From 1c555103ae48c2c452739d9b9b77e4267738965f Mon Sep 17 00:00:00 2001 From: Rahul Butani Date: Tue, 17 Jul 2018 15:06:50 -0500 Subject: [PATCH] rustfmt'ed + some clean up --- .../compiler-builtins/libm/src/math/mod.rs | 4 +- .../compiler-builtins/libm/src/math/pow.rs | 235 ++++++++++-------- 2 files changed, 127 insertions(+), 112 deletions(-) diff --git a/library/compiler-builtins/libm/src/math/mod.rs b/library/compiler-builtins/libm/src/math/mod.rs index 6dd362d00945..752a5991aeab 100644 --- a/library/compiler-builtins/libm/src/math/mod.rs +++ b/library/compiler-builtins/libm/src/math/mod.rs @@ -49,8 +49,8 @@ mod log1pf; mod log2; mod log2f; mod logf; -mod powf; mod pow; +mod powf; mod round; mod roundf; mod scalbn; @@ -111,8 +111,8 @@ pub use self::log1pf::log1pf; pub use self::log2::log2; pub use self::log2f::log2f; pub use self::logf::logf; -pub use self::powf::powf; pub use self::pow::pow; +pub use self::powf::powf; pub use self::round::round; pub use self::roundf::roundf; pub use self::scalbn::scalbn; diff --git a/library/compiler-builtins/libm/src/math/pow.rs b/library/compiler-builtins/libm/src/math/pow.rs index 3d0769b34403..69c086b0f242 100644 --- a/library/compiler-builtins/libm/src/math/pow.rs +++ b/library/compiler-builtins/libm/src/math/pow.rs @@ -8,93 +8,87 @@ * is preserved. * ==================================================== */ -/* pow(x,y) return x**y - * - * n - * Method: Let x = 2 * (1+f) - * 1. Compute and return log2(x) in two pieces: - * log2(x) = w1 + w2, - * where w1 has 53-24 = 29 bit trailing zeros. - * 2. Perform y*log2(x) = n+y' by simulating muti-precision - * arithmetic, where |y'|<=0.5. - * 3. Return x**y = 2**n*exp(y'*log2) - * - * Special cases: - * 1. (anything) ** 0 is 1 - * 2. 1 ** (anything) is 1 - * 3. (anything except 1) ** NAN is NAN - * 4. NAN ** (anything except 0) is NAN - * 5. +-(|x| > 1) ** +INF is +INF - * 6. +-(|x| > 1) ** -INF is +0 - * 7. +-(|x| < 1) ** +INF is +0 - * 8. +-(|x| < 1) ** -INF is +INF - * 9. -1 ** +-INF is 1 - * 10. +0 ** (+anything except 0, NAN) is +0 - * 11. -0 ** (+anything except 0, NAN, odd integer) is +0 - * 12. +0 ** (-anything except 0, NAN) is +INF, raise divbyzero - * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF, raise divbyzero - * 14. -0 ** (+odd integer) is -0 - * 15. -0 ** (-odd integer) is -INF, raise divbyzero - * 16. +INF ** (+anything except 0,NAN) is +INF - * 17. +INF ** (-anything except 0,NAN) is +0 - * 18. -INF ** (+odd integer) is -INF - * 19. -INF ** (anything) = -0 ** (-anything), (anything except odd integer) - * 20. (anything) ** 1 is (anything) - * 21. (anything) ** -1 is 1/(anything) - * 22. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer) - * 23. (-anything except 0 and inf) ** (non-integer) is NAN - * - * Accuracy: - * pow(x,y) returns x**y nearly rounded. In particular - * pow(integer,integer) - * always returns the correct integer provided it is - * representable. - * - * Constants : - * The hexadecimal values are the intended ones for the following - * constants. The decimal values may be used, provided that the - * compiler will convert from decimal to binary accurately enough - * to produce the hexadecimal values shown. - */ -// #include "libm.h" +/// pow(x,y) return x**y +/// +/// n +/// Method: Let x = 2 * (1+f) +/// 1. Compute and return log2(x) in two pieces: +/// log2(x) = w1 + w2, +/// where w1 has 53-24 = 29 bit trailing zeros. +/// 2. Perform y*log2(x) = n+y' by simulating muti-precision +/// arithmetic, where |y'|<=0.5. +/// 3. Return x**y = 2**n*exp(y'*log2) +/// +/// Special cases: +/// 1. (anything) ** 0 is 1 +/// 2. 1 ** (anything) is 1 +/// 3. (anything except 1) ** NAN is NAN +/// 4. NAN ** (anything except 0) is NAN +/// 5. +-(|x| > 1) ** +INF is +INF +/// 6. +-(|x| > 1) ** -INF is +0 +/// 7. +-(|x| < 1) ** +INF is +0 +/// 8. +-(|x| < 1) ** -INF is +INF +/// 9. -1 ** +-INF is 1 +/// 10. +0 ** (+anything except 0, NAN) is +0 +/// 11. -0 ** (+anything except 0, NAN, odd integer) is +0 +/// 12. +0 ** (-anything except 0, NAN) is +INF, raise divbyzero +/// 13. -0 ** (-anything except 0, NAN, odd integer) is +INF, raise divbyzero +/// 14. -0 ** (+odd integer) is -0 +/// 15. -0 ** (-odd integer) is -INF, raise divbyzero +/// 16. +INF ** (+anything except 0,NAN) is +INF +/// 17. +INF ** (-anything except 0,NAN) is +0 +/// 18. -INF ** (+odd integer) is -INF +/// 19. -INF ** (anything) = -0 ** (-anything), (anything except odd integer) +/// 20. (anything) ** 1 is (anything) +/// 21. (anything) ** -1 is 1/(anything) +/// 22. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer) +/// 23. (-anything except 0 and inf) ** (non-integer) is NAN +/// +/// Accuracy: +/// pow(x,y) returns x**y nearly rounded. In particular +/// pow(integer,integer) +/// always returns the correct integer provided it is +/// representable. +/// +/// Constants : +/// The hexadecimal values are the intended ones for the following +/// constants. The decimal values may be used, provided that the +/// compiler will convert from decimal to binary accurately enough +/// to produce the hexadecimal values shown. +/// -/* Concerns: - * - Some constants are shared; DRY? - * - FLT_EVAL_METHOD: the others sidestep this (epsilon or just always true in the case of hypot (#71)) - */ +use super::{fabs, get_high_word, scalbn, sqrt, with_set_high_word, with_set_low_word}; -use super::{fabs, scalbn, sqrt, with_set_low_word, with_set_high_word, get_high_word}; - -const BP: [f64; 2] = [1.0, 1.5]; +const BP: [f64; 2] = [1.0, 1.5]; const DP_H: [f64; 2] = [0.0, 5.84962487220764160156e-01]; /* 0x3fe2b803_40000000 */ const DP_L: [f64; 2] = [0.0, 1.35003920212974897128e-08]; /* 0x3E4CFDEB, 0x43CFD006 */ -const TWO53: f64 = 9007199254740992.0; /* 0x43400000_00000000 */ -const HUGE: f64 = 1.0e300; -const TINY: f64 = 1.0e-300; +const TWO53: f64 = 9007199254740992.0; /* 0x43400000_00000000 */ +const HUGE: f64 = 1.0e300; +const TINY: f64 = 1.0e-300; // poly coefs for (3/2)*(log(x)-2s-2/3*s**3: -const L1: f64 = 5.99999999999994648725e-01; /* 0x3fe33333_33333303 */ -const L2: f64 = 4.28571428578550184252e-01; /* 0x3fdb6db6_db6fabff */ -const L3: f64 = 3.33333329818377432918e-01; /* 0x3fd55555_518f264d */ -const L4: f64 = 2.72728123808534006489e-01; /* 0x3fd17460_a91d4101 */ -const L5: f64 = 2.30660745775561754067e-01; /* 0x3fcd864a_93c9db65 */ -const L6: f64 = 2.06975017800338417784e-01; /* 0x3fca7e28_4a454eef */ -const P1: f64 = 1.66666666666666019037e-01; /* 0x3fc55555_5555553e */ +const L1: f64 = 5.99999999999994648725e-01; /* 0x3fe33333_33333303 */ +const L2: f64 = 4.28571428578550184252e-01; /* 0x3fdb6db6_db6fabff */ +const L3: f64 = 3.33333329818377432918e-01; /* 0x3fd55555_518f264d */ +const L4: f64 = 2.72728123808534006489e-01; /* 0x3fd17460_a91d4101 */ +const L5: f64 = 2.30660745775561754067e-01; /* 0x3fcd864a_93c9db65 */ +const L6: f64 = 2.06975017800338417784e-01; /* 0x3fca7e28_4a454eef */ +const P1: f64 = 1.66666666666666019037e-01; /* 0x3fc55555_5555553e */ const P2: f64 = -2.77777777770155933842e-03; /* 0xbf66c16c_16bebd93 */ -const P3: f64 = 6.61375632143793436117e-05; /* 0x3f11566a_af25de2c */ +const P3: f64 = 6.61375632143793436117e-05; /* 0x3f11566a_af25de2c */ const P4: f64 = -1.65339022054652515390e-06; /* 0xbebbbd41_c5d26bf1 */ -const P5: f64 = 4.13813679705723846039e-08; /* 0x3e663769_72bea4d0 */ -const LG2: f64 = 6.93147180559945286227e-01; /* 0x3fe62e42_fefa39ef */ -const LG2_H: f64 = 6.93147182464599609375e-01; /* 0x3fe62e43_00000000 */ -const LG2_L: f64 = -1.90465429995776804525e-09; /* 0xbe205c61_0ca86c39 */ -const OVT: f64 = 8.0085662595372944372e-017; /* -(1024-log2(ovfl+.5ulp)) */ -const CP: f64 = 9.61796693925975554329e-01; /* 0x3feec709_dc3a03fd =2/(3ln2) */ -const CP_H: f64 = 9.61796700954437255859e-01; /* 0x3feec709_e0000000 =(float)cp */ -const CP_L: f64 = -7.02846165095275826516e-09; /* 0xbe3e2fe0_145b01f5 =tail of cp_h*/ -const IVLN2: f64 = 1.44269504088896338700e+00; /* 0x3ff71547_652b82fe =1/ln2 */ -const IVLN2_H: f64 = 1.44269502162933349609e+00; /* 0x3ff71547_60000000 =24b 1/ln2*/ -const IVLN2_L: f64 = 1.92596299112661746887e-08; /* 0x3e54ae0b_f85ddf44 =1/ln2 tail*/ +const P5: f64 = 4.13813679705723846039e-08; /* 0x3e663769_72bea4d0 */ +const LG2: f64 = 6.93147180559945286227e-01; /* 0x3fe62e42_fefa39ef */ +const LG2_H: f64 = 6.93147182464599609375e-01; /* 0x3fe62e43_00000000 */ +const LG2_L: f64 = -1.90465429995776804525e-09; /* 0xbe205c61_0ca86c39 */ +const OVT: f64 = 8.0085662595372944372e-017; /* -(1024-log2(ovfl+.5ulp)) */ +const CP: f64 = 9.61796693925975554329e-01; /* 0x3feec709_dc3a03fd =2/(3ln2) */ +const CP_H: f64 = 9.61796700954437255859e-01; /* 0x3feec709_e0000000 =(float)cp */ +const CP_L: f64 = -7.02846165095275826516e-09; /* 0xbe3e2fe0_145b01f5 =tail of cp_h*/ +const IVLN2: f64 = 1.44269504088896338700e+00; /* 0x3ff71547_652b82fe =1/ln2 */ +const IVLN2_H: f64 = 1.44269502162933349609e+00; /* 0x3ff71547_60000000 =24b 1/ln2*/ +const IVLN2_L: f64 = 1.92596299112661746887e-08; /* 0x3e54ae0b_f85ddf44 =1/ln2 tail*/ #[inline] pub fn pow(x: f64, y: f64) -> f64 { @@ -103,7 +97,7 @@ pub fn pow(x: f64, y: f64) -> f64 { let (hx, lx): (i32, u32) = ((x.to_bits() >> 32) as i32, x.to_bits() as u32); let (hy, ly): (i32, u32) = ((y.to_bits() >> 32) as i32, y.to_bits() as u32); - + let mut ix: i32 = (hx & 0x7fffffff) as i32; let iy: i32 = (hy & 0x7fffffff) as i32; @@ -118,9 +112,12 @@ pub fn pow(x: f64, y: f64) -> f64 { } /* NaN if either arg is NaN */ - if ix > 0x7ff00000 || (ix == 0x7ff00000 && lx != 0) || - iy > 0x7ff00000 || (iy == 0x7ff00000 && ly != 0) { - return x + y; + if ix > 0x7ff00000 + || (ix == 0x7ff00000 && lx != 0) + || iy > 0x7ff00000 + || (iy == 0x7ff00000 && ly != 0) + { + return x + y; } /* determine if y is an odd int when x < 0 @@ -136,16 +133,16 @@ pub fn pow(x: f64, y: f64) -> f64 { yisint = 2; /* even integer y */ } else if iy >= 0x3ff00000 { k = (iy >> 20) - 0x3ff; /* exponent */ - + if k > 20 { j = (ly >> (52 - k)) as i32; - + if (j << (52 - k)) == (ly as i32) { yisint = 2 - (j & 1); } } else if ly == 0 { j = iy >> (20 - k); - + if (j << (20 - k)) == iy { yisint = 2 - (j & 1); } @@ -156,16 +153,25 @@ pub fn pow(x: f64, y: f64) -> f64 { if ly == 0 { /* special value of y */ if iy == 0x7ff00000 { - /* y is +-inf */ + /* y is +-inf */ + return if ((ix - 0x3ff00000) | (lx as i32)) == 0 { /* (-1)**+-inf is 1 */ 1.0 } else if ix >= 0x3ff00000 { /* (|x|>1)**+-inf = inf,0 */ - if hy >= 0 { y } else { 0.0 } + if hy >= 0 { + y + } else { + 0.0 + } } else { /* (|x|<1)**+-inf = 0,inf */ - if hy >= 0 { 0.0 } else { -y } + if hy >= 0 { + 0.0 + } else { + -y + } }; } @@ -194,14 +200,14 @@ pub fn pow(x: f64, y: f64) -> f64 { if ix == 0x7ff00000 || ix == 0 || ix == 0x3ff00000 { /* x is +-0,+-inf,+-1 */ let mut z: f64 = ax; - + if hy < 0 { /* z = (1/|x|) */ z = 1.0 / z; } if hx < 0 { - if ((ix-0x3ff00000)|yisint) == 0 { + if ((ix - 0x3ff00000) | yisint) == 0 { z = (z - z) / (z - z); /* (-1)**non-int is NaN */ } else if yisint == 1 { z = -z; /* (x<0)**odd = -(|x|**odd) */ @@ -241,17 +247,25 @@ pub fn pow(x: f64, y: f64) -> f64 { /* over/underflow if x is not close to one */ if ix < 0x3fefffff { - return if hy < 0 { s * HUGE * HUGE } else { s * TINY * TINY }; + return if hy < 0 { + s * HUGE * HUGE + } else { + s * TINY * TINY + }; } if ix > 0x3ff00000 { - return if hy > 0 { s * HUGE * HUGE } else { s * TINY * TINY }; + return if hy > 0 { + s * HUGE * HUGE + } else { + s * TINY * TINY + }; } /* now |1-x| is TINY <= 2**-20, suffice to compute log(x) by x-x^2/2+x^3/3-x^4/4 */ - let t: f64 = ax - 1.0; /* t has 20 trailing zeros */ + let t: f64 = ax - 1.0; /* t has 20 trailing zeros */ let w: f64 = (t * t) * (0.5 - t * (0.3333333333333333333333 - t * 0.25)); - let u: f64 = IVLN2_H * t; /* ivln2_h has 21 sig. bits */ + let u: f64 = IVLN2_H * t; /* ivln2_h has 21 sig. bits */ let v: f64 = t * IVLN2_L - w * IVLN2; t1 = with_set_low_word(u + v, 0); t2 = v - (t1 - u); @@ -262,8 +276,8 @@ pub fn pow(x: f64, y: f64) -> f64 { if ix < 0x00100000 { /* take care subnormal number */ ax *= TWO53; - n -= 53; - ix = get_high_word(ax) as i32; + n -= 53; + ix = get_high_word(ax) as i32; } n += (ix >> 20) - 0x3ff; @@ -271,12 +285,11 @@ pub fn pow(x: f64, y: f64) -> f64 { /* determine interval */ let k: i32; - ix = j | 0x3ff00000; /* normalize ix */ + ix = j | 0x3ff00000; /* normalize ix */ if j <= 0x3988E { /* |x| f64 { /* compute ss = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */ let u: f64 = ax - BP[k as usize]; /* bp[0]=1.0, bp[1]=1.5 */ let v: f64 = 1.0 / (ax + BP[k as usize]); - let ss: f64 = u * v; + let ss: f64 = u * v; let s_h = with_set_low_word(ss, 0); /* t_h=ax+bp[k] High */ - let t_h: f64 = with_set_high_word(0.0, - ((ix as u32 >> 1) | 0x20000000) + 0x00080000 + ((k as u32) << 18)); + let t_h: f64 = with_set_high_word( + 0.0, + ((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; }