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Diffstat (limited to 'sysdeps/ia64/fpu/e_exp2.S')
| -rw-r--r-- | sysdeps/ia64/fpu/e_exp2.S | 564 |
1 files changed, 564 insertions, 0 deletions
diff --git a/sysdeps/ia64/fpu/e_exp2.S b/sysdeps/ia64/fpu/e_exp2.S new file mode 100644 index 0000000..54f652e --- /dev/null +++ b/sysdeps/ia64/fpu/e_exp2.S @@ -0,0 +1,564 @@ +.file "exp2.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 +// 09/05/02 Improved performance +// 01/17/03 Fixed to call error support when x=1024.0 +// 03/31/05 Reformatted delimiters between data tables +// +// API +//============================================================== +// double exp2(double) +// +// Overview of operation +//============================================================== +// Background +// +// Implementation +// +// Let x= (K + fh + fl + r), 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) +// +// 2^x is approximated as +// 2^K * Th [ f ] * Tl [ f ] * (1+c1*r+c2*r^2+c3*r^3+c4*r^4) + +// Note: We use the following trick to speed up conversion from FP to integer: +// +// Let x = K + r, where K is an integer, and |r| <= 0.5 +// Let N be the number of significand bits for the FP format used +// ( N=64 for double-extended, N=53 for double) +// +// Then let y = 1.5 * 2^(N-1) + x for RN mode +// K = y - 1.5 * 2^(N-1) +// r = x - K +// +// If we want to obtain the integer part and the first m fractional bits of x, +// we can use the same trick, but with a constant of 1.5 * 2^(N-1-m): +// +// Let x = K + f + r +// f = 0.b_1 b_2 ... b_m +// |r| <= 2^(-m-1) +// +// Then let y = 1.5 * 2^(N-1-m) + x for RN mode +// (K+f) = y - 1.5 * 2^(N-1-m) +// r = x - K + + +// Special values +//============================================================== +// exp2(0)= 1 +// exp2(+inf)= inf +// exp2(-inf)= 0 +// + +// Registers used +//============================================================== +// r2-r3, r14-r40 +// f6-f15, f32-f45 +// p6-p8, 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_EMIN = r25 + +GR_ROUNDVAL = r26 +GR_MASK = r27 +GR_KF0 = r28 +GR_MASK_low = r29 +GR_COEFF_START = r30 + +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_KF0 = f12 +FR_COEFF3 = f13 +FR_COEFF4 = f14 +FR_UF_LIMIT = f15 + +FR_OF_LIMIT = f32 +FR_EXPMIN = 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 + + +// Data tables +//============================================================== + +RODATA + +.align 16 + +LOCAL_OBJECT_START(poly_coeffs) + +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_LIBM_ENTRY(exp2) + + +{.mfi + alloc r32= ar.pfs, 1, 4, 4, 0 + // will continue only for non-zero normal/denormal numbers + fclass.nm p12, p0= f8, 0x1b + // GR_TBL_START= pointer to C_1...C_4 followed by T_table + addl GR_TBL_START= @ltoff(poly_coeffs), gp +} +{.mlx + mov GR_OF_LIMIT= 0xffff + 10 // Exponent of overflow limit + movl GR_ROUNDVAL= 0x5a400000 // 1.5*2^(63-10) (SP) +} +;; + +// Form special constant 1.5*2^(63-10) to give integer part and first 10 +// fractional bits of x +{.mfi + setf.s FR_ROUNDVAL= GR_ROUNDVAL // Form special constant + fcmp.lt.s1 p6, p8= f8, f0 // X<0 ? + nop.i 0 +} +{.mfb + ld8 GR_COEFF_START= [ GR_TBL_START ] // Load pointer to coeff table + nop.f 0 + (p12) br.cond.spnt SPECIAL_exp2 // Branch if nan, inf, zero +} +;; + +{.mlx + setf.exp FR_OF_LIMIT= GR_OF_LIMIT // Set overflow limit + movl GR_UF_LIMIT= 0xc4866000 // (-2^10-51) = -1075 +} +;; + +{.mfi + ldfpd FR_COEFF3, FR_COEFF4= [ GR_COEFF_START ], 16 // load C_3, C_4 + fma.s0 f8= f8, f1, f0 // normalize x + nop.i 0 +} +;; + +{.mmi + setf.s FR_UF_LIMIT= GR_UF_LIMIT // Set underflow limit + ldfe FR_COEFF1= [ GR_COEFF_START ], 16 // load C_1 + mov GR_EXP_CORR= 0xffff-126 +} +;; + +{.mfi + ldfe FR_COEFF2= [ GR_COEFF_START ], 16 // load C_2 + fma.s1 FR_KF0= f8, f1, FR_ROUNDVAL // y= x + 1.5*2^(63-10) + nop.i 0 +} +;; + +{.mfi + mov GR_MASK= 1023 + fms.s1 FR_KF= FR_KF0, f1, FR_ROUNDVAL // (K+f) + mov GR_MASK_low= 31 +} +;; + +{.mfi + getf.sig GR_KF0= FR_KF0 // (K+f)*2^10= round_to_int(y) + fcmp.ge.s1 p12, p7= f8, FR_OF_LIMIT // x >= overflow threshold ? + add GR_LOG_TBL= 256, GR_COEFF_START // Pointer to high T_table +} +;; + +{.mmi + and GR_F_low= GR_KF0, GR_MASK_low // f_low + and GR_F_high= GR_MASK, GR_KF0 // f_high*32 + shr GR_K= GR_KF0, 10 // K +} +;; + +{.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} + fnma.s1 FR_R= FR_KF, f1, f8 // r= x - (K+f) + shladd GR_Fh_ADDR= GR_Fh, 3, GR_LOG_TBL // address of 2^{f_high} +} +{.mlx + ldf8 FR_T_low= [ GR_Flow_ADDR ] // load T_low= 2^{f_low} + movl GR_EMIN= 0xc47f8000 // EMIN= -1022 +} +;; + +{.mfi + ldf8 FR_T_high= [ GR_Fh_ADDR ] // load T_high= 2^{f_high} + (p7) fcmp.lt.s1 p12, p7= f8, FR_UF_LIMIT // x<underflow threshold ? + nop.i 0 +} +;; + +{.mfi + setf.s FR_EXPMIN= GR_EMIN // FR_EXPMIN= EMIN + 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_exp2 +} +;; + +{.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 + 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 + fma.s1 FR_P14= FR_R2, FR_P34, FR_P12 // P14= P12+r2*P34 + 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 + fcmp.lt.s0 p6, p8= f8, FR_EXPMIN // underflow (x<EMIN) ? + nop.i 0 +} +;; + +{.mfi + nop.m 0 + fma.s1 FR_P= FR_P14, FR_R, f0 // P= P14*r + nop.i 0 +} +;; + +{.mfb + nop.m 0 + fma.d.s0 f8= FR_P, FR_T, FR_T // result= T+T*P + (p8) br.ret.sptk b0 // return +} +;; + +{.mfb + (p6) mov GR_Parameter_TAG= 162 + nop.f 0 + (p6) br.cond.sptk __libm_error_region +} +;; + + +SPECIAL_exp2: +{.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 // exp2(-Infinity)= 0 + (p6) br.ret.spnt b0 +} +;; + +{.mfb + nop.m 0 + nop.f 0 + (p7) br.ret.spnt b0 // exp2(+Infinity)= +Infinity +} +;; + +{.mfb + nop.m 0 + (p8) mov f8= f1 // exp2(+/-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_exp2: + +// overflow: p8= 1 + +{.mii + (p8) mov GR_EXPMAX= 0x1fffe + nop.i 0 + nop.i 0 +} +;; + +{.mmb + (p8) mov GR_Parameter_TAG= 161 + (p8) setf.exp FR_R= GR_EXPMAX + nop.b 999 +} +;; + +{.mfi + nop.m 999 + (p8) fma.d.s0 f8= FR_R, FR_R, f0 // Create overflow + nop.i 999 +} +// underflow: p6= 1 +{.mii + (p6) mov GR_Parameter_TAG= 162 + (p6) mov GR_EXPMAX= 1 + nop.i 0 +} +;; + +{.mmb + nop.m 0 + (p6) setf.exp FR_R= GR_EXPMAX + nop.b 999 +} +;; + +{.mfb + nop.m 999 + (p6) fma.d.s0 f8= FR_R, FR_R, f0 // Create underflow + nop.b 0 +} +;; + +GLOBAL_LIBM_END(exp2) + + +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# |