pow!
This commit is contained in:
Rahul Butani
parent
89c7f41c04
commit
f12ba75f67
1 changed files with 395 additions and 0 deletions
395
library/compiler-builtins/libm/src/math/pow.rs
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395
library/compiler-builtins/libm/src/math/pow.rs
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/* origin: FreeBSD /usr/src/lib/msun/src/e_pow.c */
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/*
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* ====================================================
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* Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved.
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*
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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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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/* 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, 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 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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// 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 P2: f64 = -2.77777777770155933842e-03; /* 0xbf66c16c_16bebd93 */
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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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#[inline]
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pub fn pow(x: f64, y: f64) -> f64 {
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let t1: f64;
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let t2: 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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/* x**0 = 1, even if x is NaN */
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if ((iy as u32) | ly) == 0 {
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return 1.0;
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}
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/* 1**y = 1, even if y is NaN */
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if hx == 0x3ff00000 && lx == 0 {
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return 1.0;
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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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}
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/* determine if y is an odd int when x < 0
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* yisint = 0 ... y is not an integer
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* yisint = 1 ... y is an odd int
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* yisint = 2 ... y is an even int
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*/
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let mut yisint: i32 = 0;
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let mut k: i32;
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let mut j: i32;
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if hx < 0 {
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if iy >= 0x43400000 {
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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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}
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}
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}
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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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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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} 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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};
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}
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if iy == 0x3ff00000 {
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/* y is +-1 */
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return if hy >= 0 { x } else { 1.0 / x };
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}
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if hy == 0x40000000 {
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/* y is 2 */
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return x * x;
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}
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if hy == 0x3fe00000 {
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/* y is 0.5 */
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if hx >= 0 {
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/* x >= +0 */
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return sqrt(x);
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}
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}
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}
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let mut ax: f64 = fabs(x);
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if lx == 0 {
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/* special value of x */
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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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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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}
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}
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return z;
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}
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}
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let mut s: f64 = 1.0; /* sign of result */
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if hx < 0 {
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if yisint == 0 {
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/* (x<0)**(non-int) is NaN */
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return (x - x) / (x - x);
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}
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if yisint == 1 {
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/* (x<0)**(odd int) */
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s = -1.0;
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}
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}
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/* |y| is HUGE */
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if iy > 0x41e00000 {
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/* if |y| > 2**31 */
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if iy > 0x43f00000 {
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/* if |y| > 2**64, must o/uflow */
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if ix <= 0x3fefffff {
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return if hy < 0 { HUGE * HUGE } else { TINY * TINY };
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}
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if ix >= 0x3ff00000 {
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return if hy > 0 { HUGE * HUGE } else { TINY * TINY };
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}
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}
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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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}
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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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}
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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 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 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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} else {
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// double ss,s2,s_h,s_l,t_h,t_l;
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let mut n: i32 = 0;
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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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}
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n += (ix >> 20) - 0x3ff;
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j = ix & 0x000fffff;
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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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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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/* |x|<sqrt(3) */
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k = 1;
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} else {
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k = 0;
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n += 1;
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ix -= 0x00100000;
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}
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ax = with_set_high_word(ax, ix as u32);
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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 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_l: f64 = ax - (t_h - BP[k as usize]);
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let s_l: f64 = v * ((u - s_h * t_h) - s_h * t_l);
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/* compute log(ax) */
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let s2: f64 = ss * ss;
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let mut r: f64 = s2 * s2 * (L1 + s2 * (L2 + s2 *(L3 + s2 *(L4 + s2 *(L5 + s2 * L6)))));
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r += s_l * (s_h + ss);
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let s2: f64 = s_h * s_h;
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let t_h: f64 = with_set_low_word(3.0 + s2 + r, 0);
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let t_l: f64 = r - ((t_h - 3.0) - s2);
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/* u+v = ss*(1+...) */
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let u: f64 = s_h * t_h;
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let v: f64 = s_l * t_h + t_l * ss;
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/* 2/(3log2)*(ss+...) */
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let p_h: f64 = with_set_low_word(u + v, 0);
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let p_l = v - (p_h-u);
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let z_h: f64 = CP_H * p_h; /* cp_h+cp_l = 2/(3*log2) */
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let z_l: f64 = CP_L * p_h + p_l * CP + DP_L[k as usize];
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/* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */
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let t: f64 = n as f64;
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t1 = with_set_low_word(((z_h + z_l) + DP_H[k as usize]) + t, 0);
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t2 = z_l - (((t1 - t) - DP_H[k as usize]) - z_h);
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}
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/* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
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let y1: f64 = with_set_low_word(y, 0);
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let p_l: f64 = (y - y1) * t1 + y * t2;
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let mut p_h: f64 = y1 * t1;
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let z: f64 = p_l + p_h;
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let mut j: i32 = (z.to_bits() >> 32) as i32;
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let i: i32 = z.to_bits() as i32;
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// let (j, i): (i32, i32) = ((z.to_bits() >> 32) as i32, z.to_bits() as i32);
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if j >= 0x40900000 {
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/* z >= 1024 */
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if (j - 0x40900000) | i != 0 {
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/* if z > 1024 */
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return s * HUGE * HUGE; /* overflow */
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}
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if p_l + OVT > z - p_h {
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return s * HUGE * HUGE; /* overflow */
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}
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} else if (j & 0x7fffffff) >= 0x4090cc00 {
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/* z <= -1075 */
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// FIXME: instead of abs(j) use unsigned j
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if (((j as u32) - 0xc090cc00) | (i as u32)) != 0 {
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/* z < -1075 */
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return s * TINY * TINY; /* underflow */
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}
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if p_l <= z - p_h {
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return s * TINY * TINY; /* underflow */
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}
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}
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/* compute 2**(p_h+p_l) */
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let i: i32 = j & (0x7fffffff as i32);
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k = (i >> 20) - 0x3ff;
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let mut n: i32 = 0;
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if i > 0x3fe00000 {
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/* if |z| > 0.5, set n = [z+0.5] */
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n = j + (0x00100000 >> (k + 1));
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k = ((n&0x7fffffff) >> 20) - 0x3ff; /* new k for n */
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let t: f64 = with_set_high_word(0.0, (n & !(0x000fffff >> k)) as u32);
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n = ((n & 0x000fffff) | 0x00100000) >> (20 - k);
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if j < 0 {
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n = -n;
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}
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p_h -= t;
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}
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let t: f64 = with_set_low_word(p_l + p_h, 0);
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let u: f64 = t * LG2_H;
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let v: f64 = (p_l - (t - p_h)) * LG2 + t * LG2_L;
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let mut z: f64 = u + v;
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let w: f64 = v - (z - u);
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let t: f64 = z * z;
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let t1: f64 = z - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5))));
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let r: f64 = (z * t1) / (t1 - 2.0) - (w + z*w);
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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);
|
||||
} else {
|
||||
z = with_set_high_word(z, j as u32);
|
||||
}
|
||||
|
||||
return s*z;
|
||||
}
|
||||
Loading…
Add table
Add a link
Reference in a new issue