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| author | Ulrich Drepper <drepper@gmail.com> | 2012-01-07 11:19:05 -0500 |
|---|---|---|
| committer | Ulrich Drepper <drepper@gmail.com> | 2012-01-07 11:19:05 -0500 |
| commit | d75a0a62b12c35ee85f786d5f8d155ab39909411 (patch) | |
| tree | c3479d23878ef4ab05629d4a60f4f7623269c1dd /sysdeps/ia64/fpu/s_tanl.S | |
| parent | dcc9756b5bfbb2b97f73bad863d7e1c4002bea98 (diff) | |
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Remove IA-64 support
Diffstat (limited to 'sysdeps/ia64/fpu/s_tanl.S')
| -rw-r--r-- | sysdeps/ia64/fpu/s_tanl.S | 3248 |
1 files changed, 0 insertions, 3248 deletions
diff --git a/sysdeps/ia64/fpu/s_tanl.S b/sysdeps/ia64/fpu/s_tanl.S deleted file mode 100644 index 607a271545..0000000000 --- a/sysdeps/ia64/fpu/s_tanl.S +++ /dev/null @@ -1,3248 +0,0 @@ -.file "tancotl.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: -// -// 02/02/00 (hand-optimized) -// 04/04/00 Unwind support added -// 12/28/00 Fixed false invalid flags -// 02/06/02 Improved speed -// 05/07/02 Changed interface to __libm_pi_by_2_reduce -// 05/30/02 Added cotl -// 02/10/03 Reordered header: .section, .global, .proc, .align; -// used data8 for long double table values -// 05/15/03 Reformatted data tables -// 10/26/04 Avoided using r14-31 as scratch so not clobbered by dynamic loader -// -//********************************************************************* -// -// Functions: tanl(x) = tangent(x), for double-extended precision x values -// cotl(x) = cotangent(x), for double-extended precision x values -// -//********************************************************************* -// -// Resources Used: -// -// Floating-Point Registers: f8 (Input and Return Value) -// f9-f15 -// f32-f121 -// -// General Purpose Registers: -// r32-r70 -// -// Predicate Registers: p6-p15 -// -//********************************************************************* -// -// IEEE Special Conditions for tanl: -// -// Denormal fault raised on denormal inputs -// Overflow exceptions do not occur -// Underflow exceptions raised when appropriate for tan -// (No specialized error handling for this routine) -// Inexact raised when appropriate by algorithm -// -// tanl(SNaN) = QNaN -// tanl(QNaN) = QNaN -// tanl(inf) = QNaN -// tanl(+/-0) = +/-0 -// -//********************************************************************* -// -// IEEE Special Conditions for cotl: -// -// Denormal fault raised on denormal inputs -// Overflow exceptions occur at zero and near zero -// Underflow exceptions do not occur -// Inexact raised when appropriate by algorithm -// -// cotl(SNaN) = QNaN -// cotl(QNaN) = QNaN -// cotl(inf) = QNaN -// cotl(+/-0) = +/-Inf and error handling is called -// -//********************************************************************* -// -// Below are mathematical and algorithmic descriptions for tanl. -// For cotl we use next identity cot(x) = -tan(x + Pi/2). -// So, to compute cot(x) we just need to increment N (N = N + 1) -// and invert sign of the computed result. -// -//********************************************************************* -// -// Mathematical Description -// -// We consider the computation of FPTANL of Arg. Now, given -// -// Arg = N pi/2 + alpha, |alpha| <= pi/4, -// -// basic mathematical relationship shows that -// -// tan( Arg ) = tan( alpha ) if N is even; -// = -cot( alpha ) otherwise. -// -// 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, tan(r+c) and -cot(r+c) can be -// computed very easily by 2 or 3 terms of the Taylor series -// expansion as follows: -// -// Case 2: -// ------- -// -// tan(r + c) = r + c + r^3/3 ...accurately -// -cot(r + c) = -1/(r+c) + r/3 ...accurately -// -// Case 4: -// ------- -// -// tan(r + c) = r + c + r^3/3 + 2r^5/15 ...accurately -// -cot(r + c) = -1/(r+c) + r/3 + r^3/45 ...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 greatest challenge of this task is that the second terms of -// the Taylor series for tan(r) and -cot(r) -// -// r + r^3/3 + 2 r^5/15 + ... -// -// and -// -// -1/r + r/3 + r^3/45 + ... -// -// 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^(-2), however, the second terms will be small -// enough (5 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 tan(r) and cot(r), |r| <= pi/4. -// -// Case small_r: |r| < 2^(-2) -// -------------------------- -// -// Since Arg = N pi/4 + r + c accurately, we have -// -// tan(Arg) = tan(r+c) for N even, -// = -cot(r+c) otherwise. -// -// Here for this case, both tan(r) and -cot(r) can be approximated -// by simple polynomials: -// -// tan(r) = r + P1_1 r^3 + P1_2 r^5 + ... + P1_9 r^19 -// -cot(r) = -1/r + Q1_1 r + Q1_2 r^3 + ... + Q1_7 r^13 -// -// accurately. Since |r| is relatively small, tan(r+c) and -// -cot(r+c) can be accurately approximated by replacing r with -// r+c only in the first two terms of the corresponding polynomials. -// -// Note that P1_1 (and Q1_1 for that matter) approximates 1/3 to -// almost 64 sig. bits, thus -// -// P1_1 (r+c)^3 = P1_1 r^3 + c * r^2 accurately. -// -// Hence, -// -// tan(r+c) = r + P1_1 r^3 + P1_2 r^5 + ... + P1_9 r^19 -// + c*(1 + r^2) -// -// -cot(r+c) = -1/(r+c) + Q1_1 r + Q1_2 r^3 + ... + Q1_7 r^13 -// + Q1_1*c -// -// -// Case normal_r: 2^(-2) <= |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]. -// -// The required calculation is either -// -// tan(r + c) = tan(r) + correction, or -// -cot(r + c) = -cot(r) + correction. -// -// Specifically, -// -// tan(r + c) = tan(r) + c tan'(r) + O(c^2) -// = tan(r) + c sec^2(r) + O(c^2) -// = tan(r) + c SEC_sq ...accurately -// as long as SEC_sq approximates sec^2(r) -// to, say, 5 bits or so. -// -// Similarly, -// -// -cot(r + c) = -cot(r) - c cot'(r) + O(c^2) -// = -cot(r) + c csc^2(r) + O(c^2) -// = -cot(r) + c CSC_sq ...accurately -// as long as CSC_sq approximates csc^2(r) -// to, say, 5 bits or so. -// -// We therefore concentrate on accurately calculating tan(r) and -// cot(r) for a working-precision number r, |r| <= pi/4 to within -// 0.1% or so. -// -// We will employ a table-driven approach. Let -// -// r = sgn_r * 2^k * 1.b_1 b_2 ... b_5 ... b_63 -// = sgn_r * ( B + x ) -// -// where -// -// B = 2^k * 1.b_1 b_2 ... b_5 1 -// x = |r| - B -// -// Now, -// tan(B) + tan(x) -// tan( B + x ) = ------------------------ -// 1 - tan(B)*tan(x) -// -// / \ -// | tan(B) + tan(x) | - -// = tan(B) + | ------------------------ - tan(B) | -// | 1 - tan(B)*tan(x) | -// \ / -// -// sec^2(B) * tan(x) -// = tan(B) + ------------------------ -// 1 - tan(B)*tan(x) -// -// (1/[sin(B)*cos(B)]) * tan(x) -// = tan(B) + -------------------------------- -// cot(B) - tan(x) -// -// -// Clearly, the values of tan(B), cot(B) and 1/(sin(B)*cos(B)) are -// calculated beforehand and stored in a table. Since -// -// |x| <= 2^k * 2^(-6) <= 2^(-7) (because k = -1, -2) -// -// a very short polynomial will be sufficient to approximate tan(x) -// accurately. The details involved in computing the last expression -// will be given in the next section on algorithm description. -// -// -// Now, we turn to the case where cot( B + x ) is needed. -// -// -// 1 - tan(B)*tan(x) -// cot( B + x ) = ------------------------ -// tan(B) + tan(x) -// -// / \ -// | 1 - tan(B)*tan(x) | - -// = cot(B) + | ----------------------- - cot(B) | -// | tan(B) + tan(x) | -// \ / -// -// [tan(B) + cot(B)] * tan(x) -// = cot(B) - ---------------------------- -// tan(B) + tan(x) -// -// (1/[sin(B)*cos(B)]) * tan(x) -// = cot(B) - -------------------------------- -// tan(B) + tan(x) -// -// -// Note that the values of tan(B), cot(B) and 1/(sin(B)*cos(B)) that -// are needed are the same set of values needed in the previous -// case. -// -// Finally, we can put all the ingredients together as follows: -// -// Arg = N * pi/2 + r + c ...accurately -// -// tan(Arg) = tan(r) + correction if N is even; -// = -cot(r) + correction otherwise. -// -// For Cases 2 and 4, -// -// Case 2: -// tan(Arg) = tan(r + c) = r + c + r^3/3 N even -// = -cot(r + c) = -1/(r+c) + r/3 N odd -// Case 4: -// tan(Arg) = tan(r + c) = r + c + r^3/3 + 2r^5/15 N even -// = -cot(r + c) = -1/(r+c) + r/3 + r^3/45 N odd -// -// -// For Cases 1 and 3, -// -// Case small_r: |r| < 2^(-2) -// -// tan(Arg) = r + P1_1 r^3 + P1_2 r^5 + ... + P1_9 r^19 -// + c*(1 + r^2) N even -// -// = -1/(r+c) + Q1_1 r + Q1_2 r^3 + ... + Q1_7 r^13 -// + Q1_1*c N odd -// -// Case normal_r: 2^(-2) <= |r| <= pi/4 -// -// tan(Arg) = tan(r) + c * sec^2(r) N even -// = -cot(r) + c * csc^2(r) otherwise -// -// For N even, -// -// tan(Arg) = tan(r) + c*sec^2(r) -// = tan( sgn_r * (B+x) ) + c * sec^2(|r|) -// = sgn_r * ( tan(B+x) + sgn_r*c*sec^2(|r|) ) -// = sgn_r * ( tan(B+x) + sgn_r*c*sec^2(B) ) -// -// since B approximates |r| to 2^(-6) in relative accuracy. -// -// / (1/[sin(B)*cos(B)]) * tan(x) -// tan(Arg) = sgn_r * | tan(B) + -------------------------------- -// \ cot(B) - tan(x) -// \ -// + CORR | - -// / -// where -// -// CORR = sgn_r*c*tan(B)*SC_inv(B); SC_inv(B) = 1/(sin(B)*cos(B)). -// -// For N odd, -// -// tan(Arg) = -cot(r) + c*csc^2(r) -// = -cot( sgn_r * (B+x) ) + c * csc^2(|r|) -// = sgn_r * ( -cot(B+x) + sgn_r*c*csc^2(|r|) ) -// = sgn_r * ( -cot(B+x) + sgn_r*c*csc^2(B) ) -// -// since B approximates |r| to 2^(-6) in relative accuracy. -// -// / (1/[sin(B)*cos(B)]) * tan(x) -// tan(Arg) = sgn_r * | -cot(B) + -------------------------------- -// \ tan(B) + tan(x) -// \ -// + CORR | - -// / -// where -// -// CORR = sgn_r*c*cot(B)*SC_inv(B); SC_inv(B) = 1/(sin(B)*cos(B)). -// -// -// The actual algorithm prescribes how all the mathematical formulas -// are calculated. -// -// -// 2. Algorithmic Description -// ========================== -// -// 2.1 Computation for Cases 2 and 4. -// ---------------------------------- -// -// For Case 2, we use two-term polynomials. -// -// For N even, -// -// rsq := r * r -// Poly := c + r * rsq * P1_1 -// Result := r + Poly ...in user-defined rounding -// -// For N odd, -// S_hi := -frcpa(r) ...8 bits -// S_hi := S_hi + S_hi*(1 + S_hi*r) ...16 bits -// S_hi := S_hi + S_hi*(1 + S_hi*r) ...32 bits -// S_hi := S_hi + S_hi*(1 + S_hi*r) ...64 bits -// S_lo := S_hi*( (1 + S_hi*r) + S_hi*c ) -// ...S_hi + S_lo is -1/(r+c) to extra precision -// S_lo := S_lo + Q1_1*r -// -// Result := S_hi + S_lo ...in user-defined rounding -// -// For Case 4, we use three-term polynomials -// -// For N even, -// -// rsq := r * r -// Poly := c + r * rsq * (P1_1 + rsq * P1_2) -// Result := r + Poly ...in user-defined rounding -// -// For N odd, -// S_hi := -frcpa(r) ...8 bits -// S_hi := S_hi + S_hi*(1 + S_hi*r) ...16 bits -// S_hi := S_hi + S_hi*(1 + S_hi*r) ...32 bits -// S_hi := S_hi + S_hi*(1 + S_hi*r) ...64 bits -// S_lo := S_hi*( (1 + S_hi*r) + S_hi*c ) -// ...S_hi + S_lo is -1/(r+c) to extra precision -// rsq := r * r -// P := Q1_1 + rsq*Q1_2 -// S_lo := S_lo + r*P -// -// Result := S_hi + S_lo ...in user-defined rounding -// -// -// Note that the coefficients P1_1, P1_2, Q1_1, and Q1_2 are -// the same as those used in the small_r case of Cases 1 and 3 -// below. -// -// -// 2.2 Computation for Cases 1 and 3. -// ---------------------------------- -// This is further divided into the case of small_r, -// where |r| < 2^(-2), and the case of normal_r, where |r| lies between -// 2^(-2) and pi/4. -// -// Algorithm for the case of small_r -// --------------------------------- -// -// For N even, -// rsq := r * r -// Poly1 := rsq*(P1_1 + rsq*(P1_2 + rsq*P1_3)) -// r_to_the_8 := rsq * rsq -// r_to_the_8 := r_to_the_8 * r_to_the_8 -// Poly2 := P1_4 + rsq*(P1_5 + rsq*(P1_6 + ... rsq*P1_9)) -// CORR := c * ( 1 + rsq ) -// Poly := Poly1 + r_to_the_8*Poly2 -// Poly := r*Poly + CORR -// Result := r + Poly ...in user-defined rounding -// ...note that Poly1 and r_to_the_8 can be computed in parallel -// ...with Poly2 (Poly1 is intentionally set to be much -// ...shorter than Poly2 so that r_to_the_8 and CORR can be hidden) -// -// For N odd, -// S_hi := -frcpa(r) ...8 bits -// S_hi := S_hi + S_hi*(1 + S_hi*r) ...16 bits -// S_hi := S_hi + S_hi*(1 + S_hi*r) ...32 bits -// S_hi := S_hi + S_hi*(1 + S_hi*r) ...64 bits -// S_lo := S_hi*( (1 + S_hi*r) + S_hi*c ) -// ...S_hi + S_lo is -1/(r+c) to extra precision -// S_lo := S_lo + Q1_1*c -// -// ...S_hi and S_lo are computed in parallel with -// ...the following -// rsq := r*r -// P := Q1_1 + rsq*(Q1_2 + rsq*(Q1_3 + ... + rsq*Q1_7)) -// -// Poly := r*P + S_lo -// Result := S_hi + Poly ...in user-defined rounding -// -// -// Algorithm for the case of normal_r -// ---------------------------------- -// -// Here, we first consider the computation of tan( r + c ). As -// presented in the previous section, -// -// tan( r + c ) = tan(r) + c * sec^2(r) -// = sgn_r * [ tan(B+x) + CORR ] -// CORR = sgn_r * c * tan(B) * 1/[sin(B)*cos(B)] -// -// because sec^2(r) = sec^(|r|), and B approximate |r| to 6.5 bits. -// -// tan( r + c ) = -// / (1/[sin(B)*cos(B)]) * tan(x) -// sgn_r * | tan(B) + -------------------------------- + -// \ cot(B) - tan(x) -// \ -// CORR | - -// / -// -// The values of tan(B), cot(B) and 1/(sin(B)*cos(B)) are -// calculated beforehand and stored in a table. Specifically, -// the table values are -// -// tan(B) as T_hi + T_lo; -// cot(B) as C_hi + C_lo; -// 1/[sin(B)*cos(B)] as SC_inv -// -// T_hi, C_hi are in double-precision memory format; -// T_lo, C_lo are in single-precision memory format; -// SC_inv is in extended-precision memory format. -// -// The value of tan(x) will be approximated by a short polynomial of -// the form -// -// tan(x) as x + x * P, where -// P = x^2 * (P2_1 + x^2 * (P2_2 + x^2 * P2_3)) -// -// Because |x| <= 2^(-7), cot(B) - x approximates cot(B) - tan(x) -// to a relative accuracy better than 2^(-20). Thus, a good -// initial guess of 1/( cot(B) - tan(x) ) to initiate the iterative -// division is: -// -// 1/(cot(B) - tan(x)) is approximately -// 1/(cot(B) - x) is -// tan(B)/(1 - x*tan(B)) is approximately -// T_hi / ( 1 - T_hi * x ) is approximately -// -// T_hi * [ 1 + (Thi * x) + (T_hi * x)^2 ] -// -// The calculation of tan(r+c) therefore proceed as follows: -// -// Tx := T_hi * x -// xsq := x * x -// -// V_hi := T_hi*(1 + Tx*(1 + Tx)) -// P := xsq * (P1_1 + xsq*(P1_2 + xsq*P1_3)) -// ...V_hi serves as an initial guess of 1/(cot(B) - tan(x)) -// ...good to about 20 bits of accuracy -// -// tanx := x + x*P -// D := C_hi - tanx -// ...D is a double precision denominator: cot(B) - tan(x) -// -// V_hi := V_hi + V_hi*(1 - V_hi*D) -// ....V_hi approximates 1/(cot(B)-tan(x)) to 40 bits -// -// V_lo := V_hi * ( [ (1 - V_hi*C_hi) + V_hi*tanx ] -// - V_hi*C_lo ) ...observe all order -// ...V_hi + V_lo approximates 1/(cot(B) - tan(x)) -// ...to extra accuracy -// -// ... SC_inv(B) * (x + x*P) -// ... tan(B) + ------------------------- + CORR -// ... cot(B) - (x + x*P) -// ... -// ... = tan(B) + SC_inv(B)*(x + x*P)*(V_hi + V_lo) + CORR -// ... -// -// Sx := SC_inv * x -// CORR := sgn_r * c * SC_inv * T_hi -// -// ...put the ingredients together to compute -// ... SC_inv(B) * (x + x*P) -// ... tan(B) + ------------------------- + CORR -// ... cot(B) - (x + x*P) -// ... -// ... = tan(B) + SC_inv(B)*(x + x*P)*(V_hi + V_lo) + CORR -// ... -// ... = T_hi + T_lo + CORR + -// ... Sx * V_hi + Sx * V_lo + Sx * P *(V_hi + V_lo) -// -// CORR := CORR + T_lo -// tail := V_lo + P*(V_hi + V_lo) -// tail := Sx * tail + CORR -// tail := Sx * V_hi + tail -// T_hi := sgn_r * T_hi -// -// ...T_hi + sgn_r*tail now approximate -// ...sgn_r*(tan(B+x) + CORR) accurately -// -// Result := T_hi + sgn_r*tail ...in user-defined -// ...rounding control -// ...It is crucial that independent paths be fully -// ...exploited for performance's sake. -// -// -// Next, we consider the computation of -cot( r + c ). As -// presented in the previous section, -// -// -cot( r + c ) = -cot(r) + c * csc^2(r) -// = sgn_r * [ -cot(B+x) + CORR ] -// CORR = sgn_r * c * cot(B) * 1/[sin(B)*cos(B)] -// -// because csc^2(r) = csc^(|r|), and B approximate |r| to 6.5 bits. -// -// -cot( r + c ) = -// / (1/[sin(B)*cos(B)]) * tan(x) -// sgn_r * | -cot(B) + -------------------------------- + -// \ tan(B) + tan(x) -// \ -// CORR | - -// / -// -// The values of tan(B), cot(B) and 1/(sin(B)*cos(B)) are -// calculated beforehand and stored in a table. Specifically, -// the table values are -// -// tan(B) as T_hi + T_lo; -// cot(B) as C_hi + C_lo; -// 1/[sin(B)*cos(B)] as SC_inv -// -// T_hi, C_hi are in double-precision memory format; -// T_lo, C_lo are in single-precision memory format; -// SC_inv is in extended-precision memory format. -// -// The value of tan(x) will be approximated by a short polynomial of -// the form -// -// tan(x) as x + x * P, where -// P = x^2 * (P2_1 + x^2 * (P2_2 + x^2 * P2_3)) -// -// Because |x| <= 2^(-7), tan(B) + x approximates tan(B) + tan(x) -// to a relative accuracy better than 2^(-18). Thus, a good -// initial guess of 1/( tan(B) + tan(x) ) to initiate the iterative -// division is: -// -// 1/(tan(B) + tan(x)) is approximately -// 1/(tan(B) + x) is -// cot(B)/(1 + x*cot(B)) is approximately -// C_hi / ( 1 + C_hi * x ) is approximately -// -// C_hi * [ 1 - (C_hi * x) + (C_hi * x)^2 ] -// -// The calculation of -cot(r+c) therefore proceed as follows: -// -// Cx := C_hi * x -// xsq := x * x -// -// V_hi := C_hi*(1 - Cx*(1 - Cx)) -// P := xsq * (P1_1 + xsq*(P1_2 + xsq*P1_3)) -// ...V_hi serves as an initial guess of 1/(tan(B) + tan(x)) -// ...good to about 18 bits of accuracy -// -// tanx := x + x*P -// D := T_hi + tanx -// ...D is a double precision denominator: tan(B) + tan(x) -// -// V_hi := V_hi + V_hi*(1 - V_hi*D) -// ....V_hi approximates 1/(tan(B)+tan(x)) to 40 bits -// -// V_lo := V_hi * ( [ (1 - V_hi*T_hi) - V_hi*tanx ] -// - V_hi*T_lo ) ...observe all order -// ...V_hi + V_lo approximates 1/(tan(B) + tan(x)) -// ...to extra accuracy -// -// ... SC_inv(B) * (x + x*P) -// ... -cot(B) + ------------------------- + CORR -// ... tan(B) + (x + x*P) -// ... -// ... =-cot(B) + SC_inv(B)*(x + x*P)*(V_hi + V_lo) + CORR -// ... -// -// Sx := SC_inv * x -// CORR := sgn_r * c * SC_inv * C_hi -// -// ...put the ingredients together to compute -// ... SC_inv(B) * (x + x*P) -// ... -cot(B) + ------------------------- + CORR -// ... tan(B) + (x + x*P) -// ... -// ... =-cot(B) + SC_inv(B)*(x + x*P)*(V_hi + V_lo) + CORR -// ... -// ... =-C_hi - C_lo + CORR + -// ... Sx * V_hi + Sx * V_lo + Sx * P *(V_hi + V_lo) -// -// CORR := CORR - C_lo -// tail := V_lo + P*(V_hi + V_lo) -// tail := Sx * tail + CORR -// tail := Sx * V_hi + tail -// C_hi := -sgn_r * C_hi -// -// ...C_hi + sgn_r*tail now approximates -// ...sgn_r*(-cot(B+x) + CORR) accurately -// -// Result := C_hi + sgn_r*tail in user-defined rounding control -// ...It is crucial that independent paths be fully -// ...exploited for performance's sake. -// -// 3. Implementation Notes -// ======================= -// -// Table entries T_hi, T_lo; C_hi, C_lo; SC_inv -// -// Recall that 2^(-2) <= |r| <= pi/4; -// -// r = sgn_r * 2^k * 1.b_1 b_2 ... b_63 -// -// and -// -// B = 2^k * 1.b_1 b_2 b_3 b_4 b_5 1 -// -// Thus, for k = -2, possible values of B are -// -// B = 2^(-2) * ( 1 + index/32 + 1/64 ), -// index ranges from 0 to 31 -// -// For k = -1, however, since |r| <= pi/4 = 0.78... -// possible values of B are -// -// B = 2^(-1) * ( 1 + index/32 + 1/64 ) -// index ranges from 0 to 19. -// -// - -RODATA -.align 16 - -LOCAL_OBJECT_START(TANL_BASE_CONSTANTS) - -tanl_table_1: -data8 0xA2F9836E4E44152A, 0x00003FFE // two_by_pi -data8 0xC84D32B0CE81B9F1, 0x00004016 // P_0 -data8 0xC90FDAA22168C235, 0x00003FFF // P_1 -data8 0xECE675D1FC8F8CBB, 0x0000BFBD // P_2 -data8 0xB7ED8FBBACC19C60, 0x0000BF7C // P_3 -LOCAL_OBJECT_END(TANL_BASE_CONSTANTS) - -LOCAL_OBJECT_START(tanl_table_2) -data8 0xC90FDAA22168C234, 0x00003FFE // PI_BY_4 -data8 0xA397E5046EC6B45A, 0x00003FE7 // Inv_P_0 -data8 0x8D848E89DBD171A1, 0x0000BFBF // d_1 -data8 0xD5394C3618A66F8E, 0x0000BF7C // d_2 -data4 0x3E800000 // two**-2 -data4 0xBE800000 // -two**-2 -data4 0x00000000 // pad -data4 0x00000000 // pad -LOCAL_OBJECT_END(tanl_table_2) - -LOCAL_OBJECT_START(tanl_table_p1) -data8 0xAAAAAAAAAAAAAABD, 0x00003FFD // P1_1 -data8 0x8888888888882E6A, 0x00003FFC // P1_2 -data8 0xDD0DD0DD0F0177B6, 0x00003FFA // P1_3 -data8 0xB327A440646B8C6D, 0x00003FF9 // P1_4 -data8 0x91371B251D5F7D20, 0x00003FF8 // P1_5 -data8 0xEB69A5F161C67914, 0x00003FF6 // P1_6 -data8 0xBEDD37BE019318D2, 0x00003FF5 // P1_7 -data8 0x9979B1463C794015, 0x00003FF4 // P1_8 -data8 0x8EBD21A38C6EB58A, 0x00003FF3 // P1_9 -LOCAL_OBJECT_END(tanl_table_p1) - -LOCAL_OBJECT_START(tanl_table_q1) -data8 0xAAAAAAAAAAAAAAB4, 0x00003FFD // Q1_1 -data8 0xB60B60B60B5FC93E, 0x00003FF9 // Q1_2 -data8 0x8AB355E00C9BBFBF, 0x00003FF6 // Q1_3 -data8 0xDDEBBC89CBEE3D4C, 0x00003FF2 // Q1_4 -data8 0xB3548A685F80BBB6, 0x00003FEF // Q1_5 -data8 0x913625604CED5BF1, 0x00003FEC // Q1_6 -data8 0xF189D95A8EE92A83, 0x00003FE8 // Q1_7 -LOCAL_OBJECT_END(tanl_table_q1) - -LOCAL_OBJECT_START(tanl_table_p2) -data8 0xAAAAAAAAAAAB362F, 0x00003FFD // P2_1 -data8 0x88888886E97A6097, 0x00003FFC // P2_2 -data8 0xDD108EE025E716A1, 0x00003FFA // P2_3 -LOCAL_OBJECT_END(tanl_table_p2) - -LOCAL_OBJECT_START(tanl_table_tm2) -// -// Entries T_hi double-precision memory format -// Index = 0,1,...,31 B = 2^(-2)*(1+Index/32+1/64) -// Entries T_lo single-precision memory format -// Index = 0,1,...,31 B = 2^(-2)*(1+Index/32+1/64) -// -data8 0x3FD09BC362400794 -data4 0x23A05C32, 0x00000000 -data8 0x3FD124A9DFFBC074 -data4 0x240078B2, 0x00000000 -data8 0x3FD1AE235BD4920F -data4 0x23826B8E, 0x00000000 -data8 0x3FD2383515E2701D -data4 0x22D31154, 0x00000000 -data8 0x3FD2C2E463739C2D -data4 0x2265C9E2, 0x00000000 -data8 0x3FD34E36AFEEA48B -data4 0x245C05EB, 0x00000000 -data8 0x3FD3DA317DBB35D1 -data4 0x24749F2D, 0x00000000 -data8 0x3FD466DA67321619 -data4 0x2462CECE, 0x00000000 -data8 0x3FD4F4371F94A4D5 -data4 0x246D0DF1, 0x00000000 -data8 0x3FD5824D740C3E6D -data4 0x240A85B5, 0x00000000 -data8 0x3FD611234CB1E73D -data4 0x23F96E33, 0x00000000 -data8 0x3FD6A0BEAD9EA64B -data4 0x247C5393, 0x00000000 -data8 0x3FD73125B804FD01 -data4 0x241F3B29, 0x00000000 -data8 0x3FD7C25EAB53EE83 -data4 0x2479989B, 0x00000000 -data8 0x3FD8546FE6640EED -data4 0x23B343BC, 0x00000000 -data8 0x3FD8E75FE8AF1892 -data4 0x241454D1, 0x00000000 -data8 0x3FD97B3553928BDA -data4 0x238613D9, 0x00000000 -data8 0x3FDA0FF6EB9DE4DE -data4 0x22859FA7, 0x00000000 -data8 0x3FDAA5AB99ECF92D -data4 0x237A6D06, 0x00000000 -data8 0x3FDB3C5A6D8F1796 -data4 0x23952F6C, 0x00000000 -data8 0x3FDBD40A9CFB8BE4 -data4 0x2280FC95, 0x00000000 -data8 0x3FDC6CC387943100 -data4 0x245D2EC0, 0x00000000 -data8 0x3FDD068CB736C500 -data4 0x23C4AD7D, 0x00000000 -data8 0x3FDDA16DE1DDBC31 -data4 0x23D076E6, 0x00000000 -data8 0x3FDE3D6EEB515A93 -data4 0x244809A6, 0x00000000 -data8 0x3FDEDA97E6E9E5F1 -data4 0x220856C8, 0x00000000 -data8 0x3FDF78F11963CE69 -data4 0x244BE993, 0x00000000 -data8 0x3FE00C417D635BCE -data4 0x23D21799, 0x00000000 -data8 0x3FE05CAB1C302CD3 -data4 0x248A1B1D, 0x00000000 -data8 0x3FE0ADB9DB6A1FA0 -data4 0x23D53E33, 0x00000000 -data8 0x3FE0FF724A20BA81 -data4 0x24DB9ED5, 0x00000000 -data8 0x3FE151D9153FA6F5 -data4 0x24E9E451, 0x00000000 -LOCAL_OBJECT_END(tanl_table_tm2) - -LOCAL_OBJECT_START(tanl_table_tm1) -// -// Entries T_hi double-precision memory format -// Index = 0,1,...,19 B = 2^(-1)*(1+Index/32+1/64) -// Entries T_lo single-precision memory format -// Index = 0,1,...,19 B = 2^(-1)*(1+Index/32+1/64) -// -data8 0x3FE1CEC4BA1BE39E -data4 0x24B60F9E, 0x00000000 -data8 0x3FE277E45ABD9B2D -data4 0x248C2474, 0x00000000 -data8 0x3FE324180272B110 -data4 0x247B8311, 0x00000000 -data8 0x3FE3D38B890E2DF0 -data4 0x24C55751, 0x00000000 -data8 0x3FE4866D46236871 -data4 0x24E5BC34, 0x00000000 -data8 0x3FE53CEE45E044B0 -data4 0x24001BA4, 0x00000000 -data8 0x3FE5F74282EC06E4 -data4 0x24B973DC, 0x00000000 -data8 0x3FE6B5A125DF43F9 -data4 0x24895440, 0x00000000 -data8 0x3FE77844CAFD348C -data4 0x240021CA, 0x00000000 -data8 0x3FE83F6BCEED6B92 -data4 0x24C45372, 0x00000000 -data8 0x3FE90B58A34F3665 -data4 0x240DAD33, 0x00000000 -data8 0x3FE9DC522C1E56B4 -data4 0x24F846CE, 0x00000000 -data8 0x3FEAB2A427041578 -data4 0x2323FB6E, 0x00000000 -data8 0x3FEB8E9F9DD8C373 -data4 0x24B3090B, 0x00000000 -data8 0x3FEC709B65C9AA7B -data4 0x2449F611, 0x00000000 -data8 0x3FED58F4ACCF8435 -data4 0x23616A7E, 0x00000000 -data8 0x3FEE480F97635082 -data4 0x24C2FEAE, 0x00000000 -data8 0x3FEF3E57F0ACC544 -data4 0x242CE964, 0x00000000 -data8 0x3FF01E20F7E06E4B -data4 0x2480D3EE, 0x00000000 -data8 0x3FF0A1258A798A69 -data4 0x24DB8967, 0x00000000 -LOCAL_OBJECT_END(tanl_table_tm1) - -LOCAL_OBJECT_START(tanl_table_cm2) -// -// Entries C_hi double-precision memory format -// Index = 0,1,...,31 B = 2^(-2)*(1+Index/32+1/64) -// Entries C_lo single-precision memory format -// Index = 0,1,...,31 B = 2^(-2)*(1+Index/32+1/64) -// -data8 0x400ED3E2E63EFBD0 -data4 0x259D94D4, 0x00000000 -data8 0x400DDDB4C515DAB5 -data4 0x245F0537, 0x00000000 -data8 0x400CF57ABE19A79F -data4 0x25D4EA9F, 0x00000000 -data8 0x400C1A06D15298ED -data4 0x24AE40A0, 0x00000000 -data8 0x400B4A4C164B2708 -data4 0x25A5AAB6, 0x00000000 -data8 0x400A855A5285B068 -data4 0x25524F18, 0x00000000 -data8 0x4009CA5A3FFA549F -data4 0x24C999C0, 0x00000000 -data8 0x4009188A646AF623 -data4 0x254FD801, 0x00000000 -data8 0x40086F3C6084D0E7 -data4 0x2560F5FD, 0x00000000 -data8 0x4007CDD2A29A76EE -data4 0x255B9D19, 0x00000000 -data8 0x400733BE6C8ECA95 -data4 0x25CB021B, 0x00000000 -data8 0x4006A07E1F8DDC52 -data4 0x24AB4722, 0x00000000 -data8 0x4006139BC298AD58 -data4 0x252764E2, 0x00000000 -data8 0x40058CABBAD7164B -data4 0x24DAF5DB, 0x00000000 -data8 0x40050B4BAE31A5D3 -data4 0x25EA20F4, 0x00000000 -data8 0x40048F2189F85A8A -data4 0x2583A3E8, 0x00000000 -data8 0x400417DAA862380D -data4 0x25DCC4CC, 0x00000000 -data8 0x4003A52B1088FCFE -data4 0x2430A492, 0x00000000 -data8 0x400336CCCD3527D5 -data4 0x255F77CF, 0x00000000 -data8 0x4002CC7F5760766D -data4 0x25DA0BDA, 0x00000000 -data8 0x4002660711CE02E3 -data4 0x256FF4A2, 0x00000000 -data8 0x4002032CD37BBE04 -data4 0x25208AED, 0x00000000 -data8 0x4001A3BD7F050775 -data4 0x24B72DD6, 0x00000000 -data8 0x40014789A554848A -data4 0x24AB4DAA, 0x00000000 -data8 0x4000EE65323E81B7 -data4 0x2584C440, 0x00000000 -data8 0x4000982721CF1293 -data4 0x25C9428D, 0x00000000 -data8 0x400044A93D415EEB -data4 0x25DC8482, 0x00000000 -data8 0x3FFFE78FBD72C577 -data4 0x257F5070, 0x00000000 -data8 0x3FFF4AC375EFD28E -data4 0x23EBBF7A, 0x00000000 -data8 0x3FFEB2AF60B52DDE -data4 0x22EECA07, 0x00000000 -data8 0x3FFE1F1935204180 -data4 0x24191079, 0x00000000 -data8 0x3FFD8FCA54F7E60A -data4 0x248D3058, 0x00000000 -LOCAL_OBJECT_END(tanl_table_cm2) - -LOCAL_OBJECT_START(tanl_table_cm1) -// -// Entries C_hi double-precision memory format -// Index = 0,1,...,19 B = 2^(-1)*(1+Index/32+1/64) -// Entries C_lo single-precision memory format -// Index = 0,1,...,19 B = 2^(-1)*(1+Index/32+1/64) -// -data8 0x3FFCC06A79F6FADE -data4 0x239C7886, 0x00000000 -data8 0x3FFBB91F891662A6 -data4 0x250BD191, 0x00000000 -data8 0x3FFABFB6529F155D -data4 0x256CC3E6, 0x00000000 -data8 0x3FF9D3002E964AE9 -data4 0x250843E3, 0x00000000 -data8 0x3FF8F1EF89DCB383 -data4 0x2277C87E, 0x00000000 -data8 0x3FF81B937C87DBD6 -data4 0x256DA6CF, 0x00000000 -data8 0x3FF74F141042EDE4 -data4 0x2573D28A, 0x00000000 -data8 0x3FF68BAF1784B360 -data4 0x242E489A, 0x00000000 -data8 0x3FF5D0B57C923C4C -data4 0x2532D940, 0x00000000 -data8 0x3FF51D88F418EF20 -data4 0x253C7DD6, 0x00000000 -data8 0x3FF4719A02F88DAE -data4 0x23DB59BF, 0x00000000 -data8 0x3FF3CC6649DA0788 -data4 0x252B4756, 0x00000000 -data8 0x3FF32D770B980DB8 -data4 0x23FE585F, 0x00000000 -data8 0x3FF2945FE56C987A -data4 0x25378A63, 0x00000000 -data8 0x3FF200BDB16523F6 -data4 0x247BB2E0, 0x00000000 -data8 0x3FF172358CE27778 -data4 0x24446538, 0x00000000 -data8 0x3FF0E873FDEFE692 -data4 0x2514638F, 0x00000000 -data8 0x3FF0632C33154062 -data4 0x24A7FC27, 0x00000000 -data8 0x3FEFC42EB3EF115F -data4 0x248FD0FE, 0x00000000 -data8 0x3FEEC9E8135D26F6 -data4 0x2385C719, 0x00000000 -LOCAL_OBJECT_END(tanl_table_cm1) - -LOCAL_OBJECT_START(tanl_table_scim2) -// -// Entries SC_inv in Swapped IEEE format (extended) -// Index = 0,1,...,31 B = 2^(-2)*(1+Index/32+1/64) -// -data8 0x839D6D4A1BF30C9E, 0x00004001 -data8 0x80092804554B0EB0, 0x00004001 -data8 0xF959F94CA1CF0DE9, 0x00004000 -data8 0xF3086BA077378677, 0x00004000 -data8 0xED154515CCD4723C, 0x00004000 -data8 0xE77909441C27CF25, 0x00004000 -data8 0xE22D037D8DDACB88, 0x00004000 -data8 0xDD2B2D8A89C73522, 0x00004000 -data8 0xD86E1A23BB2C1171, 0x00004000 -data8 0xD3F0E288DFF5E0F9, 0x00004000 -data8 0xCFAF16B1283BEBD5, 0x00004000 -data8 0xCBA4AFAA0D88DD53, 0x00004000 -data8 0xC7CE03CCCA67C43D, 0x00004000 -data8 0xC427BC820CA0DDB0, 0x00004000 -data8 0xC0AECD57F13D8CAB, 0x00004000 -data8 0xBD606C3871ECE6B1, 0x00004000 -data8 0xBA3A0A96A44C4929, 0x00004000 -data8 0xB7394F6FE5CCCEC1, 0x00004000 -data8 0xB45C12039637D8BC, 0x00004000 -data8 0xB1A0552892CB051B, 0x00004000 -data8 0xAF04432B6BA2FFD0, 0x00004000 -data8 0xAC862A237221235F, 0x00004000 -data8 0xAA2478AF5F00A9D1, 0x00004000 -data8 0xA7DDBB0C81E082BF, 0x00004000 -data8 0xA5B0987D45684FEE, 0x00004000 -data8 0xA39BD0F5627A8F53, 0x00004000 -data8 0xA19E3B036EC5C8B0, 0x00004000 -data8 0x9FB6C1F091CD7C66, 0x00004000 -data8 0x9DE464101FA3DF8A, 0x00004000 -data8 0x9C263139A8F6B888, 0x00004000 -data8 0x9A7B4968C27B0450, 0x00004000 -data8 0x98E2DB7E5EE614EE, 0x00004000 -LOCAL_OBJECT_END(tanl_table_scim2) - -LOCAL_OBJECT_START(tanl_table_scim1) -// -// Entries SC_inv in Swapped IEEE format (extended) -// Index = 0,1,...,19 B = 2^(-1)*(1+Index/32+1/64) -// -data8 0x969F335C13B2B5BA, 0x00004000 -data8 0x93D446D9D4C0F548, 0x00004000 -data8 0x9147094F61B798AF, 0x00004000 -data8 0x8EF317CC758787AC, 0x00004000 -data8 0x8CD498B3B99EEFDB, 0x00004000 -data8 0x8AE82A7DDFF8BC37, 0x00004000 -data8 0x892AD546E3C55D42, 0x00004000 -data8 0x8799FEA9D15573C1, 0x00004000 -data8 0x86335F88435A4B4C, 0x00004000 -data8 0x84F4FB6E3E93A87B, 0x00004000 -data8 0x83DD195280A382FB, 0x00004000 -data8 0x82EA3D7FA4CB8C9E, 0x00004000 -data8 0x821B247C6861D0A8, 0x00004000 -data8 0x816EBED163E8D244, 0x00004000 -data8 0x80E42D9127E4CFC6, 0x00004000 -data8 0x807ABF8D28E64AFD, 0x00004000 -data8 0x8031EF26863B4FD8, 0x00004000 -data8 0x800960ADAE8C11FD, 0x00004000 -data8 0x8000E1475FDBEC21, 0x00004000 -data8 0x80186650A07791FA, 0x00004000 -LOCAL_OBJECT_END(tanl_table_scim1) - -Arg = f8 -Save_Norm_Arg = f8 // For input to reduction routine -Result = f8 -r = f8 // For output from reduction routine -c = f9 // For output from reduction routine -U_2 = f10 -rsq = f11 -C_hi = f12 -C_lo = f13 -T_hi = f14 -T_lo = f15 - -d_1 = f33 -N_0 = f34 -tail = f35 -tanx = f36 -Cx = f37 -Sx = f38 -sgn_r = f39 -CORR = f40 -P = f41 -D = f42 -ArgPrime = f43 -P_0 = f44 - -P2_1 = f45 -P2_2 = f46 -P2_3 = f47 - -P1_1 = f45 -P1_2 = f46 -P1_3 = f47 - -P1_4 = f48 -P1_5 = f49 -P1_6 = f50 -P1_7 = f51 -P1_8 = f52 -P1_9 = f53 - -x = f56 -xsq = f57 -Tx = f58 -Tx1 = f59 -Set = f60 -poly1 = f61 -poly2 = f62 -Poly = f63 -Poly1 = f64 -Poly2 = f65 -r_to_the_8 = f66 -B = f67 -SC_inv = f68 -Pos_r = f69 -N_0_fix = f70 -d_2 = f71 -PI_BY_4 = f72 -TWO_TO_NEG14 = f74 -TWO_TO_NEG33 = f75 -NEGTWO_TO_NEG14 = f76 -NEGTWO_TO_NEG33 = f77 -two_by_PI = f78 -N = f79 -N_fix = f80 -P_1 = f81 -P_2 = f82 -P_3 = f83 -s_val = f84 -w = f85 -B_mask1 = f86 -B_mask2 = f87 -w2 = f88 -A = f89 -a = f90 -t = f91 -U_1 = f92 -NEGTWO_TO_NEG2 = f93 -TWO_TO_NEG2 = f94 -Q1_1 = f95 -Q1_2 = f96 -Q1_3 = f97 -Q1_4 = f98 -Q1_5 = f99 -Q1_6 = f100 -Q1_7 = f101 -Q1_8 = f102 -S_hi = f103 -S_lo = f104 -V_hi = f105 -V_lo = f106 -U_hi = f107 -U_lo = f108 -U_hiabs = f109 -V_hiabs = f110 -V = f111 -Inv_P_0 = f112 - -FR_inv_pi_2to63 = f113 -FR_rshf_2to64 = f114 -FR_2tom64 = f115 -FR_rshf = f116 -Norm_Arg = f117 -Abs_Arg = f118 -TWO_TO_NEG65 = f119 -fp_tmp = f120 -mOne = f121 - -GR_SAVE_B0 = r33 -GR_SAVE_GP = r34 -GR_SAVE_PFS = r35 -table_base = r36 -table_ptr1 = r37 -table_ptr2 = r38 -table_ptr3 = r39 -lookup = r40 -N_fix_gr = r41 -GR_exp_2tom2 = r42 -GR_exp_2tom65 = r43 -exp_r = r44 -sig_r = r45 -bmask1 = r46 -table_offset = r47 -bmask2 = r48 -gr_tmp = r49 -cot_flag = r50 - -GR_sig_inv_pi = r51 -GR_rshf_2to64 = r52 -GR_exp_2tom64 = r53 -GR_rshf = r54 -GR_exp_2_to_63 = r55 -GR_exp_2_to_24 = r56 -GR_signexp_x = r57 -GR_exp_x = r58 -GR_exp_mask = r59 -GR_exp_2tom14 = r60 -GR_exp_m2tom14 = r61 -GR_exp_2tom33 = r62 -GR_exp_m2tom33 = r63 - -GR_SAVE_B0 = r64 -GR_SAVE_PFS = r65 -GR_SAVE_GP = r66 - -GR_Parameter_X = r67 -GR_Parameter_Y = r68 -GR_Parameter_RESULT = r69 -GR_Parameter_Tag = r70 - - -.section .text -.global __libm_tanl# -.global __libm_cotl# - -.proc __libm_cotl# -__libm_cotl: -.endp __libm_cotl# -LOCAL_LIBM_ENTRY(cotl) - -{ .mlx - alloc r32 = ar.pfs, 0,35,4,0 - movl GR_sig_inv_pi = 0xa2f9836e4e44152a // significand of 1/pi -} -{ .mlx - mov GR_exp_mask = 0x1ffff // Exponent mask - movl GR_rshf_2to64 = 0x47e8000000000000 // 1.1000 2^(63+64) -} -;; - -// Check for NatVals, Infs , NaNs, and Zeros -{ .mfi - getf.exp GR_signexp_x = Arg // Get sign and exponent of x - fclass.m p6,p0 = Arg, 0x1E7 // Test for natval, nan, inf, zero - mov cot_flag = 0x1 -} -{ .mfb - addl table_base = @ltoff(TANL_BASE_CONSTANTS), gp // Pointer to table ptr - fnorm.s1 Norm_Arg = Arg // Normalize x - br.cond.sptk COMMON_PATH -};; - -LOCAL_LIBM_END(cotl) - - -.proc __libm_tanl# -__libm_tanl: -.endp __libm_tanl# -GLOBAL_IEEE754_ENTRY(tanl) - -{ .mlx - alloc r32 = ar.pfs, 0,35,4,0 - movl GR_sig_inv_pi = 0xa2f9836e4e44152a // significand of 1/pi -} -{ .mlx - mov GR_exp_mask = 0x1ffff // Exponent mask - movl GR_rshf_2to64 = 0x47e8000000000000 // 1.1000 2^(63+64) -} -;; - -// Check for NatVals, Infs , NaNs, and Zeros -{ .mfi - getf.exp GR_signexp_x = Arg // Get sign and exponent of x - fclass.m p6,p0 = Arg, 0x1E7 // Test for natval, nan, inf, zero - mov cot_flag = 0x0 -} -{ .mfi - addl table_base = @ltoff(TANL_BASE_CONSTANTS), gp // Pointer to table ptr - fnorm.s1 Norm_Arg = Arg // Normalize x - nop.i 0 -};; - -// Common path for both tanl and cotl -COMMON_PATH: -{ .mfi - setf.sig FR_inv_pi_2to63 = GR_sig_inv_pi // Form 1/pi * 2^63 - fclass.m p9, p0 = Arg, 0x0b // Test x denormal - 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 -} -;; - -// Check for everything - if false, then must be pseudo-zero or pseudo-nan. -// Branch out to deal with special values. -{ .mfi - addl gr_tmp = -1,r0 - fclass.nm p7,p0 = Arg, 0x1FF // Test x unsupported - mov GR_exp_2_to_63 = 0xffff + 63 // Exponent of 2^63 -} -{ .mfb - ld8 table_base = [table_base] // Get pointer to constant table - fms.s1 mOne = f0, f0, f1 -(p6) br.cond.spnt TANL_SPECIAL // Branch if x natval, nan, inf, zero -} -;; - -{ .mmb - setf.sig fp_tmp = gr_tmp // Make a constant so fmpy produces inexact - mov GR_exp_2_to_24 = 0xffff + 24 // Exponent of 2^24 -(p9) br.cond.spnt TANL_DENORMAL // Branch if x denormal -} -;; - -TANL_COMMON: -// Return to here if x denormal -// -// Do fcmp to generate Denormal exception -// - can't do FNORM (will generate Underflow when U is unmasked!) -// Branch out to deal with unsupporteds values. -{ .mfi - setf.exp FR_2tom64 = GR_exp_2tom64 // Form 2^-64 for scaling N_float - fcmp.eq.s0 p0, p6 = Arg, f1 // Dummy to flag denormals - add table_ptr1 = 0, table_base // Point to tanl_table_1 -} -{ .mib - setf.d FR_rshf = GR_rshf // Form right shift const 1.1000 * 2^63 - add table_ptr2 = 80, table_base // Point to tanl_table_2 -(p7) br.cond.spnt TANL_UNSUPPORTED // Branch if x unsupported type -} -;; - -{ .mfi - and GR_exp_x = GR_exp_mask, GR_signexp_x // Get exponent of x - fmpy.s1 Save_Norm_Arg = Norm_Arg, f1 // Save x if large arg reduction - dep.z bmask1 = 0x7c, 56, 8 // Form mask to get 5 msb of r - // bmask1 = 0x7c00000000000000 -} -;; - -// -// Decide about the paths to take: -// Set PR_6 if |Arg| >= 2**63 -// Set PR_9 if |Arg| < 2**24 - CASE 1 OR 2 -// OTHERWISE Set PR_8 - CASE 3 OR 4 -// -// Branch out if the magnitude of the input argument is >= 2^63 -// - do this branch before the next. -{ .mfi - ldfe two_by_PI = [table_ptr1],16 // Load 2/pi - nop.f 999 - dep.z bmask2 = 0x41, 57, 7 // Form mask to OR to produce B - // bmask2 = 0x8200000000000000 -} -{ .mib - ldfe PI_BY_4 = [table_ptr2],16 // Load pi/4 - cmp.ge p6,p0 = GR_exp_x, GR_exp_2_to_63 // Is |x| >= 2^63 -(p6) br.cond.spnt TANL_ARG_TOO_LARGE // Branch if |x| >= 2^63 -} -;; - -{ .mmi - ldfe P_0 = [table_ptr1],16 // Load P_0 - ldfe Inv_P_0 = [table_ptr2],16 // Load Inv_P_0 - nop.i 999 -} -;; - -{ .mfi - ldfe P_1 = [table_ptr1],16 // Load P_1 - fmerge.s Abs_Arg = f0, Norm_Arg // Get |x| - mov GR_exp_m2tom33 = 0x2ffff - 33 // Form signexp of -2^-33 -} -{ .mfi - ldfe d_1 = [table_ptr2],16 // Load d_1 for 2^24 <= |x| < 2^63 - nop.f 999 - mov GR_exp_2tom33 = 0xffff - 33 // Form signexp of 2^-33 -} -;; - -{ .mmi - ldfe P_2 = [table_ptr1],16 // Load P_2 - ldfe d_2 = [table_ptr2],16 // Load d_2 for 2^24 <= |x| < 2^63 - cmp.ge p8,p0 = GR_exp_x, GR_exp_2_to_24 // Is |x| >= 2^24 -} -;; - -// Use special scaling to right shift so N=Arg * 2/pi is in rightmost bits -// Branch to Cases 3 or 4 if Arg <= -2**24 or Arg >= 2**24 -{ .mfb - ldfe P_3 = [table_ptr1],16 // Load P_3 - fma.s1 N_fix = Norm_Arg, FR_inv_pi_2to63, FR_rshf_2to64 -(p8) br.cond.spnt TANL_LARGER_ARG // Branch if 2^24 <= |x| < 2^63 -} -;; - -// Here if 0 < |x| < 2^24 -// ARGUMENT REDUCTION CODE - CASE 1 and 2 -// -{ .mmf - setf.exp TWO_TO_NEG33 = GR_exp_2tom33 // Form 2^-33 - setf.exp NEGTWO_TO_NEG33 = GR_exp_m2tom33 // Form -2^-33 - fmerge.s r = Norm_Arg,Norm_Arg // Assume r=x, ok if |x| < pi/4 -} -;; - -// -// If |Arg| < pi/4, set PR_8, else pi/4 <=|Arg| < 2^24 - set PR_9. -// -// Case 2: Convert integer N_fix back to normalized floating-point value. -{ .mfi - getf.sig sig_r = Norm_Arg // Get sig_r if 1/4 <= |x| < pi/4 - fcmp.lt.s1 p8,p9= Abs_Arg,PI_BY_4 // Test |x| < pi/4 - mov GR_exp_2tom2 = 0xffff - 2 // Form signexp of 2^-2 -} -{ .mfi - ldfps TWO_TO_NEG2, NEGTWO_TO_NEG2 = [table_ptr2] // Load 2^-2, -2^-2 - fms.s1 N = N_fix, FR_2tom64, FR_rshf // Use scaling to get N floated - mov N_fix_gr = r0 // Assume N=0, ok if |x| < pi/4 -} -;; - -// -// Case 1: Is |r| < 2**(-2). -// Arg is the same as r in this case. -// r = Arg -// c = 0 -// -// Case 2: Place integer part of N in GP register. -{ .mfi -(p9) getf.sig N_fix_gr = N_fix - fmerge.s c = f0, f0 // Assume c=0, ok if |x| < pi/4 - cmp.lt p10, p0 = GR_exp_x, GR_exp_2tom2 // Test if |x| < 1/4 -} -;; - -{ .mfi - setf.sig B_mask1 = bmask1 // Form mask to get 5 msb of r - nop.f 999 - mov exp_r = GR_exp_x // Get exp_r if 1/4 <= |x| < pi/4 -} -{ .mbb - setf.sig B_mask2 = bmask2 // Form mask to form B from r -(p10) br.cond.spnt TANL_SMALL_R // Branch if 0 < |x| < 1/4 -(p8) br.cond.spnt TANL_NORMAL_R // Branch if 1/4 <= |x| < pi/4 -} -;; - -// Here if pi/4 <= |x| < 2^24 -// -// Case 1: PR_3 is only affected when PR_1 is set. -// -// -// Case 2: w = N * P_2 -// Case 2: s_val = -N * P_1 + Arg -// - -{ .mfi - nop.m 999 - fnma.s1 s_val = N, P_1, Norm_Arg - nop.i 999 -} -{ .mfi - nop.m 999 - fmpy.s1 w = N, P_2 // w = N * P_2 for |s| >= 2^-33 - nop.i 999 -} -;; - -// Case 2_reduce: w = N * P_3 (change sign) -{ .mfi - nop.m 999 - fmpy.s1 w2 = N, P_3 // w = N * P_3 for |s| < 2^-33 - nop.i 999 -} -;; - -// Case 1_reduce: r = s + w (change sign) -{ .mfi - nop.m 999 - fsub.s1 r = s_val, w // r = s_val - w for |s| >= 2^-33 - nop.i 999 -} -;; - -// Case 2_reduce: U_1 = N * P_2 + w -{ .mfi - nop.m 999 - fma.s1 U_1 = N, P_2, w2 // U_1 = N * P_2 + w for |s| < 2^-33 - nop.i 999 -} -;; - -// -// Decide between case_1 and case_2 reduce: -// Case 1_reduce: |s| >= 2**(-33) -// Case 2_reduce: |s| < 2**(-33) -// -{ .mfi - nop.m 999 - fcmp.lt.s1 p9, p8 = s_val, TWO_TO_NEG33 - nop.i 999 -} -;; - -{ .mfi - nop.m 999 -(p9) fcmp.gt.s1 p9, p8 = s_val, NEGTWO_TO_NEG33 - nop.i 999 -} -;; - -// Case 1_reduce: c = s - r -{ .mfi - nop.m 999 - fsub.s1 c = s_val, r // c = s_val - r for |s| >= 2^-33 - nop.i 999 -} -;; - -// Case 2_reduce: r is complete here - continue to calculate c . -// r = s - U_1 -{ .mfi - nop.m 999 -(p9) fsub.s1 r = s_val, U_1 - nop.i 999 -} -{ .mfi - nop.m 999 -(p9) fms.s1 U_2 = N, P_2, U_1 - nop.i 999 -} -;; - -// -// Case 1_reduce: Is |r| < 2**(-2), if so set PR_10 -// else set PR_13. -// - -{ .mfi - nop.m 999 - fand B = B_mask1, r - nop.i 999 -} -{ .mfi - nop.m 999 -(p8) fcmp.lt.unc.s1 p10, p13 = r, TWO_TO_NEG2 - nop.i 999 -} -;; - -{ .mfi -(p8) getf.sig sig_r = r // Get signif of r if |s| >= 2^-33 - nop.f 999 - nop.i 999 -} -;; - -{ .mfi -(p8) getf.exp exp_r = r // Extract signexp of r if |s| >= 2^-33 -(p10) fcmp.gt.s1 p10, p13 = r, NEGTWO_TO_NEG2 - nop.i 999 -} -;; - -// Case 1_reduce: c is complete here. -// Case 1: Branch to SMALL_R or NORMAL_R. -// c = c + w (w has not been negated.) -{ .mfi - nop.m 999 -(p8) fsub.s1 c = c, w // c = c - w for |s| >= 2^-33 - nop.i 999 -} -{ .mbb - nop.m 999 -(p10) br.cond.spnt TANL_SMALL_R // Branch if pi/4 < |x| < 2^24 and |r|<1/4 -(p13) br.cond.sptk TANL_NORMAL_R_A // Branch if pi/4 < |x| < 2^24 and |r|>=1/4 -} -;; - - -// Here if pi/4 < |x| < 2^24 and |s| < 2^-33 -// -// Is i_1 = lsb of N_fix_gr even or odd? -// if i_1 == 0, set p11, else set p12. -// -{ .mfi - nop.m 999 - fsub.s1 s_val = s_val, r - add N_fix_gr = N_fix_gr, cot_flag // N = N + 1 (for cotl) -} -{ .mfi - nop.m 999 -// -// Case 2_reduce: -// U_2 = N * P_2 - U_1 -// Not needed until later. -// - fadd.s1 U_2 = U_2, w2 -// -// Case 2_reduce: -// s = s - r -// U_2 = U_2 + w -// - nop.i 999 -} -;; - -// -// Case 2_reduce: -// c = c - U_2 -// c is complete here -// Argument reduction ends here. -// -{ .mfi - nop.m 999 - fmpy.s1 rsq = r, r - tbit.z p11, p12 = N_fix_gr, 0 ;; // Set p11 if N even, p12 if odd -} - -{ .mfi - nop.m 999 -(p12) frcpa.s1 S_hi,p0 = f1, r - nop.i 999 -} -{ .mfi - nop.m 999 - fsub.s1 c = s_val, U_1 - nop.i 999 -} -;; - -{ .mmi - add table_ptr1 = 160, table_base ;; // Point to tanl_table_p1 - ldfe P1_1 = [table_ptr1],144 - nop.i 999 ;; -} -// -// Load P1_1 and point to Q1_1 . -// -{ .mfi - ldfe Q1_1 = [table_ptr1] -// -// N even: rsq = r * Z -// N odd: S_hi = frcpa(r) -// -(p12) fmerge.ns S_hi = S_hi, S_hi - nop.i 999 -} -{ .mfi - nop.m 999 -// -// Case 2_reduce: -// c = s - U_1 -// -(p9) fsub.s1 c = c, U_2 - nop.i 999 ;; -} -{ .mfi - nop.m 999 -(p12) fma.s1 poly1 = S_hi, r, f1 - nop.i 999 ;; -} -{ .mfi - nop.m 999 -// -// N odd: Change sign of S_hi -// -(p11) fmpy.s1 rsq = rsq, P1_1 - nop.i 999 ;; -} -{ .mfi - nop.m 999 -(p12) fma.s1 S_hi = S_hi, poly1, S_hi - nop.i 999 ;; -} -{ .mfi - nop.m 999 -// -// N even: rsq = rsq * P1_1 -// N odd: poly1 = 1.0 + S_hi * r 16 bits partial account for necessary -// -(p11) fma.s1 Poly = r, rsq, c - nop.i 999 ;; -} -{ .mfi - nop.m 999 -// -// N even: Poly = c + r * rsq -// N odd: S_hi = S_hi + S_hi*poly1 16 bits account for necessary -// -(p12) fma.s1 poly1 = S_hi, r, f1 -(p11) tbit.z.unc p14, p15 = cot_flag, 0 ;; // p14=1 for tanl; p15=1 for cotl -} -{ .mfi - nop.m 999 -// -// N even: Result = Poly + r -// N odd: poly1 = 1.0 + S_hi * r 32 bits partial -// -(p14) fadd.s0 Result = r, Poly // for tanl - nop.i 999 -} -{ .mfi - nop.m 999 -(p15) fms.s0 Result = r, mOne, Poly // for cotl - nop.i 999 -} -;; - -{ .mfi - nop.m 999 -(p12) fma.s1 S_hi = S_hi, poly1, S_hi - nop.i 999 ;; -} -{ .mfi - nop.m 999 -// -// N even: Result1 = Result + r -// N odd: S_hi = S_hi * poly1 + S_hi 32 bits -// -(p12) fma.s1 poly1 = S_hi, r, f1 - nop.i 999 ;; -} -{ .mfi - nop.m 999 -// -// N odd: poly1 = S_hi * r + 1.0 64 bits partial -// -(p12) fma.s1 S_hi = S_hi, poly1, S_hi - nop.i 999 ;; -} -{ .mfi - nop.m 999 -// -// N odd: poly1 = S_hi * poly + 1.0 64 bits -// -(p12) fma.s1 poly1 = S_hi, r, f1 - nop.i 999 ;; -} -{ .mfi - nop.m 999 -// -// N odd: poly1 = S_hi * r + 1.0 -// -(p12) fma.s1 poly1 = S_hi, c, poly1 - nop.i 999 ;; -} -{ .mfi - nop.m 999 -// -// N odd: poly1 = S_hi * c + poly1 -// -(p12) fmpy.s1 S_lo = S_hi, poly1 - nop.i 999 ;; -} -{ .mfi - nop.m 999 -// -// N odd: S_lo = S_hi * poly1 -// -(p12) fma.s1 S_lo = Q1_1, r, S_lo -(p12) tbit.z.unc p14, p15 = cot_flag, 0 // p14=1 for tanl; p15=1 for cotl -} -{ .mfi - nop.m 999 -// -// N odd: Result = S_hi + S_lo -// - fmpy.s0 fp_tmp = fp_tmp, fp_tmp // Dummy mult to set inexact - nop.i 999 ;; -} -{ .mfi - nop.m 999 -// -// N odd: S_lo = S_lo + Q1_1 * r -// -(p14) fadd.s0 Result = S_hi, S_lo // for tanl - nop.i 999 -} -{ .mfb - nop.m 999 -(p15) fms.s0 Result = S_hi, mOne, S_lo // for cotl - br.ret.sptk b0 ;; // Exit for pi/4 <= |x| < 2^24 and |s| < 2^-33 -} - - -TANL_LARGER_ARG: -// Here if 2^24 <= |x| < 2^63 -// -// ARGUMENT REDUCTION CODE - CASE 3 and 4 -// - -{ .mmf - mov GR_exp_2tom14 = 0xffff - 14 // Form signexp of 2^-14 - mov GR_exp_m2tom14 = 0x2ffff - 14 // Form signexp of -2^-14 - fmpy.s1 N_0 = Norm_Arg, Inv_P_0 -} -;; - -{ .mmi - setf.exp TWO_TO_NEG14 = GR_exp_2tom14 // Form 2^-14 - setf.exp NEGTWO_TO_NEG14 = GR_exp_m2tom14// Form -2^-14 - nop.i 999 -} -;; - - -// -// Adjust table_ptr1 to beginning of table. -// N_0 = Arg * Inv_P_0 -// -{ .mmi - add table_ptr2 = 144, table_base ;; // Point to 2^-2 - ldfps TWO_TO_NEG2, NEGTWO_TO_NEG2 = [table_ptr2] - nop.i 999 -} -;; - -// -// N_0_fix = integer part of N_0 . -// -// -// Make N_0 the integer part. -// -{ .mfi - nop.m 999 - fcvt.fx.s1 N_0_fix = N_0 - nop.i 999 ;; -} -{ .mfi - setf.sig B_mask1 = bmask1 // Form mask to get 5 msb of r - fcvt.xf N_0 = N_0_fix - nop.i 999 ;; -} -{ .mfi - setf.sig B_mask2 = bmask2 // Form mask to form B from r - fnma.s1 ArgPrime = N_0, P_0, Norm_Arg - nop.i 999 -} -{ .mfi - nop.m 999 - fmpy.s1 w = N_0, d_1 - nop.i 999 ;; -} -// -// ArgPrime = -N_0 * P_0 + Arg -// w = N_0 * d_1 -// -// -// N = ArgPrime * 2/pi -// -// fcvt.fx.s1 N_fix = N -// Use special scaling to right shift so N=Arg * 2/pi is in rightmost bits -// Branch to Cases 3 or 4 if Arg <= -2**24 or Arg >= 2**24 -{ .mfi - nop.m 999 - fma.s1 N_fix = ArgPrime, FR_inv_pi_2to63, FR_rshf_2to64 - - nop.i 999 ;; -} -// Convert integer N_fix back to normalized floating-point value. -{ .mfi - nop.m 999 - fms.s1 N = N_fix, FR_2tom64, FR_rshf // Use scaling to get N floated - nop.i 999 -} -;; - -// -// N is the integer part of the reduced-reduced argument. -// Put the integer in a GP register. -// -{ .mfi - getf.sig N_fix_gr = N_fix - nop.f 999 - nop.i 999 -} -;; - -// -// s_val = -N*P_1 + ArgPrime -// w = -N*P_2 + w -// -{ .mfi - nop.m 999 - fnma.s1 s_val = N, P_1, ArgPrime - nop.i 999 -} -{ .mfi - nop.m 999 - fnma.s1 w = N, P_2, w - nop.i 999 -} -;; - -// Case 4: V_hi = N * P_2 -// Case 4: U_hi = N_0 * d_1 -{ .mfi - nop.m 999 - fmpy.s1 V_hi = N, P_2 // V_hi = N * P_2 for |s| < 2^-14 - nop.i 999 -} -{ .mfi - nop.m 999 - fmpy.s1 U_hi = N_0, d_1 // U_hi = N_0 * d_1 for |s| < 2^-14 - nop.i 999 -} -;; - -// Case 3: r = s_val + w (Z complete) -// Case 4: w = N * P_3 -{ .mfi - nop.m 999 - fadd.s1 r = s_val, w // r = s_val + w for |s| >= 2^-14 - nop.i 999 -} -{ .mfi - nop.m 999 - fmpy.s1 w2 = N, P_3 // w = N * P_3 for |s| < 2^-14 - nop.i 999 -} -;; - -// Case 4: A = U_hi + V_hi -// Note: Worry about switched sign of V_hi, so subtract instead of add. -// Case 4: V_lo = -N * P_2 - V_hi (U_hi is in place of V_hi in writeup) -// Note: the (-) is still missing for V_hi. -{ .mfi - nop.m 999 - fsub.s1 A = U_hi, V_hi // A = U_hi - V_hi for |s| < 2^-14 - nop.i 999 -} -{ .mfi - nop.m 999 - fnma.s1 V_lo = N, P_2, V_hi // V_lo = V_hi - N * P_2 for |s| < 2^-14 - nop.i 999 -} -;; - -// Decide between case 3 and 4: -// Case 3: |s| >= 2**(-14) Set p10 -// Case 4: |s| < 2**(-14) Set p11 -// -// Case 4: U_lo = N_0 * d_1 - U_hi -{ .mfi - nop.m 999 - fms.s1 U_lo = N_0, d_1, U_hi // U_lo = N_0*d_1 - U_hi for |s| < 2^-14 - nop.i 999 -} -{ .mfi - nop.m 999 - fcmp.lt.s1 p11, p10 = s_val, TWO_TO_NEG14 - nop.i 999 -} -;; - -// Case 4: We need abs of both U_hi and V_hi - dont -// worry about switched sign of V_hi. -{ .mfi - nop.m 999 - fabs V_hiabs = V_hi // |V_hi| for |s| < 2^-14 - nop.i 999 -} -{ .mfi - nop.m 999 -(p11) fcmp.gt.s1 p11, p10 = s_val, NEGTWO_TO_NEG14 - nop.i 999 -} -;; - -// Case 3: c = s_val - r -{ .mfi - nop.m 999 - fabs U_hiabs = U_hi // |U_hi| for |s| < 2^-14 - nop.i 999 -} -{ .mfi - nop.m 999 - fsub.s1 c = s_val, r // c = s_val - r for |s| >= 2^-14 - nop.i 999 -} -;; - -// For Case 3, |s| >= 2^-14, determine if |r| < 1/4 -// -// Case 4: C_hi = s_val + A -// -{ .mfi - nop.m 999 -(p11) fadd.s1 C_hi = s_val, A // C_hi = s_val + A for |s| < 2^-14 - nop.i 999 -} -{ .mfi - nop.m 999 -(p10) fcmp.lt.unc.s1 p14, p15 = r, TWO_TO_NEG2 - nop.i 999 -} -;; - -{ .mfi - getf.sig sig_r = r // Get signif of r if |s| >= 2^-33 - fand B = B_mask1, r - nop.i 999 -} -;; - -// Case 4: t = U_lo + V_lo -{ .mfi - getf.exp exp_r = r // Extract signexp of r if |s| >= 2^-33 -(p11) fadd.s1 t = U_lo, V_lo // t = U_lo + V_lo for |s| < 2^-14 - nop.i 999 -} -{ .mfi - nop.m 999 -(p14) fcmp.gt.s1 p14, p15 = r, NEGTWO_TO_NEG2 - nop.i 999 -} -;; - -// Case 3: c = (s - r) + w (c complete) -{ .mfi - nop.m 999 -(p10) fadd.s1 c = c, w // c = c + w for |s| >= 2^-14 - nop.i 999 -} -{ .mbb - nop.m 999 -(p14) br.cond.spnt TANL_SMALL_R // Branch if 2^24 <= |x| < 2^63 and |r|< 1/4 -(p15) br.cond.sptk TANL_NORMAL_R_A // Branch if 2^24 <= |x| < 2^63 and |r|>=1/4 -} -;; - - -// Here if 2^24 <= |x| < 2^63 and |s| < 2^-14 >>>>>>> Case 4. -// -// Case 4: Set P_12 if U_hiabs >= V_hiabs -// Case 4: w = w + N_0 * d_2 -// Note: the (-) is now incorporated in w . -{ .mfi - add table_ptr1 = 160, table_base // Point to tanl_table_p1 - fcmp.ge.unc.s1 p12, p13 = U_hiabs, V_hiabs - nop.i 999 -} -{ .mfi - nop.m 999 - fms.s1 w2 = N_0, d_2, w2 - nop.i 999 -} -;; - -// Case 4: C_lo = s_val - C_hi -{ .mfi - ldfe P1_1 = [table_ptr1], 16 // Load P1_1 - fsub.s1 C_lo = s_val, C_hi - nop.i 999 -} -;; - -// -// Case 4: a = U_hi - A -// a = V_hi - A (do an add to account for missing (-) on V_hi -// -{ .mfi - ldfe P1_2 = [table_ptr1], 128 // Load P1_2 -(p12) fsub.s1 a = U_hi, A - nop.i 999 -} -{ .mfi - nop.m 999 -(p13) fadd.s1 a = V_hi, A - nop.i 999 -} -;; - -// Case 4: t = U_lo + V_lo + w -{ .mfi - ldfe Q1_1 = [table_ptr1], 16 // Load Q1_1 - fadd.s1 t = t, w2 - nop.i 999 -} -;; - -// Case 4: a = (U_hi - A) + V_hi -// a = (V_hi - A) + U_hi -// In each case account for negative missing form V_hi . -// -{ .mfi - ldfe Q1_2 = [table_ptr1], 16 // Load Q1_2 -(p12) fsub.s1 a = a, V_hi - nop.i 999 -} -{ .mfi - nop.m 999 -(p13) fsub.s1 a = U_hi, a - nop.i 999 -} -;; - -// -// Case 4: C_lo = (s_val - C_hi) + A -// -{ .mfi - nop.m 999 - fadd.s1 C_lo = C_lo, A - nop.i 999 ;; -} -// -// Case 4: t = t + a -// -{ .mfi - nop.m 999 - fadd.s1 t = t, a - nop.i 999 -} -;; - -// Case 4: C_lo = C_lo + t -// Case 4: r = C_hi + C_lo -{ .mfi - nop.m 999 - fadd.s1 C_lo = C_lo, t - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fadd.s1 r = C_hi, C_lo - nop.i 999 -} -;; - -// -// Case 4: c = C_hi - r -// -{ .mfi - nop.m 999 - fsub.s1 c = C_hi, r - nop.i 999 -} -{ .mfi - nop.m 999 - fmpy.s1 rsq = r, r - add N_fix_gr = N_fix_gr, cot_flag // N = N + 1 (for cotl) -} -;; - -// Case 4: c = c + C_lo finished. -// -// Is i_1 = lsb of N_fix_gr even or odd? -// if i_1 == 0, set PR_11, else set PR_12. -// -{ .mfi - nop.m 999 - fadd.s1 c = c , C_lo - tbit.z p11, p12 = N_fix_gr, 0 -} -;; - -// r and c have been computed. -{ .mfi - nop.m 999 -(p12) frcpa.s1 S_hi, p0 = f1, r - nop.i 999 -} -{ .mfi - nop.m 999 -// -// N odd: Change sign of S_hi -// -(p11) fma.s1 Poly = rsq, P1_2, P1_1 - nop.i 999 ;; -} -{ .mfi - nop.m 999 -(p12) fma.s1 P = rsq, Q1_2, Q1_1 - nop.i 999 -} -{ .mfi - nop.m 999 -// -// N odd: Result = S_hi + S_lo (User supplied rounding mode for C1) -// - fmpy.s0 fp_tmp = fp_tmp, fp_tmp // Dummy mult to set inexact - nop.i 999 ;; -} -{ .mfi - nop.m 999 -// -// N even: rsq = r * r -// N odd: S_hi = frcpa(r) -// -(p12) fmerge.ns S_hi = S_hi, S_hi - nop.i 999 -} -{ .mfi - nop.m 999 -// -// N even: rsq = rsq * P1_2 + P1_1 -// N odd: poly1 = 1.0 + S_hi * r 16 bits partial account for necessary -// -(p11) fmpy.s1 Poly = rsq, Poly - nop.i 999 ;; -} -{ .mfi - nop.m 999 -(p12) fma.s1 poly1 = S_hi, r,f1 -(p11) tbit.z.unc p14, p15 = cot_flag, 0 // p14=1 for tanl; p15=1 for cotl -} -{ .mfi - nop.m 999 -// -// N even: Poly = Poly * rsq -// N odd: S_hi = S_hi + S_hi*poly1 16 bits account for necessary -// -(p11) fma.s1 Poly = r, Poly, c - nop.i 999 ;; -} -{ .mfi - nop.m 999 -(p12) fma.s1 S_hi = S_hi, poly1, S_hi - nop.i 999 -} -{ .mfi - nop.m 999 -// -// N odd: S_hi = S_hi * poly1 + S_hi 32 bits -// -(p14) fadd.s0 Result = r, Poly // for tanl - nop.i 999 ;; -} - -.pred.rel "mutex",p15,p12 -{ .mfi - nop.m 999 -(p15) fms.s0 Result = r, mOne, Poly // for cotl - nop.i 999 -} -{ .mfi - nop.m 999 -(p12) fma.s1 poly1 = S_hi, r, f1 - nop.i 999 ;; -} -{ .mfi - nop.m 999 -// -// N even: Poly = Poly * r + c -// N odd: poly1 = 1.0 + S_hi * r 32 bits partial -// -(p12) fma.s1 S_hi = S_hi, poly1, S_hi - nop.i 999 ;; -} -{ .mfi - nop.m 999 -(p12) fma.s1 poly1 = S_hi, r, f1 - nop.i 999 ;; -} -{ .mfi - nop.m 999 -// -// N even: Result = Poly + r (Rounding mode S0) -// N odd: poly1 = S_hi * r + 1.0 64 bits partial -// -(p12) fma.s1 S_hi = S_hi, poly1, S_hi - nop.i 999 ;; -} -{ .mfi - nop.m 999 -// -// N odd: poly1 = S_hi * poly + S_hi 64 bits -// -(p12) fma.s1 poly1 = S_hi, r, f1 - nop.i 999 ;; -} -{ .mfi - nop.m 999 -// -// N odd: poly1 = S_hi * r + 1.0 -// -(p12) fma.s1 poly1 = S_hi, c, poly1 - nop.i 999 ;; -} -{ .mfi - nop.m 999 -// -// N odd: poly1 = S_hi * c + poly1 -// -(p12) fmpy.s1 S_lo = S_hi, poly1 - nop.i 999 ;; -} -{ .mfi - nop.m 999 -// -// N odd: S_lo = S_hi * poly1 -// -(p12) fma.s1 S_lo = P, r, S_lo -(p12) tbit.z.unc p14, p15 = cot_flag, 0 ;; // p14=1 for tanl; p15=1 for cotl -} - -{ .mfi - nop.m 999 -(p14) fadd.s0 Result = S_hi, S_lo // for tanl - nop.i 999 -} -{ .mfb - nop.m 999 -// -// N odd: S_lo = S_lo + r * P -// -(p15) fms.s0 Result = S_hi, mOne, S_lo // for cotl - br.ret.sptk b0 ;; // Exit for 2^24 <= |x| < 2^63 and |s| < 2^-14 -} - - -TANL_SMALL_R: -// Here if |r| < 1/4 -// r and c have been computed. -// ***************************************************************** -// ***************************************************************** -// ***************************************************************** -// N odd: S_hi = frcpa(r) -// Get [i_1] - lsb of N_fix_gr. Set p11 if N even, p12 if N odd. -// N even: rsq = r * r -{ .mfi - add table_ptr1 = 160, table_base // Point to tanl_table_p1 - frcpa.s1 S_hi, p0 = f1, r // S_hi for N odd - add N_fix_gr = N_fix_gr, cot_flag // N = N + 1 (for cotl) -} -{ .mfi - add table_ptr2 = 400, table_base // Point to Q1_7 - fmpy.s1 rsq = r, r - nop.i 999 -} -;; - -{ .mmi - ldfe P1_1 = [table_ptr1], 16 -;; - ldfe P1_2 = [table_ptr1], 16 - tbit.z p11, p12 = N_fix_gr, 0 -} -;; - - -{ .mfi - ldfe P1_3 = [table_ptr1], 96 - nop.f 999 - nop.i 999 -} -;; - -{ .mfi -(p11) ldfe P1_9 = [table_ptr1], -16 -(p12) fmerge.ns S_hi = S_hi, S_hi - nop.i 999 -} -{ .mfi - nop.m 999 -(p11) fmpy.s1 r_to_the_8 = rsq, rsq - nop.i 999 -} -;; - -// -// N even: Poly2 = P1_7 + Poly2 * rsq -// N odd: poly2 = Q1_5 + poly2 * rsq -// -{ .mfi -(p11) ldfe P1_8 = [table_ptr1], -16 -(p11) fadd.s1 CORR = rsq, f1 - nop.i 999 -} -;; - -// -// N even: Poly1 = P1_2 + P1_3 * rsq -// N odd: poly1 = 1.0 + S_hi * r -// 16 bits partial account for necessary (-1) -// -{ .mmi -(p11) ldfe P1_7 = [table_ptr1], -16 -;; -(p11) ldfe P1_6 = [table_ptr1], -16 - nop.i 999 -} -;; - -// -// N even: Poly1 = P1_1 + Poly1 * rsq -// N odd: S_hi = S_hi + S_hi * poly1) 16 bits account for necessary -// -// -// N even: Poly2 = P1_5 + Poly2 * rsq -// N odd: poly2 = Q1_3 + poly2 * rsq -// -{ .mfi -(p11) ldfe P1_5 = [table_ptr1], -16 -(p11) fmpy.s1 r_to_the_8 = r_to_the_8, r_to_the_8 - nop.i 999 -} -{ .mfi - nop.m 999 -(p12) fma.s1 poly1 = S_hi, r, f1 - nop.i 999 -} -;; - -// -// N even: Poly1 = Poly1 * rsq -// N odd: poly1 = 1.0 + S_hi * r 32 bits partial -// - -// -// N even: CORR = CORR * c -// N odd: S_hi = S_hi * poly1 + S_hi 32 bits -// - -// -// N even: Poly2 = P1_6 + Poly2 * rsq -// N odd: poly2 = Q1_4 + poly2 * rsq -// - -{ .mmf -(p11) ldfe P1_4 = [table_ptr1], -16 - nop.m 999 -(p11) fmpy.s1 CORR = CORR, c -} -;; - -{ .mfi - nop.m 999 -(p11) fma.s1 Poly1 = P1_3, rsq, P1_2 - nop.i 999 ;; -} -{ .mfi -(p12) ldfe Q1_7 = [table_ptr2], -16 -(p12) fma.s1 S_hi = S_hi, poly1, S_hi - nop.i 999 ;; -} -{ .mfi -(p12) ldfe Q1_6 = [table_ptr2], -16 -(p11) fma.s1 Poly2 = P1_9, rsq, P1_8 - nop.i 999 ;; -} -{ .mmi -(p12) ldfe Q1_5 = [table_ptr2], -16 ;; -(p12) ldfe Q1_4 = [table_ptr2], -16 - nop.i 999 ;; -} -{ .mfi -(p12) ldfe Q1_3 = [table_ptr2], -16 -// -// N even: Poly2 = P1_8 + P1_9 * rsq -// N odd: poly2 = Q1_6 + Q1_7 * rsq -// -(p11) fma.s1 Poly1 = Poly1, rsq, P1_1 - nop.i 999 ;; -} -{ .mfi -(p12) ldfe Q1_2 = [table_ptr2], -16 -(p12) fma.s1 poly1 = S_hi, r, f1 - nop.i 999 ;; -} -{ .mfi -(p12) ldfe Q1_1 = [table_ptr2], -16 -(p11) fma.s1 Poly2 = Poly2, rsq, P1_7 - nop.i 999 ;; -} -{ .mfi - nop.m 999 -// -// N even: CORR = rsq + 1 -// N even: r_to_the_8 = rsq * rsq -// -(p11) fmpy.s1 Poly1 = Poly1, rsq - nop.i 999 ;; -} -{ .mfi - nop.m 999 -(p12) fma.s1 S_hi = S_hi, poly1, S_hi - nop.i 999 -} -{ .mfi - nop.m 999 -(p12) fma.s1 poly2 = Q1_7, rsq, Q1_6 - nop.i 999 ;; -} -{ .mfi - nop.m 999 -(p11) fma.s1 Poly2 = Poly2, rsq, P1_6 - nop.i 999 ;; -} -{ .mfi - nop.m 999 -(p12) fma.s1 poly1 = S_hi, r, f1 - nop.i 999 -} -{ .mfi - nop.m 999 -(p12) fma.s1 poly2 = poly2, rsq, Q1_5 - nop.i 999 ;; -} -{ .mfi - nop.m 999 -(p11) fma.s1 Poly2= Poly2, rsq, P1_5 - nop.i 999 ;; -} -{ .mfi - nop.m 999 -(p12) fma.s1 S_hi = S_hi, poly1, S_hi - nop.i 999 -} -{ .mfi - nop.m 999 -(p12) fma.s1 poly2 = poly2, rsq, Q1_4 - nop.i 999 ;; -} -{ .mfi - nop.m 999 -// -// N even: r_to_the_8 = r_to_the_8 * r_to_the_8 -// N odd: poly1 = S_hi * r + 1.0 64 bits partial -// -(p11) fma.s1 Poly2 = Poly2, rsq, P1_4 - nop.i 999 ;; -} -{ .mfi - nop.m 999 -// -// N even: Poly = CORR + Poly * r -// N odd: P = Q1_1 + poly2 * rsq -// -(p12) fma.s1 poly1 = S_hi, r, f1 - nop.i 999 -} -{ .mfi - nop.m 999 -(p12) fma.s1 poly2 = poly2, rsq, Q1_3 - nop.i 999 ;; -} -{ .mfi - nop.m 999 -// -// N even: Poly2 = P1_4 + Poly2 * rsq -// N odd: poly2 = Q1_2 + poly2 * rsq -// -(p11) fma.s1 Poly = Poly2, r_to_the_8, Poly1 - nop.i 999 ;; -} -{ .mfi - nop.m 999 -(p12) fma.s1 poly1 = S_hi, c, poly1 - nop.i 999 -} -{ .mfi - nop.m 999 -(p12) fma.s1 poly2 = poly2, rsq, Q1_2 - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -// -// N even: Poly = Poly1 + Poly2 * r_to_the_8 -// N odd: S_hi = S_hi * poly1 + S_hi 64 bits -// -(p11) fma.s1 Poly = Poly, r, CORR - nop.i 999 ;; -} -{ .mfi - nop.m 999 -// -// N even: Result = r + Poly (User supplied rounding mode) -// N odd: poly1 = S_hi * c + poly1 -// -(p12) fmpy.s1 S_lo = S_hi, poly1 -(p11) tbit.z.unc p14, p15 = cot_flag, 0 // p14=1 for tanl; p15=1 for cotl -} -{ .mfi - nop.m 999 -(p12) fma.s1 P = poly2, rsq, Q1_1 - nop.i 999 ;; -} -{ .mfi - nop.m 999 -// -// N odd: poly1 = S_hi * r + 1.0 -// -// -// N odd: S_lo = S_hi * poly1 -// -(p14) fadd.s0 Result = Poly, r // for tanl - nop.i 999 -} -{ .mfi - nop.m 999 -(p15) fms.s0 Result = Poly, mOne, r // for cotl - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -// -// N odd: S_lo = Q1_1 * c + S_lo -// -(p12) fma.s1 S_lo = Q1_1, c, S_lo - nop.i 999 -} -{ .mfi - nop.m 999 - fmpy.s0 fp_tmp = fp_tmp, fp_tmp // Dummy mult to set inexact - nop.i 999 ;; -} -{ .mfi - nop.m 999 -// -// N odd: Result = S_lo + r * P -// -(p12) fma.s1 Result = P, r, S_lo -(p12) tbit.z.unc p14, p15 = cot_flag, 0 ;; // p14=1 for tanl; p15=1 for cotl -} - -// -// N odd: Result = Result + S_hi (user supplied rounding mode) -// -{ .mfi - nop.m 999 -(p14) fadd.s0 Result = Result, S_hi // for tanl - nop.i 999 -} -{ .mfb - nop.m 999 -(p15) fms.s0 Result = Result, mOne, S_hi // for cotl - br.ret.sptk b0 ;; // Exit |r| < 1/4 path -} - - -TANL_NORMAL_R: -// Here if 1/4 <= |x| < pi/4 or if |x| >= 2^63 and |r| >= 1/4 -// ******************************************************************* -// ******************************************************************* -// ******************************************************************* -// -// r and c have been computed. -// -{ .mfi - nop.m 999 - fand B = B_mask1, r - nop.i 999 -} -;; - -TANL_NORMAL_R_A: -// Enter here if pi/4 <= |x| < 2^63 and |r| >= 1/4 -// Get the 5 bits or r for the lookup. 1.xxxxx .... -{ .mmi - add table_ptr1 = 416, table_base // Point to tanl_table_p2 - mov GR_exp_2tom65 = 0xffff - 65 // Scaling constant for B - extr.u lookup = sig_r, 58, 5 -} -;; - -{ .mmi - ldfe P2_1 = [table_ptr1], 16 - setf.exp TWO_TO_NEG65 = GR_exp_2tom65 // 2^-65 for scaling B if exp_r=-2 - add N_fix_gr = N_fix_gr, cot_flag // N = N + 1 (for cotl) -} -;; - -.pred.rel "mutex",p11,p12 -// B = 2^63 * 1.xxxxx 100...0 -{ .mfi - ldfe P2_2 = [table_ptr1], 16 - for B = B_mask2, B - mov table_offset = 512 // Assume table offset is 512 -} -;; - -{ .mfi - ldfe P2_3 = [table_ptr1], 16 - fmerge.s Pos_r = f1, r - tbit.nz p8,p9 = exp_r, 0 -} -;; - -// Is B = 2** -2 or B= 2** -1? If 2**-1, then -// we want an offset of 512 for table addressing. -{ .mii - add table_ptr2 = 1296, table_base // Point to tanl_table_cm2 -(p9) shladd table_offset = lookup, 4, table_offset -(p8) shladd table_offset = lookup, 4, r0 -} -;; - -{ .mmi - add table_ptr1 = table_ptr1, table_offset // Point to T_hi - add table_ptr2 = table_ptr2, table_offset // Point to C_hi - add table_ptr3 = 2128, table_base // Point to tanl_table_scim2 -} -;; - -{ .mmi - ldfd T_hi = [table_ptr1], 8 // Load T_hi -;; - ldfd C_hi = [table_ptr2], 8 // Load C_hi - add table_ptr3 = table_ptr3, table_offset // Point to SC_inv -} -;; - -// -// x = |r| - B -// -// Convert B so it has the same exponent as Pos_r before subtracting -{ .mfi - ldfs T_lo = [table_ptr1] // Load T_lo -(p9) fnma.s1 x = B, FR_2tom64, Pos_r - nop.i 999 -} -{ .mfi - nop.m 999 -(p8) fnma.s1 x = B, TWO_TO_NEG65, Pos_r - nop.i 999 -} -;; - -{ .mfi - ldfs C_lo = [table_ptr2] // Load C_lo - nop.f 999 - nop.i 999 -} -;; - -{ .mfi - ldfe SC_inv = [table_ptr3] // Load SC_inv - fmerge.s sgn_r = r, f1 - tbit.z p11, p12 = N_fix_gr, 0 // p11 if N even, p12 if odd - -} -;; - -// -// xsq = x * x -// N even: Tx = T_hi * x -// -// N even: Tx1 = Tx + 1 -// N odd: Cx1 = 1 - Cx -// - -{ .mfi - nop.m 999 - fmpy.s1 xsq = x, x - nop.i 999 -} -{ .mfi - nop.m 999 -(p11) fmpy.s1 Tx = T_hi, x - nop.i 999 -} -;; - -// -// N odd: Cx = C_hi * x -// -{ .mfi - nop.m 999 -(p12) fmpy.s1 Cx = C_hi, x - nop.i 999 -} -;; -// -// N even and odd: P = P2_3 + P2_2 * xsq -// -{ .mfi - nop.m 999 - fma.s1 P = P2_3, xsq, P2_2 - nop.i 999 -} -{ .mfi - nop.m 999 -(p11) fadd.s1 Tx1 = Tx, f1 - nop.i 999 ;; -} -{ .mfi - nop.m 999 -// -// N even: D = C_hi - tanx -// N odd: D = T_hi + tanx -// -(p11) fmpy.s1 CORR = SC_inv, T_hi - nop.i 999 -} -{ .mfi - nop.m 999 - fmpy.s1 Sx = SC_inv, x - nop.i 999 ;; -} -{ .mfi - nop.m 999 -(p12) fmpy.s1 CORR = SC_inv, C_hi - nop.i 999 ;; -} -{ .mfi - nop.m 999 -(p12) fsub.s1 V_hi = f1, Cx - nop.i 999 ;; -} -{ .mfi - nop.m 999 - fma.s1 P = P, xsq, P2_1 - nop.i 999 -} -{ .mfi - nop.m 999 -// -// N even and odd: P = P2_1 + P * xsq -// -(p11) fma.s1 V_hi = Tx, Tx1, f1 - nop.i 999 ;; -} -{ .mfi - nop.m 999 -// -// N even: Result = sgn_r * tail + T_hi (user rounding mode for C1) -// N odd: Result = sgn_r * tail + C_hi (user rounding mode for C1) -// - fmpy.s0 fp_tmp = fp_tmp, fp_tmp // Dummy mult to set inexact - nop.i 999 ;; -} -{ .mfi - nop.m 999 - fmpy.s1 CORR = CORR, c - nop.i 999 ;; -} -{ .mfi - nop.m 999 -(p12) fnma.s1 V_hi = Cx,V_hi,f1 - nop.i 999 ;; -} -{ .mfi - nop.m 999 -// -// N even: V_hi = Tx * Tx1 + 1 -// N odd: Cx1 = 1 - Cx * Cx1 -// - fmpy.s1 P = P, xsq - nop.i 999 -} -{ .mfi - nop.m 999 -// -// N even and odd: P = P * xsq -// -(p11) fmpy.s1 V_hi = V_hi, T_hi - nop.i 999 ;; -} -{ .mfi - nop.m 999 -// -// N even and odd: tail = P * tail + V_lo -// -(p11) fmpy.s1 T_hi = sgn_r, T_hi - nop.i 999 ;; -} -{ .mfi - nop.m 999 - fmpy.s1 CORR = CORR, sgn_r - nop.i 999 ;; -} -{ .mfi - nop.m 999 -(p12) fmpy.s1 V_hi = V_hi,C_hi - nop.i 999 ;; -} -{ .mfi - nop.m 999 -// -// N even: V_hi = T_hi * V_hi -// N odd: V_hi = C_hi * V_hi -// - fma.s1 tanx = P, x, x - nop.i 999 -} -{ .mfi - nop.m 999 -(p12) fnmpy.s1 C_hi = sgn_r, C_hi - nop.i 999 ;; -} -{ .mfi - nop.m 999 -// -// N even: V_lo = 1 - V_hi + C_hi -// N odd: V_lo = 1 - V_hi + T_hi -// -(p11) fadd.s1 CORR = CORR, T_lo - nop.i 999 -} -{ .mfi - nop.m 999 -(p12) fsub.s1 CORR = CORR, C_lo - nop.i 999 ;; -} -{ .mfi - nop.m 999 -// -// N even and odd: tanx = x + x * P -// N even and odd: Sx = SC_inv * x -// -(p11) fsub.s1 D = C_hi, tanx - nop.i 999 -} -{ .mfi - nop.m 999 -(p12) fadd.s1 D = T_hi, tanx - nop.i 999 ;; -} -{ .mfi - nop.m 999 -// -// N odd: CORR = SC_inv * C_hi -// N even: CORR = SC_inv * T_hi -// - fnma.s1 D = V_hi, D, f1 - nop.i 999 ;; -} -{ .mfi - nop.m 999 -// -// N even and odd: D = 1 - V_hi * D -// N even and odd: CORR = CORR * c -// - fma.s1 V_hi = V_hi, D, V_hi - nop.i 999 ;; -} -{ .mfi - nop.m 999 -// -// N even and odd: V_hi = V_hi + V_hi * D -// N even and odd: CORR = sgn_r * CORR -// -(p11) fnma.s1 V_lo = V_hi, C_hi, f1 - nop.i 999 -} -{ .mfi - nop.m 999 -(p12) fnma.s1 V_lo = V_hi, T_hi, f1 - nop.i 999 ;; -} -{ .mfi - nop.m 999 -// -// N even: CORR = COOR + T_lo -// N odd: CORR = CORR - C_lo -// -(p11) fma.s1 V_lo = tanx, V_hi, V_lo - tbit.nz p15, p0 = cot_flag, 0 // p15=1 if we compute cotl -} -{ .mfi - nop.m 999 -(p12) fnma.s1 V_lo = tanx, V_hi, V_lo - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -(p15) fms.s1 T_hi = f0, f0, T_hi // to correct result's sign for cotl - nop.i 999 -} -{ .mfi - nop.m 999 -(p15) fms.s1 C_hi = f0, f0, C_hi // to correct result's sign for cotl - nop.i 999 -};; - -{ .mfi - nop.m 999 -(p15) fms.s1 sgn_r = f0, f0, sgn_r // to correct result's sign for cotl - nop.i 999 -};; - -{ .mfi - nop.m 999 -// -// N even: V_lo = V_lo + V_hi * tanx -// N odd: V_lo = V_lo - V_hi * tanx -// -(p11) fnma.s1 V_lo = C_lo, V_hi, V_lo - nop.i 999 -} -{ .mfi - nop.m 999 -(p12) fnma.s1 V_lo = T_lo, V_hi, V_lo - nop.i 999 ;; -} -{ .mfi - nop.m 999 -// -// N even: V_lo = V_lo - V_hi * C_lo -// N odd: V_lo = V_lo - V_hi * T_lo -// - fmpy.s1 V_lo = V_hi, V_lo - nop.i 999 ;; -} -{ .mfi - nop.m 999 -// -// N even and odd: V_lo = V_lo * V_hi -// - fadd.s1 tail = V_hi, V_lo - nop.i 999 ;; -} -{ .mfi - nop.m 999 -// -// N even and odd: tail = V_hi + V_lo -// - fma.s1 tail = tail, P, V_lo - nop.i 999 ;; -} -{ .mfi - nop.m 999 -// -// N even: T_hi = sgn_r * T_hi -// N odd : C_hi = -sgn_r * C_hi -// - fma.s1 tail = tail, Sx, CORR - nop.i 999 ;; -} -{ .mfi - nop.m 999 -// -// N even and odd: tail = Sx * tail + CORR -// - fma.s1 tail = V_hi, Sx, tail - nop.i 999 ;; -} -{ .mfi - nop.m 999 -// -// N even an odd: tail = Sx * V_hi + tail -// -(p11) fma.s0 Result = sgn_r, tail, T_hi - nop.i 999 -} -{ .mfb - nop.m 999 -(p12) fma.s0 Result = sgn_r, tail, C_hi - br.ret.sptk b0 ;; // Exit for 1/4 <= |r| < pi/4 -} - -TANL_DENORMAL: -// Here if x denormal -{ .mfb - getf.exp GR_signexp_x = Norm_Arg // Get sign and exponent of x - nop.f 999 - br.cond.sptk TANL_COMMON // Return to common code -} -;; - - -TANL_SPECIAL: -TANL_UNSUPPORTED: -// -// Code for NaNs, Unsupporteds, Infs, or +/- zero ? -// Invalid raised for Infs and SNaNs. -// - -{ .mfi - nop.m 999 - fmerge.s f10 = f8, f8 // Save input for error call - tbit.nz p6, p7 = cot_flag, 0 // p6=1 if we compute cotl -} -;; - -{ .mfi - nop.m 999 -(p6) fclass.m p6, p7 = f8, 0x7 // Test for zero (cotl only) - nop.i 999 -} -;; - -.pred.rel "mutex", p6, p7 -{ .mfi -(p6) mov GR_Parameter_Tag = 225 // (cotl) -(p6) frcpa.s0 f8, p0 = f1, f8 // cotl(+-0) = +-Inf - nop.i 999 -} -{ .mfb - nop.m 999 -(p7) fmpy.s0 f8 = f8, f0 -(p7) br.ret.sptk b0 -} -;; - -GLOBAL_IEEE754_END(tanl) - - -LOCAL_LIBM_ENTRY(__libm_error_region) -.prologue - -// (1) -{ .mfi - add GR_Parameter_Y=-32,sp // Parameter 2 value - nop.f 0 -.save ar.pfs,GR_SAVE_PFS - mov GR_SAVE_PFS=ar.pfs // Save ar.pfs -} -{ .mfi -.fframe 64 - add sp=-64,sp // Create new stack - nop.f 0 - mov GR_SAVE_GP=gp // Save gp -};; - -// (2) -{ .mmi - stfe [GR_Parameter_Y] = f1,16 // STORE Parameter 2 on stack - add GR_Parameter_X = 16,sp // Parameter 1 address -.save b0, GR_SAVE_B0 - mov GR_SAVE_B0=b0 // Save b0 -};; - -.body -// (3) -{ .mib - stfe [GR_Parameter_X] = f10 // STORE Parameter 1 on stack - add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address - nop.b 0 -} -{ .mib - stfe [GR_Parameter_Y] = f8 // STORE Parameter 3 on stack - add GR_Parameter_Y = -16,GR_Parameter_Y - br.call.sptk b0=__libm_error_support# // Call error handling function -};; -{ .mmi - nop.m 0 - nop.m 0 - add GR_Parameter_RESULT = 48,sp -};; - -// (4) -{ .mmi - ldfe f8 = [GR_Parameter_RESULT] // Get return result off stack -.restore sp - add sp = 64,sp // Restore stack pointer - mov b0 = GR_SAVE_B0 // Restore return address -};; -{ .mib - mov gp = GR_SAVE_GP // Restore gp - mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs - br.ret.sptk b0 // Return -};; - -LOCAL_LIBM_END(__libm_error_region) - -.type __libm_error_support#,@function -.global __libm_error_support# - - -// ******************************************************************* -// ******************************************************************* -// ******************************************************************* -// -// 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 -// 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) -TANL_ARG_TOO_LARGE: -.prologue -{ .mfi - add table_ptr2 = 144, table_base // Point to 2^-2 - nop.f 999 -.save ar.pfs,GR_SAVE_PFS - mov GR_SAVE_PFS=ar.pfs // Save ar.pfs -} -;; - -// Load 2^-2, -2^-2 -{ .mmi - ldfps TWO_TO_NEG2, NEGTWO_TO_NEG2 = [table_ptr2] - setf.sig B_mask1 = bmask1 // Form mask to get 5 msb of r -.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.sig B_mask2 = bmask2 // Form mask to form B from r - mov GR_SAVE_GP=gp // Save gp - br.call.sptk b0=__libm_pi_by_2_reduce# -} -;; - -// -// Is |r| < 2**(-2) -// -{ .mfi - getf.sig sig_r = r // Extract significand of r - fcmp.lt.s1 p6, p0 = r, TWO_TO_NEG2 - mov gp = GR_SAVE_GP // Restore gp -} -;; - -{ .mfi - getf.exp exp_r = r // Extract signexp of r - nop.f 999 - mov b0 = GR_SAVE_B0 // Restore return address -} -;; - -// -// Get N_fix_gr -// -{ .mfi - mov N_fix_gr = r8 -(p6) fcmp.gt.unc.s1 p6, p0 = r, NEGTWO_TO_NEG2 - mov ar.pfs = GR_SAVE_PFS // Restore pfs -} -;; - -{ .mbb - nop.m 999 -(p6) br.cond.spnt TANL_SMALL_R // Branch if |r| < 1/4 - br.cond.sptk TANL_NORMAL_R // Branch if 1/4 <= |r| < pi/4 -} -;; - -LOCAL_LIBM_END(__libm_callout) - -.type __libm_pi_by_2_reduce#,@function -.global __libm_pi_by_2_reduce# |