4 // Copyright (c) 2000 - 2004, Intel Corporation
5 // All rights reserved.
7 // Contributed 2000 by the Intel Numerics Group, Intel Corporation
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41 //==============================================================
42 // 02/02/00 Initial version
43 // 03/03/00 Modified to conform to C9X, and improve speed of main path
44 // 03/14/00 Fixed case where x is a power of 2, and x > y, improved speed
45 // 04/04/00 Unwind support added
46 // 05/12/00 Fixed erroneous denormal flag setting for exponent change cases 1,3
47 // 08/15/00 Bundle added after call to __libm_error_support to properly
48 // set [the previously overwritten] GR_Parameter_RESULT.
49 // 09/09/00 Updated fcmp so that qnans do not raise invalid.
50 // 12/15/00 Fixed case of smallest long double normal to largest denormal,
51 // now adhere to C99 for two zero args, and fixed flag settings
53 // 05/20/02 Cleaned up namespace and sf0 syntax
54 // 02/10/03 Reordered header: .section, .global, .proc, .align
55 // 12/14/04 Added error handling on underflow.
58 //==============================================================
59 // long double nextafterl( long double x, long double y );
60 // input floating point f8, f9
61 // output floating point f8
64 //==============================================================
79 // r36-39 parameters for libm_error_support
87 GR_Parameter_RESULT = r38
88 GR_Parameter_TAG = r39
106 // Overview of operation
107 //==============================================================
108 // nextafterl determines the next representable value
109 // after x in the direction of y.
113 GLOBAL_LIBM_ENTRY(nextafterl)
115 // Extract signexp from x
116 // Is x < y ? p10 if yes, p11 if no
117 // Form smallest denormal significand = ulp size
120 fcmp.lt.s1 p10,p11 = f8, f9
121 addl GR_sden_sig = 0x1, r0
123 // Form largest normal significand 0xffffffffffffffff
124 // Form smallest normal exponent
126 addl GR_lnorm_sig = -0x1,r0
128 addl GR_min_pexp = 0x0c001, r0 ;;
131 // Extract significand from x
132 // Is x=y? This fcmp also sets Invalid and Denormal if required
133 // Form largest normal exponent
136 fcmp.eq.s0 p6,p0 = f8, f9
137 addl GR_max_pexp = 0x13ffe, r0
139 // Move largest normal significand to fp reg for special cases
141 setf.sig FR_lnorm_sig = GR_lnorm_sig
143 addl GR_sign_mask = 0x20000, r0 ;;
146 // Move smallest denormal significand and exp to fp regs
148 // Set p12 and p13 based on whether significand increases or decreases
149 // It increases (p12 set) if x<y and x>=0 or if x>y and x<0
150 // It decreases (p13 set) if x<y and x<0 or if x>y and x>=0
152 setf.sig FR_sden_sig = GR_sden_sig
153 fclass.m p8,p0 = f8, 0xc3
154 (p10) cmp.lt p12,p13 = GR_exp, GR_sign_mask
156 // Move smallest normal exp to fp regs
158 setf.exp FR_snorm_exp = GR_min_pexp
160 (p11) cmp.ge p12,p13 = GR_exp, GR_sign_mask ;;
163 .pred.rel "mutex",p12,p13
165 // Form expected new significand, adding or subtracting 1 ulp increment
166 // If x=y set result to y
167 // Form smallest normal significand and largest denormal significand
169 (p12) add GR_new_sig = GR_sig, GR_sden_sig
170 (p6) fmerge.s f8=f9,f9
171 dep.z GR_snorm_sig = 1,63,1 // 0x8000000000000000
174 (p13) sub GR_new_sig = GR_sig, GR_sden_sig
175 movl GR_lden_sig = 0x7fffffffffffffff ;;
178 // Move expected result significand and signexp to fp regs
180 // Form new exponent in case result exponent needs incrementing or decrementing
182 setf.exp FR_new_exp = GR_exp
183 fclass.m p9,p0 = f9, 0xc3
184 (p12) add GR_exp1 = 1, GR_exp
187 setf.sig FR_new_sig = GR_new_sig
188 (p13) add GR_exp1 = -1, GR_exp
189 (p6) br.ret.spnt b0 ;; // Exit if x=y
192 // Move largest normal signexp to fp reg for special cases
195 setf.exp FR_lnorm_exp = GR_max_pexp
196 fclass.m p7,p0 = f8, 0x7
200 setf.exp FR_den_exp = GR_min_pexp
201 (p8) fma.s0 f8 = f8,f1,f9
202 (p8) br.ret.spnt b0 ;; // Exit if x=nan
205 // Move exp+-1 and smallest normal significand to fp regs for special cases
208 setf.exp FR_exp1 = GR_exp1
209 fclass.m p6,p0 = f8, 0x23
210 addl GR_exp_mask = 0x1ffff, r0
213 setf.sig FR_snorm_sig = GR_snorm_sig
214 (p9) fma.s0 f8 = f8,f1,f9
215 (p9) br.ret.spnt b0 ;; // Exit if y=nan
218 // Move largest denormal significand to fp regs for special cases
221 setf.sig FR_lden_sig = GR_lden_sig
223 (p7) br.cond.spnt NEXT_ZERO ;; // Exit if x=0
226 // Mask off the sign to get x_exp
228 and GR_x_exp = GR_exp_mask, GR_exp
230 (p6) br.cond.spnt NEXT_INF ;; // Exit if x=inf
233 // Check 5 special cases when significand rolls over:
234 // 1 sig size incr, x_sig=max_sig, x_exp < max_exp
235 // Set p6, result is sig=min_sig, exp++
236 // 2 sig size incr, x_sig=max_sig, x_exp >= max_exp
237 // Set p7, result is inf, signal overflow
238 // 3 sig size decr, x_sig=min_sig, x_exp > min_exp
239 // Set p8, result is sig=max_sig, exp--
240 // 4 sig size decr, x_sig=min_sig, x_exp = min_exp
241 // Set p9, result is sig=max_den_sig, exp same, signal underflow and inexact
242 // 5 sig size decr, x_sig=min_den_sig, x_exp = min_exp
243 // Set p10, result is zero, sign of x, signal underflow and inexact
246 (p12) cmp.eq.unc p6,p0 = GR_new_sig, r0
247 (p13) cmp.eq.unc p9,p10 = GR_new_sig, GR_lden_sig
253 (p6) cmp.lt.unc p6,p7 = GR_x_exp, GR_max_pexp
254 (p10) cmp.eq.unc p10,p0 = GR_new_sig, r0
255 (p9) cmp.le.unc p9,p8 = GR_x_exp, GR_min_pexp
259 // Create small normal in case need to generate underflow flag
262 fmerge.se FR_tmp = FR_snorm_exp, FR_lnorm_sig
265 // Branch if cases 1, 2, 3
267 (p6) br.cond.spnt NEXT_EXPUP
268 (p7) br.cond.spnt NEXT_OVERFLOW
269 (p8) br.cond.spnt NEXT_EXPDOWN ;;
272 // Branch if cases 4, 5
275 (p9) br.cond.spnt NEXT_NORM_TO_DENORM
276 (p10) br.cond.spnt NEXT_UNDERFLOW_TO_ZERO
280 // Here if no special cases
281 // Set p6 if result will be a denormal, so can force underflow flag
282 // Case 1: x_exp=min_exp, x_sig=unnormalized
283 // Case 2: x_exp<min_exp
285 cmp.lt p6,p7 = GR_x_exp, GR_min_pexp
286 fmerge.se f8 = FR_new_exp, FR_new_sig
293 (p6) tbit.z p6,p0 = GR_new_sig, 63 ;;
297 // Force underflow and inexact if denormal result
300 (p6) fma.s0 FR_tmp = FR_tmp,FR_tmp,f0
305 fnorm.s0 f8 = f8 // Final normalization to result precision
306 (p6) br.cond.spnt NEXT_UNDERFLOW ;;
318 cmp.lt p6,p7 = GR_x_exp, GR_min_pexp
319 fmerge.se f8 = FR_exp1, FR_snorm_sig
320 br.cond.sptk NEXT_COMMON_FINISH ;;
325 cmp.lt p6,p7 = GR_x_exp, GR_min_pexp
326 fmerge.se f8 = FR_exp1, FR_lnorm_sig
327 br.cond.sptk NEXT_COMMON_FINISH ;;
333 fmerge.se f8 = FR_exp1, FR_lden_sig
336 // Force underflow and inexact
339 fma.s0 FR_tmp = FR_tmp,FR_tmp,f0
340 br.cond.sptk NEXT_UNDERFLOW ;;
343 NEXT_UNDERFLOW_TO_ZERO:
346 fmerge.s f8 = FR_save_f8,f0
347 br.cond.sptk NEXT_COMMON_FINISH ;;
351 // Here if f8 is +- infinity
353 // if f8 is +inf, no matter what y is return largest long double
354 // if f8 is -inf, no matter what y is return -largest long double
356 // Create largest long double
359 fmerge.se FR_lnorm = FR_lnorm_exp,FR_lnorm_sig
365 fmerge.s f8 = f8,FR_lnorm
371 // Here if f8 is +- zero
373 // if f8 is zero and y is +, return + smallest long double denormal
374 // if f8 is zero and y is -, return - smallest long double denormal
378 fmerge.se FR_sden = f0,FR_sden_sig
382 // Create small normal to generate underflow flag
385 fmerge.se FR_tmp = FR_snorm_exp, FR_lnorm_sig
389 // Add correct sign from direction arg
392 fmerge.s f8 = f9,FR_sden
396 // Force underflow and inexact flags
399 fma.s0 FR_tmp = FR_tmp,FR_tmp,f0
400 br.cond.sptk NEXT_UNDERFLOW ;;
404 // Here if result is a denorm, or input is finite and result is zero
405 // Call error support to report possible range error
407 alloc r32=ar.pfs,2,2,4,0
408 mov GR_Parameter_TAG = 267 // Error code
409 br.cond.sptk __libm_error_region // Branch to error call
414 // Here if input is finite, but result will be infinite
415 // Use frcpa to generate infinity of correct sign
416 // Call error support to report possible range error
418 alloc r32=ar.pfs,2,2,4,0
419 frcpa.s1 f8,p6 = FR_save_f8, f0
423 // Create largest double
426 fmerge.se FR_lnorm = FR_lnorm_exp,FR_lnorm_sig
430 // Force overflow and inexact flags to be set
432 mov GR_Parameter_TAG = 153 // Error code
433 fma.s0 FR_tmp = FR_lnorm,FR_lnorm,f0
434 br.cond.sptk __libm_error_region // Branch to error call
438 GLOBAL_LIBM_END(nextafterl)
441 LOCAL_LIBM_ENTRY(__libm_error_region)
446 add GR_Parameter_Y=-32,sp // Parameter 2 value
448 .save ar.pfs,GR_SAVE_PFS
449 mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
453 add sp=-64,sp // Create new stack
455 mov GR_SAVE_GP=gp // Save gp
461 stfe [GR_Parameter_Y] = f9,16 // STORE Parameter 2 on stack
462 add GR_Parameter_X = 16,sp // Parameter 1 address
464 mov GR_SAVE_B0=b0 // Save b0
470 stfe [GR_Parameter_X] = FR_save_f8 // STORE Parameter 1 on stack
471 add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address
475 stfe [GR_Parameter_Y] = f8 // STORE Parameter 3 on stack
476 add GR_Parameter_Y = -16,GR_Parameter_Y
477 br.call.sptk b0=__libm_error_support# // Call error handling function
482 add GR_Parameter_RESULT = 48,sp
487 ldfe f8 = [GR_Parameter_RESULT] // Get return result off stack
489 add sp = 64,sp // Restore stack pointer
490 mov b0 = GR_SAVE_B0 // Restore return address
493 mov gp = GR_SAVE_GP // Restore gp
494 mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
495 br.ret.sptk b0 // Return
498 LOCAL_LIBM_END(__libm_error_region)
501 .type __libm_error_support#,@function
502 .global __libm_error_support#