.file "libm_atan2_reg.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 //============================================================== // 2/02/00: Initial version // 4/04/00 Unwind support added #include "libm_support.h" .data .align 64 ASM_TYPE_DIRECTIVE(Constants_atan#,@object) Constants_atan: data4 0x54442D18, 0x3FF921FB, 0x248D3132, 0x3E000000 // double pi/2, single lo_pi/2, two**(-3) data4 0xAAAAAAA3, 0xAAAAAAAA, 0x0000BFFD, 0x00000000 // P_1 data4 0xCCCC54B2, 0xCCCCCCCC, 0x00003FFC, 0x00000000 // P_2 data4 0x47E4D0C2, 0x92492492, 0x0000BFFC, 0x00000000 // P_3 data4 0x58870889, 0xE38E38E0, 0x00003FFB, 0x00000000 // P_4 data4 0x290149F8, 0xBA2E895B, 0x0000BFFB, 0x00000000 // P_5 data4 0x250F733D, 0x9D88E6D4, 0x00003FFB, 0x00000000 // P_6 data4 0xFB8745A0, 0x884E51FF, 0x0000BFFB, 0x00000000 // P_7 data4 0x394396BD, 0xE1C7412B, 0x00003FFA, 0x00000000 // P_8 data4 0xAAAAA52F, 0xAAAAAAAA, 0x0000BFFD, 0x00000000 // Q_1 data4 0xC75B60D3, 0xCCCCCCCC, 0x00003FFC, 0x00000000 // Q_2 data4 0x011F1940, 0x924923AD, 0x0000BFFC, 0x00000000 // Q_3 data4 0x2A5F89BD, 0xE36F716D, 0x00003FFB, 0x00000000 // Q_4 // Entries Tbl_hi (double precision) // B = 1+Index/16+1/32 Index = 0 // Entries Tbl_lo (single precision) // B = 1+Index/16+1/32 Index = 0 data4 0xA935BD8E, 0x3FE9A000, 0x23ACA08F, 0x00000000 // Entries Tbl_hi (double precision) Index = 0,1,...,15 // B = 2^(-1)*(1+Index/16+1/32) // Entries Tbl_lo (single precision) // Index = 0,1,...,15 B = 2^(-1)*(1+Index/16+1/32) data4 0x7F175A34, 0x3FDE77EB, 0x238729EE, 0x00000000 data4 0x73C1A40B, 0x3FE0039C, 0x249334DB, 0x00000000 data4 0x5B5B43DA, 0x3FE0C614, 0x22CBA7D1, 0x00000000 data4 0x88BE7C13, 0x3FE1835A, 0x246310E7, 0x00000000 data4 0xE2CC9E6A, 0x3FE23B71, 0x236210E5, 0x00000000 data4 0x8406CBCA, 0x3FE2EE62, 0x2462EAF5, 0x00000000 data4 0x1CD41719, 0x3FE39C39, 0x24B73EF3, 0x00000000 data4 0x5B795B55, 0x3FE44506, 0x24C11260, 0x00000000 data4 0x5BB6EC04, 0x3FE4E8DE, 0x242519EE, 0x00000000 data4 0x1F732FBA, 0x3FE587D8, 0x24D4346C, 0x00000000 data4 0x115D7B8D, 0x3FE6220D, 0x24ED487B, 0x00000000 data4 0x920B3D98, 0x3FE6B798, 0x2495FF1E, 0x00000000 data4 0x8FBA8E0F, 0x3FE74897, 0x223D9531, 0x00000000 data4 0x289FA093, 0x3FE7D528, 0x242B0411, 0x00000000 data4 0x576CC2C5, 0x3FE85D69, 0x2335B374, 0x00000000 data4 0xA99CC05D, 0x3FE8E17A, 0x24C27CFB, 0x00000000 // // Entries Tbl_hi (double precision) Index = 0,1,...,15 // B = 2^(-2)*(1+Index/16+1/32) // Entries Tbl_lo (single precision) // Index = 0,1,...,15 B = 2^(-2)*(1+Index/16+1/32) // data4 0x510665B5, 0x3FD025FA, 0x24263482, 0x00000000 data4 0x362431C9, 0x3FD1151A, 0x242C8DC9, 0x00000000 data4 0x67E47C95, 0x3FD20255, 0x245CF9BA, 0x00000000 data4 0x7A823CFE, 0x3FD2ED98, 0x235C892C, 0x00000000 data4 0x29271134, 0x3FD3D6D1, 0x2389BE52, 0x00000000 data4 0x586890E6, 0x3FD4BDEE, 0x24436471, 0x00000000 data4 0x175E0F4E, 0x3FD5A2E0, 0x2389DBD4, 0x00000000 data4 0x9F5FA6FD, 0x3FD68597, 0x2476D43F, 0x00000000 data4 0x52817501, 0x3FD76607, 0x24711774, 0x00000000 data4 0xB8DF95D7, 0x3FD84422, 0x23EBB501, 0x00000000 data4 0x7CD0C662, 0x3FD91FDE, 0x23883A0C, 0x00000000 data4 0x66168001, 0x3FD9F930, 0x240DF63F, 0x00000000 data4 0x5422058B, 0x3FDAD00F, 0x23FE261A, 0x00000000 data4 0x378624A5, 0x3FDBA473, 0x23A8CD0E, 0x00000000 data4 0x0AAD71F8, 0x3FDC7655, 0x2422D1D0, 0x00000000 data4 0xC9EC862B, 0x3FDD45AE, 0x2344A109, 0x00000000 // // Entries Tbl_hi (double precision) Index = 0,1,...,15 // B = 2^(-3)*(1+Index/16+1/32) // Entries Tbl_lo (single precision) // Index = 0,1,...,15 B = 2^(-3)*(1+Index/16+1/32) // data4 0x84212B3D, 0x3FC068D5, 0x239874B6, 0x00000000 data4 0x41060850, 0x3FC16465, 0x2335E774, 0x00000000 data4 0x171A535C, 0x3FC25F6E, 0x233E36BE, 0x00000000 data4 0xEDEB99A3, 0x3FC359E8, 0x239680A3, 0x00000000 data4 0xC6092A9E, 0x3FC453CE, 0x230FB29E, 0x00000000 data4 0xBA11570A, 0x3FC54D18, 0x230C1418, 0x00000000 data4 0xFFB3AA73, 0x3FC645BF, 0x23F0564A, 0x00000000 data4 0xE8A7D201, 0x3FC73DBD, 0x23D4A5E1, 0x00000000 data4 0xE398EBC7, 0x3FC8350B, 0x23D4ADDA, 0x00000000 data4 0x7D050271, 0x3FC92BA3, 0x23BCB085, 0x00000000 data4 0x601081A5, 0x3FCA217E, 0x23BC841D, 0x00000000 data4 0x574D780B, 0x3FCB1696, 0x23CF4A8E, 0x00000000 data4 0x4D768466, 0x3FCC0AE5, 0x23BECC90, 0x00000000 data4 0x4E1D5395, 0x3FCCFE65, 0x2323DCD2, 0x00000000 data4 0x864C9D9D, 0x3FCDF110, 0x23F53F3A, 0x00000000 data4 0x451D980C, 0x3FCEE2E1, 0x23CCB11F, 0x00000000 data4 0x54442D18, 0x400921FB, 0x33145C07, 0x3CA1A626 // I two doubles data4 0x54442D18, 0x3FF921FB, 0x33145C07, 0x3C91A626 // I_by_2 two dbls data4 0x54442D18, 0x3FE921FB, 0x33145C07, 0x3C81A626 // I_by_4 two dbls data4 0x7F3321D2, 0x4002D97C, 0x4C9E8A0A, 0x3C9A7939 // 3I_by_4 two dbls ASM_SIZE_DIRECTIVE(Constants_atan#) .section .text .proc __libm_atan2_reg# .global __libm_atan2_reg# .align 64 __libm_atan2_reg: { .mfi alloc r32 = ar.pfs,0,20,4,0 (p0) mov f32 = f8 nop.i 0 } { .mmi nop.m 0 (p0) addl r39 = @ltoff(Constants_atan#), gp nop.i 999 } ;; { .mmi ld8 r39 = [r39] nop.m 999 nop.i 999 } ;; { .mfi nop 999 // EMbo added ... (p0) mov f33 = f9 nop.i 0 } { .mfi nop 999 // EMbo added ... (p0) fclass.nm.unc p9,p0 = f32 ,0x1FF nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... (p0) fclass.nm.unc p8,p0 = f33 ,0x1FF nop 999 // EMbo added ... } { .mfi nop 999 // EMbo added ... (p0) fclass.m.unc p6,p0 = f33 ,0x103 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... (p0) fclass.m.unc p7,p0 = f32 ,0x103 nop 999 // EMbo added ... } { .mfi nop 999 // EMbo added ... (p0) fclass.m.unc p12,p0 = f33 ,0x0C3 nop 999;; // EMbo added ... } { .mfb nop 999 // EMbo added ... // // Check for NatVals. // Check for EM Unsupporteds // Check for NaNs. // (p0) fclass.m.unc p13,p0 = f32 ,0x0C3 (p6) br.cond.sptk L(ATAN_NATVAL);; } { .mbb nop 999 // EMbo added ... (p7) br.cond.sptk L(ATAN_NATVAL) (p8) br.cond.sptk L(ATAN_UNSUPPORTED);; } { .mib (p0) add r40 = 96, r39 nop 999 // EMbo added ... (p9) br.cond.sptk L(ATAN_UNSUPPORTED);; } { .mib (p0) ldfd f50 = [r39],8 nop 999 // EMbo added ... (p12) br.cond.sptk L(ATAN_NAN);; } { .mfb nop 999 // EMbo added ... (p0) fnorm.s1 f33 = f33 (p13) br.cond.sptk L(ATAN_NAN);; } { .mfi (p0) ldfs f51 = [r39],4 // // Remove sign bits from exponents // Load 2**(-3) // Normalize the input argument. // (p0) fnorm.s1 f32 = f32 nop 999 // EMbo added ... } { .mfi nop 999 // EMbo added ... (p0) mov f82 = f1 nop 999;; // EMbo added ... } { .mmi nop 999;; // EMbo added ... (p0) ldfs f78 = [r39],180 nop 999;; // EMbo added ... } { .mmi (p0) getf.exp r36 = f33;; // // Get exp and sign of ArgX // Get exp and sign of ArgY // Load 2**(-3) and increment ptr to Q_4. // (p0) getf.exp r37 = f32 (p0) shr.u r36 = r36,17;; } { .mfi nop 999 // EMbo added ... (p0) fmerge.s f84 = f1,f32 (p0) shr.u r37 = r37,17;; } { .mfi nop 999 // EMbo added ... // // ArgX_abs = |ArgX| // ArgY_abs = |ArgY| // sign_X is sign bit of ArgX // sign_Y is sign bit of ArgY // (p0) fmerge.s f83 = f1,f33 (p0) cmp.eq.unc p8,p9 = 0x00000, r37;; } { .mfi nop 999 // EMbo added ... (p8) fadd.s1 f34 = f0, f1 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... (p9) fsub.s1 f34 = f0, f1 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... (p0) fmin.s1 f36 = f83, f84 nop 999 // EMbo added ... } { .mfi nop 999 // EMbo added ... (p0) fmax.s1 f35 = f83, f84 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... // // Is ArgX_abs >= ArgY_abs // Is sign_Y == 0? // (p0) fcmp.ge.s1 p6,p7 = f83,f84 nop 999;; // EMbo added ... } { .mii (p6) cmp.eq.unc p10, p11 = 0x00000, r36 (p6) add r38 = r0, r0;; // // U = max(ArgX_abs,ArgY_abs) // V = min(ArgX_abs,ArgY_abs) // if p6, swap = 0 // if p7, swap = 1 // // // Let M = 1.0 // if p8, s_Y = 1.0 // if p9, s_Y = -1.0 // (p7) add r38 = 1,r0;; } { .mfi nop 999 // EMbo added ... (p0) frcpa.s1 f37, p6 = f36, f35 nop 999;; // EMbo added ... } { .mfb nop 999 // EMbo added ... // // E = frcpa(V,U) // (p10) fsub.s1 f82 = f82, f1 (p6) br.cond.sptk L(ATAN_STEP2);; } { .mib nop 999 // EMbo added ... nop 999 // EMbo added ... // /**************************************************/ // /********************* STEP2 **********************/ // /**************************************************/ (p0) br.cond.spnt L(ATAN_SPECIAL_HANDLING);; } L(ATAN_STEP2): { .mlx nop 999 // EMbo added ... (p0) movl r47 = 0x8400000000000000 } { .mlx nop 999 // EMbo added ... (p0) movl r48 = 0x0000000000000100;; } { .mfi nop 999 // EMbo added ... (p0) fmpy.s1 f38 = f37, f36 nop 999 // EMbo added ... } { .mfi nop 999 // EMbo added ... (p0) fcmp.lt.unc.s0 p0,p9 = f9,f1 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... (p0) fcmp.lt.unc.s0 p0,p8 = f8,f1 nop 999 // EMbo added ... } { .mfi nop 999 // EMbo added ... // // Q = E * V // (p11) fadd.s1 f82 = f82, f1 nop 999;; // EMbo added ... } { .mfi (p0) getf.sig r46 = f38 (p0) fcmp.lt.unc p6,p7 = f38,f78 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... (p0) fmpy.s1 f38 = f37, f36 (p0) extr.u r42 = r46, 59, 4;; } { .mfi nop 999 // EMbo added ... (p0) fmpy.s1 f50 = f82, f50 (p0) dep r47 = r42, r47, 59, 4 } { .mfi nop 999 // EMbo added ... (p0) fmpy.s1 f51 = f82, f51 nop 999;; // EMbo added ... } { .mmi nop 999;; // EMbo added ... // // Is Q < 2**(-3)? // // // Do fcmp to raise any denormal operand // exceptions. // (p0) getf.exp r45 = f38 nop 999;; // EMbo added ... } { .mib // // lookup = b_1 b_2 b_3 B_4 // // // Generate 1.b_1 b_2 b_3 b_4 1 0 0 0 ... 0 // (p0) andcm r41 = 0x0003, r45 nop 999 // EMbo added ... // // We waited a few extra cycles so P_lo and P_hi could be calculated. // Load the constant 256 for loading up table entries. // // /**************************************************/ // /********************* STEP3 **********************/ // /**************************************************/ (p6) br.cond.spnt L(ATAN_POLY);; } { .mii (p0) setf.sig f39 = r47 (p0) cmp.eq.unc p8, p9 = 0x0000, r41 // // z_hi = s exp 1.b_1 b_2 b_3 b_4 1 0 0 0 ... 0 // point to beginning of Tbl_hi entries - k = 0. // (p0) add r40 = 16, r39 } { .mmi (p0) ldfe f73 = [r39],-16;; (p9) sub r41 = r41,r0,1 (p9) add r40 = 16,r40 } { .mfi (p8) ldfd f48 = [r40],8 (p0) fmpy.s1 f50 = f34, f50 (p0) xor r38 = r36,r38;; } { .mmi (p0) ldfe f71 = [r39],-16;; (p8) ldfs f49 = [r40],8 (p9) pmpy2.r r41 = r41,r48;; } { .mfi (p0) ldfe f69 = [r39],-16 // // Let z_hi have exponent and sign of original Q // Load the Tbl_hi(0) else, increment pointer. // (p0) fmerge.se f39 = f38,f39 (p9) shladd r42 = r42,0x0004,r41;; } { .mmi (p9) add r40 = r40, r42;; (p9) ldfd f48 = [r40],8 nop 999;; // EMbo added ... } { .mmi (p0) ldfe f67 = [r39],-16;; (p9) ldfs f49 = [r40],8 nop 999 // EMbo added ... } { .mfi nop 999 // EMbo added ... // // U_prime_hi = U + V * z_hi // Load the Tbl_lo(0) // (p0) fma.s1 f40 = f36, f39, f35 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... (p0) fnma.s1 f42 = f35, f39, f36 nop 999 // EMbo added ... } { .mfi nop 999 // EMbo added ... (p0) mov f52 = f48 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... (p0) frcpa.s1 f43, p6 = f1, f40 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... // // U_prime_lo = U - U_prime_hi // k = k * 256 - result can be 0, 256, or 512. // (p0) fsub.s1 f41 = f35, f40 (p0) cmp.eq.unc p7, p6 = 0x00000, r38 } { .mfi nop 999 // EMbo added ... (p0) fmpy.s1 f52 = f34, f52 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... (p7) fadd.s1 f54 = f0, f1 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... (p6) fsub.s1 f54 = f0, f1 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... (p0) fnma.s1 f80 = f43, f40, f1 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... (p0) fadd.s1 f79 = f41, f40 nop 999 // EMbo added ... } { .mfi nop 999 // EMbo added ... (p0) fma.s1 f41 = f36, f39, f41 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... (p0) fma.s1 f56 = f54, f52, f50 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... (p0) fma.s1 f43 = f80, f43, f43 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... // // U_prime_lo = U - U_hold // lookup -> lookup * 16 + k // // // V_prime = V - U * z_hi // U_prime_lo = V * z_hi + U_prime_lo // (p0) fsub.s1 f79 = f35, f79 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... (p0) fnma.s1 f80 = f43, f40, f1 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... // // C_hi = frcpa(1,U_prime_hi) // U_prime_lo = U_prime_lo + U_hold // // // C_hi_hold = 1 - C_hi * U_prime_hi (1) // // // C_hi = C_hi + C_hi * C_hi_hold (1) // // // C_hi_hold = 1 - C_hi * U_prime_hi (2) // (p0) fadd.s1 f41 = f41, f79 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... // // C_hi = C_hi + C_hi * C_hi_hold (2) // (p0) fma.s1 f43 = f80, f43, f43 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... // // C_hi_hold = 1 - C_hi * U_prime_hi (3) // (p0) fnma.s1 f80 = f43, f40, f1 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... // // C_hi = C_hi + C_hi * C_hi_hold (3) // (p0) fma.s1 f43 = f80, f43, f43 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... // // w_hi = V_prime * C_hi // (p0) fmpy.s1 f44 = f42, f43 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... (p0) fmpy.s1 f46 = f44, f44 nop 999 // EMbo added ... } { .mfi nop 999 // EMbo added ... // // wsq = w_hi * w_hi // w_lo = = V_prime - w_hi * U_prime_hi // (p0) fnma.s1 f45 = f44, f40, f42 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... (p0) fma.s1 f47 = f46, f73, f71 nop 999 // EMbo added ... } { .mfi nop 999 // EMbo added ... // // poly = Q_3 + wsq * Q_4 // w_lo = = w_lo - w_hi * U_prime_lo // (p0) fnma.s1 f45 = f44, f41, f45 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... (p0) fma.s1 f47 = f46, f47, f69 nop 999 // EMbo added ... } { .mfi nop 999 // EMbo added ... // // poly = Q_2 + wsq * poly // w_lo = = w_lo * C_hi // (p0) fmpy.s1 f45 = f43, f45 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... (p0) fma.s1 f47 = f46, f47, f67 nop 999 // EMbo added ... } { .mfi nop 999 // EMbo added ... // // poly = Q_1 + wsq * poly // A_lo = Tbl_lo + w_lo // swap = xor(swap,sign_X) // (p0) fadd.s1 f53 = f49, f45 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... // // Is (swap) != 0 ? // poly = wsq * poly // A_hi = Tbl_hi // (p0) fmpy.s1 f47 = f46, f47 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... // // poly = wsq * poly // // // if (p6) sigma = -1.0 // if (p7) sigma = 1.0 // (p0) fmpy.s1 f47 = f44, f47 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... // // P_hi = s_Y * P_hi // A_lo = A_lo + poly // (p0) fadd.s1 f53 = f53, f47 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... // // A_lo = A_lo + w_hi // A_hi = s_Y * A_hi // (p0) fadd.s1 f53 = f53, f44 nop 999;; // EMbo added ... } { .mfb nop 999 // EMbo added ... // // result_hi = P_hi + sigma * A_hi // result_lo = P_lo + sigma * A_lo // (p0) fma.s1 f55 = f54, f53, f51 (p0) br.cond.sptk L(RETURN_ATAN);; } // // result = result_hi + result_lo * s_Y (User Supplied Rounding Mode) // // (p0) fma.d.s0 f57 = f55, f34, f56 // // /**************************************************/ // /********************* STEP4 **********************/ // /**************************************************/ // L(ATAN_POLY): { .mmi (p0) xor r38 = r36,r38 (p0) addl r39 = @ltoff(Constants_atan#), gp nop.i 999 } ;; { .mmi ld8 r39 = [r39] nop.m 999 nop.i 999 } ;; { .mlx nop 999 // EMbo added ... (p0) movl r47 = 0x24005;; } { .mfi (p0) add r39 = 128, r39 (p0) fnma.s1 f81 = f37, f35, f1 (p0) cmp.eq.unc p7, p6 = 0x00000, r38;; } { .mmf nop 999 // EMbo added ... (p0) ldfe f77 = [r39],-16 // // Iterate 3 times E = E + E*(1.0 - E*U) // Also load P_8, P_7, P_6, P_5, P_4 // E_hold = 1.0 - E * U (1) // A_temp = Q // (p0) mov f85 = f38;; } { .mmf nop 999 // EMbo added ... (p0) ldfe f76 = [r39],-16 (p6) fsub.s1 f54 = f0, f1;; } { .mmf nop 999 // EMbo added ... (p0) ldfe f75 = [r39],-16 // // E = E + E_hold*E (1) // Point to P_8. // (p0) fma.s1 f37 = f37, f81, f37;; } { .mmf nop 999 // EMbo added ... (p0) ldfe f74 = [r39],-16 (p0) fnma.s1 f64 = f85, f35, f36;; } { .mmf nop 999 // EMbo added ... (p0) ldfe f72 = [r39],-16 (p7) fadd.s1 f54 = f0, f1;; } { .mmf nop 999 // EMbo added ... (p0) ldfe f70 = [r39],-16 // // E_hold = 1.0 - E * U (2) // (p0) fnma.s1 f81 = f37, f35, f1;; } { .mmf nop 999 // EMbo added ... (p0) ldfe f68 = [r39],-16 (p0) fmpy.s1 f50 = f34, f50;; } { .mmf nop 999 // EMbo added ... (p0) ldfe f66 = [r39],-16 (p0) fmpy.d.s0 f67 = f67, f67 } { .mfi nop 999 // EMbo added ... // // E = E + E_hold*E (2) // (p0) fma.s1 f37 = f37, f81, f37 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... // // E_hold = 1.0 - E * U (3) // (p0) fnma.s1 f81 = f37, f35, f1 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... // // E = E + E_hold*E (3) // At this point E approximates 1/U to roughly working precision // z = V*E approximates V/U // (p0) fma.s1 f37 = f37, f81, f37 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... // // z = V * E // (p0) fmpy.s1 f59 = f36, f37 nop 999 // EMbo added ... } { .mfi nop 999 // EMbo added ... (p0) fmpy.s1 f64 = f64, f37 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... // // zsq = z * z // Also load P_3 // (p0) fmpy.s1 f60 = f59, f59 nop 999 // EMbo added ... } { .mfi nop 999 // EMbo added ... (p0) fadd.s1 f52 = f85, f64 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... (p0) fma.s1 f62 = f60, f77, f76 nop 999 // EMbo added ... } { .mfi nop 999 // EMbo added ... (p0) fma.s1 f63 = f60, f70, f68 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... // // z8 = zsq * zsq // Also load P_2 // (p0) fmpy.s1 f61 = f60, f60 nop 999 // EMbo added ... } { .mfi nop 999 // EMbo added ... (p0) fsub.s1 f85 = f85, f52 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... (p0) fmerge.s f65 = f52,f52 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... (p0) fma.s1 f62 = f60, f62, f75 nop 999 // EMbo added ... } { .mfi nop 999 // EMbo added ... (p0) fma.s1 f63 = f60, f63, f66 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... // // z8 = z8 * z8 // Also load P_1 // poly1 = _4 + zsq*(P_5 + zsq*(P_6 + zsq*(P_7 + zsq*P_8))) // poly2 = zsq*(P_1 + zsq*(P_2 + zsq*P_3)) // // // poly1 = P_7 + zsq * P_8 // poly2 = P_2 + zsq * P_3 // poly1 = P_4 + zsq*(P_5 + zsq*(P_6 + zsq*poly1)) // poly2 = zsq*(P_1 + zsq*poly2) // // // poly1 = P_6 + zsq * poly1 // poly2 = P_1 + zsq * poly2 // poly1 = P_4 + zsq*(P_5 + zsq*poly1) // poly2 = zsq*poly2 // (p0) fmpy.s1 f61 = f61, f61 nop 999 // EMbo added ... } { .mfi nop 999 // EMbo added ... (p0) fadd.s1 f64 = f85, f64 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... (p0) fma.s1 f62 = f60, f62, f74 nop 999 // EMbo added ... } { .mfi nop 999 // EMbo added ... // // poly1 = P_5 + zsq * poly1 // poly2 = zsq * poly2 // poly1 = P_4 + zsq*poly1 // (p0) fmpy.s1 f63 = f63, f60 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... // // poly1 = P_4 + zsq * poly1 // swap = xor(swap,sign_X) // (p0) fma.s1 f62 = f60, f62, f72 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... // // poly = z8*poly1 + poly2 (Typo in writeup) // Is (swap) != 0 ? // // // z_lo = V - A_temp * U // if (p7) sigma = 1.0 // Writeup shows A_temp as A_hi // // // z_lo = z_lo * E // if (p6) sigma = -1.0 // z_lo = (V - A_temp * U) *E // // // Fixup added to force inexact later - // A_hi = A_temp + z_lo // z_lo = (A_temp - A_hi) + z_lo // z_lo = A_hi - z_lo -A_hi + z_lo = about 0 // (p0) fma.s1 f47 = f61, f62, f63 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... // // A_lo = z * poly + z_lo // (p0) fma.s1 f53 = f59, f47, f64 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... (p0) fadd.s1 f52 = f65, f53 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... (p0) fsub.s1 f65 = f65, f52 nop 999 // EMbo added ... } { .mfi nop 999 // EMbo added ... (p0) fmpy.s1 f52 = f34, f52 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... (p0) fadd.s1 f53 = f65, f53 nop 999 // EMbo added ... } { .mfi (p0) setf.exp f65 = r47 (p0) fma.s1 f56 = f54, f52, f50 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... (p0) fclass.m.unc p6,p0 = f53,0x007 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... // // P_hi = s_Y * P_hi // A_hi = s_Y * A_hi // // // result_hi = P_hi + sigma * A_hi // (p6) mov f53 = f65 nop 999 // EMbo added ... } { .mfi nop 999 // EMbo added ... // // tmp = P_hi - result_hi // (p0) fsub.s1 f65 = f50, f56 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... (p0) fma.s1 f65 = f52, f54, f65 nop 999 // EMbo added ... } { .mfi nop 999 // EMbo added ... // // tmp = sigma * A_hi + tmp // sigma = A_lo * sigma + P_lo // (p0) fma.s1 f54 = f53, f54, f51 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... // // result_lo = s_Y * sigma + tmp // (p0) fma.s1 f55 = f34, f54, f65 nop 999;; // EMbo added ... } { .mfb nop.m 0 mov f34 = f1 (p0) br.cond.sptk L(RETURN_ATAN);; } // // result = result_hi + result_lo (User Supplied Rounding Mode) // // (p0) fadd.d.s0 f57 = f55, f56 L(ATAN_UNSUPPORTED): L(ATAN_NATVAL): { .mfb nop 999 // EMbo added ... // // Deal with the NatVal and unsupported cases. // Raise invalid if warrented. // (p0) fmpy.d.s0 f57 = f8, f9 br.cond.sptk L(RETURN_ATAN);; } L(ATAN_NAN): { .mfb nop 999 // EMbo added ... // // If only one NaN, then generate the resulting // NaN and return - may raise invalid. // (p0) fmpy.d.s0 f57 = f8, f9 (p0) br.cond.sptk L(RETURN_ATAN);; } L(ATAN_SPECIAL_HANDLING): { .mmf (p0) addl r39 = @ltoff(Constants_atan#), gp nop.m 999 (p0) fcmp.lt.s0 p0,p7 = f8,f1 } ;; // // Raise denormal operand faults if necessary // { .mfi ld8 r39 = [r39] (p0) fcmp.lt.s0 p0,p6 = f9,f1 nop 999;; // EMbo added ... } ;; { .mfi nop 999 // EMbo added ... (p0) fclass.m.unc p6,p7 = f32,0x007 nop 999;; // EMbo added ... } { .mlx nop 999 // EMbo added ... (p0) movl r47 = 992;; } { .mib (p0) add r39 = r39, r47 nop 999 // EMbo added ... (p7) br.cond.sptk L(ATAN_ArgY_Not_ZERO);; } { .mfi nop 999 // EMbo added ... (p6) fclass.m.unc p14,p0 = f33,0x035 nop 999 // EMbo added ... } { .mfi nop 999 // EMbo added ... (p6) fclass.m.unc p15,p0 = f33,0x036 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... (p6) fclass.m.unc p13,p0 = f33,0x007 nop 999 // EMbo added ... } { .mfi (p0) ldfd f56 = [r39],8 nop 999 // EMbo added ... nop 999;; // EMbo added ... } { .mfi (p0) ldfd f55 = [r39],-8 (p14) fmerge.s f56 = f32,f0 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... // // Return sign_Y * 0 when Y = +/-0 and X > 0 // (p14) fmerge.s f55 = f32,f0 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... (p15) fmerge.s f56 = f32,f56 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... // // Return sign_Y * PI when X < -0 // // (p15) fmerge.s f55 = f32,f55 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... (p0) fadd.d.s0 f57 = f56,f55 nop.i 0 } { .bbb // // Call error support function for atan(0,0) // - expected value already computed. // nop.b 0 nop.b 0 (p0) br.cond.sptk L(RETURN_ATAN) } L(ATAN_ArgY_Not_ZERO): { .mfi nop 999 // EMbo added ... (p0) fclass.m.unc p9,p10 = f32,0x023 nop 999;; // EMbo added ... } { .mfb nop 999 // EMbo added ... (p9) fclass.m.unc p6,p0 = f33,0x017 (p10) br.cond.sptk L(ATAN_ArgY_Not_INF);; } { .mfi (p6) add r39 = 16,r39 (p9) fclass.m.unc p7,p0 = f33,0x021 nop 999;; // EMbo added ... } { .mmf nop 999 // EMbo added ... (p0) ldfd f56 = [r39],8 (p9) fclass.m.unc p8,p0 = f33,0x022;; } { .mbb (p0) ldfd f55 = [r39],-8 nop 999 // EMbo added ... nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... (p6) fmerge.s f56 = f32,f56 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... (p6) fmerge.s f55 = f32,f55 nop 999;; // EMbo added ... } { .mfb nop 999 // EMbo added ... // // Load I/2 and adjust its sign. // Return +I/2 when ArgY = +Inf and ArgX = +/-0,normal // Return -I/2 when ArgY = -Inf and ArgX = +/-0,normal // (p6) fadd.d.s0 f57 = f56, f55 (p6) br.cond.sptk L(RETURN_ATAN);; } { .mmi (p7) add r39 = 32,r39;; (p7) ldfd f56 = [r39],8 nop 999;; // EMbo added ... } { .mmi nop 999;; // EMbo added ... (p7) ldfd f55 = [r39],-8 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... (p7) fmerge.s f56 = f32,f56 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... (p7) fmerge.s f55 = f32,f55 nop 999;; // EMbo added ... } { .mfb nop 999 // EMbo added ... // // Load PI/4 and adjust its sign. // Return +PI/4 when ArgY = +Inf and ArgX = +Inf // Return -PI/4 when ArgY = -Inf and ArgX = +Inf // (p7) fadd.d.s0 f57 = f56, f55 (p7) br.cond.sptk L(RETURN_ATAN);; } { .mmi (p8) add r39 = 48,r39;; (p8) ldfd f56 =[r39],8 nop 999;; // EMbo added ... } { .mmi nop 999;; // EMbo added ... (p8) ldfd f55 =[r39],-8 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... (p8) fmerge.s f56 = f32,f56 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... (p8) fmerge.s f55 = f32,f55 nop 999;; // EMbo added ... } { .mfb nop 999 // EMbo added ... // // Load I/4 and adjust its sign. // Return +3I/4 when ArgY = +Inf and ArgX = -Inf // Return -3I/4 when ArgY = -Inf and ArgX = -Inf // (p8) fadd.d.s0 f57 = f56, f55 (p8) br.cond.sptk L(RETURN_ATAN);; } L(ATAN_ArgY_Not_INF): { .mfi nop 999 // EMbo added ... (p0) fclass.m.unc p6,p0 = f33,0x007 nop 999 // EMbo added ... } { .mfi nop 999 // EMbo added ... (p0) fclass.m.unc p7,p0 = f33,0x021 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... (p0) fclass.m.unc p8,p0 = f33,0x022 (p6) add r39 = 16,r39;; } { .mfi (p6) ldfd f56 =[r39],8 nop 999 // EMbo added ... nop 999;; // EMbo added ... } { .mmi nop 999;; // EMbo added ... (p6) ldfd f55 =[r39],-8 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... (p6) fmerge.s f56 = f32,f56 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... (p6) fmerge.s f55 = f32,f55 nop 999;; // EMbo added ... } { .mfb nop 999 // EMbo added ... // // return = sign_Y * I/2 when ArgX = +/-0 // (p6) fadd.d.s0 f57 = f56, f55 (p6) br.cond.sptk L(RETURN_ATAN);; } { .mfi nop 999 // EMbo added ... (p7) fmerge.s f56 = f32,f0 nop 999 // EMbo added ... } { .mfi nop 999 // EMbo added ... (p7) fmerge.s f55 = f32,f0 nop 999;; // EMbo added ... } { .mfb nop 999 // EMbo added ... // // return = sign_Y * 0 when ArgX = Inf // (p7) fadd.d.s0 f57 = f56, f55 (p7) br.cond.sptk L(RETURN_ATAN);; } { .mfi (p8) ldfd f56 = [r39],8 nop 999 // EMbo added ... nop 999;; // EMbo added ... } { .mmi nop 999;; // EMbo added ... (p8) ldfd f55 = [r39],-8 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... (p8) fmerge.s f56 = f32,f56 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... (p8) fmerge.s f55 = f32,f55 nop 999;; // EMbo added ... } { .mfi nop 999 // EMbo added ... // // return = sign_Y * I when ArgX = -Inf // (p8) fadd.d.s0 f57 = f56, f55 nop 999 // EMbo added ... };; L(RETURN_ATAN): // mov f8 = f57 ;; // The answer is in f57. // But Z_hi is f56 // Z_lo is f55 // s_Y is f34 // W is in f9 and untouched { .mfi nop 999 mov f8 = f56 nop.i 0 };; { .mfi nop 999 mov f10 = f55 nop.i 999 } { .mfb nop 999 mov f11 = f34 br.ret.sptk b0 };; .endp __libm_atan2_reg ASM_SIZE_DIRECTIVE(__libm_atan2_reg)