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Diffstat (limited to 'sysdeps/ia64/fpu/e_exp10.S')
| -rw-r--r-- | sysdeps/ia64/fpu/e_exp10.S | 605 |
1 files changed, 605 insertions, 0 deletions
diff --git a/sysdeps/ia64/fpu/e_exp10.S b/sysdeps/ia64/fpu/e_exp10.S new file mode 100644 index 0000000..eafa59d --- /dev/null +++ b/sysdeps/ia64/fpu/e_exp10.S @@ -0,0 +1,605 @@ +.file "exp10.s" + + +// Copyright (c) 2000 - 2005, 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 +//============================================================== +// 08/25/00 Initial version +// 05/20/02 Cleaned up namespace and sf0 syntax +// 09/06/02 Improved performance; no inexact flags on exact cases +// 01/29/03 Added missing } to bundle templates +// 12/16/04 Call error handling on underflow. +// 03/31/05 Reformatted delimiters between data tables +// +// API +//============================================================== +// double exp10(double) +// +// Overview of operation +//============================================================== +// Background +// +// Implementation +// +// Let x= (K + fh + fl + r)/log2(10), where +// K is an integer, fh= 0.b1 b2 b3 b4 b5, +// fl= 2^{-5}* 0.b6 b7 b8 b8 b10 (fh, fl >= 0), +// and |r|<2^{-11} +// Th is a table that stores 2^fh (32 entries) rounded to +// double extended precision (only mantissa is stored) +// Tl is a table that stores 2^fl (32 entries) rounded to +// double extended precision (only mantissa is stored) +// +// 10^x is approximated as +// 2^K * Th [ f ] * Tl [ f ] * (1+c1*e+c1*r+c2*r^2+c3*r^3+c4*r^4), +// where e= (x*log2(10)_hi-RN(x*log2(10)_hi))+log2(10)_lo*x + +// Note there are only 22 non-zero values that produce an exact result: +// 1.0, 2.0, ... 22.0. +// We test for these cases and use s1 to avoid setting the inexact flag. + +// Special values +//============================================================== +// exp10(0)= 1 +// exp10(+inf)= inf +// exp10(-inf)= 0 +// + +// Registers used +//============================================================== +// r2-r3, r14-r40 +// f6-f15, f32-f52 +// p6-p12 +// + + +GR_TBL_START = r2 +GR_LOG_TBL = r3 + +GR_OF_LIMIT = r14 +GR_UF_LIMIT = r15 +GR_EXP_CORR = r16 +GR_F_low = r17 +GR_F_high = r18 +GR_K = r19 +GR_Flow_ADDR = r20 + +GR_BIAS = r21 +GR_Fh = r22 +GR_Fh_ADDR = r23 +GR_EXPMAX = r24 +GR_BIAS53 = r25 + +GR_ROUNDVAL = r26 +GR_SNORM_LIMIT = r26 +GR_MASK = r27 +GR_KF0 = r28 +GR_MASK_low = r29 +GR_COEFF_START = r30 +GR_exact_limit = r31 + +GR_SAVE_B0 = r33 +GR_SAVE_PFS = r34 +GR_SAVE_GP = r35 +GR_SAVE_SP = r36 + +GR_Parameter_X = r37 +GR_Parameter_Y = r38 +GR_Parameter_RESULT = r39 +GR_Parameter_TAG = r40 + + +FR_X = f10 +FR_Y = f1 +FR_RESULT = f8 + + +FR_COEFF1 = f6 +FR_COEFF2 = f7 +FR_R = f9 +FR_LOG2_10 = f10 + +FR_2P53 = f11 +FR_KF0 = f12 +FR_COEFF3 = f13 +FR_COEFF4 = f14 +FR_UF_LIMIT = f15 + +FR_OF_LIMIT = f32 +FR_DX_L210 = f33 +FR_ROUNDVAL = f34 +FR_KF = f35 + +FR_2_TO_K = f36 +FR_T_low = f37 +FR_T_high = f38 +FR_P34 = f39 +FR_R2 = f40 + +FR_P12 = f41 +FR_T_low_K = f42 +FR_P14 = f43 +FR_T = f44 +FR_P = f45 + +FR_L2_10_low = f46 +FR_L2_10_high = f47 +FR_E0 = f48 +FR_E = f49 +FR_exact_limit = f50 + +FR_int_x = f51 +FR_SNORM_LIMIT = f52 + + +// Data tables +//============================================================== + +RODATA + +.align 16 + +LOCAL_OBJECT_START(poly_coeffs) + +data8 0xd49a784bcd1b8afe, 0x00003fcb // log2(10)*2^(10-63) +data8 0x9257edfe9b5fb698, 0x3fbf // log2(10)_low (bits 64...127) +data8 0x3fac6b08d704a0c0, 0x3f83b2ab6fba4e77 // C_3 and C_4 +data8 0xb17217f7d1cf79ab, 0x00003ffe // C_1 +data8 0xf5fdeffc162c7541, 0x00003ffc // C_2 +LOCAL_OBJECT_END(poly_coeffs) + + +LOCAL_OBJECT_START(T_table) + +// 2^{0.00000 b6 b7 b8 b9 b10} +data8 0x8000000000000000, 0x8016302f17467628 +data8 0x802c6436d0e04f50, 0x80429c17d77c18ed +data8 0x8058d7d2d5e5f6b0, 0x806f17687707a7af +data8 0x80855ad965e88b83, 0x809ba2264dada76a +data8 0x80b1ed4fd999ab6c, 0x80c83c56b50cf77f +data8 0x80de8f3b8b85a0af, 0x80f4e5ff089f763e +data8 0x810b40a1d81406d4, 0x81219f24a5baa59d +data8 0x813801881d886f7b, 0x814e67cceb90502c +data8 0x8164d1f3bc030773, 0x817b3ffd3b2f2e47 +data8 0x8191b1ea15813bfd, 0x81a827baf7838b78 +data8 0x81bea1708dde6055, 0x81d51f0b8557ec1c +data8 0x81eba08c8ad4536f, 0x820225f44b55b33b +data8 0x8218af4373fc25eb, 0x822f3c7ab205c89a +data8 0x8245cd9ab2cec048, 0x825c62a423d13f0c +data8 0x8272fb97b2a5894c, 0x828998760d01faf3 +data8 0x82a0393fe0bb0ca8, 0x82b6ddf5dbc35906 +// +// 2^{0.b1 b2 b3 b4 b5} +data8 0x8000000000000000, 0x82cd8698ac2ba1d7 +data8 0x85aac367cc487b14, 0x88980e8092da8527 +data8 0x8b95c1e3ea8bd6e6, 0x8ea4398b45cd53c0 +data8 0x91c3d373ab11c336, 0x94f4efa8fef70961 +data8 0x9837f0518db8a96f, 0x9b8d39b9d54e5538 +data8 0x9ef5326091a111ad, 0xa27043030c496818 +data8 0xa5fed6a9b15138ea, 0xa9a15ab4ea7c0ef8 +data8 0xad583eea42a14ac6, 0xb123f581d2ac258f +data8 0xb504f333f9de6484, 0xb8fbaf4762fb9ee9 +data8 0xbd08a39f580c36be, 0xc12c4cca66709456 +data8 0xc5672a115506dadd, 0xc9b9bd866e2f27a2 +data8 0xce248c151f8480e3, 0xd2a81d91f12ae45a +data8 0xd744fccad69d6af4, 0xdbfbb797daf23755 +data8 0xe0ccdeec2a94e111, 0xe5b906e77c8348a8 +data8 0xeac0c6e7dd24392e, 0xefe4b99bdcdaf5cb +data8 0xf5257d152486cc2c, 0xfa83b2db722a033a +LOCAL_OBJECT_END(T_table) + + + +.section .text +GLOBAL_IEEE754_ENTRY(exp10) + + +{.mfi + alloc r32= ar.pfs, 1, 4, 4, 0 + // will continue only for non-zero normal/denormal numbers + fclass.nm.unc p12, p7= f8, 0x1b + mov GR_BIAS53= 0xffff+63-10 +} +{.mlx + // GR_TBL_START= pointer to log2(10), C_1...C_4 followed by T_table + addl GR_TBL_START= @ltoff(poly_coeffs), gp + movl GR_ROUNDVAL= 0x3fc00000 // 1.5 (SP) +} +;; + +{.mfi + ld8 GR_COEFF_START= [ GR_TBL_START ] // Load pointer to coeff table + fcmp.lt.s1 p6, p8= f8, f0 // X<0 ? + nop.i 0 +} +;; + +{.mlx + setf.exp FR_2P53= GR_BIAS53 // 2^{63-10} + movl GR_UF_LIMIT= 0xc07439b746e36b52 // (-2^10-51) / log2(10) +} +{.mlx + setf.s FR_ROUNDVAL= GR_ROUNDVAL + movl GR_OF_LIMIT= 0x40734413509f79fe // Overflow threshold +} +;; + +{.mlx + ldfe FR_LOG2_10= [ GR_COEFF_START ], 16 // load log2(10)*2^(10-63) + movl GR_SNORM_LIMIT= 0xc0733a7146f72a41 // Smallest normal threshold +} +{.mib + nop.m 0 + nop.i 0 + (p12) br.cond.spnt SPECIAL_exp10 // Branch if nan, inf, zero +} +;; + +{.mmf + ldfe FR_L2_10_low= [ GR_COEFF_START ], 16 // load log2(10)_low + setf.d FR_OF_LIMIT= GR_OF_LIMIT // Set overflow limit + fma.s0 f8= f8, f1, f0 // normalize x +} +;; + +{.mfi + ldfpd FR_COEFF3, FR_COEFF4= [ GR_COEFF_START ], 16 // load C_3, C_4 + (p8) fcvt.fx.s1 FR_int_x = f8 // Convert x to integer + nop.i 0 +} +{.mfi + setf.d FR_UF_LIMIT= GR_UF_LIMIT // Set underflow limit + fma.s1 FR_KF0= f8, FR_LOG2_10, FR_ROUNDVAL // y= (x*log2(10)*2^10 + + // 1.5*2^63) * 2^(-63) + mov GR_EXP_CORR= 0xffff-126 +} +;; + +{.mfi + setf.d FR_SNORM_LIMIT= GR_SNORM_LIMIT // Set smallest normal limit + fma.s1 FR_L2_10_high= FR_LOG2_10, FR_2P53, f0 // FR_LOG2_10= log2(10)_hi + nop.i 0 +} +;; + +{.mfi + ldfe FR_COEFF1= [ GR_COEFF_START ], 16 // load C_1 + fms.s1 FR_KF= FR_KF0, f1, FR_ROUNDVAL // (K+f)*2^(10-63) + mov GR_MASK= 1023 +} +;; + +{.mfi + ldfe FR_COEFF2= [ GR_COEFF_START ], 16 // load C_2 + fma.s1 FR_LOG2_10= f8, FR_L2_10_high, f0 // y0= x*log2(10)_hi + mov GR_MASK_low= 31 +} +;; + +{.mlx + getf.sig GR_KF0= FR_KF0 // (K+f)*2^10= round_to_int(y) + (p8) movl GR_exact_limit= 0x41b00000 // Largest x for exact result, + // +22.0 +} +;; + +{.mfi + add GR_LOG_TBL= 256, GR_COEFF_START // Pointer to high T_table + fcmp.gt.s1 p12, p7= f8, FR_OF_LIMIT // x>overflow threshold ? + nop.i 0 +} +;; + +{.mfi + (p8) setf.s FR_exact_limit = GR_exact_limit // Largest x for exact result + (p8) fcvt.xf FR_int_x = FR_int_x // Integral part of x + shr GR_K= GR_KF0, 10 // K +} +{.mfi + and GR_F_high= GR_MASK, GR_KF0 // f_high*32 + fnma.s1 FR_R= FR_KF, FR_2P53, FR_LOG2_10 // r= x*log2(10)-2^{63-10}* + // [ (K+f)*2^{10-63} ] + and GR_F_low= GR_KF0, GR_MASK_low // f_low +} +;; + +{.mmi + shladd GR_Flow_ADDR= GR_F_low, 3, GR_COEFF_START // address of 2^{f_low} + add GR_BIAS= GR_K, GR_EXP_CORR // K= bias-2*63 + shr GR_Fh= GR_F_high, 5 // f_high +} +;; + +{.mfi + setf.exp FR_2_TO_K= GR_BIAS // 2^{K-126} + (p7) fcmp.lt.s1 p12, p7= f8, FR_UF_LIMIT // x<underflow threshold ? + shladd GR_Fh_ADDR= GR_Fh, 3, GR_LOG_TBL // address of 2^{f_high} +} +{.mfi + ldf8 FR_T_low= [ GR_Flow_ADDR ] // load T_low= 2^{f_low} + fms.s1 FR_DX_L210= f8, FR_L2_10_high, FR_LOG2_10 // x*log2(10)_hi- + // RN(x*log2(10)_hi) + nop.i 0 +} +;; + +{.mfi + ldf8 FR_T_high= [ GR_Fh_ADDR ] // load T_high= 2^{f_high} + fma.s1 FR_P34= FR_COEFF4, FR_R, FR_COEFF3 // P34= C_3+C_4*r + nop.i 0 +} +{.mfb + nop.m 0 + fma.s1 FR_R2= FR_R, FR_R, f0 // r*r + (p12) br.cond.spnt OUT_RANGE_exp10 +} +;; + +{.mfi + nop.m 0 + // e= (x*log2(10)_hi-RN(x*log2(10)_hi))+log2(10)_lo*x + fma.s1 FR_E0= f8, FR_L2_10_low, FR_DX_L210 + cmp.eq p7,p9= r0,r0 // Assume inexact result +} +{.mfi + nop.m 0 + fma.s1 FR_P12= FR_COEFF2, FR_R, FR_COEFF1 // P12= C_1+C_2*r + nop.i 0 +} +;; + +{.mfi + nop.m 0 + (p8) fcmp.eq.s1 p9,p7= FR_int_x, f8 // Test x positive integer + nop.i 0 +} +{.mfi + nop.m 0 + fma.s1 FR_T_low_K= FR_T_low, FR_2_TO_K, f0 // T= 2^{K-126}*T_low + nop.i 0 +} +;; + +{.mfi + nop.m 0 + fcmp.ge.s1 p11,p0= f8, FR_SNORM_LIMIT // Test x for normal range + nop.i 0 +} +;; + +{.mfi + nop.m 0 + fma.s1 FR_E= FR_E0, FR_COEFF1, f0 // E= C_1*e + nop.i 0 +} +{.mfi + nop.m 0 + fma.s1 FR_P14= FR_R2, FR_P34, FR_P12 // P14= P12+r2*P34 + nop.i 0 +} +;; + +// If x a positive integer, will it produce an exact result? +// p7 result will be inexact +// p9 result will be exact +{.mfi + nop.m 0 + (p9) fcmp.le.s1 p9,p7= f8, FR_exact_limit // Test x gives exact result + nop.i 0 +} +{.mfi + nop.m 0 + fma.s1 FR_T= FR_T_low_K, FR_T_high, f0 // T= T*T_high + nop.i 0 +} +;; + +{.mfi + nop.m 0 + fma.s1 FR_P= FR_P14, FR_R, FR_E // P= P14*r+E + nop.i 0 +} +;; + +.pred.rel "mutex",p7,p9 +{.mfi + nop.m 0 + (p7) fma.d.s0 f8= FR_P, FR_T, FR_T // result= T+T*P, inexact set + nop.i 0 +} +{.mfb + nop.m 0 + (p9) fma.d.s1 f8= FR_P, FR_T, FR_T // result= T+T*P, exact use s1 + (p11) br.ret.sptk b0 // return, if result normal +} +;; + +// Here if result in denormal range (and not zero) +{.mib + nop.m 0 + mov GR_Parameter_TAG= 265 + br.cond.sptk __libm_error_region // Branch to error handling +} +;; + +SPECIAL_exp10: +{.mfi + nop.m 0 + fclass.m p6, p0= f8, 0x22 // x= -Infinity ? + nop.i 0 +} +;; + +{.mfi + nop.m 0 + fclass.m p7, p0= f8, 0x21 // x= +Infinity ? + nop.i 0 +} +;; + +{.mfi + nop.m 0 + fclass.m p8, p0= f8, 0x7 // x= +/-Zero ? + nop.i 0 +} +{.mfb + nop.m 0 + (p6) mov f8= f0 // exp10(-Infinity)= 0 + (p6) br.ret.spnt b0 +} +;; + +{.mfb + nop.m 0 + nop.f 0 + (p7) br.ret.spnt b0 // exp10(+Infinity)= +Infinity +} +;; + +{.mfb + nop.m 0 + (p8) mov f8= f1 // exp10(+/-0)= 1 + (p8) br.ret.spnt b0 +} +;; + +{.mfb + nop.m 0 + fma.d.s0 f8= f8, f1, f0 // Remaining cases: NaNs + br.ret.sptk b0 +} +;; + + +OUT_RANGE_exp10: + +// underflow: p6= 1 +// overflow: p8= 1 + +.pred.rel "mutex",p6,p8 +{.mmi + (p8) mov GR_EXPMAX= 0x1fffe + (p6) mov GR_EXPMAX= 1 + nop.i 0 +} +;; + +{.mii + setf.exp FR_R= GR_EXPMAX + (p8) mov GR_Parameter_TAG= 166 + (p6) mov GR_Parameter_TAG= 265 +} +;; + +{.mfb + nop.m 0 + fma.d.s0 f8= FR_R, FR_R, f0 // Create overflow/underflow + br.cond.sptk __libm_error_region // Branch to error handling +} +;; + +GLOBAL_IEEE754_END(exp10) +weak_alias (exp10, pow10) + + +LOCAL_LIBM_ENTRY(__libm_error_region) + +.prologue +{.mfi + add GR_Parameter_Y= -32, sp // Parameter 2 value + nop.f 0 +.save ar.pfs, GR_SAVE_PFS + mov GR_SAVE_PFS= ar.pfs // Save ar.pfs +} + +{.mfi +.fframe 64 + add sp= -64, sp // Create new stack + nop.f 0 + mov GR_SAVE_GP= gp // Save gp +} +;; + +{.mmi + stfd [ GR_Parameter_Y ]= FR_Y, 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 + stfd [ GR_Parameter_X ]= FR_X // STORE Parameter 1 on stack + add GR_Parameter_RESULT= 0, GR_Parameter_Y // Parameter 3 address + nop.b 0 +} +{.mib + stfd [ GR_Parameter_Y ]= FR_RESULT // 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 + add GR_Parameter_RESULT= 48, sp + nop.m 0 + nop.i 0 +} +;; + +{.mmi + ldfd 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# |