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 Corrected behavior when both args are zero to conform to C99, and
51 // fixed flag settings for several cases
52 // 05/20/02 Cleaned up namespace and sf0 syntax
53 // 02/10/03 Reordered header: .section, .global, .proc, .align
54 // 12/14/04 Added error handling on underflow.
57 //==============================================================
58 // float nextafterf( float x, float y );
59 // input floating point f8, f9
60 // output floating point f8
63 //==============================================================
79 // r36-39 parameters for libm_error_support
87 GR_Parameter_RESULT = r38
88 GR_Parameter_TAG = r39
105 // Overview of operation
106 //==============================================================
107 // nextafterf determines the next representable value
108 // after x in the direction of y.
112 GLOBAL_LIBM_ENTRY(nextafterf)
114 // Extract signexp from x
115 // Form smallest denormal significand = ulp size
118 movl GR_sden_sig = 0x0000010000000000
120 // Form largest normal exponent
121 // Is x < y ? p10 if yes, p11 if no
122 // Form smallest normal exponent
124 addl GR_max_pexp = 0x1007e, r0
125 fcmp.lt.s1 p10,p11 = f8, f9
126 addl GR_min_pexp = 0x0ff81, r0 ;;
132 fcmp.eq.s0 p6,p0 = f8, f9
135 // Extract significand from x
136 // Form largest normal significand
139 movl GR_lnorm_sig = 0xffffff0000000000 ;;
142 // Move largest normal significand to fp reg for special cases
144 setf.sig FR_lnorm_sig = GR_lnorm_sig
146 addl GR_sign_mask = 0x20000, r0 ;;
149 // Move smallest denormal significand and signexp to fp regs
151 // Set p12 and p13 based on whether significand increases or decreases
152 // It increases (p12 set) if x<y and x>=0 or if x>y and x<0
153 // It decreases (p13 set) if x<y and x<0 or if x>y and x>=0
155 setf.sig FR_sden_sig = GR_sden_sig
156 fclass.m p8,p0 = f8, 0xc3
157 (p10) cmp.lt p12,p13 = GR_exp, GR_sign_mask
160 setf.exp FR_sden_exp = GR_min_pexp
162 (p11) cmp.ge p12,p13 = GR_exp, GR_sign_mask ;;
165 .pred.rel "mutex",p12,p13
167 // Form expected new significand, adding or subtracting 1 ulp increment
168 // If x=y set result to y
169 // Form smallest normal significand and largest denormal significand
171 (p12) add GR_new_sig = GR_sig, GR_sden_sig
172 (p6) fmerge.s f8=f9,f9
173 dep.z GR_snorm_sig = 1,63,1 // 0x8000000000000000
176 (p13) sub GR_new_sig = GR_sig, GR_sden_sig
177 movl GR_lden_sig = 0x7fffff0000000000 ;;
180 // Move expected result significand and signexp to fp regs
182 // Form new exponent in case result exponent needs incrementing or decrementing
184 setf.exp FR_new_exp = GR_exp
185 fclass.m p9,p0 = f9, 0xc3
186 (p12) add GR_exp1 = 1, GR_exp
189 setf.sig FR_new_sig = GR_new_sig
190 (p13) add GR_exp1 = -1, GR_exp
191 (p6) br.ret.spnt b0 ;; // Exit if x=y
194 // Move largest normal signexp to fp reg for special cases
197 setf.exp FR_lnorm_exp = GR_max_pexp
198 fclass.m p7,p0 = f8, 0x7
203 (p8) fma.s0 f8 = f8,f1,f9
204 (p8) br.ret.spnt b0 ;; // Exit if x=nan
207 // Move exp+-1 and smallest normal significand to fp regs for special cases
210 setf.exp FR_exp1 = GR_exp1
211 fclass.m p6,p0 = f8, 0x23
212 addl GR_exp_mask = 0x1ffff, r0
215 setf.sig FR_snorm_sig = GR_snorm_sig
216 (p9) fma.s0 f8 = f8,f1,f9
217 (p9) br.ret.spnt b0 ;; // Exit if y=nan
220 // Move largest denormal significand to fp regs for special cases
223 setf.sig FR_lden_sig = GR_lden_sig
225 (p7) br.cond.spnt NEXT_ZERO ;; // Exit if x=0
228 // Mask off the sign to get x_exp
230 and GR_x_exp = GR_exp_mask, GR_exp
232 (p6) br.cond.spnt NEXT_INF ;; // Exit if x=inf
235 // Check 6 special cases when significand rolls over:
236 // 1 sig size incr, x_sig=max_sig, x_exp < max_exp
237 // Set p6, result is sig=min_sig, exp++
238 // 2 sig size incr, x_sig=max_sig, x_exp >= max_exp
239 // Set p7, result is inf, signal overflow
240 // 3 sig size decr, x_sig=min_sig, x_exp > min_exp
241 // Set p8, result is sig=max_sig, exp--
242 // 4 sig size decr, x_sig=min_sig, x_exp = min_exp
243 // Set p9, result is sig=max_den_sig, exp same, signal underflow and inexact
244 // 5 sig size decr, x_sig=min_den_sig, x_exp = min_exp
245 // Set p10, result is zero, sign of x, signal underflow and inexact
246 // 6 sig size decr, x_sig=min_sig, x_exp < min_exp
247 // Set p14, result is zero, sign of x, signal underflow and inexact
249 // Form exponent of smallest float denormal (if normalized register format)
251 adds GR_min_den_rexp = -23, GR_min_pexp
252 (p12) cmp.eq.unc p6,p0 = GR_new_sig, r0
253 (p13) cmp.eq.unc p8,p10 = GR_new_sig, GR_lden_sig ;;
257 (p6) cmp.lt.unc p6,p7 = GR_x_exp, GR_max_pexp
258 (p8) cmp.gt.unc p8,p9 = GR_x_exp, GR_min_pexp
259 (p10) cmp.eq.unc p10,p0 = GR_new_sig, r0 ;;
262 // Create small normal in case need to generate underflow flag
264 (p10) cmp.le.unc p10,p0 = GR_x_exp, GR_min_pexp
265 fmerge.se FR_tmp = FR_sden_exp, FR_lnorm_sig
266 (p9) cmp.gt.unc p9,p14 = GR_x_exp, GR_min_den_rexp
268 // Branch if cases 1, 2, 3
270 (p6) br.cond.spnt NEXT_EXPUP
271 (p7) br.cond.spnt NEXT_OVERFLOW
272 (p8) br.cond.spnt NEXT_EXPDOWN ;;
275 // Branch if cases 4, 5, 6
277 (p9) br.cond.spnt NEXT_NORM_TO_DENORM
278 (p10) br.cond.spnt NEXT_UNDERFLOW_TO_ZERO
279 (p14) br.cond.spnt NEXT_UNDERFLOW_TO_ZERO ;;
282 // Here if no special cases
283 // Set p6 if result will be a denormal, so can force underflow flag
284 // Case 1: x_exp=min_exp, x_sig=unnormalized
285 // Case 2: x_exp<min_exp
287 cmp.lt p6,p7 = GR_x_exp, GR_min_pexp
288 fmerge.se f8 = FR_new_exp, FR_new_sig
295 (p7) tbit.z p6,p0 = GR_new_sig, 63 ;;
299 // Force underflow and inexact if denormal result
302 (p6) fma.s.s0 FR_tmp = FR_tmp,FR_tmp,f0
307 fnorm.s.s0 f8 = f8 // Final normalization to result precision
308 (p6) br.cond.spnt NEXT_UNDERFLOW ;;
320 cmp.lt p6,p7 = GR_x_exp, GR_min_pexp
321 fmerge.se f8 = FR_exp1, FR_snorm_sig
322 br.cond.sptk NEXT_COMMON_FINISH ;;
327 cmp.lt p6,p7 = GR_x_exp, GR_min_pexp
328 fmerge.se f8 = FR_exp1, FR_lnorm_sig
329 br.cond.sptk NEXT_COMMON_FINISH ;;
335 fmerge.se f8 = FR_new_exp, FR_lden_sig
338 // Force underflow and inexact
341 fma.s.s0 FR_tmp = FR_tmp,FR_tmp,f0
342 br.cond.sptk NEXT_UNDERFLOW ;;
345 NEXT_UNDERFLOW_TO_ZERO:
348 fmerge.s f8 = FR_save_f8,f0
349 br.cond.sptk NEXT_COMMON_FINISH ;;
353 // Here if f8 is +- infinity
355 // if f8 is +inf, no matter what y is return largest float
356 // if f8 is -inf, no matter what y is return -largest float
360 fmerge.se FR_lnorm = FR_lnorm_exp,FR_lnorm_sig
366 fmerge.s f8 = f8,FR_lnorm
372 // Here if f8 is +- zero
374 // if f8 is zero and y is +, return + smallest float denormal
375 // if f8 is zero and y is -, return - smallest float denormal
379 fmerge.se FR_sden = FR_sden_exp,FR_sden_sig
383 // Create small normal to generate underflow flag
386 fmerge.se FR_tmp = FR_sden_exp, FR_lnorm_sig
390 // Add correct sign from direction arg
393 fmerge.s f8 = f9,FR_sden
397 // Force underflow and inexact flags
400 fma.s.s0 FR_tmp = FR_tmp,FR_tmp,f0
401 br.cond.sptk NEXT_UNDERFLOW ;;
405 // Here if result is a denorm, or input is finite and result is zero
406 // Call error support to report possible range error
408 alloc r32=ar.pfs,2,2,4,0
409 mov GR_Parameter_TAG = 269 // Error code
410 br.cond.sptk __libm_error_region // Branch to error call
415 // Here if input is finite, but result will be infinite
416 // Use frcpa to generate infinity of correct sign
417 // Call error support to report possible range error
419 alloc r32=ar.pfs,2,2,4,0
420 frcpa.s1 f8,p6 = FR_save_f8, f0
424 // Create largest double
427 fmerge.se FR_lnorm = FR_lnorm_exp,FR_lnorm_sig
431 // Force overflow and inexact flags to be set
433 mov GR_Parameter_TAG = 155 // Error code
434 fma.s.s0 FR_tmp = FR_lnorm,FR_lnorm,f0
435 br.cond.sptk __libm_error_region // Branch to error call
439 GLOBAL_LIBM_END(nextafterf)
442 LOCAL_LIBM_ENTRY(__libm_error_region)
447 add GR_Parameter_Y=-32,sp // Parameter 2 value
449 .save ar.pfs,GR_SAVE_PFS
450 mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
454 add sp=-64,sp // Create new stack
456 mov GR_SAVE_GP=gp // Save gp
462 stfs [GR_Parameter_Y] = f9,16 // STORE Parameter 2 on stack
463 add GR_Parameter_X = 16,sp // Parameter 1 address
465 mov GR_SAVE_B0=b0 // Save b0
471 stfs [GR_Parameter_X] = FR_save_f8 // STORE Parameter 1 on stack
472 add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address
476 stfs [GR_Parameter_Y] = f8 // STORE Parameter 3 on stack
477 add GR_Parameter_Y = -16,GR_Parameter_Y
478 br.call.sptk b0=__libm_error_support# // Call error handling function
483 add GR_Parameter_RESULT = 48,sp
488 ldfs f8 = [GR_Parameter_RESULT] // Get return result off stack
490 add sp = 64,sp // Restore stack pointer
491 mov b0 = GR_SAVE_B0 // Restore return address
494 mov gp = GR_SAVE_GP // Restore gp
495 mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
496 br.ret.sptk b0 // Return
499 LOCAL_LIBM_END(__libm_error_region)
502 .type __libm_error_support#,@function
503 .global __libm_error_support#