From f73c61b76230cbbb8061118ccd228411b7b84031 Mon Sep 17 00:00:00 2001 From: Erik Date: Sat, 14 Jul 2018 01:28:00 -0400 Subject: [PATCH] implement log1p and log1pf --- library/compiler-builtins/libm/src/lib.rs | 4 - .../compiler-builtins/libm/src/math/log1p.rs | 142 ++++++++++++++++++ .../compiler-builtins/libm/src/math/log1pf.rs | 97 ++++++++++++ .../compiler-builtins/libm/src/math/mod.rs | 8 +- .../libm/test-generator/src/main.rs | 3 +- 5 files changed, 246 insertions(+), 8 deletions(-) create mode 100644 library/compiler-builtins/libm/src/math/log1p.rs create mode 100644 library/compiler-builtins/libm/src/math/log1pf.rs diff --git a/library/compiler-builtins/libm/src/lib.rs b/library/compiler-builtins/libm/src/lib.rs index 39eb71e99c9f..30f879769d0b 100644 --- a/library/compiler-builtins/libm/src/lib.rs +++ b/library/compiler-builtins/libm/src/lib.rs @@ -114,7 +114,6 @@ pub trait F32Ext: private::Sealed { #[cfg(todo)] fn exp_m1(self) -> Self; - #[cfg(todo)] fn ln_1p(self) -> Self; #[cfg(todo)] @@ -295,7 +294,6 @@ impl F32Ext for f32 { expm1f(self) } - #[cfg(todo)] #[inline] fn ln_1p(self) -> Self { log1pf(self) @@ -432,7 +430,6 @@ pub trait F64Ext: private::Sealed { #[cfg(todo)] fn exp_m1(self) -> Self; - #[cfg(todo)] fn ln_1p(self) -> Self; #[cfg(todo)] @@ -616,7 +613,6 @@ impl F64Ext for f64 { expm1(self) } - #[cfg(todo)] #[inline] fn ln_1p(self) -> Self { log1p(self) diff --git a/library/compiler-builtins/libm/src/math/log1p.rs b/library/compiler-builtins/libm/src/math/log1p.rs new file mode 100644 index 000000000000..7f7a5125bbb3 --- /dev/null +++ b/library/compiler-builtins/libm/src/math/log1p.rs @@ -0,0 +1,142 @@ +/* origin: FreeBSD /usr/src/lib/msun/src/s_log1p.c */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ +/* double log1p(double x) + * Return the natural logarithm of 1+x. + * + * Method : + * 1. Argument Reduction: find k and f such that + * 1+x = 2^k * (1+f), + * where sqrt(2)/2 < 1+f < sqrt(2) . + * + * Note. If k=0, then f=x is exact. However, if k!=0, then f + * may not be representable exactly. In that case, a correction + * term is need. Let u=1+x rounded. Let c = (1+x)-u, then + * log(1+x) - log(u) ~ c/u. Thus, we proceed to compute log(u), + * and add back the correction term c/u. + * (Note: when x > 2**53, one can simply return log(x)) + * + * 2. Approximation of log(1+f): See log.c + * + * 3. Finally, log1p(x) = k*ln2 + log(1+f) + c/u. See log.c + * + * Special cases: + * log1p(x) is NaN with signal if x < -1 (including -INF) ; + * log1p(+INF) is +INF; log1p(-1) is -INF with signal; + * log1p(NaN) is that NaN with no signal. + * + * Accuracy: + * according to an error analysis, the error is always less than + * 1 ulp (unit in the last place). + * + * 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. + * + * Note: Assuming log() return accurate answer, the following + * algorithm can be used to compute log1p(x) to within a few ULP: + * + * u = 1+x; + * if(u==1.0) return x ; else + * return log(u)*(x/(u-1.0)); + * + * See HP-15C Advanced Functions Handbook, p.193. + */ + +use core::f64; + +const LN2_HI: f64 = 6.93147180369123816490e-01; /* 3fe62e42 fee00000 */ +const LN2_LO: f64 = 1.90821492927058770002e-10; /* 3dea39ef 35793c76 */ +const LG1: f64 = 6.666666666666735130e-01; /* 3FE55555 55555593 */ +const LG2: f64 = 3.999999999940941908e-01; /* 3FD99999 9997FA04 */ +const LG3: f64 = 2.857142874366239149e-01; /* 3FD24924 94229359 */ +const LG4: f64 = 2.222219843214978396e-01; /* 3FCC71C5 1D8E78AF */ +const LG5: f64 = 1.818357216161805012e-01; /* 3FC74664 96CB03DE */ +const LG6: f64 = 1.531383769920937332e-01; /* 3FC39A09 D078C69F */ +const LG7: f64 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */ + +pub fn log1p(x: f64) -> f64 { + let mut ui: u64 = x.to_bits(); + let hfsq: f64; + let mut f: f64 = 0.; + let mut c: f64 = 0.; + let s: f64; + let z: f64; + let r: f64; + let w: f64; + let t1: f64; + let t2: f64; + let dk: f64; + let hx: u32; + let mut hu: u32; + let mut k: i32; + + hx = (ui >> 32) as u32; + k = 1; + if hx < 0x3fda827a || (hx >> 31) > 0 { + /* 1+x < sqrt(2)+ */ + if hx >= 0xbff00000 { + /* x <= -1.0 */ + if x == -1. { + return x / 0.0; /* log1p(-1) = -inf */ + } + return (x - x) / 0.0; /* log1p(x<-1) = NaN */ + } + if hx << 1 < 0x3ca00000 << 1 { + /* |x| < 2**-53 */ + /* underflow if subnormal */ + if (hx & 0x7ff00000) == 0 { + force_eval!(x as f32); + } + return x; + } + if hx <= 0xbfd2bec4 { + /* sqrt(2)/2- <= 1+x < sqrt(2)+ */ + k = 0; + c = 0.; + f = x; + } + } else if hx >= 0x7ff00000 { + return x; + } + if k > 0 { + ui = (1. + x).to_bits(); + hu = (ui >> 32) as u32; + hu += 0x3ff00000 - 0x3fe6a09e; + k = (hu >> 20) as i32 - 0x3ff; + /* correction term ~ log(1+x)-log(u), avoid underflow in c/u */ + if k < 54 { + c = if k >= 2 { + 1. - (f64::from_bits(ui) - x) + } else { + x - (f64::from_bits(ui) - 1.) + }; + c /= f64::from_bits(ui); + } else { + c = 0.; + } + /* reduce u into [sqrt(2)/2, sqrt(2)] */ + hu = (hu & 0x000fffff) + 0x3fe6a09e; + ui = (hu as u64) << 32 | (ui & 0xffffffff); + f = f64::from_bits(ui) - 1.; + } + hfsq = 0.5 * f * f; + s = f / (2.0 + f); + z = s * s; + w = z * z; + t1 = w * (LG2 + w * (LG4 + w * LG6)); + t2 = z * (LG1 + w * (LG3 + w * (LG5 + w * LG7))); + r = t2 + t1; + dk = k as f64; + return s * (hfsq + r) + (dk * LN2_LO + c) - hfsq + f + dk * LN2_HI; +} diff --git a/library/compiler-builtins/libm/src/math/log1pf.rs b/library/compiler-builtins/libm/src/math/log1pf.rs new file mode 100644 index 000000000000..c8e242259337 --- /dev/null +++ b/library/compiler-builtins/libm/src/math/log1pf.rs @@ -0,0 +1,97 @@ +/* origin: FreeBSD /usr/src/lib/msun/src/s_log1pf.c */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +use core::f32; + +const LN2_HI: f32 = 6.9313812256e-01; /* 0x3f317180 */ +const LN2_LO: f32 = 9.0580006145e-06; /* 0x3717f7d1 */ +/* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */ +const LG1: f32 = 0.66666662693; /* 0xaaaaaa.0p-24 */ +const LG2: f32 = 0.40000972152; /* 0xccce13.0p-25 */ +const LG3: f32 = 0.28498786688; /* 0x91e9ee.0p-25 */ +const LG4: f32 = 0.24279078841; /* 0xf89e26.0p-26 */ + +pub fn log1pf(x: f32) -> f32 { + let mut ui: u32 = x.to_bits(); + let hfsq: f32; + let mut f: f32 = 0.; + let mut c: f32 = 0.; + let s: f32; + let z: f32; + let r: f32; + let w: f32; + let t1: f32; + let t2: f32; + let dk: f32; + let ix: u32; + let mut iu: u32; + let mut k: i32; + + ix = ui; + k = 1; + if ix < 0x3ed413d0 || (ix >> 31) > 0 { + /* 1+x < sqrt(2)+ */ + if ix >= 0xbf800000 { + /* x <= -1.0 */ + if x == -1. { + return x / 0.0; /* log1p(-1)=+inf */ + } + return (x - x) / 0.0; /* log1p(x<-1)=NaN */ + } + if ix << 1 < 0x33800000 << 1 { + /* |x| < 2**-24 */ + /* underflow if subnormal */ + if (ix & 0x7f800000) == 0 { + force_eval!(x * x); + } + return x; + } + if ix <= 0xbe95f619 { + /* sqrt(2)/2- <= 1+x < sqrt(2)+ */ + k = 0; + c = 0.; + f = x; + } + } else if ix >= 0x7f800000 { + return x; + } + if k > 0 { + ui = (1. + x).to_bits(); + iu = ui; + iu += 0x3f800000 - 0x3f3504f3; + k = (iu >> 23) as i32 - 0x7f; + /* correction term ~ log(1+x)-log(u), avoid underflow in c/u */ + if k < 25 { + c = if k >= 2 { + 1. - (f32::from_bits(ui) - x) + } else { + x - (f32::from_bits(ui) - 1.) + }; + c /= f32::from_bits(ui); + } else { + c = 0.; + } + /* reduce u into [sqrt(2)/2, sqrt(2)] */ + iu = (iu & 0x007fffff) + 0x3f3504f3; + ui = iu; + f = f32::from_bits(ui) - 1.; + } + s = f / (2.0 + f); + z = s * s; + w = z * z; + t1 = w * (LG2 + w * LG4); + t2 = z * (LG1 + w * LG3); + r = t2 + t1; + hfsq = 0.5 * f * f; + dk = k as f32; + return s * (hfsq + r) + (dk * LN2_LO + c) - hfsq + f + dk * LN2_HI; +} diff --git a/library/compiler-builtins/libm/src/math/mod.rs b/library/compiler-builtins/libm/src/math/mod.rs index 6e514f86f9cb..fb5e3df90901 100644 --- a/library/compiler-builtins/libm/src/math/mod.rs +++ b/library/compiler-builtins/libm/src/math/mod.rs @@ -18,6 +18,8 @@ mod hypotf; mod log; mod log10; mod log10f; +mod log1p; +mod log1pf; mod log2; mod log2f; mod logf; @@ -35,9 +37,9 @@ mod truncf; pub use self::{ ceilf::ceilf, expf::expf, fabs::fabs, fabsf::fabsf, floor::floor, floorf::floorf, fmodf::fmodf, - hypot::hypot, hypotf::hypotf, log::log, log10::log10, log10f::log10f, log2::log2, log2f::log2f, - logf::logf, powf::powf, round::round, roundf::roundf, scalbn::scalbn, scalbnf::scalbnf, - sqrt::sqrt, sqrtf::sqrtf, trunc::trunc, truncf::truncf, + hypot::hypot, hypotf::hypotf, log::log, log10::log10, log10f::log10f, log1p::log1p, + log1pf::log1pf, log2::log2, log2f::log2f, logf::logf, powf::powf, round::round, roundf::roundf, + scalbn::scalbn, scalbnf::scalbnf, sqrt::sqrt, sqrtf::sqrtf, trunc::trunc, truncf::truncf, }; fn isnanf(x: f32) -> bool { diff --git a/library/compiler-builtins/libm/test-generator/src/main.rs b/library/compiler-builtins/libm/test-generator/src/main.rs index 6f8d3c68a320..be5ed0784f8b 100644 --- a/library/compiler-builtins/libm/test-generator/src/main.rs +++ b/library/compiler-builtins/libm/test-generator/src/main.rs @@ -664,6 +664,7 @@ f32_f32! { expf, // fdimf, log10f, + log1pf, log2f, logf, roundf, @@ -708,7 +709,7 @@ f64_f64! { floor, log, log10, - // log1p, + log1p, log2, round, // sin,