4 // Copyright (c) 2000 - 2005, Intel Corporation
5 // All rights reserved.
7 // Contributed 2000 by the Intel Numerics Group, Intel Corporation
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21 // products derived from this software without specific prior written
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41 //==============================================================
42 // 08/25/00 Initial version
43 // 05/20/02 Cleaned up namespace and sf0 syntax
44 // 09/06/02 Improved performance and accuracy; no inexact flags on exact cases
45 // 01/29/03 Added missing } to bundle templates
46 // 12/16/04 Call error handling on underflow.
47 // 03/31/05 Reformatted delimiters between data tables
50 //==============================================================
51 // float exp10f(float)
53 // Overview of operation
54 //==============================================================
59 // Let x= (K + fh + fl + r)/log2(10), where
60 // K is an integer, fh= 0.b1 b2 b3 b4 b5,
61 // fl= 2^{-5}* 0.b6 b7 b8 b8 b10 (fh, fl >= 0),
63 // Th is a table that stores 2^fh (32 entries) rounded to
64 // double extended precision (only mantissa is stored)
65 // Tl is a table that stores 2^fl (32 entries) rounded to
66 // double extended precision (only mantissa is stored)
68 // 10^x is approximated as
69 // 2^K * Th [ f ] * Tl [ f ] * (1+c1*r+c2*r^2)
71 // Note there are only 10 non-zero values that produce an exact result:
72 // 1.0, 2.0, ... 10.0.
73 // We test for these cases and use s1 to avoid setting the inexact flag.
76 //==============================================================
83 //==============================================================
121 GR_Parameter_RESULT = r39
122 GR_Parameter_TAG = r40
163 //==============================================================
169 LOCAL_OBJECT_START(poly_coeffs)
171 data8 0xd49a784bcd1b8afe, 0x00003fcb // log2(10)*2^(10-63)
172 data8 0xb17217f7d1cf79ab, 0x00004033 // C_1 * 2^53
173 data8 0xf5fdeffc162c7541, 0x00004066 // C_2 * 2^106
174 LOCAL_OBJECT_END(poly_coeffs)
177 LOCAL_OBJECT_START(T_table)
179 // 2^{0.00000 b6 b7 b8 b9 b10}
180 data8 0x8000000000000000, 0x8016302f17467628
181 data8 0x802c6436d0e04f50, 0x80429c17d77c18ed
182 data8 0x8058d7d2d5e5f6b0, 0x806f17687707a7af
183 data8 0x80855ad965e88b83, 0x809ba2264dada76a
184 data8 0x80b1ed4fd999ab6c, 0x80c83c56b50cf77f
185 data8 0x80de8f3b8b85a0af, 0x80f4e5ff089f763e
186 data8 0x810b40a1d81406d4, 0x81219f24a5baa59d
187 data8 0x813801881d886f7b, 0x814e67cceb90502c
188 data8 0x8164d1f3bc030773, 0x817b3ffd3b2f2e47
189 data8 0x8191b1ea15813bfd, 0x81a827baf7838b78
190 data8 0x81bea1708dde6055, 0x81d51f0b8557ec1c
191 data8 0x81eba08c8ad4536f, 0x820225f44b55b33b
192 data8 0x8218af4373fc25eb, 0x822f3c7ab205c89a
193 data8 0x8245cd9ab2cec048, 0x825c62a423d13f0c
194 data8 0x8272fb97b2a5894c, 0x828998760d01faf3
195 data8 0x82a0393fe0bb0ca8, 0x82b6ddf5dbc35906
197 // 2^{0.b1 b2 b3 b4 b5}
198 data8 0x8000000000000000, 0x82cd8698ac2ba1d7
199 data8 0x85aac367cc487b14, 0x88980e8092da8527
200 data8 0x8b95c1e3ea8bd6e6, 0x8ea4398b45cd53c0
201 data8 0x91c3d373ab11c336, 0x94f4efa8fef70961
202 data8 0x9837f0518db8a96f, 0x9b8d39b9d54e5538
203 data8 0x9ef5326091a111ad, 0xa27043030c496818
204 data8 0xa5fed6a9b15138ea, 0xa9a15ab4ea7c0ef8
205 data8 0xad583eea42a14ac6, 0xb123f581d2ac258f
206 data8 0xb504f333f9de6484, 0xb8fbaf4762fb9ee9
207 data8 0xbd08a39f580c36be, 0xc12c4cca66709456
208 data8 0xc5672a115506dadd, 0xc9b9bd866e2f27a2
209 data8 0xce248c151f8480e3, 0xd2a81d91f12ae45a
210 data8 0xd744fccad69d6af4, 0xdbfbb797daf23755
211 data8 0xe0ccdeec2a94e111, 0xe5b906e77c8348a8
212 data8 0xeac0c6e7dd24392e, 0xefe4b99bdcdaf5cb
213 data8 0xf5257d152486cc2c, 0xfa83b2db722a033a
214 LOCAL_OBJECT_END(T_table)
219 GLOBAL_IEEE754_ENTRY(exp10f)
223 alloc r32= ar.pfs, 1, 4, 4, 0
224 // will continue only for non-zero normal/denormal numbers
225 fclass.nm.unc p12, p7= f8, 0x1b
229 // GR_TBL_START= pointer to log2(10), C_1...C_4 followed by T_table
230 addl GR_TBL_START= @ltoff(poly_coeffs), gp
231 movl GR_ROUNDVAL= 0x3fc00000 // 1.5 (SP)
236 ld8 GR_COEFF_START= [ GR_TBL_START ] // Load pointer to coeff table
237 fcmp.lt.s1 p6, p8= f8, f0 // X<0 ?
244 movl GR_UF_LIMIT= 0xc2349e35 // (-2^7-22) / log2(10)
247 setf.s FR_ROUNDVAL= GR_ROUNDVAL
248 movl GR_OF_LIMIT= 0x421a209a // Overflow threshold
253 ldfe FR_LOG2_10= [ GR_COEFF_START ], 16 // load log2(10)*2^(10-63)
254 movl GR_SNORM_LIMIT= 0xc217b818 // Smallest normal threshold
259 (p12) br.cond.spnt SPECIAL_exp10 // Branch if nan, inf, zero
264 setf.s FR_OF_LIMIT= GR_OF_LIMIT // Set overflow limit
265 fma.s0 f8= f8, f1, f0 // normalize x
271 setf.s FR_SNORM_LIMIT= GR_SNORM_LIMIT // Set smallest normal limit
272 (p8) fcvt.fx.s1 FR_int_x = f8 // Convert x to integer
276 setf.s FR_UF_LIMIT= GR_UF_LIMIT // Set underflow limit
277 fma.s1 FR_KF0= f8, FR_LOG2_10, FR_ROUNDVAL // y= (x*log2(10)*2^10 +
278 // 1.5*2^63) * 2^(-63)
279 mov GR_EXP_CORR= 0xffff-126
284 ldfe FR_COEFF1= [ GR_COEFF_START ], 16 // load C_1
285 fms.s1 FR_KF= FR_KF0, f1, FR_ROUNDVAL // (K+f)*2^(10-63)
291 ldfe FR_COEFF2= [ GR_COEFF_START ], 16 // load C_2
298 getf.sig GR_KF0= FR_KF0 // (K+f)*2^10= round_to_int(y)
299 (p8) movl GR_exact_limit= 0x41200000 // Largest x for exact result,
305 add GR_LOG_TBL= 256, GR_COEFF_START // Pointer to high T_table
306 fcmp.gt.s1 p12, p7= f8, FR_OF_LIMIT // x>overflow threshold ?
312 (p8) setf.s FR_exact_limit = GR_exact_limit // Largest x for exact result
313 (p8) fcvt.xf FR_int_x = FR_int_x // Integral part of x
314 shr GR_K= GR_KF0, 10 // K
317 and GR_F_high= GR_MASK, GR_KF0 // f_high*32
318 fms.s1 FR_R= f8, FR_LOG2_10, FR_KF // r*2^(-53)= [ x*log2(10)-
319 // (K+f) ] *2^{10-63}
320 and GR_F_low= GR_KF0, GR_MASK_low // f_low
325 shladd GR_Flow_ADDR= GR_F_low, 3, GR_COEFF_START // address of 2^{f_low}
326 add GR_BIAS= GR_K, GR_EXP_CORR // K= bias-2*63
327 shr GR_Fh= GR_F_high, 5 // f_high
332 setf.exp FR_2_TO_K= GR_BIAS // 2^{K-126}
333 (p7) fcmp.lt.s1 p12, p7= f8, FR_UF_LIMIT // x<underflow threshold ?
334 shladd GR_Fh_ADDR= GR_Fh, 3, GR_LOG_TBL // address of 2^{f_high}
337 ldf8 FR_T_low= [ GR_Flow_ADDR ] // load T_low= 2^{f_low}
344 ldf8 FR_T_high= [ GR_Fh_ADDR ] // load T_high= 2^{f_high}
345 fcmp.ge.s1 p11, p0= f8, FR_SNORM_LIMIT // Test x for normal range
346 (p12) br.cond.spnt OUT_RANGE_exp10
352 fma.s1 FR_P12= FR_COEFF2, FR_R, FR_COEFF1 // P12= C_1+C_2*r
353 cmp.eq p7,p9= r0,r0 // Assume inexact result
359 (p8) fcmp.eq.s1 p9,p7= FR_int_x, f8 // Test x positive integer
364 fma.s1 FR_T_low_K= FR_T_low, FR_2_TO_K, f0 // T= 2^{K-126}*T_low
371 fma.s1 FR_P= FR_P12, FR_R, f0 // P= P12*r
376 // If x a positive integer, will it produce an exact result?
377 // p7 result will be inexact
378 // p9 result will be exact
381 (p9) fcmp.le.s1 p9,p7= f8, FR_exact_limit // Test x gives exact result
386 fma.s1 FR_T= FR_T_low_K, FR_T_high, f0 // T= T*T_high
391 .pred.rel "mutex",p7,p9
394 (p7) fma.s.s0 f8= FR_P, FR_T, FR_T // result= T+T*P, inexact set
399 (p9) fma.s.s1 f8= FR_P, FR_T, FR_T // result= T+T*P, exact use s1
400 (p11) br.ret.sptk b0 // return, if result normal
404 // Here if result in denormal range (and not zero)
407 mov GR_Parameter_TAG= 266
408 br.cond.sptk __libm_error_region // Branch to error handling
415 fclass.m p6, p0= f8, 0x22 // x= -Infinity ?
422 fclass.m p7, p0= f8, 0x21 // x= +Infinity ?
429 fclass.m p8, p0= f8, 0x7 // x= +/-Zero ?
434 (p6) mov f8= f0 // exp10(-Infinity)= 0
442 (p7) br.ret.spnt b0 // exp10(+Infinity)= +Infinity
448 (p8) mov f8= f1 // exp10(+/-0)= 1
455 fma.s.s0 f8= f8, f1, f0 // Remaining cases: NaNs
466 .pred.rel "mutex",p6,p8
468 (p8) mov GR_EXPMAX= 0x1fffe
469 (p6) mov GR_EXPMAX= 1
475 setf.exp FR_R= GR_EXPMAX
476 (p8) mov GR_Parameter_TAG= 167
477 (p6) mov GR_Parameter_TAG= 266
483 fma.s.s0 f8= FR_R, FR_R, f0 // Create overflow/underflow
484 br.cond.sptk __libm_error_region // Branch to error handling
488 GLOBAL_IEEE754_END(exp10f)
489 weak_alias (exp10f, pow10f)
492 LOCAL_LIBM_ENTRY(__libm_error_region)
496 add GR_Parameter_Y= -32, sp // Parameter 2 value
498 .save ar.pfs, GR_SAVE_PFS
499 mov GR_SAVE_PFS= ar.pfs // Save ar.pfs
504 add sp= -64, sp // Create new stack
506 mov GR_SAVE_GP= gp // Save gp
511 stfs [ GR_Parameter_Y ]= FR_Y, 16 // STORE Parameter 2 on stack
512 add GR_Parameter_X= 16, sp // Parameter 1 address
514 mov GR_SAVE_B0= b0 // Save b0
520 stfs [ GR_Parameter_X ]= FR_X // STORE Parameter 1 on stack
521 add GR_Parameter_RESULT= 0, GR_Parameter_Y // Parameter 3 address
525 stfs [ GR_Parameter_Y ]= FR_RESULT // STORE Parameter 3 on stack
526 add GR_Parameter_Y= -16, GR_Parameter_Y
527 br.call.sptk b0= __libm_error_support# // Call error handling function
532 add GR_Parameter_RESULT= 48, sp
539 ldfs f8= [ GR_Parameter_RESULT ] // Get return result off stack
541 add sp= 64, sp // Restore stack pointer
542 mov b0= GR_SAVE_B0 // Restore return address
547 mov gp= GR_SAVE_GP // Restore gp
548 mov ar.pfs= GR_SAVE_PFS // Restore ar.pfs
549 br.ret.sptk b0 // Return
554 LOCAL_LIBM_END(__libm_error_region)
556 .type __libm_error_support#, @function
557 .global __libm_error_support#