From f12ba75f67ede8582bfdf20e75eafbf423112e50 Mon Sep 17 00:00:00 2001 From: Rahul Butani Date: Tue, 17 Jul 2018 14:56:11 -0500 Subject: [PATCH 1/4] pow! --- .../compiler-builtins/libm/src/math/pow.rs | 395 ++++++++++++++++++ 1 file changed, 395 insertions(+) create mode 100644 library/compiler-builtins/libm/src/math/pow.rs diff --git a/library/compiler-builtins/libm/src/math/pow.rs b/library/compiler-builtins/libm/src/math/pow.rs new file mode 100644 index 000000000000..3d0769b34403 --- /dev/null +++ b/library/compiler-builtins/libm/src/math/pow.rs @@ -0,0 +1,395 @@ +/* origin: FreeBSD /usr/src/lib/msun/src/e_pow.c */ +/* + * ==================================================== + * Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved. + * + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * 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" + +/* 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, scalbn, sqrt, with_set_low_word, with_set_high_word, get_high_word}; + +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; + +// 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 P2: f64 = -2.77777777770155933842e-03; /* 0xbf66c16c_16bebd93 */ +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*/ + +#[inline] +pub fn pow(x: f64, y: f64) -> f64 { + let t1: f64; + let t2: 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; + + /* x**0 = 1, even if x is NaN */ + if ((iy as u32) | ly) == 0 { + return 1.0; + } + + /* 1**y = 1, even if y is NaN */ + if hx == 0x3ff00000 && lx == 0 { + return 1.0; + } + + /* NaN if either arg is NaN */ + 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 + * yisint = 0 ... y is not an integer + * yisint = 1 ... y is an odd int + * yisint = 2 ... y is an even int + */ + let mut yisint: i32 = 0; + let mut k: i32; + let mut j: i32; + if hx < 0 { + if iy >= 0x43400000 { + 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); + } + } + } + } + + if ly == 0 { + /* special value of y */ + if iy == 0x7ff00000 { + /* 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 } + } else { + /* (|x|<1)**+-inf = 0,inf */ + if hy >= 0 { 0.0 } else { -y } + }; + } + + if iy == 0x3ff00000 { + /* y is +-1 */ + return if hy >= 0 { x } else { 1.0 / x }; + } + + if hy == 0x40000000 { + /* y is 2 */ + return x * x; + } + + if hy == 0x3fe00000 { + /* y is 0.5 */ + if hx >= 0 { + /* x >= +0 */ + return sqrt(x); + } + } + } + + let mut ax: f64 = fabs(x); + if lx == 0 { + /* special value of x */ + 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 { + z = (z - z) / (z - z); /* (-1)**non-int is NaN */ + } else if yisint == 1 { + z = -z; /* (x<0)**odd = -(|x|**odd) */ + } + } + + return z; + } + } + + let mut s: f64 = 1.0; /* sign of result */ + if hx < 0 { + if yisint == 0 { + /* (x<0)**(non-int) is NaN */ + return (x - x) / (x - x); + } + + if yisint == 1 { + /* (x<0)**(odd int) */ + s = -1.0; + } + } + + /* |y| is HUGE */ + if iy > 0x41e00000 { + /* if |y| > 2**31 */ + if iy > 0x43f00000 { + /* if |y| > 2**64, must o/uflow */ + if ix <= 0x3fefffff { + return if hy < 0 { HUGE * HUGE } else { TINY * TINY }; + } + + if ix >= 0x3ff00000 { + return if hy > 0 { HUGE * HUGE } else { TINY * TINY }; + } + } + + /* over/underflow if x is not close to one */ + if ix < 0x3fefffff { + 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 }; + } + + /* 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 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 v: f64 = t * IVLN2_L - w * IVLN2; + t1 = with_set_low_word(u + v, 0); + t2 = v - (t1 - u); + } else { + // double ss,s2,s_h,s_l,t_h,t_l; + let mut n: i32 = 0; + + if ix < 0x00100000 { + /* take care subnormal number */ + ax *= TWO53; + n -= 53; + ix = get_high_word(ax) as i32; + } + + n += (ix >> 20) - 0x3ff; + j = ix & 0x000fffff; + + /* determine interval */ + let k: i32; + ix = j | 0x3ff00000; /* normalize ix */ + if j <= 0x3988E { + /* |x|> 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))))); + 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); + let t_l: f64 = r - ((t_h - 3.0) - s2); + + /* u+v = ss*(1+...) */ + let u: f64 = s_h * t_h; + let v: f64 = s_l * t_h + t_l * ss; + + /* 2/(3log2)*(ss+...) */ + let p_h: f64 = with_set_low_word(u + v, 0); + 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]; + + /* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */ + let t: f64 = n as f64; + t1 = with_set_low_word(((z_h + z_l) + DP_H[k as usize]) + t, 0); + t2 = z_l - (((t1 - t) - DP_H[k as usize]) - z_h); + } + + /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */ + 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 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); + + if j >= 0x40900000 { + /* z >= 1024 */ + if (j - 0x40900000) | i != 0 { + /* if z > 1024 */ + return s * HUGE * HUGE; /* overflow */ + } + + if p_l + OVT > z - p_h { + return s * HUGE * HUGE; /* overflow */ + } + } else if (j & 0x7fffffff) >= 0x4090cc00 { + /* z <= -1075 */ + // FIXME: instead of abs(j) use unsigned j + + if (((j as u32) - 0xc090cc00) | (i as u32)) != 0 { + /* z < -1075 */ + return s * TINY * TINY; /* underflow */ + } + + if p_l <= z - p_h { + return s * TINY * TINY; /* underflow */ + } + } + + /* compute 2**(p_h+p_l) */ + let i: i32 = j & (0x7fffffff as i32); + k = (i >> 20) - 0x3ff; + let mut n: i32 = 0; + + 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 */ + let t: f64 = with_set_high_word(0.0, (n & !(0x000fffff >> k)) as u32); + n = ((n & 0x000fffff) | 0x00100000) >> (20 - k); + if j < 0 { + n = -n; + } + p_h -= t; + } + + let t: f64 = with_set_low_word(p_l + p_h, 0); + let u: f64 = t * LG2_H; + let v: f64 = (p_l - (t - p_h)) * LG2 + t * LG2_L; + let mut z: f64 = u + v; + 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); + 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; +} From 440e835967dd4bac67a7b20ea8b063dfa347891e Mon Sep 17 00:00:00 2001 From: Rahul Butani Date: Tue, 17 Jul 2018 15:03:39 -0500 Subject: [PATCH 2/4] Enable tests and expose --- library/compiler-builtins/libm/src/lib.rs | 2 -- library/compiler-builtins/libm/src/math/mod.rs | 3 ++- library/compiler-builtins/libm/test-generator/src/main.rs | 2 +- 3 files changed, 3 insertions(+), 4 deletions(-) diff --git a/library/compiler-builtins/libm/src/lib.rs b/library/compiler-builtins/libm/src/lib.rs index 1837b9c1f9ed..06991effe1d7 100644 --- a/library/compiler-builtins/libm/src/lib.rs +++ b/library/compiler-builtins/libm/src/lib.rs @@ -343,7 +343,6 @@ pub trait F64Ext: private::Sealed + Sized { // NOTE depends on unstable intrinsics::powif64 // fn powi(self, n: i32) -> Self; - #[cfg(todo)] fn powf(self, n: Self) -> Self; fn sqrt(self) -> Self; @@ -463,7 +462,6 @@ impl F64Ext for f64 { } } - #[cfg(todo)] #[inline] fn powf(self, n: Self) -> Self { pow(self, n) diff --git a/library/compiler-builtins/libm/src/math/mod.rs b/library/compiler-builtins/libm/src/math/mod.rs index 754efa9f6dac..6dd362d00945 100644 --- a/library/compiler-builtins/libm/src/math/mod.rs +++ b/library/compiler-builtins/libm/src/math/mod.rs @@ -50,6 +50,7 @@ mod log2; mod log2f; mod logf; mod powf; +mod pow; mod round; mod roundf; mod scalbn; @@ -111,6 +112,7 @@ 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::round::round; pub use self::roundf::roundf; pub use self::scalbn::scalbn; @@ -167,7 +169,6 @@ fn get_low_word(x: f64) -> u32 { x.to_bits() as u32 } -#[allow(dead_code)] #[inline] fn with_set_high_word(f: f64, hi: u32) -> f64 { let mut tmp = f.to_bits(); diff --git a/library/compiler-builtins/libm/test-generator/src/main.rs b/library/compiler-builtins/libm/test-generator/src/main.rs index 09a9cb8f5887..4c4e420a2852 100644 --- a/library/compiler-builtins/libm/test-generator/src/main.rs +++ b/library/compiler-builtins/libm/test-generator/src/main.rs @@ -774,7 +774,7 @@ f64f64_f64! { fdim, fmod, hypot, - // pow, + pow, } // With signature `fn(f64, f64, f64) -> f64` From 1c555103ae48c2c452739d9b9b77e4267738965f Mon Sep 17 00:00:00 2001 From: Rahul Butani Date: Tue, 17 Jul 2018 15:06:50 -0500 Subject: [PATCH 3/4] 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; } From 9f920e739a0765f31b77223186dfd16c48b45936 Mon Sep 17 00:00:00 2001 From: Jorge Aparicio Date: Tue, 17 Jul 2018 19:46:12 -0500 Subject: [PATCH 4/4] cargo fmt --- .../compiler-builtins/libm/src/math/pow.rs | 97 +++++++++---------- 1 file changed, 48 insertions(+), 49 deletions(-) diff --git a/library/compiler-builtins/libm/src/math/pow.rs b/library/compiler-builtins/libm/src/math/pow.rs index 69c086b0f242..329b3955d883 100644 --- a/library/compiler-builtins/libm/src/math/pow.rs +++ b/library/compiler-builtins/libm/src/math/pow.rs @@ -9,55 +9,54 @@ * ==================================================== */ -/// 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. -/// - +// 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. +// use super::{fabs, get_high_word, scalbn, sqrt, with_set_high_word, with_set_low_word}; const BP: [f64; 2] = [1.0, 1.5];