rustfmt'ed + some clean up
This commit is contained in:
Rahul Butani
parent
440e835967
commit
1c555103ae
2 changed files with 127 additions and 112 deletions
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@ -49,8 +49,8 @@ mod log1pf;
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mod log2;
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mod log2f;
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mod logf;
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mod powf;
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mod pow;
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mod powf;
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mod round;
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mod roundf;
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mod scalbn;
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@ -111,8 +111,8 @@ pub use self::log1pf::log1pf;
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pub use self::log2::log2;
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pub use self::log2f::log2f;
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pub use self::logf::logf;
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pub use self::powf::powf;
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pub use self::pow::pow;
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pub use self::powf::powf;
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pub use self::round::round;
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pub use self::roundf::roundf;
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pub use self::scalbn::scalbn;
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@ -8,93 +8,87 @@
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* is preserved.
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* ====================================================
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*/
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/* pow(x,y) return x**y
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*
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* n
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* Method: Let x = 2 * (1+f)
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* 1. Compute and return log2(x) in two pieces:
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* log2(x) = w1 + w2,
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* where w1 has 53-24 = 29 bit trailing zeros.
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* 2. Perform y*log2(x) = n+y' by simulating muti-precision
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* arithmetic, where |y'|<=0.5.
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* 3. Return x**y = 2**n*exp(y'*log2)
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*
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* Special cases:
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* 1. (anything) ** 0 is 1
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* 2. 1 ** (anything) is 1
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* 3. (anything except 1) ** NAN is NAN
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* 4. NAN ** (anything except 0) is NAN
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* 5. +-(|x| > 1) ** +INF is +INF
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* 6. +-(|x| > 1) ** -INF is +0
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* 7. +-(|x| < 1) ** +INF is +0
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* 8. +-(|x| < 1) ** -INF is +INF
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* 9. -1 ** +-INF is 1
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* 10. +0 ** (+anything except 0, NAN) is +0
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* 11. -0 ** (+anything except 0, NAN, odd integer) is +0
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* 12. +0 ** (-anything except 0, NAN) is +INF, raise divbyzero
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* 13. -0 ** (-anything except 0, NAN, odd integer) is +INF, raise divbyzero
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* 14. -0 ** (+odd integer) is -0
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* 15. -0 ** (-odd integer) is -INF, raise divbyzero
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* 16. +INF ** (+anything except 0,NAN) is +INF
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* 17. +INF ** (-anything except 0,NAN) is +0
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* 18. -INF ** (+odd integer) is -INF
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* 19. -INF ** (anything) = -0 ** (-anything), (anything except odd integer)
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* 20. (anything) ** 1 is (anything)
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* 21. (anything) ** -1 is 1/(anything)
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* 22. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)
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* 23. (-anything except 0 and inf) ** (non-integer) is NAN
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*
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* Accuracy:
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* pow(x,y) returns x**y nearly rounded. In particular
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* pow(integer,integer)
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* always returns the correct integer provided it is
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* representable.
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*
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* Constants :
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* The hexadecimal values are the intended ones for the following
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* constants. The decimal values may be used, provided that the
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* compiler will convert from decimal to binary accurately enough
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* to produce the hexadecimal values shown.
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*/
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// #include "libm.h"
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/// pow(x,y) return x**y
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///
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/// n
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/// Method: Let x = 2 * (1+f)
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/// 1. Compute and return log2(x) in two pieces:
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/// log2(x) = w1 + w2,
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/// where w1 has 53-24 = 29 bit trailing zeros.
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/// 2. Perform y*log2(x) = n+y' by simulating muti-precision
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/// arithmetic, where |y'|<=0.5.
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/// 3. Return x**y = 2**n*exp(y'*log2)
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///
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/// Special cases:
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/// 1. (anything) ** 0 is 1
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/// 2. 1 ** (anything) is 1
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/// 3. (anything except 1) ** NAN is NAN
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/// 4. NAN ** (anything except 0) is NAN
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/// 5. +-(|x| > 1) ** +INF is +INF
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/// 6. +-(|x| > 1) ** -INF is +0
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/// 7. +-(|x| < 1) ** +INF is +0
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/// 8. +-(|x| < 1) ** -INF is +INF
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/// 9. -1 ** +-INF is 1
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/// 10. +0 ** (+anything except 0, NAN) is +0
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/// 11. -0 ** (+anything except 0, NAN, odd integer) is +0
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/// 12. +0 ** (-anything except 0, NAN) is +INF, raise divbyzero
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/// 13. -0 ** (-anything except 0, NAN, odd integer) is +INF, raise divbyzero
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/// 14. -0 ** (+odd integer) is -0
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/// 15. -0 ** (-odd integer) is -INF, raise divbyzero
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/// 16. +INF ** (+anything except 0,NAN) is +INF
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/// 17. +INF ** (-anything except 0,NAN) is +0
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/// 18. -INF ** (+odd integer) is -INF
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/// 19. -INF ** (anything) = -0 ** (-anything), (anything except odd integer)
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/// 20. (anything) ** 1 is (anything)
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/// 21. (anything) ** -1 is 1/(anything)
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/// 22. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)
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/// 23. (-anything except 0 and inf) ** (non-integer) is NAN
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///
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/// Accuracy:
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/// pow(x,y) returns x**y nearly rounded. In particular
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/// pow(integer,integer)
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/// always returns the correct integer provided it is
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/// representable.
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///
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/// Constants :
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/// The hexadecimal values are the intended ones for the following
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/// constants. The decimal values may be used, provided that the
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/// compiler will convert from decimal to binary accurately enough
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/// to produce the hexadecimal values shown.
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///
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/* Concerns:
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* - Some constants are shared; DRY?
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* - FLT_EVAL_METHOD: the others sidestep this (epsilon or just always true in the case of hypot (#71))
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*/
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use super::{fabs, get_high_word, scalbn, sqrt, with_set_high_word, with_set_low_word};
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use super::{fabs, scalbn, sqrt, with_set_low_word, with_set_high_word, get_high_word};
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const BP: [f64; 2] = [1.0, 1.5];
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const BP: [f64; 2] = [1.0, 1.5];
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const DP_H: [f64; 2] = [0.0, 5.84962487220764160156e-01]; /* 0x3fe2b803_40000000 */
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const DP_L: [f64; 2] = [0.0, 1.35003920212974897128e-08]; /* 0x3E4CFDEB, 0x43CFD006 */
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const TWO53: f64 = 9007199254740992.0; /* 0x43400000_00000000 */
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const HUGE: f64 = 1.0e300;
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const TINY: f64 = 1.0e-300;
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const TWO53: f64 = 9007199254740992.0; /* 0x43400000_00000000 */
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const HUGE: f64 = 1.0e300;
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const TINY: f64 = 1.0e-300;
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// poly coefs for (3/2)*(log(x)-2s-2/3*s**3:
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const L1: f64 = 5.99999999999994648725e-01; /* 0x3fe33333_33333303 */
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const L2: f64 = 4.28571428578550184252e-01; /* 0x3fdb6db6_db6fabff */
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const L3: f64 = 3.33333329818377432918e-01; /* 0x3fd55555_518f264d */
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const L4: f64 = 2.72728123808534006489e-01; /* 0x3fd17460_a91d4101 */
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const L5: f64 = 2.30660745775561754067e-01; /* 0x3fcd864a_93c9db65 */
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const L6: f64 = 2.06975017800338417784e-01; /* 0x3fca7e28_4a454eef */
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const P1: f64 = 1.66666666666666019037e-01; /* 0x3fc55555_5555553e */
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const L1: f64 = 5.99999999999994648725e-01; /* 0x3fe33333_33333303 */
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const L2: f64 = 4.28571428578550184252e-01; /* 0x3fdb6db6_db6fabff */
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const L3: f64 = 3.33333329818377432918e-01; /* 0x3fd55555_518f264d */
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const L4: f64 = 2.72728123808534006489e-01; /* 0x3fd17460_a91d4101 */
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const L5: f64 = 2.30660745775561754067e-01; /* 0x3fcd864a_93c9db65 */
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const L6: f64 = 2.06975017800338417784e-01; /* 0x3fca7e28_4a454eef */
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const P1: f64 = 1.66666666666666019037e-01; /* 0x3fc55555_5555553e */
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const P2: f64 = -2.77777777770155933842e-03; /* 0xbf66c16c_16bebd93 */
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const P3: f64 = 6.61375632143793436117e-05; /* 0x3f11566a_af25de2c */
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const P3: f64 = 6.61375632143793436117e-05; /* 0x3f11566a_af25de2c */
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const P4: f64 = -1.65339022054652515390e-06; /* 0xbebbbd41_c5d26bf1 */
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const P5: f64 = 4.13813679705723846039e-08; /* 0x3e663769_72bea4d0 */
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const LG2: f64 = 6.93147180559945286227e-01; /* 0x3fe62e42_fefa39ef */
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const LG2_H: f64 = 6.93147182464599609375e-01; /* 0x3fe62e43_00000000 */
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const LG2_L: f64 = -1.90465429995776804525e-09; /* 0xbe205c61_0ca86c39 */
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const OVT: f64 = 8.0085662595372944372e-017; /* -(1024-log2(ovfl+.5ulp)) */
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const CP: f64 = 9.61796693925975554329e-01; /* 0x3feec709_dc3a03fd =2/(3ln2) */
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const CP_H: f64 = 9.61796700954437255859e-01; /* 0x3feec709_e0000000 =(float)cp */
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const CP_L: f64 = -7.02846165095275826516e-09; /* 0xbe3e2fe0_145b01f5 =tail of cp_h*/
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const IVLN2: f64 = 1.44269504088896338700e+00; /* 0x3ff71547_652b82fe =1/ln2 */
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const IVLN2_H: f64 = 1.44269502162933349609e+00; /* 0x3ff71547_60000000 =24b 1/ln2*/
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const IVLN2_L: f64 = 1.92596299112661746887e-08; /* 0x3e54ae0b_f85ddf44 =1/ln2 tail*/
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const P5: f64 = 4.13813679705723846039e-08; /* 0x3e663769_72bea4d0 */
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const LG2: f64 = 6.93147180559945286227e-01; /* 0x3fe62e42_fefa39ef */
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const LG2_H: f64 = 6.93147182464599609375e-01; /* 0x3fe62e43_00000000 */
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const LG2_L: f64 = -1.90465429995776804525e-09; /* 0xbe205c61_0ca86c39 */
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const OVT: f64 = 8.0085662595372944372e-017; /* -(1024-log2(ovfl+.5ulp)) */
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const CP: f64 = 9.61796693925975554329e-01; /* 0x3feec709_dc3a03fd =2/(3ln2) */
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const CP_H: f64 = 9.61796700954437255859e-01; /* 0x3feec709_e0000000 =(float)cp */
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const CP_L: f64 = -7.02846165095275826516e-09; /* 0xbe3e2fe0_145b01f5 =tail of cp_h*/
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const IVLN2: f64 = 1.44269504088896338700e+00; /* 0x3ff71547_652b82fe =1/ln2 */
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const IVLN2_H: f64 = 1.44269502162933349609e+00; /* 0x3ff71547_60000000 =24b 1/ln2*/
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const IVLN2_L: f64 = 1.92596299112661746887e-08; /* 0x3e54ae0b_f85ddf44 =1/ln2 tail*/
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#[inline]
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pub fn pow(x: f64, y: f64) -> f64 {
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@ -103,7 +97,7 @@ pub fn pow(x: f64, y: f64) -> f64 {
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let (hx, lx): (i32, u32) = ((x.to_bits() >> 32) as i32, x.to_bits() as u32);
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let (hy, ly): (i32, u32) = ((y.to_bits() >> 32) as i32, y.to_bits() as u32);
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let mut ix: i32 = (hx & 0x7fffffff) as i32;
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let iy: i32 = (hy & 0x7fffffff) as i32;
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@ -118,9 +112,12 @@ pub fn pow(x: f64, y: f64) -> f64 {
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}
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/* NaN if either arg is NaN */
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if ix > 0x7ff00000 || (ix == 0x7ff00000 && lx != 0) ||
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iy > 0x7ff00000 || (iy == 0x7ff00000 && ly != 0) {
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return x + y;
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if ix > 0x7ff00000
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|| (ix == 0x7ff00000 && lx != 0)
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|| iy > 0x7ff00000
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|| (iy == 0x7ff00000 && ly != 0)
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{
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return x + y;
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}
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/* determine if y is an odd int when x < 0
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@ -136,16 +133,16 @@ pub fn pow(x: f64, y: f64) -> f64 {
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yisint = 2; /* even integer y */
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} else if iy >= 0x3ff00000 {
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k = (iy >> 20) - 0x3ff; /* exponent */
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if k > 20 {
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j = (ly >> (52 - k)) as i32;
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if (j << (52 - k)) == (ly as i32) {
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yisint = 2 - (j & 1);
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}
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} else if ly == 0 {
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j = iy >> (20 - k);
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if (j << (20 - k)) == iy {
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yisint = 2 - (j & 1);
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}
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@ -156,16 +153,25 @@ pub fn pow(x: f64, y: f64) -> f64 {
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if ly == 0 {
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/* special value of y */
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if iy == 0x7ff00000 {
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/* y is +-inf */
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/* y is +-inf */
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return if ((ix - 0x3ff00000) | (lx as i32)) == 0 {
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/* (-1)**+-inf is 1 */
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1.0
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} else if ix >= 0x3ff00000 {
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/* (|x|>1)**+-inf = inf,0 */
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if hy >= 0 { y } else { 0.0 }
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if hy >= 0 {
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y
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} else {
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0.0
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}
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} else {
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/* (|x|<1)**+-inf = 0,inf */
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if hy >= 0 { 0.0 } else { -y }
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if hy >= 0 {
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0.0
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} else {
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-y
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}
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};
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}
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@ -194,14 +200,14 @@ pub fn pow(x: f64, y: f64) -> f64 {
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if ix == 0x7ff00000 || ix == 0 || ix == 0x3ff00000 {
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/* x is +-0,+-inf,+-1 */
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let mut z: f64 = ax;
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if hy < 0 {
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/* z = (1/|x|) */
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z = 1.0 / z;
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}
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if hx < 0 {
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if ((ix-0x3ff00000)|yisint) == 0 {
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if ((ix - 0x3ff00000) | yisint) == 0 {
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z = (z - z) / (z - z); /* (-1)**non-int is NaN */
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} else if yisint == 1 {
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z = -z; /* (x<0)**odd = -(|x|**odd) */
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@ -241,17 +247,25 @@ pub fn pow(x: f64, y: f64) -> f64 {
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/* over/underflow if x is not close to one */
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if ix < 0x3fefffff {
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return if hy < 0 { s * HUGE * HUGE } else { s * TINY * TINY };
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return if hy < 0 {
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s * HUGE * HUGE
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} else {
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s * TINY * TINY
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};
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}
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if ix > 0x3ff00000 {
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return if hy > 0 { s * HUGE * HUGE } else { s * TINY * TINY };
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return if hy > 0 {
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s * HUGE * HUGE
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} else {
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s * TINY * TINY
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};
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}
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/* now |1-x| is TINY <= 2**-20, suffice to compute
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log(x) by x-x^2/2+x^3/3-x^4/4 */
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let t: f64 = ax - 1.0; /* t has 20 trailing zeros */
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let t: f64 = ax - 1.0; /* t has 20 trailing zeros */
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let w: f64 = (t * t) * (0.5 - t * (0.3333333333333333333333 - t * 0.25));
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let u: f64 = IVLN2_H * t; /* ivln2_h has 21 sig. bits */
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let u: f64 = IVLN2_H * t; /* ivln2_h has 21 sig. bits */
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let v: f64 = t * IVLN2_L - w * IVLN2;
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t1 = with_set_low_word(u + v, 0);
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t2 = v - (t1 - u);
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@ -262,8 +276,8 @@ pub fn pow(x: f64, y: f64) -> f64 {
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if ix < 0x00100000 {
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/* take care subnormal number */
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ax *= TWO53;
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n -= 53;
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ix = get_high_word(ax) as i32;
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n -= 53;
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ix = get_high_word(ax) as i32;
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}
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n += (ix >> 20) - 0x3ff;
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@ -271,12 +285,11 @@ pub fn pow(x: f64, y: f64) -> f64 {
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/* determine interval */
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let k: i32;
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ix = j | 0x3ff00000; /* normalize ix */
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ix = j | 0x3ff00000; /* normalize ix */
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if j <= 0x3988E {
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/* |x|<sqrt(3/2) */
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k = 0;
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}
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else if j < 0xBB67A {
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} else if j < 0xBB67A {
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/* |x|<sqrt(3) */
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k = 1;
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} else {
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@ -289,18 +302,20 @@ pub fn pow(x: f64, y: f64) -> f64 {
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/* compute ss = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
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let u: f64 = ax - BP[k as usize]; /* bp[0]=1.0, bp[1]=1.5 */
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let v: f64 = 1.0 / (ax + BP[k as usize]);
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let ss: f64 = u * v;
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let ss: f64 = u * v;
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let s_h = with_set_low_word(ss, 0);
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/* t_h=ax+bp[k] High */
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let t_h: f64 = with_set_high_word(0.0,
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((ix as u32 >> 1) | 0x20000000) + 0x00080000 + ((k as u32) << 18));
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let t_h: f64 = with_set_high_word(
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0.0,
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((ix as u32 >> 1) | 0x20000000) + 0x00080000 + ((k as u32) << 18),
|
||||
);
|
||||
let t_l: f64 = ax - (t_h - BP[k as usize]);
|
||||
let s_l: f64 = v * ((u - s_h * t_h) - s_h * t_l);
|
||||
|
||||
/* compute log(ax) */
|
||||
let s2: f64 = ss * ss;
|
||||
let mut r: f64 = s2 * s2 * (L1 + s2 * (L2 + s2 *(L3 + s2 *(L4 + s2 *(L5 + s2 * L6)))));
|
||||
let mut r: f64 = s2 * s2 * (L1 + s2 * (L2 + s2 * (L3 + s2 * (L4 + s2 * (L5 + s2 * L6)))));
|
||||
r += s_l * (s_h + ss);
|
||||
let s2: f64 = s_h * s_h;
|
||||
let t_h: f64 = with_set_low_word(3.0 + s2 + r, 0);
|
||||
|
|
@ -312,7 +327,7 @@ pub fn pow(x: f64, y: f64) -> f64 {
|
|||
|
||||
/* 2/(3log2)*(ss+...) */
|
||||
let p_h: f64 = with_set_low_word(u + v, 0);
|
||||
let p_l = v - (p_h-u);
|
||||
let p_l = v - (p_h - u);
|
||||
let z_h: f64 = CP_H * p_h; /* cp_h+cp_l = 2/(3*log2) */
|
||||
let z_l: f64 = CP_L * p_h + p_l * CP + DP_L[k as usize];
|
||||
|
||||
|
|
@ -323,10 +338,10 @@ pub fn pow(x: f64, y: f64) -> f64 {
|
|||
}
|
||||
|
||||
/* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
|
||||
let y1: f64 = with_set_low_word(y, 0);
|
||||
let y1: f64 = with_set_low_word(y, 0);
|
||||
let p_l: f64 = (y - y1) * t1 + y * t2;
|
||||
let mut p_h: f64 = y1 * t1;
|
||||
let z: f64 = p_l + p_h;
|
||||
let z: f64 = p_l + p_h;
|
||||
let mut j: i32 = (z.to_bits() >> 32) as i32;
|
||||
let i: i32 = z.to_bits() as i32;
|
||||
// let (j, i): (i32, i32) = ((z.to_bits() >> 32) as i32, z.to_bits() as i32);
|
||||
|
|
@ -363,7 +378,7 @@ pub fn pow(x: f64, y: f64) -> f64 {
|
|||
if i > 0x3fe00000 {
|
||||
/* if |z| > 0.5, set n = [z+0.5] */
|
||||
n = j + (0x00100000 >> (k + 1));
|
||||
k = ((n&0x7fffffff) >> 20) - 0x3ff; /* new k for n */
|
||||
k = ((n & 0x7fffffff) >> 20) - 0x3ff; /* new k for n */
|
||||
let t: f64 = with_set_high_word(0.0, (n & !(0x000fffff >> k)) as u32);
|
||||
n = ((n & 0x000fffff) | 0x00100000) >> (20 - k);
|
||||
if j < 0 {
|
||||
|
|
@ -379,17 +394,17 @@ pub fn pow(x: f64, y: f64) -> f64 {
|
|||
let w: f64 = v - (z - u);
|
||||
let t: f64 = z * z;
|
||||
let t1: f64 = z - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5))));
|
||||
let r: f64 = (z * t1) / (t1 - 2.0) - (w + z*w);
|
||||
let r: f64 = (z * t1) / (t1 - 2.0) - (w + z * w);
|
||||
z = 1.0 - (r - z);
|
||||
j = get_high_word(z) as i32;
|
||||
j += n << 20;
|
||||
|
||||
if (j >> 20) <= 0 {
|
||||
/* subnormal output */
|
||||
z = scalbn(z,n);
|
||||
z = scalbn(z, n);
|
||||
} else {
|
||||
z = with_set_high_word(z, j as u32);
|
||||
}
|
||||
|
||||
return s*z;
|
||||
return s * z;
|
||||
}
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue