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diff --git a/sysdeps/ia64/fpu/libm_tan.S b/sysdeps/ia64/fpu/libm_tan.S deleted file mode 100644 index 179ea9c323..0000000000 --- a/sysdeps/ia64/fpu/libm_tan.S +++ /dev/null @@ -1,3332 +0,0 @@ -.file "libm_tan.s" - -// Copyright (C) 2000, 2001, Intel Corporation -// All rights reserved. -// -// Contributed 2/2/2000 by John Harrison, Ted Kubaska, Bob Norin, Shane Story, -// and Ping Tak Peter Tang of the Computational Software Lab, Intel Corporation. -// -// 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://developer.intel.com/opensource. -// -// ********************************************************************* -// -// History: -// 02/02/00 Initial Version -// 4/04/00 Unwind support added -// 12/28/00 Fixed false invalid flags -// -// ********************************************************************* -// -// Function: tan(x) = tangent(x), for double precision x values -// -// ********************************************************************* -// -// Accuracy: Very accurate for double-precision values -// -// ********************************************************************* -// -// Resources Used: -// -// Floating-Point Registers: f8 (Input and Return Value) -// f9-f15 -// f32-f112 -// -// General Purpose Registers: -// r32-r48 -// r49-r50 (Used to pass arguments to pi_by_2 reduce routine) -// -// Predicate Registers: p6-p15 -// -// ********************************************************************* -// -// IEEE Special Conditions: -// -// 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 -// -// tan(SNaN) = QNaN -// tan(QNaN) = QNaN -// tan(inf) = QNaN -// tan(+/-0) = +/-0 -// -// ********************************************************************* -// -// Mathematical Description -// -// We consider the computation of FPTAN 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 -// Result := c + r * rsq * P1_1 -// Result := r + Result ...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 -// Result := c + r * rsq * (P1_1 + rsq * P1_2) -// Result := r + Result ...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 -// Result := r*Poly + CORR -// Result := r + Result ...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)) -// -// Result := r*P + S_lo -// Result := S_hi + Result ...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. -// -// - -#include "libm_support.h" - -#ifdef _LIBC -.rodata -#else -.data -#endif - -.align 128 - -TAN_BASE_CONSTANTS: -ASM_TYPE_DIRECTIVE(TAN_BASE_CONSTANTS,@object) -data4 0x4B800000, 0xCB800000, 0x38800000, 0xB8800000 // two**24, -two**24 - // two**-14, -two**-14 -data4 0x4E44152A, 0xA2F9836E, 0x00003FFE, 0x00000000 // two_by_pi -data4 0xCE81B9F1, 0xC84D32B0, 0x00004016, 0x00000000 // P_0 -data4 0x2168C235, 0xC90FDAA2, 0x00003FFF, 0x00000000 // P_1 -data4 0xFC8F8CBB, 0xECE675D1, 0x0000BFBD, 0x00000000 // P_2 -data4 0xACC19C60, 0xB7ED8FBB, 0x0000BF7C, 0x00000000 // P_3 -data4 0x5F000000, 0xDF000000, 0x00000000, 0x00000000 // two_to_63, -two_to_63 -data4 0x6EC6B45A, 0xA397E504, 0x00003FE7, 0x00000000 // Inv_P_0 -data4 0xDBD171A1, 0x8D848E89, 0x0000BFBF, 0x00000000 // d_1 -data4 0x18A66F8E, 0xD5394C36, 0x0000BF7C, 0x00000000 // d_2 -data4 0x2168C234, 0xC90FDAA2, 0x00003FFE, 0x00000000 // PI_BY_4 -data4 0x2168C234, 0xC90FDAA2, 0x0000BFFE, 0x00000000 // MPI_BY_4 -data4 0x3E800000, 0xBE800000, 0x00000000, 0x00000000 // two**-2, -two**-2 -data4 0x2F000000, 0xAF000000, 0x00000000, 0x00000000 // two**-33, -two**-33 -data4 0xAAAAAABD, 0xAAAAAAAA, 0x00003FFD, 0x00000000 // P1_1 -data4 0x88882E6A, 0x88888888, 0x00003FFC, 0x00000000 // P1_2 -data4 0x0F0177B6, 0xDD0DD0DD, 0x00003FFA, 0x00000000 // P1_3 -data4 0x646B8C6D, 0xB327A440, 0x00003FF9, 0x00000000 // P1_4 -data4 0x1D5F7D20, 0x91371B25, 0x00003FF8, 0x00000000 // P1_5 -data4 0x61C67914, 0xEB69A5F1, 0x00003FF6, 0x00000000 // P1_6 -data4 0x019318D2, 0xBEDD37BE, 0x00003FF5, 0x00000000 // P1_7 -data4 0x3C794015, 0x9979B146, 0x00003FF4, 0x00000000 // P1_8 -data4 0x8C6EB58A, 0x8EBD21A3, 0x00003FF3, 0x00000000 // P1_9 -data4 0xAAAAAAB4, 0xAAAAAAAA, 0x00003FFD, 0x00000000 // Q1_1 -data4 0x0B5FC93E, 0xB60B60B6, 0x00003FF9, 0x00000000 // Q1_2 -data4 0x0C9BBFBF, 0x8AB355E0, 0x00003FF6, 0x00000000 // Q1_3 -data4 0xCBEE3D4C, 0xDDEBBC89, 0x00003FF2, 0x00000000 // Q1_4 -data4 0x5F80BBB6, 0xB3548A68, 0x00003FEF, 0x00000000 // Q1_5 -data4 0x4CED5BF1, 0x91362560, 0x00003FEC, 0x00000000 // Q1_6 -data4 0x8EE92A83, 0xF189D95A, 0x00003FE8, 0x00000000 // Q1_7 -data4 0xAAAB362F, 0xAAAAAAAA, 0x00003FFD, 0x00000000 // P2_1 -data4 0xE97A6097, 0x88888886, 0x00003FFC, 0x00000000 // P2_2 -data4 0x25E716A1, 0xDD108EE0, 0x00003FFA, 0x00000000 // P2_3 -// -// 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) -// -data4 0x62400794, 0x3FD09BC3, 0x23A05C32, 0x00000000 -data4 0xDFFBC074, 0x3FD124A9, 0x240078B2, 0x00000000 -data4 0x5BD4920F, 0x3FD1AE23, 0x23826B8E, 0x00000000 -data4 0x15E2701D, 0x3FD23835, 0x22D31154, 0x00000000 -data4 0x63739C2D, 0x3FD2C2E4, 0x2265C9E2, 0x00000000 -data4 0xAFEEA48B, 0x3FD34E36, 0x245C05EB, 0x00000000 -data4 0x7DBB35D1, 0x3FD3DA31, 0x24749F2D, 0x00000000 -data4 0x67321619, 0x3FD466DA, 0x2462CECE, 0x00000000 -data4 0x1F94A4D5, 0x3FD4F437, 0x246D0DF1, 0x00000000 -data4 0x740C3E6D, 0x3FD5824D, 0x240A85B5, 0x00000000 -data4 0x4CB1E73D, 0x3FD61123, 0x23F96E33, 0x00000000 -data4 0xAD9EA64B, 0x3FD6A0BE, 0x247C5393, 0x00000000 -data4 0xB804FD01, 0x3FD73125, 0x241F3B29, 0x00000000 -data4 0xAB53EE83, 0x3FD7C25E, 0x2479989B, 0x00000000 -data4 0xE6640EED, 0x3FD8546F, 0x23B343BC, 0x00000000 -data4 0xE8AF1892, 0x3FD8E75F, 0x241454D1, 0x00000000 -data4 0x53928BDA, 0x3FD97B35, 0x238613D9, 0x00000000 -data4 0xEB9DE4DE, 0x3FDA0FF6, 0x22859FA7, 0x00000000 -data4 0x99ECF92D, 0x3FDAA5AB, 0x237A6D06, 0x00000000 -data4 0x6D8F1796, 0x3FDB3C5A, 0x23952F6C, 0x00000000 -data4 0x9CFB8BE4, 0x3FDBD40A, 0x2280FC95, 0x00000000 -data4 0x87943100, 0x3FDC6CC3, 0x245D2EC0, 0x00000000 -data4 0xB736C500, 0x3FDD068C, 0x23C4AD7D, 0x00000000 -data4 0xE1DDBC31, 0x3FDDA16D, 0x23D076E6, 0x00000000 -data4 0xEB515A93, 0x3FDE3D6E, 0x244809A6, 0x00000000 -data4 0xE6E9E5F1, 0x3FDEDA97, 0x220856C8, 0x00000000 -data4 0x1963CE69, 0x3FDF78F1, 0x244BE993, 0x00000000 -data4 0x7D635BCE, 0x3FE00C41, 0x23D21799, 0x00000000 -data4 0x1C302CD3, 0x3FE05CAB, 0x248A1B1D, 0x00000000 -data4 0xDB6A1FA0, 0x3FE0ADB9, 0x23D53E33, 0x00000000 -data4 0x4A20BA81, 0x3FE0FF72, 0x24DB9ED5, 0x00000000 -data4 0x153FA6F5, 0x3FE151D9, 0x24E9E451, 0x00000000 -// -// 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) -// -data4 0xBA1BE39E, 0x3FE1CEC4, 0x24B60F9E, 0x00000000 -data4 0x5ABD9B2D, 0x3FE277E4, 0x248C2474, 0x00000000 -data4 0x0272B110, 0x3FE32418, 0x247B8311, 0x00000000 -data4 0x890E2DF0, 0x3FE3D38B, 0x24C55751, 0x00000000 -data4 0x46236871, 0x3FE4866D, 0x24E5BC34, 0x00000000 -data4 0x45E044B0, 0x3FE53CEE, 0x24001BA4, 0x00000000 -data4 0x82EC06E4, 0x3FE5F742, 0x24B973DC, 0x00000000 -data4 0x25DF43F9, 0x3FE6B5A1, 0x24895440, 0x00000000 -data4 0xCAFD348C, 0x3FE77844, 0x240021CA, 0x00000000 -data4 0xCEED6B92, 0x3FE83F6B, 0x24C45372, 0x00000000 -data4 0xA34F3665, 0x3FE90B58, 0x240DAD33, 0x00000000 -data4 0x2C1E56B4, 0x3FE9DC52, 0x24F846CE, 0x00000000 -data4 0x27041578, 0x3FEAB2A4, 0x2323FB6E, 0x00000000 -data4 0x9DD8C373, 0x3FEB8E9F, 0x24B3090B, 0x00000000 -data4 0x65C9AA7B, 0x3FEC709B, 0x2449F611, 0x00000000 -data4 0xACCF8435, 0x3FED58F4, 0x23616A7E, 0x00000000 -data4 0x97635082, 0x3FEE480F, 0x24C2FEAE, 0x00000000 -data4 0xF0ACC544, 0x3FEF3E57, 0x242CE964, 0x00000000 -data4 0xF7E06E4B, 0x3FF01E20, 0x2480D3EE, 0x00000000 -data4 0x8A798A69, 0x3FF0A125, 0x24DB8967, 0x00000000 -// -// 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) -// -data4 0xE63EFBD0, 0x400ED3E2, 0x259D94D4, 0x00000000 -data4 0xC515DAB5, 0x400DDDB4, 0x245F0537, 0x00000000 -data4 0xBE19A79F, 0x400CF57A, 0x25D4EA9F, 0x00000000 -data4 0xD15298ED, 0x400C1A06, 0x24AE40A0, 0x00000000 -data4 0x164B2708, 0x400B4A4C, 0x25A5AAB6, 0x00000000 -data4 0x5285B068, 0x400A855A, 0x25524F18, 0x00000000 -data4 0x3FFA549F, 0x4009CA5A, 0x24C999C0, 0x00000000 -data4 0x646AF623, 0x4009188A, 0x254FD801, 0x00000000 -data4 0x6084D0E7, 0x40086F3C, 0x2560F5FD, 0x00000000 -data4 0xA29A76EE, 0x4007CDD2, 0x255B9D19, 0x00000000 -data4 0x6C8ECA95, 0x400733BE, 0x25CB021B, 0x00000000 -data4 0x1F8DDC52, 0x4006A07E, 0x24AB4722, 0x00000000 -data4 0xC298AD58, 0x4006139B, 0x252764E2, 0x00000000 -data4 0xBAD7164B, 0x40058CAB, 0x24DAF5DB, 0x00000000 -data4 0xAE31A5D3, 0x40050B4B, 0x25EA20F4, 0x00000000 -data4 0x89F85A8A, 0x40048F21, 0x2583A3E8, 0x00000000 -data4 0xA862380D, 0x400417DA, 0x25DCC4CC, 0x00000000 -data4 0x1088FCFE, 0x4003A52B, 0x2430A492, 0x00000000 -data4 0xCD3527D5, 0x400336CC, 0x255F77CF, 0x00000000 -data4 0x5760766D, 0x4002CC7F, 0x25DA0BDA, 0x00000000 -data4 0x11CE02E3, 0x40026607, 0x256FF4A2, 0x00000000 -data4 0xD37BBE04, 0x4002032C, 0x25208AED, 0x00000000 -data4 0x7F050775, 0x4001A3BD, 0x24B72DD6, 0x00000000 -data4 0xA554848A, 0x40014789, 0x24AB4DAA, 0x00000000 -data4 0x323E81B7, 0x4000EE65, 0x2584C440, 0x00000000 -data4 0x21CF1293, 0x40009827, 0x25C9428D, 0x00000000 -data4 0x3D415EEB, 0x400044A9, 0x25DC8482, 0x00000000 -data4 0xBD72C577, 0x3FFFE78F, 0x257F5070, 0x00000000 -data4 0x75EFD28E, 0x3FFF4AC3, 0x23EBBF7A, 0x00000000 -data4 0x60B52DDE, 0x3FFEB2AF, 0x22EECA07, 0x00000000 -data4 0x35204180, 0x3FFE1F19, 0x24191079, 0x00000000 -data4 0x54F7E60A, 0x3FFD8FCA, 0x248D3058, 0x00000000 -// -// 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) -// -data4 0x79F6FADE, 0x3FFCC06A, 0x239C7886, 0x00000000 -data4 0x891662A6, 0x3FFBB91F, 0x250BD191, 0x00000000 -data4 0x529F155D, 0x3FFABFB6, 0x256CC3E6, 0x00000000 -data4 0x2E964AE9, 0x3FF9D300, 0x250843E3, 0x00000000 -data4 0x89DCB383, 0x3FF8F1EF, 0x2277C87E, 0x00000000 -data4 0x7C87DBD6, 0x3FF81B93, 0x256DA6CF, 0x00000000 -data4 0x1042EDE4, 0x3FF74F14, 0x2573D28A, 0x00000000 -data4 0x1784B360, 0x3FF68BAF, 0x242E489A, 0x00000000 -data4 0x7C923C4C, 0x3FF5D0B5, 0x2532D940, 0x00000000 -data4 0xF418EF20, 0x3FF51D88, 0x253C7DD6, 0x00000000 -data4 0x02F88DAE, 0x3FF4719A, 0x23DB59BF, 0x00000000 -data4 0x49DA0788, 0x3FF3CC66, 0x252B4756, 0x00000000 -data4 0x0B980DB8, 0x3FF32D77, 0x23FE585F, 0x00000000 -data4 0xE56C987A, 0x3FF2945F, 0x25378A63, 0x00000000 -data4 0xB16523F6, 0x3FF200BD, 0x247BB2E0, 0x00000000 -data4 0x8CE27778, 0x3FF17235, 0x24446538, 0x00000000 -data4 0xFDEFE692, 0x3FF0E873, 0x2514638F, 0x00000000 -data4 0x33154062, 0x3FF0632C, 0x24A7FC27, 0x00000000 -data4 0xB3EF115F, 0x3FEFC42E, 0x248FD0FE, 0x00000000 -data4 0x135D26F6, 0x3FEEC9E8, 0x2385C719, 0x00000000 -// -// Entries SC_inv in Swapped IEEE format (extended) -// Index = 0,1,...,31 B = 2^(-2)*(1+Index/32+1/64) -// -data4 0x1BF30C9E, 0x839D6D4A, 0x00004001, 0x00000000 -data4 0x554B0EB0, 0x80092804, 0x00004001, 0x00000000 -data4 0xA1CF0DE9, 0xF959F94C, 0x00004000, 0x00000000 -data4 0x77378677, 0xF3086BA0, 0x00004000, 0x00000000 -data4 0xCCD4723C, 0xED154515, 0x00004000, 0x00000000 -data4 0x1C27CF25, 0xE7790944, 0x00004000, 0x00000000 -data4 0x8DDACB88, 0xE22D037D, 0x00004000, 0x00000000 -data4 0x89C73522, 0xDD2B2D8A, 0x00004000, 0x00000000 -data4 0xBB2C1171, 0xD86E1A23, 0x00004000, 0x00000000 -data4 0xDFF5E0F9, 0xD3F0E288, 0x00004000, 0x00000000 -data4 0x283BEBD5, 0xCFAF16B1, 0x00004000, 0x00000000 -data4 0x0D88DD53, 0xCBA4AFAA, 0x00004000, 0x00000000 -data4 0xCA67C43D, 0xC7CE03CC, 0x00004000, 0x00000000 -data4 0x0CA0DDB0, 0xC427BC82, 0x00004000, 0x00000000 -data4 0xF13D8CAB, 0xC0AECD57, 0x00004000, 0x00000000 -data4 0x71ECE6B1, 0xBD606C38, 0x00004000, 0x00000000 -data4 0xA44C4929, 0xBA3A0A96, 0x00004000, 0x00000000 -data4 0xE5CCCEC1, 0xB7394F6F, 0x00004000, 0x00000000 -data4 0x9637D8BC, 0xB45C1203, 0x00004000, 0x00000000 -data4 0x92CB051B, 0xB1A05528, 0x00004000, 0x00000000 -data4 0x6BA2FFD0, 0xAF04432B, 0x00004000, 0x00000000 -data4 0x7221235F, 0xAC862A23, 0x00004000, 0x00000000 -data4 0x5F00A9D1, 0xAA2478AF, 0x00004000, 0x00000000 -data4 0x81E082BF, 0xA7DDBB0C, 0x00004000, 0x00000000 -data4 0x45684FEE, 0xA5B0987D, 0x00004000, 0x00000000 -data4 0x627A8F53, 0xA39BD0F5, 0x00004000, 0x00000000 -data4 0x6EC5C8B0, 0xA19E3B03, 0x00004000, 0x00000000 -data4 0x91CD7C66, 0x9FB6C1F0, 0x00004000, 0x00000000 -data4 0x1FA3DF8A, 0x9DE46410, 0x00004000, 0x00000000 -data4 0xA8F6B888, 0x9C263139, 0x00004000, 0x00000000 -data4 0xC27B0450, 0x9A7B4968, 0x00004000, 0x00000000 -data4 0x5EE614EE, 0x98E2DB7E, 0x00004000, 0x00000000 -// -// Entries SC_inv in Swapped IEEE format (extended) -// Index = 0,1,...,19 B = 2^(-1)*(1+Index/32+1/64) -// -data4 0x13B2B5BA, 0x969F335C, 0x00004000, 0x00000000 -data4 0xD4C0F548, 0x93D446D9, 0x00004000, 0x00000000 -data4 0x61B798AF, 0x9147094F, 0x00004000, 0x00000000 -data4 0x758787AC, 0x8EF317CC, 0x00004000, 0x00000000 -data4 0xB99EEFDB, 0x8CD498B3, 0x00004000, 0x00000000 -data4 0xDFF8BC37, 0x8AE82A7D, 0x00004000, 0x00000000 -data4 0xE3C55D42, 0x892AD546, 0x00004000, 0x00000000 -data4 0xD15573C1, 0x8799FEA9, 0x00004000, 0x00000000 -data4 0x435A4B4C, 0x86335F88, 0x00004000, 0x00000000 -data4 0x3E93A87B, 0x84F4FB6E, 0x00004000, 0x00000000 -data4 0x80A382FB, 0x83DD1952, 0x00004000, 0x00000000 -data4 0xA4CB8C9E, 0x82EA3D7F, 0x00004000, 0x00000000 -data4 0x6861D0A8, 0x821B247C, 0x00004000, 0x00000000 -data4 0x63E8D244, 0x816EBED1, 0x00004000, 0x00000000 -data4 0x27E4CFC6, 0x80E42D91, 0x00004000, 0x00000000 -data4 0x28E64AFD, 0x807ABF8D, 0x00004000, 0x00000000 -data4 0x863B4FD8, 0x8031EF26, 0x00004000, 0x00000000 -data4 0xAE8C11FD, 0x800960AD, 0x00004000, 0x00000000 -data4 0x5FDBEC21, 0x8000E147, 0x00004000, 0x00000000 -data4 0xA07791FA, 0x80186650, 0x00004000, 0x00000000 - -Arg = f8 -Result = f8 -fp_tmp = f9 -U_2 = f10 -rsq = f11 -C_hi = f12 -C_lo = f13 -T_hi = f14 -T_lo = f15 - -N_0 = f32 -d_1 = f33 -MPI_BY_4 = 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 - -TWO_TO_63 = f54 -NEGTWO_TO_63 = f55 -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 -PI_BY_4 = f71 -NEGTWO_TO_NEG2 = f72 -TWO_TO_24 = f73 -TWO_TO_NEG14 = f74 -TWO_TO_NEG33 = f75 -NEGTWO_TO_24 = f76 -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 -c = f86 -r = f87 -Z = f88 -A = f89 -a = f90 -t = f91 -U_1 = f92 -d_2 = 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 - -GR_SAVE_B0 = r33 -GR_SAVE_GP = r34 -GR_SAVE_PFS = r35 - -delta1 = r36 -table_ptr1 = r37 -table_ptr2 = r38 -i_0 = r39 -i_1 = r40 -N_fix_gr = r41 -N_inc = r42 -exp_Arg = r43 -exp_r = r44 -sig_r = r45 -lookup = r46 -table_offset = r47 -Create_B = r48 -gr_tmp = r49 - -GR_Parameter_X = r49 -GR_Parameter_r = r50 - - - -.global __libm_tan -.section .text -.proc __libm_tan - - -__libm_tan: - -{ .mfi -alloc r32 = ar.pfs, 0,17,2,0 -(p0) fclass.m.unc p6,p0 = Arg, 0x1E7 - addl gr_tmp = -1,r0 -} -;; - -{ .mfi - nop.m 999 -(p0) fclass.nm.unc p7,p0 = Arg, 0x1FF - nop.i 999 -} -;; - -{ .mfi -(p0) addl table_ptr1 = @ltoff(TAN_BASE_CONSTANTS), gp - nop.f 999 - nop.i 999 -} -;; - -{ .mmi - ld8 table_ptr1 = [table_ptr1] - setf.sig fp_tmp = gr_tmp // Make a constant so fmpy produces inexact - nop.i 999 -} -;; - -// -// Check for NatVals, Infs , NaNs, and Zeros -// Check for everything - if false, then must be pseudo-zero -// or pseudo-nan. -// Local table pointer -// - -{ .mbb -(p0) add table_ptr2 = 96, table_ptr1 -(p6) br.cond.spnt __libm_TAN_SPECIAL -(p7) br.cond.spnt __libm_TAN_SPECIAL ;; -} -// -// Point to Inv_P_0 -// Branch out to deal with unsupporteds and special values. -// - -{ .mmf -(p0) ldfs TWO_TO_24 = [table_ptr1],4 -(p0) ldfs TWO_TO_63 = [table_ptr2],4 -// -// Load -2**24, load -2**63. -// -(p0) fcmp.eq.s0 p0, p6 = Arg, f1 ;; -} - -{ .mfi -(p0) ldfs NEGTWO_TO_63 = [table_ptr2],12 -(p0) fnorm.s1 Arg = Arg - nop.i 999 -} -// -// Load 2**24, Load 2**63. -// - -{ .mmi -(p0) ldfs NEGTWO_TO_24 = [table_ptr1],12 ;; -// -// Do fcmp to generate Denormal exception -// - can't do FNORM (will generate Underflow when U is unmasked!) -// Normalize input argument. -// -(p0) ldfe two_by_PI = [table_ptr1],16 - nop.i 999 -} - -{ .mmi -(p0) ldfe Inv_P_0 = [table_ptr2],16 ;; -(p0) ldfe d_1 = [table_ptr2],16 - nop.i 999 -} -// -// Decide about the paths to take: -// PR_1 and PR_3 set if -2**24 < Arg < 2**24 - CASE 1 OR 2 -// OTHERWISE - CASE 3 OR 4 -// Load inverse of P_0 . -// Set PR_6 if Arg <= -2**63 -// Are there any Infs, NaNs, or zeros? -// - -{ .mmi -(p0) ldfe P_0 = [table_ptr1],16 ;; -(p0) ldfe d_2 = [table_ptr2],16 - nop.i 999 -} -// -// Set PR_8 if Arg <= -2**24 -// Set PR_6 if Arg >= 2**63 -// - -{ .mmi -(p0) ldfe P_1 = [table_ptr1],16 ;; -(p0) ldfe PI_BY_4 = [table_ptr2],16 - nop.i 999 -} -// -// Set PR_8 if Arg >= 2**24 -// - -{ .mmi -(p0) ldfe P_2 = [table_ptr1],16 ;; -(p0) ldfe MPI_BY_4 = [table_ptr2],16 - nop.i 999 -} -// -// Load P_2 and PI_BY_4 -// - -{ .mfi -(p0) ldfe P_3 = [table_ptr1],16 - nop.f 999 - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -(p0) fcmp.le.unc.s1 p6,p7 = Arg,NEGTWO_TO_63 - nop.i 999 -} - -{ .mfi - nop.m 999 -(p0) fcmp.le.unc.s1 p8,p9 = Arg,NEGTWO_TO_24 - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -(p7) fcmp.ge.s1 p6,p0 = Arg,TWO_TO_63 - nop.i 999 -} - -{ .mfi - nop.m 999 -(p9) fcmp.ge.s1 p8,p0 = Arg,TWO_TO_24 - nop.i 999 ;; -} - -{ .mib - nop.m 999 - nop.i 999 -// -// Load P_3 and -PI_BY_4 -// -(p6) br.cond.spnt TAN_ARG_TOO_LARGE ;; -} - -{ .mib - nop.m 999 - nop.i 999 -// -// Load 2**(-2). -// Load -2**(-2). -// Branch out if we have a special argument. -// Branch out if the magnitude of the input argument is too large -// - do this branch before the next. -// -(p8) br.cond.spnt TAN_LARGER_ARG ;; -} -// -// Branch to Cases 3 or 4 if Arg <= -2**24 or Arg >= 2**24 -// - -{ .mfi -(p0) ldfs TWO_TO_NEG2 = [table_ptr2],4 -// ARGUMENT REDUCTION CODE - CASE 1 and 2 -// Load 2**(-2). -// Load -2**(-2). -(p0) fmpy.s1 N = Arg,two_by_PI - nop.i 999 ;; -} - -{ .mfi -(p0) ldfs NEGTWO_TO_NEG2 = [table_ptr2],12 -// -// N = Arg * 2/pi -// -(p0) fcmp.lt.unc.s1 p8,p9= Arg,PI_BY_4 - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -// -// if Arg < pi/4, set PR_8. -// -(p8) fcmp.gt.s1 p8,p9= Arg,MPI_BY_4 - nop.i 999 ;; -} -// -// Case 1: Is |r| < 2**(-2). -// Arg is the same as r in this case. -// r = Arg -// c = 0 -// - -{ .mfi -(p8) mov N_fix_gr = r0 -// -// if Arg > -pi/4, reset PR_8. -// Select the case when |Arg| < pi/4 - set PR[8] = true. -// Else Select the case when |Arg| >= pi/4 - set PR[9] = true. -// -(p0) fcvt.fx.s1 N_fix = N - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -// -// Grab the integer part of N . -// -(p8) mov r = Arg - nop.i 999 -} - -{ .mfi - nop.m 999 -(p8) mov c = f0 - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -(p8) fcmp.lt.unc.s1 p10, p11 = Arg, TWO_TO_NEG2 - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -(p10) fcmp.gt.s1 p10,p0 = Arg, NEGTWO_TO_NEG2 - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -// -// Case 2: Place integer part of N in GP register. -// -(p9) fcvt.xf N = N_fix - nop.i 999 ;; -} - -{ .mib -(p9) getf.sig N_fix_gr = N_fix - nop.i 999 -// -// Case 2: Convert integer N_fix back to normalized floating-point value. -// -(p10) br.cond.spnt TAN_SMALL_R ;; -} - -{ .mib - nop.m 999 - nop.i 999 -(p8) br.cond.sptk TAN_NORMAL_R ;; -} -// -// Case 1: PR_3 is only affected when PR_1 is set. -// - -{ .mmi -(p9) ldfs TWO_TO_NEG33 = [table_ptr2], 4 ;; -// -// Case 2: Load 2**(-33). -// -(p9) ldfs NEGTWO_TO_NEG33 = [table_ptr2], 4 - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -// -// Case 2: Load -2**(-33). -// -(p9) fnma.s1 s_val = N, P_1, Arg - nop.i 999 -} - -{ .mfi - nop.m 999 -(p9) fmpy.s1 w = N, P_2 - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -// -// Case 2: w = N * P_2 -// Case 2: s_val = -N * P_1 + Arg -// -(p0) fcmp.lt.unc.s1 p9,p8 = s_val, TWO_TO_NEG33 - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -// -// Decide between case_1 and case_2 reduce: -// -(p9) fcmp.gt.s1 p9, p8 = s_val, NEGTWO_TO_NEG33 - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -// -// Case 1_reduce: s <= -2**(-33) or s >= 2**(-33) -// Case 2_reduce: -2**(-33) < s < 2**(-33) -// -(p8) fsub.s1 r = s_val, w - nop.i 999 -} - -{ .mfi - nop.m 999 -(p9) fmpy.s1 w = N, P_3 - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -(p9) fma.s1 U_1 = N, P_2, w - nop.i 999 -} - -{ .mfi - nop.m 999 -// -// Case 1_reduce: Is |r| < 2**(-2), if so set PR_10 -// else set PR_11. -// -(p8) fsub.s1 c = s_val, r - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -// -// Case 1_reduce: r = s + w (change sign) -// Case 2_reduce: w = N * P_3 (change sign) -// -(p8) fcmp.lt.unc.s1 p10, p11 = r, TWO_TO_NEG2 - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -(p10) fcmp.gt.s1 p10, p11 = r, NEGTWO_TO_NEG2 - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -(p9) fsub.s1 r = s_val, U_1 - nop.i 999 -} - -{ .mfi - nop.m 999 -// -// Case 1_reduce: c is complete here. -// c = c + w (w has not been negated.) -// Case 2_reduce: r is complete here - continue to calculate c . -// r = s - U_1 -// -(p9) fms.s1 U_2 = N, P_2, U_1 - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -// -// Case 1_reduce: c = s - r -// Case 2_reduce: U_1 = N * P_2 + w -// -(p8) fsub.s1 c = c, w - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -(p9) fsub.s1 s_val = s_val, r - nop.i 999 -} - -{ .mfb - nop.m 999 -// -// Case 2_reduce: -// U_2 = N * P_2 - U_1 -// Not needed until later. -// -(p9) fadd.s1 U_2 = U_2, w -// -// Case 2_reduce: -// s = s - r -// U_2 = U_2 + w -// -(p10) br.cond.spnt TAN_SMALL_R ;; -} - -{ .mib - nop.m 999 - nop.i 999 -(p11) br.cond.sptk TAN_NORMAL_R ;; -} - -{ .mii - nop.m 999 -// -// Case 2_reduce: -// c = c - U_2 -// c is complete here -// Argument reduction ends here. -// -(p9) extr.u i_1 = N_fix_gr, 0, 1 ;; -(p9) cmp.eq.unc p11, p12 = 0x0000,i_1 ;; -} - -{ .mfi - nop.m 999 -// -// Is i_1 even or odd? -// if i_1 == 0, set p11, else set p12. -// -(p11) fmpy.s1 rsq = r, Z - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -(p12) frcpa.s1 S_hi,p0 = f1, r - nop.i 999 -} - -// -// Case 1: Branch to SMALL_R or NORMAL_R. -// Case 1 is done now. -// - -{ .mfi -(p9) addl table_ptr1 = @ltoff(TAN_BASE_CONSTANTS), gp -(p9) fsub.s1 c = s_val, U_1 - nop.i 999 ;; -} -;; - -{ .mmi -(p9) ld8 table_ptr1 = [table_ptr1] - nop.m 999 - nop.i 999 -} -;; - -{ .mmi -(p9) add table_ptr1 = 224, table_ptr1 ;; -(p9) ldfe P1_1 = [table_ptr1],144 - nop.i 999 ;; -} -// -// Get [i_1] - lsb of N_fix_gr . -// Load P1_1 and point to Q1_1 . -// - -{ .mfi -(p9) ldfe Q1_1 = [table_ptr1] , 0 -// -// 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 Result = r, rsq, c - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -// -// N even: Result = 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 - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -// -// N even: Result = Result + r -// N odd: poly1 = 1.0 + S_hi * r 32 bits partial -// -(p11) fadd.s0 Result = r, Result - 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 - nop.i 999 -} - -{ .mfi - nop.m 999 -// -// N odd: Result = S_hi + S_lo -// -(p0) fmpy.s0 fp_tmp = fp_tmp, fp_tmp // Dummy mult to set inexact - nop.i 999 ;; -} - -{ .mfb - nop.m 999 -// -// N odd: S_lo = S_lo + Q1_1 * r -// -(p12) fadd.s0 Result = S_hi, S_lo -(p0) br.ret.sptk b0 ;; -} - - -TAN_LARGER_ARG: - -{ .mmf -(p0) addl table_ptr1 = @ltoff(TAN_BASE_CONSTANTS), gp - nop.m 999 -(p0) fmpy.s1 N_0 = Arg, Inv_P_0 -} -;; - -// -// ARGUMENT REDUCTION CODE - CASE 3 and 4 -// -// -// Adjust table_ptr1 to beginning of table. -// N_0 = Arg * Inv_P_0 -// - - -{ .mmi -(p0) ld8 table_ptr1 = [table_ptr1] - nop.m 999 - nop.i 999 -} -;; - - -{ .mmi -(p0) add table_ptr1 = 8, table_ptr1 ;; -// -// Point to 2*-14 -// -(p0) ldfs TWO_TO_NEG14 = [table_ptr1], 4 - nop.i 999 ;; -} -// -// Load 2**(-14). -// - -{ .mmi -(p0) ldfs NEGTWO_TO_NEG14 = [table_ptr1], 180 ;; -// -// N_0_fix = integer part of N_0 . -// Adjust table_ptr1 to beginning of table. -// -(p0) ldfs TWO_TO_NEG2 = [table_ptr1], 4 - nop.i 999 ;; -} -// -// Make N_0 the integer part. -// - -{ .mfi -(p0) ldfs NEGTWO_TO_NEG2 = [table_ptr1] -// -// Load -2**(-14). -// -(p0) fcvt.fx.s1 N_0_fix = N_0 - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -(p0) fcvt.xf N_0 = N_0_fix - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -(p0) fnma.s1 ArgPrime = N_0, P_0, Arg - nop.i 999 -} - -{ .mfi - nop.m 999 -(p0) fmpy.s1 w = N_0, d_1 - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -// -// ArgPrime = -N_0 * P_0 + Arg -// w = N_0 * d_1 -// -(p0) fmpy.s1 N = ArgPrime, two_by_PI - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -// -// N = ArgPrime * 2/pi -// -(p0) fcvt.fx.s1 N_fix = N - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -// -// N_fix is the integer part. -// -(p0) fcvt.xf N = N_fix - nop.i 999 ;; -} - -{ .mfi -(p0) getf.sig N_fix_gr = N_fix - nop.f 999 - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -// -// N is the integer part of the reduced-reduced argument. -// Put the integer in a GP register. -// -(p0) fnma.s1 s_val = N, P_1, ArgPrime - nop.i 999 -} - -{ .mfi - nop.m 999 -(p0) fnma.s1 w = N, P_2, w - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -// -// s_val = -N*P_1 + ArgPrime -// w = -N*P_2 + w -// -(p0) fcmp.lt.unc.s1 p11, p10 = s_val, TWO_TO_NEG14 - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -(p11) fcmp.gt.s1 p11, p10 = s_val, NEGTWO_TO_NEG14 - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -// -// Case 3: r = s_val + w (Z complete) -// Case 4: U_hi = N_0 * d_1 -// -(p10) fmpy.s1 V_hi = N, P_2 - nop.i 999 -} - -{ .mfi - nop.m 999 -(p11) fmpy.s1 U_hi = N_0, d_1 - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -// -// Case 3: r = s_val + w (Z complete) -// Case 4: U_hi = N_0 * d_1 -// -(p11) fmpy.s1 V_hi = N, P_2 - nop.i 999 -} - -{ .mfi - nop.m 999 -(p11) fmpy.s1 U_hi = N_0, d_1 - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -// -// Decide between case 3 and 4: -// Case 3: s <= -2**(-14) or s >= 2**(-14) -// Case 4: -2**(-14) < s < 2**(-14) -// -(p10) fadd.s1 r = s_val, w - nop.i 999 -} - -{ .mfi - nop.m 999 -(p11) fmpy.s1 w = N, P_3 - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -// -// Case 4: We need abs of both U_hi and V_hi - dont -// worry about switched sign of V_hi . -// -(p11) fsub.s1 A = U_hi, V_hi - nop.i 999 -} - -{ .mfi - nop.m 999 -// -// Case 4: A = U_hi + V_hi -// Note: Worry about switched sign of V_hi, so subtract instead of add. -// -(p11) fnma.s1 V_lo = N, P_2, V_hi - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -(p11) fms.s1 U_lo = N_0, d_1, U_hi - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -(p11) fabs V_hiabs = V_hi - nop.i 999 -} - -{ .mfi - nop.m 999 -// -// Case 4: 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 . -(p10) fadd.s1 r = s_val, w - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -// -// Case 3: c = s_val - r -// Case 4: U_lo = N_0 * d_1 - U_hi -// -(p11) fabs U_hiabs = U_hi - nop.i 999 -} - -{ .mfi - nop.m 999 -(p11) fmpy.s1 w = N, P_3 - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -// -// Case 4: Set P_12 if U_hiabs >= V_hiabs -// -(p11) fadd.s1 C_hi = s_val, A - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -// -// Case 4: C_hi = s_val + A -// -(p11) fadd.s1 t = U_lo, V_lo - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -// -// Case 3: Is |r| < 2**(-2), if so set PR_7 -// else set PR_8. -// Case 3: If PR_7 is set, prepare to branch to Small_R. -// Case 3: If PR_8 is set, prepare to branch to Normal_R. -// -(p10) fsub.s1 c = s_val, r - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -// -// Case 3: c = (s - r) + w (c complete) -// -(p11) fcmp.ge.unc.s1 p12, p13 = U_hiabs, V_hiabs - nop.i 999 -} - -{ .mfi - nop.m 999 -(p11) fms.s1 w = N_0, d_2, w - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -// -// Case 4: 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 . -// -(p10) fcmp.lt.unc.s1 p14, p15 = r, TWO_TO_NEG2 - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -(p14) fcmp.gt.s1 p14, p15 = r, NEGTWO_TO_NEG2 - nop.i 999 ;; -} - -{ .mfb - nop.m 999 -// -// 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 . -// Case 4: w = w + N_0 * d_2 -// Note: the (-) is now incorporated in w . -// -(p10) fadd.s1 c = c, w -// -// Case 4: t = U_lo + V_lo -// Note: remember V_lo should be (-), subtract instead of add. NO -// -(p14) br.cond.spnt TAN_SMALL_R ;; -} - -{ .mib - nop.m 999 - nop.i 999 -(p15) br.cond.spnt TAN_NORMAL_R ;; -} - -{ .mfi - nop.m 999 -// -// Case 3: Vector off when |r| < 2**(-2). Recall that PR_3 will be true. -// The remaining stuff is for Case 4. -// -(p12) fsub.s1 a = U_hi, A -(p11) extr.u i_1 = N_fix_gr, 0, 1 ;; -} - -{ .mfi - nop.m 999 -// -// Case 4: C_lo = s_val - C_hi -// -(p11) fadd.s1 t = t, w - nop.i 999 -} - -{ .mfi - nop.m 999 -(p13) fadd.s1 a = V_hi, A - nop.i 999 ;; -} - -// -// Case 4: a = U_hi - A -// a = V_hi - A (do an add to account for missing (-) on V_hi -// - -{ .mfi -(p11) addl table_ptr1 = @ltoff(TAN_BASE_CONSTANTS), gp -(p11) fsub.s1 C_lo = s_val, C_hi - nop.i 999 -} -;; - -{ .mmi -(p11) ld8 table_ptr1 = [table_ptr1] - nop.m 999 - 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 . -// -// -// Case 4: C_lo = (s_val - C_hi) + A -// - -{ .mmi -(p11) add table_ptr1 = 224, table_ptr1 ;; -(p11) ldfe P1_1 = [table_ptr1], 16 - nop.i 999 ;; -} - -{ .mfi -(p11) ldfe P1_2 = [table_ptr1], 128 -// -// Case 4: w = U_lo + V_lo + w -// -(p12) fsub.s1 a = a, V_hi - nop.i 999 ;; -} -// -// Case 4: r = C_hi + C_lo -// - -{ .mfi -(p11) ldfe Q1_1 = [table_ptr1], 16 -(p11) fadd.s1 C_lo = C_lo, A - nop.i 999 ;; -} -// -// Case 4: c = C_hi - r -// Get [i_1] - lsb of N_fix_gr. -// - -{ .mfi -(p11) ldfe Q1_2 = [table_ptr1], 16 - nop.f 999 - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -(p13) fsub.s1 a = U_hi, a - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -(p11) fadd.s1 t = t, a - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -// -// Case 4: t = t + a -// -(p11) fadd.s1 C_lo = C_lo, t - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -// -// Case 4: C_lo = C_lo + t -// -(p11) fadd.s1 r = C_hi, C_lo - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -(p11) fsub.s1 c = C_hi, r - nop.i 999 -} - -{ .mfi - nop.m 999 -// -// Case 4: c = c + C_lo finished. -// Is i_1 even or odd? -// if i_1 == 0, set PR_4, else set PR_5. -// -// 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 -(p0) fmpy.s1 rsq = r, r - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -(p11) fadd.s1 c = c , C_lo -(p11) cmp.eq.unc p11, p12 = 0x0000, i_1 ;; -} - -{ .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 Result = 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) -// -(p0) 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 Result = rsq, Result - 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 = Result * rsq -// N odd: S_hi = S_hi + S_hi*poly1 16 bits account for necessary -// -(p11) fma.s1 Result = r, Result, 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 -// -(p11) fadd.s0 Result= r, Result - 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 = Result * 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: Result1 = Result + 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 - nop.i 999 ;; -} - -{ .mfb - nop.m 999 -// -// N odd: S_lo = S_lo + r * P -// -(p12) fadd.s0 Result = S_hi, S_lo -(p0) br.ret.sptk b0 ;; -} - - -TAN_SMALL_R: - -{ .mii - nop.m 999 -(p0) extr.u i_1 = N_fix_gr, 0, 1 ;; -(p0) cmp.eq.unc p11, p12 = 0x0000, i_1 -} - -{ .mfi - nop.m 999 -(p0) fmpy.s1 rsq = r, r - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -(p12) frcpa.s1 S_hi, p0 = f1, r - nop.i 999 -} - -{ .mfi -(p0) addl table_ptr1 = @ltoff(TAN_BASE_CONSTANTS), gp - nop.f 999 - nop.i 999 -} -;; - -{ .mmi -(p0) ld8 table_ptr1 = [table_ptr1] - nop.m 999 - nop.i 999 -} -;; - -// ***************************************************************** -// ***************************************************************** -// ***************************************************************** - -{ .mmi -(p0) add table_ptr1 = 224, table_ptr1 ;; -(p0) ldfe P1_1 = [table_ptr1], 16 - nop.i 999 ;; -} -// 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 -// |r| < 2**(-2) - -{ .mfi -(p0) ldfe P1_2 = [table_ptr1], 16 -(p11) fmpy.s1 r_to_the_8 = rsq, rsq - nop.i 999 ;; -} -// -// Set table_ptr1 to beginning of constant table. -// Get [i_1] - lsb of N_fix_gr. -// - -{ .mfi -(p0) ldfe P1_3 = [table_ptr1], 96 -// -// N even: rsq = r * r -// N odd: S_hi = frcpa(r) -// -(p12) fmerge.ns S_hi = S_hi, S_hi - nop.i 999 ;; -} -// -// Is i_1 even or odd? -// if i_1 == 0, set PR_11. -// if i_1 != 0, set PR_12. -// - -{ .mfi -(p11) ldfe P1_9 = [table_ptr1], -16 -// -// N even: Poly2 = P1_7 + Poly2 * rsq -// N odd: poly2 = Q1_5 + poly2 * rsq -// -(p11) fadd.s1 CORR = rsq, f1 - nop.i 999 ;; -} - -{ .mmi -(p11) ldfe P1_8 = [table_ptr1], -16 ;; -// -// N even: Poly1 = P1_2 + P1_3 * rsq -// N odd: poly1 = 1.0 + S_hi * r -// 16 bits partial account for necessary (-1) -// -(p11) ldfe P1_7 = [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 -// - -{ .mfi -(p11) ldfe P1_6 = [table_ptr1], -16 -// -// N even: Poly2 = P1_5 + Poly2 * rsq -// N odd: poly2 = Q1_3 + poly2 * rsq -// -(p11) fmpy.s1 r_to_the_8 = r_to_the_8, r_to_the_8 - nop.i 999 ;; -} -// -// N even: Poly1 = Poly1 * rsq -// N odd: poly1 = 1.0 + S_hi * r 32 bits partial -// - -{ .mfi -(p11) ldfe P1_5 = [table_ptr1], -16 -(p12) fma.s1 poly1 = S_hi, r, f1 - nop.i 999 ;; -} -// -// 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 -(p0) addl table_ptr2 = @ltoff(TAN_BASE_CONSTANTS), gp -(p11) ldfe P1_4 = [table_ptr1], -16 -(p11) fmpy.s1 CORR = CORR, c -} -;; - - -{ .mmi -(p0) ld8 table_ptr2 = [table_ptr2] - nop.m 999 - nop.i 999 -} -;; - - -{ .mii -(p0) add table_ptr2 = 464, table_ptr2 - nop.i 999 ;; - nop.i 999 -} - -{ .mfi - nop.m 999 -(p11) fma.s1 Poly1 = P1_3, rsq, P1_2 - nop.i 999 ;; -} - -{ .mfi -(p0) ldfe Q1_7 = [table_ptr2], -16 -(p12) fma.s1 S_hi = S_hi, poly1, S_hi - nop.i 999 ;; -} - -{ .mfi -(p0) ldfe Q1_6 = [table_ptr2], -16 -(p11) fma.s1 Poly2 = P1_9, rsq, P1_8 - nop.i 999 ;; -} - -{ .mmi -(p0) 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: Result = 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 Result = Poly, r, CORR - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -// -// N even: Result = r + Result (User supplied rounding mode) -// N odd: poly1 = S_hi * c + poly1 -// -(p12) fmpy.s1 S_lo = S_hi, poly1 - nop.i 999 -} - -{ .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 -// -(p11) fadd.s0 Result = Result, r - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -// -// N odd: S_lo = S_hi * poly1 -// -(p12) fma.s1 S_lo = Q1_1, c, S_lo - nop.i 999 -} - -{ .mfi - nop.m 999 -// -// N odd: Result = Result + S_hi (user supplied rounding mode) -// -(p0) fmpy.s0 fp_tmp = fp_tmp, fp_tmp // Dummy mult to set inexact - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -// -// N odd: S_lo = Q1_1 * c + S_lo -// -(p12) fma.s1 Result = P, r, S_lo - nop.i 999 ;; -} - -{ .mfb - nop.m 999 -// -// N odd: Result = S_lo + r * P -// -(p12) fadd.s0 Result = Result, S_hi -(p0) br.ret.sptk b0 ;; -} - - -TAN_NORMAL_R: - -{ .mfi -(p0) getf.sig sig_r = r -// ******************************************************************* -// ******************************************************************* -// ******************************************************************* -// -// r and c have been computed. -// Make sure ftz mode is set - should be automatic when using wre -// -// -// Get [i_1] - lsb of N_fix_gr alone. -// -(p0) fmerge.s Pos_r = f1, r -(p0) extr.u i_1 = N_fix_gr, 0, 1 ;; -} - -{ .mfi - nop.m 999 -(p0) fmerge.s sgn_r = r, f1 -(p0) cmp.eq.unc p11, p12 = 0x0000, i_1 ;; -} - -{ .mfi - nop.m 999 - nop.f 999 -(p0) extr.u lookup = sig_r, 58, 5 -} - -{ .mlx - nop.m 999 -(p0) movl Create_B = 0x8200000000000000 ;; -} - -{ .mfi -(p0) addl table_ptr1 = @ltoff(TAN_BASE_CONSTANTS), gp - nop.f 999 -(p0) dep Create_B = lookup, Create_B, 58, 5 -} -;; - -// -// Get [i_1] - lsb of N_fix_gr alone. -// Pos_r = abs (r) -// - - -{ .mmi - ld8 table_ptr1 = [table_ptr1] - nop.m 999 - nop.i 999 -} -;; - - -{ .mmi - nop.m 999 -(p0) setf.sig B = Create_B -// -// Set table_ptr1 and table_ptr2 to base address of -// constant table. -// -(p0) add table_ptr1 = 480, table_ptr1 ;; -} - -{ .mmb - nop.m 999 -// -// Is i_1 or i_0 == 0 ? -// Create the constant 1 00000 1000000000000000000000... -// -(p0) ldfe P2_1 = [table_ptr1], 16 - nop.b 999 -} - -{ .mmi - nop.m 999 ;; -(p0) getf.exp exp_r = Pos_r - nop.i 999 -} -// -// Get r's exponent -// Get r's significand -// - -{ .mmi -(p0) ldfe P2_2 = [table_ptr1], 16 ;; -// -// Get the 5 bits or r for the lookup. 1.xxxxx .... -// from sig_r. -// Grab lsb of exp of B -// -(p0) ldfe P2_3 = [table_ptr1], 16 - nop.i 999 ;; -} - -{ .mii - nop.m 999 -(p0) andcm table_offset = 0x0001, exp_r ;; -(p0) shl table_offset = table_offset, 9 ;; -} - -{ .mii - nop.m 999 -// -// Deposit 0 00000 1000000000000000000000... on -// 1 xxxxx yyyyyyyyyyyyyyyyyyyyyy..., -// getting rid of the ys. -// Is B = 2** -2 or B= 2** -1? If 2**-1, then -// we want an offset of 512 for table addressing. -// -(p0) shladd table_offset = lookup, 4, table_offset ;; -// -// B = ........ 1xxxxx 1000000000000000000... -// -(p0) add table_ptr1 = table_ptr1, table_offset ;; -} - -{ .mmb - nop.m 999 -// -// B = ........ 1xxxxx 1000000000000000000... -// Convert B so it has the same exponent as Pos_r -// -(p0) ldfd T_hi = [table_ptr1], 8 - nop.b 999 ;; -} - -// -// x = |r| - B -// Load T_hi. -// Load C_hi. -// - -{ .mmf -(p0) addl table_ptr2 = @ltoff(TAN_BASE_CONSTANTS), gp -(p0) ldfs T_lo = [table_ptr1] -(p0) fmerge.se B = Pos_r, B -} -;; - -{ .mmi - ld8 table_ptr2 = [table_ptr2] - nop.m 999 - nop.i 999 -} -;; - -{ .mii -(p0) add table_ptr2 = 1360, table_ptr2 - nop.i 999 ;; -(p0) add table_ptr2 = table_ptr2, table_offset ;; -} - -{ .mfi -(p0) ldfd C_hi = [table_ptr2], 8 -(p0) fsub.s1 x = Pos_r, B - nop.i 999 ;; -} - -{ .mii -(p0) ldfs C_lo = [table_ptr2],255 - nop.i 999 ;; -// -// xsq = x * x -// N even: Tx = T_hi * x -// Load T_lo. -// Load C_lo - increment pointer to get SC_inv -// - cant get all the way, do an add later. -// -(p0) add table_ptr2 = 569, table_ptr2 ;; -} -// -// N even: Tx1 = Tx + 1 -// N odd: Cx1 = 1 - Cx -// - -{ .mfi -(p0) ldfe SC_inv = [table_ptr2], 0 - nop.f 999 - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -(p0) fmpy.s1 xsq = x, x - nop.i 999 -} - -{ .mfi - nop.m 999 -(p11) fmpy.s1 Tx = T_hi, x - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -(p12) fmpy.s1 Cx = C_hi, x - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -// -// N odd: Cx = C_hi * x -// -(p0) fma.s1 P = P2_3, xsq, P2_2 - nop.i 999 -} - -{ .mfi - nop.m 999 -// -// N even and odd: P = P2_3 + P2_2 * xsq -// -(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 -(p0) 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 -(p0) 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) -// -(p0) fmpy.s0 fp_tmp = fp_tmp, fp_tmp // Dummy mult to set inexact - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -(p0) 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 -// -(p0) 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 -(p0) 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 -// -(p0) 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 -// -(p0) 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 -// -(p0) 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 - nop.i 999 -} - -{ .mfi - nop.m 999 -(p12) fnma.s1 V_lo = tanx, V_hi, V_lo - 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 -// -(p0) 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 -// -(p0) fadd.s1 tail = V_hi, V_lo - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -// -// N even and odd: tail = V_hi + V_lo -// -(p0) 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 -// -(p0) fma.s1 tail = tail, Sx, CORR - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -// -// N even and odd: tail = Sx * tail + CORR -// -(p0) 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 -(p0) br.ret.sptk b0 ;; -} - -.endp __libm_tan -ASM_SIZE_DIRECTIVE(__libm_tan) - - - -// ******************************************************************* -// ******************************************************************* -// ******************************************************************* -// -// Special Code to handle very large argument case. -// Call int pi_by_2_reduce(&x,&r) -// for |arguments| >= 2**63 -// (Arg or x) is in f8 -// Address to save r and c as double - -// (1) (2) (3) (call) (4) -// sp -> + psp -> + psp -> + sp -> + -// | | | | -// | r50 ->| <- r50 f0 ->| r50 -> | -> c -// | | | | -// sp-32 -> | <- r50 f0 ->| f0 ->| <- r50 r49 -> | -> r -// | | | | -// | r49 ->| <- r49 Arg ->| <- r49 | -> x -// | | | | -// sp -64 ->| sp -64 ->| sp -64 ->| | -// -// save pfs save b0 restore gp -// save gp restore b0 -// restore pfs - - - -.proc __libm_callout -__libm_callout: -TAN_ARG_TOO_LARGE: -.prologue -// (1) -{ .mfi - add GR_Parameter_r =-32,sp // Parameter: r address - nop.f 0 -.save ar.pfs,GR_SAVE_PFS - mov GR_SAVE_PFS=ar.pfs // Save ar.pfs -} -{ .mfi -.fframe 64 - add sp=-64,sp // Create new stack - nop.f 0 - mov GR_SAVE_GP=gp // Save gp -};; - -// (2) -{ .mmi - stfe [GR_Parameter_r ] = f0,16 // Clear Parameter r on stack - add GR_Parameter_X = 16,sp // Parameter x address -.save b0, GR_SAVE_B0 - mov GR_SAVE_B0=b0 // Save b0 -};; - -// (3) -.body -{ .mib - stfe [GR_Parameter_r ] = f0,-16 // Clear Parameter c on stack - nop.i 0 - nop.b 0 -} -{ .mib - stfe [GR_Parameter_X] = Arg // Store Parameter x on stack - nop.i 0 -(p0) br.call.sptk b0=__libm_pi_by_2_reduce# -} -;; - - -// (4) -{ .mmi - mov gp = GR_SAVE_GP // Restore gp -(p0) mov N_fix_gr = r8 - nop.i 999 -} -;; - -{ .mmi -(p0) ldfe Arg =[GR_Parameter_X],16 -(p0) ldfs TWO_TO_NEG2 = [table_ptr2],4 - nop.i 999 -} -;; - - -{ .mmb -(p0) ldfe r =[GR_Parameter_r ],16 -(p0) ldfs NEGTWO_TO_NEG2 = [table_ptr2],4 - nop.b 999 ;; -} - -{ .mfi -(p0) ldfe c =[GR_Parameter_r ] - nop.f 999 - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -// -// Is |r| < 2**(-2) -// -(p0) fcmp.lt.unc.s1 p6, p0 = r, TWO_TO_NEG2 - mov b0 = GR_SAVE_B0 // Restore return address -} -;; - -{ .mfi - nop.m 999 -(p6) fcmp.gt.unc.s1 p6, p0 = r, NEGTWO_TO_NEG2 - mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs -} -;; - -{ .mbb -.restore sp - add sp = 64,sp // Restore stack pointer -(p6) br.cond.spnt TAN_SMALL_R -(p0) br.cond.sptk TAN_NORMAL_R -} -;; -.endp __libm_callout -ASM_SIZE_DIRECTIVE(__libm_callout) - - -.proc __libm_TAN_SPECIAL -__libm_TAN_SPECIAL: - -// -// Code for NaNs, Unsupporteds, Infs, or +/- zero ? -// Invalid raised for Infs and SNaNs. -// - -{ .mfb - nop.m 999 -(p0) fmpy.s0 Arg = Arg, f0 -(p0) br.ret.sptk b0 -} -.endp __libm_TAN_SPECIAL -ASM_SIZE_DIRECTIVE(__libm_TAN_SPECIAL) - - -.type __libm_pi_by_2_reduce#,@function -.global __libm_pi_by_2_reduce# |