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Diffstat (limited to 'sysdeps/ia64/fpu/e_acosf.S')
| -rw-r--r-- | sysdeps/ia64/fpu/e_acosf.S | 694 |
1 files changed, 694 insertions, 0 deletions
diff --git a/sysdeps/ia64/fpu/e_acosf.S b/sysdeps/ia64/fpu/e_acosf.S new file mode 100644 index 0000000000..bdcac59d22 --- /dev/null +++ b/sysdeps/ia64/fpu/e_acosf.S @@ -0,0 +1,694 @@ +.file "acosf.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 +//============================================================== +// 02/02/00 Initial version +// 06/28/00 Improved speed +// 06/31/00 Changed register allocation because of some duplicate macros +// moved nan exit bundle up to gain a cycle. +// 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. +// 10/17/00 Improved speed of x=0 and x=1 paths, set D flag if x denormal. +// 03/13/01 Corrected sign of imm1 value in dep instruction. +// 05/20/02 Cleaned up namespace and sf0 syntax +// 02/06/03 Reordered header: .section, .global, .proc, .align +// 04/17/03 Moved mutex after label + + +// Description +//========================================= +// The acosf function computes the principle value of the arc sine of x. +// A doman error occurs for arguments not in the range [-1,+1]. + +// The acosf function returns the arc cosine in the range [0, +pi] radians. +// acos(1) returns +0 +// acos(x) returns a Nan and raises the invalid exception for |x| >1 + +// |x| <= sqrt(2)/2. get Ax and Bx + +// poly_p1 = x p1 +// poly_p3 = x2 p4 + p3 +// poly_p1 = x2 (poly_p1) + x = x2(x p1) + x +// poly_p2 = x2( poly_p3) + p2 = x2(x2 p4 + p3) + p2 + +// poly_Ax = x5(x2( poly_p3) + p2) + x2(x p1) + x +// = x5(x2(x2 p4 + p3) + p2) + x2(x p1) + x + +// poly_p7 = x2 p8 + p7 +// poly_p5 = x2 p6 + p5 + +// poly_p7 = x4 p9 + (x2 p8 + p7) +// poly_Bx = x4 (x4 p9 + (x2 p8 + p7)) + x2 p6 + p5 + +// sinf1 = x11(x4 (x4 p9 + (x2 p8 + p7)) + x2 p6 + p5) + x5(x2(x2 p4 + p3) + p2) + x2(x p1) + x +// = x19 p9 + x17 p8 + x15 p7 x13 p6 + x11 p5 + x9 p4 + x7 p3 + x5 p2 + x3 p1 + x +// answer1 = pi/2 - sinf1 + + + +// |x| > sqrt(2)/2 + +// Get z = sqrt(1-x2) + +// Get polynomial in t = 1-x2 + +// t2 = t t +// t4 = t2 t2 + +// poly_p4 = t p5 + p4 +// poly_p1 = t p1 + 1 + +// poly_p6 = t p7 + p6 +// poly_p2 = t p3 + p2 + +// poly_p8 = t p9 + p8 + +// poly_p4 = t2 poly_p6 + poly_p4 +// = t2 (t p7 + p6) + (t p5 + p4) + +// poly_p2 = t2 poly_p2 + poly_p1 +// = t2 (t p3 + p2) + (t p1 + 1) + +// poly_p4 = t4 poly_p8 + poly_p4 +// = t4 (t p9 + p8) + (t2 (t p7 + p6) + (t p5 + p4)) + +// P(t) = poly_p2 + t4 poly_p8 +// = t2 (t p3 + p2) + (t p1 + 1) + t4 (t4 (t p9 + p8) + (t2 (t p7 + p6) + (t p5 + p4))) +// = t3 p3 + t2 p2 + t p1 + 1 + t9 p9 + t8 p8 + t7 p7 + t6 p6 + t5 p5 + t4 p4 + + +// answer2 = sign(x) z P(t) if x>0 +// = sign(x) z P(t) + pi if x<0 + + +// +// Assembly macros +//========================================= + +// predicate registers +//acosf_pred_LEsqrt2by2 = p7 +//acosf_pred_GTsqrt2by2 = p8 + +// integer registers +ACOSF_Addr1 = r33 +ACOSF_Addr2 = r34 +ACOSF_GR_1by2 = r35 + +ACOSF_GR_3by2 = r36 +ACOSF_GR_5by2 = r37 + +GR_SAVE_B0 = r38 +GR_SAVE_PFS = r39 +GR_SAVE_GP = r40 + +GR_Parameter_X = r41 +GR_Parameter_Y = r42 +GR_Parameter_RESULT = r43 +GR_Parameter_TAG = r44 + +// floating point registers + +acosf_y = f32 +acosf_abs_x = f33 +acosf_x2 = f34 +acosf_sgn_x = f35 + +acosf_1by2 = f36 +acosf_3by2 = f37 +acosf_5by2 = f38 +acosf_coeff_P3 = f39 +acosf_coeff_P8 = f40 + +acosf_coeff_P1 = f41 +acosf_coeff_P4 = f42 +acosf_coeff_P5 = f43 +acosf_coeff_P2 = f44 +acosf_coeff_P7 = f45 + +acosf_coeff_P6 = f46 +acosf_coeff_P9 = f47 +acosf_x2 = f48 +acosf_x3 = f49 +acosf_x4 = f50 + +acosf_x8 = f51 +acosf_x5 = f52 +acosf_const_piby2 = f53 +acosf_const_sqrt2by2 = f54 +acosf_x11 = f55 + +acosf_poly_p1 = f56 +acosf_poly_p3 = f57 +acosf_sinf1 = f58 +acosf_poly_p2 = f59 +acosf_poly_Ax = f60 + +acosf_poly_p7 = f61 +acosf_poly_p5 = f62 +acosf_sgnx_t4 = f63 +acosf_poly_Bx = f64 +acosf_t = f65 + +acosf_yby2 = f66 +acosf_B = f67 +acosf_B2 = f68 +acosf_Az = f69 +acosf_dz = f70 + +acosf_Sz = f71 +acosf_d2z = f72 +acosf_Fz = f73 +acosf_z = f74 +acosf_sgnx_z = f75 + +acosf_t2 = f76 +acosf_2poly_p4 = f77 +acosf_2poly_p6 = f78 +acosf_2poly_p1 = f79 +acosf_2poly_p2 = f80 + +acosf_2poly_p8 = f81 +acosf_t4 = f82 +acosf_Pt = f83 +acosf_sgnx_2poly_p2 = f84 +acosf_sgn_x_piby2 = f85 + +acosf_poly_p7a = f86 +acosf_2poly_p4a = f87 +acosf_2poly_p4b = f88 +acosf_2poly_p2a = f89 +acosf_poly_p1a = f90 + + + + + +// Data tables +//============================================================== + +RODATA + +.align 16 + +LOCAL_OBJECT_START(acosf_coeff_1_table) +data8 0x3FC5555607DCF816 // P1 +data8 0x3F9CF81AD9BAB2C6 // P4 +data8 0x3FC59E0975074DF3 // P7 +data8 0xBFA6F4CC2780AA1D // P6 +data8 0x3FC2DD45292E93CB // P9 +data8 0x3fe6a09e667f3bcd // sqrt(2)/2 +LOCAL_OBJECT_END(acosf_coeff_1_table) + +LOCAL_OBJECT_START(acosf_coeff_2_table) +data8 0x3FA6F108E31EFBA6 // P3 +data8 0xBFCA31BF175D82A0 // P8 +data8 0x3FA30C0337F6418B // P5 +data8 0x3FB332C9266CB1F9 // P2 +data8 0x3ff921fb54442d18 // pi_by_2 +LOCAL_OBJECT_END(acosf_coeff_2_table) + + +.section .text +GLOBAL_LIBM_ENTRY(acosf) + +// Load the addresses of the two tables. +// Then, load the coefficients and other constants. + +{ .mfi + alloc r32 = ar.pfs,1,8,4,0 + fnma.s1 acosf_t = f8,f8,f1 + dep.z ACOSF_GR_1by2 = 0x3f,24,8 // 0x3f000000 +} +{ .mfi + addl ACOSF_Addr1 = @ltoff(acosf_coeff_1_table),gp + fma.s1 acosf_x2 = f8,f8,f0 + addl ACOSF_Addr2 = @ltoff(acosf_coeff_2_table),gp ;; +} + + +{ .mfi + ld8 ACOSF_Addr1 = [ACOSF_Addr1] + fmerge.s acosf_abs_x = f1,f8 + dep ACOSF_GR_3by2 = -1,r0,22,8 // 0x3fc00000 +} +{ .mlx + nop.m 999 + movl ACOSF_GR_5by2 = 0x40200000;; +} + + + +{ .mfi + setf.s acosf_1by2 = ACOSF_GR_1by2 + fmerge.s acosf_sgn_x = f8,f1 + nop.i 999 +} +{ .mfi + ld8 ACOSF_Addr2 = [ACOSF_Addr2] + nop.f 0 + nop.i 999;; +} + + +{ .mfi + setf.s acosf_5by2 = ACOSF_GR_5by2 + fcmp.lt.s1 p11,p12 = f8,f0 + nop.i 999;; +} + +{ .mmf + ldfpd acosf_coeff_P1,acosf_coeff_P4 = [ACOSF_Addr1],16 + setf.s acosf_3by2 = ACOSF_GR_3by2 + fclass.m.unc p8,p0 = f8, 0xc3 ;; //@qnan | @snan +} + + +{ .mfi + ldfpd acosf_coeff_P7,acosf_coeff_P6 = [ACOSF_Addr1],16 + fma.s1 acosf_t2 = acosf_t,acosf_t,f0 + nop.i 999 +} +{ .mfi + ldfpd acosf_coeff_P3,acosf_coeff_P8 = [ACOSF_Addr2],16 + fma.s1 acosf_x4 = acosf_x2,acosf_x2,f0 + nop.i 999;; +} + + +{ .mfi + ldfpd acosf_coeff_P9,acosf_const_sqrt2by2 = [ACOSF_Addr1] + fclass.m.unc p10,p0 = f8, 0x07 //@zero + nop.i 999 +} +{ .mfi + ldfpd acosf_coeff_P5,acosf_coeff_P2 = [ACOSF_Addr2],16 + fma.s1 acosf_x3 = f8,acosf_x2,f0 + nop.i 999;; +} + + +{ .mfi + ldfd acosf_const_piby2 = [ACOSF_Addr2] + frsqrta.s1 acosf_B,p0 = acosf_t + nop.i 999 +} +{ .mfb + nop.m 999 +(p8) fma.s.s0 f8 = f8,f1,f0 +(p8) br.ret.spnt b0 ;; // Exit if x=nan +} + + +{ .mfb + nop.m 999 + fcmp.eq.s1 p6,p0 = acosf_abs_x,f1 +(p10) br.cond.spnt ACOSF_ZERO ;; // Branch if x=0 +} + +{ .mfi + nop.m 999 + fcmp.gt.s1 p9,p0 = acosf_abs_x,f1 + nop.i 999;; +} + +{ .mfi + nop.m 999 + fma.s1 acosf_x8 = acosf_x4,acosf_x4,f0 + nop.i 999 +} +{ .mfb + nop.m 999 + fma.s1 acosf_t4 = acosf_t2,acosf_t2,f0 +(p6) br.cond.spnt ACOSF_ABS_ONE ;; // Branch if |x|=1 +} + +{ .mfi + nop.m 999 + fma.s1 acosf_x5 = acosf_x2,acosf_x3,f0 + nop.i 999 +} +{ .mfb +(p9) mov GR_Parameter_TAG = 59 + fma.s1 acosf_yby2 = acosf_t,acosf_1by2,f0 +(p9) br.cond.spnt __libm_error_region ;; // Branch if |x|>1 +} + + +{ .mfi + nop.m 999 + fma.s1 acosf_Az = acosf_t,acosf_B,f0 + nop.i 999 +} +{ .mfi + nop.m 999 + fma.s1 acosf_B2 = acosf_B,acosf_B,f0 + nop.i 999;; +} + +{ .mfi + nop.m 999 + fma.s1 acosf_poly_p1 = f8,acosf_coeff_P1,f0 + nop.i 999 +} +{ .mfi + nop.m 999 + fma.s1 acosf_2poly_p1 = acosf_coeff_P1,acosf_t,f1 + nop.i 999;; +} + +{ .mfi + nop.m 999 + fma.s1 acosf_poly_p3 = acosf_coeff_P4,acosf_x2,acosf_coeff_P3 + nop.i 999 +} +{ .mfi + nop.m 999 + fma.s1 acosf_2poly_p6 = acosf_coeff_P7,acosf_t,acosf_coeff_P6 + nop.i 999;; +} + +{ .mfi + nop.m 999 + fma.s1 acosf_poly_p7 = acosf_x2,acosf_coeff_P8,acosf_coeff_P7 + nop.i 999 +} +{ .mfi + nop.m 999 + fma.s1 acosf_2poly_p2 = acosf_coeff_P3,acosf_t,acosf_coeff_P2 + nop.i 999;; +} + + +{ .mfi + nop.m 999 + fma.s1 acosf_poly_p5 = acosf_x2,acosf_coeff_P6,acosf_coeff_P5 + nop.i 999 +} +{ .mfi + nop.m 999 + fma.s1 acosf_2poly_p4 = acosf_coeff_P5,acosf_t,acosf_coeff_P4 + nop.i 999;; +} + + +{ .mfi + nop.m 999 + fma.s1 acosf_x11 = acosf_x8,acosf_x3,f0 + nop.i 999 +} +{ .mfi + nop.m 999 + fnma.s1 acosf_dz = acosf_B2,acosf_yby2,acosf_1by2 + nop.i 999;; +} + + +{ .mfi + nop.m 999 + fma.s1 acosf_poly_p1a = acosf_x2,acosf_poly_p1,f8 + nop.i 999 +} +{ .mfi + nop.m 999 + fma.s1 acosf_2poly_p8 = acosf_coeff_P9,acosf_t,acosf_coeff_P8 + nop.i 999;; +} + + +// Get the absolute value of x and determine the region in which x lies + +{ .mfi + nop.m 999 + fcmp.le.s1 p7,p8 = acosf_abs_x,acosf_const_sqrt2by2 + nop.i 999 +} +{ .mfi + nop.m 999 + fma.s1 acosf_poly_p2 = acosf_x2,acosf_poly_p3,acosf_coeff_P2 + nop.i 999;; +} + + +{ .mfi + nop.m 999 + fma.s1 acosf_poly_p7a = acosf_x4,acosf_coeff_P9,acosf_poly_p7 + nop.i 999 +} +{ .mfi + nop.m 999 + fma.s1 acosf_2poly_p2a = acosf_2poly_p2,acosf_t2,acosf_2poly_p1 + nop.i 999;; +} + + +{ .mfi + nop.m 999 +(p8) fma.s1 acosf_sgnx_t4 = acosf_sgn_x,acosf_t4,f0 + nop.i 999 +} +{ .mfi + nop.m 999 +(p8) fma.s1 acosf_2poly_p4a = acosf_2poly_p6,acosf_t2,acosf_2poly_p4 + nop.i 999;; +} + + +{ .mfi + nop.m 999 +(p8) fma.s1 acosf_Sz = acosf_5by2,acosf_dz,acosf_3by2 + nop.i 999 +} +{ .mfi + nop.m 999 +(p8) fma.s1 acosf_d2z = acosf_dz,acosf_dz,f0 + nop.i 999;; +} + + +{ .mfi + nop.m 999 +(p8) fnma.d.s1 acosf_sgn_x_piby2 = acosf_sgn_x,acosf_const_piby2,acosf_const_piby2 + nop.i 999 +} +{ .mfi + nop.m 999 +(p7) fma.s1 acosf_poly_Ax = acosf_x5,acosf_poly_p2,acosf_poly_p1a + nop.i 999;; +} + +{ .mfi + nop.m 999 +(p7) fma.s1 acosf_poly_Bx = acosf_x4,acosf_poly_p7a,acosf_poly_p5 + nop.i 999 +} +{ .mfi + nop.m 999 +(p8) fma.s1 acosf_sgnx_2poly_p2 = acosf_sgn_x,acosf_2poly_p2a,f0 + nop.i 999;; +} + +{ .mfi + nop.m 999 + fcmp.eq.s0 p6,p0 = f8,f0 // Only purpose is to set D if x denormal + nop.i 999 +} +{ .mfi + nop.m 999 +(p8) fma.s1 acosf_2poly_p4b = acosf_2poly_p8,acosf_t4,acosf_2poly_p4a + nop.i 999;; +} + + +{ .mfi + nop.m 999 +(p8) fma.s1 acosf_Fz = acosf_d2z,acosf_Sz,acosf_dz + nop.i 999;; +} + + +{ .mfi + nop.m 999 +(p8) fma.d.s1 acosf_Pt = acosf_2poly_p4b,acosf_sgnx_t4,acosf_sgnx_2poly_p2 + nop.i 999;; +} + +{ .mfi + nop.m 999 +(p8) fma.d.s1 acosf_z = acosf_Az,acosf_Fz,acosf_Az + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +(p7) fma.d.s1 acosf_sinf1 = acosf_x11,acosf_poly_Bx,acosf_poly_Ax + nop.i 999;; +} + +.pred.rel "mutex",p8,p7 //acosf_pred_GTsqrt2by2,acosf_pred_LEsqrt2by2 +{ .mfi + nop.m 999 +(p8) fma.s.s0 f8 = acosf_z,acosf_Pt,acosf_sgn_x_piby2 + nop.i 999 +} + +{ .mfb + nop.m 999 +(p7) fms.s.s0 f8 = acosf_const_piby2,f1,acosf_sinf1 + br.ret.sptk b0 ;; +} + +ACOSF_ZERO: +// Here if x=0 +{ .mfb + nop.m 999 + fma.s.s0 f8 = acosf_const_piby2,f1,f0 // acosf(0)=pi/2 + br.ret.sptk b0 ;; +} + + +ACOSF_ABS_ONE: +.pred.rel "mutex",p11,p12 +// Here if |x|=1 +{ .mfi + nop.m 999 +(p11) fma.s.s0 f8 = acosf_const_piby2,f1,acosf_const_piby2 // acosf(-1)=pi + nop.i 999 +} +{ .mfb + nop.m 999 +(p12) fma.s.s0 f8 = f1,f0,f0 // acosf(1)=0 + br.ret.sptk b0 ;; +} + +GLOBAL_LIBM_END(acosf) + + +// Stack operations when calling error support. +// (1) (2) +// sp -> + psp -> + +// | | +// | | <- GR_Y +// | | +// | <-GR_Y Y2->| +// | | +// | | <- GR_X +// | | +// sp-64 -> + sp -> + +// save ar.pfs save b0 +// save gp + + +// Stack operations when calling error support. +// (3) (call) (4) +// psp -> + sp -> + +// | | +// R3 ->| <- GR_RESULT | -> f8 +// | | +// Y2 ->| <- GR_Y | +// | | +// X1 ->| | +// | | +// sp -> + + +// restore gp +// restore ar.pfs + + +LOCAL_LIBM_ENTRY(__libm_error_region) +.prologue +{ .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] = f1,16 // Store Parameter 2 on stack + add GR_Parameter_X = 16,sp // Parameter 1 address +.save b0, GR_SAVE_B0 + mov GR_SAVE_B0=b0 // Save b0 +};; + +.body +{ .mfi + nop.m 0 + frcpa.s0 f9,p0 = f0,f0 + nop.i 0 +};; + +{ .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] = f9 // 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# |