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02/02/2024 06:09:55 PM
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abs.go
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acos_s390x.s
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acosh.go
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acosh_s390x.s
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all_test.go
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arith_s390x.go
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arith_s390x_test.go
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asin.go
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asin_s390x.s
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asinh.go
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atan.go
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atan2.go
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atan2_s390x.s
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atan_s390x.s
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atanh.go
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atanh_s390x.s
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bits
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bits.go
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cbrt.go
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cbrt_s390x.s
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const.go
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const_test.go
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copysign.go
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cosh_s390x.s
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dim.go
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dim_amd64.s
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dim_arm64.s
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dim_asm.go
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erf.go
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erf_s390x.s
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erfc_s390x.s
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erfinv.go
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example_test.go
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exp.go
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exp2_asm.go
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exp2_noasm.go
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exp_amd64.go
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exp_amd64.s
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exp_arm64.s
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exp_asm.go
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exp_noasm.go
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exp_s390x.s
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expm1.go
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expm1_s390x.s
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export_s390x_test.go
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export_test.go
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floor.go
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floor_386.s
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floor_amd64.s
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floor_asm.go
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floor_noasm.go
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floor_ppc64x.s
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floor_s390x.s
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floor_wasm.s
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fma.go
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frexp.go
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gamma.go
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huge_test.go
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hypot.go
850 bytes
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hypot_386.s
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hypot_amd64.s
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hypot_asm.go
264 bytes
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hypot_noasm.go
297 bytes
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j0.go
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j1.go
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jn.go
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ldexp.go
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lgamma.go
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log.go
3.86 KB
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log10.go
873 bytes
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log10_s390x.s
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log1p.go
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log1p_s390x.s
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log_amd64.s
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log_asm.go
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log_s390x.s
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log_stub.go
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logb.go
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mod.go
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modf.go
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modf_arm64.s
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modf_asm.go
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modf_noasm.go
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modf_ppc64x.s
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nextafter.go
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pow.go
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pow10.go
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pow_s390x.s
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rand
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remainder.go
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signbit.go
302 bytes
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sin.go
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sin_s390x.s
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sincos.go
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sinh.go
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sinh_s390x.s
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sqrt.go
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stubs.go
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stubs_s390x.s
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tan.go
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tan_s390x.s
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tanh.go
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tanh_s390x.s
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trig_reduce.go
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unsafe.go
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Editing: exp.go
Close
// Copyright 2009 The Go Authors. All rights reserved. // Use of this source code is governed by a BSD-style // license that can be found in the LICENSE file. package math // Exp returns e**x, the base-e exponential of x. // // Special cases are: // // Exp(+Inf) = +Inf // Exp(NaN) = NaN // // Very large values overflow to 0 or +Inf. // Very small values underflow to 1. func Exp(x float64) float64 { if haveArchExp { return archExp(x) } return exp(x) } // The original C code, the long comment, and the constants // below are from FreeBSD's /usr/src/lib/msun/src/e_exp.c // and came with this notice. The go code is a simplified // version of the original 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. // ==================================================== // // // exp(x) // Returns the exponential of x. // // Method // 1. Argument reduction: // Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658. // Given x, find r and integer k such that // // x = k*ln2 + r, |r| <= 0.5*ln2. // // Here r will be represented as r = hi-lo for better // accuracy. // // 2. Approximation of exp(r) by a special rational function on // the interval [0,0.34658]: // Write // R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ... // We use a special Remez algorithm on [0,0.34658] to generate // a polynomial of degree 5 to approximate R. The maximum error // of this polynomial approximation is bounded by 2**-59. In // other words, // R(z) ~ 2.0 + P1*z + P2*z**2 + P3*z**3 + P4*z**4 + P5*z**5 // (where z=r*r, and the values of P1 to P5 are listed below) // and // | 5 | -59 // | 2.0+P1*z+...+P5*z - R(z) | <= 2 // | | // The computation of exp(r) thus becomes // 2*r // exp(r) = 1 + ------- // R - r // r*R1(r) // = 1 + r + ----------- (for better accuracy) // 2 - R1(r) // where // 2 4 10 // R1(r) = r - (P1*r + P2*r + ... + P5*r ). // // 3. Scale back to obtain exp(x): // From step 1, we have // exp(x) = 2**k * exp(r) // // Special cases: // exp(INF) is INF, exp(NaN) is NaN; // exp(-INF) is 0, and // for finite argument, only exp(0)=1 is exact. // // Accuracy: // according to an error analysis, the error is always less than // 1 ulp (unit in the last place). // // Misc. info. // For IEEE double // if x > 7.09782712893383973096e+02 then exp(x) overflow // if x < -7.45133219101941108420e+02 then exp(x) underflow // // 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. func exp(x float64) float64 { const ( Ln2Hi = 6.93147180369123816490e-01 Ln2Lo = 1.90821492927058770002e-10 Log2e = 1.44269504088896338700e+00 Overflow = 7.09782712893383973096e+02 Underflow = -7.45133219101941108420e+02 NearZero = 1.0 / (1 << 28) // 2**-28 ) // special cases switch { case IsNaN(x) || IsInf(x, 1): return x case IsInf(x, -1): return 0 case x > Overflow: return Inf(1) case x < Underflow: return 0 case -NearZero < x && x < NearZero: return 1 + x } // reduce; computed as r = hi - lo for extra precision. var k int switch { case x < 0: k = int(Log2e*x - 0.5) case x > 0: k = int(Log2e*x + 0.5) } hi := x - float64(k)*Ln2Hi lo := float64(k) * Ln2Lo // compute return expmulti(hi, lo, k) } // Exp2 returns 2**x, the base-2 exponential of x. // // Special cases are the same as [Exp]. func Exp2(x float64) float64 { if haveArchExp2 { return archExp2(x) } return exp2(x) } func exp2(x float64) float64 { const ( Ln2Hi = 6.93147180369123816490e-01 Ln2Lo = 1.90821492927058770002e-10 Overflow = 1.0239999999999999e+03 Underflow = -1.0740e+03 ) // special cases switch { case IsNaN(x) || IsInf(x, 1): return x case IsInf(x, -1): return 0 case x > Overflow: return Inf(1) case x < Underflow: return 0 } // argument reduction; x = r×lg(e) + k with |r| ≤ ln(2)/2. // computed as r = hi - lo for extra precision. var k int switch { case x > 0: k = int(x + 0.5) case x < 0: k = int(x - 0.5) } t := x - float64(k) hi := t * Ln2Hi lo := -t * Ln2Lo // compute return expmulti(hi, lo, k) } // exp1 returns e**r × 2**k where r = hi - lo and |r| ≤ ln(2)/2. func expmulti(hi, lo float64, k int) float64 { const ( P1 = 1.66666666666666657415e-01 /* 0x3FC55555; 0x55555555 */ P2 = -2.77777777770155933842e-03 /* 0xBF66C16C; 0x16BEBD93 */ P3 = 6.61375632143793436117e-05 /* 0x3F11566A; 0xAF25DE2C */ P4 = -1.65339022054652515390e-06 /* 0xBEBBBD41; 0xC5D26BF1 */ P5 = 4.13813679705723846039e-08 /* 0x3E663769; 0x72BEA4D0 */ ) r := hi - lo t := r * r c := r - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))) y := 1 - ((lo - (r*c)/(2-c)) - hi) // TODO(rsc): make sure Ldexp can handle boundary k return Ldexp(y, k) }