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* include/cln/integer.h (cl_I_to_E, cl_I_to_UE): New functions. 

* src/float/transcendental/cl_LF_exp_aux.cc: Make lq argument an uintE.
        * src/float/transcendental/cl_LF_cossin_aux.cc: Likewise.
        * src/float/transcendental/cl_LF_coshsinh_aux.cc: Likewise.
        * src/float/transcendental/cl_F_tran.h: Change declaration of lq.
        * src/float/transcendental/cl_F_lnx.cc: Fix some exponent types.
        * src/float/transcendental/cl_F_expx.cc: Likewise.
        * src/float/transcendental/cl_F_sinh.cc: Likewise.
        * src/float/transcendental/cl_F_atanx.cc: Likewise.
        * src/float/transcendental/cl_F_coshsinh.cc: Likewise.
        * src/float/transcendental/cl_LF_cossin.cc: Likewise.
        * src/float/transcendental/cl_LF_coshsinh.cc: Likewise.
master
Richard Kreckel 18 years ago
parent
308a067c42
commit
749cf017b2
13 changed files with 63 additions and 34 deletions
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  1. 15
      ChangeLog
  2. 18
      include/cln/integer.h
  3. 8
      src/float/transcendental/cl_F_atanx.cc
  4. 4
      src/float/transcendental/cl_F_coshsinh.cc
  5. 8
      src/float/transcendental/cl_F_expx.cc
  6. 8
      src/float/transcendental/cl_F_lnx.cc
  7. 2
      src/float/transcendental/cl_F_sinh.cc
  8. 6
      src/float/transcendental/cl_F_tran.h
  9. 8
      src/float/transcendental/cl_LF_coshsinh.cc
  10. 4
      src/float/transcendental/cl_LF_coshsinh_aux.cc
  11. 8
      src/float/transcendental/cl_LF_cossin.cc
  12. 4
      src/float/transcendental/cl_LF_cossin_aux.cc
  13. 4
      src/float/transcendental/cl_LF_exp_aux.cc

15
ChangeLog
View File

@ -1,3 +1,18 @@
2007-05-31 Richard B. Kreckel <kreckel@ginac.de>
* include/cln/integer.h (cl_I_to_E, cl_I_to_UE): New functions.
* src/float/transcendental/cl_LF_exp_aux.cc: Make lq argument an uintE.
* src/float/transcendental/cl_LF_cossin_aux.cc: Likewise.
* src/float/transcendental/cl_LF_coshsinh_aux.cc: Likewise.
* src/float/transcendental/cl_F_tran.h: Change declaration of lq.
* src/float/transcendental/cl_F_lnx.cc: Fix some exponent types.
* src/float/transcendental/cl_F_expx.cc: Likewise.
* src/float/transcendental/cl_F_sinh.cc: Likewise.
* src/float/transcendental/cl_F_atanx.cc: Likewise.
* src/float/transcendental/cl_F_coshsinh.cc: Likewise.
* src/float/transcendental/cl_LF_cossin.cc: Likewise.
* src/float/transcendental/cl_LF_coshsinh.cc: Likewise.
2007-04-09 Richard B. Kreckel <kreckel@ginac.de>
More memory efficient constants:

18
include/cln/integer.h
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@ -32,17 +32,22 @@ CL_DEFINE_AS_CONVERSION(cl_I)
inline unsigned int cl_I_to_uint (const cl_I& x) { return cl_I_to_UL(x); }
#endif
// Convert an integer to a 64-bit 'quad' type.
#ifdef intQsize
extern uint64 cl_I_to_UQ (const cl_I& obj);
extern sint64 cl_I_to_Q (const cl_I& obj);
#endif
// Convert an integer to a C `long' or `unsigned long'.
#if (long_bitsize==32)
inline long cl_I_to_long (const cl_I& x) { return cl_I_to_L(x); }
inline unsigned long cl_I_to_ulong (const cl_I& x) { return cl_I_to_UL(x); }
#elif (long_bitsize==64)
extern uint64 cl_I_to_UQ (const cl_I& obj);
extern sint64 cl_I_to_Q (const cl_I& obj);
inline long cl_I_to_long (const cl_I& x) { return cl_I_to_Q(x); }
inline unsigned long cl_I_to_ulong (const cl_I& x) { return cl_I_to_UQ(x); }
#endif
// Convert an integer to a counter type.
#if (intCsize==long_bitsize)
inline uintC cl_I_to_UC (const cl_I& x) { return cl_I_to_ulong(x); }
inline sintC cl_I_to_C (const cl_I& x) { return cl_I_to_long(x); }
@ -51,6 +56,15 @@ CL_DEFINE_AS_CONVERSION(cl_I)
inline sintC cl_I_to_C (const cl_I& x) { return cl_I_to_int(x); }
#endif
// Convert an integer to an exponent type.
#if (intEsize==intLsize)
inline uintE cl_I_to_UE (const cl_I& x) { return cl_I_to_UL(x); }
inline sintE cl_I_to_E (const cl_I& x) { return cl_I_to_L(x); }
#elif (intEsize==intQsize)
inline uintE cl_I_to_UE (const cl_I& x) { return cl_I_to_UQ(x); }
inline sintE cl_I_to_E (const cl_I& x) { return cl_I_to_Q(x); }
#endif
// Logische Operationen auf Integers:

8
src/float/transcendental/cl_F_atanx.cc
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@ -195,15 +195,15 @@ static const cl_LF atanx_ratseries (const cl_LF& t)
var cl_idecoded_float y_ = integer_decode_float(y);
// y = (-1)^sign * 2^exponent * mantissa
var uintC lm = integer_length(y_.mantissa);
var uintL me = cl_I_to_UL(- y_.exponent);
var uintE me = cl_I_to_UE(- y_.exponent);
var cl_I p;
var uintC lq;
var uintE lq;
var cl_boolean last_step = cl_false;
if (lm >= me) { // |y| >= 1/2 ?
p = y_.sign; // 1 or -1
lq = 1;
} else {
var uintL n = me - lm; // |y| < 2^-n with n maximal
var uintE n = me - lm; // |y| < 2^-n with n maximal
// Set p to the first n bits of |y|:
if (lm > n) {
p = y_.mantissa >> (lm - n);
@ -221,7 +221,7 @@ static const cl_LF atanx_ratseries (const cl_LF& t)
if (2*n >= lm)
last_step = cl_true;
}
z = z + scale_float(cl_I_to_LF(p,len),-(sintC)lq);
z = z + scale_float(cl_I_to_LF(p,len),-(sintE)lq);
if (last_step)
break;
var cl_LF_cos_sin_t cis_z = cl_cossin_aux(-p,lq,len);

4
src/float/transcendental/cl_F_coshsinh.cc
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@ -33,7 +33,7 @@ const cosh_sinh_t cosh_sinh (const cl_F& x)
// (scale-float (+ y (/ y)) -1) und (scale-float (- y (/ y)) -1) bilden.
// Genauigkeit wieder verringern.
var sintL e = float_exponent(x);
var sintE e = float_exponent(x);
if (e < 0) { // Exponent e abtesten
// e<0
if (zerop(x) || (e <= (1-(sintC)float_digits(x))>>1))
@ -54,7 +54,7 @@ const cosh_sinh_t cosh_sinh (const cl_F& x)
#endif
if (TheLfloat(x)->len >= 585) {
// verwende exp(x), schneller als cl_coshsinh_ratseries
var cl_LF xx = extend(x,TheLfloat(x)->len+ceiling((uintL)(-e),intDsize));
var cl_LF xx = extend(x,TheLfloat(x)->len+ceiling((uintE)(-e),intDsize));
var cl_F y = exp(xx);
var cl_F y_inv = recip(y);
return cosh_sinh_t(

8
src/float/transcendental/cl_F_expx.cc
View File

@ -139,7 +139,7 @@ const cl_LF expx_ratseries (const cl_LF& x)
var uintC len = TheLfloat(x)->len;
var cl_idecoded_float x_ = integer_decode_float(x);
// x = (-1)^sign * 2^exponent * mantissa
var uintL lq = cl_I_to_UL(- x_.exponent);
var uintE lq = cl_I_to_UE(- x_.exponent);
var const cl_I& p = x_.mantissa;
// Compute exp(p/2^lq) by splitting into pieces.
// Each piece gives rise to a factor exp(pk/2^lqk).
@ -153,12 +153,12 @@ const cl_LF expx_ratseries (const cl_LF& x)
// Values 2.5 <= c <= 3.2 seem best. Let's choose c = 2.875.
var cl_boolean first_factor = cl_true;
var cl_LF product;
var uintL b1;
var uintL b2;
var uintE b1;
var uintE b2;
for (b1 = 0, b2 = 1; b1 < lq; b1 = b2, b2 = ceiling(b2*23,8)) {
// Piece containing bits b1+1..b2 after "decimal point"
// in the binary representation of (p/2^lq).
var uintL lqk = (lq >= b2 ? b2 : lq);
var uintE lqk = (lq >= b2 ? b2 : lq);
var cl_I pk = ldb(p,cl_byte(lqk-b1,lq-lqk));
// Compute exp(pk/2^lqk).
if (!zerop(pk)) {

8
src/float/transcendental/cl_F_lnx.cc
View File

@ -201,15 +201,15 @@ const cl_LF lnx_ratseries (const cl_LF& x)
if (zerop(x1_.mantissa))
break;
var uintC lm = integer_length(x1_.mantissa);
var uintL me = cl_I_to_UL(- x1_.exponent);
var uintE me = cl_I_to_UE(- x1_.exponent);
var cl_I p;
var uintC lq;
var uintE lq;
var cl_boolean last_step = cl_false;
if (lm >= me) { // |x'| >= 1/2 ?
p = x1_.sign; // 1 or -1
lq = 1;
} else {
var uintL n = me - lm; // |x'| < 2^-n with n maximal
var uintE n = me - lm; // |x'| < 2^-n with n maximal
// Set p to the first n bits of |x'|:
if (lm > n) {
p = x1_.mantissa >> (lm - n);
@ -227,7 +227,7 @@ const cl_LF lnx_ratseries (const cl_LF& x)
if (2*n >= lm)
last_step = cl_true;
}
y = y + scale_float(cl_I_to_LF(p,len),-(sintC)lq);
y = y + scale_float(cl_I_to_LF(p,len),-(sintE)lq);
if (last_step)
break;
x = x * cl_exp_aux(-p,lq,len);

2
src/float/transcendental/cl_F_sinh.cc
View File

@ -41,7 +41,7 @@ const cl_F sinh (const cl_F& x)
// verwende exp(x), schneller als cl_coshsinh_ratseries
// (aber nur bei 0 > e > -d/2, denn wir müssen, um
// Auslöschung zu verhindern, |e| Bits dazunehmen)
var cl_LF xx = extend(x,TheLfloat(x)->len+ceiling((uintL)(-float_exponent(x)),intDsize));
var cl_LF xx = extend(x,TheLfloat(x)->len+ceiling((uintE)(-float_exponent(x)),intDsize));
var cl_F y = exp(xx);
var cl_F z = scale_float(y - recip(y), -1); // (/ (- y (/ y)) 2)
return cl_float(z,x);

6
src/float/transcendental/cl_F_tran.h
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@ -19,7 +19,7 @@ extern const cl_LF pi (uintC len); // computes it even further
// cl_exp_aux(p,lq,len) liefert die Zahl exp(p/2^lq) mit len Digits.
// 0 < |p| < 2^lq.
// Es sollte |p|^2 < 2^lq sein, sonst ist das nicht effizient.
extern const cl_LF cl_exp_aux (const cl_I& p, uintC lq, uintC len);
extern const cl_LF cl_exp_aux (const cl_I& p, uintE lq, uintC len);
// cl_cossin_aux(p,lq,len) liefert cos(p/2^lq) und sin(p/2^lq) mit len Digits.
// 0 < |p| < 2^lq.
@ -31,7 +31,7 @@ struct cl_LF_cos_sin_t {
cl_LF_cos_sin_t (const cl_LF& u, const cl_LF& v) : cos (u), sin (v) {}
cl_LF_cos_sin_t () {}
};
extern const cl_LF_cos_sin_t cl_cossin_aux (const cl_I& p, uintC lq, uintC len);
extern const cl_LF_cos_sin_t cl_cossin_aux (const cl_I& p, uintE lq, uintC len);
// cl_coshsinh_aux(p,lq,len) liefert cosh(p/2^lq) und sinh(p/2^lq) mit len Digits.
// 0 < |p| < 2^lq.
@ -43,7 +43,7 @@ struct cl_LF_cosh_sinh_t {
cl_LF_cosh_sinh_t (const cl_LF& u, const cl_LF& v) : cosh (u), sinh (v) {}
cl_LF_cosh_sinh_t () {}
};
extern const cl_LF_cosh_sinh_t cl_coshsinh_aux (const cl_I& p, uintC lq, uintC len);
extern const cl_LF_cosh_sinh_t cl_coshsinh_aux (const cl_I& p, uintE lq, uintC len);
// atanhx(x) liefert zu einem Float x (betragsmäßig <1/2) atanh(x) als Float.
extern const cl_F atanhx (const cl_F& x);

8
src/float/transcendental/cl_LF_coshsinh.cc
View File

@ -26,17 +26,17 @@ const cl_LF_cosh_sinh_t cl_coshsinh_ratseries (const cl_LF& x)
var uintC len = TheLfloat(x)->len;
var cl_idecoded_float x_ = integer_decode_float(x);
// x = (-1)^sign * 2^exponent * mantissa
var uintL lq = cl_I_to_UL(- x_.exponent);
var uintE lq = cl_I_to_UE(- x_.exponent);
var const cl_I& p = x_.mantissa;
// Compute sinh(p/2^lq) and cosh(p/2^lq) by splitting into pieces.
var cl_boolean first_factor = cl_true;
var cl_LF_cosh_sinh_t product;
var uintL b1;
var uintL b2;
var uintE b1;
var uintE b2;
for (b1 = 0, b2 = 1; b1 < lq; b1 = b2, b2 = 2*b2) {
// Piece containing bits b1+1..b2 after "decimal point"
// in the binary representation of (p/2^lq).
var uintL lqk = (lq >= b2 ? b2 : lq);
var uintE lqk = (lq >= b2 ? b2 : lq);
var cl_I pk = ldb(p,cl_byte(lqk-b1,lq-lqk));
// Compute sinh(pk/2^lqk) and cosh(pk/2^lqk).
if (!zerop(pk)) {

4
src/float/transcendental/cl_LF_coshsinh_aux.cc
View File

@ -26,10 +26,10 @@ namespace cln {
// by a power series evaluation brings 20% speedup, even more for small lengths.
#define TRIVIAL_SPEEDUP
const cl_LF_cosh_sinh_t cl_coshsinh_aux (const cl_I& p, uintC lq, uintC len)
const cl_LF_cosh_sinh_t cl_coshsinh_aux (const cl_I& p, uintE lq, uintC len)
{
{ Mutable(cl_I,p);
var uintC lp = integer_length(p); // now |p| < 2^lp.
var uintE lp = integer_length(p); // now |p| < 2^lp.
if (!(lp <= lq)) cl_abort();
lp = lq - lp; // now |p/2^lq| < 2^-lp.
// Minimize lq (saves computation time).

8
src/float/transcendental/cl_LF_cossin.cc
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@ -26,17 +26,17 @@ const cl_LF_cos_sin_t cl_cossin_ratseries (const cl_LF& x)
var uintC len = TheLfloat(x)->len;
var cl_idecoded_float x_ = integer_decode_float(x);
// x = (-1)^sign * 2^exponent * mantissa
var uintL lq = cl_I_to_UL(- x_.exponent);
var uintE lq = cl_I_to_UE(- x_.exponent);
var const cl_I& p = x_.mantissa;
// Compute sin(p/2^lq) and cos(p/2^lq) by splitting into pieces.
var cl_boolean first_factor = cl_true;
var cl_LF_cos_sin_t product;
var uintL b1;
var uintL b2;
var uintE b1;
var uintE b2;
for (b1 = 0, b2 = 1; b1 < lq; b1 = b2, b2 = 2*b2) {
// Piece containing bits b1+1..b2 after "decimal point"
// in the binary representation of (p/2^lq).
var uintL lqk = (lq >= b2 ? b2 : lq);
var uintE lqk = (lq >= b2 ? b2 : lq);
var cl_I pk = ldb(p,cl_byte(lqk-b1,lq-lqk));
// Compute sin(pk/2^lqk) and cos(pk/2^lqk).
if (!zerop(pk)) {

4
src/float/transcendental/cl_LF_cossin_aux.cc
View File

@ -26,10 +26,10 @@ namespace cln {
// by a power series evaluation brings 20% speedup, even more for small lengths.
#define TRIVIAL_SPEEDUP
const cl_LF_cos_sin_t cl_cossin_aux (const cl_I& p, uintC lq, uintC len)
const cl_LF_cos_sin_t cl_cossin_aux (const cl_I& p, uintE lq, uintC len)
{
{ Mutable(cl_I,p);
var uintC lp = integer_length(p); // now |p| < 2^lp.
var uintE lp = integer_length(p); // now |p| < 2^lp.
if (!(lp <= lq)) cl_abort();
lp = lq - lp; // now |p/2^lq| < 2^-lp.
// Minimize lq (saves computation time).

4
src/float/transcendental/cl_LF_exp_aux.cc
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@ -22,10 +22,10 @@
namespace cln {
const cl_LF cl_exp_aux (const cl_I& p, uintC lq, uintC len)
const cl_LF cl_exp_aux (const cl_I& p, uintE lq, uintC len)
{
{ Mutable(cl_I,p);
var uintC lp = integer_length(p); // now |p| < 2^lp.
var uintE lp = integer_length(p); // now |p| < 2^lp.
if (!(lp <= lq)) cl_abort();
lp = lq - lp; // now |p/2^lq| < 2^-lp.
// Minimize lq (saves computation time).

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