1 /* ------------------------------------------------------------------ */
2 /* Decimal 32-bit format module */
3 /* ------------------------------------------------------------------ */
4 /* Copyright (c) IBM Corporation, 2000, 2006. All rights reserved. */
5 /* */
6 /* This software is made available under the terms of the */
7 /* ICU License -- ICU 1.8.1 and later. */
8 /* */
9 /* The description and User's Guide ("The decNumber C Library") for */
10 /* this software is called decNumber.pdf. This document is */
11 /* available, together with arithmetic and format specifications, */
12 /* testcases, and Web links, at: http://www2.hursley.ibm.com/decimal */
13 /* */
14 /* Please send comments, suggestions, and corrections to the author: */
15 /* mfc@uk.ibm.com */
16 /* Mike Cowlishaw, IBM Fellow */
17 /* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */
18 /* ------------------------------------------------------------------ */
19 /* This module comprises the routines for decimal32 format numbers. */
20 /* Conversions are supplied to and from decNumber and String. */
21 /* */
22 /* No arithmetic routines are included; decNumber provides these. */
23 /* */
24 /* Error handling is the same as decNumber (qv.). */
25 /* ------------------------------------------------------------------ */
26 #include <string.h> // [for memset/memcpy]
27 #include <stdio.h> // [for printf]
28 #if defined(_MSVC_)
29 #pragma warning(disable:4244) // [for win64]
30 #endif /*defined(_MSVC_)*/
31
32 #define DECNUMDIGITS 7 // make decNumbers with space for 7
33 #include "decNumber.h" // base number library
34 #include "decNumberLocal.h" // decNumber local types, etc.
35 #include "decimal32.h" // our primary include
36
37 /* Utility tables and routines [in decimal64.c] */
38 extern const uInt COMBEXP[32], COMBMSD[32];
39 extern const uShort DPD2BIN[1024];
40 extern const uShort BIN2DPD[1000];
41 extern const uByte BIN2CHAR[4001];
42
43 extern void decDigitsToDPD(const decNumber *, uInt *, Int);
44 extern void decDigitsFromDPD(decNumber *, const uInt *, Int);
45
46 #if DECTRACE || DECCHECK
47 void decimal32Show(const decimal32 *); // for debug
48 extern void decNumberShow(const decNumber *); // ..
49 #endif
50
51 /* Useful macro */
52 // Clear a structure (e.g., a decNumber)
53 #define DEC_clear(d) memset(d, 0, sizeof(*d))
54
55 #if !DECENDIAN || DECTRACE || DECCHECK
56 /* compile-time endian tester [assumes sizeof(int)>1] */
57 static const Int mfcone=1; // constant 1
58 static const Flag *mfctop=(Flag *)&mfcone; // -> top byte
59 #define LITEND mfctop[0] // named flag; 1=little-endian
60 #endif
61
62 /* ------------------------------------------------------------------ */
63 /* decimal32FromNumber -- convert decNumber to decimal32 */
64 /* */
65 /* ds is the target decimal32 */
66 /* dn is the source number (assumed valid) */
67 /* set is the context, used only for reporting errors */
68 /* */
69 /* The set argument is used only for status reporting and for the */
70 /* rounding mode (used if the coefficient is more than DECIMAL32_Pmax */
71 /* digits or an overflow is detected). If the exponent is out of the */
72 /* valid range then Overflow or Underflow will be raised. */
73 /* After Underflow a subnormal result is possible. */
74 /* */
75 /* DEC_Clamped is set if the number has to be 'folded down' to fit, */
76 /* by reducing its exponent and multiplying the coefficient by a */
77 /* power of ten, or if the exponent on a zero had to be clamped. */
78 /* ------------------------------------------------------------------ */
decimal32FromNumber(decimal32 * d32,const decNumber * dn,decContext * set)79 decimal32 * decimal32FromNumber(decimal32 *d32, const decNumber *dn,
80 decContext *set) {
81 uInt status=0; // status accumulator
82 Int ae; // adjusted exponent
83 decNumber dw; // work
84 decContext dc; // ..
85 uInt *pu; // ..
86 uInt comb, exp; // ..
87 uInt targ=0; // target 32-bit
88
89 // If the number has too many digits, or the exponent could be
90 // out of range then reduce the number under the appropriate
91 // constraints. This could push the number to Infinity or zero,
92 // so this check and rounding must be done before generating the
93 // decimal32]
94 ae=dn->exponent+dn->digits-1; // [0 if special]
95 if (dn->digits>DECIMAL32_Pmax // too many digits
96 || ae>DECIMAL32_Emax // likely overflow
97 || ae<DECIMAL32_Emin) { // likely underflow
98 decContextDefault(&dc, DEC_INIT_DECIMAL32); // [no traps]
99 dc.round=set->round; // use supplied rounding
100 decNumberPlus(&dw, dn, &dc); // (round and check)
101 // [this changes -0 to 0, so enforce the sign...]
102 dw.bits|=dn->bits&DECNEG;
103 status=dc.status; // save status
104 dn=&dw; // use the work number
105 } // maybe out of range
106
107 if (dn->bits&DECSPECIAL) { // a special value
108 if (dn->bits&DECINF) targ=DECIMAL_Inf<<24;
109 else { // sNaN or qNaN
110 if ((*dn->lsu!=0 || dn->digits>1) // non-zero coefficient
111 && (dn->digits<DECIMAL32_Pmax)) { // coefficient fits
112 decDigitsToDPD(dn, &targ, 0);
113 }
114 if (dn->bits&DECNAN) targ|=DECIMAL_NaN<<24;
115 else targ|=DECIMAL_sNaN<<24;
116 } // a NaN
117 } // special
118
119 else { // is finite
120 if (decNumberIsZero(dn)) { // is a zero
121 // set and clamp exponent
122 if (dn->exponent<-DECIMAL32_Bias) {
123 exp=0; // low clamp
124 status|=DEC_Clamped;
125 }
126 else {
127 exp=dn->exponent+DECIMAL32_Bias; // bias exponent
128 if (exp>DECIMAL32_Ehigh) { // top clamp
129 exp=DECIMAL32_Ehigh;
130 status|=DEC_Clamped;
131 }
132 }
133 comb=(exp>>3) & 0x18; // msd=0, exp top 2 bits ..
134 }
135 else { // non-zero finite number
136 uInt msd; // work
137 Int pad=0; // coefficient pad digits
138
139 // the dn is known to fit, but it may need to be padded
140 exp=(uInt)(dn->exponent+DECIMAL32_Bias); // bias exponent
141 if (exp>DECIMAL32_Ehigh) { // fold-down case
142 pad=exp-DECIMAL32_Ehigh;
143 exp=DECIMAL32_Ehigh; // [to maximum]
144 status|=DEC_Clamped;
145 }
146
147 // fastpath common case
148 if (DECDPUN==3 && pad==0) {
149 targ=BIN2DPD[dn->lsu[0]];
150 if (dn->digits>3) targ|=(uInt)(BIN2DPD[dn->lsu[1]])<<10;
151 msd=(dn->digits==7 ? dn->lsu[2] : 0);
152 }
153 else { // general case
154 decDigitsToDPD(dn, &targ, pad);
155 // save and clear the top digit
156 msd=targ>>20;
157 targ&=0x000fffff;
158 }
159
160 // create the combination field
161 if (msd>=8) comb=0x18 | ((exp>>5) & 0x06) | (msd & 0x01);
162 else comb=((exp>>3) & 0x18) | msd;
163 }
164 targ|=comb<<26; // add combination field ..
165 targ|=(exp&0x3f)<<20; // .. and exponent continuation
166 } // finite
167
168 if (dn->bits&DECNEG) targ|=0x80000000; // add sign bit
169
170 // now write to storage; this may be endian, or not
171 #if DECENDIAN
172 // DECENDIAN -- direct store
173 pu=(uInt *)d32->bytes; // overlay
174 *pu=targ; // directly store the int
175 #else
176 // not DECENDIAN -- use network byte order
177 if (LITEND) { // little-endian needs reversal
178 uByte *pb; // work
179 for (pb=&d32->bytes[3]; pb>=d32->bytes; pb--) {
180 *pb=(uByte)(targ&0xff);
181 targ>>=8;
182 } // i
183 }
184 else { // big-endian; it's the right way round already
185 pu=(uInt *)d32->bytes; // overlay
186 *pu=targ; // directly store the int
187 }
188 #endif
189
190 if (status!=0) decContextSetStatus(set, status); // pass on status
191 // decimal32Show(d32);
192 return d32;
193 } // decimal32FromNumber
194
195 /* ------------------------------------------------------------------ */
196 /* decimal32ToNumber -- convert decimal32 to decNumber */
197 /* d32 is the source decimal32 */
198 /* dn is the target number, with appropriate space */
199 /* No error is possible. */
200 /* ------------------------------------------------------------------ */
decimal32ToNumber(const decimal32 * d32,decNumber * dn)201 decNumber * decimal32ToNumber(const decimal32 *d32, decNumber *dn) {
202 uInt msd; // coefficient MSD
203 uInt exp; // exponent top two bits
204 uInt comb; // combination field
205 uInt *pu; // work
206 uInt sour; // source 32-bit
207
208 // load source from storage; this may be endian, or not
209 #if DECENDIAN
210 // DECENDIAN -- direct load
211 pu=(uInt *)d32->bytes; // overlay
212 sour=*pu; // directly load the int
213 #else
214 // not DECENDIAN -- use network byte order
215 if (LITEND) { // little-endian needs reversal
216 const uByte *pb; // work
217 sour=0; // [keep compiler quiet]
218 for (pb=d32->bytes; pb<=&d32->bytes[3]; pb++) {
219 sour<<=8;
220 sour|=*pb;
221 } // i
222 }
223 else { // big-endian; it's the right way round already
224 pu=(uInt *)d32->bytes; // overlay
225 sour=*pu; // directly load the int
226 }
227 #endif
228
229 comb=(sour>>26)&0x1f; // combination field
230
231 decNumberZero(dn); // clean number
232 if (sour&0x80000000) dn->bits=DECNEG; // set sign if negative
233
234 msd=COMBMSD[comb]; // decode the combination field
235 exp=COMBEXP[comb]; // ..
236
237 if (exp==3) { // is a special
238 if (msd==0) {
239 dn->bits|=DECINF;
240 return dn; // no coefficient needed
241 }
242 else if (sour&0x02000000) dn->bits|=DECSNAN;
243 else dn->bits|=DECNAN;
244 msd=0; // no top digit
245 }
246 else { // is a finite number
247 dn->exponent=(exp<<6)+((sour>>20)&0x3f)-DECIMAL32_Bias; // unbiased
248 }
249
250 // get the coefficient
251 sour&=0x000fffff; // clean coefficient continuation
252 if (msd) { // non-zero msd
253 sour|=msd<<20; // prefix to coefficient
254 decDigitsFromDPD(dn, &sour, 3); // process 3 declets
255 return dn;
256 }
257 // msd=0
258 if (!sour) return dn; // easy: coefficient is 0
259 if (sour&0x000ffc00) // need 2 declets?
260 decDigitsFromDPD(dn, &sour, 2); // process 2 declets
261 else
262 decDigitsFromDPD(dn, &sour, 1); // process 1 declet
263 return dn;
264 } // decimal32ToNumber
265
266 /* ------------------------------------------------------------------ */
267 /* to-scientific-string -- conversion to numeric string */
268 /* to-engineering-string -- conversion to numeric string */
269 /* */
270 /* decimal32ToString(d32, string); */
271 /* decimal32ToEngString(d32, string); */
272 /* */
273 /* d32 is the decimal32 format number to convert */
274 /* string is the string where the result will be laid out */
275 /* */
276 /* string must be at least 24 characters */
277 /* */
278 /* No error is possible, and no status can be set. */
279 /* ------------------------------------------------------------------ */
decimal32ToEngString(const decimal32 * d32,char * string)280 char * decimal32ToEngString(const decimal32 *d32, char *string){
281 decNumber dn; // work
282 decimal32ToNumber(d32, &dn);
283 decNumberToEngString(&dn, string);
284 return string;
285 } // decimal32ToEngString
286
decimal32ToString(const decimal32 * d32,char * string)287 char * decimal32ToString(const decimal32 *d32, char *string){
288 uInt msd; // coefficient MSD
289 Int exp; // exponent top two bits or full
290 uInt comb; // combination field
291 char *cstart; // coefficient start
292 char *c; // output pointer in string
293 uInt *pu; // work
294 char *s, *t; // .. (source, target)
295 Int dpd; // ..
296 Int pre, e; // ..
297 const uByte *u; // ..
298 uInt sour; // source 32-bit
299
300 // load source from storage; this may be endian, or not
301 #if DECENDIAN
302 // DECENDIAN -- direct load
303 pu=(uInt *)d32->bytes; // overlay
304 sour=*pu; // directly load the int
305 #else
306 // not DECENDIAN -- use network byte order
307 if (LITEND) { // little-endian needs reversal
308 const uByte *pb; // work
309 sour=0; // [keep compiler quiet]
310 for (pb=d32->bytes; pb<=&d32->bytes[3]; pb++) {
311 sour<<=8;
312 sour|=*pb;
313 } // i
314 }
315 else { // big-endian; it's the right way round already
316 pu=(uInt *)d32->bytes; // overlay
317 sour=*pu; // directly load the int
318 }
319 #endif
320
321 c=string; // where result will go
322 if (((Int)sour)<0) *c++='-'; // handle sign
323
324 comb=(sour>>26)&0x1f; // combination field
325 msd=COMBMSD[comb]; // decode the combination field
326 exp=COMBEXP[comb]; // ..
327
328 if (exp==3) {
329 if (msd==0) { // infinity
330 strcpy(c, "Infinity");
331 return string; // easy
332 }
333 if (sour&0x02000000) *c++='s'; // sNaN
334 strcpy(c, "NaN"); // complete word
335 c+=3; // step past
336 if ((sour&0x000fffff)==0) return string; // zero payload
337 // otherwise drop through to add integer; set correct exp
338 exp=0; msd=0; // setup for following code
339 }
340 else exp=(exp<<6)+((sour>>20)&0x3f)-DECIMAL32_Bias; // unbiased
341
342 // convert 7 digits of significand to characters
343 cstart=c; // save start of coefficient
344 if (msd) *c++='0'+(char)msd; // non-zero most significant digit
345
346 // Now decode the declets. After extracting each one, it is
347 // decoded to binary and then to a 4-char sequence by table lookup;
348 // the 4-chars are a 1-char length (significant digits, except 000
349 // has length 0). This allows us to left-align the first declet
350 // with non-zero content, then remaining ones are full 3-char
351 // length. We use fixed-length memcpys because variable-length
352 // causes a subroutine call in GCC. (These are length 4 for speed
353 // and are safe because the array has an extra terminator byte.)
354 #define dpd2char u=&BIN2CHAR[DPD2BIN[dpd]*4]; \
355 if (c!=cstart) {memcpy(c, u+1, 4); c+=3;} \
356 else if (*u) {memcpy(c, u+4-*u, 4); c+=*u;}
357
358 dpd=(sour>>10)&0x3ff; // declet 1
359 dpd2char;
360 dpd=(sour)&0x3ff; // declet 2
361 dpd2char;
362
363 if (c==cstart) *c++='0'; // all zeros -- make 0
364
365 if (exp==0) { // integer or NaN case -- easy
366 *c='\0'; // terminate
367 return string;
368 }
369
370 /* non-0 exponent */
371 e=0; // assume no E
372 pre=c-cstart+exp;
373 // [here, pre-exp is the digits count (==1 for zero)]
374 if (exp>0 || pre<-5) { // need exponential form
375 e=pre-1; // calculate E value
376 pre=1; // assume one digit before '.'
377 } // exponential form
378
379 /* modify the coefficient, adding 0s, '.', and E+nn as needed */
380 s=c-1; // source (LSD)
381 if (pre>0) { // ddd.ddd (plain), perhaps with E
382 char *dotat=cstart+pre;
383 if (dotat<c) { // if embedded dot needed...
384 t=c; // target
385 for (; s>=dotat; s--, t--) *t=*s; // open the gap; leave t at gap
386 *t='.'; // insert the dot
387 c++; // length increased by one
388 }
389
390 // finally add the E-part, if needed; it will never be 0, and has
391 // a maximum length of 3 digits (E-101 case)
392 if (e!=0) {
393 *c++='E'; // starts with E
394 *c++='+'; // assume positive
395 if (e<0) {
396 *(c-1)='-'; // oops, need '-'
397 e=-e; // uInt, please
398 }
399 u=&BIN2CHAR[e*4]; // -> length byte
400 memcpy(c, u+4-*u, 4); // copy fixed 4 characters [is safe]
401 c+=*u; // bump pointer appropriately
402 }
403 *c='\0'; // add terminator
404 //printf("res %s\n", string);
405 return string;
406 } // pre>0
407
408 /* -5<=pre<=0: here for plain 0.ddd or 0.000ddd forms (can never have E) */
409 t=c+1-pre;
410 *(t+1)='\0'; // can add terminator now
411 for (; s>=cstart; s--, t--) *t=*s; // shift whole coefficient right
412 c=cstart;
413 *c++='0'; // always starts with 0.
414 *c++='.';
415 for (; pre<0; pre++) *c++='0'; // add any 0's after '.'
416 //printf("res %s\n", string);
417 return string;
418 } // decimal32ToString
419
420 /* ------------------------------------------------------------------ */
421 /* to-number -- conversion from numeric string */
422 /* */
423 /* decimal32FromString(result, string, set); */
424 /* */
425 /* result is the decimal32 format number which gets the result of */
426 /* the conversion */
427 /* *string is the character string which should contain a valid */
428 /* number (which may be a special value) */
429 /* set is the context */
430 /* */
431 /* The context is supplied to this routine is used for error handling */
432 /* (setting of status and traps) and for the rounding mode, only. */
433 /* If an error occurs, the result will be a valid decimal32 NaN. */
434 /* ------------------------------------------------------------------ */
decimal32FromString(decimal32 * result,const char * string,decContext * set)435 decimal32 * decimal32FromString(decimal32 *result, const char *string,
436 decContext *set) {
437 decContext dc; // work
438 decNumber dn; // ..
439
440 decContextDefault(&dc, DEC_INIT_DECIMAL32); // no traps, please
441 dc.round=set->round; // use supplied rounding
442
443 decNumberFromString(&dn, string, &dc); // will round if needed
444 decimal32FromNumber(result, &dn, &dc);
445 if (dc.status!=0) { // something happened
446 decContextSetStatus(set, dc.status); // .. pass it on
447 }
448 return result;
449 } // decimal32FromString
450
451 #if DECTRACE || DECCHECK
452 /* ------------------------------------------------------------------ */
453 /* decimal32Show -- display a decimal32 in hexadecimal [debug aid] */
454 /* d32 -- the number to show */
455 /* ------------------------------------------------------------------ */
456 // Also shows sign/cob/expconfields extracted - valid bigendian only
decimal32Show(const decimal32 * d32)457 void decimal32Show(const decimal32 *d32) {
458 char buf[DECIMAL32_Bytes*2+1];
459 Int i, j=0;
460
461 #if DECENDIAN
462 if (LITEND) {
463 for (i=0; i<DECIMAL32_Bytes; i++, j+=2) {
464 sprintf(&buf[j], "%02x", d32->bytes[3-i]);
465 }
466 printf(" D32> %s [S:%d Cb:%02x Ec:%02x] LittleEndian\n", buf,
467 d32->bytes[3]>>7, (d32->bytes[3]>>2)&0x1f,
468 ((d32->bytes[3]&0x3)<<4)| (d32->bytes[2]>>4));
469 }
470 else {
471 #endif
472 for (i=0; i<DECIMAL32_Bytes; i++, j+=2) {
473 sprintf(&buf[j], "%02x", d32->bytes[i]);
474 }
475 printf(" D32> %s [S:%d Cb:%02x Ec:%02x] BigEndian\n", buf,
476 decimal32Sign(d32), decimal32Comb(d32), decimal32ExpCon(d32));
477 #if DECENDIAN
478 }
479 #endif
480 } // decimal32Show
481 #endif
482