| .file "atan2f.s" |
| |
| |
| // Copyright (c) 2000 - 2003, 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 |
| //============================================================== |
| // 06/01/00 Initial version |
| // 08/15/00 Bundle added after call to __libm_error_support to properly |
| // set [the previously overwritten] GR_Parameter_RESULT. |
| // 08/17/00 Changed predicate register macro-usage to direct predicate |
| // names due to an assembler bug. |
| // 01/05/01 Fixed flag settings for denormal input. |
| // 01/19/01 Added documentation |
| // 01/30/01 Improved speed |
| // 02/06/02 Corrected .section statement |
| // 05/20/02 Cleaned up namespace and sf0 syntax |
| // 02/06/03 Reordered header: .section, .global, .proc, .align |
| |
| // Description |
| //========================================= |
| // The atan2 function computes the principle value of the arc tangent of y/x using |
| // the signs of both arguments to determine the quadrant of the return value. |
| // A domain error may occur if both arguments are zero. |
| |
| // The atan2 function returns the arc tangent of y/x in the range [-pi,+pi] radians. |
| |
| //.. |
| //..Let (v,u) = (y,x) if |y| <= |x|, and (v,u) = (x,y) otherwise. Note that |
| //..v and u can be negative. We state the relationship between atan2(y,x) and |
| //..atan(v/u). |
| //.. |
| //..Let swap = false if v = y, and swap = true if v = x. |
| //..Define C according to the matrix |
| //.. |
| //.. TABLE FOR C |
| //.. x +ve x -ve |
| //.. no swap (swap = false) sgn(y)*0 sgn(y)*pi |
| //.. swap (swap = true ) sgn(y)*pi/2 sgn(y)*pi/2 |
| //.. |
| //.. atan2(y,x) = C + atan(v/u) if no swap |
| //.. atan2(y,x) = C - atan(v/u) if swap |
| //.. |
| //..These relationship is more efficient to compute as we accommodate signs in v and u |
| //..saving the need to obtain the absolute value before computation can proceed. |
| //.. |
| //..Suppose (v,u) = (y,x), we calculate atan(v/u) as follows: |
| //..A = y * frcpa(x) (so A = (y/x)(1 - beta)) |
| //..atan(y/x) = atan(A) + atan( ((y/x)-A))/(1 + (y/x)A) ), the second term is |
| //..a correction. |
| //..atan(A) is approximated by a polynomial |
| //..A + p1 A^3 + p2 A^5 + ... + p10 A^21, |
| //..atan(G) is approximated as follows: |
| //..Let G = (y - Ax)/(x + Ay), atan(G) can be approximated by G + g * p1 |
| //..where g is a limited precision approximation to G via g = (y - Ax)*frcpa(x + Ay). |
| //.. |
| //..Suppose (v,u) = (x,y), we calculate atan(v/u) as follows: |
| //..Z = x * frcpa(y) (so Z = (x/y)(1 - beta)) |
| //..atan(x/y) = atan(Z) + atan( ((x/y)-Z))/(1 + (x/y)Z) ), the second term is |
| //..a correction. |
| //..atan(Z) is approximated by a polynomial |
| //..Z + p1 Z^3 + p2 Z^5 + ... + p10 Z^21, |
| //..atan(T) is approximated as follows: |
| //..Let T = (x - Ay)/(y + Ax), atan(T) can be approximated by T + t * p1 |
| //..where t is a limited precision approximation to T via t = (x - Ay)*frcpa(y + Ax). |
| //.. |
| //.. |
| //..A = y * frcpa(x) |
| //..atan(A) ~=~ A + p1 A^3 + ... + P10 A^21 |
| //.. |
| //..This polynomial is computed as follows: |
| //..Asq = A*A; Acub = A*Asq, A4 = Asq*Asq |
| //..A5 = Asq*Acub, A6 = Asq*A4; A11 = A5 * A6 |
| //.. |
| //..poly_A1 = p9 + Asq*p10, poly_A2 = p7 + Asq*p8, poly_A3 = p5 + Asq*p6 |
| //..poly_A1 = poly_A2 + A4 * poly_A1 |
| //..poly_A1 = poly_A3 + A4 * poly_A1 |
| //.. |
| //..poly_A4 = p1 * A |
| //,,poly_A5 = p3 + Asq * p4, poly_A4 = A + Asq*poly_A4 |
| //..poly_A5 = p2 + Asq * poly_A5 |
| //..poly_A4 = poly_A4 + A5 * poly_A5 |
| //.. |
| //..atan_A = poly_A4 + A11 * poly_A1 |
| //.. |
| //..atan(G) is approximated as follows: |
| //..G_numer = y - A*x, G_denom = x + A*y |
| //..H1 = frcpa(G_denom) |
| //..H_beta = 1 - H1 * G_denom |
| //..H2 = H1 + H1 * H_beta |
| //..H_beta2 = H_beta*H_beta |
| //..H3 = H2 + H2*H_beta2 |
| //..g = H1 * G_numer; gsq = g*g; atan_G = g*p1, atan_G = atan_G*gsq |
| //..atan_G = G_numer*H3 + atan_G |
| //.. |
| //.. |
| //..A = y * frcpa(x) |
| //..atan(A) ~=~ A + p1 A^3 + ... + P10 A^21 |
| //.. |
| //..This polynomial is computed as follows: |
| //..Asq = A*A; Acub = A*Asq, A4 = Asq*Asq |
| //..A5 = Asq*Acub, A6 = Asq*A4; A11 = A5 * A6 |
| //.. |
| //..poly_A1 = p9 + Asq*p10, poly_A2 = p7 + Asq*p8, poly_A3 = p5 + Asq*p6 |
| //..poly_A1 = poly_A2 + A4 * poly_A1 |
| //..poly_A1 = poly_A3 + A4 * poly_A1 |
| //.. |
| //..poly_A4 = p1 * A |
| //,,poly_A5 = p3 + Asq * p4, poly_A4 = A + Asq*poly_A4 |
| //..poly_A5 = p2 + Asq * poly_A5 |
| //..poly_A4 = poly_A4 + A5 * poly_A5 |
| //.. |
| //..atan_A = poly_A4 + A11 * poly_A1 |
| //.. |
| //.. |
| //..==================================================================== |
| //.. COEFFICIENTS USED IN THE COMPUTATION |
| //..==================================================================== |
| |
| //coef_pj, j = 1,2,...,10; atan(A) ~=~ A + p1 A^3 + p2 A^5 + ... + p10 A^21 |
| // |
| // coef_p1 = -.3333332707155439167401311806315789E+00 |
| // coef_p1 in dbl = BFD5 5555 1219 1621 |
| // |
| // coef_p2 = .1999967670926658391827857030875748E+00 |
| // coef_p2 in dbl = 3FC9 997E 7AFB FF4E |
| // |
| // coef_p3 = -.1427989384500152360161563301087296E+00 |
| // coef_p3 in dbl = BFC2 473C 5145 EE38 |
| // |
| // coef_p4 = .1105852823460720770079031213661163E+00 |
| // coef_p4 in dbl = 3FBC 4F51 2B18 65F5 |
| // |
| // coef_p5 = -.8811839915595312348625710228448363E-01 |
| // coef_p5 in dbl = BFB6 8EED 6A8C FA32 |
| // |
| // coef_p6 = .6742329836955067042153645159059714E-01 |
| // coef_p6 in dbl = 3FB1 42A7 3D7C 54E3 |
| // |
| // coef_p7 = -.4468571068774672908561591262231909E-01 |
| // coef_p7 in dbl = BFA6 E10B A401 393F |
| // |
| // coef_p8 = .2252333246746511135532726960586493E-01 |
| // coef_p8 in dbl = 3F97 105B 4160 F86B |
| // |
| // coef_p9 = -.7303884867007574742501716845542314E-02 |
| // coef_p9 in dbl = BF7D EAAD AA33 6451 |
| // |
| // coef_p10 = .1109686868355312093949039454619058E-02 |
| // coef_p10 in dbl = 3F52 2E5D 33BC 9BAA |
| // |
| |
| // Special values |
| //============================================================== |
| // Y x Result |
| // +number +inf +0 |
| // -number +inf -0 |
| // +number -inf +pi |
| // -number -inf -pi |
| // |
| // +inf +number +pi/2 |
| // -inf +number -pi/2 |
| // +inf -number +pi/2 |
| // -inf -number -pi/2 |
| // |
| // +inf +inf +pi/4 |
| // -inf +inf -pi/4 |
| // +inf -inf +3pi/4 |
| // -inf -inf -3pi/4 |
| // |
| // +1 +1 +pi/4 |
| // -1 +1 -pi/4 |
| // +1 -1 +3pi/4 |
| // -1 -1 -3pi/4 |
| // |
| // +number +0 +pi/2 // does not raise DBZ |
| // -number +0 -pi/2 // does not raise DBZ |
| // +number -0 +pi/2 // does not raise DBZ |
| // -number -0 -pi/2 // does not raise DBZ |
| // |
| // +0 +number +0 |
| // -0 +number -0 |
| // +0 -number +pi |
| // -0 -number -pi |
| // |
| // +0 +0 +0 // does not raise invalid |
| // -0 +0 -0 // does not raise invalid |
| // +0 -0 +pi // does not raise invalid |
| // -0 -0 -pi // does not raise invalid |
| // |
| // Nan anything quiet Y |
| // anything NaN quiet X |
| |
| // atan2(+-0/+-0) sets double error tag to 37 |
| // atan2f(+-0/+-0) sets single error tag to 38 |
| // These are domain errors. |
| |
| |
| // |
| // Assembly macros |
| //========================================= |
| |
| |
| // integer registers |
| atan2f_GR_Addr_1 = r33 |
| atan2f_GR_Addr_2 = r34 |
| GR_SAVE_B0 = r35 |
| |
| GR_SAVE_PFS = r36 |
| GR_SAVE_GP = r37 |
| |
| GR_Parameter_X = r38 |
| GR_Parameter_Y = r39 |
| GR_Parameter_RESULT = r40 |
| GR_Parameter_TAG = r41 |
| |
| // floating point registers |
| atan2f_coef_p1 = f32 |
| atan2f_coef_p10 = f33 |
| atan2f_coef_p7 = f34 |
| atan2f_coef_p6 = f35 |
| |
| atan2f_coef_p3 = f36 |
| atan2f_coef_p2 = f37 |
| atan2f_coef_p9 = f38 |
| atan2f_coef_p8 = f39 |
| atan2f_coef_p5 = f40 |
| |
| atan2f_coef_p4 = f41 |
| atan2f_const_piby2 = f42 |
| atan2f_const_pi = f43 |
| atan2f_const_piby4 = f44 |
| atan2f_const_3piby4 = f45 |
| |
| atan2f_xsq = f46 |
| atan2f_ysq = f47 |
| atan2f_xy = f48 |
| atan2f_const_1 = f49 |
| atan2f_sgn_Y = f50 |
| |
| atan2f_Z0 = f51 |
| atan2f_A0 = f52 |
| atan2f_Z = f53 |
| atan2f_A = f54 |
| atan2f_C = f55 |
| |
| atan2f_U = f56 |
| atan2f_Usq = f57 |
| atan2f_U4 = f58 |
| atan2f_U6 = f59 |
| atan2f_U8 = f60 |
| |
| atan2f_poly_u109 = f61 |
| atan2f_poly_u87 = f62 |
| atan2f_poly_u65 = f63 |
| atan2f_poly_u43 = f64 |
| atan2f_poly_u21 = f65 |
| |
| atan2f_poly_u10to7 = f66 |
| atan2f_poly_u6to3 = f67 |
| atan2f_poly_u10to3 = f68 |
| atan2f_poly_u10to0 = f69 |
| atan2f_poly_u210 = f70 |
| |
| atan2f_T_numer = f71 |
| atan2f_T_denom = f72 |
| atan2f_G_numer = f73 |
| atan2f_G_denom = f74 |
| atan2f_p1rnum = f75 |
| |
| atan2f_R_denom = f76 |
| atan2f_R_numer = f77 |
| atan2f_pR = f78 |
| atan2f_pRC = f79 |
| atan2f_pQRC = f80 |
| |
| atan2f_Q1 = f81 |
| atan2f_Q_beta = f82 |
| atan2f_Q2 = f83 |
| atan2f_Q_beta2 = f84 |
| atan2f_Q3 = f85 |
| |
| atan2f_r = f86 |
| atan2f_rsq = f87 |
| atan2f_poly_atan_U = f88 |
| |
| |
| // predicate registers |
| //atan2f_Pred_Swap = p6 // |y| > |x| |
| //atan2f_Pred_noSwap = p7 // |y| <= |x| |
| //atan2f_Pred_Xpos = p8 // x >= 0 |
| //atan2f_Pred_Xneg = p9 // x < 0 |
| |
| |
| RODATA |
| |
| .align 16 |
| |
| LOCAL_OBJECT_START(atan2f_coef_table1) |
| data8 0xBFD5555512191621 // p1 |
| data8 0x3F522E5D33BC9BAA // p10 |
| data8 0xBFA6E10BA401393F // p7 |
| data8 0x3FB142A73D7C54E3 // p6 |
| data8 0xBFC2473C5145EE38 // p3 |
| data8 0x3FC9997E7AFBFF4E // p2 |
| LOCAL_OBJECT_END(atan2f_coef_table1) |
| |
| LOCAL_OBJECT_START(atan2f_coef_table2) |
| data8 0xBF7DEAADAA336451 // p9 |
| data8 0x3F97105B4160F86B // p8 |
| data8 0xBFB68EED6A8CFA32 // p5 |
| data8 0x3FBC4F512B1865F5 // p4 |
| data8 0x3ff921fb54442d18 // pi/2 |
| data8 0x400921fb54442d18 // pi |
| data8 0x3fe921fb54442d18 // pi/4 |
| data8 0x4002d97c7f3321d2 // 3pi/4 |
| LOCAL_OBJECT_END(atan2f_coef_table2) |
| |
| |
| |
| .section .text |
| GLOBAL_IEEE754_ENTRY(atan2f) |
| |
| { .mfi |
| alloc r32 = ar.pfs,1,5,4,0 |
| frcpa.s1 atan2f_Z0,p0 = f1,f8 // Approx to 1/y |
| nop.i 999 |
| } |
| { .mfi |
| addl atan2f_GR_Addr_1 = @ltoff(atan2f_coef_table1),gp |
| fma.s1 atan2f_xsq = f9,f9,f0 |
| nop.i 999 ;; |
| } |
| |
| |
| { .mfi |
| ld8 atan2f_GR_Addr_1 = [atan2f_GR_Addr_1] |
| frcpa.s1 atan2f_A0,p0 = f1,f9 // Approx to 1/x |
| nop.i 999 |
| } |
| { .mfi |
| nop.m 999 |
| fma.s1 atan2f_ysq = f8,f8,f0 |
| nop.i 999 ;; |
| } |
| |
| { .mfi |
| nop.m 999 |
| fcmp.ge.s1 p8,p9 = f9,f0 // Set p8 if x>=0, p9 if x<0 |
| nop.i 999 |
| } |
| { .mfi |
| nop.m 999 |
| fma.s1 atan2f_xy = f9,f8,f0 |
| nop.i 999 ;; |
| } |
| |
| |
| { .mfi |
| add atan2f_GR_Addr_2 = 0x30, atan2f_GR_Addr_1 |
| fmerge.s atan2f_sgn_Y = f8,f1 |
| nop.i 999 ;; |
| } |
| |
| { .mmf |
| ldfpd atan2f_coef_p1,atan2f_coef_p10 = [atan2f_GR_Addr_1],16 |
| ldfpd atan2f_coef_p9,atan2f_coef_p8 = [atan2f_GR_Addr_2],16 |
| fclass.m p10,p0 = f9,0xe7 // Test x @inf|@snan|@qnan|@zero |
| } |
| ;; |
| |
| { .mfi |
| ldfpd atan2f_coef_p7,atan2f_coef_p6 = [atan2f_GR_Addr_1],16 |
| fma.s1 atan2f_T_denom = atan2f_Z0,atan2f_xsq,f8 |
| nop.i 999 |
| } |
| { .mfi |
| ldfpd atan2f_coef_p5,atan2f_coef_p4 = [atan2f_GR_Addr_2],16 |
| fma.s1 atan2f_Z = atan2f_Z0,f9,f0 |
| nop.i 999 ;; |
| } |
| |
| |
| { .mfi |
| ldfpd atan2f_coef_p3,atan2f_coef_p2 = [atan2f_GR_Addr_1],16 |
| fma.s1 atan2f_G_denom = atan2f_A0,atan2f_ysq,f9 |
| nop.i 999 |
| } |
| { .mfi |
| ldfpd atan2f_const_piby2,atan2f_const_pi = [atan2f_GR_Addr_2],16 |
| fma.s1 atan2f_A = atan2f_A0,f8,f0 |
| nop.i 999 ;; |
| } |
| |
| { .mfi |
| ldfpd atan2f_const_piby4,atan2f_const_3piby4 = [atan2f_GR_Addr_2] |
| fclass.m p11,p0 = f8,0xe7 // Test y @inf|@snan|@qnan|@zero |
| nop.i 999 |
| } |
| { .mfb |
| nop.m 999 |
| fnma.s1 atan2f_T_numer = atan2f_Z0,atan2f_xy,f9 |
| (p10) br.cond.spnt ATAN2F_XY_INF_NAN_ZERO ;; // Branch on x nan,inf,zero |
| } |
| |
| |
| // p6 if |y|>|x|, p7 if |x|>=|y| , use xsq and ysq for test |
| { .mfi |
| nop.m 999 |
| fcmp.gt.s1 p6,p7 = atan2f_ysq,atan2f_xsq |
| nop.i 999 |
| } |
| { .mfb |
| nop.m 999 |
| fnma.s1 atan2f_G_numer = atan2f_A0,atan2f_xy,f8 |
| (p11) br.cond.spnt ATAN2F_XY_INF_NAN_ZERO ;; // Branch on y nan,inf,zero |
| } |
| |
| |
| { .mfi |
| nop.m 999 |
| (p8) fma.s1 atan2f_const_1 = atan2f_sgn_Y,f0,f0 |
| nop.i 999 |
| } |
| { .mfi |
| nop.m 999 |
| (p9) fma.s1 atan2f_const_1 = atan2f_sgn_Y,f1,f0 |
| nop.i 999 ;; |
| } |
| |
| |
| { .mfi |
| nop.m 999 |
| (p6) fnma.s1 atan2f_U = atan2f_Z,f1,f0 |
| nop.i 999 |
| } |
| { .mfi |
| nop.m 999 |
| (p6) fma.s1 atan2f_Usq = atan2f_Z,atan2f_Z,f0 |
| nop.i 999 ;; |
| } |
| |
| |
| { .mfi |
| nop.m 999 |
| (p7) fma.s1 atan2f_U = atan2f_A,f1,f0 |
| nop.i 999 |
| } |
| { .mfi |
| nop.m 999 |
| (p7) fma.s1 atan2f_Usq = atan2f_A,atan2f_A,f0 |
| nop.i 999 ;; |
| } |
| |
| |
| { .mfi |
| nop.m 999 |
| (p6) frcpa.s1 atan2f_Q1,p0 = f1,atan2f_T_denom |
| nop.i 999 |
| } |
| { .mfi |
| nop.m 999 |
| (p6) fma.s1 atan2f_R_denom = atan2f_T_denom,f1,f0 |
| nop.i 999 ;; |
| } |
| |
| |
| { .mfi |
| nop.m 999 |
| (p7) frcpa.s1 atan2f_Q1,p0 = f1,atan2f_G_denom |
| nop.i 999 |
| } |
| { .mfi |
| nop.m 999 |
| (p7) fma.s1 atan2f_R_denom = atan2f_G_denom,f1,f0 |
| nop.i 999 ;; |
| } |
| |
| |
| { .mfi |
| nop.m 999 |
| (p6) fnma.s1 atan2f_R_numer = atan2f_T_numer,f1,f0 |
| nop.i 999 |
| } |
| { .mfi |
| nop.m 999 |
| (p7) fma.s1 atan2f_R_numer = atan2f_G_numer,f1,f0 |
| nop.i 999 ;; |
| } |
| |
| |
| { .mfi |
| nop.m 999 |
| (p6) fnma.s1 atan2f_p1rnum = atan2f_T_numer,atan2f_coef_p1,f0 |
| nop.i 999 ;; |
| } |
| { .mfi |
| nop.m 999 |
| (p7) fma.s1 atan2f_p1rnum = atan2f_G_numer,atan2f_coef_p1,f0 |
| nop.i 999 ;; |
| } |
| |
| |
| { .mfi |
| nop.m 999 |
| fma.s1 atan2f_U4 = atan2f_Usq,atan2f_Usq,f0 |
| nop.i 999 |
| } |
| { .mfi |
| nop.m 999 |
| fma.s1 atan2f_poly_u109 = atan2f_Usq,atan2f_coef_p10,atan2f_coef_p9 |
| nop.i 999 ;; |
| } |
| |
| { .mfi |
| nop.m 999 |
| fma.s1 atan2f_poly_u87 = atan2f_Usq,atan2f_coef_p8,atan2f_coef_p7 |
| nop.i 999 |
| } |
| { .mfi |
| nop.m 999 |
| fma.s1 atan2f_poly_u65 = atan2f_Usq,atan2f_coef_p6,atan2f_coef_p5 |
| nop.i 999 ;; |
| } |
| |
| |
| { .mfi |
| nop.m 999 |
| fma.s1 atan2f_poly_u43 = atan2f_Usq,atan2f_coef_p4,atan2f_coef_p3 |
| nop.i 999 |
| } |
| { .mfi |
| nop.m 999 |
| fnma.s1 atan2f_Q_beta = atan2f_Q1,atan2f_R_denom,f1 |
| nop.i 999 ;; |
| } |
| |
| |
| { .mfi |
| nop.m 999 |
| fma.s1 atan2f_poly_u21 = atan2f_Usq,atan2f_coef_p2,atan2f_coef_p1 |
| nop.i 999 |
| } |
| { .mfi |
| nop.m 999 |
| fma.s1 atan2f_r = atan2f_Q1,atan2f_R_numer,f0 |
| nop.i 999 ;; |
| } |
| |
| { .mfi |
| nop.m 999 |
| (p6) fma.s1 atan2f_C = atan2f_sgn_Y,atan2f_const_piby2,f0 |
| nop.i 999 |
| } |
| { .mfi |
| nop.m 999 |
| (p7) fma.s1 atan2f_C = atan2f_const_1,atan2f_const_pi,f0 |
| nop.i 999 ;; |
| } |
| |
| { .mfi |
| nop.m 999 |
| fma.s1 atan2f_U6 = atan2f_U4,atan2f_Usq,f0 |
| nop.i 999 |
| } |
| { .mfi |
| nop.m 999 |
| fma.s1 atan2f_U8 = atan2f_U4,atan2f_U4,f0 |
| nop.i 999 ;; |
| } |
| |
| { .mfi |
| nop.m 999 |
| fma.s1 atan2f_poly_u10to7 = atan2f_U4,atan2f_poly_u109,atan2f_poly_u87 |
| nop.i 999 |
| } |
| { .mfi |
| nop.m 999 |
| fma.s1 atan2f_pR = atan2f_p1rnum,atan2f_Q1,f0 |
| nop.i 999 ;; |
| } |
| |
| { .mfi |
| nop.m 999 |
| fma.s1 atan2f_poly_u6to3 = atan2f_U4,atan2f_poly_u65,atan2f_poly_u43 |
| nop.i 999 |
| } |
| { .mfi |
| nop.m 999 |
| fma.s1 atan2f_Q2 = atan2f_Q1,atan2f_Q_beta,atan2f_Q1 |
| nop.i 999 ;; |
| } |
| |
| { .mfi |
| nop.m 999 |
| fma.s1 atan2f_Q_beta2 = atan2f_Q_beta,atan2f_Q_beta,f0 |
| nop.i 999 |
| } |
| { .mfi |
| nop.m 999 |
| fma.s1 atan2f_rsq = atan2f_r,atan2f_r,f0 |
| nop.i 999 ;; |
| } |
| |
| { .mfi |
| nop.m 999 |
| fma.s1 atan2f_poly_u210 = atan2f_Usq,atan2f_poly_u21,f1 |
| nop.i 999 ;; |
| } |
| |
| { .mfi |
| nop.m 999 |
| fcmp.eq.s0 p8,p0 = f8,f9 // Dummy op to set flag on denormal inputs |
| nop.i 999 |
| } |
| { .mfi |
| nop.m 999 |
| fma.s1 atan2f_poly_u10to3 = atan2f_U8,atan2f_poly_u10to7,atan2f_poly_u6to3 |
| nop.i 999 ;; |
| } |
| |
| { .mfi |
| nop.m 999 |
| fma.s1 atan2f_Q3 = atan2f_Q2,atan2f_Q_beta2,atan2f_Q2 |
| nop.i 999 |
| } |
| { .mfi |
| nop.m 999 |
| fma.s1 atan2f_pRC = atan2f_rsq,atan2f_pR,atan2f_C |
| nop.i 999 ;; |
| } |
| |
| { .mfi |
| nop.m 999 |
| fma.s1 atan2f_poly_u10to0 = atan2f_U6,atan2f_poly_u10to3,atan2f_poly_u210 |
| nop.i 999 ;; |
| } |
| |
| { .mfi |
| nop.m 999 |
| fma.s1 atan2f_pQRC = atan2f_R_numer,atan2f_Q3,atan2f_pRC |
| nop.i 999 ;; |
| } |
| |
| { .mfb |
| nop.m 999 |
| fma.s.s0 f8 = atan2f_U,atan2f_poly_u10to0,atan2f_pQRC |
| br.ret.sptk b0 ;; |
| } |
| |
| |
| |
| ATAN2F_XY_INF_NAN_ZERO: |
| |
| { .mfi |
| nop.m 999 |
| fclass.m p10,p0 = f8,0xc3 // Is y nan |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| fclass.m p12,p0 = f9,0xc3 // Is x nan |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| fclass.m p6,p0 = f9,0x21 // Is x +inf |
| nop.i 999 |
| } |
| { .mfb |
| nop.m 999 |
| (p10) fma.s.s0 f8 = f9,f8,f0 // Result quietized y if y is nan |
| (p10) br.ret.spnt b0 // Exit if y is nan |
| } |
| ;; |
| |
| |
| { .mfi |
| nop.m 999 |
| (p6) fclass.m.unc p7,p8 = f8,0x23 // x +inf, is y inf |
| nop.i 999 |
| } |
| { .mfb |
| nop.m 999 |
| (p12) fnorm.s.s0 f8 = f9 // Result quietized x if x is nan, y not nan |
| (p12) br.ret.spnt b0 // Exit if x is nan, y not nan |
| } |
| ;; |
| |
| // Here if x or y inf, or x or y zero |
| { .mfi |
| nop.m 999 |
| fcmp.eq.s0 p15,p0 = f8,f9 // Dummy op to set flag on denormal inputs |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| fclass.m p11,p12 = f9,0x22 // Is x -inf |
| nop.i 999 |
| } |
| { .mfb |
| nop.m 999 |
| (p7) fma.s.s0 f8 = atan2f_sgn_Y, atan2f_const_piby4,f0 // Result +-pi/4 |
| (p7) br.ret.spnt b0 // Exit if x +inf and y inf |
| } |
| ;; |
| |
| { .mfb |
| nop.m 999 |
| (p8) fmerge.s f8 = f8,f0 // If x +inf and y not inf, result +-0 |
| (p8) br.ret.spnt b0 // Exit if x +inf and y not inf |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| (p12) fclass.m.unc p13,p0 = f8,0x23 // x not -inf, is y inf |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| (p11) fclass.m.unc p14,p15 = f8,0x23 // x -inf, is y inf |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| fclass.m p6,p7 = f9,0x7 // Is x zero |
| nop.i 999 |
| } |
| { .mfb |
| nop.m 999 |
| (p13) fma.s.s0 f8 = atan2f_sgn_Y, atan2f_const_piby2,f0 // Result +-pi/2 |
| (p13) br.ret.spnt b0 // Exit if x not -inf and y inf |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| (p14) fma.s.s0 f8 = atan2f_sgn_Y, atan2f_const_3piby4,f0 // Result +-3pi/4 |
| nop.i 999 |
| } |
| { .mfb |
| nop.m 999 |
| (p15) fma.s.s0 f8 = atan2f_sgn_Y, atan2f_const_pi,f0 // Result +-pi |
| (p11) br.ret.spnt b0 // Exit if x -inf |
| } |
| ;; |
| |
| // Here if x or y zero |
| { .mfi |
| nop.m 999 |
| (p7) fclass.m.unc p8,p9 = f9,0x19 // x not zero, y zero, is x > zero |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| (p6) fclass.m.unc p10,p11 = f8,0x7 // x zero, is y zero |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| (p8) fmerge.s f8 = f8, f0 // x > zero and y zero, result is +-zero |
| nop.i 999 |
| } |
| { .mfb |
| nop.m 999 |
| (p9) fma.s.s0 f8 = atan2f_sgn_Y, atan2f_const_pi,f0 // x < 0, y 0, result +-pi |
| (p10) br.cond.spnt __libm_error_region // Branch if x zero and y zero |
| } |
| ;; |
| |
| { .mfb |
| nop.m 999 |
| (p11) fma.s.s0 f8 = atan2f_sgn_Y, atan2f_const_piby2,f0 // x zero, y not zero |
| br.ret.sptk b0 // Final special case exit |
| } |
| ;; |
| |
| |
| GLOBAL_IEEE754_END(atan2f) |
| |
| |
| LOCAL_LIBM_ENTRY(__libm_error_region) |
| .prologue |
| mov GR_Parameter_TAG = 38 |
| fclass.m p10,p11 = f9,0x5 // @zero | @pos |
| ;; |
| (p10) fmerge.s f10 = f8, f0 |
| (p11) fma.s.s0 f10 = atan2f_sgn_Y, atan2f_const_pi,f0 |
| ;; |
| |
| { .mfi |
| add GR_Parameter_Y=-32,sp // Parameter 2 value |
| nop.f 999 |
| .save ar.pfs,GR_SAVE_PFS |
| mov GR_SAVE_PFS=ar.pfs // Save ar.pfs |
| } |
| |
| { .mfi |
| .fframe 64 |
| add sp=-64,sp // Create new stack |
| nop.f 0 |
| mov GR_SAVE_GP=gp // Save gp |
| } |
| ;; |
| |
| { .mmi |
| stfs [GR_Parameter_Y] = f9,16 // 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 |
| { .mib |
| stfs [GR_Parameter_X] = f8 // Store Parameter 1 on stack |
| add GR_Parameter_RESULT = 0,GR_Parameter_Y |
| nop.b 0 // Parameter 3 address |
| } |
| { .mib |
| stfs [GR_Parameter_Y] = f10 // 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 |
| };; |
| |
| { .mmi |
| ldfs 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# |
