (Used to pass arguments to pi_by_2 reduce routine) +// +// Predicate Registers: p6-p13 +// +//********************************************************************* +// +// IEEE Special Conditions: +// +// Denormal fault raised on denormal inputs +// Overflow exceptions do not occur +// Underflow exceptions raised when appropriate for sin +// (No specialized error handling for this routine) +// Inexact raised when appropriate by algorithm +// +// sin(SNaN) = QNaN +// sin(QNaN) = QNaN +// sin(inf) = QNaN +// sin(+/-0) = +/-0 +// cos(inf) = QNaN +// cos(SNaN) = QNaN +// cos(QNaN) = QNaN +// cos(0) = 1 +// +//********************************************************************* +// +// Mathematical Description +// ======================== +// +// The computation of FSIN and FCOS is best handled in one piece of +// code. The main reason is that given any argument Arg, computation +// of trigonometric functions first calculate N and an approximation +// to alpha where +// +// Arg = N pi/2 + alpha, |alpha| <= pi/4. +// +// Since +// +// cos( Arg ) = sin( (N+1) pi/2 + alpha ), +// +// therefore, the code for computing sine will produce cosine as long +// as 1 is added to N immediately after the argument reduction +// process. +// +// Let M = N if sine +// N+1 if cosine. +// +// Now, given +// +// Arg = M pi/2 + alpha, |alpha| <= pi/4, +// +// let I = M mod 4, or I be the two lsb of M when M is represented +// as 2's complement. I = [i_0 i_1]. Then +// +// sin( Arg ) = (-1)^i_0 sin( alpha ) if i_1 = 0, +// = (-1)^i_0 cos( alpha ) if i_1 = 1. +// +// For example: +// if M = -1, I = 11 +// sin ((-pi/2 + alpha) = (-1) cos (alpha) +// if M = 0, I = 00 +// sin (alpha) = sin (alpha) +// if M = 1, I = 01 +// sin (pi/2 + alpha) = cos (alpha) +// if M = 2, I = 10 +// sin (pi + alpha) = (-1) sin (alpha) +// if M = 3, I = 11 +// sin ((3/2)pi + alpha) = (-1) cos (alpha) +// +// The value of alpha is obtained by argument reduction and +// represented by two working precision numbers r and c where +// +// alpha = r + c accurately. +// +// The reduction method is described in a previous write up. +// The argument reduction scheme identifies 4 cases. For Cases 2 +// and 4, because |alpha| is small, sin(r+c) and cos(r+c) can be +// computed very easily by 2 or 3 terms of the Taylor series +// expansion as follows: +// +// Case 2: +// ------- +// +// sin(r + c) = r + c - r^3/6 accurately +// cos(r + c) = 1 - 2^(-67) accurately +// +// Case 4: +// ------- +// +// sin(r + c) = r + c - r^3/6 + r^5/120 accurately +// cos(r + c) = 1 - r^2/2 + r^4/24 accurately +// +// The only cases left are Cases 1 and 3 of the argument reduction +// procedure. These two cases will be merged since after the +// argument is reduced in either cases, we have the reduced argument +// represented as r + c and that the magnitude |r + c| is not small +// enough to allow the usage of a very short approximation. +// +// The required calculation is either +// +// sin(r + c) = sin(r) + correction, or +// cos(r + c) = cos(r) + correction. +// +// Specifically, +// +// sin(r + c) = sin(r) + c sin'(r) + O(c^2) +// = sin(r) + c cos (r) + O(c^2) +// = sin(r) + c(1 - r^2/2) accurately. +// Similarly, +// +// cos(r + c) = cos(r) - c sin(r) + O(c^2) +// = cos(r) - c(r - r^3/6) accurately. +// +// We therefore concentrate on accurately calculating sin(r) and +// cos(r) for a working-precision number r, |r| <= pi/4 to within +// 0.1% or so. +// +// The greatest challenge of this task is that the second terms of +// the Taylor series +// +// r - r^3/3! + r^r/5! - ... +// +// and +// +// 1 - r^2/2! + r^4/4! - ... +// +// are not very small when |r| is close to pi/4 and the rounding +// errors will be a concern if simple polynomial accumulation is +// used. When |r| < 2^-3, however, the second terms will be small +// enough (6 bits or so of right shift) that a normal Horner +// recurrence suffices. Hence there are two cases that we consider +// in the accurate computation of sin(r) and cos(r), |r| <= pi/4. +// +// Case small_r: |r| < 2^(-3) +// -------------------------- +// +// Since Arg = M pi/4 + r + c accurately, and M mod 4 is [i_0 i_1], +// we have +// +// sin(Arg) = (-1)^i_0 * sin(r + c) if i_1 = 0 +// = (-1)^i_0 * cos(r + c) if i_1 = 1 +// +// can be accurately approximated by +// +// sin(Arg) = (-1)^i_0 * [sin(r) + c] if i_1 = 0 +// = (-1)^i_0 * [cos(r) - c*r] if i_1 = 1 +// +// because |r| is small and thus the second terms in the correction +// are unneccessary. +// +// Finally, sin(r) and cos(r) are approximated by polynomials of +// moderate lengths. +// +// sin(r) = r + S_1 r^3 + S_2 r^5 + ... + S_5 r^11 +// cos(r) = 1 + C_1 r^2 + C_2 r^4 + ... + C_5 r^10 +// +// We can make use of predicates to selectively calculate +// sin(r) or cos(r) based on i_1. +// +// Case normal_r: 2^(-3) <= |r| <= pi/4 +// ------------------------------------ +// +// This case is more likely than the previous one if one considers +// r to be uniformly distributed in [-pi/4 pi/4]. Again, +// +// sin(Arg) = (-1)^i_0 * sin(r + c) if i_1 = 0 +// = (-1)^i_0 * cos(r + c) if i_1 = 1. +// +// Because |r| is now larger, we need one extra term in the +// correction. sin(Arg) can be accurately approximated by +// +// sin(Arg) = (-1)^i_0 * [sin(r) + c(1-r^2/2)] if i_1 = 0 +// = (-1)^i_0 * [cos(r) - c*r*(1 - r^2/6)] i_1 = 1. +// +// Finally, sin(r) and cos(r) are approximated by polynomials of +// moderate lengths. +// +// sin(r) = r + PP_1_hi r^3 + PP_1_lo r^3 + +// PP_2 r^5 + ... + PP_8 r^17 +// +// cos(r) = 1 + QQ_1 r^2 + QQ_2 r^4 + ... + QQ_8 r^16 +// +// where PP_1_hi is only about 16 bits long and QQ_1 is -1/2. +// The crux in accurate computation is to calculate +// +// r + PP_1_hi r^3 or 1 + QQ_1 r^2 +// +// accurately as two pieces: U_hi and U_lo. The way to achieve this +// is to obtain r_hi as a 10 sig. bit number that approximates r to +// roughly 8 bits or so of accuracy. (One convenient way is +// +// r_hi := frcpa( frcpa( r ) ).) +// +// This way, +// +// r + PP_1_hi r^3 = r + PP_1_hi r_hi^3 + +// PP_1_hi (r^3 - r_hi^3) +// = [r + PP_1_hi r_hi^3] + +// [PP_1_hi (r - r_hi) +// (r^2 + r_hi r + r_hi^2) ] +// = U_hi + U_lo +// +// Since r_hi is only 10 bit long and PP_1_hi is only 16 bit long, +// PP_1_hi * r_hi^3 is only at most 46 bit long and thus computed +// exactly. Furthermore, r and PP_1_hi r_hi^3 are of opposite sign +// and that there is no more than 8 bit shift off between r and +// PP_1_hi * r_hi^3. Hence the sum, U_hi, is representable and thus +// calculated without any error. Finally, the fact that +// +// |U_lo| <= 2^(-8) |U_hi| +// +// says that U_hi + U_lo is approximating r + PP_1_hi r^3 to roughly +// 8 extra bits of accuracy. +// +// Similarly, +// +// 1 + QQ_1 r^2 = [1 + QQ_1 r_hi^2] + +// [QQ_1 (r - r_hi)(r + r_hi)] +// = U_hi + U_lo. +// +// Summarizing, we calculate r_hi = frcpa( frcpa( r ) ). +// +// If i_1 = 0, then +// +// U_hi := r + PP_1_hi * r_hi^3 +// U_lo := PP_1_hi * (r - r_hi) * (r^2 + r*r_hi + r_hi^2) +// poly := PP_1_lo r^3 + PP_2 r^5 + ... + PP_8 r^17 +// correction := c * ( 1 + C_1 r^2 ) +// +// Else ...i_1 = 1 +// +// U_hi := 1 + QQ_1 * r_hi * r_hi +// U_lo := QQ_1 * (r - r_hi) * (r + r_hi) +// poly := QQ_2 * r^4 + QQ_3 * r^6 + ... + QQ_8 r^16 +// correction := -c * r * (1 + S_1 * r^2) +// +// End +// +// Finally, +// +// V := poly + ( U_lo + correction ) +// +// / U_hi + V if i_0 = 0 +// result := | +// \ (-U_hi) - V if i_0 = 1 +// +// It is important that in the last step, negation of U_hi is +// performed prior to the subtraction which is to be performed in +// the user-set rounding mode. +// +// +// Algorithmic Description +// ======================= +// +// The argument reduction algorithm is tightly integrated into FSIN +// and FCOS which share the same code. The following is complete and +// self-contained. The argument reduction description given +// previously is repeated below. +// +// +// Step 0. Initialization. +// +// If FSIN is invoked, set N_inc := 0; else if FCOS is invoked, +// set N_inc := 1. +// +// Step 1. Check for exceptional and special cases. +// +// * If Arg is +-0, +-inf, NaN, NaT, go to Step 10 for special +// handling. +// * If |Arg| < 2^24, go to Step 2 for reduction of moderate +// arguments. This is the most likely case. +// * If |Arg| < 2^63, go to Step 8 for pre-reduction of large +// arguments. +// * If |Arg| >= 2^63, go to Step 10 for special handling. +// +// Step 2. Reduction of moderate arguments. +// +// If |Arg| < pi/4 ...quick branch +// N_fix := N_inc (integer) +// r := Arg +// c := 0.0 +// Branch to Step 4, Case_1_complete +// Else ...cf. argument reduction +// N := Arg * two_by_PI (fp) +// N_fix := fcvt.fx( N ) (int) +// N := fcvt.xf( N_fix ) +// N_fix := N_fix + N_inc +// s := Arg - N * P_1 (first piece of pi/2) +// w := -N * P_2 (second piece of pi/2) +// +// If |s| >= 2^(-33) +// go to Step 3, Case_1_reduce +// Else +// go to Step 7, Case_2_reduce +// Endif +// Endif +// +// Step 3. Case_1_reduce. +// +// r := s + w +// c := (s - r) + w ...observe order +// +// Step 4. Case_1_complete +// +// ...At this point, the reduced argument alpha is +// ...accurately represented as r + c. +// If |r| < 2^(-3), go to Step 6, small_r. +// +// Step 5. Normal_r. +// +// Let [i_0 i_1] by the 2 lsb of N_fix. +// FR_rsq := r * r +// r_hi := frcpa( frcpa( r ) ) +// r_lo := r - r_hi +// +// If i_1 = 0, then +// poly := r*FR_rsq*(PP_1_lo + FR_rsq*(PP_2 + ... FR_rsq*PP_8)) +// U_hi := r + PP_1_hi*r_hi*r_hi*r_hi ...any order +// U_lo := PP_1_hi*r_lo*(r*r + r*r_hi + r_hi*r_hi) +// correction := c + c*C_1*FR_rsq ...any order +// Else +// poly := FR_rsq*FR_rsq*(QQ_2 + FR_rsq*(QQ_3 + ... + FR_rsq*QQ_8)) +// U_hi := 1 + QQ_1 * r_hi * r_hi ...any order +// U_lo := QQ_1 * r_lo * (r + r_hi) +// correction := -c*(r + S_1*FR_rsq*r) ...any order +// Endif +// +// V := poly + (U_lo + correction) ...observe order +// +// result := (i_0 == 0? 1.0 : -1.0) +// +// Last instruction in user-set rounding mode +// +// result := (i_0 == 0? result*U_hi + V : +// result*U_hi - V) +// +// Return +// +// Step 6. Small_r. +// +// ...Use flush to zero mode without causing exception +// Let [i_0 i_1] be the two lsb of N_fix. +// +// FR_rsq := r * r +// +// If i_1 = 0 then +// z := FR_rsq*FR_rsq; z := FR_rsq*z *r +// poly_lo := S_3 + FR_rsq*(S_4 + FR_rsq*S_5) +// poly_hi := r*FR_rsq*(S_1 + FR_rsq*S_2) +// correction := c +// result := r +// Else +// z := FR_rsq*FR_rsq; z := FR_rsq*z +// poly_lo := C_3 + FR_rsq*(C_4 + FR_rsq*C_5) +// poly_hi := FR_rsq*(C_1 + FR_rsq*C_2) +// correction := -c*r +// result := 1 +// Endif +// +// poly := poly_hi + (z * poly_lo + correction) +// +// If i_0 = 1, result := -result +// +// Last operation. Perform in user-set rounding mode +// +// result := (i_0 == 0? result + poly : +// result - poly ) +// Return +// +// Step 7. Case_2_reduce. +// +// ...Refer to the write up for argument reduction for +// ...rationale. The reduction algorithm below is taken from +// ...argument reduction description and integrated this. +// +// w := N*P_3 +// U_1 := N*P_2 + w ...FMA +// U_2 := (N*P_2 - U_1) + w ...2 FMA +// ...U_1 + U_2 is N*(P_2+P_3) accurately +// +// r := s - U_1 +// c := ( (s - r) - U_1 ) - U_2 +// +// ...The mathematical sum r + c approximates the reduced +// ...argument accurately. Note that although compared to +// ...Case 1, this case requires much more work to reduce +// ...the argument, the subsequent calculation needed for +// ...any of the trigonometric function is very little because +// ...|alpha| < 1.01*2^(-33) and thus two terms of the +// ...Taylor series expansion suffices. +// +// If i_1 = 0 then +// poly := c + S_1 * r * r * r ...any order +// result := r +// Else +// poly := -2^(-67) +// result := 1.0 +// Endif +// +// If i_0 = 1, result := -result +// +// Last operation. Perform in user-set rounding mode +// +// result := (i_0 == 0? result + poly : +// result - poly ) +// +// Return +// +// +// Step 8. Pre-reduction of large arguments. +// +// ...Again, the following reduction procedure was described +// ...in the separate write up for argument reduction, which +// ...is tightly integrated here. + +// N_0 := Arg * Inv_P_0 +// N_0_fix := fcvt.fx( N_0 ) +// N_0 := fcvt.xf( N_0_fix) + +// Arg' := Arg - N_0 * P_0 +// w := N_0 * d_1 +// N := Arg' * two_by_PI +// N_fix := fcvt.fx( N ) +// N := fcvt.xf( N_fix ) +// N_fix := N_fix + N_inc +// +// s := Arg' - N * P_1 +// w := w - N * P_2 +// +// If |s| >= 2^(-14) +// go to Step 3 +// Else +// go to Step 9 +// Endif +// +// Step 9. Case_4_reduce. +// +// ...first obtain N_0*d_1 and -N*P_2 accurately +// U_hi := N_0 * d_1 V_hi := -N*P_2 +// U_lo := N_0 * d_1 - U_hi V_lo := -N*P_2 - U_hi ...FMAs +// +// ...compute the contribution from N_0*d_1 and -N*P_3 +// w := -N*P_3 +// w := w + N_0*d_2 +// t := U_lo + V_lo + w ...any order +// +// ...at this point, the mathematical value +// ...s + U_hi + V_hi + t approximates the true reduced argument +// ...accurately. Just need to compute this accurately. +// +// ...Calculate U_hi + V_hi accurately: +// A := U_hi + V_hi +// if |U_hi| >= |V_hi| then +// a := (U_hi - A) + V_hi +// else +// a := (V_hi - A) + U_hi +// endif +// ...order in computing "a" must be observed. This branch is +// ...best implemented by predicates. +// ...A + a is U_hi + V_hi accurately. Moreover, "a" is +// ...much smaller than A: |a| <= (1/2)ulp(A). +// +// ...Just need to calculate s + A + a + t +// C_hi := s + A t := t + a +// C_lo := (s - C_hi) + A +// C_lo := C_lo + t +// +// ...Final steps for reduction +// r := C_hi + C_lo +// c := (C_hi - r) + C_lo +// +// ...At this point, we have r and c +// ...And all we need is a couple of terms of the corresponding +// ...Taylor series. +// +// If i_1 = 0 +// poly := c + r*FR_rsq*(S_1 + FR_rsq*S_2) +// result := r +// Else +// poly := FR_rsq*(C_1 + FR_rsq*C_2) +// result := 1 +// Endif +// +// If i_0 = 1, result := -result +// +// Last operation. Perform in user-set rounding mode +// +// result := (i_0 == 0? result + poly : +// result - poly ) +// Return +// +// Large Arguments: For arguments above 2**63, a Payne-Hanek +// style argument reduction is used and pi_by_2 reduce is called. +// + + +RODATA +.align 16 + +LOCAL_OBJECT_START(FSINCOS_CONSTANTS) + +data4 0x4B800000 // two**24 +data4 0xCB800000 // -two**24 +data4 0x00000000 // pad +data4 0x00000000 // pad +data8 0xA2F9836E4E44152A, 0x00003FFE // Inv_pi_by_2 +data8 0xC84D32B0CE81B9F1, 0x00004016 // P_0 +data8 0xC90FDAA22168C235, 0x00003FFF // P_1 +data8 0xECE675D1FC8F8CBB, 0x0000BFBD // P_2 +data8 0xB7ED8FBBACC19C60, 0x0000BF7C // P_3 +data4 0x5F000000 // two**63 +data4 0xDF000000 // -two**63 +data4 0x00000000 // pad +data4 0x00000000 // pad +data8 0xA397E5046EC6B45A, 0x00003FE7 // Inv_P_0 +data8 0x8D848E89DBD171A1, 0x0000BFBF // d_1 +data8 0xD5394C3618A66F8E, 0x0000BF7C // d_2 +data8 0xC90FDAA22168C234, 0x00003FFE // pi_by_4 +data8 0xC90FDAA22168C234, 0x0000BFFE // neg_pi_by_4 +data4 0x3E000000 // two**-3 +data4 0xBE000000 // -two**-3 +data4 0x00000000 // pad +data4 0x00000000 // pad +data4 0x2F000000 // two**-33 +data4 0xAF000000 // -two**-33 +data4 0x9E000000 // -two**-67 +data4 0x00000000 // pad +data8 0xCC8ABEBCA21C0BC9, 0x00003FCE // PP_8 +data8 0xD7468A05720221DA, 0x0000BFD6 // PP_7 +data8 0xB092382F640AD517, 0x00003FDE // PP_6 +data8 0xD7322B47D1EB75A4, 0x0000BFE5 // PP_5 +data8 0xFFFFFFFFFFFFFFFE, 0x0000BFFD // C_1 +data8 0xAAAA000000000000, 0x0000BFFC // PP_1_hi +data8 0xB8EF1D2ABAF69EEA, 0x00003FEC // PP_4 +data8 0xD00D00D00D03BB69, 0x0000BFF2 // PP_3 +data8 0x8888888888888962, 0x00003FF8 // PP_2 +data8 0xAAAAAAAAAAAB0000, 0x0000BFEC // PP_1_lo +data8 0xD56232EFC2B0FE52, 0x00003FD2 // QQ_8 +data8 0xC9C99ABA2B48DCA6, 0x0000BFDA // QQ_7 +data8 0x8F76C6509C716658, 0x00003FE2 // QQ_6 +data8 0x93F27DBAFDA8D0FC, 0x0000BFE9 // QQ_5 +data8 0xAAAAAAAAAAAAAAAA, 0x0000BFFC // S_1 +data8 0x8000000000000000, 0x0000BFFE // QQ_1 +data8 0xD00D00D00C6E5041, 0x00003FEF // QQ_4 +data8 0xB60B60B60B607F60, 0x0000BFF5 // QQ_3 +data8 0xAAAAAAAAAAAAAA9B, 0x00003FFA // QQ_2 +data8 0xFFFFFFFFFFFFFFFE, 0x0000BFFD // C_1 +data8 0xAAAAAAAAAAAA719F, 0x00003FFA // C_2 +data8 0xB60B60B60356F994, 0x0000BFF5 // C_3 +data8 0xD00CFFD5B2385EA9, 0x00003FEF // C_4 +data8 0x93E4BD18292A14CD, 0x0000BFE9 // C_5 +data8 0xAAAAAAAAAAAAAAAA, 0x0000BFFC // S_1 +data8 0x88888888888868DB, 0x00003FF8 // S_2 +data8 0xD00D00D0055EFD4B, 0x0000BFF2 // S_3 +data8 0xB8EF1C5D839730B9, 0x00003FEC // S_4 +data8 0xD71EA3A4E5B3F492, 0x0000BFE5 // S_5 +data4 0x38800000 // two**-14 +data4 0xB8800000 // -two**-14 +LOCAL_OBJECT_END(FSINCOS_CONSTANTS) + +// sin and cos registers + +// FR +FR_Input_X = f8 + +FR_r = f8 +FR_c = f9 + +FR_Two_to_63 = f32 +FR_Two_to_24 = f33 +FR_Pi_by_4 = f33 +FR_Two_to_M14 = f34 +FR_Two_to_M33 = f35 +FR_Neg_Two_to_24 = f36 +FR_Neg_Pi_by_4 = f36 +FR_Neg_Two_to_M14 = f37 +FR_Neg_Two_to_M33 = f38 +FR_Neg_Two_to_M67 = f39 +FR_Inv_pi_by_2 = f40 +FR_N_float = f41 +FR_N_fix = f42 +FR_P_1 = f43 +FR_P_2 = f44 +FR_P_3 = f45 +FR_s = f46 +FR_w = f47 +FR_d_2 = f48 +FR_prelim = f49 +FR_Z = f50 +FR_A = f51 +FR_a = f52 +FR_t = f53 +FR_U_1 = f54 +FR_U_2 = f55 +FR_C_1 = f56 +FR_C_2 = f57 +FR_C_3 = f58 +FR_C_4 = f59 +FR_C_5 = f60 +FR_S_1 = f61 +FR_S_2 = f62 +FR_S_3 = f63 +FR_S_4 = f64 +FR_S_5 = f65 +FR_poly_hi = f66 +FR_poly_lo = f67 +FR_r_hi = f68 +FR_r_lo = f69 +FR_rsq = f70 +FR_r_cubed = f71 +FR_C_hi = f72 +FR_N_0 = f73 +FR_d_1 = f74 +FR_V = f75 +FR_V_hi = f75 +FR_V_lo = f76 +FR_U_hi = f77 +FR_U_lo = f78 +FR_U_hiabs = f79 +FR_V_hiabs = f80 +FR_PP_8 = f81 +FR_QQ_8 = f81 +FR_PP_7 = f82 +FR_QQ_7 = f82 +FR_PP_6 = f83 +FR_QQ_6 = f83 +FR_PP_5 = f84 +FR_QQ_5 = f84 +FR_PP_4 = f85 +FR_QQ_4 = f85 +FR_PP_3 = f86 +FR_QQ_3 = f86 +FR_PP_2 = f87 +FR_QQ_2 = f87 +FR_QQ_1 = f88 +FR_N_0_fix = f89 +FR_Inv_P_0 = f90 +FR_corr = f91 +FR_poly = f92 +FR_Neg_Two_to_M3 = f93 +FR_Two_to_M3 = f94 +FR_Neg_Two_to_63 = f94 +FR_P_0 = f95 +FR_C_lo = f96 +FR_PP_1 = f97 +FR_PP_1_lo = f98 +FR_ArgPrime = f99 + +// GR +GR_Table_Base = r32 +GR_Table_Base1 = r33 +GR_i_0 = r34 +GR_i_1 = r35 +GR_N_Inc = r36 +GR_Sin_or_Cos = r37 + +GR_SAVE_B0 = r39 +GR_SAVE_GP = r40 +GR_SAVE_PFS = r41 + +// sincos combined routine registers + +// GR +GR_SINCOS_SAVE_PFS = r32 +GR_SINCOS_SAVE_B0 = r33 +GR_SINCOS_SAVE_GP = r34 + +// FR +FR_SINCOS_ARG = f100 +FR_SINCOS_RES_SIN = f101 + + +.section .text + + +GLOBAL_LIBM_ENTRY(__libm_sincos_large) + +{ .mfi + alloc GR_SINCOS_SAVE_PFS = ar.pfs,0,3,0,0 + fma.s1 FR_SINCOS_ARG = f8, f1, f0 // Save argument for sin and cos + mov GR_SINCOS_SAVE_B0 = b0 +};; + +{ .mfb + mov GR_SINCOS_SAVE_GP = gp + nop.f 0 + br.call.sptk b0 = __libm_sin_large // Call sin +};; + +{ .mfi + nop.m 0 + fma.s1 FR_SINCOS_RES_SIN = f8, f1, f0 // Save sin result + nop.i 0 +};; + +{ .mfb + nop.m 0 + fma.s1 f8 = FR_SINCOS_ARG, f1, f0 // Arg for cos + br.call.sptk b0 = __libm_cos_large // Call cos +};; + +{ .mfi + mov gp = GR_SINCOS_SAVE_GP + fma.s1 f9 = FR_SINCOS_RES_SIN, f1, f0 // Out sin result + mov b0 = GR_SINCOS_SAVE_B0 +};; + +{ .mib + nop.m 0 + mov ar.pfs = GR_SINCOS_SAVE_PFS + br.ret.sptk b0 // sincos_large exit +};; + +GLOBAL_LIBM_END(__libm_sincos_large) + + + + +GLOBAL_LIBM_ENTRY(__libm_sin_large) + +{ .mlx +alloc GR_Table_Base = ar.pfs,0,12,2,0 + movl GR_Sin_or_Cos = 0x0 ;; +} + +{ .mmi + nop.m 999 + addl GR_Table_Base = @ltoff(FSINCOS_CONSTANTS#), gp + nop.i 999 +} +;; + +{ .mmi + ld8 GR_Table_Base = [GR_Table_Base] + nop.m 999 + nop.i 999 +} +;; + + +{ .mib + nop.m 999 + nop.i 999 + br.cond.sptk SINCOS_CONTINUE ;; +} + +GLOBAL_LIBM_END(__libm_sin_large) + +GLOBAL_LIBM_ENTRY(__libm_cos_large) + +{ .mlx +alloc GR_Table_Base= ar.pfs,0,12,2,0 + movl GR_Sin_or_Cos = 0x1 ;; +} + +{ .mmi + nop.m 999 + addl GR_Table_Base = @ltoff(FSINCOS_CONSTANTS#), gp + nop.i 999 +} +;; + +{ .mmi + ld8 GR_Table_Base = [GR_Table_Base] + nop.m 999 + nop.i 999 +} +;; + +// +// Load Table Address +// +SINCOS_CONTINUE: + +{ .mmi + add GR_Table_Base1 = 96, GR_Table_Base + ldfs FR_Two_to_24 = [GR_Table_Base], 4 + nop.i 999 +} +;; + +{ .mmi + nop.m 999 +// +// Load 2**24, load 2**63. +// + ldfs FR_Neg_Two_to_24 = [GR_Table_Base], 12 + mov r41 = ar.pfs ;; +} + +{ .mfi + ldfs FR_Two_to_63 = [GR_Table_Base1], 4 +// +// Check for unnormals - unsupported operands. We do not want +// to generate denormal exception +// Check for NatVals, QNaNs, SNaNs, +/-Infs +// Check for EM unsupporteds +// Check for Zero +// + fclass.m.unc p6, p8 = FR_Input_X, 0x1E3 + mov r40 = gp ;; +} + +{ .mfi + nop.m 999 + fclass.nm.unc p8, p0 = FR_Input_X, 0x1FF +// GR_Sin_or_Cos denotes + mov r39 = b0 +} + +{ .mfb + ldfs FR_Neg_Two_to_63 = [GR_Table_Base1], 12 + fclass.m.unc p10, p0 = FR_Input_X, 0x007 +(p6) br.cond.spnt SINCOS_SPECIAL ;; +} + +{ .mib + nop.m 999 + nop.i 999 +(p8) br.cond.spnt SINCOS_SPECIAL ;; +} + +{ .mib + nop.m 999 + nop.i 999 +// +// Branch if +/- NaN, Inf. +// Load -2**24, load -2**63. +// +(p10) br.cond.spnt SINCOS_ZERO ;; +} + +{ .mmb + ldfe FR_Inv_pi_by_2 = [GR_Table_Base], 16 + ldfe FR_Inv_P_0 = [GR_Table_Base1], 16 + nop.b 999 ;; +} + +{ .mmb + nop.m 999 + ldfe FR_d_1 = [GR_Table_Base1], 16 + nop.b 999 ;; +} +// +// Raise possible denormal operand flag with useful fcmp +// Is x <= -2**63 +// Load Inv_P_0 for pre-reduction +// Load Inv_pi_by_2 +// + +{ .mmb + ldfe FR_P_0 = [GR_Table_Base], 16 + ldfe FR_d_2 = [GR_Table_Base1], 16 + nop.b 999 ;; +} +// +// Load P_0 +// Load d_1 +// Is x >= 2**63 +// Is x <= -2**24? +// + +{ .mmi + ldfe FR_P_1 = [GR_Table_Base], 16 ;; +// +// Load P_1 +// Load d_2 +// Is x >= 2**24? +// + ldfe FR_P_2 = [GR_Table_Base], 16 + nop.i 999 ;; +} + +{ .mmf + nop.m 999 + ldfe FR_P_3 = [GR_Table_Base], 16 + fcmp.le.unc.s1 p7, p8 = FR_Input_X, FR_Neg_Two_to_24 +} + +{ .mfi + nop.m 999 +// +// Branch if +/- zero. +// Decide about the paths to take: +// If -2**24 < FR_Input_X < 2**24 - CASE 1 OR 2 +// OTHERWISE - CASE 3 OR 4 +// + fcmp.le.unc.s1 p10, p11 = FR_Input_X, FR_Neg_Two_to_63 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +(p8) fcmp.ge.s1 p7, p0 = FR_Input_X, FR_Two_to_24 + nop.i 999 +} + +{ .mfi + ldfe FR_Pi_by_4 = [GR_Table_Base1], 16 +(p11) fcmp.ge.s1 p10, p0 = FR_Input_X, FR_Two_to_63 + nop.i 999 ;; +} + +{ .mmi + ldfe FR_Neg_Pi_by_4 = [GR_Table_Base1], 16 ;; + ldfs FR_Two_to_M3 = [GR_Table_Base1], 4 + nop.i 999 ;; +} + +{ .mib + ldfs FR_Neg_Two_to_M3 = [GR_Table_Base1], 12 + nop.i 999 +// +// Load P_2 +// Load P_3 +// Load pi_by_4 +// Load neg_pi_by_4 +// Load 2**(-3) +// Load -2**(-3). +// +(p10) br.cond.spnt SINCOS_ARG_TOO_LARGE ;; +} + +{ .mib + nop.m 999 + nop.i 999 +// +// Branch out if x >= 2**63. Use Payne-Hanek Reduction +// +(p7) br.cond.spnt SINCOS_LARGER_ARG ;; +} + +{ .mfi + nop.m 999 +// +// Branch if Arg <= -2**24 or Arg >= 2**24 and use pre-reduction. +// + fma.s1 FR_N_float = FR_Input_X, FR_Inv_pi_by_2, f0 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 + fcmp.lt.unc.s1 p6, p7 = FR_Input_X, FR_Pi_by_4 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +// +// Select the case when |Arg| < pi/4 +// Else Select the case when |Arg| >= pi/4 +// + fcvt.fx.s1 FR_N_fix = FR_N_float + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +// +// N = Arg * 2/pi +// Check if Arg < pi/4 +// +(p6) fcmp.gt.s1 p6, p7 = FR_Input_X, FR_Neg_Pi_by_4 + nop.i 999 ;; +} +// +// Case 2: Convert integer N_fix back to normalized floating-point value. +// Case 1: p8 is only affected when p6 is set +// + +{ .mfi +(p7) ldfs FR_Two_to_M33 = [GR_Table_Base1], 4 +// +// Grab the integer part of N and call it N_fix +// +(p6) fmerge.se FR_r = FR_Input_X, FR_Input_X +// If |x| < pi/4, r = x and c = 0 +// lf |x| < pi/4, is x < 2**(-3). +// r = Arg +// c = 0 +(p6) mov GR_N_Inc = GR_Sin_or_Cos ;; +} + +{ .mmf + nop.m 999 +(p7) ldfs FR_Neg_Two_to_M33 = [GR_Table_Base1], 4 +(p6) fmerge.se FR_c = f0, f0 +} + +{ .mfi + nop.m 999 +(p6) fcmp.lt.unc.s1 p8, p9 = FR_Input_X, FR_Two_to_M3 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +// +// lf |x| < pi/4, is -2**(-3)< x < 2**(-3) - set p8. +// If |x| >= pi/4, +// Create the right N for |x| < pi/4 and otherwise +// Case 2: Place integer part of N in GP register +// +(p7) fcvt.xf FR_N_float = FR_N_fix + nop.i 999 ;; +} + +{ .mmf + nop.m 999 +(p7) getf.sig GR_N_Inc = FR_N_fix +(p8) fcmp.gt.s1 p8, p0 = FR_Input_X, FR_Neg_Two_to_M3 ;; +} + +{ .mib + nop.m 999 + nop.i 999 +// +// Load 2**(-33), -2**(-33) +// +(p8) br.cond.spnt SINCOS_SMALL_R ;; +} + +{ .mib + nop.m 999 + nop.i 999 +(p6) br.cond.sptk SINCOS_NORMAL_R ;; +} +// +// if |x| < pi/4, branch based on |x| < 2**(-3) or otherwise. +// +// +// In this branch, |x| >= pi/4. +// + +{ .mfi + ldfs FR_Neg_Two_to_M67 = [GR_Table_Base1], 8 +// +// Load -2**(-67) +// + fnma.s1 FR_s = FR_N_float, FR_P_1, FR_Input_X +// +// w = N * P_2 +// s = -N * P_1 + Arg +// + add GR_N_Inc = GR_N_Inc, GR_Sin_or_Cos +} + +{ .mfi + nop.m 999 + fma.s1 FR_w = FR_N_float, FR_P_2, f0 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +// +// Adjust N_fix by N_inc to determine whether sine or +// cosine is being calculated +// + fcmp.lt.unc.s1 p7, p6 = FR_s, FR_Two_to_M33 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +(p7) fcmp.gt.s1 p7, p6 = FR_s, FR_Neg_Two_to_M33 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +// Remember x >= pi/4. +// Is s <= -2**(-33) or s >= 2**(-33) (p6) +// or -2**(-33) < s < 2**(-33) (p7) +(p6) fms.s1 FR_r = FR_s, f1, FR_w + nop.i 999 +} + +{ .mfi + nop.m 999 +(p7) fma.s1 FR_w = FR_N_float, FR_P_3, f0 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +(p7) fma.s1 FR_U_1 = FR_N_float, FR_P_2, FR_w + nop.i 999 +} + +{ .mfi + nop.m 999 +(p6) fms.s1 FR_c = FR_s, f1, FR_r + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +// +// For big s: r = s - w: No futher reduction is necessary +// For small s: w = N * P_3 (change sign) More reduction +// +(p6) fcmp.lt.unc.s1 p8, p9 = FR_r, FR_Two_to_M3 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +(p8) fcmp.gt.s1 p8, p9 = FR_r, FR_Neg_Two_to_M3 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +(p7) fms.s1 FR_r = FR_s, f1, FR_U_1 + nop.i 999 +} + +{ .mfb + nop.m 999 +// +// For big s: Is |r| < 2**(-3)? +// For big s: c = S - r +// For small s: U_1 = N * P_2 + w +// +// If p8 is set, prepare to branch to Small_R. +// If p9 is set, prepare to branch to Normal_R. +// For big s, r is complete here. +// +(p6) fms.s1 FR_c = FR_c, f1, FR_w +// +// For big s: c = c + w (w has not been negated.) +// For small s: r = S - U_1 +// +(p8) br.cond.spnt SINCOS_SMALL_R ;; +} + +{ .mib + nop.m 999 + nop.i 999 +(p9) br.cond.sptk SINCOS_NORMAL_R ;; +} + +{ .mfi +(p7) add GR_Table_Base1 = 224, GR_Table_Base1 +// +// Branch to SINCOS_SMALL_R or SINCOS_NORMAL_R +// +(p7) fms.s1 FR_U_2 = FR_N_float, FR_P_2, FR_U_1 +// +// c = S - U_1 +// r = S_1 * r +// +// +(p7) extr.u GR_i_1 = GR_N_Inc, 0, 1 +} + +{ .mmi + nop.m 999 ;; +// +// Get [i_0,i_1] - two lsb of N_fix_gr. +// Do dummy fmpy so inexact is always set. +// +(p7) cmp.eq.unc p9, p10 = 0x0, GR_i_1 +(p7) extr.u GR_i_0 = GR_N_Inc, 1, 1 ;; +} +// +// For small s: U_2 = N * P_2 - U_1 +// S_1 stored constant - grab the one stored with the +// coefficients. +// + +{ .mfi +(p7) ldfe FR_S_1 = [GR_Table_Base1], 16 +// +// Check if i_1 and i_0 != 0 +// +(p10) fma.s1 FR_poly = f0, f1, FR_Neg_Two_to_M67 +(p7) cmp.eq.unc p11, p12 = 0x0, GR_i_0 ;; +} + +{ .mfi + nop.m 999 +(p7) fms.s1 FR_s = FR_s, f1, FR_r + nop.i 999 +} + +{ .mfi + nop.m 999 +// +// S = S - r +// U_2 = U_2 + w +// load S_1 +// +(p7) fma.s1 FR_rsq = FR_r, FR_r, f0 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +(p7) fma.s1 FR_U_2 = FR_U_2, f1, FR_w + nop.i 999 +} + +{ .mfi + nop.m 999 +//(p7) fmerge.se FR_Input_X = FR_r, FR_r +(p7) fmerge.se FR_prelim = FR_r, FR_r + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +//(p10) fma.s1 FR_Input_X = f0, f1, f1 +(p10) fma.s1 FR_prelim = f0, f1, f1 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +// +// FR_rsq = r * r +// Save r as the result. +// +(p7) fms.s1 FR_c = FR_s, f1, FR_U_1 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +// +// if ( i_1 ==0) poly = c + S_1*r*r*r +// else Result = 1 +// +//(p12) fnma.s1 FR_Input_X = FR_Input_X, f1, f0 +(p12) fnma.s1 FR_prelim = FR_prelim, f1, f0 + nop.i 999 +} + +{ .mfi + nop.m 999 +(p7) fma.s1 FR_r = FR_S_1, FR_r, f0 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +(p7) fma.d.s1 FR_S_1 = FR_S_1, FR_S_1, f0 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +// +// If i_1 != 0, poly = 2**(-67) +// +(p7) fms.s1 FR_c = FR_c, f1, FR_U_2 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +// +// c = c - U_2 +// +(p9) fma.s1 FR_poly = FR_r, FR_rsq, FR_c + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +// +// i_0 != 0, so Result = -Result +// +(p11) fma.s1 FR_Input_X = FR_prelim, f1, FR_poly + nop.i 999 ;; +} + +{ .mfb + nop.m 999 +(p12) fms.s1 FR_Input_X = FR_prelim, f1, FR_poly +// +// if (i_0 == 0), Result = Result + poly +// else Result = Result - poly +// + br.ret.sptk b0 ;; +} +SINCOS_LARGER_ARG: + +{ .mfi + nop.m 999 + fma.s1 FR_N_0 = FR_Input_X, FR_Inv_P_0, f0 + nop.i 999 +} +;; + +// This path for argument > 2*24 +// Adjust table_ptr1 to beginning of table. +// + +{ .mmi + nop.m 999 + addl GR_Table_Base = @ltoff(FSINCOS_CONSTANTS#), gp + nop.i 999 +} +;; + +{ .mmi + ld8 GR_Table_Base = [GR_Table_Base] + nop.m 999 + nop.i 999 +} +;; + + +// +// Point to 2*-14 +// N_0 = Arg * Inv_P_0 +// + +{ .mmi + add GR_Table_Base = 688, GR_Table_Base ;; + ldfs FR_Two_to_M14 = [GR_Table_Base], 4 + nop.i 999 ;; +} + +{ .mfi + ldfs FR_Neg_Two_to_M14 = [GR_Table_Base], 0 + nop.f 999 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +// +// Load values 2**(-14) and -2**(-14) +// + fcvt.fx.s1 FR_N_0_fix = FR_N_0 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +// +// N_0_fix = integer part of N_0 +// + fcvt.xf FR_N_0 = FR_N_0_fix + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +// +// Make N_0 the integer part +// + fnma.s1 FR_ArgPrime = FR_N_0, FR_P_0, FR_Input_X + nop.i 999 +} + +{ .mfi + nop.m 999 + fma.s1 FR_w = FR_N_0, FR_d_1, f0 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +// +// Arg' = -N_0 * P_0 + Arg +// w = N_0 * d_1 +// + fma.s1 FR_N_float = FR_ArgPrime, FR_Inv_pi_by_2, f0 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +// +// N = A' * 2/pi +// + fcvt.fx.s1 FR_N_fix = FR_N_float + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +// +// N_fix is the integer part +// + fcvt.xf FR_N_float = FR_N_fix + nop.i 999 ;; +} + +{ .mfi + getf.sig GR_N_Inc = FR_N_fix + nop.f 999 + nop.i 999 ;; +} + +{ .mii + nop.m 999 + nop.i 999 ;; + add GR_N_Inc = GR_N_Inc, GR_Sin_or_Cos ;; +} + +{ .mfi + nop.m 999 +// +// N is the integer part of the reduced-reduced argument. +// Put the integer in a GP register +// + fnma.s1 FR_s = FR_N_float, FR_P_1, FR_ArgPrime + nop.i 999 +} + +{ .mfi + nop.m 999 + fnma.s1 FR_w = FR_N_float, FR_P_2, FR_w + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +// +// s = -N*P_1 + Arg' +// w = -N*P_2 + w +// N_fix_gr = N_fix_gr + N_inc +// + fcmp.lt.unc.s1 p9, p8 = FR_s, FR_Two_to_M14 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +(p9) fcmp.gt.s1 p9, p8 = FR_s, FR_Neg_Two_to_M14 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +// +// For |s| > 2**(-14) r = S + w (r complete) +// Else U_hi = N_0 * d_1 +// +(p9) fma.s1 FR_V_hi = FR_N_float, FR_P_2, f0 + nop.i 999 +} + +{ .mfi + nop.m 999 +(p9) fma.s1 FR_U_hi = FR_N_0, FR_d_1, f0 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +// +// Either S <= -2**(-14) or S >= 2**(-14) +// or -2**(-14) < s < 2**(-14) +// +(p8) fma.s1 FR_r = FR_s, f1, FR_w + nop.i 999 +} + +{ .mfi + nop.m 999 +(p9) fma.s1 FR_w = FR_N_float, FR_P_3, f0 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +// +// We need abs of both U_hi and V_hi - don't +// worry about switched sign of V_hi. +// +(p9) fms.s1 FR_A = FR_U_hi, f1, FR_V_hi + nop.i 999 +} + +{ .mfi + nop.m 999 +// +// Big s: finish up c = (S - r) + w (c complete) +// Case 4: A = U_hi + V_hi +// Note: Worry about switched sign of V_hi, so subtract instead of add. +// +(p9) fnma.s1 FR_V_lo = FR_N_float, FR_P_2, FR_V_hi + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +(p9) fms.s1 FR_U_lo = FR_N_0, FR_d_1, FR_U_hi + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +(p9) fmerge.s FR_V_hiabs = f0, FR_V_hi + nop.i 999 +} + +{ .mfi + nop.m 999 +// For big s: c = S - r +// For small s do more work: U_lo = N_0 * d_1 - U_hi +// +(p9) fmerge.s FR_U_hiabs = f0, FR_U_hi + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +// +// For big s: Is |r| < 2**(-3) +// For big s: if p12 set, prepare to branch to Small_R. +// For big s: If p13 set, prepare to branch to Normal_R. +// +(p8) fms.s1 FR_c = FR_s, f1, FR_r + nop.i 999 +} + +{ .mfi + nop.m 999 +// +// For small S: V_hi = N * P_2 +// w = N * P_3 +// Note the product does not include the (-) as in the writeup +// so (-) missing for V_hi and w. +// +(p8) fcmp.lt.unc.s1 p12, p13 = FR_r, FR_Two_to_M3 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +(p12) fcmp.gt.s1 p12, p13 = FR_r, FR_Neg_Two_to_M3 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +(p8) fma.s1 FR_c = FR_c, f1, FR_w + nop.i 999 +} + +{ .mfb + nop.m 999 +(p9) fms.s1 FR_w = FR_N_0, FR_d_2, FR_w +(p12) br.cond.spnt SINCOS_SMALL_R ;; +} + +{ .mib + nop.m 999 + nop.i 999 +(p13) br.cond.sptk SINCOS_NORMAL_R ;; +} + +{ .mfi + nop.m 999 +// +// Big s: Vector off when |r| < 2**(-3). Recall that p8 will be true. +// The remaining stuff is for Case 4. +// Small s: V_lo = N * P_2 + U_hi (U_hi is in place of V_hi in writeup) +// Note: the (-) is still missing for V_lo. +// Small s: w = w + N_0 * d_2 +// Note: the (-) is now incorporated in w. +// +(p9) fcmp.ge.unc.s1 p10, p11 = FR_U_hiabs, FR_V_hiabs + extr.u GR_i_1 = GR_N_Inc, 0, 1 ;; +} + +{ .mfi + nop.m 999 +// +// C_hi = S + A +// +(p9) fma.s1 FR_t = FR_U_lo, f1, FR_V_lo + extr.u GR_i_0 = GR_N_Inc, 1, 1 ;; +} + +{ .mfi + nop.m 999 +// +// t = U_lo + V_lo +// +// +(p10) fms.s1 FR_a = FR_U_hi, f1, FR_A + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +(p11) fma.s1 FR_a = FR_V_hi, f1, FR_A + nop.i 999 +} +;; + +{ .mmi + nop.m 999 + addl GR_Table_Base = @ltoff(FSINCOS_CONSTANTS#), gp + nop.i 999 +} +;; + +{ .mmi + ld8 GR_Table_Base = [GR_Table_Base] + nop.m 999 + nop.i 999 +} +;; + + +{ .mfi + add GR_Table_Base = 528, GR_Table_Base +// +// Is U_hiabs >= V_hiabs? +// +(p9) fma.s1 FR_C_hi = FR_s, f1, FR_A + nop.i 999 ;; +} + +{ .mmi + ldfe FR_C_1 = [GR_Table_Base], 16 ;; + ldfe FR_C_2 = [GR_Table_Base], 64 + nop.i 999 ;; +} + +{ .mmf + nop.m 999 +// +// c = c + C_lo finished. +// Load C_2 +// + ldfe FR_S_1 = [GR_Table_Base], 16 +// +// C_lo = S - C_hi +// + fma.s1 FR_t = FR_t, f1, FR_w ;; +} +// +// r and c have been computed. +// Make sure ftz mode is set - should be automatic when using wre +// |r| < 2**(-3) +// Get [i_0,i_1] - two lsb of N_fix. +// Load S_1 +// + +{ .mfi + ldfe FR_S_2 = [GR_Table_Base], 64 +// +// t = t + w +// +(p10) fms.s1 FR_a = FR_a, f1, FR_V_hi + cmp.eq.unc p9, p10 = 0x0, GR_i_0 +} + +{ .mfi + nop.m 999 +// +// For larger u than v: a = U_hi - A +// Else a = V_hi - A (do an add to account for missing (-) on V_hi +// + fms.s1 FR_C_lo = FR_s, f1, FR_C_hi + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +(p11) fms.s1 FR_a = FR_U_hi, f1, FR_a + cmp.eq.unc p11, p12 = 0x0, GR_i_1 +} + +{ .mfi + nop.m 999 +// +// If u > v: a = (U_hi - A) + V_hi +// Else a = (V_hi - A) + U_hi +// In each case account for negative missing from V_hi. +// + fma.s1 FR_C_lo = FR_C_lo, f1, FR_A + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +// +// C_lo = (S - C_hi) + A +// + fma.s1 FR_t = FR_t, f1, FR_a + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +// +// t = t + a +// + fma.s1 FR_C_lo = FR_C_lo, f1, FR_t + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +// +// C_lo = C_lo + t +// Adjust Table_Base to beginning of table +// + fma.s1 FR_r = FR_C_hi, f1, FR_C_lo + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +// +// Load S_2 +// + fma.s1 FR_rsq = FR_r, FR_r, f0 + nop.i 999 +} + +{ .mfi + nop.m 999 +// +// Table_Base points to C_1 +// r = C_hi + C_lo +// + fms.s1 FR_c = FR_C_hi, f1, FR_r + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +// +// if i_1 ==0: poly = S_2 * FR_rsq + S_1 +// else poly = C_2 * FR_rsq + C_1 +// +//(p11) fma.s1 FR_Input_X = f0, f1, FR_r +(p11) fma.s1 FR_prelim = f0, f1, FR_r + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +//(p12) fma.s1 FR_Input_X = f0, f1, f1 +(p12) fma.s1 FR_prelim = f0, f1, f1 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +// +// Compute r_cube = FR_rsq * r +// +(p11) fma.s1 FR_poly = FR_rsq, FR_S_2, FR_S_1 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +(p12) fma.s1 FR_poly = FR_rsq, FR_C_2, FR_C_1 + nop.i 999 +} + +{ .mfi + nop.m 999 +// +// Compute FR_rsq = r * r +// Is i_1 == 0 ? +// + fma.s1 FR_r_cubed = FR_rsq, FR_r, f0 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +// +// c = C_hi - r +// Load C_1 +// + fma.s1 FR_c = FR_c, f1, FR_C_lo + nop.i 999 +} + +{ .mfi + nop.m 999 +// +// if i_1 ==0: poly = r_cube * poly + c +// else poly = FR_rsq * poly +// +//(p10) fms.s1 FR_Input_X = f0, f1, FR_Input_X +(p10) fms.s1 FR_prelim = f0, f1, FR_prelim + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +// +// if i_1 ==0: Result = r +// else Result = 1.0 +// +(p11) fma.s1 FR_poly = FR_r_cubed, FR_poly, FR_c + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +(p12) fma.s1 FR_poly = FR_rsq, FR_poly, f0 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +// +// if i_0 !=0: Result = -Result +// +(p9) fma.s1 FR_Input_X = FR_prelim, f1, FR_poly + nop.i 999 ;; +} + +{ .mfb + nop.m 999 +(p10) fms.s1 FR_Input_X = FR_prelim, f1, FR_poly +// +// if i_0 == 0: Result = Result + poly +// else Result = Result - poly +// + br.ret.sptk b0 ;; +} +SINCOS_SMALL_R: + +{ .mii + nop.m 999 + extr.u GR_i_1 = GR_N_Inc, 0, 1 ;; +// +// +// Compare both i_1 and i_0 with 0. +// if i_1 == 0, set p9. +// if i_0 == 0, set p11. +// + cmp.eq.unc p9, p10 = 0x0, GR_i_1 ;; +} + +{ .mfi + nop.m 999 + fma.s1 FR_rsq = FR_r, FR_r, f0 + extr.u GR_i_0 = GR_N_Inc, 1, 1 ;; +} + +{ .mfi + nop.m 999 +// +// Z = Z * FR_rsq +// +(p10) fnma.s1 FR_c = FR_c, FR_r, f0 + cmp.eq.unc p11, p12 = 0x0, GR_i_0 +} +;; + +// ****************************************************************** +// ****************************************************************** +// ****************************************************************** +// r and c have been computed. +// We know whether this is the sine or cosine routine. +// Make sure ftz mode is set - should be automatic when using wre +// |r| < 2**(-3) +// +// Set table_ptr1 to beginning of constant table. +// Get [i_0,i_1] - two lsb of N_fix_gr. +// + +{ .mmi + nop.m 999 + addl GR_Table_Base = @ltoff(FSINCOS_CONSTANTS#), gp + nop.i 999 +} +;; + +{ .mmi + ld8 GR_Table_Base = [GR_Table_Base] + nop.m 999 + nop.i 999 +} +;; + + +// +// Set table_ptr1 to point to S_5. +// Set table_ptr1 to point to C_5. +// Compute FR_rsq = r * r +// + +{ .mfi +(p9) add GR_Table_Base = 672, GR_Table_Base +(p10) fmerge.s FR_r = f1, f1 +(p10) add GR_Table_Base = 592, GR_Table_Base ;; +} +// +// Set table_ptr1 to point to S_5. +// Set table_ptr1 to point to C_5. +// + +{ .mmi +(p9) ldfe FR_S_5 = [GR_Table_Base], -16 ;; +// +// if (i_1 == 0) load S_5 +// if (i_1 != 0) load C_5 +// +(p9) ldfe FR_S_4 = [GR_Table_Base], -16 + nop.i 999 ;; +} + +{ .mmf +(p10) ldfe FR_C_5 = [GR_Table_Base], -16 +// +// Z = FR_rsq * FR_rsq +// +(p9) ldfe FR_S_3 = [GR_Table_Base], -16 +// +// Compute FR_rsq = r * r +// if (i_1 == 0) load S_4 +// if (i_1 != 0) load C_4 +// + fma.s1 FR_Z = FR_rsq, FR_rsq, f0 ;; +} +// +// if (i_1 == 0) load S_3 +// if (i_1 != 0) load C_3 +// + +{ .mmi +(p9) ldfe FR_S_2 = [GR_Table_Base], -16 ;; +// +// if (i_1 == 0) load S_2 +// if (i_1 != 0) load C_2 +// +(p9) ldfe FR_S_1 = [GR_Table_Base], -16 + nop.i 999 +} + +{ .mmi +(p10) ldfe FR_C_4 = [GR_Table_Base], -16 ;; +(p10) ldfe FR_C_3 = [GR_Table_Base], -16 + nop.i 999 ;; +} + +{ .mmi +(p10) ldfe FR_C_2 = [GR_Table_Base], -16 ;; +(p10) ldfe FR_C_1 = [GR_Table_Base], -16 + nop.i 999 +} + +{ .mfi + nop.m 999 +// +// if (i_1 != 0): +// poly_lo = FR_rsq * C_5 + C_4 +// poly_hi = FR_rsq * C_2 + C_1 +// +(p9) fma.s1 FR_Z = FR_Z, FR_r, f0 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +// +// if (i_1 == 0) load S_1 +// if (i_1 != 0) load C_1 +// +(p9) fma.s1 FR_poly_lo = FR_rsq, FR_S_5, FR_S_4 + nop.i 999 +} + +{ .mfi + nop.m 999 +// +// c = -c * r +// dummy fmpy's to flag inexact. +// +(p9) fma.d.s1 FR_S_4 = FR_S_4, FR_S_4, f0 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +// +// poly_lo = FR_rsq * poly_lo + C_3 +// poly_hi = FR_rsq * poly_hi +// + fma.s1 FR_Z = FR_Z, FR_rsq, f0 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +(p9) fma.s1 FR_poly_hi = FR_rsq, FR_S_2, FR_S_1 + nop.i 999 +} + +{ .mfi + nop.m 999 +// +// if (i_1 == 0): +// poly_lo = FR_rsq * S_5 + S_4 +// poly_hi = FR_rsq * S_2 + S_1 +// +(p10) fma.s1 FR_poly_lo = FR_rsq, FR_C_5, FR_C_4 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +// +// if (i_1 == 0): +// Z = Z * r for only one of the small r cases - not there +// in original implementation notes. +// +(p9) fma.s1 FR_poly_lo = FR_rsq, FR_poly_lo, FR_S_3 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +(p10) fma.s1 FR_poly_hi = FR_rsq, FR_C_2, FR_C_1 + nop.i 999 +} + +{ .mfi + nop.m 999 +(p10) fma.d.s1 FR_C_1 = FR_C_1, FR_C_1, f0 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +(p9) fma.s1 FR_poly_hi = FR_poly_hi, FR_rsq, f0 + nop.i 999 +} + +{ .mfi + nop.m 999 +// +// poly_lo = FR_rsq * poly_lo + S_3 +// poly_hi = FR_rsq * poly_hi +// +(p10) fma.s1 FR_poly_lo = FR_rsq, FR_poly_lo, FR_C_3 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +(p10) fma.s1 FR_poly_hi = FR_poly_hi, FR_rsq, f0 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +// +// if (i_1 == 0): dummy fmpy's to flag inexact +// r = 1 +// +(p9) fma.s1 FR_poly_hi = FR_r, FR_poly_hi, f0 + nop.i 999 +} + +{ .mfi + nop.m 999 +// +// poly_hi = r * poly_hi +// + fma.s1 FR_poly = FR_Z, FR_poly_lo, FR_c + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +(p12) fms.s1 FR_r = f0, f1, FR_r + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +// +// poly_hi = Z * poly_lo + c +// if i_0 == 1: r = -r +// + fma.s1 FR_poly = FR_poly, f1, FR_poly_hi + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +(p12) fms.s1 FR_Input_X = FR_r, f1, FR_poly + nop.i 999 +} + +{ .mfb + nop.m 999 +// +// poly = poly + poly_hi +// +(p11) fma.s1 FR_Input_X = FR_r, f1, FR_poly +// +// if (i_0 == 0) Result = r + poly +// if (i_0 != 0) Result = r - poly +// + br.ret.sptk b0 ;; +} +SINCOS_NORMAL_R: + +{ .mii + nop.m 999 + extr.u GR_i_1 = GR_N_Inc, 0, 1 ;; +// +// Set table_ptr1 and table_ptr2 to base address of +// constant table. + cmp.eq.unc p9, p10 = 0x0, GR_i_1 ;; +} + +{ .mfi + nop.m 999 + fma.s1 FR_rsq = FR_r, FR_r, f0 + extr.u GR_i_0 = GR_N_Inc, 1, 1 ;; +} + +{ .mfi + nop.m 999 + frcpa.s1 FR_r_hi, p6 = f1, FR_r + cmp.eq.unc p11, p12 = 0x0, GR_i_0 +} +;; + +// ****************************************************************** +// ****************************************************************** +// ****************************************************************** +// +// r and c have been computed. +// We known whether this is the sine or cosine routine. +// Make sure ftz mode is set - should be automatic when using wre +// Get [i_0,i_1] - two lsb of N_fix_gr alone. +// + +{ .mmi + nop.m 999 + addl GR_Table_Base = @ltoff(FSINCOS_CONSTANTS#), gp + nop.i 999 +} +;; + +{ .mmi + ld8 GR_Table_Base = [GR_Table_Base] + nop.m 999 + nop.i 999 +} +;; + + +{ .mfi +(p10) add GR_Table_Base = 384, GR_Table_Base +//(p12) fms.s1 FR_Input_X = f0, f1, f1 +(p12) fms.s1 FR_prelim = f0, f1, f1 +(p9) add GR_Table_Base = 224, GR_Table_Base ;; +} + +{ .mmf + nop.m 999 +(p10) ldfe FR_QQ_8 = [GR_Table_Base], 16 +// +// if (i_1==0) poly = poly * FR_rsq + PP_1_lo +// else poly = FR_rsq * poly +// +//(p11) fma.s1 FR_Input_X = f0, f1, f1 ;; +(p11) fma.s1 FR_prelim = f0, f1, f1 ;; +} + +{ .mmf +(p10) ldfe FR_QQ_7 = [GR_Table_Base], 16 +// +// Adjust table pointers based on i_0 +// Compute rsq = r * r +// +(p9) ldfe FR_PP_8 = [GR_Table_Base], 16 + fma.s1 FR_r_cubed = FR_r, FR_rsq, f0 ;; +} + +{ .mmf +(p9) ldfe FR_PP_7 = [GR_Table_Base], 16 +(p10) ldfe FR_QQ_6 = [GR_Table_Base], 16 +// +// Load PP_8 and QQ_8; PP_7 and QQ_7 +// + frcpa.s1 FR_r_hi, p6 = f1, FR_r_hi ;; +} +// +// if (i_1==0) poly = PP_7 + FR_rsq * PP_8. +// else poly = QQ_7 + FR_rsq * QQ_8. +// + +{ .mmb +(p9) ldfe FR_PP_6 = [GR_Table_Base], 16 +(p10) ldfe FR_QQ_5 = [GR_Table_Base], 16 + nop.b 999 ;; +} + +{ .mmb +(p9) ldfe FR_PP_5 = [GR_Table_Base], 16 +(p10) ldfe FR_S_1 = [GR_Table_Base], 16 + nop.b 999 ;; +} + +{ .mmb +(p10) ldfe FR_QQ_1 = [GR_Table_Base], 16 +(p9) ldfe FR_C_1 = [GR_Table_Base], 16 + nop.b 999 ;; +} + +{ .mmi +(p10) ldfe FR_QQ_4 = [GR_Table_Base], 16 ;; +(p9) ldfe FR_PP_1 = [GR_Table_Base], 16 + nop.i 999 ;; +} + +{ .mmf +(p10) ldfe FR_QQ_3 = [GR_Table_Base], 16 +// +// if (i_1=0) corr = corr + c*c +// else corr = corr * c +// +(p9) ldfe FR_PP_4 = [GR_Table_Base], 16 +(p10) fma.s1 FR_poly = FR_rsq, FR_QQ_8, FR_QQ_7 ;; +} +// +// if (i_1=0) poly = rsq * poly + PP_5 +// else poly = rsq * poly + QQ_5 +// Load PP_4 or QQ_4 +// + +{ .mmf +(p9) ldfe FR_PP_3 = [GR_Table_Base], 16 +(p10) ldfe FR_QQ_2 = [GR_Table_Base], 16 +// +// r_hi = frcpa(frcpa(r)). +// r_cube = r * FR_rsq. +// +(p9) fma.s1 FR_poly = FR_rsq, FR_PP_8, FR_PP_7 ;; +} +// +// Do dummy multiplies so inexact is always set. +// + +{ .mfi +(p9) ldfe FR_PP_2 = [GR_Table_Base], 16 +// +// r_lo = r - r_hi +// +(p9) fma.s1 FR_U_lo = FR_r_hi, FR_r_hi, f0 + nop.i 999 ;; +} + +{ .mmf + nop.m 999 +(p9) ldfe FR_PP_1_lo = [GR_Table_Base], 16 +(p10) fma.s1 FR_corr = FR_S_1, FR_r_cubed, FR_r +} + +{ .mfi + nop.m 999 +(p10) fma.s1 FR_poly = FR_rsq, FR_poly, FR_QQ_6 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +// +// if (i_1=0) U_lo = r_hi * r_hi +// else U_lo = r_hi + r +// +(p9) fma.s1 FR_corr = FR_C_1, FR_rsq, f0 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +// +// if (i_1=0) corr = C_1 * rsq +// else corr = S_1 * r_cubed + r +// +(p9) fma.s1 FR_poly = FR_rsq, FR_poly, FR_PP_6 + nop.i 999 +} + +{ .mfi + nop.m 999 +(p10) fma.s1 FR_U_lo = FR_r_hi, f1, FR_r + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +// +// if (i_1=0) U_hi = r_hi + U_hi +// else U_hi = QQ_1 * U_hi + 1 +// +(p9) fma.s1 FR_U_lo = FR_r, FR_r_hi, FR_U_lo + nop.i 999 +} + +{ .mfi + nop.m 999 +// +// U_hi = r_hi * r_hi +// + fms.s1 FR_r_lo = FR_r, f1, FR_r_hi + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +// +// Load PP_1, PP_6, PP_5, and C_1 +// Load QQ_1, QQ_6, QQ_5, and S_1 +// + fma.s1 FR_U_hi = FR_r_hi, FR_r_hi, f0 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +(p10) fma.s1 FR_poly = FR_rsq, FR_poly, FR_QQ_5 + nop.i 999 +} + +{ .mfi + nop.m 999 +(p10) fnma.s1 FR_corr = FR_corr, FR_c, f0 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +// +// if (i_1=0) U_lo = r * r_hi + U_lo +// else U_lo = r_lo * U_lo +// +(p9) fma.s1 FR_corr = FR_corr, FR_c, FR_c + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +(p9) fma.s1 FR_poly = FR_rsq, FR_poly, FR_PP_5 + nop.i 999 +} + +{ .mfi + nop.m 999 +// +// if (i_1 =0) U_hi = r + U_hi +// if (i_1 =0) U_lo = r_lo * U_lo +// +// +(p9) fma.d.s1 FR_PP_5 = FR_PP_5, FR_PP_4, f0 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +(p9) fma.s1 FR_U_lo = FR_r, FR_r, FR_U_lo + nop.i 999 +} + +{ .mfi + nop.m 999 +(p10) fma.s1 FR_U_lo = FR_r_lo, FR_U_lo, f0 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +// +// if (i_1=0) poly = poly * rsq + PP_6 +// else poly = poly * rsq + QQ_6 +// +(p9) fma.s1 FR_U_hi = FR_r_hi, FR_U_hi, f0 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +(p10) fma.s1 FR_poly = FR_rsq, FR_poly, FR_QQ_4 + nop.i 999 +} + +{ .mfi + nop.m 999 +(p10) fma.s1 FR_U_hi = FR_QQ_1, FR_U_hi, f1 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +(p10) fma.d.s1 FR_QQ_5 = FR_QQ_5, FR_QQ_5, f0 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +// +// if (i_1!=0) U_hi = PP_1 * U_hi +// if (i_1!=0) U_lo = r * r + U_lo +// Load PP_3 or QQ_3 +// +(p9) fma.s1 FR_poly = FR_rsq, FR_poly, FR_PP_4 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +(p9) fma.s1 FR_U_lo = FR_r_lo, FR_U_lo, f0 + nop.i 999 +} + +{ .mfi + nop.m 999 +(p10) fma.s1 FR_U_lo = FR_QQ_1,FR_U_lo, f0 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +(p9) fma.s1 FR_U_hi = FR_PP_1, FR_U_hi, f0 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +(p10) fma.s1 FR_poly = FR_rsq, FR_poly, FR_QQ_3 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +// +// Load PP_2, QQ_2 +// +(p9) fma.s1 FR_poly = FR_rsq, FR_poly, FR_PP_3 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +// +// if (i_1==0) poly = FR_rsq * poly + PP_3 +// else poly = FR_rsq * poly + QQ_3 +// Load PP_1_lo +// +(p9) fma.s1 FR_U_lo = FR_PP_1, FR_U_lo, f0 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +// +// if (i_1 =0) poly = poly * rsq + pp_r4 +// else poly = poly * rsq + qq_r4 +// +(p9) fma.s1 FR_U_hi = FR_r, f1, FR_U_hi + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +(p10) fma.s1 FR_poly = FR_rsq, FR_poly, FR_QQ_2 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +// +// if (i_1==0) U_lo = PP_1_hi * U_lo +// else U_lo = QQ_1 * U_lo +// +(p9) fma.s1 FR_poly = FR_rsq, FR_poly, FR_PP_2 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +// +// if (i_0==0) Result = 1 +// else Result = -1 +// + fma.s1 FR_V = FR_U_lo, f1, FR_corr + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +(p10) fma.s1 FR_poly = FR_rsq, FR_poly, f0 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +// +// if (i_1==0) poly = FR_rsq * poly + PP_2 +// else poly = FR_rsq * poly + QQ_2 +// +(p9) fma.s1 FR_poly = FR_rsq, FR_poly, FR_PP_1_lo + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +(p10) fma.s1 FR_poly = FR_rsq, FR_poly, f0 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +// +// V = U_lo + corr +// +(p9) fma.s1 FR_poly = FR_r_cubed, FR_poly, f0 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +// +// if (i_1==0) poly = r_cube * poly +// else poly = FR_rsq * poly +// + fma.s1 FR_V = FR_poly, f1, FR_V + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +//(p12) fms.s1 FR_Input_X = FR_Input_X, FR_U_hi, FR_V +(p12) fms.s1 FR_Input_X = FR_prelim, FR_U_hi, FR_V + nop.i 999 +} + +{ .mfb + nop.m 999 +// +// V = V + poly +// +//(p11) fma.s1 FR_Input_X = FR_Input_X, FR_U_hi, FR_V +(p11) fma.s1 FR_Input_X = FR_prelim, FR_U_hi, FR_V +// +// if (i_0==0) Result = Result * U_hi + V +// else Result = Result * U_hi - V +// + br.ret.sptk b0 ;; +} + +// +// If cosine, FR_Input_X = 1 +// If sine, FR_Input_X = +/-Zero (Input FR_Input_X) +// Results are exact, no exceptions +// +SINCOS_ZERO: + +{ .mmb + cmp.eq.unc p6, p7 = 0x1, GR_Sin_or_Cos + nop.m 999 + nop.b 999 ;; +} + +{ .mfi + nop.m 999 +(p7) fmerge.s FR_Input_X = FR_Input_X, FR_Input_X + nop.i 999 +} + +{ .mfb + nop.m 999 +(p6) fmerge.s FR_Input_X = f1, f1 + br.ret.sptk b0 ;; +} + +SINCOS_SPECIAL: + +// +// Path for Arg = +/- QNaN, SNaN, Inf +// Invalid can be raised. SNaNs +// become QNaNs +// + +{ .mfb + nop.m 999 + fmpy.s1 FR_Input_X = FR_Input_X, f0 + br.ret.sptk b0 ;; +} +GLOBAL_LIBM_END(__libm_cos_large) + + +// ******************************************************************* +// ******************************************************************* +// ******************************************************************* +// +// Special Code to handle very large argument case. +// Call int __libm_pi_by_2_reduce(x,r,c) for |arguments| >= 2**63 +// The interface is custom: +// On input: +// (Arg or x) is in f8 +// On output: +// r is in f8 +// c is in f9 +// N is in r8 +// Be sure to allocate at least 2 GP registers as output registers for +// __libm_pi_by_2_reduce. This routine uses r49-50. These are used as +// scratch registers within the __libm_pi_by_2_reduce routine (for speed). +// +// We know also that __libm_pi_by_2_reduce preserves f10-15, f71-127. We +// use this to eliminate save/restore of key fp registers in this calling +// function. +// +// ******************************************************************* +// ******************************************************************* +// ******************************************************************* + +LOCAL_LIBM_ENTRY(__libm_callout_2) +SINCOS_ARG_TOO_LARGE: + +.prologue +// Readjust Table ptr +{ .mfi + adds GR_Table_Base1 = -16, GR_Table_Base1 + nop.f 999 +.save ar.pfs,GR_SAVE_PFS + mov GR_SAVE_PFS=ar.pfs // Save ar.pfs +};; + +{ .mmi + ldfs FR_Two_to_M3 = [GR_Table_Base1],4 + mov GR_SAVE_GP=gp // Save gp +.save b0, GR_SAVE_B0 + mov GR_SAVE_B0=b0 // Save b0 +};; + +.body +// +// Call argument reduction with x in f8 +// Returns with N in r8, r in f8, c in f9 +// Assumes f71-127 are preserved across the call +// +{ .mib + ldfs FR_Neg_Two_to_M3 = [GR_Table_Base1],0 + nop.i 0 + br.call.sptk b0=__libm_pi_by_2_reduce# +};; + +{ .mfi + add GR_N_Inc = GR_Sin_or_Cos,r8 + fcmp.lt.unc.s1 p6, p0 = FR_r, FR_Two_to_M3 + mov b0 = GR_SAVE_B0 // Restore return address +};; + +{ .mfi + mov gp = GR_SAVE_GP // Restore gp +(p6) fcmp.gt.unc.s1 p6, p0 = FR_r, FR_Neg_Two_to_M3 + mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs +};; + +{ .mbb + nop.m 999 +(p6) br.cond.spnt SINCOS_SMALL_R // Branch if |r| < 1/4 + br.cond.sptk SINCOS_NORMAL_R ;; // Branch if 1/4 <= |r| < pi/4 +} + +LOCAL_LIBM_END(__libm_callout_2) + +.type __libm_pi_by_2_reduce#,@function +.global __libm_pi_by_2_reduce# + |